{"Spatial econometrics": {"categories": ["All stub articles", "Econometric modeling", "Econometrics stubs", "Regional science", "Spatial data analysis"], "title": "Spatial econometrics", "method": "Spatial econometrics", "url": "https://en.wikipedia.org/wiki/Spatial_econometrics", "summary": "Spatial econometrics is the field where spatial analysis and econometrics intersect. The term \u201cspatial econometrics\u201d was introduced for the first time by the Belgian economist Jean Paelinck (universally recognised as the father of the discipline) in the general address he delivered to the annual meeting of the Dutch Statistical Association in May 1974 (Paelinck and Klaassen, 1979).\nIn general, econometrics differs from other branches of statistics in focusing on theoretical models, whose parameters are estimated using regression analysis. Spatial econometrics is a refinement of this, where either the theoretical model involves interactions between different entities, or the data observations are not truly independent. Thus, models incorporating spatial auto-correlation or neighborhood effects can be estimated using spatial econometric methods. Such models are common in regional science, real estate economics, education economics, housing market and many others. Adopting a more general view, in the by-law of the Spatial Econometrics Association, the discipline is defined as the set of \u201cmodels and theoretical instruments of spatial statistics and spatial data analysis to analyse various economic effects such as externalities, interactions, spatial concentration and many others\u201d (Spatial Econometrics Association, 2006). Recent developments tend to include also methods and models from social network econometrics.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170527191524%21Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170519203409%21Emoji_u1f4c8.svg"], "links": ["Complete spatial randomness", "Correlation", "Digital object identifier", "Econometrics", "Education economics", "Geographic information science", "Giuseppe Arbia", "Housing market", "Luc Anselin", "Modifiable Areal Unit Problem", "Neighborhood effects", "Real estate economics", "Regional science", "Regression analysis", "Social network", "Spatial Econometrics Association", "Spatial analysis", "Spatial auto-correlation", "Spatial autocorrelation"], "references": ["http://doi.org/10.1111/j.1435-5957.2010.00279.x"]}, "Geometric median": {"categories": ["Descriptive statistics", "Geometric algorithms", "Mathematical optimization", "Means", "Multivariate statistics", "Nonparametric statistics"], "title": "Geometric median", "method": "Geometric median", "url": "https://en.wikipedia.org/wiki/Geometric_median", "summary": "The geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions. It is also known as the 1-median, spatial median, Euclidean minisum point, or Torricelli point.The geometric median is an important estimator of location in statistics, where it is also known as the L1 estimator. It is also a standard problem in facility location, where it models the problem of locating a facility to minimize the cost of transportation.The special case of the problem for three points in the plane (that is, m = 3 and n = 2 in the definition below) is sometimes also known as Fermat's problem; it arises in the construction of minimal Steiner trees, and was originally posed as a problem by Pierre de Fermat and solved by Evangelista Torricelli. Its solution is now known as the Fermat point of the triangle formed by the three sample points. The geometric median may in turn be generalized to the problem of minimizing the sum of weighted distances, known as the Weber problem after Alfred Weber's discussion of the problem in his 1909 book on facility location. Some sources instead call Weber's problem the Fermat\u2013Weber problem, but others use this name for the unweighted geometric median problem.Wesolowsky (1993) provides a survey of the geometric median problem. See Fekete, Mitchell & Beurer (2005) for generalizations of the problem to non-discrete point sets.", "images": [], "links": ["Alfred Weber", "Andrew V\u00e1zsonyi", "Annals of Statistics", "ArXiv", "Arg min", "Association for Computing Machinery", "Bernd Sturmfels", "Bibcode", "Breakdown point", "Cartesian coordinates", "Center of mass", "Central tendency", "Centroid", "Chandrajit Bajaj", "Closed-form expression", "Collinear", "Computational Geometry (journal)", "Convex function", "Coplanar", "Digital object identifier", "Discrete and Computational Geometry", "Endre Weiszfeld", "Equivariant", "Estimator", "Euclidean distance", "Euclidean space", "Evangelista Torricelli", "Facility location", "Fermat point", "Frank Plastria", "Fr\u00e9chet mean", "Gary Miller (computer scientist)", "Giovanni Fagnano", "Harold W. Kuhn", "International Standard Book Number", "Iteratively re-weighted least squares", "J. B. S. Haldane", "JSTOR", "James R. Thompson (statistician)", "Jit Bose", "Joseph S. B. Mitchell", "Journal of Symbolic Computation", "K-median problem", "Line (geometry)", "Local optimum", "Location parameter", "Mathematical Programming", "Mathematical Reviews", "Mathematics Magazine", "Median", "Median (geometry)", "Metric space", "Model of computation", "Operations Research (journal)", "Peter Rousseeuw", "Pierre de Fermat", "PubMed Central", "PubMed Identifier", "Quadrilateral", "Radon point", "Riemannian manifold", "Robust estimator", "Rotation (mathematics)", "Ruler and compass", "Semidefinite programming", "Similarity (geometry)", "Steiner tree", "Symposium on Theory of Computing", "Tohoku Mathematical Journal", "Translation (geometry)", "Univariate", "Weber problem", "Zentralblatt MATH"], "references": ["http://mosi.vub.ac.be/papers/Plastria2005_Fegnano.pdf", "http://www.scs.carleton.ca/~jit/publications/papers/bmm01.ps", "http://adsabs.harvard.edu/abs/2000PNAS...97.1423V", "http://adsabs.harvard.edu/abs/2007math......2005N", "http://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1415&context=cstech", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC26449", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2735114", "http://www.ncbi.nlm.nih.gov/pubmed/19056498", "http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA390709", "http://www.ams.org/mathscinet-getitem?mr=1362958", "http://www.ams.org/mathscinet-getitem?mr=1473041", "http://www.ams.org/mathscinet-getitem?mr=1573157", "http://www.ams.org/mathscinet-getitem?mr=1740461", "http://www.ams.org/mathscinet-getitem?mr=1933966", "http://arxiv.org/abs/cs.CG/0310027", "http://arxiv.org/abs/math/0702005", "http://doi.org/10.1007%2FBF01584648", "http://doi.org/10.1007%2FBF01587094", "http://doi.org/10.1007%2FBF01592245", "http://doi.org/10.1007%2FBF02187906", "http://doi.org/10.1016%2FS0747-7171(86)80015-3", "http://doi.org/10.1016%2FS0925-7721(02)00102-5", "http://doi.org/10.1016%2Fj.neuroimage.2008.10.052", "http://doi.org/10.1073%2Fpnas.97.4.1423", "http://doi.org/10.1093%2Fbiomet%2F35.3-4.414", "http://doi.org/10.1093%2Fimaman%2F8.3.215", "http://doi.org/10.1093%2Fimaman%2Fdpl007", "http://doi.org/10.1214%2Faos%2F1176347978", "http://doi.org/10.1287%2Fopre.1040.0137", "http://doi.org/10.1287%2Fopre.26.4.597", "http://doi.org/10.2307%2F2688541", "http://www.jstor.org/stable/2241852", "http://www.jstor.org/stable/2688541", "http://www.jstor.org/stable/2690672?origin=pubexport", "http://zbmath.org/?format=complete&q=an:1126.90046", "https://books.google.com/books?id=4E0r3oWkn6AC&pg=PA3", "https://books.google.com/books?id=6bQ8JJ_Rx6sC&pg=PA6", "https://books.google.com/books?id=sxpcsGN7K1YC&pg=PA1"]}, "Concordance correlation coefficient": {"categories": ["CS1 maint: Multiple names: authors list", "Covariance and correlation", "Inter-rater reliability"], "title": "Concordance correlation coefficient", "method": "Concordance correlation coefficient", "url": "https://en.wikipedia.org/wiki/Concordance_correlation_coefficient", "summary": "In statistics, the concordance correlation coefficient measures the agreement between two variables, e.g., to evaluate reproducibility or for inter-rater reliability.\n\n", "images": [], "links": ["Biometrics (journal)", "Carol A. E. Nickerson", "Cohen's kappa", "Digital object identifier", "Functional magnetic resonance imaging", "Inter-rater reliability", "Intra-class correlation", "JSTOR", "Jossey-Bass", "Klaus Krippendorff", "Mean", "NIWA", "NeuroImage", "Pearson product-moment correlation coefficient", "PubMed Identifier", "Reproducibility", "Robert L. Savoy", "San Francisco", "Sociological Methodology", "Statistics", "Statistics in Medicine (journal)", "Variance"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/10458943", "http://www.ncbi.nlm.nih.gov/pubmed/2720055", "http://www.ncbi.nlm.nih.gov/pubmed/7701147", "http://doi.org/10.1002%2Fsim.4780132310", "http://doi.org/10.1006%2Fnimg.1999.0472", "http://doi.org/10.1111%2Fj.0006-341X.2000.00324.x", "http://doi.org/10.2307%2F2532051", "http://doi.org/10.2307%2F2533516", "http://doi.org/10.2307%2F270787", "http://www.jstor.org/stable/2532051", "http://www.jstor.org/stable/2533516", "https://www.academia.edu/attachments/52086555/download_file?st=MTQ4OTA1OTg4MSwxOTYuMzQuMjUwLjE4LDEyMjEwMTI%3D&s=profile", "https://www.niwa.co.nz/node/104318/concordance"]}, "Bayes error rate": {"categories": ["All articles with unsourced statements", "All stub articles", "Articles with unsourced statements from February 2013", "Bayesian statistics", "Statistical classification", "Statistics stubs", "Wikipedia articles needing clarification from February 2013"], "title": "Bayes error rate", "method": "Bayes error rate", "url": "https://en.wikipedia.org/wiki/Bayes_error_rate", "summary": "In statistical classification, Bayes error rate is the lowest possible error rate for any classifier of a random outcome (into, for example, one of two categories) and is analogous to the irreducible error.A number of approaches to the estimation of the Bayes error rate exist. One method seeks to obtain analytical bounds which are inherently dependent on distribution parameters, and hence difficult to estimate. Another approach focuses on class densities, while yet another method combines and compares various classifiers.The Bayes error rate finds important use in the study of patterns and machine learning techniques.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["International Standard Book Number", "Machine learning", "Multiclass classifier", "Naive Bayes classifier", "Statistical classification", "Statistics"], "references": ["https://web.stanford.edu/~hastie/ElemStatLearn/"]}, "Meadow's law": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from April 2008", "Articles with unsourced statements from April 2008", "Criminology", "Medical statistics"], "title": "Meadow's law", "method": "Meadow's law", "url": "https://en.wikipedia.org/wiki/Meadow%27s_law", "summary": "Now discredited, Meadow's Law was a precept much in use until recently in the field of child protection, specifically by those investigating cases of multiple cot or crib death \u2013 SIDS \u2013 within a single family.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Beverley Allitt", "Case history", "Cot-death", "Daily Record (Scotland)", "Digital object identifier", "Double murder", "Fabricated or Induced Illness", "Gene", "General Medical Council", "Guilt (law)", "Likelihood function", "London School of Hygiene and Tropical Medicine", "Pathology", "Pediatrics", "Probability", "Prosecutor's fallacy", "Roy Meadow", "Sally Clark", "Statistical independence", "Statistician", "Statistics", "Sudden infant death syndrome", "United Kingdom", "United States", "Verdict"], "references": ["http://www.abc.net.au/rn/talks/8.30/helthrpt/stories/s1288472.htm", "http://www.docstoc.com/docs/24341288/Cot-Death-or-Murder", "http://doi.org/10.1111%2Fj.1365-3016.2004.00560.x", "http://www.cse.salford.ac.uk/staff/RHill/ppe_5601.pdf", "http://www.dailyrecord.co.uk/news/scottish-news/2010/04/30/top-doctor-casts-doubt-on-conviction-of-waiter-mohammad-ullah-for-killing-baby-stepson-86908-22222501/", "http://observer.guardian.co.uk/print/0,,4221973-102285,00.html", "http://www.timesonline.co.uk/tol/news/uk/article544402.ece", "https://www.telegraph.co.uk/news/main.jhtml?xml=/news/2008/03/11/sm_sallyclark15.xml&page=3"]}, "Moment-generating function": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from February 2010", "Generating functions", "Moment (mathematics)"], "title": "Moment-generating function", "method": "Moment-generating function", "url": "https://en.wikipedia.org/wiki/Moment-generating_function", "summary": "In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple results for the moment-generating functions of distributions defined by the weighted sums of random variables. However, not all random variables have moment-generating functions.\nAs its name implies, the moment generating function can be used to compute a distribution\u2019s moments: the nth moment about 0 is the nth derivative of the moment-generating function, evaluated at 0.\nIn addition to real-valued distributions (univariate distributions), moment-generating functions can be defined for vector- or matrix-valued random variables, and can even be extended to more general cases.\nThe moment-generating function of a real-valued distribution does not always exist, unlike the characteristic function. There are relations between the behavior of the moment-generating function of a distribution and properties of the distribution, such as the existence of moments.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Almost all", "Bernoulli distribution", "Binomial distribution", "Cauchy distribution", "Central moment", "Characteristic function (probability theory)", "Chi-squared distribution", "Combinant", "Convolution", "Cumulant", "Cumulant-generating function", "Cumulative distribution function", "Degenerate distribution", "Discrete uniform distribution", "Dot product", "Entropic value at risk", "Expected value", "Exponential distribution", "Exponential generating function", "Exponential order", "Factorial moment generating function", "Fourier transform", "Gamma distribution", "Generating function", "Geometric distribution", "Hamburger moment problem", "Hoeffding's lemma", "Indeterminate form", "Integral transform", "International Standard Book Number", "Jensen's inequality", "Kurtosis", "L-moment", "Laplace distribution", "Logarithmically convex function", "Lognormal distribution", "Markov's inequality", "Measure (mathematics)", "Moment-generating function", "Moment (mathematics)", "Multivariate Cauchy distribution", "Multivariate normal distribution", "Negative binomial distribution", "Noncentral chi-squared distribution", "Normal distribution", "Oxford University Press", "Poisson distribution", "Probability-generating function", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Quantile function", "Random variable", "Random vector", "Rate function", "Raw moment", "Real number", "Riemann\u2013Stieltjes integral", "Skewness", "Standard deviation", "Statistics", "Two-sided Laplace transform", "Uniform distribution (continuous)", "Variance", "Wick rotation"], "references": []}, "Age adjustment": {"categories": ["Demography", "Design of experiments", "Epidemiology"], "title": "Age adjustment", "method": "Age adjustment", "url": "https://en.wikipedia.org/wiki/Age_adjustment", "summary": "In epidemiology and demography, age adjustment, also called age standardization, is a technique used to allow populations to be compared when the age profiles of the populations are quite different.", "images": [], "links": ["Circulatory system", "Demography", "Digital object identifier", "Epidemiology", "Indigenous Australian", "Morbidity", "Prevalence", "PubMed Identifier", "Simpson's paradox", "Standardized mortality ratio", "Weighting"], "references": ["http://www.ausstats.abs.gov.au/ausstats/subscriber.nsf/0/3B1917236618A042CA25711F00185526/$File/43640_2004-05.pdf", "http://www.ausstats.abs.gov.au/ausstats/subscriber.nsf/0/B1BCF4E6DD320A0BCA25714C001822BC/$File/47150_2004-05.pdf", "http://ec.europa.eu/eurostat/documents/3859598/5926869/KS-RA-13-028-EN.PDF", "http://aspe.hhs.gov/datacncl/ageadj.htm", "http://www.ncbi.nlm.nih.gov/pubmed/10495462", "http://www.who.int/healthinfo/paper31.pdf", "http://doi.org/10.1002%2F(SICI)1097-0258(19991015)18:19%3C2645::AID-SIM184%3E3.0.CO;2-Q"]}, "Half circle distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2017", "Continuous distributions", "Pages using deprecated image syntax"], "title": "Wigner semicircle distribution", "method": "Half circle distribution", "url": "https://en.wikipedia.org/wiki/Wigner_semicircle_distribution", "summary": "The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution supported on the interval [\u2212R, R] the graph of whose probability density function f is a semicircle of radius R centered at (0, 0) and then suitably normalized (so that it is really a semi-ellipse):\n\n \n \n \n f\n (\n x\n )\n =\n \n \n 2\n \n \u03c0\n \n R\n \n 2\n \n \n \n \n \n \n \n \n R\n \n 2\n \n \n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n \n \n {\\displaystyle f(x)={2 \\over \\pi R^{2}}{\\sqrt {R^{2}-x^{2}\\,}}\\,}\n for \u2212R \u2264 x \u2264 R, and f(x) = 0 if |x| > R.\nThis distribution arises as the limiting distribution of eigenvalues of many random symmetric matrices as the size of the matrix approaches infinity.\nIt is a scaled beta distribution, more precisely, if Y is beta distributed with parameters \u03b1 = \u03b2 = 3/2, then X = 2RY \u2013 R has the above Wigner semicircle distribution.\nA higher-dimensional generalization is a parabolic distribution in three dimensional space, namely the marginal distribution function of a spherical (parametric) distribution\n \n \n \n \n f\n \n X\n ,\n Y\n ,\n Z\n \n \n (\n x\n ,\n y\n ,\n z\n )\n =\n \n \n 3\n \n 4\n \u03c0\n \n \n \n ,\n \n \n \n x\n \n 2\n \n \n +\n \n y\n \n 2\n \n \n +\n \n z\n \n 2\n \n \n \u2264\n 1\n ,\n \n \n {\\displaystyle f_{X,Y,Z}(x,y,z)={\\frac {3}{4\\pi }},\\qquad \\qquad x^{2}+y^{2}+z^{2}\\leq 1,}\n \n\n \n \n \n \n f\n \n X\n \n \n (\n x\n )\n =\n \n \u222b\n \n \u2212\n \n \n 1\n \u2212\n \n y\n \n 2\n \n \n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n +\n \n \n 1\n \u2212\n \n y\n \n 2\n \n \n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n \n \u222b\n \n \u2212\n \n \n 1\n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n +\n \n \n 1\n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n \n \n \n 3\n \n d\n \n y\n \n \n 4\n \u03c0\n \n \n \n =\n 3\n (\n 1\n \u2212\n \n x\n \n 2\n \n \n )\n \n /\n \n 4.\n \n \n {\\displaystyle f_{X}(x)=\\int _{-{\\sqrt {1-y^{2}-x^{2}}}}^{+{\\sqrt {1-y^{2}-x^{2}}}}\\int _{-{\\sqrt {1-x^{2}}}}^{+{\\sqrt {1-x^{2}}}}{\\frac {3\\mathrm {d} y}{4\\pi }}=3(1-x^{2})/4.}\n \nNote that R=1.\nWhile Wigner's semicircle distribution pertains to the distribution of eigenvalues, Wigner surmise deals with the probability density of the differences between consecutive eigenvalues.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/53/WignerS_distribution_CDF.svg", "https://upload.wikimedia.org/wikipedia/commons/6/66/WignerS_distribution_PDF.svg"], "links": ["ARGUS distribution", "Abramowitz and Stegun", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bessel function", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Catalan number", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chebyshev polynomials", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulant", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Eigenvalues", "Elliptical distribution", "Eric W. Weisstein", "Erlang distribution", "Eugene Wigner", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Free Poisson distribution", "Free probability", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "If and only if", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kesten\u2013McKay measure", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Moment (mathematics)", "Moment generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "N-sphere", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Noncrossing partition", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normalizing constant", "Number theory", "Orthogonal polynomials", "Parabolic fractal distribution", "Pareto distribution", "Partition of a set", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Radius", "Raised cosine distribution", "Random matrices", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Sato\u2013Tate conjecture", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner surmise", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.math.sfu.ca/~cbm/aands/page_360.htm", "http://www.math.sfu.ca/~cbm/aands/page_376.htm", "http://mathworld.wolfram.com/StruveFunction.html", "http://mathworld.wolfram.com/WignersSemicircleLaw.html", "http://www.dtic.upf.edu/~alozano/papers/ThesisIlaria.pdf", "http://doi.org/10.1109%2FAPS.2011.5996900", "http://doi.org/10.1109%2FRADAR.2017.7944181", "http://ieeexplore.ieee.org/document/7944181/", "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5996900"]}, "Classical definition of probability": {"categories": ["All accuracy disputes", "All articles with unsourced statements", "Articles with disputed statements from March 2016", "Articles with unsourced statements from March 2016", "Probability interpretations"], "title": "Classical definition of probability", "method": "Classical definition of probability", "url": "https://en.wikipedia.org/wiki/Classical_definition_of_probability", "summary": "The classical definition or interpretation of probability is identified with the works of Jacob Bernoulli and Pierre-Simon Laplace. As stated in Laplace's Th\u00e9orie analytique des probabilit\u00e9s,\n\nThe probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur more than any other, which renders them, for us, equally possible.This definition is essentially a consequence of the principle of indifference. If elementary events are assigned equal probabilities, then the probability of a disjunction of elementary events is just the number of events in the disjunction divided by the total number of elementary events.\nThe classical definition of probability was called into question by several writers of the nineteenth century, including John Venn and George Boole. The frequentist definition of probability became widely accepted as a result of their criticism, and especially through the works of R.A. Fisher. The classical definition enjoyed a revival of sorts due to the general interest in Bayesian probability, because Bayesian methods require a prior probability distribution and the principle of indifference offers one source of such a distribution. Classical probability can offer prior probabilities that reflect ignorance which often seems appropriate before an experiment is conducted.", "images": [], "links": ["Bayesian probability", "Blaise Pascal", "Caramuel", "Charles-Benjamin de Lubi\u00e8res", "Chevalier de M\u00e9r\u00e9", "Christiaan Huygens", "Digital object identifier", "Elementary events", "Encyclop\u00e9die", "Frequency probability", "Frequentist probability", "Geometry", "George Boole", "Gerolamo Cardano", "Gilles de Roberval", "International Standard Book Number", "Interpretations of probability", "Jacob Bernoulli", "John Venn", "Laplace", "Luca Pacioli", "Pierre-Simon Laplace", "Pierre de Fermat", "Principle of indifference", "Probability", "Probability interpretations", "Probability theory", "Problem of points", "R.A. Fisher", "Theory of probability", "Th\u00e9orie analytique des probabilit\u00e9s"], "references": ["http://hdl.handle.net/2027/spo.did2222.0000.983", "http://doi.org/10.1016%2F0304-4076(95)01766-6", "http://doi.org/10.1214%2Fss%2F1177011360", "http://mathforum.org/isaac/problems/prob1.html"]}, "Vapnik\u2013Chervonenkis theory": {"categories": ["Computational learning theory", "Empirical process"], "title": "Vapnik\u2013Chervonenkis theory", "method": "Vapnik\u2013Chervonenkis theory", "url": "https://en.wikipedia.org/wiki/Vapnik%E2%80%93Chervonenkis_theory", "summary": "Vapnik\u2013Chervonenkis theory (also known as VC theory) was developed during 1960\u20131990 by Vladimir Vapnik and Alexey Chervonenkis. The theory is a form of computational learning theory, which attempts to explain the learning process from a statistical point of view.\nVC theory is related to statistical learning theory and to empirical processes. Richard M. Dudley and Vladimir Vapnik, among others, have applied VC-theory to empirical processes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["0-1 loss", "Aad van der Vaart", "Alexey Chervonenkis", "Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Central limit theorem", "Cluster analysis", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Consistency (statistics)", "Convolutional neural network", "Covering number", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Dimensionality reduction", "Dirac measure", "Dudley's theorem", "Empirical processes", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature engineering", "Feature learning", "Gated recurrent unit", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "Hoeffding's inequality", "Hypograph (mathematics)", "Independent component analysis", "International Conference on Machine Learning", "International Standard Book Number", "Jensen's inequality", "John Wiley & Sons", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Law of large numbers", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Mean-shift", "Multilayer perceptron", "Naive Bayes classifier", "Non-negative matrix factorization", "OPTICS algorithm", "Occam learning", "Online machine learning", "Outline of machine learning", "Perceptron", "Principal component analysis", "Probably approximately correct learning", "Q-learning", "Rademacher complexity", "Random forest", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Richard M. Dudley", "Sauer\u2013Shelah lemma", "Self-organizing map", "Semi-supervised learning", "Shattered set", "Slutsky's theorem", "Springer-Verlag", "Stability (learning theory)", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "U-Net", "Unsupervised learning", "VC dimension", "Vladimir Vapnik"], "references": ["https://arxiv.org/list/cs.LG/recent", "https://books.google.com.ua/books?id=zdDkBwAAQBAJ"]}, "Partial autocorrelation function": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2011", "Covariance and correlation", "Time domain analysis", "Time series", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Partial autocorrelation function", "method": "Partial autocorrelation function", "url": "https://en.wikipedia.org/wiki/Partial_autocorrelation_function", "summary": "In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a time series with its own lagged values, controlling for the values of the time series at all shorter lags. It contrasts with the autocorrelation function, which does not control for other lags.\nThis function plays an important role in data analysis aimed at identifying the extent of the lag in an autoregressive model. The use of this function was introduced as part of the Box\u2013Jenkins approach to time series modelling, whereby plotting the partial autocorrelative functions one could determine the appropriate lags p in an AR (p) model or in an extended ARIMA (p,d,q) model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autocorrelation function", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4463.htm"]}, "Statistical semantics": {"categories": ["All articles with dead external links", "Applied statistics", "Articles with dead external links from May 2018", "Articles with permanently dead external links", "Artificial intelligence applications", "Computational linguistics", "Information retrieval techniques", "Semantics", "Statistical natural language processing"], "title": "Statistical semantics", "method": "Statistical semantics", "url": "https://en.wikipedia.org/wiki/Statistical_semantics", "summary": "In linguistics, statistical semantics applies the methods of statistics to the problem of determining the meaning of words or phrases, ideally through unsupervised learning, to a degree of precision at least sufficient for the purpose of information retrieval. \n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/de/Globe_of_letters.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/de/20170906045643%21Globe_of_letters.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/de/20170824110555%21Globe_of_letters.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/de/20170824102703%21Globe_of_letters.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/de/20170824100912%21Globe_of_letters.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/de/20100309111323%21Globe_of_letters.svg"], "links": ["ACM Transactions on Information Systems", "Anthropological linguistics", "Applied linguistics", "ArXiv", "Bell System Technical Journal", "Bibcode", "Borovets", "COLING", "Cambridge, Massachusetts", "CiteSeerX", "Co-occurrence", "Cognitive Science Society", "Cognitive grammar", "Computational Linguistics (journal)", "Computational linguistics", "Computational semantics", "Constraint-based grammar", "Dependency grammar", "Digital object identifier", "Discourse analysis", "Distributional hypothesis", "Etymology", "Forensic linguistics", "Functional theories of grammar", "Generative grammar", "George Furnas", "Grammar", "Historical linguistics", "History of linguistics", "Index of linguistics articles", "Information Retrieval (journal)", "Information retrieval", "International Joint Conference on Artificial Intelligence", "International Standard Book Number", "Internet linguistics", "J. R. Firth", "John Rupert Firth", "Journal of Experimental and Theoretical Artificial Intelligence", "KDD Conference", "LGBT linguistics", "Language acquisition", "Latent semantic analysis", "Latent semantic indexing", "Lexicography", "Lexicon", "Linguistic anthropology", "Linguistic description", "Linguistic prescription", "Linguistics", "MIT Press", "Machine Learning (journal)", "Machine translation", "Morphology (linguistics)", "Natural language processing", "Neurolinguistics", "OCLC", "Origin of language", "Origin of speech", "Orthography", "Outline of linguistics", "Philological Society", "Philosophy of language", "Phonetics", "Phonology", "Pragmatics", "Psycholinguistics", "Psychological Review", "Second-language acquisition", "Semantic analytics", "Semantic similarity", "Semantics", "Similarity-based generalization", "Sociolinguistics", "Statistical natural language processing", "Statistics", "Stochastic grammar", "Structural linguistics", "Studies in Linguistic Analysis", "Syntax", "Text corpus", "Text mining", "Thames and Hudson", "Unsupervised learning", "Warren Weaver", "Web mining", "Word sense disambiguation"], "references": ["http://lsa.colorado.edu/papers/plato/plato.annote.html", "http://adsabs.harvard.edu/abs/2003cs........8033T", "http://adsabs.harvard.edu/abs/2003cs........9035T", "http://adsabs.harvard.edu/abs/2004cs........7065T", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.100.3751", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.104.7535", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.1829", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.6771", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.9041", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.8734", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.3598", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.184.4759", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.701", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.2939", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.8007", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.9.6425", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.90.9819", "http://psych.stanford.edu/~michael/papers/Draft_Yarlett_Similarity.pdf", "http://locutus.ucr.edu/reprintPDFs/lba95csp.pdf", "http://furnas.people.si.umich.edu/Papers/FurnasEtAl1983_BSTJ_p1753.pdf", "http://acl.ldc.upenn.edu/C/C92/C92-2082.pdf", "http://acl.ldc.upenn.edu/N/N03/N03-1032.pdf", "http://www.mt-archive.info/Weaver-1949.pdf", "http://arxiv.org/abs/cs/0212015", "http://arxiv.org/abs/cs/0212020", "http://arxiv.org/abs/cs/0308033", "http://arxiv.org/abs/cs/0309034", "http://arxiv.org/abs/cs/0309035", "http://arxiv.org/abs/cs/0407065", "http://arxiv.org/abs/cs/0508103", "http://arxiv.org/abs/cs/0608100", "http://cogprints.org/3163/", "http://cogprints.org/3164/", "http://cogprints.org/3732/", "http://cogprints.org/4518/", "http://cogprints.org/5098/", "http://doi.org/10.1002%2Fj.1538-7305.1983.tb03513.x", "http://doi.org/10.1007%2Fs10994-005-0913-1", "http://doi.org/10.1023%2FA:1009976227802", "http://doi.org/10.1037%2F0033-295x.104.2.211", "http://doi.org/10.1080%2F09528130110100270", "http://doi.org/10.1145%2F775047.775138", "http://doi.org/10.1145%2F944012.944013", "http://doi.org/10.1162%2Fcoli.2006.32.3.379", "http://doi.org/10.3115%2F1073445.1073477", "http://doi.org/10.3115%2F992133.992154", "http://www.worldcat.org/oclc/1001646", "http://www.worldcat.org/oclc/123573912", "http://soda.swedish-ict.se/3941/1/sahlgren.distr-hypo.pdf", "http://homepages.inf.ed.ac.uk/smcdonal/cogsci2001.pdf", "https://web.archive.org/web/20140419012951/http://psych.stanford.edu/~michael/papers/Draft_Yarlett_Similarity.pdf", "https://web.archive.org/web/20160304093738/http://furnas.people.si.umich.edu/Papers/FurnasEtAl1983_BSTJ_p1753.pdf"]}, "Cointegration": {"categories": ["All articles needing expert attention", "Articles needing expert attention from December 2010", "Articles needing expert attention with no reason or talk parameter", "Mathematical finance", "Statistics articles needing expert attention", "Time series", "Wikipedia articles with GND identifiers"], "title": "Cointegration", "method": "Cointegration", "url": "https://en.wikipedia.org/wiki/Cointegration", "summary": "Cointegration is a statistical property of a collection (X1, X2, ..., Xk) of time series variables. First, all of the series must be integrated of order d (see Order of integration). Next, if a linear combination of this collection is integrated of order zero, then the collection is said to be co-integrated. Formally, if (X,Y,Z) are each integrated of order d, and there exist coefficients a,b,c such that aX + bY + cZ is integrated of order 0, then X, Y, and Z are cointegrated. Cointegration has become an important property in contemporary time series analysis. Time series often have trends\u2014either deterministic or stochastic. In an influential paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends\u2014these are also called unit root processes, or processes integrated of order \n \n \n \n 1\n :\n I\n (\n 1\n )\n \n \n {\\displaystyle 1:I(1)}\n . They also showed that unit root processes have non-standard statistical properties, so that conventional econometric theory methods do not apply to them.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Charles Plosser", "Chemometrics", "Chi-squared test", "CiteSeerX", "Clinical study design", "Clinical trial", "Clive Granger", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrica", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical Economics", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Error correction model", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fumio Hayashi", "Futures contract", "G-test", "G. S. Maddala", "GNP", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Integrated Authority File", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Econometrics", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order of integration", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Paul Newbold", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter C. B. Phillips", "Phillips\u2013Perron test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R-squared", "Radar chart", "Random assignment", "Random walk", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robert Engle", "Robust regression", "Robust statistics", "Run chart", "Sam Ouliaris", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spurious correlation", "Standard deviation", "Standard error", "Stationary process", "Stationary subspace analysis", "Statistic", "Statistical", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistically significant", "Statistics", "Stem-and-leaf display", "Stochastic", "Stock market index", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The American Statistician", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Unit root", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Wilmott Magazine", "Z-test"], "references": ["http://davegiles.blogspot.com/2013/06/ardl-models-part-ii-bounds-tests.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.353.2946", "http://www-stat.wharton.upenn.edu/~steele/Courses/434/434Context/Co-integration/Murray93DrunkAndDog.pdf", "http://doi.org/10.1002%2Fjae.616", "http://doi.org/10.1002%2Fwilm.10167", "http://doi.org/10.1007%2Fs00181-007-0175-9", "http://doi.org/10.1016%2F0304-3932(82)90012-5", "http://doi.org/10.1016%2F0304-4076(69)41685-7", "http://doi.org/10.1016%2F0304-4076(74)90034-7", "http://doi.org/10.1016%2F0304-4076(81)90079-8", "http://doi.org/10.1080%2F00031305.1994.10476017", "http://www.jstor.org/stable/1913236", "http://www.jstor.org/stable/2938339", "https://books.google.com/books?id=llXBvougICMC&pg=PA155", "https://d-nb.info/gnd/4347470-6", "https://ideas.repec.org/a/spr/empeco/v35y2008i3p497-505.html", "https://www.wikidata.org/wiki/Q1751675"]}, "Scheff\u00e9's method": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2012", "Multiple comparisons", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Scheff\u00e9's method", "method": "Scheff\u00e9's method", "url": "https://en.wikipedia.org/wiki/Scheff%C3%A9%27s_method", "summary": "In statistics, Scheff\u00e9's method, named after the American statistician Henry Scheff\u00e9, is a method for adjusting significance levels in a linear regression analysis to account for multiple comparisons. It is particularly useful in analysis of variance (a special case of regression analysis), and in constructing simultaneous confidence bands for regressions involving basis functions.\nScheff\u00e9's method is a single-step multiple comparison procedure which applies to the set of estimates of all possible contrasts among the factor level means, not just the pairwise differences considered by the Tukey\u2013Kramer method. It works on similar principles as the Working\u2013Hotelling procedure for estimating mean responses in regression, which applies to the set of all possible factor levels.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["ANOVA", "Analysis of variance", "Basis functions", "Confidence band", "Contrast (statistics)", "Copyright status of work by the U.S. government", "Errors and residuals in statistics", "Family-wise error rate", "Henry Scheff\u00e9", "International Standard Book Number", "JSTOR", "Journal of the Royal Statistical Society", "Linear regression", "Mean", "Multiple comparisons", "National Institute of Standards and Technology", "Statistical significance", "Statistician", "Statistics", "Tukey\u2013Kramer method", "United States", "Working\u2013Hotelling procedure"], "references": ["http://www.itl.nist.gov/div898/handbook/prc/section4/prc472.htm", "http://www.nist.gov", "http://www.jstor.org/stable/2984571"]}, "Polynomial and rational function modeling": {"categories": ["CS1 maint: Multiple names: authors list", "Interpolation", "Pages with citations lacking titles", "Regression models", "Statistical ratios", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Polynomial and rational function modeling", "method": "Polynomial and rational function modeling", "url": "https://en.wikipedia.org/wiki/Polynomial_and_rational_function_modeling", "summary": "In statistical modeling (especially process modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annales de math\u00e9matiques pures et appliqu\u00e9es", "Approximation theory", "Arithmetic mean", "Asymptote", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calibration curve", "Calyampudi Radhakrishna Rao", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational statistics", "Confidence interval", "Confounding", "Constant function", "Contingency table", "Continuous probability distribution", "Control chart", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cubic function", "Curve fitting", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation theory", "Experiment", "Exponential family", "Exponential smoothing", "Extrapolation", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "Harmonic mean", "Heteroscedasticity", "Histogram", "Historia Mathematica", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Integer", "Interaction (statistics)", "International Standard Book Number", "Interpolation", "Interquartile range", "Interval estimation", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jack Kiefer (statistician)", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Joseph Diaz Gergonne", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lawrence D. Brown", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear function", "Linear least squares (mathematics)", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Metric (mathematics)", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving least squares", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Neil Sloane", "Nelson\u2013Aalen estimator", "Non-linear least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial function", "Polynomial interpolation", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Process modeling", "Proportional hazards model", "Psychometrics", "Quadratic function", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rational function", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Ridge regression", "Robust regression", "Robust statistics", "Run chart", "Runge's phenomenon", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaling (geometry)", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical modeling", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen M. Stigler", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Translation (geometry)", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://neilsloane.com/doc/design.pdf", "http://neilsloane.com/doc/doeh.pdf", "http://neilsloane.com/doc/meatball.pdf", "http://support.sas.com/publishing/bbu/companion_site/index_author.html#tobias", "http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-20/2/df451ec5fbb7c044d0f4d900af80ec86", "http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-1Y/2/680c7ada0198761e9866197d53512ab4", "http://www.itl.nist.gov/div898/handbook/pmd/section6/pmd642.htm", "http://www.nist.gov", "http://doi.org/10.1016%2F0315-0860(74)90033-0", "http://doi.org/10.1016%2F0315-0860(74)90034-2", "http://doi.org/10.1093%2Fbiomet%2F12.1-2.1", "http://www.jstor.org/stable/2331929", "http://biomet.oxfordjournals.org/cgi/content/citation/12/1-2/1", "http://stats.lse.ac.uk/atkinson/", "http://www.maths.manchester.ac.uk/~adonev/", "https://books.google.com/books?id=oIHsrw6NBmoC"]}, "Meta-regression": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from July 2012", "Articles with unsourced statements from July 2018", "Meta-analysis", "Regression analysis"], "title": "Meta-regression", "method": "Meta-regression", "url": "https://en.wikipedia.org/wiki/Meta-regression", "summary": "Meta-regression is a tool used in meta-analysis to examine the impact of moderator variables on study effect size using regression-based techniques. Meta-regression is more effective at this task than are standard meta-analytic techniques", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Digital object identifier", "International Standard Book Number", "Literature survey", "Meta-analysis", "Moderator variable", "PubMed Identifier", "Regression analysis", "Systematic review"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/12111920", "http://www.ncbi.nlm.nih.gov/pubmed/19719359", "http://doi.org/10.1002/sim.1187", "http://doi.org/10.1037/a0016619"]}, "Outliers in statistics": {"categories": ["All articles with unsourced statements", "Articles with inconsistent citation formats", "Articles with unsourced statements from October 2016", "Commons category link is on Wikidata", "Robust statistics", "Statistical charts and diagrams", "Statistical outliers", "Webarchive template wayback links", "Wikipedia articles with BNF identifiers", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with SUDOC identifiers"], "title": "Outlier", "method": "Outliers in statistics", "url": "https://en.wikipedia.org/wiki/Outlier", "summary": "In statistics, an outlier is an observation point that is distant from other observations. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set. An outlier can cause serious problems in statistical analyses.\nOutliers can occur by chance in any distribution, but they often indicate either measurement error or that the population has a heavy-tailed distribution. In the former case one wishes to discard them or use statistics that are robust to outliers, while in the latter case they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two distinct sub-populations, or may indicate 'correct trial' versus 'measurement error'; this is modeled by a mixture model.\nIn most larger samplings of data, some data points will be further away from the sample mean than what is deemed reasonable. This can be due to incidental systematic error or flaws in the theory that generated an assumed family of probability distributions, or it may be that some observations are far from the center of the data. Outlier points can therefore indicate faulty data, erroneous procedures, or areas where a certain theory might not be valid. However, in large samples, a small number of outliers is to be expected (and not due to any anomalous condition).\nOutliers, being the most extreme observations, may include the sample maximum or sample minimum, or both, depending on whether they are extremely high or low. However, the sample maximum and minimum are not always outliers because they may not be unusually far from other observations.\nNaive interpretation of statistics derived from data sets that include outliers may be misleading. For example, if one is calculating the average temperature of 10 objects in a room, and nine of them are between 20 and 25 degrees Celsius, but an oven is at 175 \u00b0C, the median of the data will be between 20 and 25 \u00b0C but the mean temperature will be between 35.5 and 40 \u00b0C. In this case, the median better reflects the temperature of a randomly sampled object (but not the temperature in the room) than the mean; naively interpreting the mean as \"a typical sample\", equivalent to the median, is incorrect. As illustrated in this case, outliers may indicate data points that belong to a different population than the rest of the sample set.\nEstimators capable of coping with outliers are said to be robust: the median is a robust statistic of central tendency, while the mean is not. However, the mean is generally more precise estimator.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Michelsonmorley-boxplot.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Standard_deviation_diagram_micro.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7e/Wiki_q_inter_def.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["ASTM", "American Academy of Arts and Sciences", "Anomaly (natural sciences)", "Anomaly detection", "Arithmetic mean", "Average", "Benjamin Peirce", "Biblioth\u00e8que nationale de France", "Binomial distribution", "Box plot", "Cauchy distribution", "Censoring (statistics)", "Central tendency", "Charles Sanders Peirce", "Chauvenet's criterion", "Coast Survey", "Cook's distance", "Data analysis", "Data mining", "Data set", "Data transformation (statistics)", "Degrees Celsius", "Digital object identifier", "Dixon's Q test", "Encyclopedia of Mathematics", "Estimation of covariance matrices", "Estimator", "Fat tails", "G. S. Maddala", "Grubbs' test for outliers", "Hans-Peter Kriegel", "Heavy-tailed distribution", "Hierarchical Bayes model", "Integrated Authority File", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "JSTOR", "K-nearest neighbor", "King effect", "Leverage (statistics)", "Library of Congress Control Number", "Local Outlier Factor", "Mahalanobis distance", "MathWorld", "Measurement error", "Median", "Michelson\u2013Morley experiment", "Michiel Hazewinkel", "Mixture model", "Normal distribution", "Normal probability plot", "OCLC", "Outlier (disambiguation)", "Peirce's criterion", "Peter Rousseeuw", "Poisson distribution", "Probability distribution", "Quartile", "Regression analysis", "Relaxed intersection", "Robust regression", "Robust statistics", "SIGMOD", "Sample (statistics)", "Sample maximum", "Sample minimum", "Set estimation", "Skewness", "Standard deviation", "Statistical population", "Statistical significance", "Statistics", "Studentized residual", "Systematic error", "Syst\u00e8me universitaire de documentation", "Theory", "Three sigma rule", "Truncation (statistics)", "Wayback Machine", "Winsorising", "Winsorizing"], "references": ["http://mathworld.wolfram.com/CauchyDistribution.html", "http://mathworld.wolfram.com/Outlier.html", "http://www.dbs.ifi.lmu.de/Publikationen/Papers/LOF.pdf", "http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1852AJ......2..161P;data_type=PDF_HIGH", "http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1852AJ......2..176P;data_type=PDF_HIGH", "http://data.bnf.fr/ark:/12148/cb12127529t", "http://www.ensta-bretagne.fr/jaulin/paper_probint_0.pdf", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda35h.htm", "http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0019.PDF#page=215", "http://doi.org/10.1002%2Fsam.11161", "http://doi.org/10.1002%2Fwidm.1280", "http://doi.org/10.1007%2Fs007780050006", "http://doi.org/10.1007%2Fs10618-012-0300-z", "http://doi.org/10.1023%2FB:AIRE.0000045502.10941.a9", "http://doi.org/10.1049%2Fip-vis:19941330", "http://doi.org/10.1080%2F00401706.1969.10490657", "http://doi.org/10.1145%2F335191.335388", "http://doi.org/10.1145%2F342009.335437", "http://doi.org/10.1214%2Faoms%2F1177705900", "http://doi.org/10.2307%2F25138498", "http://www.jstor.org/stable/25138498", "http://projecteuclid.org/download/pdf_1/euclid.aoms/1177705900", "http://www.worldcat.org/issn/1942-4787", "http://www.worldcat.org/oclc/3058187", "http://www.stats.ox.ac.uk/pub/StatMeth/Robust.pdf", "https://books.google.com/books?id=H-lkYmatYtAC&pg=PA60&lpg=PA60&dq=median+is+less+precise+than+mean&source=bl&ots=s9bMWI9vDo&sig=qSxlmBY4JhbRS_JWMyapx2A6Ofc&hl=lv&sa=X&ved=0ahUKEwjT-_ah8uzSAhVMWCwKHT6UDZIQ6AEITTAH#v=onepage&q=median%20is%20less%20precise%20than%20mean&f=false", "https://books.google.com/books?id=nBS3AAAAIAAJ&pg=PA89", "https://link.springer.com/article/10.1007%2Fs10994-013-5422-z", "https://catalogue.bnf.fr/ark:/12148/cb12127529t", "https://www.idref.fr/029709113", "https://id.loc.gov/authorities/subjects/sh85096171", "https://d-nb.info/gnd/4510494-3", "https://web.archive.org/web/20121021081319/http://www.stats.ox.ac.uk/pub/StatMeth/Robust.pdf", "https://www.encyclopediaofmath.org/index.php?title=O/o110080", "https://www.jstor.org/stable/2345543?seq=1#page_scan_tab_contents", "https://www.wikidata.org/wiki/Q779824"]}, "Quadratic classifier": {"categories": ["All articles needing additional references", "Articles needing additional references from December 2009", "Classification algorithms", "Statistical classification"], "title": "Quadratic classifier", "method": "Quadratic classifier", "url": "https://en.wikipedia.org/wiki/Quadratic_classifier", "summary": "A quadratic classifier is used in machine learning and statistical classification to separate measurements of two or more classes of objects or events by a quadric surface. It is a more general version of the linear classifier.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Circle", "Conic sections", "Covariance", "Digital object identifier", "Dot product", "Ellipse", "Hyperbola", "Kernel trick", "Likelihood-ratio test", "Line (geometry)", "Linear classifier", "Linear discriminant analysis", "Machine learning", "Normal distribution", "Parabola", "Probability vector", "PubMed Identifier", "Quadratic (disambiguation)", "Quadric surface", "Statistical classification", "Support vector machine", "Training set", "VC dimension", "Wolfram Demonstrations Project"], "references": ["http://demonstrations.wolfram.com/PatternRecognitionPrimerII", "http://www.ncbi.nlm.nih.gov/pubmed/18255613", "http://doi.org/10.1109%2F72.554194", "http://doi.org/10.1109%2Fpgec.1965.264137", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4038449", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=554194"]}, "Tukey lambda distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax", "Probability distributions with non-finite variance", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Tukey lambda distribution", "method": "Tukey lambda distribution", "url": "https://en.wikipedia.org/wiki/Tukey_lambda_distribution", "summary": "Formalized by John Tukey, the Tukey lambda distribution is a continuous, symmetric probability distribution defined in terms of its quantile function. It is typically used to identify an appropriate distribution (see the comments below) and not used in statistical models directly.\nThe Tukey lambda distribution has a single shape parameter, \u03bb, and as with other probability distributions, it can be transformed with a location parameter, \u03bc, and a scale parameter, \u03c3. Since the general form of probability distribution can be expressed in terms of the standard distribution, the subsequent formulas are given for the standard form of the function.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/25/Several_samples_of_the_pdfs_of_the_Tukey_lambda_distributions.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["ARGUS distribution", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Concave function", "Continuous uniform distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Copyright status of work by the U.S. government", "Correlation", "Cumulative distribution function", "Dagum distribution", "Data set", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Histogram", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "John Tukey", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the Royal Statistical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "L-moments", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "National Institute of Standards and Technology", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "PPCC plot", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Reflection symmetry", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical model", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.itl.nist.gov/div898/handbook/eda/section3/eda366f.htm", "http://www.nist.gov", "http://arxiv.org/abs/0903.1592", "http://arxiv.org/abs/math/0701405", "http://doi.org/10.1016%2Fj.csda.2007.06.021", "http://doi.org/10.2307%2F2283943", "http://www.jstor.org/stable/2283943"]}, "Pooled variance": {"categories": ["All articles needing additional references", "All articles to be expanded", "All articles with empty sections", "All articles with unsourced statements", "Analysis of variance", "Articles needing additional references from June 2011", "Articles to be expanded from June 2017", "Articles using small message boxes", "Articles with empty sections from June 2017", "Articles with unsourced statements from November 2010", "Statistical deviation and dispersion"], "title": "Pooled variance", "method": "Pooled variance", "url": "https://en.wikipedia.org/wiki/Pooled_variance", "summary": "In statistics, pooled variance (also known as combined, composite, or overall variance) is a method for estimating variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same. The numerical estimate resulting from the use of this method is also called the pooled variance.\nUnder the assumption of equal population variances, the pooled sample variance provides a higher precision estimate of variance than the individual sample variances. This higher precision can lead to increased statistical power when used in statistical tests that compare the populations, such as the t-test.\nThe square root of a pooled variance estimator is known as a pooled standard deviation (also known as combined, composite, or overall standard deviation).", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a7/Split-arrows.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bessel's correction", "Covariance", "Digital object identifier", "Effect size", "Efficiency (statistics)", "Estimation theory", "Mean", "Pooled covariance matrix", "Pooled degree of freedom", "Pooled mean", "Precision (statistics)", "PubMed Central", "PubMed Identifier", "Random error", "Sample size", "Sample variance", "Standard deviation", "Statistical hypothesis testing", "Statistical independence", "Statistical power", "Statistical test", "Statistics", "T-test", "Variance", "Weighted average"], "references": ["http://web.psych.utoronto.ca/~psy379/Stats%20PPT.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1473027", "http://www.ncbi.nlm.nih.gov/pubmed/15869691", "http://doi.org/10.1111%2Fj.0956-7976.2005.01538.x", "http://goldbook.iupac.org/P04758.html", "https://web.archive.org/web/20020624174749/http://www.isixsigma.com/dictionary/Pooled_Standard_Deviation-295.htm"]}, "Weighted sample": {"categories": ["All articles needing additional references", "All articles needing expert attention", "All articles that are too technical", "Articles needing additional references from February 2008", "Articles needing expert attention from June 2014", "Articles with multiple maintenance issues", "Covariance and correlation", "Estimation methods", "Matrices", "Summary statistics", "U-statistics", "Wikipedia articles that are too technical from June 2014"], "title": "Sample mean and covariance", "method": "Weighted sample", "url": "https://en.wikipedia.org/wiki/Sample_mean_and_covariance", "summary": "The sample mean or empirical mean and the sample covariance are statistics computed from a collection (the sample) of data on one or more random variables.\nThe sample mean and sample covariance are estimators of the population mean and population covariance, where the term population refers to the set from which the sample was taken.\nThe sample mean is a vector each of whose elements is the sample mean of one of the random variables \u2013 that is, each of whose elements is the arithmetic average of the observed values of one of the variables. The sample covariance matrix is a square matrix whose i, j element is the sample covariance (an estimate of the population covariance) between the sets of observed values of two of the variables and whose i, i element is the sample variance of the observed values of one of the variables. If only one variable has had values observed, then the sample mean is a single number (the arithmetic average of the observed values of that variable) and the sample covariance matrix is also simply a single value (a 1x1 matrix containing a single number, the sample variance of the observed values of that variable).\nDue to their ease of calculation and other desirable characteristics, the sample mean and sample covariance are widely used in statistics and applications to numerically represent the location and dispersion, respectively, of a distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Arithmetic average", "Arithmetic mean", "Bart Kosko", "Bessel's correction", "Bias of an estimator", "Covariance", "Covariance matrix", "Estimation of covariance matrices", "Estimator", "Estimators", "Gaussian distribution", "International Standard Book Number", "Interquartile range", "Location parameter", "Matrix (mathematics)", "Maximum likelihood", "Mean", "Multivariate random variable", "Normalizing constant", "Outliers", "Positive semi-definite matrix", "Probability distribution", "Quantile", "Random variable", "Random variables", "Random vector", "Realization (probability)", "Robust statistics", "Sample (statistics)", "Sample median", "Sample variance", "Scatter matrix", "Standard error of the mean", "Statistic", "Statistical dispersion", "Statistical population", "Trimmed estimator", "Trimmed mean", "Unbiased estimation of standard deviation", "Vector (mathematics)", "Weighted mean", "Winsorising", "Winsorized mean"], "references": ["http://www.edge.org/q2008/q08_16.html#kosko", "https://books.google.com/books?id=gFWcQgAACAAJ", "https://www.gnu.org/software/gsl/manual", "https://www.gnu.org/software/gsl/manual/html_node/Weighted-Samples.html"]}, "Dendrogram": {"categories": ["All articles needing additional references", "Articles needing additional references from January 2017", "CS1 maint: Multiple names: authors list", "Cluster analysis", "Graph drawing", "Statistical charts and diagrams", "Trees (data structures)"], "title": "Dendrogram", "method": "Dendrogram", "url": "https://en.wikipedia.org/wiki/Dendrogram", "summary": "A dendrogram is a diagram representing a tree. This diagrammatic representation is frequently used in different contexts:\n\nin hierarchical clustering, it illustrates the arrangement of the clusters produced by the corresponding analyses.\nin computational biology, it shows the clustering of genes or samples, sometimes in the margins of heatmaps.\nin phylogenetics, it displays the evolutionary relationships among various biological taxa. In this case, the dendrogram is also called a phylogenetic tree.The name dendrogram derives from the two ancient greek words \u03b4\u03ad\u03bd\u03b4\u03c1\u03bf\u03bd (d\u00e9ndron), meaning \"tree\", and \u03b3\u03c1\u03ac\u03bc\u03bc\u03b1 (gr\u00e1mma), meaning \"drawing, mathematical figure\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/83/Global-Diversity-of-Sponges-%28Porifera%29-pone.0035105.s008.tif", "https://upload.wikimedia.org/wikipedia/commons/1/16/Heatmap_RNAseqV2_1.png", "https://upload.wikimedia.org/wikipedia/commons/7/70/Phylogenetic_tree.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c5/UPGMA_Dendrogram_Hierarchical.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Ancient greek", "Bibcode", "Carl Woese", "Cladogram", "Computational biology", "Dendrogramma", "Diagram", "Digital object identifier", "Distance matrices in phylogeny", "Evolution", "Freeware", "Gene", "Genetic distances", "Heat map", "Hierarchical clustering", "International Standard Book Number", "Last universal common ancestor", "MEGA, Molecular Evolutionary Genetics Analysis", "OCLC", "Otto Kandler", "Phylogenetic tree", "Phylogenetics", "PubMed Central", "PubMed Identifier", "RNA-Seq", "R (programming language)", "Taxa", "Tree (graph theory)", "Tree of Life", "UPGMA", "YEd"], "references": ["http://www.tabularium.be/bailly/", "http://adsabs.harvard.edu/abs/1990PNAS...87.4576W", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3338747", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4817050", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC54159", "http://www.ncbi.nlm.nih.gov/pubmed/2112744", "http://www.ncbi.nlm.nih.gov/pubmed/22558119", "http://www.ncbi.nlm.nih.gov/pubmed/26209431", "http://doi.org/10.1073%2Fpnas.87.12.4576", "http://doi.org/10.1093%2Fbioinformatics%2Fbtv428", "http://doi.org/10.1198%2Ftas.2009.0033", "http://doi.org/10.1371%2Fjournal.pone.0035105", "http://www.pnas.org/content/87/12/4576.full.pdf", "http://www.worldcat.org/oclc/461974285", "https://www.britannica.com/science/phylogenetic-tree", "https://cran.r-project.org/web/packages/dendextend/vignettes/Cluster_Analysis.html#the-3-clusters-from-the-complete-method-vs-the-real-species-category", "https://www.worldcat.org/oclc/461974285"]}, "Statistical theory": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from January 2015", "CS1 maint: Multiple names: authors list", "Statistical theory"], "title": "Statistical theory", "method": "Statistical theory", "url": "https://en.wikipedia.org/wiki/Statistical_theory", "summary": "The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches. Within a given approach, statistical theory gives ways of comparing statistical procedures; it can find a best possible procedure within a given context for given statistical problems, or can provide guidance on the choice between alternative procedures.Apart from philosophical considerations about how to make statistical inferences and decisions, much of statistical theory consists of mathematical statistics, and is closely linked to probability theory, to utility theory, and to optimization.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "American Journal of Education", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Applied statistics", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "C. R. Rao", "Cambridge University Press", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chapman & Hall", "Charles Sanders Peirce", "Charles Sanders Peirce bibliography", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data analysis", "Data analyst", "Data collection", "David Freedman (statistician)", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension reduction", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Estimation theory", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Foundations of statistics", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Ian Hacking", "Index of dispersion", "Ingram Olkin", "Interaction (statistics)", "International Standard Book Number", "Interpreting statistical data", "Interquartile range", "Interval estimation", "Isis (journal)", "Isotonic regression", "JSTOR", "Jack Kiefer (mathematician)", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Wiley & Sons", "Jonckheere's trend test", "Joseph Jastrow", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lawrence D. 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It is focused on providing facilities for users with little statistical experience. It combines data frames, contingency tables, random numbers, matrices in a user friendly virtual worksheet. This worksheet allows users to explore the possibilities of calculations, analysis, simulations and manipulation of data.\nFor mathematical calculations, the Statistical Lab uses the R package, which is a free implementation of the language S Plus (originally developed by Bell Laboratories).", "images": [], "links": ["Bell Laboratories", "Business administration", "Computer program", "Digital object identifier", "Economics", "Free University of Berlin", "GPL", "Humanities", "International Standard Book Number", "Microsoft Windows 2000", "Microsoft Windows XP", "Operating system", "R (programming language)", "SPSS", "Social sciences", "Software categories", "Software developer", "Software license", "Software release life cycle", "Statistical", "Statistics", "Windows 7"], "references": ["http://www.cedis.fu-berlin.de", "http://forum.statistiklabor.de", "http://tutorials.statistiklabor.de", "http://www.statistiklabor.de/en/", "http://www.statistiklabor.de/en/Download/SetupAndInstallation/index.html", "http://www.statistiklabor.de/en/index.html", "http://doi.org/10.1007%2Fs10182-006-0236-y", "http://statistiklabor.tigris.org/"]}, "Heteroscedasticity-consistent standard errors": {"categories": ["Regression analysis", "Simultaneous equation methods (econometrics)"], "title": "Heteroscedasticity-consistent standard errors", "method": "Heteroscedasticity-consistent standard errors", "url": "https://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors", "summary": "The topic of heteroscedasticity-consistent (HC) standard errors arises in statistics and econometrics in the context of linear regression as well as time series analysis. These are also known as Eicker\u2013Huber\u2013White standard errors (also Huber\u2013White standard errors or White standard errors), to recognize the contributions of Friedhelm Eicker, Peter J. Huber, and Halbert White.In regression and time-series modelling, basic forms of models make use of the assumption that the errors or disturbances ui have the same variance across all observation points. When this is not the case, the errors are said to be heteroscedastic, or to have heteroscedasticity, and this behaviour will be reflected in the residuals \n \n \n \n \n \n \n \n \n u\n \n i\n \n \n ^\n \n \n \n \n \n \n {\\displaystyle \\scriptstyle {\\widehat {u_{i}}}}\n estimated from a fitted model. Heteroscedasticity-consistent standard errors are used to allow the fitting of a model that does contain heteroscedastic residuals. The first such approach was proposed by Huber (1967), and further improved procedures have been produced since for cross-sectional data, time-series data and GARCH estimation.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["BLUE", "CiteSeerX", "Digital object identifier", "EViews", "Econometrica", "Econometrics", "Errors and residuals in statistics", "Friedhelm Eicker", "GARCH", "Generalized estimating equation", "Generalized least squares", "Generalized method of moments", "Halbert White", "Heteroscedasticity", "International Standard Book Number", "JSTOR", "James G. MacKinnon", "Journal of Econometrics", "Leverage (statistics)", "Linear regression", "Logit", "MATLAB", "Mathematical Reviews", "Maximum likelihood estimation", "Newey\u2013West estimator", "Ordinary least squares", "Peter J. Huber", "Probit", "Python (programming language)", "RATS (statistical package)", "R (programming language)", "Stata", "Statistics", "Time-series", "Time series analysis", "Uncorrelated", "Weighted least squares", "White test", "William Greene (economist)", "Zentralblatt MATH"], "references": ["http://davegiles.blogspot.com/2013/05/robust-standard-errors-for-nonlinear.html", "http://www.eviews.com/EViews8/ev8ecrobust_n.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.7646", "http://www.ams.org/mathscinet-getitem?mr=0214223", "http://www.ams.org/mathscinet-getitem?mr=0216620", "http://www.ams.org/mathscinet-getitem?mr=0575027", "http://doi.org/10.1016/0304-4076(85)90158-7", "http://doi.org/10.2307/1912934", "http://doi.org/10.3758/BF03192961", "http://www.jstor.org/stable/1912934", "http://projecteuclid.org/euclid.bsmsp/1200512981", "http://projecteuclid.org/euclid.bsmsp/1200512988", "http://www.r-project.org/useR-2006/Slides/Kleiber+Zeileis.pdf", "http://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.RegressionResults.html", "http://zbmath.org/?format=complete&q=an:0212.21504", "http://zbmath.org/?format=complete&q=an:0217.51201", "https://books.google.com/books?id=86rWI7WzFScC&pg=PA106", "https://www.mathworks.com/help/econ/hac.html", "https://www.stata.com/manuals13/p_robust.pdf", "https://www.stata.com/manuals13/rregress.pdf", "https://web.archive.org/web/20070422030316/http://www.r-project.org/useR-2006/Slides/Kleiber+Zeileis.pdf", "https://cran.r-project.org/web/packages/sandwich/index.html"]}, "Independent component analysis": {"categories": ["All articles needing additional references", "All articles needing expert attention", "All articles with unsourced statements", "Articles needing additional references from October 2011", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Articles with unsourced statements from May 2013", "Articles with unsourced statements from October 2012", "Dimension reduction", "Signal estimation", "Statistics articles needing expert attention"], "title": "Independent component analysis", "method": "Independent component analysis", "url": "https://en.wikipedia.org/wiki/Independent_component_analysis", "summary": "In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that the subcomponents are non-Gaussian signals and that they are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the \"cocktail party problem\" of listening in on one person's speech in a noisy room.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/82/A-Local-Learning-Rule-for-Independent-Component-Analysis-srep28073-s3.ogv", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b8/Independent_component_analysis_in_EEGLAB.png", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Blind deconvolution", "Blind signal separation", "Blind source separation", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Cell (biology)", "Central Limit Theorem", "Central limit theorem", "Cluster analysis", "Cocktail party problem", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "Cumulative distribution functions", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Differential entropy", "Digital object identifier", "Dimension reduction", "Dimensionality reduction", "EEG", "EEGLAB", "Eigenvalue decomposition", "Electroencephalogram", "Empirical risk minimization", "Ensemble learning", "Entropy", "Expectation\u2013maximization algorithm", "FMRI", "FMRIB Software Library", "Factor analysis", "Factorial code", "FastICA", "Feature engineering", "Feature learning", "Gated recurrent unit", "Glossary of artificial intelligence", "Gradient descent", "Gram-Schmidt", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "Hilbert spectrum", "Image processing", "Infomax", "International Conference on Machine Learning", "International Standard Book Number", "International Standard Serial Number", "Internet resource management", "JADE (ICA)", "Jacobian matrix", "Journal of Machine Learning Research", "J\u00fcrgen Schmidhuber", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kernel-independent component analysis", "Kullback\u2013Leibler divergence", "Kurtosis", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Maximum likelihood", "Mean-shift", "Medical diagnosis", "Multi-cluster assignment", "Multilayer perceptron", "Multilinear principal component analysis", "Multilinear subspace learning", "Multivariate statistics", "Mutual information", "Naive Bayes classifier", "Negentropy", "Network tomography", "Non-negative matrix factorization", "Nonlinear ICA", "Nonlinear dimensionality reduction", "OPTICS algorithm", "Occam learning", "Online machine learning", "Outline of machine learning", "Perceptron", "Principal component analysis", "Principle of maximum entropy", "Probability density function", "Probably approximately correct learning", "Projection pursuit", "Pseudo inverse", "PubMed Central", "PubMed Identifier", "Q-learning", "RIKEN", "RNA-sequencing", "Random forest", "Random vector", "Rank (linear algebra)", "Recurrent neural network", "Regression analysis", "Regularization (mathematics)", "Reinforcement learning", "Relevance vector machine", "Resting state fMRI", "Restricted Boltzmann machine", "Round number", "Sample mean", "Self-organizing map", "Semi-supervised learning", "Signal processing", "Singular value decomposition", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical independence", "Statistical learning theory", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Terry Sejnowski", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory", "Variance", "Varimax rotation", "Whitening transformation"], "references": ["http:ftp://ftp.idsia.ch/pub/juergen/lococode.pdf", "http://brandon-merkl.blogspot.com/2005/12/independent-component-analysis.html", "http://isp.imm.dtu.dk/toolbox/", "http://mlsp.cs.cmu.edu/courses/fall2012/lectures/ICA.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.8895", "http://www.ece.ucsb.edu/wcsl/courses/ECE594/594C_F10Madhow/comon94.pdf", "http://sccn.ucsd.edu/eeglab/", "http://sccn.ucsd.edu/fmrlab/", "http://nic.uoregon.edu/projects/hipersat/index.php", "http://www.cs.helsinki.fi/u/ahyvarin/papers/NN00new.pdf", "http://www.cs.helsinki.fi/u/ahyvarin/whatisica.shtml", "http://www.cis.hut.fi/aapo/papers/IJCNN99_tutorialweb/IJCNN99_tutorial3.html", "http://www.cis.hut.fi/projects/ica/book/", "http://www.cis.hut.fi/projects/ica/book/intro.pdf", "http://www.cis.hut.fi/projects/ica/cocktail/cocktail_en.cgi", "http://www.cis.hut.fi/projects/ica/fastica/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2882863", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2895624", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4122333", "http://www.ncbi.nlm.nih.gov/pubmed/10946390", "http://www.ncbi.nlm.nih.gov/pubmed/12814576", "http://www.ncbi.nlm.nih.gov/pubmed/17188898", "http://www.ncbi.nlm.nih.gov/pubmed/24658644", "http://www.ncbi.nlm.nih.gov/pubmed/9425547", "http://www.ncbi.nlm.nih.gov/pubmed/9730022", "http://www.nbtwiki.net/doku.php?id=tutorial:compute_independent_component_analysis", "http://icatb.sourceforge.net/", "http://mdp-toolkit.sourceforge.net/", "http://doi.org/10.1016%2FS1053-8119(03)00097-1", "http://doi.org/10.1016%2Fj.neuroimage.2006.11.004", "http://doi.org/10.1016%2Fs0042-6989(97)00121-1", "http://doi.org/10.1016%2Fs0166-2236(00)01683-0", "http://doi.org/10.1016%2Fs0893-6080(00)00026-5", "http://doi.org/10.1038%2Fnbt.2859", "http://doi.org/10.1038%2Fsrep28073", "http://doi.org/10.1142%2Fs0129065797000458", "http://doi.org/10.1162%2F089976699300016629", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5753957", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6875048&tag=1", "http://www.worldcat.org/issn/0899-7667", "https://web.archive.org/web/20060630205321/http://www.bsp.brain.riken.go.jp/ICALAB/", "https://arxiv.org/abs/1404.2986", "https://arxiv.org/list/cs.LG/recent", "https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/MELODIC"]}, "Biased random walk (biochemistry)": {"categories": ["All articles lacking reliable references", "All articles needing additional references", "All articles with specifically marked weasel-worded phrases", "All articles with unsourced statements", "All pages needing factual verification", "Articles lacking reliable references from March 2017", "Articles needing additional references from September 2015", "Articles with specifically marked weasel-worded phrases from April 2017", "Articles with specifically marked weasel-worded phrases from March 2017", "Articles with unsourced statements from March 2017", "Commons category link is on Wikidata", "Motile cells", "Perception", "Taxes (biology)", "Transmembrane receptors", "Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference", "Wikipedia articles needing factual verification from March 2017", "Wikipedia articles needing page number citations from March 2017"], "title": "Chemotaxis", "method": "Biased random walk (biochemistry)", "url": "https://en.wikipedia.org/wiki/Chemotaxis", "summary": "Chemotaxis (from chemo- + taxis) is the movement of an organism in response to a chemical stimulus. Somatic cells, bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals in their environment. This is important for bacteria to find food (e.g., glucose) by swimming toward the highest concentration of food molecules, or to flee from poisons (e.g., phenol). In multicellular organisms, chemotaxis is critical to early development (e.g., movement of sperm towards the egg during fertilization) and subsequent phases of development (e.g., migration of neurons or lymphocytes) as well as in normal function and health (e.g., migration of leukocytes during injury or infection). In addition, it has been recognized that mechanisms that allow chemotaxis in animals can be subverted during cancer metastasis.\nPositive chemotaxis occurs if the movement is toward a higher concentration of the chemical in question; negative chemotaxis if the movement is in the opposite direction. Chemically prompted kinesis (randomly directed or nondirectional) can be called chemokinesis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/23/Chemotaxis1.jpg", "https://upload.wikimedia.org/wikipedia/commons/d/d8/Chtx-AttrRep-en.png", "https://upload.wikimedia.org/wikipedia/commons/f/ff/ChtxAspRec.png", "https://upload.wikimedia.org/wikipedia/commons/2/2e/ChtxCCW_CW_%28Fixed%29.png", "https://upload.wikimedia.org/wikipedia/commons/6/60/ChtxCRF2.png", "https://upload.wikimedia.org/wikipedia/commons/4/46/ChtxChemkinStr2.png", "https://upload.wikimedia.org/wikipedia/commons/1/10/ChtxChemokineStruct.png", "https://upload.wikimedia.org/wikipedia/commons/5/5e/Chtxbaceukkl1.png", "https://upload.wikimedia.org/wikipedia/commons/2/22/Chtxbactsign1.png", "https://upload.wikimedia.org/wikipedia/commons/c/ce/Chtxphenomen1.png", "https://upload.wikimedia.org/wikipedia/commons/2/2c/Chtxsel.png", "https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["12-Hydroxyeicosatetraenoic acid", "12-Hydroxyheptadecatrienoic acid", "15-Hydroxyeicosatetraenoic acid", "5-Hydroxyeicosatetraenoic acid", "5-Hydroxyicosatetraenoic acid", "5-oxo-eicosatetraenoic acid", "AIDS", "ALOX12", "ALOX15", "ALOX5", "Actin", "Adenosine triphosphate", "Allergy", "Ameboid", "Amino acids", "Amoeba (genus)", "Angiogenesis", "Apoptosis", "Arachidonic acid", "Arthritis", "Asbestos", "Atherosclerosis", "BLT", "BLT2", "Bacillus subtilis", "Bacteria", "Bacterial", "Basal body", "Benzpyrene", "Bibcode", "Brucellosis", "C3 (complement)", "Cancer", "Cell membrane", "Che proteins", "Chemical", "Chemical substance", "Chemokine receptor", "Chemokines", "Chemokinesis", "Chemotactic range fitting", "Chemotactic selection", "Chemotaxis assay", "Chromium", "Ch\u00e9diak\u2013Higashi syndrome", "Cilia", "Ciliate", "Cilium", "CiteSeerX", "Complement component 5a", "Complement system", "Cyclic nucleotide", "Cyclooxygenase 1", "Cyclooxygenase 2", "Cytokines", "Cytosol", "Demethylase", "Diffusion", "Digital object identifier", "Dipeptide", "Durotaxis", "Eicosanoid", "Electric current", "Embryogenesis", "Encyclop\u00e6dia Britannica Eleventh Edition", "Endothelial cells", "Eosinophil", "Eosinophils", "Escherichia coli", "Eukaryotic", "Extracellular matrix", "Fertilization", "Fibroblast", "Flagellin", "Flagellum", "Fluid flow", "Formyl", "Formyl peptide receptor", "Formyl peptide receptors", "G protein", "G protein\u2013coupled receptor", "Galactose", "Genome", "Germ layers", "Glucose", "Glutamate", "Gradient", "Granulocyte", "Gravitaxis", "Gravity", "Guanosine triphosphate", "Haptotaxis", "Henry Harris (scientist)", "Herbert Spencer Jennings", "Higher vertebrate", "Hodgkin disease", "Immune system", "Inflammation", "Inorganic", "Insulin", "Interleukin 8", "International Standard Book Number", "International Standard Serial Number", "Julius Adler (biochemist)", "Kartagener syndrome", "Kinesis (biology)", "Leeuwenhoek", "Leukotriene B4", "Leukotriene receptor", "Leukotrienes", "Ligand", "Ligands", "Light", "Listeria monocytogenes", "Lymphocyte", "Macrophage", "Magnetic field", "Magnetotaxis", "Male infertility", "Mast cell", "McCutcheon index", "Mead acid", "Mechanotaxis", "Mercury (element)", "Metastases", "Metastasis", "Metastatic tumor", "Methyl-accepting chemotaxis protein", "Methylation", "Microtubule", "Moisture", "Monocyte", "Monocytes", "Multicellular", "Multiple sclerosis", "N-formylmethioninyl", "Necrosis", "Necrotaxis", "Netrin-1 peptide", "Neuron", "Neutrophil", "Neutrophils", "Nociceptin", "Organic compound", "Oxoeicosanoid receptor 1", "Oxygen", "Ozone", "PACAP-38", "PIP3", "Paramecium", "Pathogen", "Peptide", "Periodontitis", "Periplasmatic space", "Phagocytosis", "Phenol", "Phosphatidylinositol (3,4,5)-trisphosphate", "Phosphorylation", "Phototaxis", "Plasma membrane", "Plithotaxis", "Poison", "Polymerisation", "Polyunsaturated fatty acid", "Pressure", "Prostaglandin D2", "Prostaglandin DP2 receptor", "Protein-glutamate methylesterase", "Pseudopods", "Psoriasis", "PubMed Central", "PubMed Identifier", "R. spheroids", "RANTES", "Random walk", "Ras subfamily", "Reperfusion injury", "Rheotaxis", "Ribose", "S. meliloti", "Serine", "Single-cell organism", "Somatic cell", "Somatosensory system", "Spatial ecology", "Sperm", "Stiffness", "T helper cell", "Taxis", "Temperature", "Tetrahymena", "Theodor Wilhelm Engelmann", "Thermotaxis", "Toll-like receptor", "Transferase", "Transmembrane receptor", "Tropism", "Two-component regulatory system", "Uropod (immunology)", "White blood cell", "Wilhelm Pfeffer", "Wind", "\u00c9lie Metchnikoff"], "references": ["http://www.mathworks.com/matlabcentral/fileexchange/9732-taxi-movement-of-bacteria-to-the-food", "http://chemotaxis.tiddlyspot.com/", "http://www.rpgroup.caltech.edu/courses/aph161/2007/lectures/ChemotaxisLecture.pdf", "http://adsabs.harvard.edu/abs/1967Natur.213..256C", "http://adsabs.harvard.edu/abs/1972PNAS...69.2509M", "http://adsabs.harvard.edu/abs/1974Sci...184.1292A", "http://adsabs.harvard.edu/abs/1975PNAS...72.1059S", "http://adsabs.harvard.edu/abs/2000Sci...287.1652C", "http://adsabs.harvard.edu/abs/2007BpJ....92.2329M", "http://adsabs.harvard.edu/abs/2010PNAS..10717079X", "http://adsabs.harvard.edu/abs/2013PhT....66b..24L", "http://adsabs.harvard.edu/abs/2014PNAS..11114448S", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.318.4824", "http://www.isn.ucsd.edu/courses/Beng221/problems/2012/BENG221_Project%20-%20Roberts%20Chung%20Yu%20Li.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1864821", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC208443", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2096533", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2109936", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2138524", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2951443", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC340952", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3577161", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3867297", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3989901", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC419924", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4210025", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC426976", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC432465", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4830718", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5367630", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5710732", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5710736", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5901339", "http://www.ncbi.nlm.nih.gov/pubmed/10611962", "http://www.ncbi.nlm.nih.gov/pubmed/10698740", "http://www.ncbi.nlm.nih.gov/pubmed/10735174", "http://www.ncbi.nlm.nih.gov/pubmed/1093163", "http://www.ncbi.nlm.nih.gov/pubmed/14966542", "http://www.ncbi.nlm.nih.gov/pubmed/15187186", "http://www.ncbi.nlm.nih.gov/pubmed/15539117", "http://www.ncbi.nlm.nih.gov/pubmed/17208965", "http://www.ncbi.nlm.nih.gov/pubmed/17557195", "http://www.ncbi.nlm.nih.gov/pubmed/17767353", "http://www.ncbi.nlm.nih.gov/pubmed/18404496", "http://www.ncbi.nlm.nih.gov/pubmed/18685153", "http://www.ncbi.nlm.nih.gov/pubmed/19203648", "http://www.ncbi.nlm.nih.gov/pubmed/19747082", "http://www.ncbi.nlm.nih.gov/pubmed/199132", "http://www.ncbi.nlm.nih.gov/pubmed/20864631", "http://www.ncbi.nlm.nih.gov/pubmed/22994495", "http://www.ncbi.nlm.nih.gov/pubmed/23308365", "http://www.ncbi.nlm.nih.gov/pubmed/23653726", "http://www.ncbi.nlm.nih.gov/pubmed/2403544", "http://www.ncbi.nlm.nih.gov/pubmed/24056189", "http://www.ncbi.nlm.nih.gov/pubmed/24363460", "http://www.ncbi.nlm.nih.gov/pubmed/25249632", "http://www.ncbi.nlm.nih.gov/pubmed/25449650", "http://www.ncbi.nlm.nih.gov/pubmed/25480980", "http://www.ncbi.nlm.nih.gov/pubmed/264125", "http://www.ncbi.nlm.nih.gov/pubmed/26928542", "http://www.ncbi.nlm.nih.gov/pubmed/27123011", "http://www.ncbi.nlm.nih.gov/pubmed/27231052", "http://www.ncbi.nlm.nih.gov/pubmed/29064685", "http://www.ncbi.nlm.nih.gov/pubmed/29461522", "http://www.ncbi.nlm.nih.gov/pubmed/4560688", "http://www.ncbi.nlm.nih.gov/pubmed/4598187", "http://www.ncbi.nlm.nih.gov/pubmed/4873021", "http://www.ncbi.nlm.nih.gov/pubmed/6030602", "http://www.ncbi.nlm.nih.gov/pubmed/7117406", "http://www.ncbi.nlm.nih.gov/pubmed/8807851", "http://www.ncbi.nlm.nih.gov/pubmed/8906847", "http://www.ncbi.nlm.nih.gov/pubmed/9702410", "http://www.chemotaxis.usn.hu", "http://www.cellmigration.org/index.shtml", "http://doi.org/10.1002%2F9780470015902.a0001251.pub3", "http://doi.org/10.1006%2Fcyto.1997.0328", "http://doi.org/10.1007%2F978-3-319-32211-7_5", "http://doi.org/10.1007%2Fs10911-007-9046-4", "http://doi.org/10.1007%2Fs11302-005-6213-1", "http://doi.org/10.1016%2F0014-4827(82)90139-2", "http://doi.org/10.1016%2FS0065-2164(08)00803-4", "http://doi.org/10.1016%2Fbs.mcb.2015.11.003", "http://doi.org/10.1016%2Fj.bbalip.2014.10.008", "http://doi.org/10.1016%2Fj.camwa.2015.12.019", "http://doi.org/10.1016%2Fj.plipres.2013.09.001", "http://doi.org/10.1016%2Fj.soilbio.2013.11.019", "http://doi.org/10.1016%2Fj.tim.2004.10.003", "http://doi.org/10.1016%2Fs1074-5521(96)90103-9", "http://doi.org/10.1021%2Fja3091615", "http://doi.org/10.1021%2Fjacs.7b08783", "http://doi.org/10.1038%2F213256a0", "http://doi.org/10.1038%2Fnchem.2905", "http://doi.org/10.1038%2Fnri.2016.49", "http://doi.org/10.1063%2FPT.3.1884", "http://doi.org/10.1073%2Fpnas.1007333107", "http://doi.org/10.1073%2Fpnas.1011271107", "http://doi.org/10.1073%2Fpnas.1412197111", "http://doi.org/10.1073%2Fpnas.69.9.2509", "http://doi.org/10.1073%2Fpnas.72.3.1059", "http://doi.org/10.1084%2Fjem.128.2.259", "http://doi.org/10.1093%2Fjb%2Fmvu078", "http://doi.org/10.1100%2Ftsw.2007.182", "http://doi.org/10.1126%2Fscience.184.4143.1292", "http://doi.org/10.1126%2Fscience.287.5458.1652", "http://doi.org/10.1128%2FMMBR.68.2.301-319.2004", "http://doi.org/10.1128%2Fjb.172.1.383-388.1990", "http://doi.org/10.1128%2Fjmbe.v11i2.216", "http://doi.org/10.1146%2Fannurev-micro-092611-150120", "http://doi.org/10.1146%2Fannurev.cellbio.15.1.231", "http://doi.org/10.1155%2F2016%2F7142868", "http://doi.org/10.1242%2Fjcs.018077", "http://doi.org/10.1371%2Fjournal.pbio.0020049", "http://doi.org/10.1515%2FBC.2009.130", "http://doi.org/10.1529%2Fbiophysj.106.097808", "http://doi.org/10.2478%2Fs11536-012-0130-9", "http://www.pnas.org/content/72/3/1059.full.pdf", "http://www.worldcat.org/issn/0002-7863", "http://www.worldcat.org/issn/1755-4330", "http://wormweb.org/bacteriachemo", "https://www.nature.com/articles/nchem.2905", "https://www.youtube.com/watch?v=h4lv7cBYVug", "https://www.physik.uni-muenchen.de/lehre/vorlesungen/wise_16_17/Biophysics_of_Systems/013_BakterChemotaxis_DB_WS16.pdf", "https://scholarship.rice.edu/bitstream/1911/77450/1/PT.3.1884.pdf", "https://www.ncbi.nlm.nih.gov/books/NBK26822/#2878", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2919929/"]}, "Burr distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax"], "title": "Burr distribution", "method": "Burr distribution", "url": "https://en.wikipedia.org/wiki/Burr_distribution", "summary": "In probability theory, statistics and econometrics, the Burr Type XII distribution or simply the Burr distribution is a continuous probability distribution for a non-negative random variable. It is also known as the Singh\u2013Maddala distribution and is one of a number of different distributions sometimes called the \"generalized log-logistic distribution\". It is most commonly used to model household income (See: Household income in the U.S. and compare to magenta graph at right).\nThe Burr (Type XII) distribution has probability density function:\n\n \n \n \n f\n (\n x\n ;\n c\n ,\n k\n )\n =\n c\n k\n \n \n \n x\n \n c\n \u2212\n 1\n \n \n \n (\n 1\n +\n \n x\n \n c\n \n \n \n )\n \n k\n +\n 1\n \n \n \n \n \n \n \n \n {\\displaystyle f(x;c,k)=ck{\\frac {x^{c-1}}{(1+x^{c})^{k+1}}}\\!}\n \n\n \n \n \n f\n (\n x\n ;\n c\n ,\n k\n ,\n \u03bb\n )\n =\n \n \n \n c\n k\n \n \u03bb\n \n \n \n \n (\n \n \n x\n \u03bb\n \n \n )\n \n \n c\n \u2212\n 1\n \n \n \n \n [\n \n 1\n +\n \n \n (\n \n \n x\n \u03bb\n \n \n )\n \n \n c\n \n \n \n ]\n \n \n \u2212\n k\n \u2212\n 1\n \n \n \n \n {\\displaystyle f(x;c,k,\\lambda )={\\frac {ck}{\\lambda }}\\left({\\frac {x}{\\lambda }}\\right)^{c-1}\\left[1+\\left({\\frac {x}{\\lambda }}\\right)^{c}\\right]^{-k-1}}\n and cumulative distribution function:\n\n \n \n \n F\n (\n x\n ;\n c\n ,\n k\n )\n =\n 1\n \u2212\n \n \n (\n \n 1\n +\n \n x\n \n c\n \n \n \n )\n \n \n \u2212\n k\n \n \n \n \n {\\displaystyle F(x;c,k)=1-\\left(1+x^{c}\\right)^{-k}}\n \n\n \n \n \n F\n (\n x\n ;\n c\n ,\n k\n ,\n \u03bb\n )\n =\n 1\n \u2212\n \n \n [\n \n 1\n +\n \n \n (\n \n \n x\n \u03bb\n \n \n )\n \n \n c\n \n \n \n ]\n \n \n \u2212\n k\n \n \n \n \n {\\displaystyle F(x;c,k,\\lambda )=1-\\left[1+\\left({\\frac {x}{\\lambda }}\\right)^{c}\\right]^{-k}}\n Note when c = 1, the Burr distribution becomes the Pareto Type II (Lomax) distribution. When k = 1, the Burr distribution is a special case of the Champernowne distribution, often referred to as the Fisk distribution.The Burr Type XII distribution is a member of a system of continuous distributions introduced by Irving W. Burr (1942), which comprises 12 distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5c/Burr_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d4/Burr_pdf.svg"], "links": ["ARGUS distribution", "Annals of Mathematical Statistics", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biometrika", "Bivariate von Mises distribution", "Borel distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Champernowne distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Econometrica", "Econometrics", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Fisk distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Household income", "Household income in the United States", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irving W. Burr", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Magenta", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.causascientia.org/math_stat/Dists/Compendium.pdf", "http://doi.org/10.1093%2Fbiomet%2F64.1.129", "http://doi.org/10.1214%2Faoms%2F1177731607", "http://doi.org/10.2307%2F1402945", "http://doi.org/10.2307%2F1907644", "http://www.jstor.org/stable/1402945", "http://www.jstor.org/stable/1911538", "http://www.jstor.org/stable/2235756"]}, "Uniform distribution (discrete)": {"categories": ["Discrete distributions", "Location-scale family probability distributions", "Pages using deprecated image syntax"], "title": "Discrete uniform distribution", "method": "Uniform distribution (discrete)", "url": "https://en.wikipedia.org/wiki/Discrete_uniform_distribution", "summary": "In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying \"discrete uniform distribution\" would be \"a known, finite number of outcomes equally likely to happen\".\nA simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the dice is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.\nThe discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by all integers in an interval [a,b], so that a and b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n). With these conventions, the cumulative distribution function (CDF) of the discrete uniform distribution can be expressed, for any k \u2208 [a,b], as\n\n \n \n \n F\n (\n k\n ;\n a\n ,\n b\n )\n =\n \n \n \n \u230a\n k\n \u230b\n \u2212\n a\n +\n 1\n \n \n b\n \u2212\n a\n +\n 1\n \n \n \n \n \n {\\displaystyle F(k;a,b)={\\frac {\\lfloor k\\rfloor -a+1}{b-a+1}}}", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/77/Dis_Uniform_distribution_CDF.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1f/Uniform_discrete_pmf_svg.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial coefficient", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Capture-recapture", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Complete statistic", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dice", "Digital object identifier", "Dirac delta distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "German tank problem", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hockey-stick identity", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maximum spacing estimation", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Minimum-variance unbiased estimator", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Probability mass function", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random permutation", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rencontres numbers", "Rice distribution", "Sample maximum", "Sample size", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Sufficient statistic", "Support (mathematics)", "Symmetric distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Unbiased estimator", "Uniform distribution (continuous)", "Uniformly minimum variance unbiased estimator", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "World War II", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://doi.org/10.1111%2Fj.1467-9639.1994.tb00688.x", "http://www.rsscse.org.uk/ts/index.htm"]}, "Finite-dimensional distribution": {"categories": ["All articles lacking sources", "Articles lacking sources from December 2009", "Measure theory", "Stochastic processes"], "title": "Finite-dimensional distribution", "method": "Finite-dimensional distribution", "url": "https://en.wikipedia.org/wiki/Finite-dimensional_distribution", "summary": "In mathematics, finite-dimensional distributions are a tool in the study of measures and stochastic processes. A lot of information can be gained by studying the \"projection\" of a measure (or process) onto a finite-dimensional vector space (or finite collection of times).", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Law (stochastic processes)", "Mathematics", "Measurable", "Measure space", "Measure theory", "Probability measure", "Probability space", "Product space", "Pushforward measure", "Rectangle", "Stochastic process", "Stochastic processes", "Tightness of measures", "Vector space", "Weak convergence of measures"], "references": []}, "Duncan's new multiple range test": {"categories": ["Multiple comparisons", "Statistical tests"], "title": "Duncan's new multiple range test", "method": "Duncan's new multiple range test", "url": "https://en.wikipedia.org/wiki/Duncan%27s_new_multiple_range_test", "summary": "In statistics, Duncan's new multiple range test (MRT) is a multiple comparison procedure developed by David B. Duncan in 1955. Duncan's MRT belongs to the general class of multiple comparison procedures that use the studentized range statistic qr to compare sets of means.\nDavid B. Duncan developed this test as a modification of the Student\u2013Newman\u2013Keuls method that would have greater power. Duncan's MRT is especially protective against false negative (Type II) error at the expense of having a greater risk of making false positive (Type I) errors. Duncan's test is commonly used in agronomy and other agricultural research.\nThe result of the test is a set of subsets of means, where in each subset means have been found not to be significantly different from one another.\n\n", "images": [], "links": ["Agronomy", "Biometrics (journal)", "Cluster analysis", "David B. Duncan", "Degrees of freedom", "Digital object identifier", "False discovery rate", "Familywise error rate", "Henry Scheff\u00e9", "Hierarchical Clustering", "John W. Tukey", "Loss function", "Loss functions", "Multiple comparisons", "Newman\u2013Keuls procedure", "Null hypotheses", "Null hypothesis", "Pairwise comparison", "Pairwise comparisons", "Probability", "Quantile", "Standard error", "Statistical power", "Statistics", "Student's t-test", "Studentized range", "Studentized range distribution", "Student\u2013Newman\u2013Keuls method", "Tukey's range test", "Type I and type II errors", "Type I error rate", "Variance", "Yoav Benjamini", "Yosi Hochberg"], "references": ["http://www.ime.usp.br/~abe/lista/pdfepXJ7Z5yxl.pdf", "http://doi.org/10.1016%2FS0378-3758(99)00042-7", "http://doi.org/10.1016%2FS0378-3758(99)00044-0", "http://doi.org/10.2307%2F3001478"]}, "Empirical statistical laws": {"categories": ["Statistical laws"], "title": "Empirical statistical laws", "method": "Empirical statistical laws", "url": "https://en.wikipedia.org/wiki/Empirical_statistical_laws", "summary": "An empirical statistical law or (in popular terminology) a law of statistics represents a type of behaviour that has been found across a number of datasets and, indeed, across a range of types of data sets. Many of these observances have been formulated and proved as statistical or probabilistic theorems and the term \"law\" has been carried over to these theorems. There are other statistical and probabilistic theorems that also have \"law\" as a part of their names that have not obviously derived from empirical observations. However, both types of \"law\" may be considered instances of a scientific law in the field of statistics. What distinguishes an empirical statistical law from a formal statistical theorem is the way these patterns simply appear in natural distributions, without a prior theoretical reasoning about the data.", "images": [], "links": ["Benford's law", "Central limit theorem", "Digital object identifier", "Forgetting", "International Standard Book Number", "International Standard Serial Number", "Law of averages", "Law of large numbers", "Law of truly large numbers", "Linguistics", "Pareto principle", "Probability axioms", "Rank-size distribution", "Regression towards the mean", "Safety in numbers", "Scientific law", "Statistical regularity", "Statistics", "Zipf's law"], "references": ["http://www.crn.com/news/security/18821726/microsofts-ceo-80-20-rule-applies-to-bugs-not-just-features.htm?itc=refresh", "http://www.investopedia.com/terms/1/80-20-rule.asp", "http://www.springerlink.com/content/3pfylb1vw03q7950", "http://act-r.psy.cmu.edu/wordpress/wp-content/uploads/2012/12/37JRA_LS_PS_1991.pdf", "http://pages.stern.nyu.edu/~xgabaix/papers/zipf.pdf", "http://doi.org/10.1111%2Fj.1467-9280.1991.tb00174.x", "http://www.worldcat.org/issn/0362-4331", "https://www.nytimes.com/2008/03/03/business/03juran.html", "https://archive.ahrq.gov/research/findings/factsheets/costs/expriach/expriach1.html"]}, "Twisting properties": {"categories": ["Algorithmic inference", "All Wikipedia articles needing context", "All articles lacking in-text citations", "All pages needing cleanup", "Articles lacking in-text citations from September 2009", "Computational statistics", "Wikipedia articles needing context from January 2009", "Wikipedia introduction cleanup from January 2009"], "title": "Twisting properties", "method": "Twisting properties", "url": "https://en.wikipedia.org/wiki/Twisting_properties", "summary": "Starting with a sample \n \n \n \n {\n \n x\n \n 1\n \n \n ,\n \u2026\n ,\n \n x\n \n m\n \n \n }\n \n \n {\\displaystyle \\{x_{1},\\ldots ,x_{m}\\}}\n observed from a random variable X having a given distribution law with a non-set parameter, a parametric inference problem consists of computing suitable values \u2013 call them estimates \u2013 of this parameter precisely on the basis of the sample. An estimate is suitable if replacing it with the unknown parameter does not cause major damage in next computations. In algorithmic inference, suitability of an estimate reads in terms of compatibility with the observed sample. \nIn turn, parameter compatibility is a probability measure that we derive from the probability distribution of the random variable to which the parameter refers. In this way we identify a random parameter \u0398 compatible with an observed sample.\nGiven a sampling mechanism \n \n \n \n \n M\n \n X\n \n \n =\n (\n \n g\n \n \u03b8\n \n \n ,\n Z\n )\n \n \n {\\displaystyle M_{X}=(g_{\\theta },Z)}\n , the rationale of this operation lies in using the Z seed distribution law to determine both the X distribution law for the given \u03b8, and the \u0398 distribution law given an X sample. Hence, we may derive the latter distribution directly from the former if we are able to relate domains of the sample space to subsets of \u0398 support. In more abstract terms, we speak about twisting properties of samples with properties of parameters and identify the former with statistics that are suitable for this exchange, so denoting a well behavior w.r.t. the unknown parameters. The operational goal is to write the analytic expression of the cumulative distribution function \n \n \n \n \n F\n \n \u0398\n \n \n (\n \u03b8\n )\n \n \n {\\displaystyle F_{\\Theta }(\\theta )}\n , in light of the observed value s of a statistic S, as a function of the S distribution law when the X parameter is exactly \u03b8.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f0/Gamma3D.png", "https://upload.wikimedia.org/wikipedia/commons/e/ef/GammaK2D.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Algorithmic inference", "Cumulative distribution function", "Digital object identifier", "Estimator", "Fiducial inference", "Fox's H function", "Gamma distribution", "Incomplete gamma function", "Method of moments (statistics)", "Parametric statistics", "Random variable", "Sample (statistics)", "Support (mathematics)", "Well-behaved statistic"], "references": ["http://doi.org/10.1111/j.1469-1809.1935.tb02120.x", "http://doi.org/10.2307/2334048"]}, "Conditional probability distribution": {"categories": ["All articles needing additional references", "Articles needing additional references from April 2013", "Conditional probability", "Theory of probability distributions", "Wikipedia articles needing clarification from June 2017"], "title": "Conditional probability distribution", "method": "Conditional probability distribution", "url": "https://en.wikipedia.org/wiki/Conditional_probability_distribution", "summary": "In probability theory and statistics, given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X is the probability distribution of Y when X is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value x of X as a parameter. When both \"X\" and \"Y\" are categorical variables, a conditional probability table is typically used to represent the conditional probability. The conditional distribution contrasts with the marginal distribution of a random variable, which is its distribution without reference to the value of the other variable.\nIf the conditional distribution of Y given X is a continuous distribution, then its probability density function is known as the conditional density function. The properties of a conditional distribution, such as the moments, are often referred to by corresponding names such as the conditional mean and conditional variance.\nMore generally, one can refer to the conditional distribution of a subset of a set of more than two variables; this conditional distribution is contingent on the values of all the remaining variables, and if more than one variable is included in the subset then this conditional distribution is the conditional joint distribution of the included variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/57/Multivariate_Gaussian.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayes' theorem", "Bivariate normal distribution", "Borel's paradox", "Categorical variable", "Conditional expectation", "Conditional mean", "Conditional probability", "Conditional probability table", "Conditional variance", "Conditioning (probability)", "Continuous distribution", "Continuous random variable", "Dice", "Discrete random variable", "Indicator function", "Joint density function", "Joint distribution", "Joint probability distribution", "Likelihood function", "Marginal density", "Marginal distribution", "Moment (mathematics)", "Patrick Billingsley", "Plane (geometry)", "Probability density function", "Probability distribution", "Probability measure", "Probability theory", "Random variable", "Regular conditional probability", "Statistical independence", "Statistics"], "references": ["https://books.google.com/books?id=a3gavZbxyJcC"]}, "Total least squares": {"categories": ["All articles with unsourced statements", "Applied mathematics", "Articles with unsourced statements from July 2009", "Least squares", "Wikipedia articles needing page number citations from June 2012"], "title": "Total least squares", "method": "Total least squares", "url": "https://en.wikipedia.org/wiki/Total_least_squares", "summary": "In applied statistics, total least squares is a type of errors-in-variables regression, a least squares data modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models.\nThe total least squares approximation of the data is generically equivalent to the best, in the Frobenius norm, low-rank approximation of the data matrix.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/8/81/Total_least_squares.svg"], "links": ["Analysis of covariance", "Analysis of variance", "Applied statistics", "Approximation theory", "Augmented matrix", "Bayesian experimental design", "Bayesian linear regression", "Bayesian multivariate linear regression", "Binomial regression", "Calibration curve", "Charles F. Van Loan", "Chebyshev nodes", "Chebyshev polynomials", "Computational statistics", "Condition equations", "Confounding", "Correlation and dependence", "Curve fitting", "Deming regression", "Design of experiments", "Determination of equilibrium constants", "Digital object identifier", "Discrete choice", "Distance from a point to a line", "Eckart\u2013Young theorem", "Errors-in-variables model", "Errors-in-variables models", "Errors-in-variables regression", "Errors and residuals in statistics", "Fixed effects model", "Frobenius norm", "GNU Octave", "Gaussian quadrature", "Gauss\u2013Markov theorem", "Gene H. Golub", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Growth curve (statistics)", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Kendall tau rank correlation coefficient", "Lagrange multipliers", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "List of statistics articles", "Local regression", "Logistic regression", "Low-rank approximation", "Mahalanobis distance", "Mallows's Cp", "Maximum-likelihood", "Mean and predicted response", "Minimum mean-square error", "Mixed logit", "Mixed model", "Model selection", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate analysis of variance", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Objective function", "Optimal design", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Orthogonal regression", "Outline of statistics", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Paul Samuelson", "Pearson product-moment correlation coefficient", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Rank correlation", "Regression analysis", "Regression model validation", "Regularized least squares", "Response surface methodology", "Ridge regression", "Robust regression", "Sabine Van Huffel", "Scale invariance", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Singular value decomposition", "Social Science Research Network", "Spearman's rank correlation coefficient", "Statistical model", "Statistics", "Stepwise regression", "Studentized residual", "System identification", "The Johns Hopkins University Press", "Tikhonov regularization", "Variance-covariance matrix", "Weighted least squares"], "references": ["http:ftp://ftp.sam.math.ethz.ch/pub/sam-reports/reports/reports2010/2010-38.pdf", "http://www.dspcsp.com/pubs/euclreg.pdf", "http://www.mathpages.com/home/kmath110.htm", "http://ssrn.com/abstract=1077322", "http://ssrn.com/abstract=2707593", "http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471934127.html", "http://engold.ui.ac.ir/~amiri/JGS_Amiri_Jazaeri_2012.pdf", "http://doi.org/10.1017%2FS1464793106007007", "http://doi.org/10.1139%2Ff75-172", "http://doi.org/10.2307%2F1907024", "http://www.jstor.org/stable/1907024", "http://www.netlib.org/vanhuffel/index.html", "http://eprints.ecs.soton.ac.uk/13855/1/tls_overview.pdf", "https://web.archive.org/web/20120724080908/http://www.fp.tul.cz/~plesinger/my_publications/doctoral_thesis/thesis.pdf", "https://arxiv.org/pdf/math.RA/9805076/", "https://doi.org/10.1137%2F040616991", "https://doi.org/10.1137%2F0717073", "https://doi.org/10.1137%2F1.9781611971002"]}, "Univariate analysis": {"categories": ["Exploratory data analysis"], "title": "Univariate analysis", "method": "Univariate analysis", "url": "https://en.wikipedia.org/wiki/Univariate_analysis", "summary": "Univariate analysis is perhaps the simplest form of statistical analysis. Like other forms of statistics, it can be inferential or descriptive. The key fact is that only one variable is involved.", "images": [], "links": ["Arithmetic mean", "Central tendency", "Coding (social sciences)", "Coefficient of variation", "Descriptive statistics", "Exploratory data analysis", "Frequency table", "Geometric mean", "Harmonic mean", "Inferential statistics", "International Standard Book Number", "Kurtosis", "Level of measurement", "Median", "Mode (statistics)", "Multivariate analysis", "Range (statistics)", "Sign test", "Skewness", "Standard deviation", "Statistical analysis", "T-test", "Univariate", "Wilcoxon signed rank test"], "references": ["http://www.vassarstats.net/csfit.html"]}, "Gamma variate": {"categories": ["All articles with incomplete citations", "All articles with unsourced statements", "Articles with incomplete citations from November 2012", "Articles with unsourced statements from September 2012", "Conjugate prior distributions", "Continuous distributions", "Exponential family distributions", "Factorial and binomial topics", "Infinitely divisible probability distributions", "Survival analysis", "Wikipedia articles needing clarification from July 2018"], "title": "Gamma distribution", "method": "Gamma variate", "url": "https://en.wikipedia.org/wiki/Gamma_distribution", "summary": "In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are three different parametrizations in common use:\n\nWith a shape parameter k and a scale parameter \u03b8.\nWith a shape parameter \u03b1 = k and an inverse scale parameter \u03b2 = 1/\u03b8, called a rate parameter.\nWith a shape parameter k and a mean parameter \u03bc = k\u03b8 = \u03b1/\u03b2.In each of these three forms, both parameters are positive real numbers.\nThe gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and with respect to a 1/x base measure) for a random variable X for which E[X] = k\u03b8 = \u03b1/\u03b2 is fixed and greater than zero, and E[ln(X)] = \u03c8(k) + ln(\u03b8) = \u03c8(\u03b1) \u2212 ln(\u03b2) is fixed (\u03c8 is the digamma function).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8b/Gamma-KL-3D.png", "https://upload.wikimedia.org/wikipedia/commons/b/b1/Gamma-PDF-3D.png", "https://upload.wikimedia.org/wikipedia/commons/8/8d/Gamma_distribution_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e6/Gamma_distribution_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg"], "links": ["ARGUS distribution", "Accelerated life testing", "Arcsine distribution", "Asymmetric Laplace distribution", "Bacterial genetics", "Balding\u2013Nichols model", "Bates distribution", "Bayesian inference", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "ChIP-chip", "ChIP-seq", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "CiteSeerX", "Compound Poisson distribution", "Compound distribution", "Compound gamma distribution", "Conjugate prior", "Constitutively expressed", "Conway\u2013Maxwell\u2013Poisson distribution", "Copy number analysis", "Cumulative distribution function", "Dagum distribution", "David Blei", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Econometrics", "Elliptical distribution", "Encyclopedia of Mathematics", "Eric W. Weisstein", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential dispersion model", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma function", "Gamma process", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Gene expression", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized gamma distribution", "Generalized integer gamma distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Genomics", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Herman Rubin", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Incomplete gamma function", "Independent and identically-distributed random variables", "Independent and identically distributed random variables", "Infinite divisibility (probability)", "Information entropy", "Insurance policy", "Integer", "International Standard Book Number", "International Standard Serial Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse gamma distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "K-distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kullback\u2013Leibler divergence", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "Laplace transform", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "MathWorld", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Method of moments (statistics)", "Michiel Hazewinkel", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Natural parameters", "Natural statistics", "Negative binomial distribution", "Negative multinomial distribution", "Neuroscience", "Newton's method", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Parametrization", "Pareto distribution", "Peak calling", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poisson process", "Poisson regression", "Poly-Weibull distribution", "Polygamma function", "Prior probability", "Probability density function", "Probability distribution", "Probability theory", "Protein molecule", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rate parameter", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Rejection sampling", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Robert V. Hogg", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Statistics", "Student's t-distribution", "Support (mathematics)", "Temporal coding", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.wise.xmu.edu.cn/Master/Download/..%5C..%5CUploadFiles%5Cpaper-masterdownload%5C2009519932327055475115776.pdf", "http://www.biomedcentral.com/1471-2164/14/834", "http://www.epixanalytics.com/modelassist/AtRisk/Model_Assist.htm#Distributions/Continuous_distributions/Gamma.htm", "http://www.springerlink.com/content/u750hg4630387205/", "http://mathworld.wolfram.com/GammaDistribution.html", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.157.5540&rep=rep1&type=pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.3828", "http://www.stat.washington.edu/thompson/S341_10/Notes/week4.pdf", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm", "http://www.ams.org/journals/proc/1994-121-01/S0002-9939-1994-1195477-8/S0002-9939-1994-1195477-8.pdf", "http://luc.devroye.org/rnbookindex.html", "http://doi.org/10.1007%2FBF02293108", "http://doi.org/10.1007%2FBF02613934", "http://doi.org/10.1016%2Fj.jeconom.2008.12.014", "http://doi.org/10.1080%2F00401706.1969.10490731", "http://doi.org/10.1145%2F358315.358390", "http://doi.org/10.1145%2F358407.358414", "http://bioinformatics.oxfordjournals.org/content/24/3/396.full.pdf+html", "http://commons.wikimedia.org/wiki/File:Gamma-PDF-3D-by-Theta.png", "http://commons.wikimedia.org/wiki/File:Gamma-PDF-3D-by-k.png", "http://commons.wikimedia.org/wiki/File:Gamma-PDF-3D-by-x.png", "http://journals.tubitak.gov.tr/engineering/issues/muh-00-24-6/muh-24-6-7-9909-13.pdf", "https://tminka.github.io/papers/minka-gamma.pdf", "https://arxiv.org/pdf/1311.1704v3.pdf", "https://arxiv.org/pdf/math/0609442.pdf", "https://dx.doi.org/10.1016/0167-7152(86)90044-1", "https://www.encyclopediaofmath.org/index.php?title=p/g043300", "https://www.worldcat.org/search?fq=x0:jrnl&q=n2:0167-7152"]}, "Correlation implies causation": {"categories": ["All accuracy disputes", "All articles with unsourced statements", "Articles with disputed statements from November 2017", "Articles with short description", "Articles with unsourced statements from August 2016", "Articles with unsourced statements from July 2009", "Articles with unsourced statements from July 2015", "Articles with unsourced statements from June 2017", "CS1 maint: Multiple names: authors list", "Causal fallacies", "Causal inference", "Covariance and correlation", "English phrases", "Misuse of statistics", "Webarchive template wayback links", "Wikipedia articles needing clarification from August 2016"], "title": "Correlation does not imply causation", "method": "Correlation implies causation", "url": "https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation", "summary": "In statistics, many statistical tests calculate correlations between variables and when two variables are found to be correlated, it is tempting to assume that this shows that one variable causes the other. That \"correlation proves causation\" is considered a questionable cause logical fallacy when two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known as cum hoc ergo propter hoc, Latin for \"with this, therefore because of this\", and \"false cause\". A similar fallacy, that an event that followed another was necessarily a consequence of the first event, is the post hoc ergo propter hoc (Latin for \"after this, therefore because of this.\") fallacy.\nFor example, in a widely studied case, numerous epidemiological studies showed that women taking combined hormone replacement therapy (HRT) also had a lower-than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD. But randomized controlled trials showed that HRT caused a small but statistically significant increase in risk of CHD. Re-analysis of the data from the epidemiological studies showed that women undertaking HRT were more likely to be from higher socio-economic groups (ABC1), with better-than-average diet and exercise regimens. The use of HRT and decreased incidence of coronary heart disease were coincident effects of a common cause (i.e. the benefits associated with a higher socioeconomic status), rather than a direct cause and effect, as had been supposed.As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not imply that the resulting conclusion is false. In the instance above, if the trials had found that hormone replacement therapy does in fact have a negative incidence on the likelihood of coronary heart disease the assumption of causality would have been correct, although the logic behind the assumption would still have been flawed. Indeed, a few go further, using correlation as a basis for testing a hypothesis to try to establish a true causal relationship; examples are the Granger causality test, convergent cross mapping, and Liang-Kleeman information flow.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["Accident (fallacy)", "Affirming the consequent", "Al-Ghazali", "Alignments of random points", "Ambiguity", "Anecdotal evidence", "Animistic fallacy", "Apophenia", "Argument from analogy", "Aristotle", "Bald\u2013hairy", "Base rate fallacy", "Begging the question", "Bible code", "Biology", "Body mass index", "British Medical Association", "Butterfly effect", "CNN", "Carbon dioxide", "Causality", "Causality (physics)", "Cherry picking", "Cheshire, Connecticut", "Cholesterol", "Circular analysis", "Circular cause and consequence", "Circular logic", "Circular reasoning", "Classical mechanics", "Coefficient of determination", "Coincidence", "Complex question", "Confounding", "Confusion of the inverse", "Conjunction fallacy", "Continuum fallacy", "Convergent cross mapping", "Converse accident", "Coronary heart disease", "Correlation and dependence", "Correlation does not imply causation", "Correlative-based fallacies", "Counterfactual", "Data dredging", "David Hume", "Denying the correlative", "Dependent and independent variables", "Descartes", "Design of experiments", "Digital object identifier", "Direct election", "Discipline (specialism)", "Double-barreled question", "Double-blind", "Double counting (fallacy)", "Drunkenness", "East Lansing, Michigan", "Ecological fallacy", "Economics", "Education economics", "Edward Tufte", "Effect size", "Epidemiological study", "Equivocation", "Exogenous", "Experiment", "Fallacies of illicit transference", "Fallacy", "Fallacy of accent", "Fallacy of composition", "Fallacy of division", "Fallacy of the single cause", "False attribution", "False dilemma", "False equivalence", "False precision", "Faulty generalization", "Fever", "Field (physics)", "Four causes", "French paradox", "Furtive fallacy", "GDP", "Gambler's fallacy", "Gateway drug theory", "George Davey Smith", "Granger causality", "Graphics Press", "High-density lipoprotein", "Hormone replacement therapy (menopause)", "How to Lie with Statistics", "Human capital", "Human swimming", "Illusory correlation", "Immanuel Kant", "Impact (mechanics)", "Impression management", "Inertia", "Infant", "Informal fallacy", "Instrumental variables", "International Standard Book Number", "Inverse gambler's fallacy", "JSTOR", "Joint effect", "Journal of the American Statistical Association", "Latin", "Law", "Leading question", "Lies, damned lies, and statistics", "Life-time of correlation", "List of fallacies", "Loaded language", "Loaded question", "Logic", "Logical consequence", "Loki's Wager", "London", "Look-elsewhere effect", "Louse", "Lurking variable", "Marijuana", "Material conditional", "McNamara fallacy", "Mechanism (philosophy)", "Michigan State University Press", "Middle Ages", "Mierscheid law", "Misleading graph", "Misuse of statistics", "Moving the goalposts", "Multiple comparisons problem", "Myopia", "NRS social grade", "Nate Silver", "Nature (journal)", "Nature Publishing Group", "New York City", "Nirvana fallacy", "No true Scotsman", "Nonlinear system", "Normally distributed and uncorrelated does not imply independent", "Obesity", "Occasionalism", "Ohio State University", "Overwhelming exception", "P-value", "Penguin Books", "Penn Presbyterian Medical Center", "Philosophy", "Physical activity", "Physical law", "Physics", "Pirates in terms of global warming", "Post hoc analysis", "Post hoc ergo propter hoc", "Potential energy", "Predation", "Problem of induction", "Psychiatric disorder", "PubMed Identifier", "Quantum mechanics", "Questionable cause", "Quoting out of context", "Randomized controlled trials", "Recreational drug use", "Redskins Rule", "Regression analysis", "Regression fallacy", "Reification (fallacy)", "Reproducibility", "Ronald Fisher", "Sampling bias", "Screening (economics)", "Second law of thermodynamics", "Secundum quid", "Self medication", "Signalling (economics)", "Slippery slope", "Slothful induction", "Social Democratic Party of Germany", "Social science", "Socio-economic group", "Sorites paradox", "Spacetime", "Spurious relationship", "Statistical mechanics", "Statistical significance", "Statistical tests", "Statistics", "Sufficient condition", "Suppressed correlative", "Syntactic ambiguity", "Television", "Testing hypotheses suggested by the data", "Texas sharpshooter fallacy", "The BMJ", "The Signal and the Noise", "Thermodynamic free energy", "Thermodynamics", "Thermometer", "Tobacco and lung cancer", "Tobacco industry", "Twin study", "United States Presidential Election 2004", "United States Presidential Election 2012", "University of Pennsylvania", "Vagueness", "Variable (mathematics)", "Verificationism", "Washington Redskins", "Wayback Machine"], "references": ["http://www.cnn.com/HEALTH/9905/12/children.lights/index.html", "http://www.edwardtufte.com/tufte/powerpoint", "http://www.huffingtonpost.com/dr-dean-ornish/cholesterol-the-good-the-_b_870655.html", "http://www.opifexphoenix.com/reasoning/fallacies/ignorecc.htm", "http://tylervigen.com/spurious-correlations", "http://www.tylervigen.com/", "http://researchnews.osu.edu/archive/nitelite.htm", "http://plato.stanford.edu/archives/spr2001/entries/hume/#CausationN", "http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf", "http://singapore.cs.ucla.edu/LECTURE/lecture_sec1.htm", "http://www.ncbi.nlm.nih.gov/pubmed/10335839", "http://www.ncbi.nlm.nih.gov/pubmed/10724157", "http://www.ncbi.nlm.nih.gov/pubmed/10724158", "http://www.ncbi.nlm.nih.gov/pubmed/15166201", "http://www.ncbi.nlm.nih.gov/pubmed/29957352", "http://www.americanscientist.org/issues/pub/what-everyone-should-know-about-statistical-correlation", "http://doi.org/10.1016%2Fj.envint.2018.06.023", "http://doi.org/10.1038%2F182108a0", "http://doi.org/10.1038%2F182596a0", "http://doi.org/10.1038%2F20094", "http://doi.org/10.1038%2F35004661", "http://doi.org/10.1038%2F35004663", "http://doi.org/10.1038%2F35004665", "http://doi.org/10.1080%2F01621459.1986.10478354", "http://doi.org/10.1093%2Fije%2Fdyh124", "http://doi.org/10.1136%2Fbmj.2.5035.43", "http://doi.org/10.1136%2Fbmj.2.5039.297-b", "http://doi.org/10.1163%2F156852876x00101", "http://doi.org/10.1214%2Fss%2F1177009870", "http://www.jstor.org/stable/2246135", "http://www.jstor.org/stable/25383068", "http://www.jstor.org/stable/25383439", "http://www.jstor.org/stable/4181986", "http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/", "http://www.sciencebasedmedicine.org/evidence-in-medicine-correlation-and-causation/", "http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/", "http://www.economics.soton.ac.uk/staff/aldrich/spurious.pdf", "https://books.google.com/books?id=1gJPXv5wQbIC", "https://books.google.com/books?id=yWWEIvNgUQ4C", "https://www.mdpi.com/1099-4300/15/1/327", "https://krugman.blogs.nytimes.com/2013/04/16/reinhart-rogoff-continued/?_r=0", "https://www.sciencedirect.com/science/article/pii/S0160412018307098", "https://web.archive.org/web/20060219042545/http://www.economics.soton.ac.uk/staff/aldrich/spurious.pdf", "https://web.archive.org/web/20060901152949/http://researchnews.osu.edu/archive/nitelite.htm", "https://web.archive.org/web/20090522103015/http://www.opifexphoenix.com/reasoning/fallacies/ignorecc.htm", "https://www.york.ac.uk/depts/maths/histstat/fisher272.pdf", "https://www.york.ac.uk/depts/maths/histstat/fisher274.pdf", "https://www.york.ac.uk/depts/maths/histstat/fisher275.pdf", "https://www.york.ac.uk/depts/maths/histstat/fisher276.pdf"]}, "Tukey median": {"categories": ["Euclidean geometry", "Means", "Multi-dimensional geometry"], "title": "Centerpoint (geometry)", "method": "Tukey median", "url": "https://en.wikipedia.org/wiki/Centerpoint_(geometry)", "summary": "In statistics and computational geometry, the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space. Given a set of points in d-dimensional space, a centerpoint of the set is a point such that any hyperplane that goes through that point divides the set of points in two roughly equal subsets: the smaller part should have at least a 1/(d + 1) fraction of the points. Like the median, a centerpoint need not be one of the data points. Every non-empty set of points (with no duplicates) has at least one centerpoint.", "images": [], "links": ["Approximation algorithm", "Computational geometry", "David Eppstein", "Digital object identifier", "Discrete and Computational Geometry", "Euclidean plane", "Euclidean space", "Gary Miller (professor)", "Geometric median", "Half-space (geometry)", "Helly's theorem", "Herbert Edelsbrunner", "International Standard Book Number", "John Tukey", "Kenneth L. Clarkson", "Linear time", "Mathematical Reviews", "Median", "Randomized algorithm", "Shang-Hua Teng", "Statistics", "Timothy M. Chan"], "references": ["http://www.almaden.ibm.com/u/kclarkson/center/p.pdf", "http://portal.acm.org/citation.cfm?id=982792.982853", "http://www.ams.org/mathscinet-getitem?mr=1409651", "http://doi.org/10.1007/BF02574382"]}, "Variable rules analysis": {"categories": ["Linguistic research software", "Logistic regression", "Sociolinguistics"], "title": "Variable rules analysis", "method": "Variable rules analysis", "url": "https://en.wikipedia.org/wiki/Variable_rules_analysis", "summary": "In linguistics, variable rules analysis is a set of statistical analysis methods commonly used in sociolinguistics and historical linguistics to describe patterns of variation between alternative forms in language use. It is also sometimes known as Varbrul analysis, after the name of a software package dedicated to carrying out the relevant statistical computations (Varbrul, from \"variable rule\"). The method goes back to a theoretical approach developed by the sociolinguist William Labov in the late 1960s and early 1970s, and its mathematical implementation was developed by Henrietta Cedergren and David Sankoff in 1974.A variable rules analysis is designed to provide a quantitative model of a situation where speakers alternate between different forms that have the same meaning and stand in free variation, but in such a way that the probability of choice of either the one or the other form is conditioned by a variety of context factors or social characteristics. Such a situation, where variation is not entirely random but rule-governed, is also known as \"structured variation\". A variable rules analysis computes a multivariate statistical model, on the basis of observed token counts, such that each determining factor is assigned a numerical factor weight that describes how it influences the probabilities of choice of either form. This is done by means of stepwise logistic regression, using a maximum likelihood algorithm.\nAlthough the necessary computations required for a variable rules analysis can be carried out with the help of mainstream general-purpose statistics software packages such as SPSS, it is more often done by means of a specialised software dedicated to the needs of linguists, called Varbrul. It was originally written by David Sankoff and currently exists in freeware implementations for Mac OS and Microsoft Windows, under the title of Goldvarb X. There are also versions implemented in the statistical language R and therefore available on most platforms. These include R-Varb and Rbrul.Variable rules approaches are commonly employed for the analysis of data in sociolinguistic research, especially in studies that aim to investigate how reflexes of linguistic change through time appear in the shape of structured variation patterns within a speech community.\n\n", "images": [], "links": ["David Sankoff", "Diaphoneme", "Free variation", "Freeware", "Historical linguistics", "Logistic regression", "Mac OS", "Maximum likelihood", "Microsoft Windows", "Multivariate analysis", "R (programming language)", "SPSS", "Sociolinguistics", "Statistical analysis", "Stepwise regression", "Variation (linguistics)", "William Labov"], "references": ["http://individual.utoronto.ca/tagliamonte/goldvarb.html", "http://www.danielezrajohnson.com/rbrul.html"]}, "Response surface methodology": {"categories": ["Articles with missing files", "CS1 errors: external links", "CS1 maint: Multiple names: authors list", "Design of experiments", "Industrial engineering", "Mathematical optimization", "Optimal decisions", "Pages with citations lacking titles", "Sequential experiments", "Statistical process control", "Systems engineering"], "title": "Response surface methodology", "method": "Response surface methodology", "url": "https://en.wikipedia.org/wiki/Response_surface_methodology", "summary": "In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process.\nStatistical approaches such as RSM can be employed to maximize the production of a special substance by optimization of operational factors. In contrast to conventional methods, the interaction among process variables can be determined by statistical techniques. The work by Box and co-workers was summarized in the book . Other important textbooks in RSM with a more recent set of topics other than those originally studied by Box and co-workers in the 50's and 60's are .", "images": [], "links": ["Analysis of covariance", "Analysis of variance", "Approximation theory", "Bayesian experimental design", "Bayesian linear regression", "Bias (statistics)", "Binomial regression", "Blind experiment", "Blocking (statistics)", "Box\u2013Behnken design", "Calibration curve", "Calyampudi Radhakrishna Rao", "Central composite design", "Charles Sanders Peirce", "Charles Sanders Peirce bibliography", "Chebyshev nodes", "Chebyshev polynomials", "Cochran's theorem", "Comparing means", "Completely randomized design", "Computational statistics", "Confounding", "Contrast (statistics)", "Correlation and dependence", "Covariate", "Crossover study", "Curve fitting", "Degree of a polynomial", "Design of experiments", "Digital object identifier", "Effect size", "Errors and residuals in statistics", "Experiment", "Experimental unit", "Explanatory variable", "External validity", "Factorial experiment", "Fractional factorial design", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Generalized randomized block design", "George E. P. Box", "Glossary of experimental design", "Goodness of fit", "Gradient-Enhanced Kriging (GEK)", "Graeco-Latin square", "Growth curve (statistics)", "Hierarchical Bayes model", "Hierarchical linear modeling", "IOSO", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jack Kiefer (mathematician)", "Joseph Diaz Gergonne", "Journal of the Royal Statistical Society", "Kendall tau rank correlation coefficient", "Latin hypercube sampling", "Latin square", "Lawrence D. Brown", "Least squares", "Linear least squares (mathematics)", "Linear regression", "List of statistics articles", "Local regression", "Logistic regression", "Mallows's Cp", "Mean and predicted response", "Minimum mean-square error", "Mixed model", "Model selection", "Moving least squares", "Multiobjective optimization", "Multiple comparison", "Multivariate analysis of variance", "Neil Sloane", "Non-linear least squares", "Nonlinear regression", "Nonparametric regression", "Nuisance variable", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "OCLC", "Optimal design", "Ordinary least squares", "Orthogonal array", "Orthogonal polynomials", "Orthogonality", "Outline of statistics", "Pareto efficiency", "Partial correlation", "Partial least squares", "Partition of sums of squares", "Pearson product-moment correlation coefficient", "Plackett-Burman design", "Plackett\u2013Burman design", "Poisson regression", "Polynomial", "Polynomial and rational function modeling", "Polynomial regression", "Probabilistic design", "Quantile regression", "Random assignment", "Random effect", "Randomization", "Randomized block design", "Randomized controlled trial", "Rank correlation", "Regression analysis", "Regression model validation", "Repeated measures design", "Replication (statistics)", "Response variable", "Restricted randomization", "Ridge regression", "Robust regression", "Sample size", "Scientific control", "Scientific method", "Segmented regression", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Simple linear regression", "Society for Industrial and Applied Mathematics", "Spearman's rank correlation coefficient", "Spherical design", "Statistical inference", "Statistical model", "Stephen M. Stigler", "Stepwise regression", "Studentized residual", "Surrogate model", "System identification", "Taguchi methods", "Total least squares", "Validity (statistics)", "Weighted least squares"], "references": ["http://www.ua.ac.be/main.aspx?c=peter.goos", "http://users.telenet.be/peter.goos/springer.htm", "http://www.webdoe.cc/publications/kirstine.php", "http://www.ec-securehost.com/SIAM/CL50.html", "http://neilsloane.com/doc/design.pdf", "http://neilsloane.com/doc/doeh.pdf", "http://neilsloane.com/doc/meatball.pdf", "http://www.us.oup.com/us/catalog/general/subject/Mathematics/ProbabilityStatistics/~~/dmlldz11c2EmY2k9OTc4MDE5OTI5NjYwNg==", "http://support.sas.com/publishing/bbu/companion_site/index_author.html#tobias", "http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-20/2/df451ec5fbb7c044d0f4d900af80ec86", "http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-1Y/2/680c7ada0198761e9866197d53512ab4", "http://www.sciencedirect.com/science/article/pii/S0169716196130327", "http://www.math.uni-augsburg.de/stochastik/pukelsheim/", "http://www.itl.nist.gov/div898/handbook/pri/section3/pri336.htm", "http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0025.PDF#page=222", "http://www.bbrc.in", "http://doi.org/10.1016%2F0315-0860(74)90033-0", "http://doi.org/10.1016%2F0315-0860(74)90034-2", "http://doi.org/10.1016%2FS0169-7161(96)13032-7", "http://doi.org/10.1016%2Fj.biortech.2016.12.073", "http://doi.org/10.1287%2Fopre.15.4.643", "http://doi.org/10.2307%2F2331929", "http://dx.doi.org/10.1002/0470072768", "http://www.jstor.org/stable/2331929", "http://worldcat.org/oclc/783405607", "http://www.worldcat.org/oclc/783405607", "http://stats.lse.ac.uk/atkinson/", "http://www.maths.manchester.ac.uk/~adonev/", "https://books.google.com/books?id=5ZcfDZUJ4F8C", "https://books.google.com/books?id=oIHsrw6NBmoC", "https://www.springer.com/series/694", "https://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-95515-5", "https://www.researchgate.net/publication/311881656_Optimization_of_organosolv_pretreatment_of_rice_straw_for_enhanced_biohydrogen_production_using_Enterobacter_aerogenes", "https://www.researchgate.net/publication/326072519_Statistical_Monitoring_and_Optimization_of_Electrochemical_Machining_using_Shewhart_Charts_and_Response_Surface_Methodology", "https://doi.org/10.26776/ijemm.03.02.2018.01", "https://www.jstor.org/stable/168276"]}, "Gaussian function": {"categories": ["All articles needing additional references", "Articles containing proofs", "Articles needing additional references from August 2009", "Articles with example MATLAB/Octave code", "Exponentials", "Gaussian function", "Wikipedia articles needing clarification from August 2016"], "title": "Gaussian function", "method": "Gaussian function", "url": "https://en.wikipedia.org/wiki/Gaussian_function", "summary": "In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the form:\n\n \n \n \n f\n (\n x\n )\n =\n a\n \n e\n \n \u2212\n \n \n \n (\n x\n \u2212\n b\n \n )\n \n 2\n \n \n \n \n 2\n \n c\n \n 2\n \n \n \n \n \n \n \n \n \n {\\displaystyle f(x)=ae^{-{\\frac {(x-b)^{2}}{2c^{2}}}}}\n for arbitrary real constants a, b and non zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric \"bell curve\" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the \"bell\".\nGaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value \u03bc = b and variance \u03c32 = c2. In this case, the Gaussian is of the form:\n\n \n \n \n g\n (\n x\n )\n =\n \n \n 1\n \n \u03c3\n \n \n 2\n \u03c0\n \n \n \n \n \n \n e\n \n \u2212\n \n \n 1\n 2\n \n \n \n \n (\n \n \n \n x\n \u2212\n \u03bc\n \n \u03c3\n \n \n )\n \n \n 2\n \n \n \n \n .\n \n \n {\\displaystyle g(x)={\\frac {1}{\\sigma {\\sqrt {2\\pi }}}}e^{-{\\frac {1}{2}}\\left({\\frac {x-\\mu }{\\sigma }}\\right)^{2}}.}\n Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensional Gaussians are used for Gaussian blurs, and in mathematics to solve heat equations and diffusion equations and to define the Weierstrass transform.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/84/Discrete_Gaussian_kernel.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Gaussian_2d.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d9/Gaussian_2d_1.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Gaussian_2d_2.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b0/Gaussian_2d_3.svg", "https://upload.wikimedia.org/wikipedia/commons/7/74/Normal_Distribution_PDF.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Affine shn", "Airy disk", "Analytic function", "Antiderivative", "Artificial neural network", "Basis set (chemistry)", "Bell (instrument)", "Carl Friedrich Gauss", "Central limit theorem", "Computational chemistry", "Computer vision", "Concave function", "Convolution", "Cram\u00e9r\u2013Rao bound", "Derivative", "Diffusion", "Diffusion equation", "Digital signal processing", "Dirac delta", "Discrete Gaussian kernel", "Eigenfunction", "Elementary function (differential algebra)", "Emission spectrum", "Engineering", "Error function", "Expected value", "Exponential function", "Fluorescence microscopy", "Fourier transform", "Fraunhofer diffraction", "Full width at half maximum", "Function (mathematics)", "GNU Octave", "Gaussian Curve", "Gaussian Curve (band)", "Gaussian beam", "Gaussian blur", "Gaussian filter", "Gaussian integral", "Gaussian orbital", "Geostatistics", "Graph of a function", "Green's function", "Ground state", "Heat equation", "Heat kernel", "Hermite functions", "Hermite polynomial", "Image processing", "Independent and identically-distributed random variables", "Inflection point", "Integral", "Iteratively reweighted least squares", "Least squares", "Limit (mathematics)", "Linear combination", "List of logarithmic identities", "Logarithm", "Lorentzian function", "MathWorld", "Mathematics", "Modified Bessel function", "Molecular orbital", "Multivariate normal distribution", "Natural sciences", "Normal distribution", "Normalizing constant", "Partial differential equation", "Photographic slide", "Photometry (astronomy)", "Point source", "Poisson distribution", "Poisson summation formula", "Positive-definite matrix", "Probability density function", "Probability distribution", "Probability theory", "Quadratic function", "Quantum field theory", "Quantum harmonic oscillator", "Radial basis function kernel", "Random variable", "Real number", "Root mean square", "Sampled Gaussian kernel", "Scale space", "Scale space implementation", "Signal processing", "Social sciences", "Standard deviation", "Statistics", "Training image", "Transmittance", "Transpose", "Vacuum state", "Variance", "Visual system", "Wave function", "Weierstrass transform"], "references": ["http://www.aor.com/anonymous/pub/commands.pdf", "http://www.mathpages.com/home/kmath045/kmath045.htm", "http://mathworld.wolfram.com/FourierTransformGaussian.html", "http://mathworld.wolfram.com/GaussianFunction.html", "http://www.nada.kth.se/~tony/abstracts/Lin90-PAMI.html", "https://github.com/dwaithe/generalMacros/tree/master/gaussian_fitting", "https://github.com/frecker/gaussian-distribution/", "https://dx.doi.org/10.1007/s11004-010-9276-7", "https://dx.doi.org/10.1016/j.tpb.2007.08.001", "https://dx.doi.org/10.1109/MSP.2011.941846", "https://dx.doi.org/10.1364/AO.46.005374", "https://dx.doi.org/10.1364/AO.47.006842", "https://upload.wikimedia.org/wikipedia/commons/a/a2/Cumulative_function_n_dimensional_Gaussians_12.2013.pdf"]}, "Probability of precipitation": {"categories": ["Climate and weather statistics", "Numerical climate and weather models", "Weather forecasting"], "title": "Probability of precipitation", "method": "Probability of precipitation", "url": "https://en.wikipedia.org/wiki/Probability_of_precipitation", "summary": "A probability of precipitation (POP), (also expressed as: \"chance of precipitation,\" \"chance of rain\") is a description of the likelihood of precipitation that is often published with weather forecasts. Generally it refers to the probability that at least some minimum quantity of precipitation will occur within a specified forecast period and location.", "images": [], "links": ["AccuWeather", "Bibcode", "Digital object identifier", "Ensemble forecasting", "Environment Canada", "Haleakal\u0101", "Maui", "Met Office", "Nate Silver", "National Weather Service", "Plain English Campaign", "Precipitation (meteorology)", "Probability", "Probability of exceedance", "Quantitative precipitation forecast", "Rain gauge", "The Weather Channel", "Weather forecasts", "Wet bias"], "references": ["http://www.ec.gc.ca/meteo-weather/default.asp?lang=En&n=2D8EBDE4-1#c2", "http://adsabs.harvard.edu/abs/2009BAMS...90..185J", "http://pajk.arh.noaa.gov/Articles/articles/survey/poptext.html", "http://www.nws.noaa.gov/directives/010/archive/pd01005003b.pdf", "http://www.srh.noaa.gov/ffc/?n=pop", "http://www.srh.noaa.gov/jax/?n=probability_of_precipitation", "http://www.weather.gov/bgm/forecast_terms", "http://doi.org/10.1175%2F2008BAMS2509.1", "http://www.plainenglish.co.uk/campaigning/awards/2011-awards/golden-bull-awards.html", "http://blog.metoffice.gov.uk/2011/12/09/a-golden-conundrum/", "http://www.metoffice.gov.uk/news/in-depth/science-behind-probability-of-precipitation", "https://ec.gc.ca/meteo-weather/default.asp?lang=En&n=B8CD636F-1&def=show02B55773D", "https://www.nytimes.com/2012/09/09/magazine/the-weatherman-is-not-a-moron.html?pagewanted=all&_r=0", "https://blogs.wsj.com/numbers/deciphering-a-20-chance-of-rain-470/", "https://www.bbc.co.uk/news/uk-16100112", "https://www.telegraph.co.uk/news/weather/8880438/Chance-of-a-shower-You-decide-as-Met-Office-launches-new-style-weather-forecasts.html"]}, "Pattern recognition": {"categories": ["Accuracy disputes from May 2014", "All accuracy disputes", "All articles needing additional references", "All articles with unsourced statements", "All pages needing cleanup", "Articles needing additional references from November 2014", "Articles needing cleanup from May 2014", "Articles with disputed statements from November 2014", "Articles with multiple maintenance issues", "Articles with unsourced statements from January 2011", "Articles with unsourced statements from May 2014", "CS1 maint: Archived copy as title", "CS1 maint: Multiple names: authors list", "Computational fields of study", "Formal sciences", "Machine learning", "Pattern recognition", "Webarchive template archiveis links", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers", "Wikipedia list cleanup from May 2014"], "title": "Pattern recognition", "method": "Pattern recognition", "url": "https://en.wikipedia.org/wiki/Pattern_recognition", "summary": "Pattern recognition is the automated recognition of patterns and regularities in data. Pattern recognition is closely related to artificial intelligence and machine learning, together with applications such as data mining and knowledge discovery in databases (KDD), and is often used interchangeably with these terms. However, these are distinguished: machine learning is one approach to pattern recognition, while other approaches include hand-crafted (not learned) rules or heuristics; and pattern recognition is one approach to artificial intelligence, while other approaches include symbolic artificial intelligence. A modern definition of pattern recognition is:\n\nThe field of pattern recognition is concerned with the automatic discovery of regularities in data through the use of computer algorithms and with the use of these regularities to take actions such as classifying the data into different categories.\nThis article focuses on machine learning approaches to pattern recognition. Pattern recognition systems are in many cases trained from labeled \"training\" data (supervised learning), but when no labeled data are available other algorithms can be used to discover previously unknown patterns (unsupervised learning). Machine learning is the common term for supervised learning methods and originates from artificial intelligence, whereas KDD and data mining have a larger focus on unsupervised methods and stronger connection to business use. Pattern recognition has its origins in engineering, and the term is popular in the context of computer vision: a leading computer vision conference is named Conference on Computer Vision and Pattern Recognition. In pattern recognition, there may be a higher interest to formalize, explain and visualize the pattern, while machine learning traditionally focuses on maximizing the recognition rates. Yet, all of these domains have evolved substantially from their roots in artificial intelligence, engineering and statistics, and they've become increasingly similar by integrating developments and ideas from each other.\nIn machine learning, pattern recognition is the assignment of a label to a given input value. In statistics, discriminant analysis was introduced for this same purpose in 1936. An example of pattern recognition is classification, which attempts to assign each input value to one of a given set of classes (for example, determine whether a given email is \"spam\" or \"non-spam\"). However, pattern recognition is a more general problem that encompasses other types of output as well. Other examples are regression, which assigns a real-valued output to each input; sequence labeling, which assigns a class to each member of a sequence of values (for example, part of speech tagging, which assigns a part of speech to each word in an input sentence); and parsing, which assigns a parse tree to an input sentence, describing the syntactic structure of the sentence.Pattern recognition algorithms generally aim to provide a reasonable answer for all possible inputs and to perform \"most likely\" matching of the inputs, taking into account their statistical variation. This is opposed to pattern matching algorithms, which look for exact matches in the input with pre-existing patterns. A common example of a pattern-matching algorithm is regular expression matching, which looks for patterns of a given sort in textual data and is included in the search capabilities of many text editors and word processors. In contrast to pattern recognition, pattern matching is not generally a type of machine learning, although pattern-matching algorithms (especially with fairly general, carefully tailored patterns) can sometimes succeed in providing similar-quality output of the sort provided by pattern-recognition algorithms.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d9/800px-Cool_Kids_of_Death_Off_Festival_p_146-face_selected.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/1/17/System-search.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["A priori and a posteriori", "Adaptive resonance theory", "Anomaly detection", "Archive.is", "Artificial intelligence", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayes' rule", "Bayes error rate", "Bayes rule", "Bayesian inference", "Bayesian network", "Bayesian statistics", "Beta distribution", "Bias-variance dilemma", "Black box", "Boosting (machine learning)", "Boosting (meta-algorithm)", "Bootstrap aggregating", "Branch and bound", "CURE data clustering algorithm", "Cache language model", "Canonical correlation analysis", "Categorical data", "Classification (machine learning)", "Cluster analysis", "Community ecology", "Compound term processing", "Computational learning theory", "Computer-aided diagnosis", "Computer vision", "Conditional random field", "Conference on Computer Vision and Pattern Recognition", "Conference on Neural Information Processing Systems", "Conjugate prior distribution", "Contextual image classification", "Continuous distribution", "Convolutional neural network", "Correctness (computer science)", "Correlation clustering", "Covariance matrix", "DBSCAN", "Data", "Data clustering", "Data mining", "Decision list", "Decision theory", "Decision tree", "Decision tree learning", "DeepDream", "Deep Learning", "Deep learning", "Digital object identifier", "Dimensionality reduction", "Dirichlet distribution", "Discriminative model", "Distance", "Document classification", "Dot product", "Dynamic time warping", "Empirical risk minimization", "Engineering", "Ensemble averaging", "Ensemble learning", "Expectation\u2013maximization algorithm", "Expected value", "Face detection", "Face recognition", "Factor analysis", "Feature engineering", "Feature extraction", "Feature learning", "Feature selection", "Feature vector", "Fisher discriminant analysis", "Free On-line Dictionary of Computing", "Frequentist inference", "GNU Free Documentation License", "Gated recurrent unit", "Gaussian distribution", "Gaussian process regression", "Gene expression programming", "Generative model", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Handwriting recognition", "Heuristic", "Hidden Markov model", "Hierarchical clustering", "Hierarchical mixture of experts", "Image analysis", "Image recognition", "Independent component analysis", "Integer", "Integral", "Integrated Authority File", "International Conference on Machine Learning", "International Standard Book Number", "International Standard Serial Number", "Journal of Machine Learning Research", "K-means clustering", "K-nearest-neighbor", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kalman filter", "Kernel principal component analysis", "Knowledge discovery in databases", "Learning to rank", "License plate recognition", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "List of datasets for machine learning research", "List of numerical analysis software", "List of numerical libraries", "Local outlier factor", "Logistic regression", "Long short-term memory", "Loss function", "Machine Learning (journal)", "Machine learning", "Markov random field", "Maximum a posteriori", "Maximum entropy Markov model", "Maximum entropy classifier", "Maximum likelihood", "Mean-shift", "Meta-algorithm", "Mixture model", "Mixture of experts", "Multilayer perceptron", "Multilinear principal component analysis", "Multilinear subspace learning", "Multinomial logistic regression", "Naive Bayes classifier", "National Diet Library", "Neocognitron", "Neural network", "Nominal data", "Non-negative matrix factorization", "OCLC", "OPTICS algorithm", "Occam's Razor", "Occam learning", "Online machine learning", "Optimization problem", "Ordinal data", "Outline of machine learning", "Parse tree", "Parsing", "Part of speech", "Part of speech tagging", "Particle filter", "Pattern Recognition (journal)", "Pattern matching", "Pattern recognition (disambiguation)", "Pattern recognition (psychology)", "Perception", "Perceptron", "Perceptual learning", "Peter E. Hart", "Posterior probability", "Powerset", "Predictive analytics", "Principal component analysis", "Principal components analysis", "Prior knowledge for pattern recognition", "Prior probability", "Probabilistic classifier", "Probability", "Probability distribution", "Probability theory", "Probably approximately correct learning", "Q-learning", "Quadratic classifier", "Random forest", "Real number", "Recurrent neural network", "Recurrent neural networks", "Regression analysis", "Regular expression", "Regularization (mathematics)", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Self-organizing map", "Semi-supervised learning", "Sequence labeling", "Sequence mining", "Similarity measure", "Space (mathematics)", "Speech recognition", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical inference", "Statistical learning theory", "Structured prediction", "Supervised learning", "Support vector machine", "Symbolic artificial intelligence", "Syntactic structure", "T-distributed stochastic neighbor embedding", "Template matching", "Temporal difference learning", "Tensor", "Text editor", "Training set", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory", "Variable kernel density estimation", "Vector space", "Word processor", "Zero-one loss function"], "references": ["http://cgm.cs.mcgill.ca/~godfried/teaching/pr-web.html", "http://cds.cern.ch/record/998831/files/9780387310732_TOC.pdf", "http://www.openpr.org.cn/", "http://www.docentes.unal.edu.co/morozcoa/docs/pr.php", "http://anpr-tutorial.com/", "http://www.dontveter.com/basisofai/basisofai.html", "http://www.inderscience.com/ijapr", "http://www.sciencedirect.com/science/journal/00313203", "http://www.worldscinet.com/ijprai/mkt/archive.shtml", "http://cmp.felk.cvut.cz/cmp/software/stprtool/examples/ocr_system.gif", "http://www.cs.cmu.edu/afs/cs.cmu.edu/usr/mitchell/ftp/faces.html", "http://www-vis.lbl.gov/~romano/mlgroup/papers/guyon03a.pdf", "http://www.egmont-petersen.nl/classifiers.htm", "http://dl.acm.org/citation.cfm?id=1324656", "http://doi.org/10.1016%2FS0031-3203(01)00178-9", "http://doi.org/10.1016%2FS0031-3203(99)00041-2", "http://doi.org/10.1016%2Fj.patcog.2007.08.018", "http://doi.org/10.1049%2Fiet-bmt.2017.0065", "http://doi.org/10.1108%2F03684920710743466", "http://doi.org/10.1109%2F34.824819", "http://doi.org/10.1109%2FT-C.1972.223519", "http://doi.org/10.1109%2FTSMC.1987.4309029", "http://dx.doi.org/10.1108/03684920710743466", "http://health-asia.org/papnet-for-cervical-screening/", "http://www.iapr.org", "http://ieeexplore.ieee.org/document/8302747/", "http://www.jprr.org", "http://worldcat.org/oclc/799802313", "http://www.worldcat.org/issn/0368-492X", "http://www.worldcat.org/oclc/799802313", "http://www.s-cool.co.uk/a-level/psychology/attention/revise-it/pattern-recognition", "https://www.academia.edu/31957815/Improved_Pattern_Matching_Applied_to_Surface_Mounting_Devices_Components_Localization_on_Automated_Optical_Inspection", "https://pubweb.eng.utah.edu/~cs6961/slides/seq-labeling1.4ps.pdf", "https://d-nb.info/gnd/4040936-3", "https://archive.is/20120708211332/http://health-asia.org/papnet-for-cervical-screening/", "https://id.ndl.go.jp/auth/ndlna/00569072", "https://arxiv.org/list/cs.LG/recent", "https://deepai.org/machine-learning-glossary-and-terms/training-pattern", "https://www.wikidata.org/wiki/Q378859"]}, "Bochner's theorem": {"categories": ["Statistical theorems", "Theorems in Fourier analysis", "Theorems in functional analysis", "Theorems in harmonic analysis", "Theorems in measure theory"], "title": "Bochner's theorem", "method": "Bochner's theorem", "url": "https://en.wikipedia.org/wiki/Bochner%27s_theorem", "summary": "In mathematics, Bochner's theorem (named for Salomon Bochner) characterizes the Fourier transform of a positive finite Borel measure on the real line. More generally in harmonic analysis, Bochner's theorem asserts that under Fourier transform a continuous positive definite function on a locally compact abelian group corresponds to a finite positive measure on the Pontryagin dual group.", "images": [], "links": ["Abelian group", "Absolutely continuous", "Autocovariance function", "Borel measure", "C*-algebra", "Characteristic function (probability theory)", "Covariance", "Discrete group", "Dominated convergence theorem", "Fourier transform", "Harmonic analysis", "Herglotz", "Herglotz representation theorem", "Hilbert space", "Inner product", "International Standard Book Number", "Isomorphism", "Locally compact group", "Mathematics", "Multiplier algebra", "Pontryagin duality", "Positive-definite function on a group", "Positive definite function on a group", "Probability measure", "Pull-back", "Radon-Nikodym derivative", "Salomon Bochner", "Serial correlation", "Shift operator", "Spectral density", "State (functional analysis)", "Stationary stochastic process", "Statistics", "Strong operator topology", "Time series", "Unitary representation"], "references": []}, "Small area estimation": {"categories": ["Estimation methods"], "title": "Small area estimation", "method": "Small area estimation", "url": "https://en.wikipedia.org/wiki/Small_area_estimation", "summary": "Small area estimation is any of several statistical techniques involving the estimation of parameters for small sub-populations, generally used when the sub-population of interest is included in a larger survey.\nThe term \"small area\" in this context generally refers to a small geographical area such as a county. It may also refer to a \"small domain\", i.e. a particular demographic within an area. If a survey has been carried out for the population as a whole (for example, a nation or statewide survey), the sample size within any particular small area may be too small to generate accurate estimates from the data. To deal with this problem, it may be possible to use additional data (such as census records) that exists for these small areas in order to obtain estimates.\nOne of the more common small area models in use today is the 'nested area unit level regression model', first used in 1988 to model corn and soybean crop areas in Iowa. The initial survey data, in which farmers reported the area they had growing either corn or soybeans, was compared to estimates obtained from satellite mapping of the farms.\nThe final model resulting from this for unit/farm 'j' in county 'i' is \n \n \n \n \n y\n \n i\n j\n \n \n =\n \n x\n \n i\n j\n \n \u2032\n \n \u03b2\n +\n \n \u03bc\n \n i\n \n \n +\n \n \u03f5\n \n i\n j\n \n \n \n \n \n {\\displaystyle y_{ij}=x_{ij}'\\beta +\\mu _{i}+\\epsilon _{ij}\\,}\n , where 'y' denotes the reported crop area, \n \n \n \n \u03b2\n \n \n \n {\\displaystyle \\beta \\,}\n is the regression coefficient, 'x' is the farm-level estimate for either corn or soybean usage from\nthe satellite data and \n \n \n \n \u03bc\n \n \n \n {\\displaystyle \\mu \\,}\n represents the county-level effect of any area characteristics unaccounted for.", "images": [], "links": ["Census", "Demographic", "Estimation", "International Standard Book Number", "Linear regression", "Parameter", "Sample size", "Statistical", "Statistical survey", "Sub-population"], "references": ["http://projecteuclid.org/euclid.ss/1177010647", "https://www.jstor.org/stable/2288915"]}, "Circular uniform distribution": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2010", "Continuous distributions", "Directional statistics"], "title": "Circular uniform distribution", "method": "Circular uniform distribution", "url": "https://en.wikipedia.org/wiki/Circular_uniform_distribution", "summary": "In probability theory and directional statistics, a circular uniform distribution is a probability distribution on the unit circle whose density is uniform for all angles.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/86/CircUniformDistOfMean.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bessel function", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central limit theorem for directional statistics", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Entropy (information theory)", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent and identically-distributed random variables", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kronecker delta", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://ieeexplore.ieee.org/document/7944181/", "https://www.amazon.com/Topics-Circular-Statistics-Rao-Jammalamadaka/dp/9810237782#reader_9810237782"]}, "Well-behaved statistic": {"categories": ["All articles lacking in-text citations", "All articles with style issues", "Articles lacking in-text citations from November 2010", "Articles with multiple maintenance issues", "CS1 maint: Uses authors parameter", "Statistical inference", "Wikipedia articles with style issues from September 2009"], "title": "Well-behaved statistic", "method": "Well-behaved statistic", "url": "https://en.wikipedia.org/wiki/Well-behaved_statistic", "summary": "Although the term well-behaved statistic often seems to be used in the scientific literature in somewhat the same way as is well-behaved in mathematics, that is, to mean 'non-pathological' it can also be assigned precise mathematical meaning, and in more than one way. In the former case, the meaning of this term will vary from context to context. In the latter case, the mathematical conditions can be used to derive classes of combinations of distributions with statistics which are well-behaved in each sense.\nFirst Definition: The variance of a well-behaved statistical estimator is finite and one condition on its mean is that it is differentiable in the parameter being estimated.Second Definition: The statistic is monotonic, well-defined, and locally sufficient.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Algorithmic inference", "Bernoulli distribution", "Data mining", "Digital object identifier", "Estimator", "Exponential distribution", "Pareto distribution", "R. R. Bahadur", "Statistic", "Statistical inference", "Sufficient statistics", "Uniform distribution (continuous)", "Variance", "Well-behaved"], "references": ["http://www.stat.purdue.edu/~dasgupta/528-5.pdf", "http://www-personal.umich.edu/~jdinardo/lawsofgenius.pdf", "http://resource.owen.vanderbilt.edu/facultyadmin/data/research/2359abstract.pdf", "http://doi.org/10.1214%2Faoms%2F1177728604"]}, "Analytic and enumerative statistical studies": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2010", "Philosophy of statistics", "Quality", "Webarchive template wayback links"], "title": "Analytic and enumerative statistical studies", "method": "Analytic and enumerative statistical studies", "url": "https://en.wikipedia.org/wiki/Analytic_and_enumerative_statistical_studies", "summary": "Analytic and enumerative statistical studies are two types of scientific studies:\nIn any statistical study the ultimate aim is to provide a rational basis for action. Enumerative and analytic studies differ by where the action is taken. Deming first published on this topic in 1942. Deming summarized the distinction between enumerative and analytic studies as follows:\n\nEnumerative study: A statistical study in which action will be taken on the material in the frame being studied.\nAnalytic study: A statistical study in which action will be taken on the process or cause-system that produced the frame being studied. The aim being to improve practice in the future.\n\n(In a statistical study, the frame is the set from which the sample is taken.)\nThese terms were introduced in Some Theory of Sampling (1950, Chapter 7) by W. Edwards Deming.\nIn other words, an enumerative study is a statistical study in which the focus is on judgment of results, and an analytic study is one in which the focus is on improvement of the process or system which created the results being evaluated and which will continue creating results in the future. A statistical study can be enumerative or analytic, but it cannot be both.\nStatistical theory in enumerative studies is used to describe the precision of estimates and the validity of hypotheses for the population studied. In analytical studies, the standard error of a statistic does not address the most important source of uncertainty, namely, the change in study conditions in the future. Although analytical studies need to take into account the uncertainty due to sampling, as in enumerative studies, the attributes of the study design and analysis of the data primarily deal with the uncertainty resulting from extrapolation to the future (generalisation to the conditions in future time periods). The methods used in analytical studies encourage the exploration of mechanisms through multifactor designs, contextual variables introduced through blocking and replication over time.This distinction between enumerative and analytic studies is the theory behind the Fourteen Points for Management. Dr. Deming's philosophy is that management should be analytic instead of enumerative. In other words, management should focus on improvement of processes for the future instead of on judgment of current results.\n\n\"Use of data requires knowledge about the different sources of uncertainty.\nMeasurement is a process. Is the system of measurement stable or unstable? Use\n\nof data requires also understanding of the distinction between enumerative studies and analytic problems.\"\n\"The interpretation of results of a test or experiment is something else. It is\nprediction that a specific change in a process or procedure will be a wise choice, or that no change would be better. Either way the choice is prediction. This is known as an analytic problem, or a problem of inference, prediction.\"\nStatistician Dr. Mike Tveite has pointed out the dangers of attempting to use an enumerative study for prediction.Co-presenter and author Henry Neave discusses the issues associated with enumerative and analytic studies along with the many contributions made by Deming in his 1990 book, \"The Deming Dimension {reference added} and the 12 Days to Deming Course made accessible by the British Deming Association at: http://www.franbo.uk/deming/the-course/\nProvost wrote about the distinction of analytic studies in health care.", "images": [], "links": ["Digital object identifier", "Fourteen Points for Management", "Improvement of the process", "International Standard Serial Number", "Mike Tveite", "PubMed Central", "Sample (statistics)", "Scientific studies", "W. Edwards Deming", "Wayback Machine"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3066849", "http://doi.org/10.1080%2F07408179208964218", "http://doi.org/10.1136%2Fbmjqs.2011.051557", "http://doi.org/10.2307%2F2279212", "http://dx.doi.org/10.1080/07408179208964218", "http://dx.doi.org/10.1136/bmjqs.2011.051557", "http://dx.doi.org/10.2307/2279212", "http://www.worldcat.org/issn/0162-1459", "http://www.worldcat.org/issn/0740-817X", "http://www.worldcat.org/issn/2044-5415", "http://www.franbo.uk/deming/the-course/", "https://web.archive.org/web/20100920162902/http://homepage.mac.com/dfkerridge/.Public/DEN/Reality.pdf"]}, "Cluster randomised controlled trial": {"categories": ["Clinical research", "Design of experiments"], "title": "Cluster randomised controlled trial", "method": "Cluster randomised controlled trial", "url": "https://en.wikipedia.org/wiki/Cluster_randomised_controlled_trial", "summary": "A cluster randomised controlled trial is a type of randomised controlled trial in which groups of subjects (as opposed to individual subjects) are randomised. Cluster randomised controlled trials are also known as cluster randomised trials, group-randomised trials, and place-randomized trials.A 2004 bibliometric study documented an increasing number of publications in the medical literature on cluster randomised controlled trials since the 1980s. Advantages of cluster randomised controlled trials over individually randomised controlled trials include the ability to study interventions that cannot be directed toward selected individuals (e.g., a radio show about lifestyle changes) and the ability to control for \"contamination\" across individuals (e.g., one individual's changing behaviors may influence another individual to do so).Disadvantages compared with individually randomised controlled trials include greater complexity in design and analysis, and a requirement for more participants to obtain the same statistical power. Specifically, the cluster randomised designs introduce dependence (or clustering) between individual units sampled. An example would be an educational intervention in which schools are randomised to one of several new teaching methods. When comparing differences in outcome achieved under the new methods, researchers must account for the fact that two students sampled from a single school are more likely to be similar (in terms of outcomes) than two students sampled from different schools. Multilevel or similar statistical models are typically used to correct for this non-independence.", "images": [], "links": ["American Behavioral Scientist", "Bibliometrics", "Digital object identifier", "Frederick Mosteller", "International Standard Book Number", "Multilevel model", "PubMed Central", "PubMed Identifier", "Randomised controlled trial", "Randomized controlled trial", "Statistical power", "Statistics", "Zelen's design"], "references": ["http://www.biomedcentral.com/1471-2288/4/21", "http://www.bmj.com/cgi/content/full/318/7195/1407", "http://www.bmj.com/cgi/content/full/328/7441/702", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1115783", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1448268", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1551970", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC381234", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC515302", "http://www.ncbi.nlm.nih.gov/pubmed/10334756", "http://www.ncbi.nlm.nih.gov/pubmed/14998806", "http://www.ncbi.nlm.nih.gov/pubmed/15031246", "http://www.ncbi.nlm.nih.gov/pubmed/15310402", "http://www.ncbi.nlm.nih.gov/pubmed/16873760", "http://ajph.aphapublications.org/cgi/content/full/94/3/423", "http://ajph.aphapublications.org/cgi/content/full/96/9/1582", "http://doi.org/10.1136%2Fbmj.318.7195.1407", "http://doi.org/10.1136%2Fbmj.328.7441.702", "http://doi.org/10.1177%2F0002764203259291", "http://doi.org/10.1186%2F1471-2288-4-21", "http://doi.org/10.2105%2FAJPH.2004.047399", "http://doi.org/10.2105%2FAJPH.94.3.423", "http://spabs.highwire.org/cgi/content/abstract/47/5/608"]}, "Little's law": {"categories": ["Queueing theory"], "title": "Little's law", "method": "Little's law", "url": "https://en.wikipedia.org/wiki/Little%27s_law", "summary": "In queueing theory, a discipline within the mathematical theory of probability, Little's result, theorem, lemma, law, or formula is a theorem by John Little which states that the long-term average number L of customers in a stationary system is equal to the long-term average effective arrival rate \u03bb multiplied by the average time W that a customer spends in the system. Expressed algebraically the law is\n\n \n \n \n L\n =\n \u03bb\n W\n .\n \n \n {\\displaystyle L=\\lambda W.}\n Although it looks intuitively easy, it is quite a remarkable result, as the relationship is \"not influenced by the arrival process distribution, the service distribution, the service order, or practically anything else.\"The result applies to any system, and particularly, it applies to systems within systems. So in a bank, the customer line might be one subsystem, and each of the tellers another subsystem, and Little's result could be applied to each one, as well as the whole thing. The only requirements are that the system be stable and non-preemptive; this rules out transition states such as initial startup or shutdown.\nIn some cases it is possible not only to mathematically relate the average number in the system to the average wait but even to relate the entire probability distribution (and moments) of the number in the system to the wait.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival theorem", "BCMP network", "Balance equation", "Bank teller", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "CreateSpace", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Erlang (unit)", "Erlang distribution", "FIFO (computing and electronics)", "First come, first served", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "International Standard Book Number", "JSTOR", "Jackson network", "John Little (academic)", "Julian Keilson", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "List of eponymous laws", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Michael Trick", "Network congestion", "Network scheduler", "Operations Research (journal)", "Philip M. Morse", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Preemption (computing)", "Probability distribution", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Response time (technology)", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Stationary process", "Teletraffic engineering", "Traffic equations", "Ward Whitt"], "references": ["http://www.epmonthly.com/subspecialties/management/littles-law-the-science-behind-proper-staffing/", "http://www.onjava.com/pub/a/onjava/2005/01/19/j2ee-bottlenecks.html", "http://www.columbia.edu/~ks20/stochastic-I/stochastic-I-LL.pdf", "http://www.columbia.edu/~ww2040/LL_OR.pdf", "http://dspace.mit.edu/handle/1721.1/5305", "http://web.mit.edu/dbertsim/www/papers/Queuing%20Theory/The%20distributional%20Little's%20law%20and%20its%20applications.pdf", "http://web.mit.edu/sgraves/www/papers/Little's%20Law-Published.pdf", "http://doi.org/10.1007%2F978-0-387-73699-0_5", "http://doi.org/10.1007%2F978-1-4612-1482-3_5", "http://doi.org/10.1016%2F0167-6377(88)90035-1", "http://doi.org/10.1287%2Fopre.1110.0940", "http://doi.org/10.1287%2Fopre.1110.0941", "http://doi.org/10.1287%2Fopre.15.6.1109", "http://doi.org/10.1287%2Fopre.17.5.915", "http://doi.org/10.1287%2Fopre.2.1.70", "http://doi.org/10.1287%2Fopre.20.6.1115", "http://doi.org/10.1287%2Fopre.2013.1193", "http://doi.org/10.1287%2Fopre.22.2.417", "http://doi.org/10.1287%2Fopre.43.2.298", "http://doi.org/10.1287%2Fopre.9.3.383", "http://www.informs.org/content/download/255808/2414681/file/little_paper.pdf", "http://www.jstor.org/stable/166539", "http://www.jstor.org/stable/167570", "http://www.jstor.org/stable/168368", "http://www.jstor.org/stable/168616", "http://www.jstor.org/stable/169301", "http://www.jstor.org/stable/169601", "http://www.jstor.org/stable/171838", "http://www.jstor.org/stable/23013126", "https://www.amazon.com/Every-Computer-Performance-Book-Computers/dp/1482657759/", "https://arxiv.org/abs/cs/0404043"]}, "Tukey's test of additivity": {"categories": ["All articles lacking in-text citations", "Analysis of variance", "Articles lacking in-text citations from February 2010", "Statistical tests"], "title": "Tukey's test of additivity", "method": "Tukey's test of additivity", "url": "https://en.wikipedia.org/wiki/Tukey%27s_test_of_additivity", "summary": "In statistics, Tukey's test of additivity, named for John Tukey, is an approach used in two-way ANOVA (regression analysis involving two qualitative factors) to assess whether the factor variables are additively related to the expected value of the response variable. It can be applied when there are no replicated values in the data set, a situation in which it is impossible to directly estimate a fully general non-additive regression structure and still have information left to estimate the error variance. The test statistic proposed by Tukey has one degree of freedom under the null hypothesis, hence this is often called \"Tukey's one-degree-of-freedom test.\"", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Analysis of Variance", "Digital object identifier", "Expected value", "F-distribution", "JSTOR", "John Tukey", "Regression analysis", "Statistics", "Test statistic", "Tukey's range test"], "references": ["http://doi.org/10.2307%2F3001938", "http://www.jstor.org/stable/3001938"]}, "Glossary of experimental design": {"categories": ["Design of experiments", "Glossaries of mathematics", "Glossaries of science", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Glossary of experimental design", "method": "Glossary of experimental design", "url": "https://en.wikipedia.org/wiki/Glossary_of_experimental_design", "summary": "The following is a glossary of terms. It is not intended to be all-inclusive.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average treatment effect", "Balanced design", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Block effect", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparative design", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Control group", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossed factor", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design", "Design matrix", "Design of Experiments", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation theory", "Experiment", "Experimental design", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fixed effect", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary", "Glossary of probability and statistics", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Internal validity", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistical topics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nested factors", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Notation in probability and statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Paradigm (experimental)", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Random error", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression discontinuity design", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Rotatability", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaling factor level", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Screening design", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Test plan", "Time domain", "Time series", "Tolerance interval", "Treatment combination", "Treatment group", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Variance component", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.itl.nist.gov/div898/handbook/pmd/section3/pmd31.htm", "http://www.itl.nist.gov/div898/handbook/pri/section7/pri7.htm", "http://www.nist.gov"]}, "Quadratic form (statistics)": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from December 2009", "Articles with unsourced statements from September 2018", "Quadratic forms", "Statistical theory"], "title": "Quadratic form (statistics)", "method": "Quadratic form (statistics)", "url": "https://en.wikipedia.org/wiki/Quadratic_form_(statistics)", "summary": "In multivariate statistics, if \n \n \n \n \u03b5\n \n \n {\\displaystyle \\varepsilon }\n is a vector of \n \n \n \n n\n \n \n {\\displaystyle n}\n random variables, and \n \n \n \n \u039b\n \n \n {\\displaystyle \\Lambda }\n is an \n \n \n \n n\n \n \n {\\displaystyle n}\n -dimensional symmetric matrix, then the scalar quantity \n \n \n \n \n \u03b5\n \n T\n \n \n \u039b\n \u03b5\n \n \n {\\displaystyle \\varepsilon ^{T}\\Lambda \\varepsilon }\n is known as a quadratic form in \n \n \n \n \u03b5\n \n \n {\\displaystyle \\varepsilon }\n .", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Bias of an estimator", "Central moment", "Chi-squared distribution", "Covariance", "Covariance matrix", "Errors and residuals in statistics", "Expected value", "Idempotent matrix", "International Standard Book Number", "Matrix representation of conic sections", "Multivariate normal distribution", "Multivariate statistics", "Noncentral chi-squared distribution", "OCLC", "Operator matrix", "Quadratic form", "Random variable", "Residual sum of squares", "Scalar (mathematics)", "Symmetric matrix", "Trace (linear algebra)", "Vector space"], "references": ["http://www.stat.wisc.edu/~st849-1/lectures/Ch02.pdf", "http://www.worldcat.org/oclc/212120778"]}, "Procrustes analysis": {"categories": ["Articles containing Greek-language text", "Biometrics", "Commons category link is on Wikidata", "Euclidean symmetries", "Greek mythology studies", "Greek words and phrases", "Multivariate statistics"], "title": "Procrustes analysis", "method": "Procrustes analysis", "url": "https://en.wikipedia.org/wiki/Procrustes_analysis", "summary": "In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes. The name Procrustes (Greek: \u03a0\u03c1\u03bf\u03ba\u03c1\u03bf\u03cd\u03c3\u03c4\u03b7\u03c2) refers to a bandit from Greek mythology who made his victims fit his bed either by stretching their limbs or cutting them off.\nIn mathematics:\n\nan orthogonal Procrustes problem is a method which can be used to find out the optimal rotation and/or reflection (i.e., the optimal orthogonal linear transformation) for the PS of an object with respect to another.\na constrained orthogonal Procrustes problem, subject to det(R) = 1 (where R is a rotation matrix), is a method which can be used to determine the optimal rotation for the PS of an object with respect to another (reflection is not allowed). In some contexts, this method is called the Kabsch algorithm.When a shape is compared to another, or a set of shapes is compared to an arbitrarily selected reference shape, Procrustes analysis is sometimes further qualified as classical or ordinary, as opposed to Generalized Procrustes analysis (GPA), which compares three or more shapes to an optimally determined \"mean shape\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f5/Procrustes_superimposition.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Active shape model", "Alignments of random points", "Biological data", "Biometrics", "Centroid", "David George Kendall", "Determinant", "Equivalence class", "Generalized Procrustes analysis", "Geometry", "Greek language", "Image registration", "Kabsch algorithm", "Kent distribution", "Landmark point", "Least squares", "Manifold", "Mean", "Morphometrics", "Orientation (geometry)", "Orthogonal Procrustes problem", "Procrustes", "Reflection (mathematics)", "Root mean square", "Rotation (mathematics)", "Rotation matrix", "Scaling (geometry)", "Shape", "Singular value decomposition", "Standing stones", "Statistical shape analysis", "Statistics", "Translation (geometry)"], "references": ["http://www.rps.psu.edu/mar94/goodall.html", "http://petitjeanmichel.free.fr/itoweb.petitjean.shape.html", "https://www.jstor.org/stable/2245331"]}, "Seasonal subseries plot": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2016", "Statistical charts and diagrams", "Time series", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Seasonal subseries plot", "method": "Seasonal subseries plot", "url": "https://en.wikipedia.org/wiki/Seasonal_subseries_plot", "summary": "Seasonal subseries plots are a graphical tool to visualize and detect seasonality in a time series. Seasonal subseries plots involves the extraction of the seasons from a time series into a subseries. Based on a selected periodicity, it is an alternative plot that emphasizes the seasonal patterns are where the data for each season are collected together in separate mini time plots.Seasonal subseries plots enables the underlying seasonal pattern to be seen clearly, and also shows the changes in seasonality over time. Especially, it allows to detect changes between different seasons, changes within a particular season over time.\nHowever, this plot is only useful if the period of the seasonality is already known. In many cases, this will in fact be known. For example, monthly data typically has a period of 12. If the period is not known, an autocorrelation plot or spectral plot can be used to determine it. If there is a large number of observations, then a box plot may be preferable.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/91/Seasonal_sub-series_plot.png", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Autocorrelation plot", "Box plot", "Copyright status of work by the U.S. government", "National Institute of Standards and Technology", "Outlier", "Periodic point", "R (programming language)", "Recurrence plot", "Response variable", "Run sequence plot", "Seasonality", "Spectral plot", "Time series"], "references": ["http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4431.htm", "http://www.nist.gov", "https://www.otexts.org/fpp/2/1"]}, "Studentized residual": {"categories": ["Accuracy disputes from February 2014", "All accuracy disputes", "All articles needing additional references", "Articles needing additional references from May 2015", "Articles with multiple maintenance issues", "Errors and residuals", "Statistical deviation and dispersion", "Statistical outliers", "Statistical ratios"], "title": "Studentized residual", "method": "Studentized residual", "url": "https://en.wikipedia.org/wiki/Studentized_residual", "summary": "In statistics, a studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation. Typically the standard deviations of residuals in a sample vary greatly from one data point to another even when the errors all have the same standard deviation, particularly in regression analysis; thus it does not make sense to compare residuals at different data points without first studentizing. It is a form of a Student's t-statistic, with the estimate of error varying between points.\nThis is an important technique in the detection of outliers. It is among several named in honor of William Sealey Gosset, who wrote under the pseudonym Student. Dividing a statistic by a sample standard deviation is called studentizing, in analogy with standardizing and normalizing.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/1/17/System-search.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Beta distribution", "Chapman and Hall", "Data point", "Degrees of freedom (statistics)", "Design matrix", "Digital object identifier", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "Estimator", "Estimators", "Expected value", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Hat matrix", "Influence function (statistics)", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Least-angle regression", "Least absolute deviations", "Least squares", "Leverage (statistics)", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Mean and predicted response", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate distribution", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Normal distribution", "Normalization (statistics)", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal projection", "Outlier", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probability distribution", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression coefficient", "Regression model validation", "Regularized least squares", "Robust regression", "Sample standard deviation", "Samuelson's inequality", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Standard deviation", "Standard score", "Standardizing", "Statistical independence", "Statistics", "Student", "Student's t-distribution", "Student's t-statistic", "Studentization", "Tau coefficient", "Tau distribution", "Tikhonov regularization", "Total least squares", "Uniform distribution (continuous)", "Univariate distribution", "Weighted least squares", "William Sealey Gosset", "William Sealy Gosset"], "references": ["http://www.stat.umn.edu/rir/", "http://www.ngs.noaa.gov/PUBS_LIB/TRNOS65NGS1.pdf", "http://doi.org/10.1214%2Faoms%2F1177732567"]}, "Rule of three (medicine)": {"categories": ["Clinical trials", "Medical statistics", "Nursing research", "Statistical approximations"], "title": "Rule of three (statistics)", "method": "Rule of three (medicine)", "url": "https://en.wikipedia.org/wiki/Rule_of_three_(statistics)", "summary": "In statistical analysis, the rule of three states that if a certain event did not occur in a sample with n subjects, the interval from 0 to 3/n is a 95% confidence interval for the rate of occurrences in the population. When n is greater than 30, this is a good approximation of results from more sensitive tests. For example, a pain-relief drug is tested on 1500 human subjects, and no adverse event is recorded. From the rule of three, it can be concluded with 95% confidence that fewer than 1 person in 500 (or 3/1500) will experience an adverse event. By symmetry, one could expect for only successes, the 95% confidence interval is [1\u22123/n,1].\nThe rule is useful in the interpretation of clinical trials generally, particularly in phase II and phase III where often there are limitations in duration or statistical power. The rule of three applies well beyond medical research, to any trial done n times. If 300 parachutes are randomly tested and all open successfully, then it is concluded with 95% confidence that fewer than 1 in 100 parachutes with the same characteristics (3/300) will fail.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c9/Rule_of_three.svg"], "links": ["Adverse event", "Bernoulli trial", "Binomial distribution", "Binomial proportion confidence interval", "Cantelli's inequality", "Chebyshev's inequality", "Clinical trial", "Confidence interval", "Design of experiments", "Digital object identifier", "Human subjects research", "International Standard Book Number", "Natural logarithm", "Phases of clinical research", "Population (statistics)", "PubMed Central", "PubMed Identifier", "Rule of succession", "Rule of three (disambiguation)", "Statistical analysis", "Statistical power", "Three-sigma rule", "Unimodal function", "Variance", "Vysochanskij\u2013Petunin inequality"], "references": ["http://www.bmj.com/cgi/content/full/311/7005/619", "http://www.pmean.com/01/zeroevents.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2550668", "http://www.ncbi.nlm.nih.gov/pubmed/6827763", "http://www.ncbi.nlm.nih.gov/pubmed/7663258", "http://doi.org/10.1001%2Fjama.1983.03330370053031", "http://doi.org/10.1136%2Fbmj.311.7005.619"]}, "SAS (software)": {"categories": ["4GL", "Articles with example code", "Articles with inconsistent citation formats", "Business intelligence", "CS1 maint: Extra text: authors list", "C software", "Data mining and machine learning software", "Data warehousing", "Extract, transform, load tools", "Good articles", "Mathematical optimization software", "Numerical software", "Proprietary commercial software for Linux", "Proprietary cross-platform software", "Science software for Linux"], "title": "SAS (software)", "method": "SAS (software)", "url": "https://en.wikipedia.org/wiki/SAS_(software)", "summary": "SAS (previously \"Statistical Analysis System\") is a software suite developed by SAS Institute for advanced analytics, multivariate analyses, business intelligence, data management, and predictive analytics.\nSAS was developed at North Carolina State University from 1966 until 1976, when SAS Institute was incorporated. SAS was further developed in the 1980s and 1990s with the addition of new statistical procedures, additional components and the introduction of JMP. A point-and-click interface was added in version 9 in 2004. A social media analytics product was added in 2010.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/9/97/%E0%A6%B8%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B8_%E0%A6%B2%E0%A7%8B%E0%A6%97%E0%A7%8B.png", "https://upload.wikimedia.org/wikipedia/en/e/e8/SAS_9_on_Microsoft_Windows.png", "https://upload.wikimedia.org/wikipedia/en/9/94/Symbol_support_vote.svg"], "links": ["ADMB", "Alpine Data Labs", "Analyse-it", "Analysis of variance", "Anthony James Barr", "Apple Macintosh", "Assembly language", "BMC Health Services Research", "BMDP", "BV4.1 (software)", "Business Intelligence", "Business intelligence", "CSPro", "C (programming language)", "C programming language", "Clinical trial", "Commercial software", "Comparison of OLAP Servers", "Comparison of numerical analysis software", "Comparison of statistical packages", "Compilers", "Conversational Monitor System", "Cross-platform", "CumFreq", "Customer Relationship Management", "Customer intelligence", "DAP (software)", "Data Desk", "Data management", "Data mining", "Dataplot", "Digital object identifier", "EMC Greenplum", "EViews", "Econometrics", "Epi Info", "European Court of Justice", "Food and Drug Administration", "Fortran", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "General linear model", "Gertrude Mary Cox", "GraphPad InStat", "GraphPad Prism", "Graphical user interface", "Gretl", "H2O (software)", "High-performance computing", "High Court of Justice", "High Performance Computing", "IBM Cognos", "IBM System/360", "IBM mainframe", "InformationWeek", "International Standard Book Number", "International Standard Serial Number", "JASP", "JMP (statistical software)", "JMulTi", "JSTOR", "James Goodnight", "John Sall", "Journal of Marriage and Family", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Linux", "List of statistical packages", "MATLAB", "MLwiN", "MS-DOS", "Macintosh", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Multiple regression", "Multivariate analyses", "NCSS (statistical software)", "National Institute of Health", "North Carolina State University", "Numerical analysis", "OCLC", "OS/2", "Open-source software", "OpenBUGS", "OpenVMS", "Open architecture", "Operating system", "Oracle Hyperion", "Orange (software)", "OxMetrics", "PL/I", "PSPP", "Performance indicator", "Power BI", "Power user", "Predictive analytics", "Primos", "Proprietary software", "PubMed Central", "PubMed Identifier", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAP BusinessObjects", "SAS (disambiguation)", "SAS Institute", "SAS Institute Inc.", "SAS Institute Inc. and World Programming Limited", "SAS Institute lawsuit with World Programming", "SAS language", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "Sentiment analysis", "SigmaStat", "SigmaXL", "Silicon Graphics", "SimFiT", "SmartPLS", "Social media analytics", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "StatsDirect", "TSP (econometrics software)", "Teradata", "Text mining", "The Unscrambler", "Time Series Analysis", "UNISTAT", "UNIX", "University Statisticians of the Southern Experiment Stations", "University of California, Los Angeles", "Unix", "Usability", "WinBUGS", "Windows", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe", "Z/OS"], "references": ["http://www.bi-verdict.com/fileadmin/FreeAnalyses/consolidations.htm", "http://www.clickz.com/clickz/column/2353618/just-how-big-is-the-big-data-market", "http://money.cnn.com/2010/01/21/technology/sas_best_companies.fortune/", "http://www.drdobbs.com/tools/228200027?queryText=SAS%2BJMP", "http://www.eweek.com/c/a/Channel/SAS-to-Extend-Its-Supply-Chain-Offerings/#sthash.DcJjCKou.dpuf", "http://www.eweek.com/c/a/Finance-IT/SAS-to-Add-to-Analytical-CRM-Arsenal/", "http://www.gartner.com/technology/reprints.do?id=1-1DZLPEP&ct=130207&st=sb", "http://gcn.com/Articles/2013/05/10/Social-media-analysis-predictive-coding-enlisted-to-fight-fraud.aspx?Page=3", "http://www.gleanster.com/#/solution/sas-for-governance-risk-and-compliance", "http://www.globalstatements.com/sas/differences/", "http://www.google.com/translate?hl=en&ie=UTF8&sl=auto&tl=en&u=http://www.diarioti.com/noticia/SAS_lanza_JMP_8_para_Mac/24733", "http://idcdocserv.com/241689e_sas", "http://www.information-management.com/news/SAS-GRC-compliance-software-Forrester-McClean-10022461-1.html", "http://informationweek.com/blog/software/228900553?queryText=SAS+announced", "http://informationweek.com/news/18700087?queryText=SAS+announced", "http://informationweek.com/news/software/bi/211100027?queryText=SAS+announced", "http://www.informationweek.com/sas-ships-customer-intelligence-app/d/d-id/1025026?", "http://www.informationweek.com/software/information-management/low-cost-options-for-predictive-analytics-challenge-sas-ibm/d/d-id/1099191?page_number=1", "http://www.insurancenetworking.com/news/business_intelligence_analytics_cloud_computing_fraud_insurance_technology-12069-1.html", "http://archive.itmanagementnews.com/itmanagementnews-54-20040922SASLaunchesSuiteofSolutionsforIT.html", "http://www.itworld.com/article/2915374/sas-enlarges-its-palette-for-big-data-analysis.html", "http://www.itworldcanada.com/article/sas-expands-cloud-analytics-business/98450#ixzz3IzvMFJ9l", "http://www.jmp.com/about/newsletters/jmpercable/pdf/26_winter_2010.pdf", "http://www.jmp.com/landing/foreword_pdf/JMPForeward_72dpi.pdf", "http://www.jmp.com/support/downloads/pdf/jmp9/jmp9_new_features.pdf", "http://jtonedm.com/2011/08/10/first-look-jmp-pro/", "http://jtonedm.com/2011/11/11/first-look-sas-enterprise-miner-7-1/", "http://www.newsobserver.com/2012/01/20/1790587/sas-revenue-up-12-in-2011.html", "http://www.oregonlive.com/finance/index.ssf/2013/08/what_to_do_with_that_false_pos.html", "http://ovum.com/2011/10/17/sas-adds-in-memory-to-high-performance-computing/", "http://www.protiviti.com/en-US/Documents/About-Us/The-Forrester-Wave-Enterprise-Governance-Risk-and-Compliance-Platforms-Q4-2011.pdf", "http://support.sas.com/supportos/list", "http://www.sas.com", "http://www.sas.com/company/about/history.html#s1=5", "http://www.sas.com/en_us/home.html", "http://www2.sas.com/proceedings/sugi30/134-30.pdf", "http://www.techrepublic.com/blog/big-data-analytics/see-if-the-r-language-fits-in-your-big-data-toolkit/", "http://searchbusinessanalytics.techtarget.com/news/2240102699/SAS-ups-big-data-ante-with-high-performance-computing-platform", "http://onlinelibrary.wiley.com/doi/10.1111/j.1741-3737.2005.00196.x/full", "http://www.wral.com/business/story/9211429/", "http://www.zdnet.com/blog/crm/the-crm-watchlist-part-ii-the-usual-suspects/2419?tag=mantle_skin;content", "http://css.its.psu.edu/news/nlsu02/sas.html", "http://www.ats.ucla.edu/stat/mult_pkg/compare_packages.htm", "http://www.ats.ucla.edu/stat/sas/seminars/sas_macros_introduction/default.htm", "http://docsouth.unc.edu/sohp/I-0073/excerpts/excerpt_976.html", "http://www.cabnr.unr.edu/gf/apst650/sassoftbusiness.pdf", "http://curia.europa.eu/jcms/upload/docs/application/pdf/2012-05/cp120053en.pdf", "http://curia.europa.eu/juris/document/document.jsf?docid=82474&doclang=en&mode=&part=1", "http://www.fda.gov/ohrms/dockets/dockets/00n0001/ts00016.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3205033", "http://www.ncbi.nlm.nih.gov/pubmed/21977990", "http://www.bailii.org/ew/cases/EWHC/Ch/2010/1829.html#para36", "http://www.clinmedres.org/content/8/3-4/189.3", "http://doi.org/10.1111%2Fj.1467-985X.2009.00588_2.x", "http://doi.org/10.1111%2Fj.1741-3737.2005.00196.x", "http://doi.org/10.1177%2F0049124195023003006", "http://doi.org/10.1186%2F1472-6963-11-252", "http://doi.org/10.2307%2F1402812", "http://doi.org/10.3121%2Fcmr.2010.943.c-c1-04", "http://doi.org/10.4135%2F9781412961288", "http://www.jstor.org/stable/1402812", "http://www.nesug.org/Proceedings/nesug12/ma/ma10.pdf", "http://www.nesug.org/proceedings/nesug02/et/et004.pdf", "http://www.pharmasug.org/proceedings/2012/DG/PharmaSUG-2012-DG01.pdf", "http://www.sascommunity.org/wiki/Main_Page", "http://www.worldcat.org/issn/0306-7734", "http://www.worldcat.org/oclc/4984363", "http://www.worldcat.org/title/statistical-analysis-system/oclc/5728643", "http://www.worldcatlibraries.org/oclc/1325510", "http://www.worldcatlibraries.org/oclc/4984363", "http://www.fsn.co.uk/channel_bi_bpm_cpm/pr_sas_spm_strategic_performance_management", "https://www.forbes.com/sites/quentinhardy/2011/06/09/sas-ibms-bad-culture-how-well-win/", "https://books.google.com/books?id=WtZZ6sYA2_QC&pg=PA6", "https://books.google.com/books?id=a0Fc9dJby7EC&pg=PA321&dq=sas+%22library+engine%22+%22remote+library+services%22&hl=en&sa=X&ei=pmZNUsnbI6SHygHt4oHYAQ&ved=0CEsQ6AEwAQ#v=onepage&q=Glossary&f=false", "https://books.google.com/books?id=kBL_aEB6RX0C&pg=PA149", "https://books.google.com/books?id=kPGJUiUCJZkC&pg=PA177", "https://books.google.com/books?id=o9nVu8Xsd6kC&pg=PA365", "https://books.google.com/books?id=qNVP2L6iKi0C&pg=SL3-PA22", "https://books.google.com/books?id=vTDCtLEo5UcC&pg=PA5", "https://books.google.com/books?id=vjqSNRhEnQcC&pg=PA64", "https://books.google.com/books?id=xdg9nkBFh1UC&pg=PA23", "https://news.google.com/newspapers?nid=1734&dat=20020205&id=ljUgAAAAIBAJ&sjid=GFMEAAAAIBAJ&pg=4836,3215963", "https://news.google.com/newspapers?nid=1916&dat=20010505&id=nPpIAAAAIBAJ&sjid=oAUNAAAAIBAJ&pg=3476,727402", "https://blogs.sas.com/content/iml/2013/08/02/how-old-is-your-version-of-sas-release-dates-for-sas-software.html", "https://www.sas.com/en_us/company-information.html#history", "https://www.sas.com/products/", "https://www.sas.com/store/books/categories/usage-and-reference/proc-sql-beyond-the-basics-using-sas-second-edition/prodBK_62432_en.html", "https://online.wsj.com/news/articles/SB10001424127887324144304578619811891715262", "https://www.stat.berkeley.edu/classes/s100/sas.pdf", "https://web.archive.org/web/20111129010236/http://money.cnn.com/2010/01/21/technology/sas_best_companies.fortune/", "https://web.archive.org/web/20131012065352/http://www.stat.berkeley.edu/classes/s100/sas.pdf"]}, "Statistical relational learning": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from June 2011", "Articles with unsourced statements from December 2016", "Computational statistics", "Machine learning"], "title": "Statistical relational learning", "method": "Statistical relational learning", "url": "https://en.wikipedia.org/wiki/Statistical_relational_learning", "summary": "Statistical relational learning (SRL) is a subdiscipline of artificial intelligence and machine learning that is concerned with domain models that exhibit both uncertainty (which can be dealt with using statistical methods) and complex, relational structure. Note that SRL is sometimes called Relational Machine Learning (RML) in the literature. Typically, the knowledge representation formalisms developed in SRL use (a subset of) first-order logic to describe relational properties of a domain in a general manner (universal quantification) and draw upon probabilistic graphical models (such as Bayesian networks or Markov networks) to model the uncertainty; some also build upon the methods of inductive logic programming. Significant contributions to the field have been made since the late 1990s.As is evident from the characterization above, the field is not strictly limited to learning aspects; it is equally concerned with reasoning (specifically probabilistic inference) and knowledge representation. Therefore, alternative terms that reflect the main foci of the field include statistical relational learning and reasoning (emphasizing the importance of reasoning) and first-order probabilistic languages (emphasizing the key properties of the languages with which models are represented).", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Artificial intelligence", "Association rule learning", "BLOG model", "Bayesian logic program", "Bayesian network", "Ben Taskar", "Classification (machine learning)", "Cluster analysis", "Collaborative filtering", "Collective classification", "Digital object identifier", "Domain model", "First-order logic", "Formal concept analysis", "Fuzzy logic", "Grammar induction", "Inductive logic programming", "International Standard Book Number", "Knowledge representation", "Lecture Notes in Computer Science", "Link-based clustering", "Link prediction", "Lise Getoor", "Machine learning", "Markov logic network", "Markov network", "Multi-entity Bayesian network", "Probabilistic graphical model", "Probabilistic soft logic", "Reasoning", "Record linkage", "Recursive random field", "Relation (mathematics)", "Relational Bayesian network", "Relational Kalman filtering", "Relational Markov network", "Relational dependency network", "Social network", "Statistical inference", "Uncertainty", "Universal quantification"], "references": ["http:ftp://nozdr.ru/biblio/kolxo3/Cs/CsLn/Inductive%20Logic%20Programming,%2016%20conf.,%20ILP%202006(LNCS4455,%20Springer,%202006)(ISBN%203540738460)(466s).pdf#page=20", "http://www.cs.ubc.ca/~hkhosrav/pub/survey.pdf", "http://www.ai.sri.com/~braz/papers/sci-chapter.pdf", "http://www.cs.washington.edu/homes/pedrod/papers/mlj05.pdf", "http://www.jair.org/media/3659/live-3659-6589-jair.pdf", "https://books.google.com/books?id=lSkIewOw2WoC&printsec=frontcover#v=onepage&q&f=false", "https://www.biostat.wisc.edu/~page/lprm-ijcai99.pdf", "https://doi.org/10.1016%2Fj.cose.2010.02.002"]}, "Numerical data": {"categories": ["All articles with unsourced statements", "Articles with inconsistent citation formats", "Articles with unsourced statements from July 2012", "Cognitive science", "Measurement", "Pages containing links to subscription-only content", "Scientific method", "Statistical data types", "Subscription required using via"], "title": "Level of measurement", "method": "Numerical data", "url": "https://en.wikipedia.org/wiki/Level_of_measurement", "summary": "Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement originated in psychology and is widely criticized by scholars in other disciplines. Other classifications include those by Mosteller and Tukey, and by Chrisman.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute zero", "Accelerated failure time model", "Actuarial science", "Affine line", "Affine space", "Akaike information criterion", "American Psychologist", "Analysis of covariance", "Analysis of variance", "Analytic hierarchy process", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavioral sciences", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "British Association for the Advancement of Science", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cognitive", "Cohen's kappa", "Coherence (units of measurement)", "Cointegration", "Colorimetry", "Completeness (statistics)", "Concatenation (mathematics)", "Confidence interval", "Confounding", "Constructivist epistemology", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "D.J. Bartholomew", "Data collection", "Decomposition of time series", "Degree Celsius", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Electric charge", "Elliptical distribution", "Empirical distribution function", "Energy", "Engineering statistics", "Environmental statistics", "Epidemiology", "Equality (mathematics)", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frederick Mosteller", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Georg Rasch", "Geostatistics", "Globally unique identifier", "Goodness of fit", "Grammar", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hume's principle", "Index of dispersion", "Inequality (mathematics)", "Inter-rater reliability", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Tukey", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kelvin", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "L. L. Thurstone", "Law of comparative judgment", "Lehmann\u2013Scheff\u00e9 theorem", "Length", "Level sensor", "Library of Congress Control Number", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logarithmic scale", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mass", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nicholas Mackintosh", "Nobel prize", "Nominal variable", "Non-trivial", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Norman Cliff", "Norman Robert Campbell", "Observational study", "Official statistics", "One- and two-tailed tests", "Operation (mathematics)", "Operationalization", "Opinion", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal data", "Ordinary least squares", "Otto H\u00f6lder", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Parts of speech", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Percy Bridgman", "Permutation test", "Pie chart", "Pivotal quantity", "Plane angle", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Power projection", "Prediction interval", "Prima facie", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometric", "Psychometrics", "PubMed Central", "PubMed Identifier", "Qualitative property", "Quality control", "Quantitative property", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R. Duncan Luce", "Radar chart", "Ramsey\u2013Lewis method", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank order", "Rank statistics", "Rao\u2013Blackwell theorem", "Rasch model", "Real versus nominal value (economics)", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "SPSS", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Science (journal)", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set membership", "Set theory", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Software engineering", "Sone", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standardized moment", "Stanley Smith Stevens", "Stationary process", "Statistic", "Statistical classification", "Statistical data type", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stock", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized range", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taxonomic rank", "Taylor & Francis", "Theory of conjoint measurement", "Time", "Time domain", "Time series", "Tolerance interval", "Transaction Publishers", "Trap (computing)", "Trend estimation", "Truth value", "U-statistic", "Uniformly most powerful test", "Units of measurement", "V-statistic", "Validity (logic)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Rozeboom", "Z-test"], "references": ["http://www.crcpress.com/product/isbn/9781584888147", "http://www.tandfonline.com/doi/abs/10.1559/152304098782383043", "http://adsabs.harvard.edu/abs/1946Sci...103..677S", "http://www.courses.msstate.edu/jmg1/4123/Spring2008/Readings/Lord1953.pdf", "http://www.ats.ucla.edu/stat/mult_pkg/whatstat/nominal_ordinal_interval.htm", "http://www4.uwsp.edu/geo/faculty/gmartin/geog476/Lecture/BeySt.htm", "http://lccn.loc.gov/68011394", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3157145", "http://www.ncbi.nlm.nih.gov/pubmed/11178923", "http://www.ncbi.nlm.nih.gov/pubmed/17750512", "http://www.ncbi.nlm.nih.gov/pubmed/21897729", "http://www.cambridge.org/catalogue/catalogue.asp?isbn=978-0-521-54478-8", "http://doi.org/10.1006%2Fjmps.1999.1293", "http://doi.org/10.1007%2F978-1-4020-5614-7_1971", "http://doi.org/10.1007%2Fbf00337695", "http://doi.org/10.1007%2Fbf00485356", "http://doi.org/10.1007%2Fbf02342603", "http://doi.org/10.1016%2F0022-2496(64)90015-x", "http://doi.org/10.1016%2F0022-2496(81)90045-6", "http://doi.org/10.1016%2F0022-2496(85)90019-7", "http://doi.org/10.1016%2F0022-2496(86)90017-9", "http://doi.org/10.1016%2F0022-2496(87)90012-5", "http://doi.org/10.1037%2F0033-2909.100.3.398", "http://doi.org/10.1037%2Fh0063675", "http://doi.org/10.1080%2F15366360802035489", "http://doi.org/10.1086%2F289875", "http://doi.org/10.1111%2Fj.1523-1739.2006.00531.x", "http://doi.org/10.1111%2Fj.2044-8295.1997.tb02641.x", "http://doi.org/10.1111%2Fj.2044-8295.1997.tb02645.x", "http://doi.org/10.1126%2Fscience.103.2684.677", "http://doi.org/10.1177%2F0146621605276938", "http://doi.org/10.1559%2F152304098782383043", "http://doi.org/10.2307%2F2684788", "http://doi.org/10.4103%2F0976-500X.83300", "http://www.jstor.org/stable/2684788", "http://science.sciencemag.org/content/103/2684/677", "http://www.worldcat.org/issn/1523-0406", "http://www.academic.cmru.ac.th/phraisin/au/prasit/stevens/Stevens_Measurement.pdf", "https://books.google.com/?id=d11bUmyCRCYC&pg=PR3", "https://books.google.com/books?id=VfQpW6PYGKMC&pg=PA402", "https://link.springer.com/referenceworkentry/10.1007/978-1-4020-5614-7_1971", "https://web.archive.org/web/20070926232755/http://www2.umassd.edu/swpi/ISERN/isern-95-04.pdf", "https://web.archive.org/web/20110720003408/http://www.courses.msstate.edu/jmg1/4123/Spring2008/Readings/Lord1953.pdf", "https://web.archive.org/web/20111125054925/http://www.academic.cmru.ac.th/phraisin/au/prasit/stevens/Stevens_Measurement.pdf", "https://www.jstor.org/stable/1162101"]}, "Asymptotic normality": {"categories": ["Asymptotic theory (statistics)", "Types of probability distributions"], "title": "Asymptotic distribution", "method": "Asymptotic normality", "url": "https://en.wikipedia.org/wiki/Asymptotic_distribution", "summary": "In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the \"limiting\" distribution of a sequence of distributions. One of the main uses of the idea of an asymptotic distribution is in providing approximations to the cumulative distribution functions of statistical estimators.", "images": [], "links": ["Asymptotic analysis", "Asymptotic theory (statistics)", "Central limit theorem", "Convergence in distribution", "Convergence of random variables", "Cumulative distribution function", "De Moivre\u2013Laplace theorem", "Degenerate distribution", "Estimator", "Iid", "Independent and identically distributed", "International Standard Book Number", "Limiting density of discrete points", "Local asymptotic normality", "Mathematics", "Normal distribution", "Probability distribution", "Random variable", "Regular parametric model", "Sequence", "Statistical model", "Statistics"], "references": ["https://books.google.com/books?id=UQ9yIrZpMToC", "https://books.google.com/books?id=z39jQgAACAAJ&pg=PA357"]}, "Categorical data": {"categories": ["Categorical data", "Statistical data types"], "title": "Categorical variable", "method": "Categorical data", "url": "https://en.wikipedia.org/wiki/Categorical_variable", "summary": "In statistics, a categorical variable is a variable that can take on one of a limited, and usually fixed number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property. In computer science and some branches of mathematics, categorical variables are referred to as enumerations or enumerated types. Commonly (though not in this article), each of the possible values of a categorical variable is referred to as a level. The probability distribution associated with a random categorical variable is called a categorical distribution.\nCategorical data is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data. More specifically, categorical data may derive from observations made of qualitative data that are summarised as counts or cross tabulations, or from observations of quantitative data grouped within given intervals. Often, purely categorical data are summarised in the form of a contingency table. However, particularly when considering data analysis, it is common to use the term \"categorical data\" to apply to data sets that, while containing some categorical variables, may also contain non-categorical variables.\nA categorical variable that can take on exactly two values is termed a binary variable or dichotomous variable; an important special case is the Bernoulli variable. Categorical variables with more than two possible values are called polytomous variables; categorical variables are often assumed to be polytomous unless otherwise specified. Discretization is treating continuous data as if it were categorical. Dichotomization is treating continuous data or polytomous variables as if they were binary variables. Regression analysis often treats category membership with one or more quantitative dummy variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA", "A priori (epistemology)", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alphabetical order", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli distribution", "Bernoulli variable", "Bias of an estimator", "Binary variable", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Blood type", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical distribution", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Chinese characters", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Complex numbers", "Confidence interval", "Confounding", "Contingency table", "Continuous function", "Continuous probability distribution", "Control chart", "Control group", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cross tabulation", "Cyrillic", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dichotomization", "Dickey\u2013Fuller test", "Dirichlet process", "Discrete choice", "Discretization", "Divergence (statistics)", "Dummy variable (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Enumerated types", "Enumerations", "Environmental statistics", "Epidemiology", "Equivalence relation", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental group", "Exponential family", "Exponential smoothing", "F-test", "F statistic", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Friendly, Michael", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Grand mean", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Igneous", "Independent variable", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Language", "Language model", "Latin alphabet", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of analyses of categorical data", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean (statistics)", "Median", "Median-unbiased estimator", "Median (statistics)", "Medical statistics", "Metamorphic rock", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multinomial logistic regression", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nominal category", "Nominal scale", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal scale", "Ordinal variable", "Ordinary least squares", "Orthogonality", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Political party", "Population (statistics)", "Population statistics", "Post hoc test", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probit regression", "Proportional hazards model", "Psychometrics", "Qualitative data", "Qualitative property", "Quality control", "Quantitative data", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real numbers", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Sedimentary", "Semiparametric regression", "Set membership", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standardized variable", "Stationary process", "Statistic", "Statistical classification", "Statistical data type", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical test", "Statistical theory", "Statistics", "Steffen L. Lauritzen", "Stem-and-leaf display", "Stephen Fienberg", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variable (research)", "Variance", "Vector autoregression", "W. H. Freeman and Company", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Word", "Word embedding", "Y-intercept", "Yvonne Bishop", "Z-test"], "references": ["http://datavis.ca/papers/casm/casm.pdf", "http://bcs.whfreeman.com/yates2e/", "http://www.itl.nist.gov/div898/handbook/", "http://www.ams.org/mathscinet-getitem?mr=0381130", "http://www.ams.org/mathscinet-getitem?mr=1633357", "http://www.stats.ox.ac.uk/~steffen/papers/cont.pdf", "https://web.archive.org/web/20050209001108/http://bcs.whfreeman.com/yates2e/#"]}, "Chernoff face": {"categories": ["All articles with dead external links", "Articles with dead external links from September 2018", "Articles with permanently dead external links", "Statistical charts and diagrams"], "title": "Chernoff face", "method": "Chernoff face", "url": "https://en.wikipedia.org/wiki/Chernoff_face", "summary": "Chernoff faces, invented by Herman Chernoff in 1973, display multivariate data in the shape of a human face. The individual parts, such as eyes, ears, mouth and nose represent values of the variables by their shape, size, placement and orientation. The idea behind using faces is that humans easily recognize faces and notice small changes without difficulty. Chernoff faces handle each variable differently. Because the features of the faces vary in perceived importance, the way in which variables are mapped to the features should be carefully chosen (e.g. eye size and eyebrow-slant have been found to carry significant weight).", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/17/Chernoff_faces_for_evaluations_of_US_judges.svg"], "links": ["American Marketing Association", "American Statistical Association", "Asymmetrical", "Blindsight (Watts novel)", "Degrees of Freedom", "Digital object identifier", "Edward Tufte", "Eyebrow", "Herman Chernoff", "Identical twin", "International Standard Book Number", "JSTOR", "Journal of Accounting Research", "Journal of the American Statistical Association", "Karl Schroeder", "MATLAB", "Mac OS X", "Matplotlib", "Multivariate statistics", "Python (programming language)", "R programming language", "The American Statistician", "The Journal of Marketing", "The New York Times"], "references": ["http://bradandkathy.com/software/faces.html", "http://dl.dropbox.com/u/85192141/1980-turner.pdf", "http://dl.dropbox.com/u/85192141/1981-flury.pdf", "http://dl.dropbox.com/u/85192141/1981-kleiner.pdf", "http://flowingdata.com/2010/08/31/how-to-visualize-data-with-cartoonish-faces/", "http://healthyalgorithms.com/2012/11/12/dataviz-in-python-chernoff-faces-with-matplotlib/", "http://www.research.ibm.com/people/c/cjmorris/publications/Chernoff_990402.pdf", "http://www.mathworks.com/help/stats/glyphplot.html", "http://www.mathworks.com/products/statistics/", "http://www.novospark.com", "http://www2.sas.com/proceedings/sugi26/p195-26.pdf", "http://www.stata-journal.com/sjpdf.html?articlenum=gr0038", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.9200", "http://people.cs.uchicago.edu/~wiseman/chernoff/", "http://www.apprendre-en-ligne.net/mathematica/3.3/chernoff.pdf", "http://doi.org/10.2307%2F2284077", "http://doi.org/10.2307%2F2287565", "http://eagereyes.org/VisCrit/ChernoffFaces.html", "http://www.jstor.org/stable/2284077", "http://www.jstor.org/stable/2287565", "http://www.cs.ucl.ac.uk/staff/a.loizides/218.pdf", "https://thegrid.ai/kgw/end-notes-from-karl-schroeders-degrees-of-freedom/", "https://www.nytimes.com/2008/04/01/science/01prof.html", "https://archive.is/20121219203010/http://rgm2.lab.nig.ac.jp/RGM2/func.php?rd_id=aplpack:faces", "https://web.archive.org/web/20041217153643/http://gis.esri.com/library/userconf/educ04/papers/pap5000.pdf", "https://web.archive.org/web/20070521104703/http://kspark.kaist.ac.kr/Human%20Engineering.files/Chernoff/Chernoff%20Faces.htm", "https://web.archive.org/web/20120415030406/http://www.apprendre-en-ligne.net/mathematica/3.3/chernoff.pdf", "https://web.archive.org/web/20130916002111/http://blogs.iq.harvard.edu/sss/archives/2006/11/chernoff_faces_1.shtml", "https://web.archive.org/web/20140326100742/http://129.96.12.107/confpapers/CRPITV24Lee.pdf"]}, "Kingman's formula": {"categories": ["Single queueing nodes"], "title": "Kingman's formula", "method": "Kingman's formula", "url": "https://en.wikipedia.org/wiki/Kingman%27s_formula", "summary": "In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula also known as the VUT equation, is an approximation for the mean waiting time in a G/G/1 queue. The formula is the product of three terms which depend on utilization (U), variability (V) and service time (T). It was first published by John Kingman in his 1961 paper The single server queue in heavy traffic. It is known to be generally very accurate, especially for a system operating close to saturation.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Coefficient of variation", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Erlang (unit)", "Erlang distribution", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "International Standard Book Number", "JSTOR", "Jackson network", "John Kingman", "Kelly network", "Kendall's notation", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markovian arrival process", "Mathematical Proceedings of the Cambridge Philosophical Society", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Peter G. Harrison", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations"], "references": ["http://doi.org/10.1017/S0305004100036094", "http://doi.org/10.1109/TASE.2007.906348", "http://www.jstor.org/stable/2984229"]}, "Owen's T function": {"categories": ["All stub articles", "Computational statistics", "Functions related to probability distributions", "Normal distribution", "Statistics stubs"], "title": "Owen's T function", "method": "Owen's T function", "url": "https://en.wikipedia.org/wiki/Owen%27s_T_function", "summary": "In mathematics, Owen's T function T(h, a), named after statistician Donald Bruce Owen, is defined by\n\n \n \n \n T\n (\n h\n ,\n a\n )\n =\n \n \n 1\n \n 2\n \u03c0\n \n \n \n \n \u222b\n \n 0\n \n \n a\n \n \n \n \n \n e\n \n \u2212\n \n \n 1\n 2\n \n \n \n h\n \n 2\n \n \n (\n 1\n +\n \n x\n \n 2\n \n \n )\n \n \n \n 1\n +\n \n x\n \n 2\n \n \n \n \n \n d\n x\n \n \n (\n \n \u2212\n \u221e\n <\n h\n ,\n a\n <\n +\n \u221e\n \n )\n \n .\n \n \n {\\displaystyle T(h,a)={\\frac {1}{2\\pi }}\\int _{0}^{a}{\\frac {e^{-{\\frac {1}{2}}h^{2}(1+x^{2})}}{1+x^{2}}}dx\\quad \\left(-\\infty <h,a<+\\infty \\right).}\n The function was first introduced by Owen in 1956.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Bivariate normal distribution", "Error bound", "Gaussian quadrature", "LGPL", "List of integrals of Gaussian functions", "Mathematica", "Multivariate normal distribution", "Normal distribution", "Random variable", "Standard normal distribution", "Statistically independent", "Statistician", "Statistics"], "references": ["http://blog.wolfram.com/2010/10/07/why-you-should-care-about-the-obscure/", "http://reference.wolfram.com/mathematica/ref/OwenT.html", "http://people.sc.fsu.edu/~burkardt/f_src/owens/owens.html", "http://people.sc.fsu.edu/~jburkardt/m_src/asa076/tfn.m", "http://www.jstatsoft.org/v05/i05/paper"]}, "Type-1 Gumbel distribution": {"categories": ["All stub articles", "Continuous distributions", "Probability stubs"], "title": "Type-1 Gumbel distribution", "method": "Type-1 Gumbel distribution", "url": "https://en.wikipedia.org/wiki/Type-1_Gumbel_distribution", "summary": "In probability theory, the Type-1 Gumbel density function is\n\n \n \n \n f\n (\n x\n \n |\n \n a\n ,\n b\n )\n =\n a\n b\n \n e\n \n \u2212\n (\n b\n \n e\n \n \u2212\n a\n x\n \n \n +\n a\n x\n )\n \n \n \n \n {\\displaystyle f(x|a,b)=abe^{-(be^{-ax}+ax)}}\n for\n\n \n \n \n \u2212\n \u221e\n <\n x\n <\n \u221e\n .\n \n \n {\\displaystyle -\\infty <x<\\infty .}\n The distribution is mainly used in the analysis of extreme values and in survival analysis (also known as duration analysis or event-history modelling).", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "Extreme value theory", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Student's t-distribution", "Survival analysis", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["https://www.gnu.org/software/gsl/manual/gsl-ref_19.html#SEC309"]}, "Generalised hyperbolic distribution": {"categories": ["Continuous distributions", "Wikipedia articles needing clarification from January 2018"], "title": "Generalised hyperbolic distribution", "method": "Generalised hyperbolic distribution", "url": "https://en.wikipedia.org/wiki/Generalised_hyperbolic_distribution", "summary": "The generalised hyperbolic distribution (GH) is a continuous probability distribution defined as the normal variance-mean mixture where the mixing distribution is the generalized inverse Gaussian distribution (GIG). Its probability density function (see the box) is given in terms of modified Bessel function of the second kind, denoted by \n \n \n \n \n K\n \n \u03bb\n \n \n \n \n {\\displaystyle K_{\\lambda }}\n . It was introduced by Ole Barndorff-Nielsen, who studied it in the context of physics of wind-blown sand.", "images": [], "links": ["ARGUS distribution", "Aeolian processes", "Affine transformation", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Infinite divisibility (probability)", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Modified Bessel function", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal-inverse chi-squared distribution", "Normal-inverse gamma distribution", "Normal distribution", "Normal variance-mean mixture", "Ole Barndorff-Nielsen", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Statistical analysis of financial markets", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://doi.org/10.1098%2Frspa.1977.0041", "http://www.jstor.org/stable/79167"]}, "Financial econometrics": {"categories": ["All articles with style issues", "Econometrics", "Financial economics", "Mathematical finance", "Wikipedia articles with style issues from December 2015"], "title": "Financial econometrics", "method": "Financial econometrics", "url": "https://en.wikipedia.org/wiki/Financial_econometrics", "summary": "Financial econometrics is the application of statistical methods to financial market data. Financial econometrics is a branch of financial economics, in the field of economics. Areas of study include capital markets, financial institutions, corporate finance and corporate governance. Topics often revolve around asset valuation of individual stocks, bonds, derivatives, currencies and other financial instruments.\nIt differs from other forms of econometrics because the emphasis is usually on analyzing the prices of financial assets traded at competitive, liquid markets.\nPeople working in the finance industry or researching the finance sector often use econometric techniques in a range of activities \u2013 for example, in support of portfolio management and in the valuation of securities. Financial econometrics is essential for risk management when it is important to know how often 'bad' investment outcomes are expected to occur over future days, weeks, months and years.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Andrew Lo", "Arbitrage pricing theory", "Autoregressive conditional heteroskedasticity", "Capital asset pricing model", "Chris Brooks (academic)", "Clive Granger", "Cointegration", "Econometrica", "Econometrics", "Economics", "Eric Ghysels", "Eugene Fama", "Event study", "Exponential smoothing", "Financial economics", "International Standard Book Number", "Investment management", "John Y. Campbell", "Journal of Business & Economic Statistics", "Journal of Econometrics", "Lars Peter Hansen", "Market data", "Modern portfolio theory", "Neil Shephard", "Nobel Memorial Prize in Economic Sciences", "Random walk hypothesis", "Realized variance", "Returns-based style analysis", "RiskMetrics", "Risk management", "Robert F. Engle", "Robert J. Shiller", "Stephen Taylor (economist)", "Tim Bollerslev", "Value at risk", "Volatility (finance)", "Yield curve"], "references": ["http://sofie.stern.nyu.edu/", "http://jfec.oxfordjournals.org/", "https://web.archive.org/web/20091124061843/http://jfec.oxfordjournals.org/", "https://web.archive.org/web/20121117124501/http://sofie.stern.nyu.edu/", "https://web.archive.org/web/20170602020545/http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2003/", "https://web.archive.org/web/20170602022022/http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/", "https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2003/", "https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/", "https://scholar.google.co.uk/citations?view_op=search_authors&hl=en&mauthors=label:financial_econometrics"]}, "Confidence region": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2011", "Estimation theory"], "title": "Confidence region", "method": "Confidence region", "url": "https://en.wikipedia.org/wiki/Confidence_region", "summary": "In statistics, a confidence region is a multi-dimensional generalization of a confidence interval. It is a set of points in an n-dimensional space, often represented as an ellipsoid around a point which is an estimated solution to a problem, although other shapes can occur.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Bootstrapping (statistics)", "Chi-squared distribution", "Circular error probable", "Confidence band", "Confidence interval", "Covariance", "Degrees of freedom (statistics)", "Dependent variable", "Ellipsoid", "F-distribution", "F distribution", "Generalized least squares", "Hotelling's T-squared statistic", "Identity matrix", "Independent variable", "International Standard Book Number", "Linear regression", "Multivariate normal distribution", "Normal distribution", "Off-diagonal elements", "Ordinary least squares", "Prior probability", "Quantile function", "Reduced chi-squared", "Singular value decomposition", "Statistical independence", "Statistical significance", "Statistics", "Transpose", "Uncertainty Quantification", "Variance", "Weighted least squares"], "references": []}, "Z-test": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2009", "Normal distribution", "Statistical tests"], "title": "Z-test", "method": "Z-test", "url": "https://en.wikipedia.org/wiki/Z-test", "summary": "A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. Because of the central limit theorem, many test statistics are approximately normally distributed for large samples. For each significance level, the Z-test has a single critical value (for example, 1.96 for 5% two tailed) which makes it more convenient than the Student's t-test which has separate critical values for each sample size. Therefore, many statistical tests can be conveniently performed as approximate Z-tests if the sample size is large or the population variance is known. If the population variance is unknown (and therefore has to be estimated from the sample itself) and the sample size is not large (n < 30), the Student's t-test may be more appropriate. \nIf T is a statistic that is approximately normally distributed under the null hypothesis, the next step in performing a Z-test is to estimate the expected value \u03b8 of T under the null hypothesis, and then obtain an estimate s of the standard deviation of T. After that the standard score Z = (T \u2212 \u03b8) / s is calculated, from which one-tailed and two-tailed p-values can be calculated as \u03a6(\u2212Z) (for upper-tailed tests), \u03a6(Z) (for lower-tailed tests) and 2\u03a6(\u2212|Z|) (for two-tailed tests) where \u03a6 is the standard normal cumulative distribution function.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptomatic carrier", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Auxology", "Bachelor of Science in Public Health", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavior change (public health)", "Behavioural change theories", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biological hazard", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Carl Rogers Darnall", "Cartography", "Case\u2013control study", "Categorical variable", "Census", "Centers for Disease Control and Prevention", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Chief Medical Officer", "Child mortality", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Community health", "Completeness (statistics)", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Council on Education for Public Health", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cultural competence in health care", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Deviance (sociology)", "Dickey\u2013Fuller test", "Diffusion of innovations", "Disease surveillance", "Divergence (statistics)", "Doctor of Public Health", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Emergency sanitation", "Empirical distribution function", "Engineering statistics", "Environmental health", "Environmental statistics", "Epidemic", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Family planning", "Fan chart (statistics)", "Fecal\u2013oral route", "First-hitting-time model", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Genetically modified food", "Geographic information system", "Geometric mean", "Geostatistics", "Germ theory of disease", "Global health", "Globalization and disease", "Good agricultural practice", "Good manufacturing practice", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "HACCP", "Hand washing", "Harmonic mean", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human factors and ergonomics", "Human nutrition", "Hygiene", "ISO 22000", "Index of dispersion", "Infant mortality", "Infection control", "Injury prevention", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Snow (physician)", "Jonckheere's trend test", "Joseph Lister", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of epidemics", "List of fields of application of statistics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location test", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Margaret Sanger", "Mary Mallon", "Maternal health", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical anthropology", "Medical sociology", "Medical statistics", "Mental health", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Ministry of Health and Family Welfare", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo method", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Notifiable disease", "Nuisance parameter", "Null hypothesis", "Observational study", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Official statistics", "One- and two-tailed tests", "One-tailed", "Open defecation", "Opinion poll", "Optimal decision", "Optimal design", "Oral hygiene", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "P-values", "PRECEDE-PROCEED model", "Paired difference test", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Patient safety", "Patient safety organization", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pharmaceutical policy", "Pharmacovigilance", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population health", "Population statistics", "Positive deviance", "Posterior probability", "Power (statistics)", "Prediction interval", "Preventive healthcare", "Preventive nutrition", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Professional degrees of public health", "Proportional hazards model", "Psychometrics", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quality control", "Quarantine", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "ROC curve", "Race and health", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative risk", "Reliability engineering", "Replication (statistics)", "Reproductive health", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Safe sex", "Sample median", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sexually transmitted infection", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Slutsky's theorem", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Social statistics", "Sociology of health and illness", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Standard normal table", "Standard score", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "Test statistic", "Theory of planned behavior", "Time domain", "Time series", "Tolerance interval", "Transtheoretical model", "Trend estimation", "Tropical disease", "U-statistic", "U statistic", "Uniformly most powerful test", "United States Public Health Service", "V-statistic", "Vaccination", "Vaccine trial", "Variance", "Vector autoregression", "Vector control", "Wald test", "Waterborne diseases", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "World Health Organization", "World Toilet Organization"], "references": []}, "National Health Interview Survey": {"categories": ["Centers for Disease Control and Prevention", "Demographics of the United States", "Health economics", "Surveys"], "title": "National Health Interview Survey", "method": "National Health Interview Survey", "url": "https://en.wikipedia.org/wiki/National_Health_Interview_Survey", "summary": "The National Health Interview Survey (NHIS) is an annual, cross-sectional survey intended to provide nationally representative estimates on a wide range of health status and utilization measures among the nonmilitary, noninstitutionalized population of the United States. Each annual data set can be used to examine the disease burden and access to care that individuals and families are currently experiencing in the United States.\nNHIS is designed by the CDC's National Center for Health Statistics (NCHS) \u2013 the government agency tasked to monitor the population's health status and behavior \u2013 and administered by the U.S. Census Bureau. NHIS has been administered since 1957, although the core content and questionnaires undergo major revisions every 10\u201315 years. NHIS allows both governmental and outside researchers to obtain estimates on a variety of health-related topics among either the entire nation or specific demographic groups of the population. Also, since the survey design is cross-sectional rather than longitudinal, health information can be trended for demographic groups and the country as a whole, but not for individuals or families.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/33/Medical_debt_in_USA._National_Health_Interview_Survey.gif"], "links": ["Alternative medicine", "Behavior change (public health)", "Cancer", "Cancer screening", "Centers for Disease Control and Prevention", "Confidence interval", "Cross-sectional study", "Demographics", "Department of Health and Human Services", "Diet (nutrition)", "Digital object identifier", "Disease burden", "Exercise", "Families", "Family history (medicine)", "Health", "Health disparities", "Health effects of sun exposure", "Health insurance coverage in the United States", "Health status indicators", "Household", "Illness", "Immunizations", "Individuals", "Injuries", "Injury", "List of household surveys in the United States", "Longitudinal study", "Medical Expenditure Panel Survey", "Medical facility", "Mental health", "Morbidity", "National Cancer Institute", "National Center for Health Statistics", "National Institute for Occupational Safety and Health", "Occupational health", "Occupational injury", "Outcomes research", "Population", "PubMed Central", "PubMed Identifier", "Questionnaire", "Questionnaires", "R (software)", "Researchers", "Risk factors", "SAS (software)", "SPSS", "Sample survey", "Simple random sample", "Smoking", "Standard error (statistics)", "Stata", "U.S. Census Bureau", "U.S. Public Health Service", "United States", "Utilization management"], "references": ["http:ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Dataset_Documentation/NHIS/2010/househld_summary.pdf", "http:ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Dataset_Documentation/NHIS/2010/personsx_summary.pdf", "http:ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Dataset_Documentation/NHIS/2010/srvydesc.pdf", "http:ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Dataset_Documentation/NHIS/2010/injpoiep_layout.pdf", "http:ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Dataset_Documentation/NHIS/2010/injverbt_summary.pdf", "http:ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Survey_Questionnaires/NHIS/2010/2010_Q_Reference_Guide.pdf", "http://www.meps.ahrq.gov/mepsweb/data_stats/more_info_download_data_files.jsp#hc-nhis", "http://aspe.hhs.gov/insurance/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4557701", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4557703", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4559280", "http://www.ncbi.nlm.nih.gov/pubmed/22495886", "http://www.ncbi.nlm.nih.gov/pubmed/22674651", "http://www.ncbi.nlm.nih.gov/pubmed/22821700", "http://www.ncbi.nlm.nih.gov/pubmed/22911666", "http://www.ncbi.nlm.nih.gov/pubmed/23023603", "http://doi.org/10.1002%2Fajim.22048", "http://doi.org/10.1002%2Fajim.22080", "http://doi.org/10.1002%2Fajim.22089", "http://doi.org/10.1002%2Fajim.22108", "http://doi.org/10.1002%2Fajim.22123", "https://scholar.google.com/scholar?hl=en&q='national+health+interview+survey'+'health+behavior'", "https://www.cdc.gov/nccdphp/", "https://www.cdc.gov/nchs/data/factsheets/factsheet_nhis.htm", "https://www.cdc.gov/nchs/data/nhis/2006var.pdf", "https://www.cdc.gov/nchs/data/nhis/brochure2010January.pdf", "https://www.cdc.gov/nchs/data/series/sr_01/sr01_011acc.pdf", "https://www.cdc.gov/nchs/healthy_people.htm", "https://www.cdc.gov/nchs/ndi.htm", "https://www.cdc.gov/nchs/nhis/about_nhis.htm", "https://www.cdc.gov/nchs/nhis/index.htm", "https://www.cdc.gov/nchs/nhis/nhis_2010_data_release.htm", "https://www.cdc.gov/nchs/nhis/quest_data_related_1997_forward.htm", "https://www.cdc.gov/nchs/nhis/supplements_cosponsors.htm", "https://www.cdc.gov/nchs/products/databriefs.htm", "https://www.cdc.gov/nchs/products/nhsr.htm", "https://www.cdc.gov/nchs/products/series/series10.htm", "https://www.cdc.gov/niosh/topics/nhis", "https://www.cdc.gov/rdc/", "https://www.cdc.gov/rdc/B1DataType/Dt100.htm", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2031124/"]}, "Unit root": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2010", "Regression with time series structure"], "title": "Unit root", "method": "Unit root", "url": "https://en.wikipedia.org/wiki/Unit_root", "summary": "In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary but does not always have a trend.\nIf the other roots of the characteristic equation lie inside the unit circle\u2014that is, have a modulus (absolute value) less than one\u2014then the first difference of the process will be stationary; otherwise, the process will need to be differenced multiple times to become stationary. Due to this characteristic, unit root processes are also called difference stationary.Unit root processes may sometimes be confused with trend-stationary processes; while they share many properties, they are different in many aspects. It is possible for a time series to be non-stationary, yet have no unit root and be trend-stationary. In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent impact on the mean (i.e. no convergence over time).If a root of the process's characteristic equation is larger than 1, then it is called an explosive process, even though such processes are sometimes inaccurately called unit roots processes.\nThe presence of a unit root can be tested using a unit root test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/89/Unit_root_hypothesis_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/89/20100208054142%21Unit_root_hypothesis_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/89/20100208053300%21Unit_root_hypothesis_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/89/20100208052451%21Unit_root_hypothesis_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/89/20100208051935%21Unit_root_hypothesis_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/89/20100208051233%21Unit_root_hypothesis_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/89/20100207231108%21Unit_root_hypothesis_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/89/20100207230749%21Unit_root_hypothesis_diagram.svg"], "links": ["ADF-GLS test", "Absolute value", "Alok Bhargava", "Augmented Dickey\u2013Fuller test", "Autoregressive", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernd Lucke", "Characteristic equation (calculus)", "Characteristic polynomial", "Clive Granger", "Coefficient of determination", "Cointegration", "Dickey-Fuller test", "Dickey\u2013Fuller test", "Digital object identifier", "Econometrica", "Economic output", "Errors and residuals in statistics", "Finite difference", "First difference", "GDP", "GNP", "International Monetary Fund", "JSTOR", "John Denis Sargan", "Journal of Econometrics", "Journal of Monetary Economics", "KPSS tests", "Lag operator", "Model (abstract)", "Multiplicity (mathematics)", "Null hypothesis", "Order of integration", "Ordinary least squares", "Paul Krugman", "Phillips-Perron test", "Phillips\u2013Perron test", "Probability theory", "Random walk", "Regression analysis", "Root of a function", "Sample size", "Stationary process", "Statistical inference", "Statistics", "Stochastic process", "Structural break", "T-statistic", "Time series", "Trend stationary", "Unit root test"], "references": ["http://uk.mathworks.com/help/econ/trend-stationary-vs-difference-stationary.html", "http://www.wiso-net.de/genios1.pdf?START=0A1&ANR=215850&DBN=ZECO&ZNR=1&ZHW=-4&WID=59162-3020953-72523_1", "http://www.econ.ku.dk/metrics/Econometrics2_05_II/Slides/08_unitroottests_2pp.pdf", "http://pages.stern.nyu.edu/~churvich/Forecasting/Handouts/UnitRoot.pdf", "http://doi.org/10.1016%2F0304-3932(82)90012-5", "http://doi.org/10.1016%2F0304-4076(74)90034-7", "http://doi.org/10.2307%2F1912159", "http://doi.org/10.2307%2F1912252", "http://www.imf.org/external/pubs/ft/fandd/2009/09/blanchardindex.htm", "http://www.jstor.org/stable/1912159", "http://www.jstor.org/stable/1912252", "http://www.jstor.org/stable/20111955", "http://www.stats.ox.ac.uk/~burke/Autocorrelation/Non-Stationary%20Series.pdf", "https://krugman.blogs.nytimes.com/2009/03/03/roots-of-evil-wonkish/"]}, "Dataplot": {"categories": ["All stub articles", "Free plotting software", "Public-domain software with source code", "Science software stubs"], "title": "Dataplot", "method": "Dataplot", "url": "https://en.wikipedia.org/wiki/Dataplot", "summary": "Dataplot is a public domain software system for scientific visualization and statistical analysis. It was developed at the National Institute of Standards and Technology. Dataplot's source code is available.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/31/Free_and_open-source_software_logo_%282009%29.svg", "https://upload.wikimedia.org/wikipedia/commons/7/75/Science-symbol-2.svg"], "links": ["ADMB", "Analyse-it", "BMDP", "BV4.1 (software)", "CSPro", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "EViews", "Epi Info", "Fortran", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Linux", "List of statistical packages", "MATLAB", "MLwiN", "Mac OS X", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "National Institute of Standards and Technology", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Public-domain software", "Public domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "Scientific software", "Scientific visualization", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software categories", "Software developer", "Source code", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistical analysis", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "Unix", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["https://www.nist.gov/itl/sed/dataplot"]}, "Bonferroni inequalities": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from February 2012", "CS1 Italian-language sources (it)", "Probabilistic inequalities", "Statistical inequalities", "Wikipedia articles incorporating text from PlanetMath"], "title": "Boole's inequality", "method": "Bonferroni inequalities", "url": "https://en.wikipedia.org/wiki/Boole%27s_inequality", "summary": "In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. Boole's inequality is named after George Boole.\nFormally, for a countable set of events A1, A2, A3, ..., we have\n\n \n \n \n \n P\n \n \n (\n \n \n \u22c3\n \n i\n \n \n \n A\n \n i\n \n \n \n )\n \n \u2264\n \n \u2211\n \n i\n \n \n \n \n P\n \n \n (\n \n A\n \n i\n \n \n )\n .\n \n \n {\\displaystyle \\mathbb {P} \\left(\\bigcup _{i}A_{i}\\right)\\leq \\sum _{i}{\\mathbb {P} }(A_{i}).}\n In measure-theoretic terms, Boole's inequality follows from the fact that a measure (and certainly any probability measure) is \u03c3-sub-additive.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Associative", "Bayes' theorem", "Carlo Emilio Bonferroni", "Complementary event", "Conditional independence", "Conditional probability", "Countable", "Digital object identifier", "Diluted inclusion\u2013exclusion principle", "Elementary event", "Encyclopedia of Mathematics", "Even and odd numbers", "Event (probability theory)", "Finite set", "Finite unions", "Fr\u00e9chet inequalities", "George Boole", "Inclusion\u2013exclusion principle", "Independence (probability theory)", "International Standard Book Number", "JSTOR", "Janos Galambos", "Joint probability distribution", "Law of large numbers", "Law of total probability", "Marginal distribution", "Mathematical Reviews", "Measure theory", "Michiel Hazewinkel", "PlanetMath", "Probability Axioms", "Probability axioms", "Probability measure", "Probability space", "Probability theory", "Random variable", "Sample space", "Schuette\u2013Nesbitt formula", "Set (mathematics)", "Springer-Verlag", "Statistics", "Subadditivity", "Tree diagram (probability theory)", "Upper bound", "Venn diagram", "Zentralblatt MATH"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0448478", "http://www.ams.org/mathscinet-getitem?mr=1402242", "http://www.ams.org/mathscinet-getitem?mr=2019293", "http://doi.org/10.1214%2Faop%2F1176995765", "http://www.jstor.org/stable/2243081", "http://projecteuclid.org/euclid.aop/1176995765", "http://zbmath.org/?format=complete&q=an:0016.41103", "http://zbmath.org/?format=complete&q=an:0369.60018", "http://zbmath.org/?format=complete&q=an:0869.60014", "http://zbmath.org/?format=complete&q=an:1026.05009", "https://books.google.com/books?id=0x_vAAAAMAAJ&pg=PA11", "https://www.encyclopediaofmath.org/index.php?title=Bonferroni_inequalities"]}, "Empirical": {"categories": ["All articles that may contain original research", "All articles with unsourced statements", "Articles that may contain original research from October 2016", "Articles with unsourced statements from November 2012", "Empiricism", "Epistemology of science", "Evidence", "Justification", "Observation", "Philosophy of science", "Sampling (statistics)", "Science experiments", "Sources of knowledge", "Wikipedia articles needing page number citations from February 2014"], "title": "Empirical evidence", "method": "Empirical", "url": "https://en.wikipedia.org/wiki/Empirical_evidence", "summary": "Empirical evidence is the information received by means of the senses, particularly by observation and documentation of patterns and behavior through experimentation. The term comes from the Greek word for experience, \u1f10\u03bc\u03c0\u03b5\u03b9\u03c1\u03af\u03b1 (empeir\u00eda). \nAfter Immanuel Kant, in philosophy, it is common to call the knowledge gained a posteriori knowledge (in contrast to a priori knowledge).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg"], "links": ["A posteriori", "A priori and a posteriori", "Ab initio", "Albert Einstein", "Alchemy", "Alfred North Whitehead", "Analytic\u2013synthetic distinction", "Ancient Greek", "Anecdotal evidence", "Anti-realism", "Argument", "Aristotle", "Auguste Comte", "Averroes", "Avicenna", "Axiom", "Bas van Fraassen", "Bertrand Russell", "C. D. Broad", "Carl Gustav Hempel", "Causality", "Charles Sanders Peirce", "Coherentism", "Commensurability (philosophy of science)", "Confirmation holism", "Consilience", "Construct (philosophy)", "Constructive empiricism", "Constructive realism", "Constructivist epistemology", "Contextualism", "Conventionalism", "Creative synthesis", "Criticism of science", "Critique of Pure Reason", "Daniel Dennett", "David Hume", "Deductive-nomological model", "Deductive reasoning", "Demarcation problem", "Design of experiments", "Determinism", "Dominicus Gundissalinus", "Empirical", "Empirical (disambiguation)", "Empirical distribution function", "Empirical formula", "Empirical measure", "Empirical research", "Empiricism", "Epicureanism", "Epistemological anarchism", "Epistemology", "Evolutionism", "Experiential knowledge", "Experiment", "Explanatory power", "Fact", "Faith and rationality", "Fallibilism", "Falsifiability", "Feminist method", "First principle", "Foundationalism", "Francis Bacon", "Friedrich Wilhelm Joseph Schelling", "Galileo Galilei", "Ground truth", "Hans Reichenbach", "Henri Poincar\u00e9", "Herbert Spencer", "History and philosophy of science", "History of evolutionary thought", "History of science", "Houghton Mifflin", "Hugh of Saint Victor", "Hypothesis", "Hypothetico-deductive model", "Ian Hacking", "Ignoramus et ignorabimus", "Immanuel Kant", "Imre Lakatos", "Index of philosophy of science articles", "Inductionism", "Inductive reasoning", "Information", "Inquiry", "Instrumentalism", "International Standard Book Number", "Internet Encyclopedia of Philosophy", "Intertheoretic reduction", "Isaac Newton", "John Stuart Mill", "J\u00fcrgen Habermas", "Karl Pearson", "Karl Popper", "Larry Laudan", "List of philosophers of science", "Logic", "Metaphysics", "Michael Polanyi", "Model-dependent realism", "Naturalism (philosophy)", "Nature (philosophy)", "Objectivity (philosophy)", "Observation", "Otto Neurath", "Paradigm", "Paul Feyerabend", "Peer review", "Phenomenology (philosophy)", "Philosophical analysis", "Philosophy of artificial intelligence", "Philosophy of biology", "Philosophy of chemistry", "Philosophy of computer science", "Philosophy of engineering", "Philosophy of environment", "Philosophy of geography", "Philosophy of information", "Philosophy of mind", "Philosophy of motion", "Philosophy of perception", "Philosophy of physics", "Philosophy of psychiatry", "Philosophy of psychology", "Philosophy of science", "Philosophy of social science", "Philosophy of space and time", "Philosophy of technology", "Philosophy of thermal and statistical physics", "Physicalism", "Pierre Duhem", "Pierre Gassendi", "Plato", "Positivism", "Pragmatism", "Problem of induction", "Proposition", "Pseudoscience", "Rationalism", "Reason", "Received view of theories", "Reductionism", "Relationship between religion and science", "Ren\u00e9 Descartes", "Rhetoric of science", "Robert Kilwardby", "Roger Bacon", "Rudolf Carnap", "Rudolf Steiner", "Science", "Scientific Method", "Scientific community", "Scientific essentialism", "Scientific evidence", "Scientific formalism", "Scientific law", "Scientific literature", "Scientific method", "Scientific realism", "Scientific revolution", "Scientific skepticism", "Scientific theory", "Scientism", "Semantic view of theories", "Senses", "Sociology of scientific ignorance", "Sociology of scientific knowledge", "Statement (logic)", "Stoicism", "Structuralism (philosophy of science)", "Testability", "The Cambridge Dictionary of Philosophy", "Theory", "Theory-ladenness", "Theory choice", "Thomas Hobbes", "Thomas Kuhn", "Thomas S. Kuhn", "Truth", "Underdetermination", "Uniformitarianism", "Unity of science", "Vitalism", "Wilhelm Windelband", "Wilhelm Wundt", "Willard Van Orman Quine", "William Whewell", "William of Ockham"], "references": ["http://plato.stanford.edu/archives/fall2013/entries/thomas-kuhn/#4.2", "http://www.iep.utm.edu/apriori"]}, "Labour Force Survey": {"categories": ["Articles with limited geographic scope from November 2009", "International Labour Organization", "Quantitative research", "Social statistics data", "Statistical data agreements", "Unemployment", "Use dmy dates from December 2010"], "title": "Labour Force Survey", "method": "Labour Force Survey", "url": "https://en.wikipedia.org/wiki/Labour_Force_Survey", "summary": "Labour Force Surveys are statistical surveys conducted in a number of countries designed to capture data about the labour market. All European Union member states are required to conduct a Labour Force Survey annually. Labour Force Surveys are also carried out in some non-EU countries. They are used to calculate the International Labour Organization (ILO)-defined unemployment rate. The ILO agrees the definitions and concepts employed in Labour Force Surveys.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/bd/Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20120912112036%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20090504090119%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20090429055401%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081116011312%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081116010712%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081114061656%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112053306%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112013744%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112013034%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112012748%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112012546%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20080503023049%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20080503022818%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20080503022500%21Ambox_globe_content.svg"], "links": ["Australia", "Australian Bureau of Statistics", "Coding (social sciences)", "European Community", "European Free Trade Association", "European Union", "Eurostat", "Fieldwork", "Future enlargement of the European Union", "Iceland", "International Labour Organization", "International Standard Book Number", "International Standard Serial Number", "Labour market", "List of capitals in Australia", "New Zealand", "Norway", "Office for National Statistics", "Official statistics", "Questionnaire", "Sample (statistics)", "Statistical survey", "Switzerland", "Underemployment", "Unemployment", "United Kingdom"], "references": ["http://www.abs.gov.au/AUSSTATS/abs@.nsf/Previousproducts/1301.0Feature%20Article162005?opendocument&tabname=Summary&prodno=1301.0&issue=2005&num=&view=", "http://europa.eu/estatref/info/sdds/en/lfsi/lfsi_sm.htm", "http://epp.eurostat.ec.europa.eu/portal/page/portal/microdata/lfs", "http://laborsta.ilo.org/applv8/data/SSM3/E/NZ.html", "http://laborsta.ilo.org/applv8/data/SSM3/E/SSM3.html", "http://www.ilo.org/dyn/lfsurvey/lfsurvey.home", "http://www.worldcat.org/issn/0312-4746", "http://www.esds.ac.uk/government/lfs/usage/", "http://www.esds.ac.uk/government/lfs/usage/LFSusage2008.pdf", "http://webarchive.nationalarchives.gov.uk/20020625191833/http://www.statistics.gov.uk/ssd/surveys/labour_force_survey.asp", "http://webarchive.nationalarchives.gov.uk/20031222022152/http://www.statistics.gov.uk/downloads/theme_labour/What_exactly_is_LFS1.pdf", "http://www.statistics.gov.uk/downloads/theme_labour/What_exactly_is_LFS1.pdf", "http://www.statistics.gov.uk/ssd/surveys/labour_force_survey.asp", "https://books.google.com/books?id=AOp4mP5EuQcC&pg=PA569&lpg=PA569&dq=ILO+unemployment+LFS&source=web&ots=Kvf_vpl00q&sig=0LFYepiCd-xbUtMVpgKxOApj15E&hl=en&sa=X&oi=book_result&resnum=10&ct=result", "https://web.archive.org/web/20110812222412/http://epp.eurostat.ec.europa.eu/portal/page/portal/microdata/lfs"]}, "Moving least squares": {"categories": ["All stub articles", "Applied mathematics stubs", "Least squares"], "title": "Moving least squares", "method": "Moving least squares", "url": "https://en.wikipedia.org/wiki/Moving_least_squares", "summary": "Moving least squares is a method of reconstructing continuous functions from a set of unorganized point samples via the calculation of a weighted least squares measure biased towards the region around the point at which the reconstructed value is requested.\nIn computer graphics, the moving least squares method is useful for reconstructing a surface from a set of points. Often it is used to create a 3D surface from a point cloud through either downsampling or upsampling.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a3/Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f3/Moving_Least_Squares2.png"], "links": ["Applied mathematics", "Computer graphics", "Continuous function", "Diffuse element method", "Downsampling", "Local regression", "Measure (mathematics)", "Moving average", "Point cloud", "Set (mathematics)", "Upsampling", "Weighted least squares"], "references": ["http://www.sciencedirect.com/science/article/pii/S0045794905000726/", "http://www.springerlink.com/content/v7164702238848p1/", "http://www.nealen.net/projects/mls/asapmls.pdf", "http://dl.acm.org/citation.cfm?id=301704", "http://www.ams.org/mcom/1998-67-224/S0025-5718-98-00974-0/S0025-5718-98-00974-0.pdf"]}, "Bayesian vector autoregression": {"categories": ["All stub articles", "Bayesian statistics", "Econometrics stubs", "Multivariate time series"], "title": "Bayesian vector autoregression", "method": "Bayesian vector autoregression", "url": "https://en.wikipedia.org/wiki/Bayesian_vector_autoregression", "summary": "In statistics, Bayesian vector autoregression (BVAR) uses Bayesian methods to estimate a vector autoregression (VAR). In that respect, the difference with standard VAR models lies in the fact that the model parameters are treated as random variables, and prior probabilities are assigned to them.\nVector autoregressions are flexible statistical models that typically include many free parameters. Given the limited length of standard macroeconomic datasets, Bayesian methods have become an increasingly popular way of dealing with this problem of over-parameterization. The general idea is to use informative priors to shrink the unrestricted model towards a parsimonious na\u00efve benchmark, thereby reducing parameter uncertainty and improving forecast accuracy (see for a survey). A typical example is the shrinkage prior proposed by Robert Litterman, and subsequently developed by other researchers at University of Minnesota, which is known in the BVAR literature as the \"Minnesota prior\". The informativeness of the prior can be set by treating it as an additional parameter, based on a hierarchical interpretation of the model.Recent research has shown that Bayesian vector autoregression is an appropriate tool for modelling large data sets.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg"], "links": ["Bayesian econometrics", "Bayesian inference", "CiteSeerX", "Digital object identifier", "Econometric Reviews", "Econometrics", "Helmut L\u00fctkepohl", "International Standard Book Number", "Journal of Applied Econometrics", "Prior probability", "Random variable", "Robert Litterman", "Social Science Research Network", "Statistics", "University of Minnesota", "Vector autoregression"], "references": ["http://ssrn.com/abstract=1514412", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.164.7962", "http://doi.org/10.1002/jae.1137", "http://doi.org/10.1016/B978-0-444-62731-5.00015-4", "http://doi.org/10.1080/07474938408800053", "http://doi.org/10.1162/rest_a_00483", "http://doi.org/10.1561/0800000013", "http://minneapolisfed.org/research/DP/DP14.pdf", "http://www.minneapolisfed.org/research/WP/WP115.pdf", "https://books.google.com/books?id=muorJ6FHIiEC&pg=PA223", "https://ideas.repec.org/p/hhs/oruesi/2012_012.html", "https://ideas.repec.org/p/nbr/nberwo/18467.html"]}, "Dirichlet process": {"categories": ["CS1 maint: Multiple names: authors list", "Nonparametric Bayesian statistics", "Stochastic processes"], "title": "Dirichlet process", "method": "Dirichlet process", "url": "https://en.wikipedia.org/wiki/Dirichlet_process", "summary": "In probability theory, Dirichlet processes (after Peter Gustav Lejeune Dirichlet) are a family of stochastic processes whose realizations are probability distributions. In other words, a Dirichlet process is a probability distribution whose range is itself a set of probability distributions. It is often used in Bayesian inference to describe the prior knowledge about the distribution of random variables\u2014how likely it is that the random variables are distributed according to one or another particular distribution.\nThe Dirichlet process is specified by a base distribution \n \n \n \n H\n \n \n {\\displaystyle H}\n and a positive real number \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n called the concentration parameter (also known as scaling parameter). The base distribution is the expected value of the process, i.e., the Dirichlet process draws distributions \"around\" the base distribution the way a normal distribution draws real numbers around its mean. However, even if the base distribution is continuous, the distributions drawn from the Dirichlet process are almost surely discrete. The scaling parameter specifies how strong this discretization is: in the limit of \n \n \n \n \u03b1\n \u2192\n 0\n \n \n {\\displaystyle \\alpha \\rightarrow 0}\n , the realizations are all concentrated at a single value, while in the limit of \n \n \n \n \u03b1\n \u2192\n \u221e\n \n \n {\\displaystyle \\alpha \\rightarrow \\infty }\n the realizations become continuous. Between the two extremes the realizations are discrete distributions with less and less concentration as \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n increases.\nThe Dirichlet process can also be seen as the infinite-dimensional generalization of the Dirichlet distribution. In the same way as the Dirichlet distribution is the conjugate prior for the categorical distribution, the Dirichlet process is the conjugate prior for infinite, nonparametric discrete distributions. A particularly important application of Dirichlet processes is as a prior probability distribution in infinite mixture models.\nThe Dirichlet process was formally introduced by Thomas Ferguson in 1973\nand has since been applied in data mining and machine learning, among others for natural language processing, computer vision and bioinformatics.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/93/Chinese_Restaurant_Process_for_DP%280.5%2CH%29.webm", "https://upload.wikimedia.org/wikipedia/commons/d/db/DP_clustering_simulation.png", "https://upload.wikimedia.org/wikipedia/commons/d/d3/Dirichlet_process_draws.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f5/Parameter_estimation_process_infinite_Gaussian_mixture_model.webm"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost surely", "Annals of Statistics", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bayesian inference", "Bernoulli distribution", "Bernoulli process", "Bessel process", "Beta distribution", "Biased random walk on a graph", "Bioinformatics", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Categorical distribution", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Computer vision", "Conditional independence", "Conjugate prior", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous distribution", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Data clustering", "Data mining", "De Finetti's theorem", "Diffusion process", "Digital object identifier", "Dirichlet distribution", "Discrete-time stochastic process", "Discrete distribution", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Expected value", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Gibbs sampler", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hierarchical Dirichlet process", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Imprecise Dirichlet process", "Independence (probability theory)", "Independent and identically distributed random variables", "Indicator function", "Infinite mixture model", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "K-means clustering", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical Reviews", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Measurable set", "Mixing (mathematics)", "Moran process", "Moving-average model", "Multivariate normal distribution", "Natural language processing", "Nils Lid Hjort", "Non-homogeneous Poisson process", "Non-parametric statistics", "Nonparametric statistics", "Normal distribution", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Partition of a set", "Percolation theory", "Peter Gustav Lejeune Dirichlet", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Posterior distribution", "Potts model", "Predictable process", "Prior probability", "Probability distribution", "Probability mass function", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "P\u00f3lya urn model", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random variate", "Random walk", "Real number", "Realization (probability)", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sample path", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Sign test", "Simplex", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistical inference", "Statistics", "Stick-breaking process", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Thomas Ferguson (statistician)", "Time reversibility", "Time series", "Time series analysis", "Uncountable set", "Uniform integrability", "Unsupervised learning", "Usual hypotheses", "Variance", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilcoxon rank sum test", "Wilcoxon signed-rank test", "Wilkie investment model"], "references": ["http://www.sciencedirect.com/science/article/pii/S0921889012000334", "http://www.sciencedirect.com/science/article/pii/S0925231213005523", "http://topicmodels.west.uni-koblenz.de/ckling/tmt/crp.html?parameters=0.5&dp=1#", "http://www.cs.berkeley.edu/~jordan/nips-tutorial05.ps", "http://cs.brown.edu/~sudderth/papers/sudderthPhD.pdf", "http://www.ams.org/mathscinet-getitem?mr=0350949", "http://ClusterAnalysis.org", "http://doi.org/10.1214%2Faos%2F1176342360", "http://ieeexplore.ieee.org/document/6320657/", "http://www.maths.bris.ac.uk/~maxvd/cribsheet.pdf", "http://www.stats.bris.ac.uk/~peter/papers/GreenCDP.pdf", "http://learning.eng.cam.ac.uk/zoubin/talks/uai05tutorial-b.pdf", "http://www.gatsby.ucl.ac.uk/~edward/pub/inf.mix.nips.99.pdf", "http://www.gatsby.ucl.ac.uk/~ywteh/research/npbayes/Teh2010a.pdf", "https://www.ee.washington.edu/techsite/papers/documents/UWEETR-2010-0006.pdf", "https://archive.is/20121215093339/http://www.ece.sunysb.edu/~zyweng/dpcluster.html", "https://web.archive.org/web/20070524045420/http://www.cs.toronto.edu/~beal/npbayes/"]}, "Bivariate analysis": {"categories": ["Multivariate statistics"], "title": "Bivariate analysis", "method": "Bivariate analysis", "url": "https://en.wikipedia.org/wiki/Bivariate_analysis", "summary": "Bivariate analysis is one of the simplest forms of quantitative (statistical) analysis. It involves the analysis of two variables (often denoted as X, Y), for the purpose of determining the empirical relationship between them.Bivariate analysis can be helpful in testing simple hypotheses of association. Bivariate analysis can help determine to what extent it becomes easier to know and predict a value for one variable (possibly a dependent variable) if we know the value of the other variable (possibly the independent variable) (see also correlation and simple linear regression).Bivariate analysis can be contrasted with univariate analysis in which only one variable is analysed. Like univariate analysis, bivariate analysis can be descriptive or inferential. It is the analysis of the relationship between the two variables. Bivariate analysis is a simple (two variable) special case of multivariate analysis (where multiple relations between multiple variables are examined simultaneously).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0f/Oldfaithful3.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Association (statistics)", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coding (social sciences)", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Discriminant correlation analysis", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Earl R. Babbie", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypotheses", "Independent variable", "Index of dispersion", "Inferential statistics", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Logit", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Mosaic plot", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "Old Faithful Geyser", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordered logit", "Ordered probit", "Ordinal data", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probit", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scatterplot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simple regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Univariate analysis", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Wyoming", "Yellowstone National Park", "Z-test"], "references": ["http://sociologyindex.com/bivariate_analysis.htm", "http://ieeexplore.ieee.org/document/7470527/"]}, "Leftover hash-lemma": {"categories": ["Probability theorems", "Theory of cryptography"], "title": "Leftover hash lemma", "method": "Leftover hash-lemma", "url": "https://en.wikipedia.org/wiki/Leftover_hash_lemma", "summary": "The leftover hash lemma is a lemma in cryptography first stated by Russell Impagliazzo, Leonid Levin, and Michael Luby.\nImagine that you have a secret key X that has n uniform random bits, and you would like to use this secret key to encrypt a message. Unfortunately, you were a bit careless with the key, and know that an adversary was able to learn about t < n bits of that key, but you do not know which. Can you still use your key, or do you have to throw it away and choose a new key? The leftover hash lemma tells us that we can produce a key of about n - t bits, over which the adversary has almost no knowledge. Since the adversary knows all but n - t bits, this is almost optimal.\nMore precisely, the leftover hash lemma tells us that we can extract a length asymptotic to \n \n \n \n \n H\n \n \u221e\n \n \n (\n X\n )\n \n \n {\\displaystyle H_{\\infty }(X)}\n (the min-entropy of X) bits from a random variable X that are almost uniformly distributed. In other words, an adversary who has some partial knowledge about X, will have almost no knowledge about the extracted value. That is why this is also called privacy amplification (see privacy amplification section in the article Quantum key distribution).\nRandomness extractors achieve the same result, but use (normally) less randomness.\nLet X be a random variable over \n \n \n \n \n \n X\n \n \n \n \n {\\displaystyle {\\mathcal {X}}}\n and let \n \n \n \n m\n >\n 0\n \n \n {\\displaystyle m>0}\n . Let \n \n \n \n h\n :\n \n \n S\n \n \n \u00d7\n \n \n X\n \n \n \u2192\n {\n 0\n ,\n \n 1\n \n }\n \n m\n \n \n \n \n {\\textstyle h\\colon {\\mathcal {S}}\\times {\\mathcal {X}}\\rightarrow \\{0,\\,1\\}^{m}}\n be a 2-universal hash function. If \n\n \n \n \n m\n \u2264\n \n H\n \n \u221e\n \n \n (\n X\n )\n \u2212\n 2\n log\n \u2061\n \n (\n \n \n 1\n \u03b5\n \n \n )\n \n \n \n {\\textstyle m\\leq H_{\\infty }(X)-2\\log \\left({\\frac {1}{\\varepsilon }}\\right)}\n then for S uniform over \n \n \n \n \n \n S\n \n \n \n \n {\\displaystyle {\\mathcal {S}}}\n and independent of X, we have: \n\n \n \n \n \u03b4\n \n [\n \n (\n h\n (\n S\n ,\n X\n )\n ,\n S\n )\n ,\n (\n U\n ,\n S\n )\n \n ]\n \n \u2264\n \u03b5\n .\n \n \n {\\textstyle \\delta \\left[(h(S,X),S),(U,S)\\right]\\leq \\varepsilon .}\n where U is uniform over \n \n \n \n {\n 0\n ,\n 1\n \n }\n \n m\n \n \n \n \n {\\displaystyle \\{0,1\\}^{m}}\n and independent of S.\n \n \n \n \n H\n \n \u221e\n \n \n (\n X\n )\n =\n \u2212\n log\n \u2061\n \n max\n \n x\n \n \n Pr\n [\n X\n =\n x\n ]\n \n \n {\\textstyle H_{\\infty }(X)=-\\log \\max _{x}\\Pr[X=x]}\n is the min-entropy of X, which measures the amount of randomness X has. The min-entropy is always less than or equal to the Shannon entropy. Note that \n \n \n \n \n max\n \n x\n \n \n Pr\n [\n X\n =\n x\n ]\n \n \n {\\textstyle \\max _{x}\\Pr[X=x]}\n is the probability of correctly guessing X. (The best guess is to guess the most probable value.) Therefore, the min-entropy measures how difficult it is to guess X.\n\n \n \n \n 0\n \u2264\n \u03b4\n (\n X\n ,\n Y\n )\n =\n \n \n 1\n 2\n \n \n \n \u2211\n \n v\n \n \n \n |\n \n Pr\n [\n X\n =\n v\n ]\n \u2212\n Pr\n [\n Y\n =\n v\n ]\n \n |\n \n \u2264\n 1\n \n \n {\\textstyle 0\\leq \\delta (X,Y)={\\frac {1}{2}}\\sum _{v}\\left|\\Pr[X=v]-\\Pr[Y=v]\\right|\\leq 1}\n is a statistical distance between X and Y.", "images": [], "links": ["Adversary (cryptography)", "Almost all", "Almost optimal", "Bit", "Cryptography", "Hash function", "Information theoretic security", "K-independent hashing", "Key (cryptography)", "Lemma (mathematics)", "Leonid Levin", "Michael Luby", "Min-entropy", "Quantum key distribution", "Random variable", "Randomness extractor", "Russell Impagliazzo", "R\u00e9nyi entropy", "Shannon entropy", "Statistical distance", "Universal hashing"], "references": ["http://people.csail.mit.edu/ronitt/COURSE/S08/drafts/22.pdf", "http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=312213", "http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=45477", "http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=73009", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=10153&arnumber=476316&type=ref"]}, "Observed information": {"categories": ["Estimation theory", "Information theory"], "title": "Observed information", "method": "Observed information", "url": "https://en.wikipedia.org/wiki/Observed_information", "summary": "In statistics, the observed information, or observed Fisher information, is the negative of the second derivative (the Hessian matrix) of the \"log-likelihood\" (the logarithm of the likelihood function). It is a sample-based version of the Fisher information.", "images": [], "links": ["Asymptotic normality", "Biometrika", "Bradley Efron", "David V. Hinkley", "Digital object identifier", "Expected information", "Expected value", "Fisher information", "Fisher information matrix", "Fisher information metric", "Hessian matrix", "International Standard Book Number", "JSTOR", "Likelihood function", "Mathematical Reviews", "Maximum likelihood", "Random variable", "Statistics"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0521817", "http://doi.org/10.1093%2Fbiomet%2F65.3.457", "http://www.jstor.org/stable/2335893"]}, "Total sum of squares": {"categories": ["Least squares"], "title": "Total sum of squares", "method": "Total sum of squares", "url": "https://en.wikipedia.org/wiki/Total_sum_of_squares", "summary": "In statistical data analysis the total sum of squares (TSS or SST) is a quantity that appears as part of a standard way of presenting results of such analyses. It is defined as being the sum, over all observations, of the squared differences of each observation from the overall mean.In statistical linear models, (particularly in standard regression models), the TSS is the sum of the squares of the difference of the dependent variable and its mean:\n\n \n \n \n \n T\n S\n S\n \n =\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n \n (\n \n \n y\n \n i\n \n \n \u2212\n \n \n \n y\n \u00af\n \n \n \n \n )\n \n \n 2\n \n \n \n \n {\\displaystyle \\mathrm {TSS} =\\sum _{i=1}^{n}\\left(y_{i}-{\\bar {y}}\\right)^{2}}\n where \n \n \n \n \n \n \n y\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {y}}}\n is the mean.\nFor wide classes of linear models, the total sum of squares equals the explained sum of squares plus the residual sum of squares. For a proof of this in the multivariate OLS case, see partitioning in the general OLS model.\nIn analysis of variance (ANOVA) the total sum of squares is the sum of the so-called \"within-samples\" sum of squares and \"between-samples\" sum of squares, i.e., partitioning of the sum of squares.\nIn multivariate analysis of variance (MANOVA) the following equation applies\n\n \n \n \n \n T\n \n =\n \n W\n \n +\n \n B\n \n ,\n \n \n {\\displaystyle \\mathbf {T} =\\mathbf {W} +\\mathbf {B} ,}\n where T is the total sum of squares and products (SSP) matrix, W is the within-samples SSP matrix and B is the between-samples SSP matrix.\nSimilar terminology may also be used in linear discriminant analysis, where W and B are respectively referred to as the within-groups and between-groups SSP matrices.", "images": [], "links": ["Academic Press", "Analysis of variance", "Explained sum of squares", "International Standard Book Number", "K. V. Mardia", "Lack-of-fit sum of squares", "Linear discriminant analysis", "Linear model", "Matrix (mathematics)", "Mean", "Multivariate analysis of variance", "Regression model", "Residual sum of squares", "Square (algebra)", "Statistics", "Sum of squares (statistics)", "Summation"], "references": []}, "Principle of indifference": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from April 2010", "Articles with unsourced statements from July 2013", "Probability theory", "Statistical principles"], "title": "Principle of indifference", "method": "Principle of indifference", "url": "https://en.wikipedia.org/wiki/Principle_of_indifference", "summary": "The principle of indifference (also called principle of insufficient reason) is a rule for assigning epistemic probabilities. Suppose that there are n > 1 mutually exclusive and collectively exhaustive possibilities. The principle of indifference states that if the n possibilities are indistinguishable except for their names, then each possibility should be assigned a probability equal to 1/n.\nIn Bayesian probability, this is the simplest non-informative prior. The principle of indifference is meaningless under the frequency interpretation of probability, in which probabilities are relative frequencies rather than degrees of belief in uncertain propositions, conditional upon state information.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Admissible decision rule", "Approximate Bayesian computation", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernstein\u2013von Mises theorem", "Bertrand's paradox (probability)", "Bertrand paradox (probability)", "Cambridge University Press", "Coin", "Coin flipping", "Collectively exhaustive", "Conjugate prior", "Continuous uniform distribution", "Credible interval", "Cromwell's rule", "Dice", "Digital object identifier", "E.T. Jaynes", "Edwin T. Jaynes", "Empirical Bayes method", "Epistemic probability", "Equipossibility", "Equiprobability", "Frequency probability", "George Boole", "Gottfried Leibniz", "Hyperparameter", "Hyperprior", "International Standard Book Number", "JSTOR", "Jacob Bernoulli", "Jeffreys prior", "John Arbuthnot", "John Maynard Keynes", "John Venn", "Likelihood function", "Liouville's theorem (Hamiltonian)", "Macroscopic", "Markov chain Monte Carlo", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Moment generating function", "Mutually exclusive", "Non-informative prior", "Persi Diaconis", "Philosophy", "Pierre Simon Laplace", "Playing cards", "Posterior predictive distribution", "Posterior probability", "Principle of maximum entropy", "Principle of sufficient reason", "Principle of transformation groups", "Prior probability", "Probability density function", "Probability interpretations", "Radical probabilism", "Rule of succession", "Schwarz criterion", "Shuffling playing cards", "Statistical physics", "Statistics", "Symmetry", "Thermodynamic equilibrium", "Uniform distribution (continuous)"], "references": ["http://doi.org/10.2307%2F2324089", "http://www.jstor.org/stable/2324089", "https://books.google.com/books?id=M7yvkERHIIMC", "https://books.google.com/books?id=YmCvAAAAIAAJ&pg=PA41", "https://books.google.com/books?id=tTN4HuUNXjgC"]}, "Symmetric design": {"categories": ["Combinatorics", "Design of experiments", "Design theory", "Set families"], "title": "Block design", "method": "Symmetric design", "url": "https://en.wikipedia.org/wiki/Block_design", "summary": "In combinatorial mathematics, a block design is a set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties that are deemed useful for a particular application. These applications come from many areas, including experimental design, finite geometry, software testing, cryptography, and algebraic geometry. Many variations have been examined, but the most intensely studied are the balanced incomplete block designs (BIBDs or 2-designs) which historically were related to statistical issues in the design of experiments.A block design in which all the blocks have the same size is called uniform. The designs discussed in this article are all uniform. Pairwise balanced designs (PBDs) are examples of block designs that are not necessarily uniform.", "images": [], "links": ["15 schoolgirl problem", "Affine plane (incidence geometry)", "Algebraic geometry", "Analysis of covariance", "Analysis of variance", "Annals of Eugenics", "Annals of Mathematical Statistics", "Anne Penfold Street", "ArXiv", "Association scheme", "Bayesian experimental design", "Bayesian linear regression", "Bhat-Nayak Vasanti N.", "Binary relation", "Blind experiment", "Block code", "Blocking (statistics)", "Box\u2013Behnken design", "Bruck\u2013Ryser\u2013Chowla theorem", "Cambridge University Press", "Central composite design", "Cochran's theorem", "Combinatorial design", "Combinatorics", "Comparing means", "Completely randomized design", "Confounding", "Contrast (statistics)", "Covariate", "Crossover study", "Cryptography", "Damaraju Raghavarao", "Design of experiments", "Digital object identifier", "Digon", "Effect size", "Eric W. Weisstein", "Error correcting code", "Experiment", "Experimental design", "Experimental unit", "External validity", "Factorial experiment", "Family of sets", "Fano plane", "Finite geometry", "Fisher's inequality", "Fractional factorial design", "Generalized randomized block design", "Glossary of experimental design", "Graeco-Latin square", "H. J. Ryser", "Hadamard matrix", "Hierarchical Bayes model", "Hierarchical linear modeling", "Identity relation", "Incidence geometry", "Incidence matrix", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Journal of Combinatorial Theory", "Latin hypercube sampling", "Latin square", "Linear regression", "List of statistics articles", "MathWorld", "Mathematical Reviews", "Mathematics", "Mixed model", "Multiple comparison", "Multivariate analysis of variance", "M\u00f6bius plane", "Nuisance variable", "Optimal design", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Ovoid (projective geometry)", "Paley construction", "Paley digraph", "Partition of a set", "Peter Cameron (mathematician)", "Plackett-Burman design", "Polynomial and rational function modeling", "Projective linear group", "Projective plane", "Projective special linear group", "Pulse-position modulation", "Quadratic form", "Quadric (projective geometry)", "R", "R. C. Bose", "Random assignment", "Random effect", "Randomization", "Randomized block design", "Randomized controlled trial", "Raymond Paley", "Regular Hadamard matrix", "Repeated measures design", "Replication (statistics)", "Response surface methodology", "Restricted randomization", "Ronald Fisher", "S. S. Shrikhande", "Sample size", "Scientific control", "Scientific method", "Sequential analysis", "Sequential probability ratio test", "Set (mathematics)", "Software testing", "Statistical inference", "Statistical model", "Statistics", "Steiner system", "Taguchi methods", "Validity (statistics)"], "references": ["http://mathworld.wolfram.com/BlockDesign.html", "http://www.ams.org/mathscinet-getitem?mr=2384014", "http://arxiv.org/abs/1203.5378", "http://designtheory.org", "http://doi.org/10.1002%2Fjcd.20145", "http://doi.org/10.1016%2F0097-3165(71)90054-9", "http://doi.org/10.1016%2F0097-3165(78)90002-X", "http://doi.org/10.1080%2F01621459.1952.10501161", "http://doi.org/10.1109%2FLCOMM.2012.042512.120457", "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6205424", "http://www.neverendingbooks.org/DATA/biplanesingerman.pdf", "http://www.maths.qmul.ac.uk/~pjc/design/resources.html", "https://cran.r-project.org/package=agricolae"]}, "Kish grid": {"categories": ["All articles lacking in-text citations", "All stub articles", "Articles lacking in-text citations from January 2013", "Sampling techniques", "Statistics stubs"], "title": "Kish grid", "method": "Kish grid", "url": "https://en.wikipedia.org/wiki/Kish_grid", "summary": "The Kish grid or Kish selection grid is a method for selecting members within a household to be interviewed. It uses a pre-assigned table of random numbers to find the person to be interviewed. It was developed by statistician Leslie Kish in 1949.It is a technique widely used in survey research. However, in telephone surveys, the next-birthday method is sometimes preferred to the Kish grid.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Digital object identifier", "Household", "International Standard Book Number", "Interview", "JSTOR", "Leslie Kish", "Next-birthday method", "Statistics", "Survey research"], "references": ["http://www.encyclopedia.com/doc/1O88-Kishgrid.html", "http://srmo.sagepub.com/view/the-sage-encyclopedia-of-social-science-research-methods/n464.xml", "http://doi.org/10.1080/01621459.1949.10483314", "http://doi.org/10.1086/203642", "http://doi.org/10.1086/268785", "http://doi.org/10.1093/poq/nfi006", "http://doi.org/10.4135/9781412950589", "http://www.jstor.org/stable/2280236", "http://www.jstor.org/stable/2743408", "http://www.jstor.org/stable/2749026"]}, "Line chart": {"categories": ["Financial charts", "Quality control tools", "Statistical charts and diagrams"], "title": "Line chart", "method": "Line chart", "url": "https://en.wikipedia.org/wiki/Line_chart", "summary": "A line chart or line graph is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments. It is a basic type of chart common in many fields. It is similar to a scatter plot except that the measurement points are ordered (typically by their x-axis value) and joined with straight line segments. A line chart is often used to visualize a trend in data over intervals of time \u2013 a time series \u2013 thus the line is often drawn chronologically. In these cases they are known as run charts.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0b/Dwiggins_graph.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f7/Graph_%28PSF%29.png", "https://upload.wikimedia.org/wikipedia/commons/0/02/ScientificGraphSpeedVsTime.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Best-fit", "Chart", "Curve fitting", "Data table", "Francis Hauksbee", "Gradient", "Johann Heinrich Lambert", "Linear equation", "List of graphing software", "List of information graphics software", "Michael Friendly", "Nicolaus Samuel Cruquius", "Run chart", "Scatter plot", "Spreadsheet", "Time series", "William Playfair"], "references": ["http://www.math.yorku.ca/SCS/Gallery/milestone/milestone.pdf", "http://physics.info/curve-fitting/"]}, "K-medoids": {"categories": ["All articles with style issues", "All articles with unsourced statements", "Articles with unsourced statements from February 2016", "Cluster analysis algorithms", "Wikipedia articles with style issues from September 2015"], "title": "K-medoids", "method": "K-medoids", "url": "https://en.wikipedia.org/wiki/K-medoids", "summary": "The k-medoids algorithm is a clustering algorithm related to the k-means algorithm and the medoidshift algorithm. Both the k-means and k-medoids algorithms are partitional (breaking the dataset up into groups) and both attempt to minimize the distance between points labeled to be in a cluster and a point designated as the center of that cluster. In contrast to the k-means algorithm, k-medoids chooses datapoints as centers (medoids or exemplars) and works with a generalization of the Manhattan Norm to define distance between datapoints instead of \n \n \n \n \n l\n \n 2\n \n \n \n \n {\\displaystyle l_{2}}\n . This method was proposed in 1987 for the work with \n \n \n \n \n l\n \n 1\n \n \n \n \n {\\displaystyle l_{1}}\n norm and other distances.\nk-medoid is a classical partitioning technique of clustering, which clusters the data set of n objects into k clusters, with the number k of clusters assumed known a priori. If unknown, k can be determined with methods such as silhouette.\nIt is more robust to noise and outliers as compared to k-means because it minimizes a sum of pairwise dissimilarities instead of a sum of squared Euclidean distances.\nA medoid can be defined as the object of a cluster whose average dissimilarity to all the objects in the cluster is minimal. i.e. it is a most centrally located point in the cluster.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b3/K-means_versus_k-medoids.png", "https://upload.wikimedia.org/wikipedia/commons/e/e1/Kmedoid1.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/82/Kmedoid2.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Kmedoid3.jpg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Algorithm", "Data clustering", "ELKI", "Julia language", "K-means", "K-means clustering", "KNIME", "Lloyd's algorithm", "MATLAB", "Manhattan distance", "Medoid", "Medoids", "Medoidshift", "Norm (mathematics)", "R (programming language)", "RapidMiner", "Silhouette (clustering)"], "references": ["http://www.math.le.ac.uk/people/ag153/homepage/KmeansKmedoids/Kmeans_Kmedoids.html"]}, "Unitized risk": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from February 2018", "Articles with unsourced statements from September 2016", "CS1 errors: dates", "Statistical deviation and dispersion", "Statistical ratios", "Use dmy dates from October 2017", "Webarchive template wayback links"], "title": "Coefficient of variation", "method": "Unitized risk", "url": "https://en.wikipedia.org/wiki/Coefficient_of_variation", "summary": "In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation \n \n \n \n \n \u03c3\n \n \n {\\displaystyle \\ \\sigma }\n to the mean \n \n \n \n \n \u03bc\n \n \n {\\displaystyle \\ \\mu }\n (or its absolute value, \n \n \n \n \n |\n \n \u03bc\n \n |\n \n \n \n {\\displaystyle |\\mu |}\n ). \nThe CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R. In addition, CV is utilized by economists and investors in economic models and in determining the volatility of a security.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA gauge R&R", "Absolute error", "Absolute value", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Analytical chemistry", "Anderson\u2013Darling test", "Arithmetic mean", "Assay", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Biased estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Celsius", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimensionless number", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Economic model", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Fahrenheit", "Failure rate", "Fan chart (statistics)", "Fano factor", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Gini coefficient", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hyper-exponential distribution", "Hypothesis test", "Image processing", "Income inequality metrics", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Interval scale", "Intraclass correlation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kelvin", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-normal", "Log-normal distribution", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McKay's approximation for the coefficient of variation", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Midhinge", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiplicative inverse", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural log", "Nelson\u2013Aalen estimator", "Non-central t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normalization (statistics)", "Normally distributed", "Observational study", "Official statistics", "Omega ratio", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Physics", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quartile coefficient of dispersion", "Quasi-experiment", "Questionnaire", "Queueing theory", "Q\u2013Q plot", "RMSD", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rankine scale", "Rao\u2013Blackwell theorem", "Ratio scale", "Regression analysis", "Regression model validation", "Reliability engineering", "Reliability theory", "Renewal theory", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Security (finance)", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal-to-noise ratio (imaging)", "Signal processing", "Signal to noise ratio", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Standardized (statistics)", "Standardized moment", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-to-mean ratio", "Vector autoregression", "Volatility (finance)", "Wald test", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.graphpad.com/faq/viewfaq.cfm?faq=1089", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC130103", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4112421", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4478151", "http://www.ncbi.nlm.nih.gov/pubmed/10709801", "http://www.ncbi.nlm.nih.gov/pubmed/12414755", "http://www.ncbi.nlm.nih.gov/pubmed/1601532", "http://www.ncbi.nlm.nih.gov/pubmed/24728329", "http://www.ncbi.nlm.nih.gov/pubmed/25757675", "http://www.ncbi.nlm.nih.gov/pubmed/25987306", "http://www.ncbi.nlm.nih.gov/pubmed/27581804", "http://www.ncbi.nlm.nih.gov/pubmed/4370388", "http://doi.org/10.1002%2F(SICI)1097-0258(19960330)15:6%3C647::AID-SIM184%3E3.0.CO;2-P", "http://doi.org/10.1002%2Fajhb.22690", "http://doi.org/10.1007%2Fs00180-013-0445-2", "http://doi.org/10.1080%2F00031305.1996.10473537", "http://doi.org/10.1080%2F03610920802187448", "http://doi.org/10.1081%2FBIP-100101013", "http://doi.org/10.1093%2Fbiomet%2F51.1-2.25", "http://doi.org/10.1093%2Fije%2Fdyw191", "http://doi.org/10.1128%2FCDLI.9.6.1235-1239.2002", "http://doi.org/10.1136%2Fannrheumdis-2014-205228", "http://doi.org/10.1214%2Faoms%2F1177732503", "http://doi.org/10.1641%2F0006-3568(2001)051%5B0341:LNDATS%5D2.0.CO;2", "http://doi.org/10.2307%2F1267363", "http://doi.org/10.3758%2Fs13428-015-0600-5", "http://www.fao.org/docs/up/easypol/448/simple_inequality_mesures_080en.pdf", "http://www.jstor.org/stable/1267363", "http://www.jstor.org/stable/2530139", "http://www.jstor.org/stable/2685039", "http://www.jstor.org/stable/2957564", "http://ije.oxfordjournals.org/content/early/2016/08/30/ije.dyw191.extract", "http://pharmasug.org/proceedings/2011/PO/PharmaSUG-2011-PO08.pdf", "http://www.worldcat.org/issn/0300-5771", "http://www.worldcat.org/issn/1554-3528", "http://pub.epsilon.slu.se/4489/1/forkman_j_110214.pdf", "https://books.google.com/?id=qd4PAQAAMAAJ&q=%22unitized+risk%22", "https://scholarworks.gsu.edu/math_theses/124", "https://www.powderprocess.net/Measuring_Degree_Mixing.html", "https://web.archive.org/web/20081215175508/http://graphpad.com/faq/viewfaq.cfm?faq=1089", "https://web.archive.org/web/20110824094357/http://pharmasug.org/proceedings/2011/PO/PharmaSUG-2011-PO08.pdf", "https://web.archive.org/web/20131206021229/http://pub.epsilon.slu.se/4489/1/forkman_j_110214.pdf", "https://web.archive.org/web/20140301102042/http://scholarworks.gsu.edu/cgi/viewcontent.cgi?article=1116&context=math_theses", "https://web.archive.org/web/20160805101141/http://www.fao.org/docs/up/easypol/448/simple_inequality_mesures_080en.pdf", "https://web.archive.org/web/20171114145327/https://www.powderprocess.net/Measuring_Degree_Mixing.html", "https://cran.r-project.org/package=cvequality"]}, "McCullagh's parametrization of the Cauchy distributions": {"categories": ["Continuous distributions"], "title": "McCullagh's parametrization of the Cauchy distributions", "method": "McCullagh's parametrization of the Cauchy distributions", "url": "https://en.wikipedia.org/wiki/McCullagh%27s_parametrization_of_the_Cauchy_distributions", "summary": "In probability theory, the \"standard\" Cauchy distribution is the probability distribution whose probability density function (pdf) is\n\n \n \n \n f\n (\n x\n )\n =\n \n \n 1\n \n \u03c0\n (\n 1\n +\n \n x\n \n 2\n \n \n )\n \n \n \n \n \n {\\displaystyle f(x)={1 \\over \\pi (1+x^{2})}}\n for x real. This has median 0, and first and third quartiles respectively \u22121 and +1. Generally, a Cauchy distribution is any probability distribution belonging to the same location-scale family as this one. Thus, if X has a standard Cauchy distribution and \u03bc is any real number and \u03c3 > 0, then Y = \u03bc + \u03c3X has a Cauchy distribution whose median is \u03bc and whose first and third quartiles are respectively \u03bc \u2212 \u03c3 and \u03bc + \u03c3.\nMcCullagh's parametrization, introduced by Peter McCullagh, professor of statistics at the University of Chicago uses the two parameters of the non-standardised distribution to form a single complex-valued parameter, specifically, the complex number \u03b8 = \u03bc + i\u03c3, where i is the imaginary unit. It also extends the usual range of scale parameter to include \u03c3 < 0.\nAlthough the parameter is notionally expressed using a complex number, the density is still a density over the real line. In particular the density can be written using the real-valued parameters \u03bc and \u03c3, which can each take positive or negative values, as\n\n \n \n \n f\n (\n x\n )\n =\n \n \n 1\n \n \u03c0\n \n |\n \u03c3\n |\n \n (\n 1\n +\n \n \n \n (\n x\n \u2212\n \u03bc\n \n )\n \n 2\n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n )\n \n \n \n \n ,\n \n \n {\\displaystyle f(x)={1 \\over \\pi \\left\\vert \\sigma \\right\\vert (1+{\\frac {(x-\\mu )^{2}}{\\sigma ^{2}}})}\\,,}\n where the distribution is regarded as degenerate if \u03c3 = 0. \nAn alternative form for the density can be written using the complex parameter \u03b8 = \u03bc + i\u03c3 as\n\n \n \n \n f\n (\n x\n )\n =\n \n \n \n |\n \n \u2111\n \n \u03b8\n \n \n |\n \n \n \u03c0\n \n \n |\n \n x\n \u2212\n \u03b8\n \n |\n \n \n 2\n \n \n \n \n \n \n ,\n \n \n {\\displaystyle f(x)={\\left\\vert \\Im {\\theta }\\right\\vert \\over \\pi \\left\\vert x-\\theta \\right\\vert ^{2}}\\,,}\n where \n \n \n \n \u2111\n \n \u03b8\n \n =\n \u03c3\n \n \n {\\displaystyle \\Im {\\theta }=\\sigma }\n .\nTo the question \"Why introduce complex numbers when only real-valued random variables are involved?\", McCullagh wrote:\n\nIn other words, if the random variable Y has a Cauchy distribution with complex parameter \u03b8, then the random variable Y * defined above has a Cauchy distribution with parameter (a\u03b8 + b)/(c\u03b8 + d).\nMcCullagh also wrote, \"The distribution of the first exit point from the upper half-plane of a Brownian particle starting at \u03b8 is the Cauchy density on the real line with parameter \u03b8.\" In addition, McCullagh shows that the complex-valued parameterisation allows a simple relationship to be made between the Cauchy and the \"circular Cauchy distribution\".", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biometrika", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Complex number", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Imaginary number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location-scale family", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Peter McCullagh", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "University of Chicago", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wiener process", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.stat.uchicago.edu/~pmcc/pubs/paper18.pdf", "http://biomet.oxfordjournals.org/cgi/content/abstract/79/2/247"]}, "Multiscale decision making": {"categories": ["Decision analysis", "Markov processes", "Mechanism design"], "title": "Multiscale decision-making", "method": "Multiscale decision making", "url": "https://en.wikipedia.org/wiki/Multiscale_decision-making", "summary": "Multiscale decision-making, also referred to as multiscale decision theory (MSDT), is an approach in operations research that combines game theory, multi-agent influence diagrams, in particular dependency graphs, and Markov decision processes to solve multiscale challenges in sociotechnical systems. MSDT considers interdependencies within and between the following scales: system level, time and information.\nMultiscale decision theory builds upon decision theory and multiscale mathematics. Multiscale decision theory can model and analyze complex decision-making networks that exhibit multiscale phenomena. The theory's results can be used by mechanism designers and decision-makers in organizations and complex systems to improve system performance and decision quality.\nMultiscale decision theory has been applied to manufacturing enterprise enterprises, service systems, supply chain management, healthcare, systems engineering, among others. In healthcare, for example, MSDT has been used to identify multi-level incentives that can improve healthcare value (quality of outcomes per dollar spent). The Multiscale Decision Making Laboratory at Virginia Tech directed by Dr. Christian Wernz is working at the forefront of MSDT theory and applications.\nMultiscale decision theory is related to:\n\nMultiscale modeling\nDecision analysis\nCooperative distributed problem solving\nDecentralized decision making\n\n", "images": [], "links": ["Complex system", "Cooperative distributed problem solving", "Decentralized decision making", "Decision-making", "Decision analysis", "Decision theory", "Dependency graph", "Digital object identifier", "Game theory", "Healthcare", "Influence diagram", "International Standard Book Number", "Markov decision process", "Mechanism design", "Multi-agent system", "Multiscale mathematics", "Multiscale modeling", "Network (mathematics)", "Operations research", "Service system", "Sociotechnical system", "Supply chain management", "Systems engineering", "Virginia Tech"], "references": ["http://scholarworks.umass.edu/dissertations/AAI3336994/", "http://www.msdm.ise.vt.edu/index.html", "http://science.energy.gov/~/media/ascr/pdf/research/am/docs/Multiscale_math_workshop_3.pdf", "http://stinet.dtic.mil/cgi-bin/GetTRDoc?AD=ADA465613&Location=U2&doc=GetTRDoc.pdf", "http://doi.org/10.1007%2Fs10479-014-1735-y", "http://doi.org/10.1016%2Fj.ejor.2009.06.022", "http://doi.org/10.1016%2Fj.jmsy.2007.10.003", "http://doi.org/10.1287%2Fserv.1.4.270", "https://www.nsf.gov/awardsearch/showAward?AWD_ID=1549896&HistoricalAwards=false", "https://www.researchgate.net/profile/Christian_Wernz/publication/280937533_Aligning_Incentives_in_Health_Care_A_Multiscale_Decision_Theory_Approach/links/55ccd7d208aebebb8f5779da.pdf?origin=publication_detail&ev=pub_int_prw_xdl&msrp=mc3WuAURvCsZdXwILOYGGiF1Cg-1Fb80eXnlcteV-2ul0v7VShlai5YI8W8dnDODQnrUq7OeCfGleFEp32LpBQ.o-xPiLgepmggWWsCzSEsKKetFLw-Wc96HP450Ci5bxHPdh2KVTwBbDbKtXtnUSuM9_4BlEamgcCI2H7VJ3zQLw.iFZPYLyBiQR8eEZQXtDTViLF4hFhgL_788UWEH40DNUkcI6CEJnOMc2eUtmaKOqBjBpPr45vgnmTAbdXrsEHIw"]}, "Data analysis": {"categories": ["All articles with specifically marked weasel-worded phrases", "Articles with specifically marked weasel-worded phrases from March 2018", "Computational fields of study", "Data analysis", "Scientific method", "Wikipedia articles needing clarification from March 2018", "Wikipedia articles with GND identifiers"], "title": "Data analysis", "method": "Data analysis", "url": "https://en.wikipedia.org/wiki/Data_analysis", "summary": "Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, while being used in different business, science, and social science domains.\nData mining is a particular data analysis technique that focuses on modeling and knowledge discovery for predictive rather than purely descriptive purposes, while business intelligence covers data analysis that relies heavily on aggregation, focusing mainly on business information. In statistical applications, data analysis can be divided into descriptive statistics, exploratory data analysis (EDA), and confirmatory data analysis (CDA). EDA focuses on discovering new features in the data while CDA focuses on confirming or falsifying existing hypotheses. Predictive analytics focuses on application of statistical models for predictive forecasting or classification, while text analytics applies statistical, linguistic, and structural techniques to extract and classify information from textual sources, a species of unstructured data. All of the above are varieties of data analysis.\nData integration is a precursor to data analysis, and data analysis is closely linked to data visualization and data dissemination. The term data analysis is sometimes used as a synonym for data modeling.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/b/ba/Data_visualization_process_v1.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/5/54/Rayleigh-Taylor_instability.jpg", "https://upload.wikimedia.org/wikipedia/commons/e/ee/Relationship_of_data%2C_information_and_intelligence.png", "https://upload.wikimedia.org/wikipedia/commons/9/9b/Social_Network_Analysis_Visualization.png", "https://upload.wikimedia.org/wikipedia/commons/f/fb/Total_Revenues_and_Outlays_as_Percent_GDP_2013.png", "https://upload.wikimedia.org/wikipedia/commons/7/7e/U.S._Phillips_Curve_2000_to_2013.png", "https://upload.wikimedia.org/wikipedia/commons/d/db/US_Employment_Statistics_-_March_2015.png", "https://upload.wikimedia.org/wikipedia/commons/8/80/User-activities.png", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg"], "links": ["ANCOVA", "ANOVA", "ASCE", "Actuarial science", "Ad\u00e8r, H.J.", "Algorithms", "Analytics", "Area chart", "Bar chart", "Ben Shneiderman", "Bifurcation theory", "Big data", "Bonferroni correction", "Bootstrapping (statistics)", "Boris Galerkin", "Boundary element method", "Boxplot", "Bush tax cuts", "Business intelligence", "CERN", "Cartogram", "Causality", "Censoring (statistics)", "Chaos theory", "Chartjunk", "Cognitive bias", "Collectively exhaustive events", "Common-method variance", "Competing on Analytics", "Computational fluid dynamics", "Computational physics", "Computer simulation", "Confirmation bias", "Congressional Budget Office", "Contextualization (computer science)", "Control chart", "Correlation and dependence", "Cronbach's alpha", "Cross-validation (statistics)", "Daniel Patrick Moynihan", "Data", "Data (computing)", "Data Analysis", "Data Presentation Architecture", "Data acquisition", "Data archaeology", "Data blending", "Data cleansing", "Data collection", "Data compression", "Data corruption", "Data curation", "Data degradation", "Data editing", "Data farming", "Data format management", "Data fusion", "Data governance", "Data integration", "Data integrity", "Data library", "Data loss", "Data management", "Data migration", "Data mining", "Data model", "Data modeling", "Data pre-processing", "Data preservation", "Data quality", "Data recovery", "Data reduction", "Data retention", "Data science", "Data scraping", "Data scrubbing", "Data security", "Data stewardship", "Data storage", "Data system", "Data transformation", "Data transformation (statistics)", "Data validation", "Data visualization", "Data warehouse", "Data wrangling", "Database", "David Hand (statistician)", "Descriptive statistics", "DevInfo", "Digital object identifier", "Digital signal processing", "Dimension reduction", "Dissipative particle dynamics", "Doing Data Science", "Dropout (electronics)", "DuPont analysis", "ELKI", "Early case assessment", "Education", "Edward Norton Lorenz", "Edward Tufte", "Exploratory data analysis", "FHWA", "Fact", "Fernanda Vi\u00e9gas", "Financial statement analysis", "Finite difference method", "Finite element method", "Finite volume method", "Fourier analysis", "General linear model", "Generalized linear model", "Gibbs sampling", "Gideon J. Mellenbergh", "Hadley Wickham", "Harmonics", "Herman J. Ad\u00e8r", "Histogram", "Hypotheses", "Hypothesis testing", "Inferential statistics", "Infographic", "Information", "Information design", "Information displays", "Information privacy", "Integrated Authority File", "Intelligence cycle", "Interactive data visualization", "Internal consistency", "International Standard Book Number", "Item response theory", "John Tukey", "John W. Tukey", "John von Neumann", "KNIME", "Kaggle", "Kenneth G. Wilson", "LTPP International Data Analysis Contest", "Lattice Boltzmann methods", "Lennard-Jones potential", "Line chart", "MANOVA", "MECE principle", "Machine learning", "Manipulation check", "McKinsey and Company", "Measuring instrument", "Median", "Metropolis\u2013Hastings algorithm", "Misleading graph", "Missing data", "Molecular dynamics", "Monte Carlo integration", "Monte Carlo method", "Morse/Long-range potential", "Morse potential", "Multilinear principal component analysis", "Multilinear subspace learning", "Multiway data analysis", "Mutually exclusive events", "N-body simulation", "Nearest neighbor search", "Nonlinear system", "Nonlinear system identification", "Normal distribution", "Numeracy", "Numerical analysis", "OCLC", "Opinion", "Orange (software)", "Outlier", "Over-the-counter data", "Pandas (software)", "Pareto chart", "Particle-in-cell", "Phillips Curve", "Physics Analysis Workstation", "Pie chart", "Plot (graphics)", "Potential", "Predictive analytics", "Principal component analysis", "Probability distribution", "Problem solving", "Process theory", "Propensity score matching", "Qualitative research", "ROOT", "R (programming language)", "Randomization", "Regression analysis", "Reliability (statistics)", "Response rate (survey)", "Richard Veryard", "Richards Heuer", "Riemann solver", "Run chart", "Scatter plot", "Scatterplot", "SciPy", "Scientific computing", "Scientific visualization", "Sensitivity analysis", "Sergei K. Godunov", "Small multiple", "Smoothed-particle hydrodynamics", "Sparkline", "Standard deviation", "Stanislaw Ulam", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistics", "Stem-and-leaf display", "Structural equation modelling", "Structured data analysis (statistics)", "Subharmonics", "System identification", "T test", "Table (information)", "Tamara Munzner", "Test method", "Text analytics", "Turbulence modeling", "Type 1 error", "Type I and type II errors", "United Nations Development Group", "Unstructured data", "Visual perception", "Wavelet", "Yukawa potential"], "references": ["http://www.martingrandjean.ch/wp-content/uploads/2015/02/Grandjean-2014-Connaissance-reseau.pdf", "http://www.bloombergview.com/articles/2014-10-28/bad-math-that-passes-for-insight", "http://www.mdnpress.com/wmn/pdfs/chi94-pro-formas-2.pdf", "http://research.microsoft.com/en-us/projects/datacleaning/", "http://www.perceptualedge.com/articles/b-eye/quantitative_data.pdf", "http://www.perceptualedge.com/articles/ie/the_right_graph.pdf", "http://www.perceptualedge.com/articles/misc/Graph_Selection_Matrix.pdf", "http://search.proquest.com/docview/202710770?accountid=28180", "http://db.cs.berkeley.edu/jmh/papers/cleaning-unece.pdf", "http://www.cs.cmu.edu/~Compose/ftp/shaw-fin-etaps.pdf", "http://www.cc.gatech.edu/~stasko/papers/infovis05.pdf", "http://cll.stanford.edu/~willb/course/behrens97pm.pdf", "http://www.cbo.gov/publication/21670", "http://www.itl.nist.gov/div898/handbook/", "http://doi.org/10.1016%2Fj.procs.2016.04.213", "http://doi.org/10.3166%2Flcn.10.3.37-54", "http://projecteuclid.org/download/pdf_1/euclid.aoms/1177704711", "http://www.symmetrymagazine.org/article/july-2014/the-machine-learning-community-takes-on-the-higgs/", "http://www.worldcat.org/oclc/905799857", "http://www.worldcat.org/title/advising-on-research-methods-a-consultants-companion/oclc/905799857/viewport", "https://sas.elluminate.com/site/external/recording/playback/link/table/dropin?sid=2008350&suid=D.4DF60C7117D5A77FE3AED546909ED2", "https://www.suntecindia.com/blog/clean-data-in-crm-the-key-to-generate-sales-ready-leads-and-boost-your-revenue-pool/", "https://scholarspace.manoa.hawaii.edu/handle/10125/41879", "https://www.cia.gov/library/center-for-the-study-of-intelligence/csi-publications/books-and-monographs/psychology-of-intelligence-analysis/art3.html", "https://www.fhwa.dot.gov/research/tfhrc/programs/infrastructure/pavements/ltpp/2016_2017_asce_ltpp_contest_guidelines.cfm", "https://www.fhwa.dot.gov/research/tfhrc/programs/infrastructure/pavements/ltpp/", "https://d-nb.info/gnd/4123037-1", "https://www.erim.eur.nl/centres/necessary-condition-analysis/", "https://folk.uio.no/ohammer/past/", "https://web.archive.org/web/20171018181046/https://spotlessdata.com/blog/exploring-data-analysis", "https://www.wikidata.org/wiki/Q1988917"]}, "Clinical utility of diagnostic tests": {"categories": ["Medical tests", "Pathology"], "title": "Medical test", "method": "Clinical utility of diagnostic tests", "url": "https://en.wikipedia.org/wiki/Medical_test", "summary": "A medical test is a medical procedure performed to detect, diagnose, or monitor diseases, disease processes, susceptibility, or to determine a course of treatment. Medical tests relate to clinical chemistry and molecular diagnostics, and are typically performed in a medical laboratory.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/85/Lung_scintigraphy_keosys.JPG", "https://upload.wikimedia.org/wikipedia/commons/f/fb/X-ray_by_Wilhelm_R%C3%B6ntgen_of_Albert_von_K%C3%B6lliker%27s_hand_-_18960123-02.jpg"], "links": ["3D ultrasound", "ABO blood group system", "ACTH stimulation test", "ART4", "AST/ALT ratio", "Abdominal auscultation", "Abdominal palpation", "Abdominal ultrasonography", "Abdominal x-ray", "Absolute neutrophil count", "Accuracy and precision", "Acid\u2013base homeostasis", "Activated clotting time", "Agglutination (biology)", "Alanine transaminase", "Albumin", "Albuminuria", "Alkaline phosphatase", "Aminoaciduria", "Amylase", "Anatomical pathology", "Angiocardiography", "Angiography", "Anion gap", "Anti-Jo1", "Anti-SSA/Ro autoantibodies", "Anti-actin antibodies", "Anti-apolipoprotein antibodies", "Anti-cardiolipin antibodies", "Anti-centromere antibodies", "Anti-dsDNA", "Anti-ganglioside antibodies", "Anti-gliadin antibodies", "Anti-glomerular basement membrane antibody", "Anti-glutamate receptor antibodies", "Anti-glycoprotein-210 antibodies", "Anti-mitochondrial antibody", "Anti-nRNP", "Anti-neutrophil cytoplasmic antibody", "Anti-nuclear antibody", "Anti-p62 antibodies", "Anti-smooth muscle antibody", "Anti-sp100 antibodies", "Anti-streptolysin O", "Anti-thrombin antibodies", "Anti-thyroid peroxidase antibody", "Anti-topoisomerase antibodies", "Anti-transglutaminase antibodies", "Antiphospholipid syndrome", "Anti\u2013citrullinated protein antibody", "Aortography", "Apheresis", "Apoptosis", "Apt\u2013Downey test", "Aquaporin 3", "Arterial blood gas", "Arthrogram", "Artificially binary value", "Aspartate transaminase", "Atrophy", "Audition", "Autoantibody", "Autopsy", "BDNA test", "BUN-to-creatinine ratio", "Bacterial infection", "Bacteriuria", "Baricity", "Base excess", "Basigin", "Bayesian probability", "Bicarbonate", "Bilirubin", "Bilirubinuria", "Binary classification", "Bleeding time", "Blood", "Blood bank", "Blood culture", "Blood donation", "Blood film", "Blood lipids", "Blood plasma", "Blood product", "Blood substitute", "Blood sugar", "Blood test", "Blood transfusion", "Blood type", "Blood urea nitrogen", "Blood values", "Bone scintigraphy", "Brain positron emission tomography", "Breast MRI", "Breast cancer", "Breast ultrasound", "Bronchial challenge test", "Bronchography", "C-ANCA", "C-reactive protein", "C1GALT1", "CD151", "CFU-GM", "CO2 content", "CPK-MB test", "CSF/serum albumin ratio", "CSF/serum glucose ratio", "CSF albumin", "CSF glucose", "CT pulmonary angiogram", "CT scan", "Calcium", "Calcium in biology", "Cardiac MRI perfusion", "Cardiac PET", "Cardiac magnetic resonance imaging", "Cardiac marker", "Cardiovascular system", "Carotid ultrasonography", "Caseous necrosis", "Cause (medicine)", "Cell damage", "Cell death", "Cellular adaptation", "Central nervous system", "Cerebrospinal fluid", "Cervical cancer", "Chemical test", "Chest pain", "Chest radiograph", "Cholangiography", "Cholecystography", "Cholescintigraphy", "Cholesterol test", "Chromatin immunoprecipitation", "Chromatography", "Chyluria", "Clinical chemistry", "Clinical pathology", "Coagulation", "Coagulative necrosis", "Coeliac disease", "Cognitive bias", "Colton antigen system", "Complement component 4", "Complement fixation test", "Complement receptor 1", "Complete blood count", "Comprehensive Therapy", "Computed tomography angiography", "Computed tomography of the abdomen and pelvis", "Computed tomography of the head", "Computed tomography of the thyroid", "Confocal microscopy", "Congenital hypothyroidism", "Contact thermography", "Contraction stress test", "Contrast-enhanced ultrasound", "Contrast medium", "Coombs test", "Coronary CT angiography", "Coronary CT calcium scan", "Counterimmunoelectrophoresis", "Creatinine", "Cross-matching", "Cryoprecipitate", "Cryosupernatant", "Crystalluria", "Current Procedural Terminology", "Cutoff (reference value)", "Cystography", "Cytopathology", "Cytoplasm", "D-dimer", "DMSA scan", "Dacryoscintigraphy", "Decay-accelerating factor", "Dengue fever", "Dental radiography", "Diabetes mellitus", "Diagnostic immunology", "Diagnostic test", "Diego antigen system", "Differential diagnosis", "Diffusion MRI", "Digestion", "Digital X-ray radiogrammetry", "Digital object identifier", "Dilute Russell's viper venom time", "Direct fluorescent antibody", "Disease", "Doppler echocardiography", "Doppler ultrasonography", "Dual-energy X-ray absorptiometry", "Duffy antigen system", "Duplex ultrasonography", "Dynamic angiothermography", "Dysplasia", "ELISA", "ELISPOT", "ERMAP", "Ecarin clotting time", "Echocardiography", "Echoencephalography", "Electrocardiogram", "Electrocardiography", "Electrocochleography", "Electrodiagnostic medicine", "Electroencephalography", "Electrogastrogram", "Electrolyte", "Electromyography", "Electron beam tomography", "Electron microscopy", "Electronystagmography", "Electrooculography", "Electroretinography", "Emergency ultrasound", "Emission computed tomography", "Endocrine system", "Endomicroscopy", "Endoscopic ultrasound", "Enzyme assay", "Enzyme multiplied immunoassay technique", "Eosinophiluria", "Epitope mapping", "Epstein\u2013Barr virus", "Er blood group collection", "Erythrocyte sedimentation rate", "Euglobulin lysis time", "Exchange transfusion", "Extractable nuclear antigen", "FTA-ABS", "Facial electromyography", "False positive", "Fat necrosis", "Ferritin", "Fetal hemoglobin", "Fever", "Fibrinoid necrosis", "Fibrinolysis", "Flow cytometry", "Fluorescence in situ hybridization", "Fluoroscopy", "Focused assessment with sonography for trauma", "Forensic pathology", "Forssman antigen system", "Fresh frozen plasma", "Full-body CT scan", "Functional magnetic resonance imaging", "Gallium 67 scan", "Gamma ray", "Gangrene", "Gastric emptying scan", "General anesthesia", "Genetic testing", "Glandular metaplasia", "Globoside", "Glucose", "Gluten challenge test", "Glycogen phosphorylase isoenzyme BB", "Glycophorin C", "Glycosuria", "Gold standard (test)", "Gross examination", "Gynecologic ultrasonography", "HIV", "HIV test", "Haptoglobin", "Harvard University", "Heart", "HelicoCARE direct", "Helicobacter", "Hemagglutination", "Hemagglutinin", "Hematocrit", "Hematopathology", "Hematuria", "Hemodynamics", "Hemoglobin", "Hemoglobinuria", "Hemorheology", "Hemosiderin", "Heterophile antibody test", "Hh blood group", "High resolution CT", "Histopathology", "Human blood group systems", "Human chorionic gonadotropin", "Human eye", "Human red cell antigens", "Human serum albumin", "Hyperplasia", "Hypersthenuria", "Hypertrophy", "Hyperuricosuria", "Hypouricosuria", "Hysterosalpingography", "ICAM4", "ICD-10 Chapter XVIII: Symptoms, signs and abnormal clinical and laboratory findings", "ICD-10 Procedure Coding System", "ICD-9-CM Volume 3", "ISBT 128", "Ii antigen system", "Immunoassay", "Immunocytochemistry", "Immunodiffusion", "Immunoelectrophoresis", "Immunofluorescence", "Immunohistochemistry", "Immunology", "Immunopathology", "Immunoprecipitation", "Immunoscintigraphy", "Indian blood group system", "Indication (medicine)", "Indium-111 WBC scan", "Infant", "Infection", "Inflammation", "Information bias (psychology)", "Informed consent", "International Society of Blood Transfusion", "Intracranial EEG", "Intraoperative blood salvage", "Intravascular ultrasound", "Iron tests", "Ischemia", "Isosthenuria", "Junior blood group system", "Karyolysis", "Karyorrhexis", "Kell antigen system", "Ketone bodies", "Ketonuria", "Kidd antigen system", "Kidneys, ureters, and bladder x-ray", "Kleihauer\u2013Betke test", "LSm", "Lactate dehydrogenase", "Lan blood group system", "Laser", "Latex fixation test", "Leukapheresis", "Leukocyte esterase", "Lewis antigen system", "Likelihood ratios in diagnostic testing", "Lipase", "Lipochrome", "Lipofuscin", "Liquefactive necrosis", "List of ICD-9 codes 780\u2013799: symptoms, signs, and ill-defined conditions", "Liver function tests", "Lower gastrointestinal series", "Lung cancer", "Lupus anticoagulant", "Lutheran antigen system", "Lymphocyte", "Lymphogram", "Lymphoma", "MChip", "MELISA", "MNS antigen system", "MRI sequence", "Magnetic resonance angiography", "Magnetic resonance cholangiopancreatography", "Magnetic resonance imaging", "Magnetic resonance imaging of the brain", "Magnetic resonance neurography", "Magnetocardiography", "Magnetoencephalography", "Magnetogastrography", "Mammography", "Manometry", "Mass concentration (chemistry)", "Mass spectrometry", "Mean corpuscular hemoglobin", "Mean corpuscular hemoglobin concentration", "Mean corpuscular volume", "Mean platelet volume", "Mediastinoscopy", "Medical Subject Headings", "Medical diagnosis", "Medical history", "Medical imaging", "Medical laboratory", "Medical microbiology", "Medical procedure", "Medical sign", "Medical ultrasonography", "Melanin", "Mentzer index", "Metabolism", "Metaplasia", "Microalbuminuria", "Microbiological culture", "Microscopic hematuria", "Molecular diagnostics", "Molecular pathology", "Monitoring (medicine)", "Myelography", "Myeloid", "Myocardial perfusion imaging", "Myoglobin", "Myoglobinuria", "NS1 antigen test", "Nailbed assessment", "Necrosis", "Negative medical test", "Neoplasia", "Nephelometry", "Nerve conduction study", "Newborn screening", "Nitro blue tetrazolium chloride", "Non-contact thermography", "Nuclear medicine", "Nurse practitioner", "Obstetric ultrasonography", "Octreotide scan", "Operation of computed tomography", "Optical coherence tomography", "Optical imaging", "Optical tomography", "Oral and maxillofacial pathology", "Oral food challenge", "Orthogonal polarization spectral imaging", "Osmolality", "Ouchterlony double immunodiffusion", "P-ANCA", "PET-CT", "P antigen system", "Packed red blood cells", "Pallor", "Pancreas", "Pancreatic lipase", "Panoramic radiograph", "Pap smear", "Pap test", "Partial thromboplastin time", "Passive smoke", "Patch test", "Pathogen", "Pathogenesis", "Pathogenic bacteria", "Pathognomonic", "Pathology", "Perfusion MRI", "Peripheral nervous system", "Phlegm", "Physical examination", "Physician", "Physician assistant", "Pigment", "Plasma frozen within 24 hours", "Plasma osmolality", "Plasmapheresis", "Platelet", "Platelet count", "Plateletpheresis", "Pneumoencephalography", "Point-of-care testing", "Positive test", "Positron", "Positron emission mammography", "Positron emission tomography", "Positron emission tomography\u2013magnetic resonance imaging", "Post-test probability", "Posthumous diagnosis", "Potassium in biology", "Pre- and post-test probability", "Pre- and posttest probability", "Pre-hospital ultrasound", "Predictive values", "Pregnancy test", "Primary biliary cirrhosis", "Procalcitonin", "Prognosis", "Programmed cell death", "Projectional radiography", "Proteinuria", "Prothrombin time", "Protozoan infection", "PubMed Identifier", "Pyelogram", "Pyknosis", "Quantitative computed tomography", "RHAG", "Radial immunodiffusion", "Radioactive iodine uptake test", "Radioallergosorbent test", "Radiobinding assay", "Radiographic testing", "Radiography", "Radioimmunoassay", "Radioisotope renography", "Radiologic", "Radionuclide angiography", "Radionuclide ventriculography", "Rapid plasma reagin", "Rare disease", "Red blood cell", "Red blood cell distribution width", "Red blood cell indices", "Reference group", "Relative risk", "Renal function", "Reptilase time", "Reticulocyte index", "Rh blood group system", "Rheumatoid arthritis", "Rheumatoid factor", "Rickettsia", "Ristocetin-induced platelet aggregation", "SEMA7A", "Sabin\u2013Feldman dye test", "Scintigraphy", "Scintimammography", "Screening (medicine)", "Screening test", "Sensitivity and specificity", "Serology", "Serum chloride", "Serum iron", "Serum osmolal gap", "Serum sodium", "Serum total protein", "Sestamibi parathyroid scintigraphy", "Sialography", "Side effects", "Sine qua non", "Single-photon emission computed tomography", "Sj\u00f6gren's syndrome", "Skeletal survey", "Skin allergy test", "Small-bowel follow-through", "Small molecule", "Sputum", "Squamous metaplasia", "Steatosis", "Stereoelectroencephalography", "Stool test", "Streptococcus", "Surgical pathology", "Symptom", "Synthetic MRI", "Syphilis", "Test panel", "Therapy", "Thermography", "Thrombin time", "Thrombodynamics test", "Thromboelastography", "Thyroid-stimulating hormone", "Thyroid function tests", "Total complement activity", "Total iron-binding capacity", "Toxoplasmosis", "Tractography", "Transaminase", "Transcranial Doppler", "Transesophageal echocardiogram", "Transferrin", "Transferrin receptor", "Transferrin saturation", "Transfusion medicine", "Transrectal ultrasonography", "Transscrotal ultrasound", "Transthoracic echocardiogram", "Troponin test", "Upper gastrointestinal series", "Urinalysis", "Urinary cast", "Urination", "Urine", "Urine anion gap", "Urine osmolality", "Urine specific gravity", "Urobilinogen", "Vectorcardiography", "Vel blood group", "Venereal Disease Research Laboratory test", "Venography", "Ventilation/perfusion scan", "Viral disease", "Virtual colonoscopy", "Von Willebrand factor", "Wassermann test", "Weil\u2013Felix test", "White blood cell", "Whole blood", "Whole body imaging", "Wound healing", "X-ray", "X-ray microtomography", "X-ray motion analysis", "X-rays", "XK (protein)", "Xg antigen system", "Yt antigen system"], "references": ["http://www.edma-ivd.be/#/About-In-Vitro-Diagnostics", "http://www.health.harvard.edu/a_to_z/electrocardiogram-ekg", "http://www.health.harvard.edu/diagnostic-tests/", "http://www.health.harvard.edu/diagnostic-tests/mediastinoscopy.htm", "http://www.health.harvard.edu/diagnostic-tests/pap-smear.htm", "http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:1998:331:0001:0037:EN:PDF", "http://www.ncbi.nlm.nih.gov/pubmed/12783911", "http://www.ncbi.nlm.nih.gov/pubmed/17709921", "http://www.ncbi.nlm.nih.gov/pubmed/3021937", "http://www.ncbi.nlm.nih.gov/pubmed/7655958", "http://www.ncbi.nlm.nih.gov/pubmed/8062543", "http://www.annals.org/content/155/8/529.abstract", "http://doi.org/10.1001%2Fjama.289.21.2810", "http://doi.org/10.1097%2F00043764-198610000-00003", "http://doi.org/10.1097%2F00043764-199502000-00016", "http://doi.org/10.1159%2F000104806", "http://doi.org/10.7326%2F0003-4819-155-8-201110180-00009", "http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-25-22423", "http://www.labtestsonline.org.uk/understanding/analytes/glucose/tab/test", "http://www.labtestsonline.org.uk/understanding/analytes/liver-panel/", "http://www.labtestsonline.org.uk/understanding/analytes/lytes", "https://www.nlm.nih.gov/cgi/mesh/2016/MB_cgi?field=uid&term=D019937", "https://www.osha.gov/SLTC/medicalsurveillance/screening.html", "https://web.archive.org/web/20070608072504/http://www.health.harvard.edu/diagnostic-tests/pap-smear.htm", "https://web.archive.org/web/20120211100230/http://www.annals.org/content/155/8/529.abstract"]}, "Statistical epidemiology": {"categories": ["All orphaned articles", "Biostatistics", "Demography", "Epidemiology", "Orphaned articles from April 2012"], "title": "Statistical epidemiology", "method": "Statistical epidemiology", "url": "https://en.wikipedia.org/wiki/Statistical_epidemiology", "summary": "Statistical epidemiology is an emerging branch of the disciplines of epidemiology and biostatistics that aims to:\n\nBring more statistical rigour to bear in the field of epidemiology\nRecognise the importance of applied statistics, especially with respect to the context in which statistical methods are appropriate and inappropriate\nAid and improve our interpretation of observations", "images": ["https://upload.wikimedia.org/wikipedia/en/6/6c/Wiki_letter_w.svg"], "links": ["American Statistical Association", "Bayesian method", "Biology", "Biostatistics", "Complex data", "Computer science", "Digital object identifier", "Economics", "Epidemiology", "Mathematics", "Observational study", "Operations research", "PubMed Identifier", "Quantitative methods", "Royal Statistical Society", "Statistical analysis", "Statistics"], "references": ["http://www.bca.edu.au/", "http://www.blackwellpublishing.com/journal.asp?ref=0006-341x", "http://edwardbetts.com/find_link?q=Statistical_epidemiology", "http://www.epidem.com", "http://www3.interscience.wiley.com/cgi-bin/jhome/2988?CRETRY=1&SRETRY=0", "http://www.ncbi.nlm.nih.gov/pubmed/14001013", "http://doi.org/10.1002/1097-0142(196304)16:4%3C510::aid-cncr2820160412%3E3.0.co;2-l", "http://aje.oxfordjournals.org/", "http://biostatistics.oxfordjournals.org/", "http://ije.oxfordjournals.org/", "http://statisticalepidemiology.org/", "http://www.tibs.org/Interior.aspx", "http://www1.ic.ac.uk/medicine/research/researchthemes/publicandint/ide/research_groups/stats/", "http://www.leeds.ac.uk/light/staff/Mark-S-Gilthorpe", "https://web.archive.org/web/20060323060012/http://www.bepress.com/ijb/"]}, "Method of simulated moments": {"categories": ["All stub articles", "Econometrics stubs", "Estimation methods"], "title": "Method of simulated moments", "method": "Method of simulated moments", "url": "https://en.wikipedia.org/wiki/Method_of_simulated_moments", "summary": "In econometrics, the method of simulated moments (MSM) (also called simulated method of moments) is a structural estimation technique introduced by Daniel McFadden. It extends the generalized method of moments to cases where theoretical moment functions cannot be evaluated directly, such as when moment functions involve high-dimensional integrals. MSM's earliest and principal applications have been to research in industrial organization, after its development by Ariel Pakes, David Pollard, and others, though applications in consumption are emerging.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170527191524%21Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170519203409%21Emoji_u1f4c8.svg"], "links": ["Ariel Pakes", "Consumption (economics)", "Daniel McFadden", "Digital object identifier", "Econometrica", "Econometrics", "Generalized method of moments", "Indirect Inference", "Industrial organization", "Integral", "JSTOR", "John Haltiwanger", "Moment function", "Structural estimation"], "references": ["http://www.econ.yale.edu/smith/palgrave7.pdf", "http://doi.org/10.3386/w13115", "http://www.jstor.org/stable/1913621"]}, "Rice distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2012", "CS1 maint: Uses authors parameter", "Continuous distributions", "Pages using deprecated image syntax", "Use dmy dates from September 2010", "Wikipedia articles needing clarification from June 2012"], "title": "Rice distribution", "method": "Rice distribution", "url": "https://en.wikipedia.org/wiki/Rice_distribution", "summary": "In probability theory, the Rice distribution, Rician distribution or Ricean distribution is the probability distribution of the magnitude of a circular bivariate normal random variable with potentially non-zero mean. It was named after Stephen O. Rice.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a3/Rice_distribution_motivation.svg", "https://upload.wikimedia.org/wikipedia/commons/4/41/Rice_distributiona_CDF.png", "https://upload.wikimedia.org/wikipedia/commons/a/a0/Rice_distributiona_PDF.png"], "links": ["ARGUS distribution", "Abramowitz and Stegun", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bessel function", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central moment", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Confluent hypergeometric function", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Estimating equations", "Euclidean norm", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Fixed point (mathematics)", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Georgios B. Giannakis", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Horn function", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Laguerre polynomials", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Marcum Q-function", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Method of maximum likelihood", "Method of moments (statistics)", "Mittag-Leffler distribution", "Mixture distribution", "Modified Bessel function of the first kind", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral chi distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normal random vector", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Raw moments", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rician fading", "Rising factorial", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Signal-to-noise ratio", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Stephen O. Rice", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://webh01.ua.ac.be/visielab/papers/sijbers/ieee98.pdf", "http://www.math.sfu.ca/~cbm/aands/page_508.htm", "http://ballistipedia.com/index.php?title=Closed_Form_Precision#How_many_sighter_shots_do_you_need.3F", "http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=14237&objectType=FILE", "http://apps.nrbook.com/bateman/Vol1.pdf", "http://www.sciencedirect.com/science/article/pii/S0022460X17301074", "http://users.ece.gatech.edu/mrichard/Rice%20power%20pdf.pdf", "http://doi.org/10.1006%2Fjmrb.1996.0166", "http://doi.org/10.1016%2Fj.ejmp.2014.05.002", "http://doi.org/10.1016%2Fj.jsv.2007.07.038", "http://doi.org/10.1121%2F1.400532", "http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/26/18877/00871398.pdf?temp=x", "http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/7693/4350290/04350297.pdf?arnumber=4350297", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=913150", "https://doi.org/10.1016/j.jmr.2006.01.016", "https://dx.doi.org/10.1109/4234.913150"]}, "Grand mean": {"categories": ["Descriptive statistics", "Means"], "title": "Grand mean", "method": "Grand mean", "url": "https://en.wikipedia.org/wiki/Grand_mean", "summary": "The grand mean is the mean of the means of several subsamples, as long as the subsamples have the same number of data points. For example, consider several lots, each containing several items. The items from each lot are sampled for a measure of some variable and the means of the measurements from each lot are computed. The mean of the measures from each lot constitutes the subsample mean. The mean of these subsample means is then the grand mean.", "images": [], "links": ["ANOVA", "Arithmetic mean", "International Standard Book Number", "Mean", "Measurement", "Pooled variance", "Sampling (statistics)", "Standard deviation", "Total sum of squares"], "references": []}, "Q-Gaussian distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from February 2012", "Continuous distributions", "Pages using deprecated image syntax", "Probability distributions with non-finite variance", "Statistical mechanics"], "title": "Q-Gaussian distribution", "method": "Q-Gaussian distribution", "url": "https://en.wikipedia.org/wiki/Q-Gaussian_distribution", "summary": "The q-Gaussian is a probability distribution arising from the maximization of the Tsallis entropy under appropriate constraints. It is one example of a Tsallis distribution. The q-Gaussian is a generalization of the Gaussian in the same way that Tsallis entropy is a generalization of standard Boltzmann\u2013Gibbs entropy or Shannon entropy. The normal distribution is recovered as q \u2192 1.\nThe q-Gaussian has been applied to problems in the fields of statistical mechanics, geology, anatomy, astronomy, economics, finance, and machine learning. The distribution is often favored for its heavy tails in comparison to the Gaussian for 1 < q < 3. For \n \n \n \n q\n <\n 1\n \n \n {\\displaystyle q<1}\n the q-Gaussian distribution is the PDF of a bounded random variable. This makes in biology and other domains the q-Gaussian distribution more suitable than Gaussian distribution to model the effect of external stochasticity. A generalized q-analog of the classical central limit theorem was proposed in 2008, in which the independence constraint for the i.i.d. variables is relaxed to an extent defined by the q parameter, with independence being recovered as q \u2192 1. However, a proof of such a theorem is still lacking.In the heavy tail regions, the distribution is equivalent to the Student's t-distribution with a direct mapping between q and the degrees of freedom. A practitioner using one of these distributions can therefore parameterize the same distribution in two different ways. The choice of the q-Gaussian form may arise if the system is non-extensive, or if there is lack of a connection to small samples sizes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/35/The_PDF_of_QGaussian.svg"], "links": ["ARGUS distribution", "Anatomy", "ArXiv", "Arcsine distribution", "Astronomy", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Box\u2013Muller transform", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compact space", "Compound Poisson distribution", "Constantino Tsallis", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Economics", "Elliptical distribution", "Entropy (information theory)", "Entropy (statistical thermodynamics)", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Finance", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geology", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heavy tails", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent and identically distributed random variables", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Machine learning", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonextensive entropy", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "PubMed Identifier", "Q-Weibull distribution", "Q-analog", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical mechanics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tsallis distribution", "Tsallis entropy", "Tsallis statistics", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "White noise", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://e1.newcastle.edu.au/coffee/pubs/wp/2007/07-10.pdf", "http://www.cbpf.br/GrupPesq/StatisticalPhys/pdftheo/UmarovTsallisSteinberg2008.pdf", "http://adsabs.harvard.edu/abs/2006PhRvL..96k0601D", "http://adsabs.harvard.edu/abs/2010JSMTE..10..023H", "http://www.cscs.umich.edu/~crshalizi/notebooks/tsallis.html", "http://www.ncbi.nlm.nih.gov/pubmed/16605807", "http://arxiv.org/abs/1008.4259", "http://doi.org/10.1007%2Fs00032-008-0087-y", "http://doi.org/10.1088%2F1742-5468%2F2010%2F10%2FP10023", "http://doi.org/10.1103%2FPhysRevLett.96.110601", "http://discovery.ucl.ac.uk/142750/1/142750.pdf"]}, "Ewens's sampling formula": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from August 2011", "Discrete distributions", "Population genetics", "Theory of probability distributions"], "title": "Ewens's sampling formula", "method": "Ewens's sampling formula", "url": "https://en.wikipedia.org/wiki/Ewens%27s_sampling_formula", "summary": "In population genetics, Ewens's sampling formula, describes the probabilities associated with counts of how many different alleles are observed a given number of times in the sample.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["ARGUS distribution", "Allele", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biomathematics", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Chinese restaurant process", "Circular distribution", "Circular uniform distribution", "Coalescent theory", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamete", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Gene", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Genetic drift", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Infinite-alleles model", "Integer partition", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Locus (genetics)", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Mutation", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Population genetics", "Population mutation rate", "Probabilities", "Probability", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random permutation", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Sample (statistics)", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Unified neutral theory of biodiversity", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Warren Ewens", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["https://www.researchgate.net/publication/280311472_The_Ubiquitous_Ewens_Sampling_Formula"]}, "Data dredging": {"categories": ["All articles needing additional references", "Articles needing additional references from October 2016", "Bias", "Cognitive biases", "Data mining", "Design of experiments", "Misuse of statistics", "Statistical hypothesis testing"], "title": "Data dredging", "method": "Data dredging", "url": "https://en.wikipedia.org/wiki/Data_dredging", "summary": "Data dredging (also data fishing, data snooping, data butchery, and p-hacking) is the misuse of data analysis to find patterns in data that can be presented as statistically significant when in fact there is no real underlying effect. This is done by performing many statistical tests on the data and only paying attention to those that come back with significant results, instead of stating a single hypothesis about an underlying effect before the analysis and then conducting a single test for it.\nThe process of data dredging involves automatically testing huge numbers of hypotheses about a single data set by exhaustively searching\u2014perhaps for combinations of variables that might show a correlation, and perhaps for groups of cases or observations that show differences in their mean or in their breakdown by some other variable.\nConventional tests of statistical significance are based on the probability that a particular result would arise if chance alone were at work, and necessarily accept some risk of mistaken conclusions of a certain type (mistaken rejections of the null hypothesis). This level of risk is called the significance. When large numbers of tests are performed, some produce false results of this type, hence 5% of randomly chosen hypotheses turn out to be significant at the 5% level, 1% turn out to be significant at the 1% significance level, and so on, by chance alone. When enough hypotheses are tested, it is virtually certain that some will be statistically significant but misleading, since almost every data set with any degree of randomness is likely to contain (for example) some spurious correlations. If they are not cautious, researchers using data mining techniques can be easily misled by these results.\nThe multiple comparisons hazard is common in data dredging. Moreover, subgroups are sometimes explored without alerting the reader to the number of questions at issue, which can lead to misinformed conclusions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0c/Spurious_correlations_-_spelling_bee_spiders.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abacavir", "Aliasing", "Base rate fallacy", "Bias", "Bible code", "Bonferroni correction", "Bonferroni inequalities", "Cancer cluster", "Cherry picking", "Coin throw", "Correlation", "Covariate", "Cross-validation (statistics)", "Data analysis", "Data set", "Demographic data", "Digital object identifier", "European Journal of Personality", "Exhaustive search", "Exploratory data analysis", "False discovery rate", "Frequency probability", "George Davey Smith", "HARKing", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "John P. A. Ioannidis", "Lincoln\u2013Kennedy coincidences urban legend", "Linear regression", "Look-elsewhere effect", "Mean square error", "Meteorology", "Misuse of statistics", "Multiple comparisons", "Nature Human Behaviour", "Neuroskeptic", "Null hypothesis", "Observational study", "Open science", "Out-of-sample test", "Overfitting", "P-value", "PLoS Medicine", "Pareidolia", "Post hoc analysis", "Predictive analytics", "Predictive modelling", "Predictive power", "PubMed Central", "PubMed Identifier", "Publication bias", "Randomized", "Registered report", "Reproducibility", "Scheff\u00e9 test", "Significance test", "Skeptical Inquirer", "Statistical hypothesis testing", "Statistical population", "Statistical significance", "Statistical test", "Stepwise regression", "Testing hypotheses suggested by the data", "Texas sharpshooter fallacy", "Tukey range test", "YouTube"], "references": ["http://data-snooping.martinsewell.com/", "http://www.tylervigen.com/spurious-correlations", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1124898", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182327", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4359000", "http://www.ncbi.nlm.nih.gov/pubmed/12493654", "http://www.ncbi.nlm.nih.gov/pubmed/16060722", "http://www.ncbi.nlm.nih.gov/pubmed/25768323", "http://doi.org/10.1007%2Fs10940-009-9077-7", "http://doi.org/10.1038%2Fs41562-016-0034", "http://doi.org/10.1080%2F00031305.1966.10480401", "http://doi.org/10.1111%2Fj.1740-9713.2011.00506.x", "http://doi.org/10.1136%2Fbmj.325.7378.1437", "http://doi.org/10.1371%2Fjournal.pbio.1002106", "http://doi.org/10.1371%2Fjournal.pmed.0020124", "http://www.jstor.org/stable/2681493", "http://www.niss.org/sites/default/files/Young%20Karr%20Obs%20Study%20Problem.pdf", "http://www.plosmedicine.org/article/info:doi%2F10.1371%2Fjournal.pmed.0020124", "http://www.worldcat.org/issn/1549-1277", "https://www.ejp-blog.com/blog/2017/2/3/streamlined-review-and-registered-reports-coming-soon", "https://www.youtube.com/watch?v=A0vEGuOMTyA", "https://www.youtube.com/watch?v=UFhJefdVCjE", "https://www.nimh.nih.gov/about/directors/thomas-insel/blog/2014/p-hacking.shtml", "https://books.google.co.nz/books?id=B-EoDwAAQBAJ", "https://web.archive.org/web/20180805142806/https://www.csicop.org/specialarticles/show/p-hacker_confessions_daryl_bem_and_me"]}, "Tikhonov regularization": {"categories": ["Estimation methods", "Inverse problems", "Linear algebra", "Pages using citations with accessdate and no URL"], "title": "Tikhonov regularization", "method": "Tikhonov regularization", "url": "https://en.wikipedia.org/wiki/Tikhonov_regularization", "summary": "Tikhonov regularization, named for Andrey Tikhonov, is the most commonly used method of regularization of ill-posed problems. In statistics, the method is known as ridge regression, in machine learning it is known as weight decay, and with multiple independent discoveries, it is also variously known as the Tikhonov\u2013Miller method, the Phillips\u2013Twomey method, the constrained linear inversion method, and the method of linear regularization. It is related to the Levenberg\u2013Marquardt algorithm for non-linear least-squares problems.\nSuppose that for a known matrix \n \n \n \n A\n \n \n {\\displaystyle A}\n and vector \n \n \n \n \n b\n \n \n \n {\\displaystyle \\mathbf {b} }\n , we wish to find a vector \n \n \n \n \n x\n \n \n \n {\\displaystyle \\mathbf {x} }\n such that\n\n \n \n \n A\n \n x\n \n =\n \n b\n \n .\n \n \n {\\displaystyle A\\mathbf {x} =\\mathbf {b} .}\n The standard approach is ordinary least squares linear regression. However, if no \n \n \n \n \n x\n \n \n \n {\\displaystyle \\mathbf {x} }\n satisfies the equation or more than one \n \n \n \n \n x\n \n \n \n {\\displaystyle \\mathbf {x} }\n does\u2014that is, the solution is not unique\u2014the problem is said to be ill posed. In such cases, ordinary least squares estimation leads to an overdetermined (over-fitted), or more often an underdetermined (under-fitted) system of equations. Most real-world phenomena have the effect of low-pass filters in the forward direction where \n \n \n \n A\n \n \n {\\displaystyle A}\n maps \n \n \n \n \n x\n \n \n \n {\\displaystyle \\mathbf {x} }\n to \n \n \n \n \n b\n \n \n \n {\\displaystyle \\mathbf {b} }\n . Therefore, in solving the inverse-problem, the inverse mapping operates as a high-pass filter that has the undesirable tendency of amplifying noise (eigenvalues / singular values are largest in the reverse mapping where they were smallest in the forward mapping). In addition, ordinary least squares implicitly nullifies every element of the reconstructed version of \n \n \n \n \n x\n \n \n \n {\\displaystyle \\mathbf {x} }\n that is in the null-space of \n \n \n \n A\n \n \n {\\displaystyle A}\n , rather than allowing for a model to be used as a prior for \n \n \n \n \n x\n \n \n \n {\\displaystyle \\mathbf {x} }\n .\nOrdinary least squares seeks to minimize the sum of squared residuals, which can be compactly written as\n\n \n \n \n \u2016\n A\n \n x\n \n \u2212\n \n b\n \n \n \u2016\n \n 2\n \n \n 2\n \n \n ,\n \n \n {\\displaystyle \\|A\\mathbf {x} -\\mathbf {b} \\|_{2}^{2},}\n where \n \n \n \n \u2016\n \u22c5\n \n \u2016\n \n 2\n \n \n \n \n {\\displaystyle \\|\\cdot \\|_{2}}\n is the Euclidean norm.\nIn order to give preference to a particular solution with desirable properties, a regularization term can be included in this minimization:\n\n \n \n \n \u2016\n A\n \n x\n \n \u2212\n \n b\n \n \n \u2016\n \n 2\n \n \n 2\n \n \n +\n \u2016\n \u0393\n \n x\n \n \n \u2016\n \n 2\n \n \n 2\n \n \n \n \n {\\displaystyle \\|A\\mathbf {x} -\\mathbf {b} \\|_{2}^{2}+\\|\\Gamma \\mathbf {x} \\|_{2}^{2}}\n for some suitably chosen Tikhonov matrix \n \n \n \n \u0393\n \n \n {\\displaystyle \\Gamma }\n . In many cases, this matrix is chosen as a multiple of the identity matrix (\n \n \n \n \u0393\n =\n \u03b1\n I\n \n \n {\\displaystyle \\Gamma =\\alpha I}\n ), giving preference to solutions with smaller norms; this is known as L2 regularization. In other cases, high-pass operators (e.g., a difference operator or a weighted Fourier operator) may be used to enforce smoothness if the underlying vector is believed to be mostly continuous.\nThis regularization improves the conditioning of the problem, thus enabling a direct numerical solution. An explicit solution, denoted by \n \n \n \n \n \n \n x\n ^\n \n \n \n \n \n {\\displaystyle {\\hat {x}}}\n , is given by\n\n \n \n \n \n \n \n x\n ^\n \n \n \n =\n (\n \n A\n \n \u22a4\n \n \n A\n +\n \n \u0393\n \n \u22a4\n \n \n \u0393\n \n )\n \n \u2212\n 1\n \n \n \n A\n \n \u22a4\n \n \n \n b\n \n .\n \n \n {\\displaystyle {\\hat {x}}=(A^{\\top }A+\\Gamma ^{\\top }\\Gamma )^{-1}A^{\\top }\\mathbf {b} .}\n The effect of regularization may be varied by the scale of matrix \n \n \n \n \u0393\n \n \n {\\displaystyle \\Gamma }\n . For \n \n \n \n \u0393\n =\n 0\n \n \n {\\displaystyle \\Gamma =0}\n this reduces to the unregularized least-squares solution, provided that (ATA)\u22121 exists.\nL2 regularization is used in many contexts aside from linear regression, such as classification with logistic regression or support vector machines, and matrix factorization.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Andrew Ng", "Andrey Nikolayevich Tikhonov", "Arthur E. Hoerl", "Bayes' theorem", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bias of an estimator", "Cholesky factorization", "Compact operator", "Condition number", "Covariance matrix", "Cross-validation (statistics)", "Difference operator", "Digital object identifier", "Discrepancy principle", "Discrete choice", "Discrete fourier transform", "Doklady Akademii Nauk SSSR", "Effective number of degrees of freedom", "Eigenvalues", "Errors-in-variables models", "Errors and residuals in statistics", "Expected value", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Generalized singular-value decomposition", "Goodness of fit", "Grace Wahba", "Hermitian adjoint", "High-pass filter", "Hilbert space", "Homoscedasticity", "Identity matrix", "Ill-posed problem", "Integral equation", "International Conference on Machine Learning", "International Standard Book Number", "Inverse problem", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Journal of Machine Learning Research", "Kriging", "L-curve method", "Lasso (statistics)", "Least-angle regression", "Least absolute deviations", "Least squares", "Levenberg\u2013Marquardt algorithm", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Low-pass filters", "Machine learning", "Mahalanobis distance", "Matrix regularization", "Maximum a posteriori", "Mean and predicted response", "Minimum mean square error", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate normal distribution", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonnegative matrix factorization", "Nonparametric regression", "Norm (mathematics)", "Normal distribution", "Ordered logit", "Ordered probit", "Ordinary least squares", "Over-fitted", "Overdetermined system", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Prior probability", "Probit model", "Quantile regression", "Random effects model", "Rank (linear algebra)", "Regression analysis", "Regression model validation", "Regularization (mathematics)", "Regularized least squares", "Residual (numerical analysis)", "Residual sum of squares", "Restricted maximum likelihood", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Singular-value decomposition", "Standard deviation", "Statistical classification", "Statistical independence", "Statistics", "Studentized residual", "Support vector machine", "Takeshi Amemiya", "Total least squares", "Unbiased predictive risk estimator", "Under-fitted", "Underdetermined system", "Weighted least squares", "Well-posed problem", "Whitening transformation", "Wiener filter"], "references": ["http://apps.nrbook.com/empanel/index.html#pg=1006", "http://www.stat.wisc.edu/~wahba/ftp1/oldie/golub.heath.wahba.pdf", "http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/SIAM/index.html", "http://doi.org/10.1080%2F00401706.1979.10489751", "http://doi.org/10.1137%2F0109031", "http://doi.org/10.1145%2F321105.321114", "http://doi.org/10.2307%2F1267351", "http://www.jstor.org/stable/1271436", "http://a-server.math.nsc.ru/IPP/BASE_WORK/tihon_en.html", "https://icml.cc/Conferences/2004/proceedings/papers/354.pdf", "https://www.springer.com/us/book/9780792335832", "https://www.springer.com/us/book/9789401751698"]}, "Seismic to simulation": {"categories": ["Economic geology", "Geology software", "Geophysics", "Geostatistics", "Petroleum geology", "Scientific modeling", "Seismology"], "title": "Reservoir modeling", "method": "Seismic to simulation", "url": "https://en.wikipedia.org/wiki/Reservoir_modeling", "summary": "In the oil and gas industry, reservoir modeling involves the construction of a computer model of a petroleum reservoir, for the purposes of improving estimation of reserves and making decisions regarding the development of the field, predicting future production, placing additional wells, and evaluating alternative reservoir management scenarios. \nA reservoir model represents the physical space of the reservoir by an array of discrete cells, delineated by a grid which may be regular or irregular. The array of cells is usually three-dimensional, although 1D and 2D models are sometimes used. Values for attributes such as porosity, permeability and water saturation are associated with each cell. The value of each attribute is implicitly deemed to apply uniformly throughout the volume of the reservoir represented by the cell.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/84/Contour_map_software_screen_snapshot_of_isopach_map_for_8500ft_deep_OIL_reservoir_with_a_Fault_line.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["1967 Oil Embargo", "1973 oil crisis", "1979 energy crisis", "1980s oil glut", "1990 oil price shock", "2000s energy crisis", "2010s oil glut", "Abu Dhabi National Oil Company", "Acoustic impedance", "Algorithm", "Amec Foster Wheeler", "Anadarko Petroleum", "Apache Corporation", "Argus Sour Crude Index", "Artificial lift", "BG Group", "BP", "Baker Hughes", "Bayesian inference", "Benchmark (crude oil)", "Big Oil", "Blowout (well drilling)", "Bonny Light oil", "Brent Crude", "CGG (company)", "CH2M Hill", "Cameron International", "Caspian Sea", "Cenovus Energy", "Chevron Corporation", "Chicago Bridge & Iron Company", "China National Offshore Oil Corporation", "China National Petroleum Corporation", "China Oilfield Services", "Christmas tree (oil well)", "Compa\u00f1\u00eda Espa\u00f1ola de Petr\u00f3leos", "Completion (oil and gas wells)", "Computer model", "Computer simulation", "ConocoPhillips", "Contour map", "Core sample", "Corner-point grid", "Devon Energy", "Differential sticking", "Directional drilling", "Downstream (petroleum industry)", "Drill stem test", "Drilling engineering", "Drilling fluid", "Drilling fluid invasion", "Dubai Crude", "East Midlands Oil Province", "East Texas Oil Field", "Ecopetrol", "Elastic modulus", "Enbridge", "Energy trading", "Enhanced oil recovery", "Eni", "Ensco plc", "Equinor", "Erath, Louisiana", "Exploration geophysics", "Extraction of petroleum", "ExxonMobil", "Fault line", "Finite difference methods", "Fredrik Ljungstr\u00f6m", "GE Energy", "Galp Energia", "Gas Exporting Countries Forum", "Gas lift", "Gas reinjection", "Gasoline and diesel usage and pricing", "Gazprom", "Geologic modelling", "Geologist", "Geophysicist", "Geostatistics", "Geosteering", "Glencore", "Grupa Lotos", "Gulf of Mexico", "Gunvor (company)", "Halliburton", "Heavy crude oil", "Hess Corporation", "Histogram", "History of the petroleum industry", "Husky Energy", "Hydrocarbon exploration", "Imperial Oil", "Indian Basket", "Indian Oil Corporation", "Indonesian Crude Price", "Integrated asset modelling", "International Association of Oil & Gas Producers", "International Energy Agency", "International Petroleum Exchange", "International Standard Book Number", "Iraq National Oil Company", "Isthmus-34 Light", "JXTG Holdings", "Japan Crude Cocktail", "KazMunayGas", "Kuwait Petroleum Corporation", "List of acronyms in oil and gas exploration and production", "List of countries by natural gas consumption", "List of countries by natural gas exports", "List of countries by natural gas imports", "List of countries by natural gas production", "List of countries by natural gas proven reserves", "List of countries by oil consumption", "List of countries by oil exports", "List of countries by oil imports", "List of countries by oil production", "List of countries by proven oil reserves", "List of natural gas fields", "List of oil exploration and production companies", "List of oil fields", "List of oilfield service companies", "Lithology", "Lost circulation", "Lukoil", "Marathon Oil", "Markov chain Monte Carlo", "Measurement while drilling", "Mercuria Energy Group", "Midstream", "Mitigation of peak oil", "Nabors Industries", "Naftiran Intertrade", "National Iranian Oil Company", "National Iranian South Oil Company", "National Oilwell Varco", "National oil company", "Nationalization of oil supplies", "Natural gas prices", "Niger Delta", "Nigerian National Petroleum Corporation", "North Sea oil", "OMV", "OPEC", "OPEC Reference Basket", "Occidental Petroleum", "Oil and Gas Development Company", "Oil and Natural Gas Corporation", "Oil refinery", "Oil reserves", "Oil reserves in Russia", "Oil reserves in Venezuela", "Oil reservoir", "Oil sands", "Oil shale", "Oil shale gas", "Oil well", "PDVSA", "PKN Orlen", "PTT Public Company Limited", "Peak oil", "Pemex", "Permeability (earth sciences)", "Permian Basin (North America)", "Persian Gulf", "Pertamina", "PetroChina", "Petrobangla", "Petrobras", "Petrocurrency", "Petrodollar recycling", "Petrofac", "Petroleum", "Petroleum engineering", "Petroleum fiscal regime", "Petroleum geology", "Petroleum industry", "Petroleum industry in Iraq", "Petroleum licensing", "Petroleum product", "Petroleum reservoir", "Petronas", "Petrophysics", "Petrovietnam", "Pipeline transport", "Porosity", "Port Harcourt Refining Company", "Posted price", "Predicting the timing of peak oil", "Price of oil", "Primary energy", "Probability distribution function", "Production planning", "Production sharing agreement", "Prudhoe Bay Oil Field", "Pumpjack", "Qatar Petroleum", "Realization (probability)", "Reflection seismology", "Refraction", "Reliance Industries", "Repsol", "Reservoir engineering", "Reservoir petrophysics", "Reservoir simulation", "Reservoir simulator", "Rise in Core", "Rosneft", "Royal Dutch Shell", "SOCAR", "Saipem", "Saudi Aramco", "Schlumberger", "Seismic grid", "Seismic inversion", "Seismic source", "Seismic to simulation", "Seven Sisters (oil companies)", "Shale band", "Shale gas", "Shale oil extraction", "Sinopec", "Snam", "Society of Petroleum Engineers", "Sonangol Group", "Sonatrach", "Sonic logging", "Squeeze job", "Standard Oil", "Steam injection (oil industry)", "Stratigraphy", "Submersible pump", "Subsea 7", "Suncor Energy", "Surgutneftegas", "Swing producer", "TNK-BP", "Tapis crude", "Total S.A.", "Tracer use in the oil industry", "Trafigura", "TransCanada Corporation", "Transocean", "Tullow Oil", "T\u00fcpra\u015f", "T\u00fcrkiye Petrolleri Anonim Ortakl\u0131\u011f\u0131", "Unconventional oil", "Underbalanced drilling", "Upstream (petroleum industry)", "Urals oil", "Variogram", "Vermilion Parish", "Vitol", "Water content", "Water injection (oil production)", "Water saturation", "Weatherford International", "Well intervention", "Well logging", "West Texas Intermediate", "Western Canadian Sedimentary Basin", "Western Canadian Select", "Wood Group", "World Petroleum Council", "YPF"], "references": ["http://www.estdco.com"]}, "Information theory": {"categories": ["Cybernetics", "Formal sciences", "Information Age", "Information theory", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Information theory", "method": "Information theory", "url": "https://en.wikipedia.org/wiki/Information_theory", "summary": "Information theory studies the quantification, storage, and communication of information. It was originally proposed by Claude E. Shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper entitled \"A Mathematical Theory of Communication\". Applications of fundamental topics of information theory include lossless data compression (e.g. ZIP files), lossy data compression (e.g. MP3s and JPEGs), and channel coding (e.g. for digital subscriber line (DSL)). Its impact has been crucial to the success of the Voyager missions to deep space, the invention of the compact disc, the feasibility of mobile phones, the development of the Internet, the study of linguistics and of human perception, the understanding of black holes, and numerous other fields.\nA key measure in information theory is \"entropy\". Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a die (with six equally likely outcomes). Some other important measures in information theory are mutual information, channel capacity, error exponents, and relative entropy.\nThe field is at the intersection of mathematics, statistics, computer science, physics, neurobiology, information engineering, and electrical engineering. The theory has also found applications in other areas, including statistical inference, natural language processing, cryptography, neurobiology, human vision, the evolution and function of molecular codes (bioinformatics), model selection in statistics, thermal physics, quantum computing, linguistics, plagiarism detection, pattern recognition, and anomaly detection. Important sub-fields of information theory include source coding, channel coding, algorithmic complexity theory, algorithmic information theory, information-theoretic security, and measures of information.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/22/Binary_entropy_plot.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b6/Binary_erasure_channel.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b5/Binary_symmetric_channel.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5a/CDSCRATCHES.jpg", "https://upload.wikimedia.org/wikipedia/commons/c/c7/Channel_model.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/89/Symbol_book_class2.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/5/5c/Symbol_template_class.svg"], "links": ["A-law algorithm", "ACM Computing Classification System", "A Mathematical Theory of Communication", "Abstract algebra", "Active networking", "Adaptive Huffman coding", "Adaptive differential pulse-code modulation", "Adaptive system", "Alan Turing", "Alexander Lerner", "Alfred Radcliffe-Brown", "Algebra", "Algebraic code-excited linear prediction", "Algebraic geometry", "Algorithm", "Algorithm design", "Algorithmic complexity theory", "Algorithmic efficiency", "Algorithmic information theory", "Algorithmic probability", "Allenna Leonard", "Analysis of algorithms", "Analytic geometry", "Andrey Kolmogorov", "Anomaly detection", "Anthony Wilden", "Anticipatory system", "Application security", "Applied mathematics", "ArXiv", "Areas of mathematics", "Arithmetic", "Arithmetic coding", "Artificial intelligence", "Asymmetric numeral systems", "Audio codec", "Automata theory", "Automated planning and scheduling", "Average bitrate", "Ban (unit)", "Bayesian inference", "Bell Labs", "Bell System Technical Journal", "Bernoulli trial", "Bibcode", "Binary entropy function", "Binary erasure channel", "Binary logarithm", "Binary symmetric channel", "Biocybernetics", "Bioinformatics", "Biomedical cybernetics", "Biorobotics", "Biosemiotics", "Bit", "Bit rate", "Black hole", "Black hole information paradox", "Block cipher", "Boltzmann's constant", "Brain\u2013computer interface", "Broadcast channel", "Brotli", "Brute force attack", "Buckminster Fuller", "Burrows\u2013Wheeler transform", "Byte", "Byte pair encoding", "Calculus", "Canonical Huffman code", "Catastrophe theory", "Category theory", "Chain code", "Channel capacity", "Channel code", "Channel coding", "Charles Fran\u00e7ois (systems scientist)", "Chess", "Chroma subsampling", "Cipher", "Ciphertext", "Claude Bernard", "Claude E. 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C. 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Brown", "Grammatical Man", "Graph theory", "Graphics processing unit", "Green computing", "Gregory Bateson", "Hamming distance", "Hardware acceleration", "Harry Nyquist", "Hartley (unit)", "Health informatics", "Heinz von Foerster", "History of information theory", "History of mathematics", "Homeostasis", "Hubert Yockey", "Huffman coding", "Human\u2013computer interaction", "Humberto Maturana", "Igor Aleksander", "Image compression", "Image resolution", "Independent and identically distributed", "Independent identically distributed random variables", "Inductive probability", "Info-metrics", "Informatics (academic field)", "Information", "Information-theoretic security", "Information algebra", "Information asymmetry", "Information engineering (field)", "Information entropy", "Information field theory", "Information geometry", "Information retrieval", "Information science", "Information security", "Information system", "Information theoretic security", "Information theory and measure theory", "Integrated Authority File", "Integrated circuit", "Integrated development environment", "Intelligence (information gathering)", "Interaction design", "Interlaced video", "International Standard Book Number", "International Standard Serial Number", "Internet", "Interpreter (computing)", "Intrusion detection system", "J. Willard Gibbs", "JPEG", "Jacque Fresco", "Jakob von Uexk\u00fcll", "James Gleick", "Jason Jixuan Hu", "Jay Wright Forrester", "Jennifer Wilby", "John N. Warfield", "Joint entropy", "Karhunen\u2013Lo\u00e8ve theorem", "Kevin Warwick", "Key (cryptography)", "Knowledge representation and reasoning", "Kolmogorov complexity", "Kullback\u2013Leibler divergence", "LZ4 (compression algorithm)", "LZ77 and LZ78", "LZFSE", "LZJB", "LZRW", "LZWL", "LZX (algorithm)", "Lapped transform", "Latency (audio)", "Lempel\u2013Ziv\u2013Markov chain algorithm", "Lempel\u2013Ziv\u2013Oberhumer", "Lempel\u2013Ziv\u2013Stac", "Lempel\u2013Ziv\u2013Storer\u2013Szymanski", "Lempel\u2013Ziv\u2013Welch", "Levenshtein coding", "Library (computing)", "Library of Congress Control Number", "Likelihood-ratio test", "Line spectral pairs", "Linear algebra", "Linear predictive coding", "Linguistics", "List of important publications in theoretical computer science", "List of unsolved problems in information theory", "Lists of mathematics topics", "Log area ratio", "Logic in computer science", "Logic of information", "Lossless compression", "Lossless data compression", "Lossy compression", "Lossy data compression", "Ludwig Boltzmann", "Ludwig von Bertalanffy", "MP3", "Machine learning", "Macroblock", "Maleyka Abbaszadeh", "Management cybernetics", "Manfred Clynes", "Margaret Mead", "Marian Mazur", "Mathematical analysis", "Mathematical logic", "Mathematical optimization", "Mathematical physics", "Mathematical software", "Mathematical statistics", "Mathematics", "Mathematics and art", "Mathematics education", "Medical cybernetics", "Metric (mathematics)", "Michiel Hazewinkel", "Middleware", "Min-entropy", "Minimum description length", "Minimum message length", "Mixed reality", "Mobile phone", "Model of computation", "Model selection", "Modeling language", "Modified Huffman coding", "Modified discrete cosine transform", "Motion compensation", "Move-to-front transform", "Multi-task learning", "Multilinear algebra", "Multimedia database", "Multinomial distribution", "Multiprocessing", "Multithreading (computer architecture)", "Musical composition", "Mutual information", "N. Katherine Hayles", "Nat (unit)", "Natalia Bekhtereva", "National Diet Library", "Natural language processing", "Natural logarithm", "Network architecture", "Network coding", "Network information theory", "Network performance", "Network protocol", "Network scheduler", "Network security", "Network service", "Networking hardware", "Neurobiology", "Niklas Luhmann", "Noisy-channel coding theorem", "Norbert Wiener", "Noth, Winfried", "Number theory", "Numerical analysis", "Nyquist\u2013Shannon sampling theorem", "One-time pad", "Open-source software", "Operating system", "Operations research", "Order theory", "Outline of mathematics", "PAQ", "Parallel computing", "Pattern recognition", "Peak signal-to-noise ratio", "Pearson's chi-squared test", "Peripheral", "Petro Grigorenko", "Philosophy of artificial intelligence", "Philosophy of information", "Philosophy of mathematics", "Photo manipulation", "Physics", "Pixel", "Plagiarism detection", "Plaintext", "Pointwise mutual information", "Posterior probability", "Prediction by partial matching", "Printed circuit board", "Prior probability", "Probability", "Probability distribution", "Probability mass function", "Probability theory", "Process control", "Programming language", "Programming language theory", "Programming paradigm", "Programming team", "Programming tool", "Pseudorandom number generator", "Psychoacoustics", "PubMed Identifier", "Public-key cryptography", "Pure mathematics", "Pyramid (image processing)", "Qian Xuesen", "Quantification (science)", "Quantities of information", "Quantization (image processing)", "Quantization (signal processing)", "Quantum computing", "Quantum information science", "Ralph Hartley", "Random process", "Random seed", "Random variable", "Randomized algorithm", "Range encoding", "Ranulph Glanville", "Rate\u2013distortion theory", "Real-time computing", "Receiver (information theory)", "Recreational mathematics", "Redundancy (information theory)", "Reflection seismology", "Reinforcement learning", "Relative entropy", "Relay channel", "Rendering (computer graphics)", "Requirements analysis", "Reza, F", "Robert K. Logan", "Robert McEliece", "Robert Trappl", "Rolf Landauer", "Rubric (academic)", "Run-length encoding", "R\u00e9nyi entropy", "Sampling (signal processing)", "Second-order cybernetics", "Security service (telecommunication)", "Self-information", "Semantics (computer science)", "Semiotic information theory", "Semiotics", "Sequence of symbols", "Sergei P. Kurdyumov", "Set partitioning in hierarchical trees", "Set theory", "Shannon (unit)", "Shannon coding", "Shannon\u2013Fano coding", "Shannon\u2013Fano\u2013Elias coding", "Shannon\u2013Hartley law", "Shannon\u2013Hartley theorem", "Signal (electrical engineering)", "Signal noise", "Signal processing", "Snappy (compression)", "Social computing", "Social software", "Sociocybernetics", "Software configuration management", "Software construction", "Software deployment", "Software design", "Software development", "Software development process", "Software framework", "Software maintenance", "Software quality", "Software repository", "Solid modeling", "Sound quality", "Source coding", "Source coding theorem", "Speech coding", "Stafford Beer", "Standard test image", "Stationary process", "Statistical independence", "Statistical inference", "Statistics", "Stochastic process", "Stuart Kauffman", "Stuart Umpleby", "Sub-band coding", "Subjectivity", "Supervised learning", "Surprisal", "Symmetric-key algorithm", "Symmetric function", "Synergetics (Haken)", "System on a chip", "Systems science", "Talcott Parsons", "Telecommunication", "The Chinese University of Hong Kong", "The Information: A History, a Theory, a Flood", "Theory of computation", "Thermal physics", "Thermodynamics", "Thomas M. Cover", "Timeline of information theory", "Topology", "Triangle inequality", "Trigonometry", "Tunstall coding", "Turing", "Ubiquitous computing", "Ulla Mitzdorf", "Ultra", "Umberto Eco", "Unary coding", "Unicity distance", "Units of measurement", "Universal code (data compression)", "University of Illinois Press", "Unsupervised learning", "Urbana, Illinois", "Valentin Turchin", "Valentino Braitenberg", "Variable bitrate", "Variety (cybernetics)", "Venona project", "Very Large Scale Integration", "Victory in Europe Day", "Video", "Video codec", "Video compression picture types", "Video games", "Video quality", "Virtual machine", "Virtual reality", "Visualization (computer graphics)", "Voyager program", "W. Ross Ashby", "Walter Bradford Cannon", "Walter Pitts", "Warped linear predictive coding", "Warren Sturgis McCulloch", "Warren Weaver", "Wavelet transform", "Wiley-Interscience", "William Grey Walter", "Word processor", "World Wide Web", "ZIP (file format)", "Zstandard", "\u039c-law algorithm"], "references": ["http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html", "http://betbubbles.com/wp-content/uploads/2017/07/kelly.pdf", "http://www.dotrose.com/etext/90_Miscellaneous/transmission_of_information_1928b.pdf", "http://www.research.ibm.com/journal/rd/441/landauerii.pdf", "http://sciamdigital.com/index.cfm?fa=Products.ViewIssuePreview&ARTICLEID_CHAR=08B64096-0772-4904-9D48227D5C9FAC75", "http://adsabs.harvard.edu/abs/1957PhRv..106..620J", "http://adsabs.harvard.edu/abs/2001Sci...294.2310H", "http://adsabs.harvard.edu/abs/2003SciAm.288f..76B", "http://adsabs.harvard.edu/abs/2016NatSR...636038D", "http://alum.mit.edu/www/toms/", "http://jchemed.chem.wisc.edu/Journal/Issues/1999/Oct/abs1385.html", "http://bayes.wustl.edu/", "http://lccn.loc.gov/49-11922", "http://www.ncbi.nlm.nih.gov/pubmed/12764940", "http://iest2.ie.cuhk.edu.hk/~whyeung/book/", "http://iest2.ie.cuhk.edu.hk/~whyeung/book2/", "http://www.inc.cuhk.edu.hk/InformationTheory/index.html", "http://aicanderson2.home.comcast.net/~aicanderson2/home.pdf", "http://arxiv.org/abs/1111.6857", "http://arxiv.org/archive/cs.IT", "http://doi.org/10.1016%2Fs0378-1119(98)00269-8", "http://doi.org/10.1038%2Fscientificamerican0603-76", "http://doi.org/10.1038%2Fsrep36038", "http://doi.org/10.1103%2Fphysrev.106.620", "http://doi.org/10.1126%2Fscience.1065889", "http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=615478", "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6773024", "http://www.itsoc.org/", "http://monoskop.org/images/b/be/Shannon_Claude_E_Weaver_Warren_The_Mathematical_Theory_of_Communication_1963.pdf", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Information+theory", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Information+theory&library=0CHOOSE0", "http://www.worldcat.org/issn/2045-2322", "http://www.inference.phy.cam.ac.uk/mackay/itila/book.html", "http://jim-stone.staff.shef.ac.uk/BookInfoTheory/InfoTheoryBookMain.html", "https://books.google.com/books?id=RtzpRAiX6OgC&pg=PA8&dq=intitle:%22An+Introduction+to+Information+Theory%22++%22entropy+of+a+simple+source%22", "https://books.google.com/books?id=aqQ2Ry6spu0C&pg=PA56&dq=entropy-rate+conditional#PPA57,M1", "https://books.google.com/books?id=ngZhvUfF0UIC&pg=PA16&dq=intitle:information+intitle:theory+inauthor:ash+conditional+uncertainty", "https://www.nature.com/articles/srep36038", "https://www.springer.com/computer/image+processing/book/978-1-84882-296-2", "https://d-nb.info/gnd/4026927-9", "https://id.ndl.go.jp/auth/ndlna/00575012", "https://web.archive.org/web/20110723045720/http://aicanderson2.home.comcast.net/~aicanderson2/home.pdf", "https://www.encyclopediaofmath.org/index.php?title=p/i051040", "https://www.itsoc.org/resources/surveys", "https://www.wikidata.org/wiki/Q131222"]}, "Self-selection bias": {"categories": ["Bias", "Design of experiments", "Sampling (statistics)"], "title": "Self-selection bias", "method": "Self-selection bias", "url": "https://en.wikipedia.org/wiki/Self-selection_bias", "summary": "In statistics, self-selection bias arises in any situation in which individuals select themselves into a group, causing a biased sample with nonprobability sampling. It is commonly used to describe situations where the characteristics of the people which cause them to select themselves in the group create abnormal or undesirable conditions in the group. It is closely related to the non-response bias, describing when the group of people responding has different responses than the group of people not responding.\nSelf-selection bias is a major problem in research in sociology, psychology, economics and many other social sciences. In such fields, a poll suffering from such bias is termed a self-selected listener opinion poll or \"SLOP\".\nThe term is also used in criminology to describe the process by which specific predispositions may lead an offender to choose a criminal career and lifestyle.\nWhile the effects of self-selection bias are closely related to those of selection bias, the problem arises for rather different reasons; thus there may be a purposeful intent on the part of respondents leading to self-selection bias whereas other types of selection bias may arise more inadvertently, possibly as the result of mistakes by those designing any given study.", "images": [], "links": ["Academic bias", "Accidental sampling", "Acquiescence bias", "Anchoring", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "Belief bias", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Biased sample", "Causation (sociology)", "Choice-supportive bias", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Confirmation bias", "Congruence bias", "Criminology", "Cultural bias", "Debiasing", "Digital object identifier", "Distinction bias", "Dunning\u2013Kruger effect", "Economics", "Egocentric bias", "Emotional bias", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Forecast bias", "Fundamental attribution error", "Funding bias", "Group (sociology)", "Halo effect", "Healthy user bias", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "Impact bias", "In-group favoritism", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "International Standard Book Number", "Lead time bias", "Length time bias", "List of cognitive biases", "List of memory biases", "Market research", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Negativity bias", "Net bias", "Non-response bias", "Nonprobability sampling", "Normalcy bias", "Omission bias", "Omitted-variable bias", "Optimism bias", "Outcome bias", "Overton window", "Participation bias", "Precision bias", "Pro-innovation bias", "Program evaluation", "Psychology", "Publication bias", "Recall bias", "Reporting bias", "Response bias", "Restraint bias", "Roy model", "Sampling bias", "Selection bias", "Self-serving bias", "Social comparison bias", "Social desirability bias", "Social sciences", "Sociology", "Spectrum bias", "Statistics", "Status quo bias", "Survivorship bias", "Systematic error", "Systemic bias", "Time-saving bias", "Trait ascription bias", "United States news media and the Vietnam War", "Verification bias", "Von Restorff effect", "Weak anthropic principle", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://www.skepdic.com/selectionbias.html", "http://moneyterms.co.uk/self-selection-bias/", "https://doi.org/10.1007%2Fs00181-008-0231-0"]}, "Eddy covariance": {"categories": ["All articles needing additional references", "Articles needing additional references from July 2018", "Boundary layer meteorology", "CS1 maint: Multiple names: authors list", "Covariance and correlation", "Wikipedia external links cleanup from October 2018", "Wikipedia spam cleanup from October 2018"], "title": "Eddy covariance", "method": "Eddy covariance", "url": "https://en.wikipedia.org/wiki/Eddy_covariance", "summary": "The eddy covariance (also known as eddy correlation and eddy flux) technique is a key atmospheric measurement technique to measure and calculate vertical turbulent fluxes within atmospheric boundary layers. The method analyzes high-frequency wind and scalar atmospheric data series, and yields values of fluxes of these properties. It is a statistical method used in meteorology and other applications (micrometeorology, oceanography, hydrology, agricultural sciences, industrial and regulatory applications, etc.) to determine exchange rates of trace gases over natural ecosystems and agricultural fields, and to quantify gas emissions rates from other land and water areas. It is frequently used to estimate momentum, heat, water vapour, carbon dioxide and methane fluxes.The technique is also used extensively for verification and tuning of global climate models, mesoscale and weather models, complex biogeochemical and ecological models, and remote sensing estimates from satellites and aircraft. The technique is mathematically complex, and requires significant care in setting up and processing data. To date, there is no uniform terminology or a single methodology for the Eddy Covariance technique, but much effort is being made by flux measurement networks (e.g., FluxNet, Ameriflux, ICOS, CarboEurope, Fluxnet Canada, OzFlux, NEON, and iLEAPS) to unify the various approaches.\n\nThe technique has additionally proven applicable under water to the benthic zone for measuring oxygen fluxes between seafloor and overlying water. In these environments, the technique is generally known as the eddy correlation technique, or just eddy correlation. Oxygen fluxes are extracted from raw measurements largely following the same principles as used in the atmosphere, and they are typically used as a proxy for carbon exchange, which is important for local and global carbon budgets. For most benthic ecosystems, eddy correlation is the most accurate technique for measuring in-situ fluxes. The technique's development and its applications under water remains a fruitful area of research.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5f/EddyCovariance_diagram_2.jpg", "https://upload.wikimedia.org/wikipedia/commons/5/52/Eddy_Covariance_IRGA_Sonic.jpg", "https://upload.wikimedia.org/wikipedia/commons/e/e1/Eddycorrelationsystem.jpg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Py%C3%B6rrekovarianssi-tekniikan_kaaviokuva.jpg", "https://upload.wikimedia.org/wikipedia/en/5/59/EddyCovariance_equations_part_1.jpg", "https://upload.wikimedia.org/wikipedia/en/8/81/EddyCovariance_equations_part_2.jpg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Average", "Benthic zone", "Bibcode", "Carbon Sequestration", "Carbon dioxide", "Closed-source", "Covariance", "Digital object identifier", "Ecosystem respiration", "Eddy (fluid dynamics)", "Evaporation", "Evapotranspiration", "Flux", "FluxNet", "Flux footprint", "Global climate model", "Greenhouse gas emissions", "Heat flux", "Hydraulic fracturing", "International Standard Serial Number", "Irrigation", "Landfill", "Latent heat flux", "Matlab", "Meteorology", "Methane emissions", "Momentum", "Open-source software", "Planetary boundary layer", "Proprietary software", "R (programming language)", "Reactive trace gas", "Scalar (physics)", "Statistics", "Transpiration", "Wind"], "references": ["http://www.scu.edu.au/coastal-biogeochemistry/index.php/49/", "http://www.ozflux.org.au/", "http://fluxnet.ccrp.ec.gc.ca/e_about.htm", "http://dfmcginnis.com/EddyCorrelation.html", "http://www.google.com/search?q=eddy+covariance&btnG=Search+Books&tbm=bks&tbo=1", "http://www.licor.com/env/products/eddy_covariance/ec_book.html", "http://www.licor.com/env/products/eddy_covariance/software.html", "http://www.mpi-bremen.de/en/Eddy_Correlation_System.html", "http://myweb.fsu.edu/mhuettel/Projects/NSF_Eddy.html", "http://adsabs.harvard.edu/abs/2016AMT.....9..509O", "http://adsabs.harvard.edu/abs/2017EGUGA..1918076S", "http://faculty.virginia.edu/berg/", "http://www.icos-infrastructure.eu/", "http://ameriflux.lbl.gov/", "http://gaia.agraria.unitus.it/eco2s", "http://www.biogeosciences.net/5/451/2008/bg-5-451-2008.pdf", "http://www.climatexchange.nl/projects/alteddy/index.htm", "http://www.carboeurope.org/", "http://doi.org/10.1029%2FJD090iD01p02119", "http://doi.org/10.1175%2F1520-0426(1990)007%3C0349:fmwcs%3E2.0.co;2", "http://doi.org/10.3402%2Ftellusb.v65i0.19940", "http://doi.org/10.5194%2Famt-9-509-2016", "http://www.ileaps.org/", "http://www.neoninc.org/", "http://www.worldcat.org/issn/1867-8548", "https://www.licor.com/env/help/eddypro/topics_eddypro/EddyPro_Home.html", "https://www.springer.com/earth+sciences+and+geography/atmospheric+sciences/book/978-94-007-2350-4", "https://www.bgc-jena.mpg.de/www/uploads/Publications/TechnicalReports/tech_report10.pdf", "https://epub.uni-bayreuth.de/342/", "https://www.atmos-meas-tech.net/9/509/2016/", "https://web.archive.org/web/20080821152535/http://www.met.wau.nl/", "https://www.geos.ed.ac.uk/homes/jbm/micromet/EdiRe/"]}, "Birth\u2013death process": {"categories": ["Markov processes", "Queueing theory"], "title": "Birth\u2013death process", "method": "Birth\u2013death process", "url": "https://en.wikipedia.org/wiki/Birth%E2%80%93death_process", "summary": "The birth\u2013death process is a special case of continuous-time Markov process where the state transitions are of only two types: \"births\", which increase the state variable by one and \"deaths\", which decrease the state by one. The model's name comes from a common application, the use of such models to represent the current size of a population where the transitions are literal births and deaths. Birth\u2013death processes have many applications in demography, queueing theory, performance engineering, epidemiology and biology. They may be used, for example to study the evolution of bacteria, the number of people with a disease within a population, or the number of customers in line at the supermarket.\nWhen a birth occurs, the process goes from state n to n + 1. When a death occurs, the process goes from state n to state n \u2212 1. The process is specified by birth rates \n \n \n \n {\n \n \u03bb\n \n i\n \n \n \n }\n \n i\n =\n 0\n \u2026\n \u221e\n \n \n \n \n {\\displaystyle \\{\\lambda _{i}\\}_{i=0\\dots \\infty }}\n and death rates \n \n \n \n {\n \n \u03bc\n \n i\n \n \n \n }\n \n i\n =\n 1\n \u2026\n \u221e\n \n \n \n \n {\\displaystyle \\{\\mu _{i}\\}_{i=1\\dots \\infty }}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/28/BD-proces.png"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bacteria", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Biology", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time Markov process", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Demography", "Difference equations", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Epidemiology", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Erlang unit", "Exchangeable random variables", "Exponential distribution", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kendall's notation", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 model", "M/M/1 queue", "M/M/c model", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Performance engineering", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Population size", "Potts model", "Predictable process", "Probability", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Quasi-birth\u2013death process", "Queueing model", "Queueing models", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://www.netlab.tkk.fi/opetus/s383143/kalvot/E_bdpros.pdf"]}, "Regenerative process": {"categories": ["Stochastic processes"], "title": "Regenerative process", "method": "Regenerative process", "url": "https://en.wikipedia.org/wiki/Regenerative_process", "summary": "In applied probability, a regenerative process is a class of stochastic process with the property that certain portions of the process can be treated as being statistically independent of each other. This property can be used in the derivation of theoretical properties of such processes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/52/Warehouse_md17.jpg", "https://upload.wikimedia.org/wikipedia/commons/archive/5/52/20160427091014%21Warehouse_md17.jpg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Applied probability", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Bibcode", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Harris chain", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "JSTOR", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Measurable function", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability theory", "Proceedings of the Royal Society A", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflected Brownian motion", "Reflection principle (Wiener process)", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistically independent", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "Walter L. Smith", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://adsabs.harvard.edu/abs/1955RSPSA.232....6S", "http://doi.org/10.1007%2F0-387-21525-5_6", "http://doi.org/10.1007%2F0-387-21552-2_6", "http://doi.org/10.1016%2FB978-0-12-375686-2.00003-0", "http://doi.org/10.1098%2Frspa.1955.0198", "http://doi.org/10.1287%2Fmoor.4.1.70", "http://doi.org/10.1287%2Fopre.15.3.467", "http://www.jstor.org/stable/168455", "http://www.jstor.org/stable/3689240"]}, "Risk\u2013benefit analysis": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2012", "Ethics and statistics", "Medical statistics", "Risk analysis"], "title": "Risk\u2013benefit ratio", "method": "Risk\u2013benefit analysis", "url": "https://en.wikipedia.org/wiki/Risk%E2%80%93benefit_ratio", "summary": "A risk\u2013benefit ratio is the ratio of the risk of an action to its potential benefits. Risk\u2013benefit analysis is analysis that seeks to quantify the risk and benefits and hence their ratio. \nAnalyzing a risk can be heavily dependent on the human factor. A certain level of risk in our lives is accepted as necessary to achieve certain benefits. For example, driving an automobile is a risk most people take daily, also since it is mitigated by the controlling factor of their perception of their individual ability to manage the risk-creating situation. When individuals are exposed to involuntary risk (a risk over which they have no control), they make risk aversion their primary goal. Under these circumstances individuals require the probability of risk to be as much as one thousand times smaller than for the same situation under their perceived control (a notable example being the common bias in the perception of risk in flying vs. driving).", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Academic clinical trials", "Adaptive clinical trial", "Analysis", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Benefit shortfall", "Biomedical research", "Blind experiment", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Consolidated Standards of Reporting Trials", "Correlation does not imply causation", "Cost\u2013benefit analysis", "Cross-sectional study", "Cumulative incidence", "Declaration of Helsinki", "Design of experiments", "Ecological study", "Epidemiological methods", "Ethical", "Evidence-based medicine", "Experiment", "First-in-man study", "Glossary of clinical research", "Hazard ratio", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Intention-to-treat analysis", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds algorithm", "Odds ratio", "Open-label trial", "Optimism bias", "Period prevalence", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "Quantification (science)", "Randomized controlled trial", "Ratio", "Reference class forecasting", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk", "Risk difference", "Risk ratio", "Scientific control", "Seeding trial", "Selection bias", "Specificity and sensitivity", "Survivorship bias", "Systematic review", "Vaccine trial", "Virulence", "World Medical Association"], "references": ["http://capita.wustl.edu/me567_informatics/concepts/riskben.html", "http://www.wma.net/en/30publications/10policies/b3/17c.pdf", "http://www.consort-statement.org/", "https://web.archive.org/web/20131029201115/http://capita.wustl.edu/me567_informatics/concepts/riskben.html"]}, "Regression control chart": {"categories": ["All stub articles", "Quality control tools", "Statistical charts and diagrams", "Statistics stubs", "Wikipedia articles needing clarification from December 2010"], "title": "Regression control chart", "method": "Regression control chart", "url": "https://en.wikipedia.org/wiki/Regression_control_chart", "summary": "In statistical quality control, the regression control chart allows for monitoring a change in a process where two or more variables are correlated. The change in a dependent variable can be detected and compensatory change in the independent variable can be recommended. Examples from the Post Office Department provide an application of such models.Regression control chart differs from a traditional control chart in four main aspects:\n\nIt is designed to control a varying (rather than a constant) average.\nThe control limit lines are parallel to the regression line rather than the horizontal line.\nThe computations here are much more complex.\nIt is appropriate for use in more complex situations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Control chart", "Correlation and dependence", "Dependent variable", "Independent variable", "Statistical quality control", "Statistics"], "references": ["http://faculty.washington.edu/htamura/qm520/mandel.pdf"]}, "Bhattacharya coefficient": {"categories": ["All articles needing expert attention", "Articles needing expert attention from May 2008", "Articles needing expert attention with no reason or talk parameter", "Mathematics articles needing expert attention", "Statistical deviation and dispersion", "Statistical distance"], "title": "Bhattacharyya distance", "method": "Bhattacharya coefficient", "url": "https://en.wikipedia.org/wiki/Bhattacharyya_distance", "summary": "In statistics, the Bhattacharyya distance measures the similarity of two probability distributions. It is closely related to the Bhattacharyya coefficient which is a measure of the amount of overlap between two statistical samples or populations. Both measures are named after Anil Kumar Bhattacharya, a statistician who worked in the 1930s at the Indian Statistical Institute.The coefficient can be used to determine the relative closeness of the two samples being considered. It is used to measure the separability of classes in classification and it is considered to be more reliable than the Mahalanobis distance, as the Mahalanobis distance is a particular case of the Bhattacharyya distance when the standard deviations of the two classes are the same. Consequently, when two classes have similar means but different standard deviations, the Mahalanobis distance would tend to zero, whereas the Bhattacharyya distance grows depending on the difference between the standard deviations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["Anil Kumar Bhattacharya", "ArXiv", "Bhattacharyya angle", "Bhattacharyya distance", "Calcutta Mathematical Society", "Chernoff bound", "Digital object identifier", "Domain of a function", "Encyclopedia of Mathematics", "Hellinger distance", "IEEE Transactions on Pattern Analysis and Machine Intelligence", "Indian Statistical Institute", "Integral", "International Standard Book Number", "Kullback\u2013Leibler divergence", "Linear discriminant analysis", "Mahalanobis distance", "Mathematical Reviews", "Measurement", "Michiel Hazewinkel", "Multivariate normal", "Partition of an interval", "Probability distribution", "R\u00e9nyi entropy", "Similarity measure", "Statistical classification", "Statistician", "Statistics", "Triangle inequality"], "references": ["http://www.mtm.ufsc.br/~taneja/book/node20.html", "http://coewww.rutgers.edu/riul/research/papers/pdf/trackmo.pdf", "http://www.ams.org/mathscinet-getitem?mr=0010358", "http://arxiv.org/abs/1004.5049", "http://doi.org/10.1109%2F34.41388", "http://doi.org/10.1109%2FTCOM.1967.1089532", "http://doi.org/10.1109%2FTIT.2011.2159046", "https://arxiv.org/pdf/1709.10498.pdf", "https://www.encyclopediaofmath.org/index.php?title=p/b110490"]}, "Fat-tailed distribution": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from April 2010", "Articles with unsourced statements from March 2014", "Behavioral finance", "Tails of probability distributions"], "title": "Fat-tailed distribution", "method": "Fat-tailed distribution", "url": "https://en.wikipedia.org/wiki/Fat-tailed_distribution", "summary": "A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. In common usage, the term fat tailed and heavy-tailed are synonymous, but different research communities favor one or the other largely for historical reasons. Fat-tailed distributions have been empirically encountered in a variety of areas: physics, earth sciences, economics and political science. The class of fat-tailed distributions includes those whose tails decay like a power law, which is a common point of reference in their use in the scientific literature. However, fat-tailed distributions also include other slowly-decaying distributions, such as the log-normal.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/66/BrownianMotion.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Cauchy_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d0/LevyFlight.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["1998 Russian financial crisis", "80-20 rule", "Behavioral finance", "Beno\u00eet Mandelbrot", "Big O notation", "Black Monday (1987)", "Black swan theory", "Black\u2013Scholes", "Brownian motion", "Catastrophic event", "Cauchy distribution", "Central limit theorem", "Commodity market", "Cumulative distribution function", "Digital object identifier", "Dot-com bubble", "Exponential distribution", "Finance", "Heavy tailed distribution", "Ian Bremmer", "Kurtosis", "Late-2000s financial crisis", "Leptokurtic", "Log-normal distribution", "Long-Term Capital Management", "L\u00e9vy flight", "Marketing", "Mean", "Moneyness", "Music industry", "Nassim Taleb", "Normal distribution", "Option (finance)", "Phonographic market", "Power-law distribution", "Power law", "Preston Keat", "Probability distribution", "Random variable", "Risk", "Seven states of randomness", "Skewness", "Stable distribution", "Stable distributions", "Standard deviation", "Taleb distribution", "The Fat Tail: The Power of Political Knowledge for Strategic Investing", "Variance", "Well-behaved", "William Safire"], "references": ["http://www.fattails.ca/distribution.html", "http://www.sciencedirect.com/science/article/pii/S0378437112004281?v=s5", "http://www.math.unl.edu/~sdunbar1/MathematicalFinance/Lessons/BlackScholes/Limitations/limitations.xml", "http://web.williams.edu/Mathematics/sjmiller/public_html/341Fa09/econ/Mandelbroit_VariationCertainSpeculativePrices.pdf", "http://doi.org/10.1016%2Fj.physa.2012.05.057", "http://doi.org/10.1086%2F294632", "http://www.skew-lognormal-cascade-distribution.org/apps/", "https://books.google.com/books?id=A9KumbRohY4C&pg=PA487", "https://books.google.com/books?id=jy0WU884hW0C&pg=PA288", "https://www.nytimes.com/2009/02/08/magazine/08wwln-safire-t.html"]}, "Hyperparameter": {"categories": ["Bayesian statistics", "Sensitivity analysis"], "title": "Hyperparameter", "method": "Hyperparameter", "url": "https://en.wikipedia.org/wiki/Hyperparameter", "summary": "In Bayesian statistics, a hyperparameter is a parameter of a prior distribution; the term is used to distinguish them from parameters of the model for the underlying system under analysis.\nFor example, if one is using a beta distribution to model the distribution of the parameter p of a Bernoulli distribution, then:\n\np is a parameter of the underlying system (Bernoulli distribution), and\n\u03b1 and \u03b2 are parameters of the prior distribution (beta distribution), hence hyperparameters.One may take a single value for a given hyperparameter, or one can iterate and take a probability distribution on the hyperparameter itself, called a hyperprior.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg"], "links": ["Admissible decision rule", "Andrew Gelman", "Approximate Bayesian computation", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernoulli distribution", "Bernstein\u2013von Mises theorem", "Beta distribution", "Conjugate prior", "Credible interval", "Credible intervals", "Cromwell's rule", "Empirical Bayes method", "Hyperparameter (machine learning)", "Hyperprior", "International Standard Book Number", "Likelihood function", "Markov chain Monte Carlo", "Maximum a posteriori estimation", "Parametric family", "Posterior predictive distribution", "Posterior probability", "Principle of indifference", "Principle of maximum entropy", "Prior distribution", "Prior probability", "Probability interpretations", "Radical probabilism", "Schwarz criterion", "Sensitivity analysis", "Statistics"], "references": ["http://www.roma1.infn.it/~dagos/rpp/node30.html", "http://www.roma1.infn.it/~dagos/rpp/rpp.html", "https://books.google.com/books?id=11nSgIcd7xQC", "https://books.google.com/books?id=ZRMJ-CebFm4C&pg=PA241", "https://books.google.com/books?id=lV3DIdV0F9AC&pg=PA251"]}, "Philosophy of probability": {"categories": ["All articles needing additional references", "Articles needing additional references from April 2011", "CS1 errors: dates", "Epistemology", "Interpretation (philosophy)", "Probability interpretations", "Probability theory", "Use dmy dates from September 2010", "Wikipedia articles needing clarification from April 2010"], "title": "Probability interpretations", "method": "Philosophy of probability", "url": "https://en.wikipedia.org/wiki/Probability_interpretations", "summary": "The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical tendency of something to occur or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory.\nThere are two broad categories of probability interpretations which can be called \"physical\" and \"evidential\" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given type of event (such as a die yielding a six) tends to occur at a persistent rate, or \"relative frequency\", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies. The two main kinds of theory of physical probability are frequentist accounts (such as those of Venn, Reichenbach and von Mises) and propensity accounts (such as those of Popper, Miller, Giere and Fetzer).Evidential probability, also called Bayesian probability, can be assigned to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility, or the degree to which the statement is supported by the available evidence. On most accounts, evidential probabilities are considered to be degrees of belief, defined in terms of dispositions to gamble at certain odds. The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage), the epistemic or inductive interpretation (Ramsey, Cox) and the logical interpretation (Keynes and Carnap). There are also evidential interpretations of probability covering groups, which are often labelled as 'intersubjective' (proposed by Gillies and Rowbottom).\nSome interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing. The physical interpretation, for example, is taken by followers of \"frequentist\" statistical methods, such as Ronald Fisher, Jerzy Neyman and Egon Pearson. Statisticians of the opposing Bayesian school typically accept the existence and importance of physical probabilities, but also consider the calculation of evidential probabilities to be both valid and necessary in statistics. This article, however, focuses on the interpretations of probability rather than theories of statistical inference.\nThe terminology of this topic is rather confusing, in part because probabilities are studied within a variety of academic fields. The word \"frequentist\" is especially tricky. To philosophers it refers to a particular theory of physical probability, one that has more or less been abandoned. To scientists, on the other hand, \"frequentist probability\" is just another name for physical (or objective) probability. Those who promote Bayesian inference view \"frequentist statistics\" as an approach to statistical inference that recognises only physical probabilities. Also the word \"objective\", as applied to probability, sometimes means exactly what \"physical\" means here, but is also used of evidential probabilities that are fixed by rational constraints, such as logical and epistemic probabilities.\n\nIt is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6a/Dice.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/26/Roulette_wheel.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/07/Tokyo_Racecourse_3.jpg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["A Treatise on Probability", "Aleatory", "Andrey Kolmogorov", "Arthur W. Burks", "Atom", "Axiom", "Bayesian probability", "Belief", "Blaise Pascal", "Brian Skyrms", "British Journal for the Philosophy of Science", "Bruno de Finetti", "CRC Press", "Celestial mechanics", "Charles Sanders Peirce", "Charles Sanders Peirce bibliography", "Classical definition of probability", "Coherence (physics)", "Coin", "Credence (statistics)", "David Kellogg Lewis", "David Miller (philosopher)", "Determinism", "Dice", "Digital object identifier", "Donald A. Gillies", "Edward N. Zalta", "Egon Pearson", "Electrical charge", "Elsevier", "Empirical evidence", "Entailment", "Epistemic", "Epistemology", "Estimation theory", "Evidence-based medicine", "Exchangeability", "Frank P. Ramsey", "Frequency (statistics)", "Frequency probability", "Frequentist probability", "Gambling", "Games of chance", "Hans Reichenbach", "Ian Hacking", "Indiana Philosophy Ontology Project", "Infinity", "International Standard Book Number", "JSTOR", "Jerzy Neyman", "John Maynard Keynes", "John Venn", "Karl Popper", "Laurence Jonathan Cohen", "Law of large numbers", "Laws of probability", "Leonard Jimmie Savage", "Logic", "Logical consequence", "Ludlow, Massachusetts", "Mathematics", "Negative probability", "Patrick Suppes", "Paul Humphreys (philosopher)", "PhilPapers", "Philosophy of mathematics", "Philosophy of statistics", "Pierre-Simon Laplace", "Pierre de Fermat", "Pignistic probability", "Playing card", "Predictive inference", "Principle of indifference", "Prior probability", "Probabilistic logic", "Probabilistically checkable proof", "Probability", "Probability amplitude", "Probability axioms", "Probability theory", "Propensity probability", "Quantum physics", "Radioactive decay", "Randomness", "Reference class problem", "Richard Threlkeld Cox", "Richard von Mises", "Roger Ludlow", "Ronald Fisher", "Ronald N. Giere", "Roulette", "Rudolf Carnap", "Seymour Geisser", "Six sigma", "Stanford Encyclopedia of Philosophy", "Statistical hypothesis testing", "Statistical inference", "String theory landscape", "Sunrise problem", "Susan Haack", "Theory of justification", "Thomas Bayes", "Thought experiment", "Urn model"], "references": ["http://www.nlx.com/collections/95", "http://www.sciencedirect.com/science/article/pii/S0049237X09703805", "http://www.sciencedirect.com/science/bookseries/0049237X", "http://plato.stanford.edu/archives/win2012/entries/probability-interpret/", "http://www.socsci.uci.edu/~bskyrms/bio/readings/pascal_fermat.pdf", "http://www.tc.umn.edu/~pemeehl/167GroveMeehlClinstix.pdf", "http://philosophy.elte.hu/colloquium/2001/October/Szabo/angol011008/angol011008.html", "http://philosophy.elte.hu/leszabo/Preprints/lesz_no_probability_preprint.pdf", "http://doi.org/10.1037%2F1076-8971.2.2.293", "http://doi.org/10.1093%2Fbjps%2F26.2.123", "http://doi.org/10.1175%2Fmwr2913.1", "http://fitelson.org/probability/ramsey.pdf", "http://www.jstor.org/stable/4106816", "http://bjps.oxfordjournals.org", "https://books.google.com/books?id=es0AAAAAcAAJ", "https://books.google.com/books?id=wfdlBZ_iwZoC", "https://www.stat.berkeley.edu/~stark/Preprints/611.pdf", "https://inpho.cogs.indiana.edu/idea/1155", "https://plato.stanford.edu/entries/probability-interpret/", "https://web.archive.org/web/20111030214359/http://www.tc.umn.edu/~pemeehl/167GroveMeehlClinstix.pdf", "https://www.gutenberg.org/ebooks/32625", "https://philpapers.org/browse/interpretation-of-probability/"]}, "Scatter plot": {"categories": ["Commons category link is on Wikidata", "Quality control tools", "Statistical charts and diagrams"], "title": "Scatter plot", "method": "Scatter plot", "url": "https://en.wikipedia.org/wiki/Scatter_plot", "summary": "A scatter plot (also called a scatterplot, scatter graph, scatter chart, scattergram, or scatter diagram) is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are color-coded, one additional variable can be displayed.\nThe data are displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a5/Matriz_de_gr%C3%A1ficos_de_dispers%C3%A3o.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Oldfaithful3.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/af/Scatter_diagram_for_quality_characteristic_XXX.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c4/Scatter_plot.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "American Society for Quality", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "AnyChart", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Bubble chart", "Canonical correlation", "Cartesian coordinate system", "Cartography", "Categorical variable", "Causality", "Census", "Central limit theorem", "Central tendency", "Check sheet", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curve fitting", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fluctuation diagram", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent variable", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Ishikawa diagram", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Herschel", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line chart", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical diagram", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Milwaukee, Wisconsin", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Mosaic plot", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "Old Faithful Geyser", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameter", "Parametric statistics", "Pareto chart", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plot (graphics)", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality (business)", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter diagram", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Seven Basic Tools of Quality", "Seven basic tools of quality", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variable (mathematics)", "Variance", "Vector autoregression", "Vertical axis", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Wyoming", "Yellowstone National Park", "Z-test"], "references": ["http://docs.anychart.com/7.9.0/Basic_Charts_Types/Scatter_Chart", "http://www.psychwiki.com/wiki/What_is_a_scatterplot%3F", "http://www.r-bloggers.com/ggplot2-for-big-data/", "http://www.r-statistics.com/2010/04/correlation-scatter-plot-matrix-for-ordered-categorical-data/", "http://www.tandfonline.com/doi/ref/10.1080/10618600.2012.694762", "http://www.itl.nist.gov/div898/handbook/eda/section3/scatplma.htm", "http://www.asq.org/learn-about-quality/seven-basic-quality-tools/overview/overview.html", "http://doi.org/10.1002%2Fjhbs.20078", "http://doi.org/10.1080%2F10618600.2012.694762", "https://yodalearning.com/tutorials/create-scatter-plots-excel/", "https://wci.llnl.gov/codes/visit/gallery.html"]}, "Armitage\u2013Doll multistage model of carcinogenesis": {"categories": ["All stub articles", "Carcinogenesis", "Medical statistics", "Oncology stubs", "Statistics stubs"], "title": "Armitage\u2013Doll multistage model of carcinogenesis", "method": "Armitage\u2013Doll multistage model of carcinogenesis", "url": "https://en.wikipedia.org/wiki/Armitage%E2%80%93Doll_multistage_model_of_carcinogenesis", "summary": "The Armitage\u2013Doll model is a statistical model of carcinogenesis, proposed in 1954 by Peter Armitage and Richard Doll, which suggested that a sequence of multiple distinct genetic events preceded the onset of cancer. The original paper has recently been reprinted with a set of commentary articles.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9f/Mitotic_Metaphase.svg"], "links": ["Carcinogenesis", "Digital object identifier", "Oncology", "Peter Armitage", "Richard Doll", "Statistics"], "references": ["http://www.nature.com/bjc/journal/v91/n12/pdf/6602297a.pdf", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2007940/pdf/brjcancer00386-0010.pdf", "https://doi.org/10.1038%2Fsj.bjc.6602297", "https://doi.org/10.1093%2Fije%2Fdyh216", "https://doi.org/10.1093%2Fije%2Fdyh222", "https://doi.org/10.1093%2Fije%2Fdyh288", "https://doi.org/10.1093%2Fije%2Fdyh359"]}, "Large deviations of Gaussian random functions": {"categories": ["Stochastic processes"], "title": "Large deviations of Gaussian random functions", "method": "Large deviations of Gaussian random functions", "url": "https://en.wikipedia.org/wiki/Large_deviations_of_Gaussian_random_functions", "summary": "A random function \u2013 of either one variable (a random process), or two or more variables\n(a random field) \u2013 is called Gaussian if every finite-dimensional distribution is a multivariate normal distribution. Gaussian random fields on the sphere are useful (for example) when analysing\n\nthe anomalies in the cosmic microwave background radiation (see, pp. 8\u20139);\nbrain images obtained by positron emission tomography (see, pp. 9\u201310).Sometimes, a value of a Gaussian random function deviates from its expected value by several standard deviations. This is a large deviation. Though rare in a small domain (of space or/and time), large deviations may be quite usual in a large domain.\n\n", "images": [], "links": ["Almost surely", "Connected space", "Continuously differentiable", "Correlation function", "Cosmic microwave background radiation", "Directional derivative", "Ellipse", "Empty set", "Euler characteristic", "Expected value", "Finite-dimensional distribution", "Gaussian process", "Gaussian random field", "Gauss\u2013Bonnet theorem", "International Standard Book Number", "Large deviations theory", "Multivariate normal distribution", "Poincar\u00e9\u2013Hopf theorem", "Positron emission tomography", "Random field", "Random process", "Relative error", "Rice's formula", "Set (mathematics)", "Sphere", "Standard deviation", "Standard normal distribution", "Tangential", "Torus"], "references": ["http://www.tau.ac.il/~tsirel/Courses/Gauss2/syllabus.html", "https://arxiv.org/abs/0805.1031", "https://dx.doi.org/10.1214/aoap/1019737664"]}, "Marginal distribution": {"categories": ["Theory of probability distributions"], "title": "Marginal distribution", "method": "Marginal distribution", "url": "https://en.wikipedia.org/wiki/Marginal_distribution", "summary": "In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables.\nMarginal variables are those variables in the subset of variables being retained. These concepts are \"marginal\" because they can be found by summing values in a table along rows or columns, and writing the sum in the margins of the table. The distribution of the marginal variables (the marginal distribution) is obtained by marginalizing \u2013 that is, focusing on the sums in the margin \u2013 over the distribution of the variables being discarded, and the discarded variables are said to have been marginalized out.\nThe context here is that the theoretical studies being undertaken, or the data analysis being done, involves a wider set of random variables but that attention is being limited to a reduced number of those variables. In many applications, an analysis may start with a given collection of random variables, then first extend the set by defining new ones (such as the sum of the original random variables) and finally reduce the number by placing interest in the marginal distribution of a subset (such as the sum). Several different analyses may be done, each treating a different subset of variables as the marginal variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8e/MultivariateNormal.png", "https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png"], "links": ["Bayes' theorem", "Boole's inequality", "Complementary event", "Compound probability distribution", "Conditional distribution", "Conditional independence", "Conditional probability", "Continuous random variable", "Data analysis", "Discrete random variable", "Elementary event", "Event (probability theory)", "Expected value", "Frequency distribution", "Independence (probability theory)", "Indexed family", "International Standard Book Number", "Joint distribution", "Joint probability", "Joint probability distribution", "Law of large numbers", "Law of the unconscious statistician", "Law of total probability", "Multivariate distribution", "Mutual information", "Probability axioms", "Probability density function", "Probability distribution", "Probability mass function", "Probability measure", "Probability space", "Probability theory", "Random variable", "Sample space", "Statistics", "Subset", "Tree diagram (probability theory)", "Venn diagram", "Wasserstein metric"], "references": []}, "NumXL": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2017", "Econometrics software", "Official website different in Wikidata and Wikipedia", "Time series software"], "title": "NumXL", "method": "NumXL", "url": "https://en.wikipedia.org/wiki/NumXL", "summary": "Numerical Analysis for Excel (NumXL) is an econometrics and time series analysis add-in for Microsoft Excel. Developed by Spider Financial, NumXL provides a wide variety of statistical and time series analysis techniques, including linear and nonlinear time series modeling, statistical tests and others.\nAlthough NumXL is intended as an analytical add-in for Excel, it extends Excel\u2019s user-interface (UI) and offers many wizards, menus and toolbars to automate the mundane phases of time series analysis. The features include summary statistics, test of hypothesis, correlogram analysis, modeling, calibration, residuals diagnosis, back-testing and forecast.\nNumXL users have varied backgrounds in finance, economics, engineering and science. NumXL is used in academic and research institutions and industrial enterprises.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/69/NumXLlogo.png", "https://upload.wikimedia.org/wikipedia/commons/archive/6/69/20110615033826%21NumXLlogo.png"], "links": ["ADMB", "AREMOS", "Akaike information criterion", "Analyse-it", "Augmented Dickey\u2013Fuller test", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive\u2013moving-average model", "BMDP", "BV4.1 (software)", "Bayesian information criterion", "Binomial distribution", "C++", "CSPro", "C (programming language)", "Chow test", "Commercial software", "Comparison of statistical packages", "Cross-correlation", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "Deviance (statistics)", "Discrete Fourier transform", "EViews", "Econometrics software", "Epi Info", "Excess kurtosis", "Exponential power distribution", "Exponential smoothing", "Freeware", "GARCH", "GAUSS (software)", "GNU Octave", "Gaussian distribution", "GenStat", "Generalized linear model", "Goodness of fit", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "Hodrick\u2013Prescott filter", "Integral operator", "Interpolation", "JASP", "JMP (statistical software)", "JMulTi", "Jarque\u2013Bera test", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Lag operator", "Likelihood function", "List of statistical packages", "Ljung\u2013Box test", "Logit", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Moving average", "Multicollinearity", "Multiple linear regression", "NCSS (statistical software)", "Natural logarithm", "Normal distribution", "Normality test", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Partial autocorrelation function", "Poisson distribution", "Portmanteau test", "Power transform", "Principal component", "Probit", "Public-domain software", "R-squared", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Rcmdr", "Regression Analysis of Time Series", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "Seasonal adjustment", "SegReg", "Shapiro\u2013Wilk test", "SigmaStat", "SigmaXL", "SimFiT", "Simple linear regression", "Skewness", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "StatsDirect", "Stepwise regression", "Student t distribution", "TSP (econometrics software)", "The Unscrambler", "Trialware", "UNISTAT", "User-interface", "WinBUGS", "Windows", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://support.numxl.com/forums/21692403-Release-notes", "http://support.numxl.com/hc/articles/207842203", "http://support.numxl.com/hc/categories/201159123", "http://support.numxl.com/hc/community/topics", "http://support.numxl.com/hc/sections/203146523", "http://www.numxl.com", "http://spiderfinancial.com", "http://www.spiderfinancial.com/tips-demos", "https://www.facebook.com/spiderfinancial", "https://www.twitter.com/spiderfinancial"]}, "Uncomfortable science": {"categories": ["Philosophy of statistics", "Statistical hypothesis testing"], "title": "Uncomfortable science", "method": "Uncomfortable science", "url": "https://en.wikipedia.org/wiki/Uncomfortable_science", "summary": "Uncomfortable science, as identified by statistician John Tukey, comprises situations in which there is a need to draw an inference from a limited sample of data, where further samples influenced by the same cause system will not be available. More specifically, it involves the analysis of a finite natural phenomenon for which it is difficult to overcome the problem of using a common sample of data for both exploratory data analysis and confirmatory data analysis. This leads to the danger of systematic bias through testing hypotheses suggested by the data.\nA typical example is Bode's law, which provides a simple numerical rule for the distances of the planets in the solar system from the Sun. Once the rule has been derived, through the trial and error matching of various rules with the observed data (exploratory data analysis), there are not enough planets remaining for a rigorous and independent test of the hypothesis (confirmatory data analysis). We have exhausted the natural phenomena. The agreement between data and the numerical rule should be no surprise, as we have deliberately chosen the rule to match the data. If we are concerned about what Bode's law tells us about the cause system of planetary distribution then we demand confirmation that will not be available until better information about other planetary systems becomes available.", "images": [], "links": ["Cause system", "Confirmatory data analysis", "Cosmic variance", "Data", "Data mining", "Digital object identifier", "Exploratory data analysis", "Hypothesis", "International Standard Book Number", "John Tukey", "P. Diaconis", "Phenomenon", "Planet", "PubMed Central", "PubMed Identifier", "Sample (statistics)", "Solar system", "Statistical inference", "Statistician", "Sun", "Systematic bias", "Testing hypotheses suggested by the data", "Titius-Bode law", "Trial and error"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3261704", "http://www.ncbi.nlm.nih.gov/pubmed/21988833", "http://doi.org/10.1038%2Fmsb.2011.70"]}, "Inverse distance weighting": {"categories": ["Geostatistics", "Multivariate interpolation"], "title": "Inverse distance weighting", "method": "Inverse distance weighting", "url": "https://en.wikipedia.org/wiki/Inverse_distance_weighting", "summary": "Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points.\nThe name given to this type of methods was motivated by the weighted average applied, since it resorts to the inverse of the distance to each known point (\"amount of proximity\") when assigning weights.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/58/Shepard_interpolation_1_dimension.png", "https://upload.wikimedia.org/wikipedia/commons/7/71/Shepard_interpolation_2.png"], "links": ["Association for Computing Machinery", "Deterministic algorithm", "Digital object identifier", "Geographic information system", "Kd-tree", "Kernel density estimation", "Metric (mathematics)", "Multivariate interpolation", "Netlib", "Parallel computing", "Probability distribution", "Statistical error", "Tuple", "Voronoi diagram", "Weighted mean", "William Warntz", "\u0141ukaszyk\u2013Karmowski metric"], "references": ["http://isites.harvard.edu/fs/docs/icb.topic39008.files/History_LCG.pdf", "http://doi.org/10.1007%2Fs00466-003-0532-2", "http://doi.org/10.1145%2F800186.810616"]}, "Strong prior": {"categories": ["All articles lacking sources", "All stub articles", "Articles lacking sources from December 2009", "Bayesian statistics", "Statistics stubs"], "title": "Strong prior", "method": "Strong prior", "url": "https://en.wikipedia.org/wiki/Strong_prior", "summary": "In Bayesian statistics, a strong prior is a preceding assumption, theory, concept or idea upon which, after taking account of new information, a current assumption, theory, concept or idea is founded. The term is used to contrast the case of a weak or uninformative prior probability. A strong prior would be a type of informative prior in which the information contained in the prior distribution dominates the information contained in the data being analysed. The Bayesian analysis combines the information contained in the prior with that extracted from the data to produce the posterior distribution which, in the case of a \"strong prior\", would be little changed from the prior distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayesian analysis", "Bayesian statistics", "Posterior distribution", "Prior distribution", "Prior probability", "Statistics"], "references": []}, "Cheeger bound": {"categories": ["All stub articles", "Probabilistic inequalities", "Statistical inequalities", "Statistics stubs", "Stochastic processes"], "title": "Cheeger bound", "method": "Cheeger bound", "url": "https://en.wikipedia.org/wiki/Cheeger_bound", "summary": "In mathematics, the Cheeger bound is a bound of the second largest eigenvalue of the transition matrix of a finite-state, discrete-time, reversible stationary Markov chain. It can be seen as a special case of Cheeger inequalities in expander graphs.\nLet \n \n \n \n X\n \n \n {\\displaystyle X}\n be a finite set and let \n \n \n \n K\n (\n x\n ,\n y\n )\n \n \n {\\displaystyle K(x,y)}\n be the transition probability for a reversible Markov chain on \n \n \n \n X\n \n \n {\\displaystyle X}\n . Assume this chain has stationary distribution \n \n \n \n \u03c0\n \n \n {\\displaystyle \\pi }\n .\nDefine\n\n \n \n \n Q\n (\n x\n ,\n y\n )\n =\n \u03c0\n (\n x\n )\n K\n (\n x\n ,\n y\n )\n \n \n {\\displaystyle Q(x,y)=\\pi (x)K(x,y)}\n and for \n \n \n \n A\n ,\n B\n \u2282\n X\n \n \n {\\displaystyle A,B\\subset X}\n define\n\n \n \n \n Q\n (\n A\n \u00d7\n B\n )\n =\n \n \u2211\n \n x\n \u2208\n A\n ,\n y\n \u2208\n B\n \n \n Q\n (\n x\n ,\n y\n )\n .\n \n \n {\\displaystyle Q(A\\times B)=\\sum _{x\\in A,y\\in B}Q(x,y).}\n Define the constant \n \n \n \n \u03a6\n \n \n {\\displaystyle \\Phi }\n as\n\n \n \n \n \u03a6\n =\n \n min\n \n S\n \u2282\n X\n ,\n \u03c0\n (\n S\n )\n \u2264\n \n \n 1\n 2\n \n \n \n \n \n \n \n Q\n (\n S\n \u00d7\n \n S\n \n c\n \n \n )\n \n \n \u03c0\n (\n S\n )\n \n \n \n .\n \n \n {\\displaystyle \\Phi =\\min _{S\\subset X,\\pi (S)\\leq {\\frac {1}{2}}}{\\frac {Q(S\\times S^{c})}{\\pi (S)}}.}\n The operator \n \n \n \n K\n ,\n \n \n {\\displaystyle K,}\n acting on the space of functions from \n \n \n \n \n |\n \n X\n \n |\n \n \n \n {\\displaystyle |X|}\n to \n \n \n \n \n |\n \n X\n \n |\n \n \n \n {\\displaystyle |X|}\n , defined by\n\n \n \n \n (\n K\n \u03d5\n )\n (\n x\n )\n =\n \n \u2211\n \n y\n \n \n K\n (\n x\n ,\n y\n )\n \u03d5\n (\n y\n )\n \n \n {\\displaystyle (K\\phi )(x)=\\sum _{y}K(x,y)\\phi (y)}\n has eigenvalues \n \n \n \n \n \u03bb\n \n 1\n \n \n \u2265\n \n \u03bb\n \n 2\n \n \n \u2265\n \u22ef\n \u2265\n \n \u03bb\n \n n\n \n \n \n \n {\\displaystyle \\lambda _{1}\\geq \\lambda _{2}\\geq \\cdots \\geq \\lambda _{n}}\n . It is known that \n \n \n \n \n \u03bb\n \n 1\n \n \n =\n 1\n \n \n {\\displaystyle \\lambda _{1}=1}\n . The Cheeger bound is a bound on the second largest eigenvalue \n \n \n \n \n \u03bb\n \n 2\n \n \n \n \n {\\displaystyle \\lambda _{2}}\n .\n Theorem (Cheeger bound):\n\n \n \n \n 1\n \u2212\n 2\n \u03a6\n \u2264\n \n \u03bb\n \n 2\n \n \n \u2264\n 1\n \u2212\n \n \n \n \u03a6\n \n 2\n \n \n 2\n \n \n .\n \n \n {\\displaystyle 1-2\\Phi \\leq \\lambda _{2}\\leq 1-{\\frac {\\Phi ^{2}}{2}}.}", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Cheeger constant", "Eigenvalue", "Expander graph", "Expander graphs", "Markov chain", "Mathematics", "Poincar\u00e9 bound", "Space of functions", "Stationary distribution", "Statistics", "Stochastic matrix"], "references": []}, "Likert scale": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "CS1 maint: Uses authors parameter", "Educational psychology research methods", "Psychometrics", "Questionnaire construction"], "title": "Likert scale", "method": "Likert scale", "url": "https://en.wikipedia.org/wiki/Likert_scale", "summary": "A Likert scale ( LIK-\u0259rt but more commonly pronounced LY-k\u0259rt) is a psychometric scale commonly involved in research that employs questionnaires. It is the most widely used approach to scaling responses in survey research, such that the term (or more accurately the Likert-type scale) is often used interchangeably with rating scale, although there are other types of rating scales.\nThe scale is named after its inventor, psychologist Rensis Likert. Likert distinguished between a scale proper, which emerges from collective responses to a set of items (usually eight or more), and the format in which responses are scored along a range. Technically speaking, a Likert scale refers only to the former. The difference between these two concepts has to do with the distinction Likert made between the underlying phenomenon being investigated and the means of capturing variation that points to the underlying phenomenon.When responding to a Likert item, respondents specify their level of agreement or disagreement on a symmetric agree-disagree scale for a series of statements. Thus, the range captures the intensity of their feelings for a given item.A scale can be created as the simple sum or average of questionnaire responses over the set of individual items (questions). In so doing, Likert scaling assumes distances between each choice (answer option) are equal. Many researchers employ a set of such items that are highly correlated (that show high internal consistency) but also that together will capture the full domain under study (which requires less-than perfect correlations). Others hold to a standard by which \"All items are assumed to be replications of each other or in other words items are considered to be parallel instruments\" (p. 197). By contrast, modern test theory treats the difficulty of each item (the ICCs) as information to be incorporated in scaling items.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/cc/Example_Likert_Scale.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e4/Social_Network_Diagram_%28segment%29.svg"], "links": ["Acquiescence bias", "Analysis of variance", "Armstrong's axioms", "Axiom", "Bibliography of sociology", "Binomial distribution", "Bogardus Social Distance Scale", "Borg scale", "Central limit theorem", "Central tendency", "Chi-squared test", "Cochran's Q test", "Comparative historical research", "Computational sociology", "Conflict theories", "Consensus based assessment (CBA)", "Criminology", "Critical theory", "Demography", "Development theory", "Deviance (sociology)", "Diamond of opposites", "Digital object identifier", "Discan", "Distance metric", "Economic sociology", "Environmental sociology", "Ethnography", "Ethnomethodology", "Feminist sociology", "Guttman scale", "Historical sociology", "History of sociology", "Hypothesis", "Index of sociology articles", "Industrial sociology", "Institutionalization", "Internal consistency", "International Standard Book Number", "Ipsative", "Item response theory", "Kruskal\u2013Wallis test", "Kurtosis", "Level of measurement", "List of sociological associations", "List of sociologists", "List of sociology journals", "Mann\u2013Whitney test", "Mathematical sociology", "McNemar test", "Measure theory", "Medical sociology", "Military sociology", "Minnesota Multiphasic Personality Inventory", "Mokken scale", "Organizational theory", "Outline of sociology", "Phrase completions", "Political sociology", "Polytomous Rasch model", "Positivism", "Psychologist", "Psychometrics", "PubMed Identifier", "Qualitative research", "Quantitative research", "Questionnaire", "Questionnaire construction", "Rating scale", "Rating sites", "Rensis Likert", "Rosenberg self-esteem scale", "Rural sociology", "Satisficing", "Scale (social sciences)", "Semantic differential", "Skewness", "Social change", "Social conflict", "Social construction of technology", "Social constructionism", "Social desirability bias", "Social inequality", "Social movement", "Social network analysis", "Social psychology (sociology)", "Social research", "Social stratification", "Sociological theory", "Sociology", "Sociology of culture", "Sociology of education", "Sociology of gender", "Sociology of health and illness", "Sociology of immigration", "Sociology of knowledge", "Sociology of law", "Sociology of literature", "Sociology of race and ethnic relations", "Sociology of religion", "Sociology of scientific knowledge", "Sociology of terrorism", "Sociology of the family", "Statistically significant", "Structural functionalism", "Subfields of sociology", "Symbolic interactionism", "Thurstone scale", "Timeline of sociology", "Urban sociology", "Visual analogue scale", "Voting system", "Wilcoxon signed-rank test"], "references": ["http://core.ecu.edu/psyc/wuenschk/StatHelp/Likert.htm", "http://files.eric.ed.gov/fulltext/ED399296.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/18697664", "http://www.comp.dit.ie/dgordon/Courses/ResearchMethods/likertscales.pdf", "http://www.socialresearchmethods.net/kb/scallik.php", "http://asq.org/quality-progress/2007/07/statistics/likert-scales-and-data-analyses.html", "http://doi.org/10.1046%2Fj.1365-2648.1994.20010196.x", "http://doi.org/10.1080%2F01621459.1959.10501526", "http://doi.org/10.2307%2F2574595", "http://doi.org/10.2466%2Fpms.1987.64.2.359", "http://doi.org/10.3758%2FBRM.40.3.699", "http://doi.org/10.3844%2Fjssp.2007.106.116", "http://www.icbl.hw.ac.uk/ltdi/cookbook/info_likert_scale/index.html", "https://www.r-statistics.com/2010/04/correlation-scatter-plot-matrix-for-ordered-categorical-data/", "https://wwww.surveyking.com/help/likert-scale-example", "https://twitter.com/seanjtaylor/status/968251357814665216"]}, "Group method of data handling": {"categories": ["All articles with failed verification", "Articles with failed verification from July 2015", "Artificial neural networks", "Classification algorithms", "Computational statistics", "Regression variable selection"], "title": "Group method of data handling", "method": "Group method of data handling", "url": "https://en.wikipedia.org/wiki/Group_method_of_data_handling", "summary": "Group method of data handling (GMDH) is a family of inductive algorithms for computer-based mathematical modeling of multi-parametric datasets that features fully automatic structural and parametric optimization of models.\nGMDH is used in such fields as data mining, knowledge discovery, prediction, complex systems modeling, optimization and pattern recognition. Li et. al. (2017)'s results showed that GMDH neural network performed better than the classical forecasting algorithms such as Single Exponential Smooth, Double Exponential Smooth, ARIMA and back-propagation neural network. GMDH algorithms are characterized by inductive procedure that performs sorting-out of gradually complicated polynomial models and selecting the best solution by means of the so-called external criterion.\nA GMDH model with multiple inputs and one output is a subset of components of the base function (1):\n\n \n \n \n Y\n (\n \n x\n \n 1\n \n \n ,\n \u2026\n ,\n \n x\n \n n\n \n \n )\n =\n \n a\n \n 0\n \n \n +\n \n \u2211\n \n i\n =\n 1\n \n \n m\n \n \n \n a\n \n i\n \n \n \n f\n \n i\n \n \n \n \n {\\displaystyle Y(x_{1},\\dots ,x_{n})=a_{0}+\\sum \\limits _{i=1}^{m}a_{i}f_{i}}\n where f are elementary functions dependent on different sets of inputs, a are coefficients and m is the number of the base function components.\nIn order to find the best solution GMDH algorithms consider various component subsets of the base function (1) called partial models. Coefficients of these models are estimated by the least squares method. GMDH algorithms gradually increase the number of partial model components and find a model structure with optimal complexity indicated by the minimum value of an external criterion. This process is called self-organization of models.\nThe most popular base function used in GMDH is the gradually complicated Kolmogorov-Gabor polynomial (2):\n\n \n \n \n Y\n (\n \n x\n \n 1\n \n \n ,\n \u2026\n ,\n \n x\n \n n\n \n \n )\n =\n \n a\n \n 0\n \n \n +\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n \n a\n \n i\n \n \n \n \n x\n \n i\n \n \n +\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n \n \u2211\n \n j\n =\n i\n \n \n n\n \n \n \n \n a\n \n i\n j\n \n \n \n \n \n x\n \n i\n \n \n \n x\n \n j\n \n \n +\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n \n \u2211\n \n j\n =\n i\n \n \n n\n \n \n \n \n \u2211\n \n k\n =\n j\n \n \n n\n \n \n \n \n a\n \n i\n j\n k\n \n \n \n \n \n \n x\n \n i\n \n \n \n x\n \n j\n \n \n \n x\n \n k\n \n \n +\n \u22ef\n \n \n {\\displaystyle Y(x_{1},\\dots ,x_{n})=a_{0}+\\sum \\limits _{i=1}^{n}{a_{i}}x_{i}+\\sum \\limits _{i=1}^{n}{\\sum \\limits _{j=i}^{n}{a_{ij}}}x_{i}x_{j}+\\sum \\limits _{i=1}^{n}{\\sum \\limits _{j=i}^{n}{\\sum \\limits _{k=j}^{n}{a_{ijk}}}}x_{i}x_{j}x_{k}+\\cdots }\n The resulting models are also known as polynomial neural networks. J\u00fcrgen Schmidhuber cites GDMH as one of the earliest deep learning methods, remarking that it was used to train eight-layer neural nets as early as 1971.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/Combinatorial_GMDH_optimal_complexity.png", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/0/0d/Photo_of_Prof._Alexey_G._Ivakhnenko.jpg"], "links": ["Alexey Grigorevich Ivakhnenko", "ArXiv", "Artificial Neural Network", "Complex systems", "Data mining", "Deep learning", "Digital object identifier", "Forecasting", "J\u00fcrgen Schmidhuber", "Kiev", "Knowledge discovery", "Least squares", "MATLAB", "Optimization (mathematics)", "Pattern recognition", "Shannon's Theorem", "Ukrainian Soviet Socialist Republic", "Weka (machine learning)", "Wiener series"], "references": ["http://www.gmdhshell.com", "http://pnn.pnnsoft.com/index.html", "http://www.sciencedirect.com/science/article/pii/S0140700716301165", "http://www.tandfonline.com/doi/citedby/10.1080/14445921.2016.1225149?scroll=top&needAccess=true", "http://neuron.felk.cvut.cz/game/project.html", "http://www.knowledgeminer.eu/about.html", "http://wgmdh.irb.hr/en/project/", "http://research.guilan.ac.ir/gevom/", "http://www.gmdh.net", "http://sourceforge.net/projects/sciengyrpf/", "http://arxiv.org/abs/1404.7828", "http://doi.org/10.1016%2Fj.ijrefrig.2016.05.011", "http://doi.org/10.1016%2Fj.neunet.2014.09.003", "https://cran.r-project.org/web/packages/GMDH/"]}, "Polynomial regression": {"categories": ["All articles to be merged", "All articles with unsourced statements", "Articles to be merged from April 2018", "Articles with unsourced statements from March 2018", "Regression analysis"], "title": "Polynomial regression", "method": "Polynomial regression", "url": "https://en.wikipedia.org/wiki/Polynomial_regression", "summary": "In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x), and has been used to describe nonlinear phenomena such as the growth rate of tissues, the distribution of carbon isotopes in lake sediments, and the progression of disease epidemics. Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression.\nThe explanatory (independent) variables resulting from the polynomial expansion of the \"baseline\" variables are known as higher-degree terms. Such variables are also used in classification settings.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8b/Polyreg_scheffe.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Adrien-Marie Legendre", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Analytic function", "Anderson\u2013Darling test", "Approximation theory", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Basis function", "Basis functions", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calibration curve", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational statistics", "Conditional expectation", "Confidence band", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curve fitting", "Data", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete choice", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Estimation", "Estimation theory", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fixed effects model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gauss", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent variable", "Index of dispersion", "Infinitesimal", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Joseph Diaz Gergonne", "Journal of Machine Learning Research", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kernel methods", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least-angle regression", "Least absolute deviations", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line regression", "Linear discriminant analysis", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local polynomial regression", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multiple linear regression", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "PhET", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial", "Polynomial and rational function modeling", "Polynomial interpolation", "Polynomial kernel", "Polynomial least squares", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal component regression", "Prior probability", "Probabilistic design", "Probability distribution", "Probit model", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Radial basis function", "Random assignment", "Random effects model", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regularized least squares", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Ridge regression", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scalar (mathematics)", "Scale parameter", "Scatter plot", "Scheff\u00e9's method", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smoothing", "Smoothing spline", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spline (mathematics)", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen M. Stigler", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Support vector regression", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total derivative", "Total least squares", "Trend estimation", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "V-statistic", "Vandermonde matrix", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.webdoe.cc/publications/kirstine.php", "http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-20/2/df451ec5fbb7c044d0f4d900af80ec86", "http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-1Y/2/680c7ada0198761e9866197d53512ab4", "http://jmlr.csail.mit.edu/papers/v11/chang10a.html", "http://www.ncbi.nlm.nih.gov/pubmed/11423656", "http://www.ncbi.nlm.nih.gov/pubmed/16572172", "http://www.ncbi.nlm.nih.gov/pubmed/7548341", "http://doi.org/10.1016%2F0315-0860(74)90033-0", "http://doi.org/10.1016%2F0315-0860(74)90034-2", "http://doi.org/10.1038%2Fnature04513", "http://doi.org/10.1097%2F00001648-199507000-00005", "http://doi.org/10.1126%2Fscience.1059612", "http://doi.org/10.2307%2F2331929", "http://doi.org/10.2307%2F2685560", "http://www.jstor.org/stable/2331929", "http://www.jstor.org/stable/2685560", "http://www.jstor.org/stable/3702080", "https://phet.colorado.edu/en/simulation/curve-fitting", "https://facultystaff.richmond.edu/~cstevens/301/Excel4.html"]}, "Jonckheere's trend test": {"categories": ["Statistical tests"], "title": "Jonckheere's trend test", "method": "Jonckheere's trend test", "url": "https://en.wikipedia.org/wiki/Jonckheere%27s_trend_test", "summary": "In statistics, the Jonckheere trend test (sometimes called the Jonckheere\u2013Terpstra test) is a test for an ordered alternative hypothesis within an independent samples (between-participants) design. It is similar to the Kruskal\u2013Wallis test in that the null hypothesis is that several independent samples are from the same population. However, with the Kruskal\u2013Wallis test there is no a priori ordering of the populations from which the samples are drawn. When there is an a priori ordering, the Jonckheere test has more statistical power than the Kruskal\u2013Wallis test. The test was developed by A. R. Jonckheere, who was a psychologist and statistician at University College London.\nThe null and alternative hypotheses can be conveniently expressed in terms of population medians for k populations (where k > 2). Letting \u03b8i be the population median for the ith population, the null hypothesis is:\n\n \n \n \n \n H\n \n 0\n \n \n :\n \n \u03b8\n \n 1\n \n \n =\n \n \u03b8\n \n 2\n \n \n =\n \u22ef\n =\n \n \u03b8\n \n k\n \n \n \n \n {\\displaystyle H_{0}:\\theta _{1}=\\theta _{2}=\\cdots =\\theta _{k}}\n The alternative hypothesis is that the population medians have an a priori ordering e.g.:\n\n \n \n \n \n H\n \n A\n \n \n :\n \n \u03b8\n \n 1\n \n \n \n \n {\\displaystyle H_{A}:\\theta _{1}}\n \u2264 \n \n \n \n \n \u03b8\n \n 2\n \n \n \n \n {\\displaystyle \\theta _{2}}\n \u2264 \n \n \n \n \u22ef\n \n \n {\\displaystyle \\cdots }\n \u2264 \n \n \n \n \n \u03b8\n \n k\n \n \n \n \n {\\displaystyle \\theta _{k}}\n with at least one strict inequality.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Aimable Robert Jonckheere", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent variable", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kruskal\u2013Wallis test", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maurice Kendall", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Page's trend test", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard normal distribution", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistically significant", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "University College London", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://oai.cwi.nl/oai/asset/8258/8258A.pdf", "http://doi.org/10.1016%2FS0022-5371(74)80011-3", "http://doi.org/10.2307%2F2282965", "http://doi.org/10.2307%2F2333011", "https://books.google.com/books?id=0hPvAAAAMAAJ&pg=PA234"]}, "Nonparametric skew": {"categories": ["All articles with incomplete citations", "Articles with incomplete citations from November 2012", "Summary statistics", "Wikipedia articles needing clarification from July 2012"], "title": "Nonparametric skew", "method": "Nonparametric skew", "url": "https://en.wikipedia.org/wiki/Nonparametric_skew", "summary": "In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values. It is a measure of the skewness of a random variable's distribution\u2014that is, the distribution's tendency to \"lean\" to one side or the other of the mean. Its calculation does not require any knowledge of the form of the underlying distribution\u2014hence the name nonparametric. It has some desirable properties: it is zero for any symmetric distribution; it is \nunaffected by a scale shift; and it reveals either left- or right-skewness equally well. Although its use has been mentioned in older textbooks it appears to have gone out of fashion. In statistical samples it has been shown to be less powerful than the usual measures of skewness in detecting departures of the population from normality.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute value", "Accelerated failure time model", "Actuarial science", "Affine transformation", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "ArXiv", "Arithmetic mean", "Arthur Lyon Bowley", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Beta distribution", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Birnbaum\u2013Saunders distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Characteristic function (probability theory)", "Chemometrics", "Chi-squared test", "Chi square distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulative distribution function", "Dagum distribution", "Data collection", "Decomposition of time series", "Degrees of freedom", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Edgeworth expansion", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Euler's constant", "Expected value", "Experiment", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Exponentially modified Gaussian distribution", "F-test", "F distribution", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma distribution", "General linear model", "Generalized Pareto distribution", "Generalized linear model", "Generalized normal distribution", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-normal distribution", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Integer", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Isotonic regression", "J. B. S. Haldane", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Weibull distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logistic regression", "Lomax distribution", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maurice Kendall", "Maximum a posteriori estimation", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Nakagami distribution", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile function", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Real number", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sample standard deviation", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Symmetric distribution", "Symmetric probability distribution", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Udny Yule", "Uniformly most powerful test", "Unimodal distribution", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wilcoxon signed-rank test", "Yulia Gel", "Z-test"], "references": ["http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1037&context=rgp_rsr", "http://web.ipac.caltech.edu/staff/fmasci/home/statistics_refs/UsefulDistributions.pdf", "http://www.math.ucla.edu/~tom/papers/unpublished/meanmed.pdf", "http://www.se16.info/hgb/median.htm", "http://www.amstat.org/publications/jse/v13n2/vonhippel.html", "http://www.amstat.org/publications/jse/v13n3/lesser_letter.html", "http://www.amstat.org/publications/jse/v19n2/doane.pdf", "http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research/steel/steel_homepage/techrep/mosrevcsda.pdf", "https://doi.org/10.1093%2Fbiomet%2F11.4.425", "https://doi.org/10.1214%2Faoms%2F1177704482"]}, "Likelihood interval": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2016", "Bayesian statistics", "Maximum likelihood estimation"], "title": "Likelihood function", "method": "Likelihood interval", "url": "https://en.wikipedia.org/wiki/Likelihood_function", "summary": "In frequentist inference, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, given specific observed data. Likelihood functions play a key role in frequentist inference, especially methods of estimating a parameter from a set of statistics. In informal contexts, \"likelihood\" is often used as a synonym for \"probability\". In mathematical statistics, the two terms have different meanings. Probability in this mathematical context describes the plausibility of a random outcome, given a model parameter value, without reference to any observed data. Likelihood describes the plausibility of a model parameter value, given specific observed data.\nIn Bayesian inference, although one can speak about the likelihood of any proposition or random variable given another random variable: for example the likelihood of a parameter value or of a statistical model (see marginal likelihood), given specified data or other evidence, the likelihood function remains the same entity, with the additional interpretations of (i) a conditional density of the data given the parameter (since it is then a random variable) and (ii) a measure or amount of information brought by the data about the parameter value or even the model. Due to the introduction of a probability structure on the parameter space or on the collection of models, it is a possible occurrence that a parameter value or a statistical model have a large likelihood value for a given specified observed data, and yet have a low probability, or vice versa. This is often the case in medical contexts. Following Bayes' Rule, the likelihood when seen as a conditional density can be multiplied by the prior probability density of the parameter and then normalized, to give a posterior probability density.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5a/LikelihoodFunctionAfterHH.png", "https://upload.wikimedia.org/wikipedia/commons/2/20/LikelihoodFunctionAfterHHT.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["A. W. F. Edwards", "Accelerated failure time model", "Actuarial science", "Akaike Information Criterion", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anders Hald", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes' Rule", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Bioinformatics (journal)", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Cambridge University Press", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chapman & Hall", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional entropy", "Conditional probability", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Counting measure", "Coverage probability", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "David Cox (statistician)", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Derivative", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Divergent series", "Donald A. S. Fraser", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical likelihood", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "Exponentiation", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's exact test", "Forest plot", "Fourier analysis", "Francis Ysidro Edgeworth", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Function (mathematics)", "Fundamental theorem of calculus", "G-test", "Gamma distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "German tank problem", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Harvard University Press", "Heteroscedasticity", "Histogram", "History of probability", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypergeometric distribution", "IID", "Identifiability analysis", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval (mathematics)", "Interval estimate", "Interval estimation", "Inverse probability", "Isotonic regression", "Iverson bracket", "JSTOR", "Jackknife resampling", "Jahrbuch \u00fcber die Fortschritte der Mathematik", "Jarque\u2013Bera test", "Johansen test", "John W. Pratt", "John Wiley & Sons", "Johns Hopkins University Press", "Jonckheere's trend test", "Journal of the Royal Statistical Society, Series A", "Journal of the Royal Statistical Society, Series B", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L'H\u00f4pital's rule", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood interval", "Likelihood principle", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marginal likelihood", "Mathematical Reviews", "Mathematical statistics", "Maximum", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimate", "Maximum likelihood estimation", "McNemar's test", "Mean", "Mean value", "Median", "Median-unbiased estimator", "Medical statistics", "Method of maximum likelihood", "Method of moments (statistics)", "Methods engineering", "Middle English", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural logarithm", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Nuisance parameter", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameterized family", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial derivative", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Philosophical Transactions of the Royal Society", "Phylogenetics", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principle of maximum entropy", "Prior probability", "Probabilistic design", "Probability", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Proportional hazards model", "Prosecutor's fallacy", "Pseudolikelihood", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Radon\u2013Nikodym theorem", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Residual maximum likelihood", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score (statistics)", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shorter Oxford English Dictionary", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Stationary process", "Statistic", "Statistical Science", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistically independent", "Statistics", "Stem-and-leaf display", "Stephen Stigler", "Stratified sampling", "Strictly increasing", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The Annals of Statistics", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tunghai University", "U-statistic", "Uncertainty analysis", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://digital.library.adelaide.edu.au/dspace/handle/2440/15172", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3324512", "http://www.ncbi.nlm.nih.gov/pubmed/19505944", "http://www.ncbi.nlm.nih.gov/pubmed/22355081", "http://www.ams.org/mathscinet-getitem?mr=0400509", "http://doi.org/10.1002/9781118341544", "http://doi.org/10.1007%2Fs00362-007-0056-5", "http://doi.org/10.1093%2Fbioinformatics%2Fbtp358", "http://doi.org/10.1093%2Fbioinformatics%2Fbts088", "http://doi.org/10.1093%2Fbiomet%2F62.2.269", "http://doi.org/10.1098%2Frsta.1922.0009", "http://doi.org/10.1214%2Faos%2F1176343457", "http://doi.org/10.1214%2Fss%2F1009212248", "http://doi.org/10.1214%2Fss%2F1030037905", "http://doi.org/10.2307%2F2344804", "http://www.jstor.org/stable/2344804", "http://www.jstor.org/stable/2676741", "http://www.jstor.org/stable/2958222", "http://www.jstor.org/stable/91208", "http://bioinformatics.oxfordjournals.org/content/28/8/1130.long", "http://planetmath.org/likelihoodfunction", "http://projecteuclid.org/download/pdf_1/euclid.ss/1009212248", "http://zbmath.org/?format=complete&q=an:48.1280.02", "http://www.math.uni.wroc.pl/~pms/files/15/Article/15.21.pdf", "http://web.thu.edu.tw/wenwei/www/glmpdfmargin.htm", "https://academic.oup.com/bioinformatics/article/25/15/1923/213246", "https://projecteuclid.org/euclid.ss/1030037905", "https://books.google.co.uk/books?id=hyN6gXHvSo0C"]}, "Variational Bayesian methods": {"categories": ["Accuracy disputes from April 2018", "All articles lacking in-text citations", "Articles lacking in-text citations from September 2010", "Bayesian statistics"], "title": "Variational Bayesian methods", "method": "Variational Bayesian methods", "url": "https://en.wikipedia.org/wiki/Variational_Bayesian_methods", "summary": "Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning. They are typically used in complex statistical models consisting of observed variables (usually termed \"data\") as well as unknown parameters and latent variables, with various sorts of relationships among the three types of random variables, as might be described by a graphical model. As is typical in Bayesian inference, the parameters and latent variables are grouped together as \"unobserved variables\". Variational Bayesian methods are primarily used for two purposes:\n\nTo provide an analytical approximation to the posterior probability of the unobserved variables, in order to do statistical inference over these variables.\nTo derive a lower bound for the marginal likelihood (sometimes called the \"evidence\") of the observed data (i.e. the marginal probability of the data given the model, with marginalization performed over unobserved variables). This is typically used for performing model selection, the general idea being that a higher marginal likelihood for a given model indicates a better fit of the data by that model and hence a greater probability that the model in question was the one that generated the data. (See also the Bayes factor article.)In the former purpose (that of approximating a posterior probability), variational Bayes is an alternative to Monte Carlo sampling methods \u2014 particularly, Markov chain Monte Carlo methods such as Gibbs sampling \u2014 for taking a fully Bayesian approach to statistical inference over complex distributions that are difficult to directly evaluate or sample from. In particular, whereas Monte Carlo techniques provide a numerical approximation to the exact posterior using a set of samples, Variational Bayes provides a locally-optimal, exact analytical solution to an approximation of the posterior.\nVariational Bayes can be seen as an extension of the EM (expectation-maximization) algorithm from maximum a posteriori estimation (MAP estimation) of the single most probable value of each parameter to fully Bayesian estimation which computes (an approximation to) the entire posterior distribution of the parameters and latent variables. As in EM, it finds a set of optimal parameter values, and it has the same alternating structure as does EM, based on a set of interlocked (mutually dependent) equations that cannot be solved analytically. \nFor many applications, variational Bayes produces solutions of comparable accuracy to Gibbs sampling at greater speed. However, deriving the set of equations used to iteratively update the parameters often requires a large amount of work compared with deriving the comparable Gibbs sampling equations. This is the case even for many models that are conceptually quite simple, as is demonstrated below in the case of a basic non-hierarchical model with only two parameters and no latent variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2a/Bayesian-gaussian-mixture-vb.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2e/Bregman_divergence_Pythagorean.png", "https://upload.wikimedia.org/wikipedia/commons/1/17/System-search.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["ArXiv", "Bayes factor", "Bayesian inference", "Bayesian network", "Bibcode", "Bregman divergence", "Calculus of variations", "Categorical distribution", "Categorical variable", "Christopher M. Bishop", "Circular dependency", "Completing the square", "Conditional probability distribution", "Conditionally independent", "Conjugate prior", "Covariance matrix", "Credible interval", "David J.C. MacKay", "Digital object identifier", "Dirichlet distribution", "Expectation-maximization", "Expectation-maximization algorithm", "Expectation maximization", "Expectation propagation", "Expected value", "Exponential family", "Gamma distribution", "Gaussian-Wishart distribution", "Gaussian-gamma distribution", "Gaussian distribution", "Gaussian mixture model", "Generalized filtering", "Gibbs sampling", "Graphical model", "Hyperparameter", "Hyperparameters", "Independent identically distributed", "Integral", "International Standard Book Number", "Iterative", "Joint probability", "Kullback\u2013Leibler divergence", "Latent variable", "Limit of a sequence", "Lower bound", "Machine learning", "Marginal likelihood", "Marginal probability", "Markov chain Monte Carlo", "Maximum Entropy Discrimination", "Maximum a posteriori", "Maximum a posteriori estimation", "Maximum likelihood", "Mean", "Mixture model", "Mode (statistics)", "Model evidence", "Model selection", "Moment (mathematics)", "Monte Carlo sampling", "Multinomial distribution", "Multivariate Gaussian distribution", "Nonlinear", "Normal-scaled inverse gamma distribution", "Normal distribution", "Normalization constant", "Normalizing constant", "One-to-one correspondence", "Parameter", "Partition of a set", "Plate notation", "Posterior distribution", "Posterior probability", "Precision (statistics)", "Precision matrix", "Prior distribution", "Probability density function", "Probability distribution", "Random variable", "Sample (statistics)", "Statistical independence", "Statistical inference", "Statistical model", "Thermodynamic free energy", "Variance", "Variational message passing", "Variational method (quantum mechanics)", "Wishart distribution"], "references": ["http://www.cse.buffalo.edu/faculty/mbeal/thesis/index.html", "http://adsabs.harvard.edu/abs/2014Entrp..16.6338A", "http://www.cs.jhu.edu/~jason/tutorials/variational.html", "http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf", "http://arxiv.org/abs/1803.10998", "http://arxiv.org/archive/cs.IT", "http://doi.org/10.3390%2Fe16126338", "http://www.inference.phy.cam.ac.uk/mackay/itila/", "http://www.robots.ox.ac.uk/~sjrob/Pubs/fox_vbtut.pdf", "http://www.gatsby.ucl.ac.uk/vbayes/", "https://arxiv.org/abs/1803.10998", "https://doi.org/10.1007%2Fs10462-011-9236-8"]}, "Second moment method": {"categories": ["All pages needing cleanup", "Articles containing proofs", "Articles needing cleanup from January 2009", "Cleanup tagged articles without a reason field from January 2009", "Moment (mathematics)", "Probabilistic inequalities", "Wikipedia pages needing cleanup from January 2009"], "title": "Second moment method", "method": "Second moment method", "url": "https://en.wikipedia.org/wiki/Second_moment_method", "summary": "In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive. More generally, the \"moment method\" consists of bounding the probability that a random variable fluctuates far from its mean, by using its moments.The method is often quantitative, in that one can often deduce a lower bound on the probability that the random variable is larger than some constant times its expectation. The method involves comparing the second moment of random variables to the square of the first moment.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Analysis", "ArXiv", "Bernoulli bond percolation", "Binary tree", "Cauchy\u2013Schwarz inequality", "Converge in law", "Digital object identifier", "Fubini's theorem", "Glossary of graph theory", "Handle System", "Integral", "Markov's inequality", "Moment (mathematics)", "Paley\u2013Zygmund inequality", "Probability theory", "Random variable", "Reverse Fatou lemma", "Terence Tao", "Tree (graph theory)"], "references": ["http://terrytao.wordpress.com/2008/06/18/the-strong-law-of-large-numbers/", "http://mypage.iu.edu/~rdlyons/prbtree/prbtree.html", "http://hdl.handle.net/1773%2F2194", "http://arxiv.org/abs/math/9701225", "http://doi.org/10.1214%2Faop%2F1022855639", "http://doi.org/10.1214%2Faop%2F1176989540"]}, "Feature extraction": {"categories": ["All articles lacking sources", "Articles lacking sources from January 2016", "Dimension reduction", "Feature detection (computer vision)"], "title": "Feature extraction", "method": "Feature extraction", "url": "https://en.wikipedia.org/wiki/Feature_extraction", "summary": "In machine learning, pattern recognition and in image processing, feature extraction starts from an initial set of measured data and builds derived values (features) intended to be informative and non-redundant, facilitating the subsequent learning and generalization steps, and in some cases leading to better human interpretations. Feature extraction is a dimensionality reduction process, where an initial set of raw variables is reduced to more manageable groups (features) for processing, while still accurately and completely describing the original data set.When the input data to an algorithm is too large to be processed and it is suspected to be redundant (e.g. the same measurement in both feet and meters, or the repetitiveness of images presented as pixels), then it can be transformed into a reduced set of features (also named a feature vector). Determining a subset of the initial features is called feature selection. The selected features are expected to contain the relevant information from the input data, so that the desired task can be performed by using this reduced representation instead of the complete initial data.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Algorithm", "Autocorrelation", "Autoencoder", "Blob detection", "Blob extraction", "Cluster analysis", "Connected-component labeling", "Corner detection", "Data mining", "Digitized image", "Dimensionality reduction", "Edge detection", "Feature (machine learning)", "Feature detection (computer vision)", "Feature engineering", "Feature selection", "Feature vector", "Hough transform", "Image processing", "Independent component analysis", "International Standard Book Number", "Isomap", "Kernel PCA", "Latent semantic analysis", "List of statistical packages", "MATLAB", "Machine learning", "Motion detection", "Multifactor dimensionality reduction", "Multilinear PCA", "Multilinear subspace learning", "Nonlinear dimensionality reduction", "NumPy", "Optical character recognition", "Optical flow", "Overfitting", "Partial least squares", "Pattern recognition", "Principal component analysis", "R (programming language)", "Raster image", "Ridge detection", "Scale-invariant feature transform", "SciLab", "Segmentation (image processing)", "Semidefinite embedding", "Space mapping", "Statistical classification", "Template matching", "Thresholding (image processing)", "Video stream"], "references": ["https://reality.ai/", "https://reality.ai/it-is-all-about-the-features/", "https://books.google.com/books?id=7f5bBAAAQBAJ&printsec=frontcover#v=onepage&q=%22feature%20(extraction%20OR%20selection)%22&f=false", "https://deepai.org/machine-learning-glossary-and-terms/feature-extraction"]}, "Winsorising": {"categories": ["Robust statistics", "Statistical data transformation"], "title": "Winsorizing", "method": "Winsorising", "url": "https://en.wikipedia.org/wiki/Winsorizing", "summary": "Winsorizing or winsorization is the transformation of statistics by limiting extreme values in the statistical data to reduce the effect of possibly spurious outliers. It is named after the engineer-turned-biostatistician Charles P. Winsor (1895\u20131951). The effect is the same as clipping in signal processing.\nThe distribution of many statistics can be heavily influenced by outliers. A typical strategy is to set all outliers to a specified percentile of the data; for example, a 90% winsorization would see all data below the 5th percentile set to the 5th percentile, and data above the 95th percentile set to the 95th percentile.\nWinsorized estimators are usually more robust to outliers than their more standard forms, although there are alternatives, such as trimming, that will achieve a similar effect.\n\n", "images": [], "links": ["Annals of Mathematical Statistics", "Censoring (statistics)", "Clipping (signal processing)", "Digital object identifier", "Estimator", "Extreme value", "Huber loss", "JSTOR", "John Tukey", "NumPy", "Order statistics", "Outlier", "Outliers", "Percentile", "Python (programming language)", "Robust regression", "Robust statistics", "SciPy", "Statistic", "Statistics", "Trimmed estimator", "Truncated mean", "Truncation (statistics)", "Weighted average", "Winsorized mean"], "references": ["http://doi.org/10.1214%2Faoms%2F1177704711", "http://doi.org/10.1214%2Faoms%2F1177705900", "http://doi.org/10.1214%2Faoms%2F1177730388", "http://www.jstor.org/stable/2237638", "https://www.r-bloggers.com/winsorization/"]}, "Bland\u2013Altman plot": {"categories": ["Analytical chemistry", "Medical statistics", "Statistical charts and diagrams"], "title": "Bland\u2013Altman plot", "method": "Bland\u2013Altman plot", "url": "https://en.wikipedia.org/wiki/Bland%E2%80%93Altman_plot", "summary": "A Bland\u2013Altman plot (Difference plot) in analytical chemistry or biomedicine is a method of data plotting used in analyzing the agreement between two different assays. It is identical to a Tukey mean-difference plot, the name by which it is known in other fields, but was popularised in medical statistics by J. Martin Bland and Douglas G. Altman.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f8/Bland-Alman_Plot_with_CI%27s_on_LOA.png"], "links": ["Analyse-it", "Analytical chemistry", "Assay", "Cartesian coordinate system", "Correlation", "Data plot", "Deming regression", "Digital object identifier", "Doug Altman", "Estimation statistics", "Gold standard (test)", "International Standard Book Number", "International Standard Serial Number", "J. Martin Bland", "John Tukey", "Limits of agreement", "MA plot", "Mean", "MedCalc", "Medical statistics", "NCSS (statistical software)", "OCLC", "Outlier", "PubMed Central", "PubMed Identifier", "R (programming language)", "Standard deviation", "Statistical Methods in Medical Research", "StatsDirect", "Student's t-test"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2944826", "http://www.ncbi.nlm.nih.gov/pubmed/10501650", "http://www.ncbi.nlm.nih.gov/pubmed/18560291", "http://www.ncbi.nlm.nih.gov/pubmed/25355343", "http://www.ncbi.nlm.nih.gov/pubmed/2868172", "http://doi.org/10.1016%2FS0140-6736(86)90837-8", "http://doi.org/10.1038%2F514550a", "http://doi.org/10.1097%2F01.AACN.0000318125.41512.a3", "http://doi.org/10.1097%2FOPX.0000000000000513", "http://doi.org/10.1191%2F096228099673819272", "http://doi.org/10.2307%2F2987937", "http://www.worldcat.org/issn/0028-0836", "http://www.worldcat.org/oclc/29456028", "https://www.worldcat.org/oclc/29456028", "https://www-users.york.ac.uk/~mb55/meas/ba.pdf"]}, "M-estimator": {"categories": ["All articles to be merged", "Articles to be merged from October 2017", "Estimator", "M-estimators", "Robust regression", "Robust statistics"], "title": "M-estimator", "method": "M-estimator", "url": "https://en.wikipedia.org/wiki/M-estimator", "summary": "In statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. Both non-linear least squares and maximum likelihood estimation are special cases of M-estimators. The definition of M-estimators was motivated by robust statistics, which contributed new types of M-estimators. The statistical procedure of evaluating an M-estimator on a data set is called M-estimation.\nMore generally, an M-estimator may be defined to be a zero of an estimating function. This estimating function is often the derivative of another statistical function. For example, a maximum-likelihood estimate is the point where the derivative of the likelihood function with respect to the parameter is zero; thus, a maximum-likelihood estimator is a critical point of the score function. In many applications, such M-estimators can be thought of as estimating characteristics of the population.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrap (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "CiteSeerX", "Class (mathematics)", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Critical point (mathematics)", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "Extremum estimator", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Iid", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iteratively re-weighted least squares", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-estimator", "L-moment", "Law of large numbers", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McNemar's test", "Mean", "Measurable function", "Median", "Median-unbiased estimator", "Median absolute deviation", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Newton\u2013Raphson", "Non-linear least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Objective function", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter J. Huber", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R-estimator", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Redescending M-estimator", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "S-estimator", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sara van de Geer", "Scale parameter", "Scatter plot", "Scientific control", "Score (statistics)", "Score test", "Seasonal adjustment", "Seemingly unrelated regressions", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Two-step M-estimators involving MLE", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald-type test", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://research.microsoft.com/en-us/um/people/zhang/INRIA/Publis/Tutorial-Estim/node24.html#SECTION000104000000000000000", "http://apps.nrbook.com/empanel/index.html#pg=818", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.2288", "http://www.ams.org/mathscinet-getitem?mr=1792795", "http://doi.org/10.1007%2Fb98823", "http://doi.org/10.1080%2F01621459.1982.10477894", "http://doi.org/10.1214%2Faos%2F1015952006", "http://doi.org/10.2277%2F052165002X", "http://www.jstor.org/stable/2287314", "http://www.jstor.org/stable/2674061", "https://davegiles.blogspot.com/2012/07/concentrating-or-profiling-likelihood.html", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA447"]}, "Laplace distribution": {"categories": ["Continuous distributions", "Exponential family distributions", "Geometric stable distributions", "Location-scale family probability distributions", "Pages using deprecated image syntax", "Pierre-Simon Laplace"], "title": "Laplace distribution", "method": "Laplace distribution", "url": "https://en.wikipedia.org/wiki/Laplace_distribution", "summary": "In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together back-to-back, although the term is also sometimes used to refer to the Gumbel distribution. The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time. Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b1/Laplace_Surinam.png", "https://upload.wikimedia.org/wikipedia/commons/a/ad/Laplace_cdf_mod.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0a/Laplace_pdf_mod.svg"], "links": ["ARGUS distribution", "Absolute difference", "Absolute value", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Besov measure", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Brownian motion", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Confidence belt", "Conway\u2013Maxwell\u2013Poisson distribution", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Differential privacy", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Fourier transform", "Discrete Weibull distribution", "Discrete cosine transform", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Encyclopedia of Mathematics", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential integral", "Exponential power distribution", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Function space", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hydrology", "Hyper-Erlang distribution", "Hyperbolic distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Iid", "Independent identically-distributed random variables", "Information entropy", "Integral", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Keynes", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace motion", "Lasso (statistics)", "Least absolute deviations", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Michiel Hazewinkel", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Pierre-Simon Laplace", "Plotting position", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Robert M. Norton", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "The American Statistician", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Variance gamma process", "Variate", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://openaccess.uoc.edu/webapps/o2/bitstream/10609/6263/6/jei-jpeg.pdf", "http://eo.uit.no/publications/TE-SPL-06.pdf", "http://doi.org/10.1109%2FLSP.2006.870353", "http://doi.org/10.1117%2F1.1344592", "http://doi.org/10.2307%2F2683252", "http://www.jstor.org/stable/2683252", "https://books.google.com/books?id=cb8B07hwULUC&lpg=PA22&dq=laplace%20distribution%20exponential%20characteristic%20function&hl=fr&pg=PA23#v=onepage&q=laplace%20distribution%20exponential%20characteristic%20function&f=false", "https://www.waterlog.info/composite.htm", "https://www.waterlog.info/cumfreq.htm", "https://www.encyclopediaofmath.org/index.php?title=p/l057460"]}, "Probability density function": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from November 2017", "Articles with unsourced statements from October 2013", "Concepts in physics", "Functions related to probability distributions", "Webarchive template wayback links"], "title": "Probability density function", "method": "Probability density function", "url": "https://en.wikipedia.org/wiki/Probability_density_function", "summary": "In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample. In other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there are an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would equal one sample compared to the other sample.\nIn a more precise sense, the PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable\u2019s PDF over that range\u2014that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.\nThe terms \"probability distribution function\" and \"probability function\" have also sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. In other sources, \"probability distribution function\" may be used when the probability distribution is defined as a function over general sets of values, or it may refer to the cumulative distribution function, or it may be a probability mass function (PMF) rather than the density. \"Density function\" itself is also used for the probability mass function, leading to further confusion. In general though, the PMF is used in the context of discrete random variables (random variables that take values on a discrete set), while PDF is used in the context of continuous random variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Boxplot_vs_PDF.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/3/33/Visualisation_mode_median_mean.svg"], "links": ["Absolute continuity", "Almost everywhere", "Andrey Kolmogorov", "Atomic orbital", "Bijective", "Borel set", "Boxplot", "Cantor distribution", "Cauchy distribution", "Central moment", "Characteristic function (probability theory)", "Combinant", "Continuous probability distribution", "Continuous random variable", "Conversion of units", "Convolution", "Counting measure", "Cumulant", "Cumulative distribution function", "Density estimation", "Derivative", "Differentiable function", "Dirac delta", "Dirac delta function", "Discrete random variable", "Domain of a function", "Encyclopedia of Mathematics", "Eric W. Weisstein", "Expected value", "Function (mathematics)", "Home range", "Integer", "Integral", "International Standard Book Number", "Interval (mathematics)", "Inverse function", "Jacobian matrix", "Jacobian matrix and determinant", "Kernel (statistics)", "Kernel density estimation", "Kurtosis", "L-moment", "Law of the unconscious statistician", "Lebesgue integration", "Lebesgue measure", "Likelihood function", "List of convolutions of probability distributions", "List of probability distributions", "Marginalizing out", "MathWorld", "Mean", "Mean (statistics)", "Measurable space", "Measure theory", "Measure zero", "Median (statistics)", "Michiel Hazewinkel", "Mode (statistics)", "Moment-generating function", "Monotonic", "Monotonic function", "Normal distribution", "Normalization factor", "OCLC", "One-to-one function", "Parameter", "Patrick Billingsley", "Pierre Simon de Laplace", "Probability-generating function", "Probability axioms", "Probability distribution", "Probability mass function", "Probability theory", "Product distribution", "Quantile function", "Rademacher distribution", "Radon\u2013Nikodym derivative", "Random variable", "Ratio distribution", "Raw moment", "Sample space", "Secondary measure", "Skewness", "Standard deviation", "Standard normal distribution", "Statistical independence", "Statistical physics", "Uniform distribution (continuous)", "Univariate distribution", "Variance", "Wayback Machine"], "references": ["http://apstatsreview.tumblr.com/post/50058615236/density-curves-and-the-normal-distributions?action=purge", "http://mathworld.wolfram.com/ProbabilityDensityFunction.html", "http://mathworld.wolfram.com/ProbabilityFunction.html", "http://planetmath.org/?method=png&from=objects&id=2884&op=getobj", "http://www.worldcat.org/oclc/851313783", "https://web.archive.org/web/20110807023948/http://planetmath.org/?method=png&from=objects&id=2884&op=getobj", "https://www.encyclopediaofmath.org/index.php?title=D/d031110", "https://www.worldcat.org/oclc/851313783"]}, "Random regular graph": {"categories": ["Random graphs", "Regular graphs"], "title": "Random regular graph", "method": "Random regular graph", "url": "https://en.wikipedia.org/wiki/Random_regular_graph", "summary": "A random r-regular graph is a graph selected from \n \n \n \n \n \n \n G\n \n \n \n n\n ,\n r\n \n \n \n \n {\\displaystyle {\\mathcal {G}}_{n,r}}\n , which denotes the probability space of all r-regular graphs on n vertices, where 3 \u2264 r < n and nr is even. It is therefore a particular kind of random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.", "images": [], "links": ["Almost surely", "Brendan McKay", "B\u00e9la Bollob\u00e1s", "Connectivity (graph theory)", "Diameter (graph theory)", "Graph (discrete mathematics)", "Multigraph", "Random graph", "Regular graph"], "references": ["http://cs.anu.edu.au/~bdm/papers/RandRegGen.pdf"]}, "Generalized least squares": {"categories": ["All articles needing additional references", "All pages needing cleanup", "Articles needing additional references from July 2009", "Articles needing cleanup from May 2010", "Articles with multiple maintenance issues", "Cleanup tagged articles without a reason field from May 2010", "Least squares", "Wikipedia pages needing cleanup from May 2010"], "title": "Generalized least squares", "method": "Generalized least squares", "url": "https://en.wikipedia.org/wiki/Generalized_least_squares", "summary": "In statistics, generalized least squares (GLS) is a technique for estimating the unknown parameters in a linear regression model when there is a certain degree of correlation between the residuals in a regression model. In these cases, ordinary least squares and weighted least squares can be statistically inefficient, or even give misleading inferences. GLS was first described by Alexander Aitken in 1934.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Alexander Aitken", "Asymptotic distribution", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bias of an estimator", "Blue (statistics)", "Cholesky decomposition", "Conditional mean", "Confidence region", "Consistent estimator", "Correlation", "Covariance matrix", "Degrees of freedom (statistics)", "Design matrix", "Digital object identifier", "Discrete choice", "Efficiency (statistics)", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized linear model", "Goodness of fit", "Heteroscedasticity", "Heteroscedasticity-consistent standard errors", "Identity matrix", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Jan Kmenta", "John Johnston (econometrician)", "Journal of Econometrics", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Mahalanobis distance", "Mean and predicted response", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Parameter", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistical inference", "Statistical residual", "Statistical unit", "Statistics", "Studentized residual", "Takeshi Amemiya", "Tikhonov regularization", "Total least squares", "Variance", "Weighted least squares"], "references": ["http://doi.org/10.1016%2Fj.jeconom.2006.07.011", "https://books.google.com/books?id=0bzGQE14CwEC&pg=PA181", "https://books.google.com/books?id=BZtvwZAGyV0C&pg=PA208", "https://books.google.com/books?id=Bxq7AAAAIAAJ&pg=PA607"]}, "Cover's theorem": {"categories": ["All stub articles", "Artificial neural networks", "Computational learning theory", "Pages incorrectly using the quote template", "Statistical classification", "Statistics stubs"], "title": "Cover's theorem", "method": "Cover's theorem", "url": "https://en.wikipedia.org/wiki/Cover%27s_theorem", "summary": "Cover's Theorem is a statement in computational learning theory and is one of the primary theoretical motivations for the use of non-linear kernel methods in machine learning applications. The theorem states that given a set of training data that is not linearly separable, one can with high probability transform it into a training set that is linearly separable by projecting it into a higher-dimensional space via some non-linear transformation. The theorem is named after the information theorist Thomas M. Cover who stated it in 1965.\nThe proof is easy. A deterministic mapping may be used. Indeed, suppose there are \n \n \n \n n\n \n \n {\\displaystyle n}\n samples. Lift them onto the vertices of the simplex in the \n \n \n \n n\n \u2212\n 1\n \n \n {\\displaystyle n-1}\n dimensional real space. Every partition of the samples into two sets is separable by a linear separator. QED.\n\nA complex pattern-classification problem, cast in a high-dimensional space nonlinearly, is more likely to be linearly separable than in a low-dimensional space, provided that the space is not densely populated.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Computational learning theory", "Digital object identifier", "Higher-dimensional space", "International Standard Book Number", "Kernel methods", "Linear separability", "Linearly separable", "Machine learning", "Map (mathematics)", "Mathematical proof", "Non-linear transformation", "Partition of a set", "Pattern recognition", "Simplex", "Statistics", "Thomas M. Cover"], "references": ["http://doi.org/10.1109/pgec.1965.264137", "https://books.google.com/books?id=6d68Y4Wq_R4C&pg=PA88"]}, "Killed process": {"categories": ["Stochastic processes"], "title": "Killed process", "method": "Killed process", "url": "https://en.wikipedia.org/wiki/Killed_process", "summary": "In probability theory \u2014 specifically, in stochastic analysis \u2014 a killed process is a stochastic process that is forced to assume an undefined or \"killed\" state at some (possibly random) time.\n\n", "images": [], "links": ["Bernt \u00d8ksendal", "Index set", "International Standard Book Number", "Measurable space", "Ordered set", "Probability space", "Probability theory", "Process state", "Stochastic processes", "Stopped process"], "references": []}, "Stochastic investment model": {"categories": ["All articles lacking in-text citations", "All pages needing cleanup", "Articles lacking in-text citations from June 2012", "Articles needing cleanup from January 2012", "Articles with multiple maintenance issues", "Articles with sections that need to be turned into prose from January 2012", "Financial models", "Monte Carlo methods in finance", "Wikipedia articles needing clarification from January 2012"], "title": "Stochastic investment model", "method": "Stochastic investment model", "url": "https://en.wikipedia.org/wiki/Stochastic_investment_model", "summary": "A stochastic investment model tries to forecast how returns and prices on different assets or asset classes, (e. g. equities or bonds) vary over time. Stochastic models are not applied for making point estimation rather interval estimation and they use different stochastic processes. Investment models can be classified into single-asset and multi-asset models. They are often used for actuarial work and financial planning to allow optimization in asset allocation or asset-liability-management (ALM).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Actuary", "Asset allocation", "Asset liability management", "Binomial model", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Chen model", "Cox\u2013Ingersoll\u2013Ross model", "Financial plan", "Fixed income", "Geometric Brownian motion", "Ho\u2013Lee model", "Hull\u2013White model", "Interval estimation", "JSTOR", "Kalotay\u2013Williams\u2013Fabozzi model", "LIBOR market model", "Longstaff\u2013Schwartz model", "Merton model", "Point estimation", "Price", "Rate of return", "Rendleman\u2013Bartter model", "Stochastic process", "Vasicek model", "Wilkie investment model"], "references": ["http://www.actuaries.org.uk/sites/all/files/documents/pdf/0341-0403.pdf", "https://www.jstor.org/stable/2946287", "https://www.jstor.org/stable/3439055"]}, "Ramsey RESET test": {"categories": ["Regression diagnostics", "Statistical tests"], "title": "Ramsey RESET test", "method": "Ramsey RESET test", "url": "https://en.wikipedia.org/wiki/Ramsey_RESET_test", "summary": "In statistics, the Ramsey Regression Equation Specification Error Test (RESET) test is a general specification test for the linear regression model. More specifically, it tests whether non-linear combinations of the fitted values help explain the response variable. The intuition behind the test is that if non-linear combinations of the explanatory variables have any power in explaining the response variable, the model is misspecified in the sense that the data generating process might be better approximated by a polynomial or another non-linear functional form.\nThe test was developed by James B. Ramsey as part of his Ph.D. thesis at the University of Wisconsin\u2013Madison in 1968, and later published in the Journal of the Royal Statistical Society in 1969.\n\n", "images": [], "links": ["Digital object identifier", "Explanatory variable", "F-test", "Harvey\u2013Collier test", "International Standard Book Number", "J. Scott Long", "JSTOR", "James B. Ramsey", "Jeffrey Wooldridge", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society", "Journal of the Royal Statistical Society, Series B", "Linear regression", "Polynomial", "Response variable", "Specification (regression)", "Statistics", "University of Wisconsin\u2013Madison"], "references": ["http://doi.org/10.1080%2F01621459.1977.10480627", "http://www.jstor.org/stable/2286231", "http://www.jstor.org/stable/2984219", "https://books.google.com/books?id=4TZnpwAACAAJ", "https://books.google.com/books?id=BhO3AAAAIAAJ&pg=PA13"]}, "Unimodal function": {"categories": ["CS1 Russian-language sources (ru)", "CS1 maint: Uses authors parameter", "Functions and mappings", "Mathematical relations", "Theory of probability distributions"], "title": "Unimodality", "method": "Unimodal function", "url": "https://en.wikipedia.org/wiki/Unimodality", "summary": "In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e2/Bimodal.png", "https://upload.wikimedia.org/wikipedia/commons/b/bc/Bimodal_geological.PNG", "https://upload.wikimedia.org/wikipedia/commons/f/fb/Normal_distribution_pdf.svg"], "links": ["American Statistician", "Bimodal distribution", "Binomial distribution", "Carl Friedrich Gauss", "Cauchy distribution", "Characteristic function (probability theory)", "Chebychev's inequality", "Chebyshev inequality", "Chi-squared distribution", "Computational geometry", "Concave function", "Convex function", "Cumulative distribution function", "Digital object identifier", "Encyclopedia of Mathematics", "Eric W. Weisstein", "Euclidean space", "Exponential distribution", "Extremum", "Function (mathematics)", "Gauss's inequality", "Golden section search", "International Standard Book Number", "JSTOR", "Kurtosis", "Laplace\u2013Stieltjes transform", "Local unimodal sampling", "MathWorld", "Mathematics", "Maximum", "Michiel Hazewinkel", "Mode (statistics)", "Monotonic", "Multimodal distribution", "Normal distribution", "Pascal triangle", "Poisson distribution", "Probability density function", "Probability distribution", "Probability mass function", "Quadratic polynomial", "Quasiconvex function", "Real number", "Schwarzian derivative", "Search algorithm", "Skewness", "SkyTran", "Statistics", "Student's t-distribution", "Successive parabolic interpolation", "Tent map", "Ternary search", "Uniform distribution (continuous)", "Unimodal", "Unimodal distribution", "Vysochanski\u00ef\u2013Petunin inequality"], "references": ["http://homepage.univie.ac.at/thibaut.barthelemy/METRIC.pdf", "http://www.akademiai.com/content/j5012306777g764n/", "http://mathworld.wolfram.com/Mode.html", "http://mathworld.wolfram.com/Unimodal.html", "http://doi.org/10.1007%2Fbf00979872", "http://doi.org/10.1007%2Fbf02018665", "http://doi.org/10.2307%2F1971501", "http://doi.org/10.2307%2F2684690", "http://glossary.computing.society.informs.org/second.php?page=U.html", "http://www.jstor.org/stable/2684690", "http://epubs.siam.org/doi/pdf/10.1137/S0040585X97975447", "https://www.encyclopediaofmath.org/index.php?title=U/u095330"]}, "Luby transform code": {"categories": ["Coding theory", "Pages using RFC magic links"], "title": "Luby transform code", "method": "Luby transform code", "url": "https://en.wikipedia.org/wiki/Luby_transform_code", "summary": "In computer science, Luby transform codes (LT codes) are the first class of practical fountain codes that are near-optimal erasure correcting codes. They were invented by Michael Luby in 1998 and published in 2002. Like some other fountain codes, LT codes depend on sparse bipartite graphs to trade reception overhead for encoding and decoding speed. The distinguishing characteristic of LT codes is in employing a particularly simple algorithm based on the exclusive or operation (\n \n \n \n \u2295\n \n \n {\\displaystyle \\oplus }\n ) to encode and decode the message.LT codes are rateless because the encoding algorithm can in principle produce an infinite number of message packets (i.e., the percentage of packets that must be received to decode the message can be arbitrarily small). They are erasure correcting codes because they can be used to transmit digital data reliably on an erasure channel.\nThe next generation beyond LT codes are raptor codes (see for example IETF RFC 5053 or IETF RFC 6330), which have linear time encoding and decoding. Raptor codes use two encoding stages for encoding, where the second stage is an LT encoding.", "images": [], "links": ["Binary erasure channel", "Bipartite graph", "Bit", "Computer science", "Cyclic redundancy check", "Erasure correcting code", "Exclusive or", "Fountain code", "Michael Luby", "Online codes", "Pseudorandom number generator", "Raptor code", "Raptor codes", "Soliton distribution", "Tornado codes"], "references": ["http://www.codeproject.com/Articles/425456/Your-Digital-Fountain", "http://switzernet.com/people/emin-gabrielyan/060112-capillary-references/ref/MacKay05.pdf", "http://www.netlab.tkk.fi/tutkimus/abi/publ/lt-resim-2006.pdf", "http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1181950", "https://franpapers.com/en/algorithmic/2018-introduction-to-fountain-codes-lt-codes-with-python/"]}, "Bayes classifier": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2013", "Bayesian statistics", "Statistical classification"], "title": "Bayes classifier", "method": "Bayes classifier", "url": "https://en.wikipedia.org/wiki/Bayes_classifier", "summary": "In statistical classification the Bayes classifier minimizes the probability of misclassification.", "images": [], "links": ["Classification rule", "Conditional distribution", "Consistency (statistics)", "International Standard Book Number", "Misclassification", "Naive Bayes classifier", "Probability", "Risk (statistics)", "Statistical classification"], "references": []}, "Goodman and Kruskal's lambda": {"categories": ["Accuracy disputes from December 2011", "All accuracy disputes", "All articles lacking reliable references", "Articles lacking reliable references from July 2012", "Statistical ratios", "Summary statistics for contingency tables"], "title": "Goodman and Kruskal's lambda", "method": "Goodman and Kruskal's lambda", "url": "https://en.wikipedia.org/wiki/Goodman_and_Kruskal%27s_lambda", "summary": "In probability theory and statistics, Goodman & Kruskal's lambda (\n \n \n \n \u03bb\n \n \n {\\displaystyle \\lambda }\n ) is a measure of proportional reduction in error in cross tabulation analysis. For any sample with a nominal independent variable and dependent variable (or ones that can be treated nominally), it indicates the extent to which the modal categories and frequencies for each value of the independent variable differ from the overall modal category and frequency, i.e. for all values of the independent variable together. \n \n \n \n \u03bb\n \n \n {\\displaystyle \\lambda }\n can be calculated with the equation\n\n \n \n \n \u03bb\n =\n \n \n \n \n \u03b5\n \n 1\n \n \n \u2212\n \n \u03b5\n \n 2\n \n \n \n \n \u03b5\n \n 1\n \n \n \n \n .\n \n \n {\\displaystyle \\lambda ={\\frac {\\varepsilon _{1}-\\varepsilon _{2}}{\\varepsilon _{1}}}.}\n where\n\n \n \n \n \n \u03b5\n \n 1\n \n \n \n \n {\\displaystyle \\varepsilon _{1}}\n is the overall non-modal frequency, and\n\n \n \n \n \n \u03b5\n \n 2\n \n \n \n \n {\\displaystyle \\varepsilon _{2}}\n is the sum of the non-modal frequencies for each value of the independent variable.Values for lambda range from zero (no association between independent and dependent variables) to one (perfect association).", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/17/System-search.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accord (statistics)", "Cross tabulation", "Digital object identifier", "Independent variable", "JSTOR", "Journal of the American Statistical Association", "Level of measurement", "Perfect association", "Probability theory", "Proportional reduction in loss", "Statistics"], "references": ["http://www.nssl.noaa.gov/users/brooks/public_html/feda/papers/goodmankruskal1.pdf", "https://bitbucket.org/mhunter/readinglists/src/d8e8010f0b0d/ReadingList_NotreDame/GoodmanKruskal1959CrossClassificationMeasures2.pdf", "https://doi.org/10.1080%2F01621459.1963.10500850", "https://www.jstor.org/stable/2282143", "https://www.jstor.org/stable/2283271", "https://www.jstor.org/stable/281536"]}, "Markov network": {"categories": ["Graphical models", "Markov networks", "Wikipedia articles needing clarification from July 2018"], "title": "Markov random field", "method": "Markov network", "url": "https://en.wikipedia.org/wiki/Markov_random_field", "summary": "In the domain of physics and probability, a Markov random field (often abbreviated as MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it satisfies Markov properties.\nA Markov network or MRF is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies); on the other hand, it can't represent certain dependencies that a Bayesian network can (such as induced dependencies). The underlying graph of a Markov random field may be finite or infinite.\nWhen the joint probability density of the random variables is strictly positive, it is also referred to as a Gibbs random field, because, according to the Hammersley\u2013Clifford theorem, it can then be represented by a Gibbs measure for an appropriate (locally defined) energy function. The prototypical Markov random field is the Ising model; indeed, the Markov random field was introduced as the general setting for the Ising model.\nIn the domain of artificial intelligence, a Markov random field is used to model various low- to mid-level tasks in image processing and computer vision.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f7/Markov_random_field_example.png"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Andrew McCallum", "Andrey Markov, Jr.", "Artificial intelligence", "Association for Computing Machinery", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bayesian network", "Belief propagation", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Carla Brodley", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Chordal graph", "Chow\u2013Liu tree", "Classical Wiener space", "Clique (graph theory)", "Compound Poisson process", "Computer graphics (computer science)", "Computer stereo vision", "Computer vision", "Conditional distribution", "Conditional independence", "Conditional random field", "Conference on Neural Information Processing Systems", "Configuration space (physics)", "Constant elasticity of variance model", "Constraint Composite Graph", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Correlation function", "Covariance matrix", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Daphne Koller", "Determinant", "Diffusion process", "Digital object identifier", "Directed acyclic graph", "Dirichlet process", "Discrete-time stochastic process", "Discriminative model", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dot product", "Dynkin's formula", "Econometrics", "Empirical process", "Entropy", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exact inference", "Exchangeable random variables", "Expectation value", "Extreme value theory", "Factor graph", "Feller-continuous process", "Feller process", "Fernando C.N. Pereira", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Graphical model", "Hammersley\u2013Clifford theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Hopfield network", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Image processing", "Image registration", "Incidence matrix", "Independent and identically distributed random variables", "Indicator function", "Infinitesimal generator (stochastic processes)", "Information retrieval", "Interacting particle system", "International Conference on Machine Learning", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "John D. Lafferty", "Joint probability distribution", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Log-linear analysis", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "MIT Press", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov chain Monte Carlo", "Markov logic network", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical Reviews", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "Maximum a posteriori", "Maximum entropy method", "Maximum likelihood estimate", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Multivariate normal distribution", "Neighborhood (graph theory)", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Partition function (mathematics)", "Percolation theory", "Perturbation theory", "Physics", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potential energy", "Potts model", "Precision matrix", "Predictable process", "Probability", "Probability density function", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sharp-P-complete", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistical mechanics", "Statistics", "Stochastic analysis", "Stochastic cellular automata", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Super-resolution", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Texture synthesis", "Time reversibility", "Time series", "Time series analysis", "Trace (linear algebra)", "Undirected graph", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Variational method", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://icml.cc/2013/?page_id=21", "http://papers.nips.cc/paper/3117-using-combinatorial-optimization-within-max-product-belief-propagation", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.649.303&rep=rep1&type=pdf", "http://www.tiny-clues.eu/Research/Petitjean2013-ICDM.pdf", "http://www.cmap.polytechnique.fr/~rama/ehess/mrfbook.pdf", "http://www.ams.org/mathscinet-getitem?mr=0432132", "http://www.ams.org/mathscinet-getitem?mr=0620955", "http://doi.org/10.1007%2FBF01011714", "http://doi.org/10.1145%2F1015330.1015444", "http://doi.org/10.2140%2Fmemocs.2017..101", "https://books.google.com/books?id=rDsObhDkCIAC&printsec=frontcover#v=onepage&q&f=false", "https://bitbucket.org/rukletsov/b"]}, "Latent class model": {"categories": ["CS1 maint: Multiple names: authors list", "Classification algorithms", "Latent variable models", "Market research", "Market segmentation", "Wikipedia articles with GND identifiers"], "title": "Latent class model", "method": "Latent class model", "url": "https://en.wikipedia.org/wiki/Latent_class_model", "summary": "In statistics, a latent class model (LCM) relates a set of observed (usually discrete) multivariate variables to a set of latent variables. It is a type of latent variable model. It is called a latent class model because the latent variable is discrete. A class is characterized by a pattern of conditional probabilities that indicate the chance that variables take on certain values.\nLatent class analysis (LCA) is a subset of structural equation modeling, used to find groups or subtypes of cases in multivariate categorical data. These subtypes are called \"latent classes\".Confronted with a situation as follows, a researcher might choose to use LCA to understand the data: Imagine that symptoms a-d have been measured in a range of patients with diseases X Y and Z, and that disease X is associated with the presence of symptoms a, b, and c, disease Y with symptoms b, c, d, and disease Z with symptoms a, c and d.\nThe LCA will attempt to detect the presence of latent classes (the disease entities), creating patterns of association in the symptoms. As in factor analysis, the LCA can also be used to classify case according to their maximum likelihood class membership.Because the criterion for solving the LCA is to achieve latent classes within which there is no longer any association of one symptom with another (because the class is the disease which causes their association), and the set of diseases a patient has (or class a case is a member of) causes the symptom association, the symptoms will be \"conditionally independent\", i.e., conditional on class membership, they are no longer related.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20161201223606%21Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20120912121406%21Blue_pencil.svg"], "links": ["Allan L. McCutcheon", "Anton K. Formann", "Behavior Genetics", "Biometrika", "Cluster analysis", "Collaborative filtering", "Conditional probabilities", "Contingency table", "Digital object identifier", "Integrated Authority File", "International Standard Book Number", "John Wiley & Sons", "Latent profile analysis", "Latent variable", "Latent variable model", "Leo A. Goodman", "Local independence", "Maximum likelihood", "Multiple choice", "Multivariate random variable", "Non-negative matrix factorization", "Paul F. Lazarsfeld", "Penn State", "Probabilistic latent semantic analysis", "Sage Publications", "Statistically independent", "Statistics", "Structural equation modeling"], "references": ["http://www.john-uebersax.com/stat/index.htm", "http://www.nature.com/nrmicro/journal/v8/n12_supp/full/nrmicro1523.html", "http://www.statisticalinnovations.com/", "http://doi.org/10.1007%2Fbf01067550", "http://doi.org/10.1038%2Fsrep11861", "http://doi.org/10.1093%2Fbiomet%2F61.2.215", "http://doi.org/10.1109%2FTSMCA.2003.818877", "https://d-nb.info/gnd/4166857-1", "https://web.archive.org/web/20110404023118/http://methodology.psu.edu/ra/lcalta", "https://www.wikidata.org/wiki/Q1806878"]}, "Median": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2012", "Articles with unsourced statements from May 2012", "Articles with unsourced statements from October 2015", "Means", "Robust statistics", "Webarchive template wayback links", "Wikipedia articles incorporating text from PlanetMath"], "title": "Median", "method": "Median", "url": "https://en.wikipedia.org/wiki/Median", "summary": "The median is the value separating the higher half from the lower half of a data sample (a population or a probability distribution). For a data set, it may be thought of as the \"middle\" value. For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6, the fourth largest, and also the fourth smallest, number in the sample. For a continuous probability distribution, the median is the value such that a number is equally likely to fall above or below it.\nThe median is a commonly used measure of the properties of a data set in statistics and probability theory. The basic advantage of the median in describing data compared to the mean (often simply described as the \"average\") is that it is not skewed so much by extremely large or small values, and so it may give a better idea of a \"typical\" value. For example, in understanding statistics like household income or assets which vary greatly, a mean may be skewed by a small number of extremely high or low values. Median income, for example, may be a better way to suggest what a \"typical\" income is.\nBecause of this, the median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median will not give an arbitrarily large or small result.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/de/Comparison_mean_median_mode.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cf/Finding_the_median.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/3/33/Visualisation_mode_median_mean.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["A Treatise on Probability", "Abraham Wald", "Absolute continuity", "Absolute deviation", "Accelerated failure time model", "Actuarial science", "Adrien-Marie Legendre", "Akaike information criterion", "Allan Birnbaum", "An inequality on location and scale parameters", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Mathematical Statistics", "Annals of Statistics", "Antoine Augustin Cournot", "Arithmetic mean", "Array (data structure)", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Banach space", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Big O notation", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breakdown point", "Breusch\u2013Godfrey test", "Canonical correlation", "Cantelli's inequality", "Carl Friedrich Gauss", "Cartography", "Categorical variable", "Cauchy distribution", "Census", "Centerpoint (geometry)", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Compass", "Completeness (statistics)", "Computational complexity theory", "Concentration of measure", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decile", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension (linear algebra)", "Distance metric", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Edward Wright (mathematician)", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empty set", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Euclidean norm", "Expected loss", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Francis Galton", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gauss", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric median", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gustav Theodor Fechner", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Image processing", "Income inequality metrics", "Index of dispersion", "Injective function", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval (mathematics)", "Interval estimation", "Iowa", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen's inequality", "Johansen test", "John Tukey", "Jonckheere's trend test", "Journal of the American Statistical Association", "K-means clustering", "K-medians clustering", "K-medoids", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "L1-norm", "L1 norm", "Laplace", "Least squares", "Lebesgue\u2013Stieltjes integral", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Lipschitz functions", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location theory", "Location\u2013scale family", "Log-normal distribution", "Log-rank test", "Logistic regression", "Loss function", "Loss functions", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "MathWorld", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean absolute deviation", "Median-unbiased estimator", "Median (disambiguation)", "Median (geometry)", "Median absolute deviation", "Median filter", "Median graph", "Median search", "Median slope", "Median voter theory", "Medical statistics", "Medoid", "Method of moments (statistics)", "Methods engineering", "Metric (mathematics)", "Michiel Hazewinkel", "Mid-range", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monochrome", "Monotone likelihood ratio", "Multiple comparisons", "Multiset", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate median", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New York (state)", "Noise reduction", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normed space", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Pareto distribution", "Pareto interpolation", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Rousseeuw", "Pie chart", "Pierre-Simon Laplace", "Pivotal quantity", "PlanetMath", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Power law", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability theory", "Proceedings of the National Academy of Sciences of the United States of America", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quartile", "Quasi-experiment", "Questionnaire", "Quicksort", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raster image", "Rate parameter", "Real number", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Resistant statistic", "Risk", "Robust estimator", "Robust regression", "Robust statistics", "Roger Joseph Boscovich", "Run chart", "Salt and pepper noise", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Selection algorithm", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singleton (mathematics)", "Skewness", "Slope", "Social statistics", "Sorting algorithm", "South Dakota", "Spatial analysis", "Spatial median", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen Stigler", "Stratified sampling", "Strictly convex function", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Summary statistic", "Survey methodology", "Survival analysis", "Survival function", "Symmetric distribution", "System identification", "Talmud", "Theil\u2013Sen estimator", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Trimmed estimator", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "Unimodal distribution", "V-statistic", "Variance", "Vector autoregression", "Vector space", "Wald test", "Wavelet", "Wayback Machine", "Weak ordering", "Weibull distribution", "Weighted median", "Whittle likelihood", "Wilcoxon signed-rank test", "Yisrael Aumann", "Z-test", "Zentralblatt MATH"], "references": ["http://www.montefiore.ulg.ac.be/~kvansteen/MATH0008-2/ac20112012/Class3/Chapter2_ac1112_vfinalPartII.pdf", "http://wis.kuleuven.be/stat/robust/papers/publications-1990/rousseeuwbassett-remedian-jasa-1990.pdf", "http://www.statcan.gc.ca/edu/power-pouvoir/ch11/median-mediane/5214872-eng.htm", "http://www.accessecon.com/pubs/EB/2004/Volume3/EB-04C10011A.pdf", "http://www.celiagreen.com/charlesmccreery/statistics/meanmedianmode.pdf", "http://danadler.com/blog/2014/12/31/talmud-and-modern-economics/", "http://apstatsreview.tumblr.com/post/50058615236/density-curves-and-the-normal-distributions?action=purge", "http://mathworld.wolfram.com/StatisticalMedian.html", "http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.8162", "http://www.personal.psu.edu/users/e/c/ecb5/Courses/M475W/WeeklyReadings/Week%2013/DevelopmentOfModernStatistics.pdf", "http://www.stat.psu.edu/old_resources/ClassNotes/ljs_07/sld008.htm", "http://www.iowa.gov/tax/locgov/Statistical_Calculation_Definitions.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC26449", "http://www.ncbi.nlm.nih.gov/pubmed/10677477", "http://www.tax.ny.gov/research/property/reports/cod/2010mvs/reporttext.htm", "http://www.wisdom.weizmann.ac.il/math/AABeyond12/presentations/Aumann.pdf", "http://mathschallenge.net/index.php?section=problems&show=true&titleid=average_problem", "http://repository.tudelft.nl/islandora/object/uuid:8e67fb99-7cb7-4b11-8e6a-02039c7ed1bb/datastream/OBJ/view", "http://www.ams.org/mathscinet-getitem?mr=0125674", "http://www.ams.org/mathscinet-getitem?mr=0326872", "http://www.ams.org/mathscinet-getitem?mr=0902264", "http://www.ams.org/mathscinet-getitem?mr=0949228", "http://www.ams.org/mathscinet-getitem?mr=1291393", "http://www.ams.org/mathscinet-getitem?mr=1604954", "http://www.ams.org/mathscinet-getitem?mr=2598854", "http://www.amstat.org/publications/jse/v13n2/vonhippel.html", "http://doi.org/10.1002%2Fbimj.200410148", "http://doi.org/10.1002%2Fspe.4380231105", "http://doi.org/10.1007%2F978-1-4419-0468-3", "http://doi.org/10.1007%2FBF00356105", "http://doi.org/10.1016%2Fj.spl.2004.11.010", "http://doi.org/10.1073%2Fpnas.97.4.1423", "http://doi.org/10.1080%2F00031305.1991.10475815", "http://doi.org/10.1080%2F01621459.1960.10482056", "http://doi.org/10.1080%2F01621459.1990.10475311", "http://doi.org/10.1093%2Fbiomet%2F60.3.439", "http://doi.org/10.1117%2F12.946562", "http://doi.org/10.1137%2FS0040585X97975447", "http://doi.org/10.1214%2Faoms%2F1177705051", "http://doi.org/10.1214%2Faoms%2F1177705145", "http://doi.org/10.1214%2Faoms%2F1177729549", "http://doi.org/10.1214%2Faoms%2F1177730349", "http://doi.org/10.1214%2Faoms%2F1177731868", "http://doi.org/10.1214%2Faos%2F1176344552", "http://doi.org/10.1214%2Faos%2F1176347263", "http://doi.org/10.1214%2Faos%2F1176347978", "http://doi.org/10.1214%2Faos%2F1176350511", "http://www.jstor.org/stable/2235677", "http://www.jstor.org/stable/2236236", "http://www.jstor.org/stable/2236928", "http://www.jstor.org/stable/2237612", "http://www.jstor.org/stable/2237754", "http://www.jstor.org/stable/2241717", "http://www.jstor.org/stable/2241852", "http://www.jstor.org/stable/2334992", "http://www.jstor.org/stable/25047749", "http://www.jstor.org/stable/2958830", "http://projecteuclid.org/euclid.aos/1176343543", "http://www.poorcity.richcity.org/cgi-bin/inequality.cgi", "http://www.poorcity.richcity.org/oei/#GiniHooverTheil", "http://zbmath.org/?format=complete&q=an:0045.08606", "http://www3.stat.sinica.edu.tw/statistica/password.asp?vol=14&num=4&art=11", "http://www.state.sd.us/drr2/publications/assess1199.pdf", "https://books.google.com/books?id=YSFb4QX2UIoC&pg=PA207", "https://books.google.com/books?id=bmwhcJqq01cC&pg=PA7", "https://books.google.com/books?id=cTwwtyBX7PAC&pg=PA26", "https://web.archive.org/web/20090510034115/http://www.state.sd.us/drr2/publications/assess1199.pdf", "https://web.archive.org/web/20100730032416/http://www.stat.psu.edu/old_resources/ClassNotes/ljs_07/sld008.htm", "https://web.archive.org/web/20101111214903/http://iowa.gov/tax/locgov/Statistical_Calculation_Definitions.pdf", "https://web.archive.org/web/20110310043642/http://www.universityofcalifornia.edu/senate/inmemoriam/georgewbrown.htm", "https://web.archive.org/web/20121106015231/http://www.tax.ny.gov/research/property/reports/cod/2010mvs/reporttext.htm", "https://arxiv.org/abs/0806.3301", "https://arxiv.org/pdf/cond-mat/0412004.pdf", "https://www.biodiversitylibrary.org/item/94448", "https://doi.org/10.1214%2Faos%2F1176343543", "https://doi.org/10.2307%2F1403809", "https://www.encyclopediaofmath.org/index.php/Galton,_Francis", "https://www.encyclopediaofmath.org/index.php?title=p/m063310", "https://www.jstor.org/stable/1403809"]}, "Regression analysis": {"categories": ["Actuarial science", "All articles with unsourced statements", "Articles with unsourced statements from February 2010", "Articles with unsourced statements from March 2011", "Commons category link is on Wikidata", "Estimation theory", "Regression analysis", "Wikipedia articles with BNF identifiers", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers"], "title": "Regression analysis", "method": "Regression analysis", "url": "https://en.wikipedia.org/wiki/Regression_analysis", "summary": "In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors'). More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.\nMost commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables \u2013 that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, a function of the independent variables called the regression function is to be estimated. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the prediction of the regression function using a probability distribution. A related but distinct approach is Necessary Condition Analysis (NCA), which estimates the maximum (rather than average) value of the dependent variable for a given value of the independent variable (ceiling line rather than central line) in order to identify what value of the independent variable is necessary but not sufficient for a given value of the dependent variable.\nRegression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable.\nMany techniques for carrying out regression analysis have been developed. Familiar methods such as linear regression and ordinary least squares regression are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional.\nThe performance of regression analysis methods in practice depends on the form of the data generating process, and how it relates to the regression approach being used. Since the true form of the data-generating process is generally not known, regression analysis often depends to some extent on making assumptions about this process. These assumptions are sometimes testable if a sufficient quantity of data is available. Regression models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally. However, in many applications, especially with small effects or questions of causality based on observational data, regression methods can give misleading results.In a narrower sense, regression may refer specifically to the estimation of continuous response (dependent) variables, as opposed to the discrete response variables used in classification. The case of a continuous dependent variable may be more specifically referred to as metric regression to distinguish it from related problems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c7/CurveWeightHeight.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Adrien-Marie Legendre", "Adrien Marie Legendre", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anomaly detection", "Approximation theory", "Arithmetic mean", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Asymptomatic carrier", "Asymptotic theory (statistics)", "Autocorrelation", "Autoencoder", "Automated machine learning", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Auxology", "Average value", "BIRCH", "Bachelor of Science in Public Health", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian method", "Bayesian multivariate linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Behavior change (public health)", "Behavioural change theories", "Bias-variance dilemma", "Bias of an estimator", "Biblioth\u00e8que nationale de France", "Binomial regression", "Bioinformatics", "Biological hazard", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Boosting (machine learning)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "CURE data clustering algorithm", "Calibration curve", "Canonical correlation", "Canonical correlation analysis", "Carl Friedrich Gauss", "Carl Rogers Darnall", "Cartography", "Case\u2013control study", "Categorical variable", "Causality", "Censored regression model", "Census", "Centers for Disease Control and Prevention", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Chief Medical Officer", "Child mortality", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Community health", "Completeness (statistics)", "Computational learning theory", "Computational statistics", "Conditional distribution", "Conditional expectation", "Conditional random field", "Conference on Neural Information Processing Systems", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Convolutional neural network", "Correlation and dependence", "Correlogram", "Council on Education for Public Health", "Count data", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cultural competence in health care", "Curve fitting", "D.V. Lindley", "DBSCAN", "Data", "Data collection", "Data mining", "Decision tree learning", "Decomposition of time series", "DeepDream", "Deep learning", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Dependent variable", "Descriptive statistics", "Design of experiments", "Deviance (sociology)", "Diagonal matrix", "Dickey\u2013Fuller test", "Diffusion of innovations", "Digital object identifier", "Dimension", "Dimensionality reduction", "Discrete choice", "Disease surveillance", "Divergence (statistics)", "Doctor of Public Health", "Durbin\u2013Watson statistic", "Econometric model", "Econometrics", "Edinburgh", "Effect size", "Efficiency (statistics)", "Efficient (statistics)", "Elliptical distribution", "Emergency sanitation", "Empirical distribution function", "Empirical risk minimization", "Encyclopedia of Mathematics", "Engineering statistics", "Ensemble learning", "Environmental health", "Environmental statistics", "Epidemic", "Epidemiology", "Errors-in-variables model", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Estimation Theory", "Estimation theory", "Euclidean vector", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Expectation\u2013maximization algorithm", "Experiment", "Exponential family", "Exponential smoothing", "Extrapolation", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Family planning", "Fan chart (statistics)", "Feature engineering", "Feature learning", "Fecal\u2013oral route", "First-hitting-time model", "Fixed effects model", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Forecasting", "Forest plot", "Fourier analysis", "Fraction of variance unexplained", "Francis Galton", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Function (mathematics)", "Function approximation", "G-test", "G. Udny Yule", "Gated recurrent unit", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Generalized linear models", "Genetically modified food", "Geographic information system", "Geometric mean", "Geostatistics", "Germ theory of disease", "Global health", "Globalization and disease", "Glossary of artificial intelligence", "Good agricultural practice", "Good manufacturing practice", "Goodness of fit", "Grammar induction", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "HACCP", "Hand washing", "Harmonic mean", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Heckman correction", "Heteroscedasticity", "Hidden Markov model", "Hierarchical clustering", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human factors and ergonomics", "Human nutrition", "Hygiene", "Hypothesis test", "ISO 22000", "Independent component analysis", "Independent variable", "Index of dispersion", "Infant mortality", "Infection control", "Injury prevention", "Integrated Authority File", "Interaction (statistics)", "International Conference on Machine Learning", "International Standard Book Number", "Interpolation", "Interquartile range", "Interval estimation", "Invertible matrix", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Snow (physician)", "Joint distribution", "Jonckheere's trend test", "Joseph Lister", "Journal of Machine Learning Research", "Judith Tanur", "Julian C. Stanley", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Learning to rank", "Least-angle regression", "Least absolute deviations", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Library of Congress Control Number", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Limited dependent variable", "Linear combination", "Linear discriminant analysis", "Linear least squares", "Linear least squares (mathematics)", "Linear probability model", "Linear regression", "Linearly independent", "List of datasets for machine-learning research", "List of epidemics", "List of fields of application of statistics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Local outlier factor", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Long short-term memory", "Loss function", "Lp space", "M-estimator", "Machine Learning (journal)", "Machine learning", "Mallows's Cp", "Mann\u2013Whitney U test", "Margaret Sanger", "Mary Mallon", "Maternal health", "Maximum a posteriori estimation", "Maximum likelihood", "McGraw Hill", "McNemar's test", "Mean", "Mean-shift", "Mean and predicted response", "Mean square error", "Median", "Median-unbiased estimator", "Medical anthropology", "Medical sociology", "Medical statistics", "Mental health", "Method of least squares", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Ministry of Health and Family Welfare", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Modifiable areal unit problem", "Moment (mathematics)", "Monotone likelihood ratio", "Moving average", "Moving least squares", "Multilayer perceptron", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate probit", "Multivariate statistics", "Naive Bayes classifier", "National Diet Library", "National accounts", "Natural experiment", "Necessity and sufficiency", "Negative binomial", "Nelson\u2013Aalen estimator", "New Palgrave: A Dictionary of Economics", "Non-linear least squares", "Non-negative least squares", "Non-negative matrix factorization", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Notifiable disease", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "OPTICS algorithm", "Observational study", "Occam learning", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Official statistics", "One- and two-tailed tests", "Online machine learning", "Open defecation", "Opinion poll", "Optimal decision", "Optimal design", "Oral hygiene", "Order statistic", "Ordered logit", "Ordered probit", "Ordinal regression", "Ordinal variable", "Ordinary least squares", "Orthogonal polynomials", "Outline of machine learning", "Outline of statistics", "Overdetermined system", "PRECEDE-PROCEED model", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Patient safety", "Patient safety organization", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perceptron", "Permutation test", "Pharmaceutical policy", "Pharmacovigilance", "Phillip Good", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polychoric correlation", "Polynomial regression", "Population (statistics)", "Population health", "Population parameter", "Population statistics", "Positive deviance", "Posterior probability", "Power (statistics)", "Prediction", "Prediction interval", "Preventive healthcare", "Preventive nutrition", "Principal component analysis", "Principal component regression", "Prior probability", "Probabilistic design", "Probability distribution", "Probably approximately correct learning", "Probit model", "Professional degrees of public health", "Proportional hazards model", "Psychometrics", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Q-learning", "Quality control", "Quantile", "Quantile regression", "Quarantine", "Quasi-experiment", "Quasi-variance", "Questionnaire", "Q\u2013Q plot", "R-squared", "ROC curve", "Race and health", "Radar chart", "Random assignment", "Random effects model", "Random forest", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recurrent neural network", "Regression analysis", "Regression diagnostics", "Regression intercept", "Regression model validation", "Regression toward the mean", "Regression validation", "Regressor", "Regularized least squares", "Reinforcement learning", "Relative risk", "Relevance vector machine", "Reliability engineering", "Replication (statistics)", "Reproductive health", "Resampling (statistics)", "Residual sum of squares", "Response surface methodology", "Restricted Boltzmann machine", "Ridge regression", "Robust regression", "Robust statistics", "Ronald A. Fisher", "Run chart", "Safe sex", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scalar (physics)", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Self-organizing map", "Semi-supervised learning", "Semiparametric regression", "Sexually transmitted infection", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal processing", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smoking cessation", "Social Science Research Network", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Social statistics", "Sociology of health and illness", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spreadsheet", "Standard deviation", "Standard error", "Standard error (statistics)", "State\u2013action\u2013reward\u2013state\u2013action", "Stationary process", "Statistic", "Statistical assumption", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Structured prediction", "Student's t-test", "Studentized residual", "Sufficient statistic", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-distributed stochastic neighbor embedding", "T-test", "Temporal difference learning", "Theory of planned behavior", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Transtheoretical model", "Trend analysis", "Trend estimation", "Tropical disease", "U-Net", "U-statistic", "Udny Yule", "Uncorrelated", "Uniformly most powerful test", "United States Public Health Service", "Unsupervised learning", "V-statistic", "Vaccination", "Vaccine trial", "Vapnik\u2013Chervonenkis theory", "Variance", "Vector autoregression", "Vector control", "Wald test", "Waterborne diseases", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "William Kruskal", "World Health Organization", "World Toilet Organization", "Yadolah Dodge", "Z-test"], "references": ["http://psychclassics.yorku.ca/Fisher/Methods/", "http://ssrn.com/abstract=1406472", "http://jeff560.tripod.com/r.html", "http://onlinelibrary.wiley.com/doi/10.1002/for.3980140502/abstract", "http://pages.cs.wisc.edu/~huangyz/caip09_Long.pdf", "http://data.bnf.fr/ark:/12148/cb119445648", "http://www.incertitudes.fr/book.pdf", "http://www.erim.eur.nl/centres/necessary-condition-analysis/", "http://doi.org/10.1016%2Fj.patrec.2007.07.019", "http://doi.org/10.1068%2Fa231025", "http://doi.org/10.1093%2Fbiomet%2F2.2.211", "http://doi.org/10.1214%2F088342305000000331", "http://doi.org/10.1214%2Fss%2F1177012581", "http://doi.org/10.2139%2Fssrn.1406472", "http://doi.org/10.2307%2F2341124", "http://doi.org/10.2307%2F2979746", "http://www.imf.org/external/pubs/ft/fandd/2006/03/basics.htm", "http://www.jstor.org/stable/20061201", "http://www.jstor.org/stable/2245330", "http://www.jstor.org/stable/2331683", "http://www.jstor.org/stable/2341124", "http://www.jstor.org/stable/2979746", "http://www.vias.org/simulations/simusoft_regrot.html", "https://books.google.com/books?id=BuPNIbaN5v4C&lpg=PA274&dq=regression%20extrapolation&pg=PA274#v=onepage&q=regression%20extrapolation&f=false", "https://books.google.com/books?id=FRcOAAAAQAAJ", "https://books.google.com/books?id=ZQ8OAAAAQAAJ&printsec=frontcover&dq=Theoria+combinationis+observationum+erroribus+minimis+obnoxiae&as_brr=3#v=onepage&q=&f=false", "https://catalogue.bnf.fr/ark:/12148/cb119445648", "https://id.loc.gov/authorities/subjects/sh85112392", "https://d-nb.info/gnd/4129903-6", "https://id.ndl.go.jp/auth/ndlna/00564579", "https://web.archive.org/web/20100108055346/http://pages.cs.wisc.edu/~huangyz/caip09_Long.pdf", "https://arxiv.org/list/cs.LG/recent", "https://www.encyclopediaofmath.org/index.php?title=p/r080620", "https://www.jstor.org/stable/270724", "https://www.wikidata.org/wiki/Q208042"]}, "Systematic error": {"categories": ["Accuracy and precision", "All articles needing additional references", "Articles needing additional references from September 2016", "Errors and residuals"], "title": "Observational error", "method": "Systematic error", "url": "https://en.wikipedia.org/wiki/Observational_error", "summary": "Observational error (or measurement error) is the difference between a measured value of a quantity and its true value. In statistics, an error is not a \"mistake\". Variability is an inherent part of the results of measurements and of the measurement process.\nMeasurement errors can be divided into two components: random error and systematic error.Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by an inaccuracy (involving either the observation or measurement process) inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Accuracy and precision", "Ammeter", "Averaged", "Biophysical environment", "Calibration", "Causality", "Central limit theorem", "Coefficient of determination", "Computational mechanics", "Constant (mathematics)", "Correction for attenuation", "Dependent variable", "Diffraction grating", "Digital object identifier", "Distance", "Dynamic model", "Electromagnetic spectrum", "Error", "Errors-in-variables models", "Errors and residuals in statistics", "Experiment", "Fiducial marker", "Hypothesis test", "Independent variable", "Instrument error", "International Standard Book Number", "JSTOR", "Mathematical model", "Mean", "Measurement", "Measurement error", "Measurement in quantum mechanics", "Measurement uncertainty", "Metrology", "Multitrait-multimethod matrix", "Non-sampling error", "Normal distribution", "Observation", "Observations", "Oscillation frequency", "Pendulum", "Percentage error", "Physical law", "Physical quantity", "Probability theory", "Propagation of uncertainty", "Radar", "Random variable", "Regression dilution", "Replication (statistics)", "Ruler", "Science", "Sodium", "Speaking clock", "Spectrometer", "Standard deviation", "Statistical model", "Statistical theory", "Statistics", "Stochastic drift", "Stopwatch", "Surroundings", "System", "Systemic bias", "Test method", "Time-invariant", "Vernier scale", "Voltmeter", "Wavelength"], "references": ["http://www.merriam-webster.com/dictionary/systematic%20error", "http://sqp.upf.edu", "http://essedunet.nsd.uib.no/cms/topics/measurement/", "http://doi.org/10.1007%2Fs11205-015-1002-x", "http://doi.org/10.2307%2F1267450", "http://www.jstor.org/stable/1267450", "https://books.google.com/books?id=giFQcZub80oC&pg=PA94", "https://www.google.com/webhp?sourceid=chrome-instant&rlz=1CASMAG_enUS602US603&ion=1&espv=2&ie=UTF-8#q=systematic%20error%20definition"]}, "Random multinomial logit": {"categories": ["All articles with dead external links", "Articles with dead external links from May 2017", "Articles with permanently dead external links", "Articles with short description", "CS1 maint: Uses authors parameter", "Classification algorithms", "Computational statistics", "Decision theory", "Decision trees", "Ensemble learning", "Machine learning"], "title": "Random forest", "method": "Random multinomial logit", "url": "https://en.wikipedia.org/wiki/Random_forest", "summary": "Random forests or random decision forests are an ensemble learning method for classification, regression and other tasks, that operate by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees. Random decision forests correct for decision trees' habit of overfitting to their training set.The first algorithm for random decision forests was created by Tin Kam Ho using the random subspace method, which, in Ho's formulation, is a way to implement the \"stochastic discrimination\" approach to classification proposed by Eugene Kleinberg.An extension of the algorithm was developed by Leo Breiman and Adele Cutler, and \"Random Forests\" is their trademark. The extension combines Breiman's \"bagging\" idea and random selection of features, introduced first by Ho and later independently by Amit and Geman in order to construct a collection of decision trees with controlled variance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Annals of Mathematics and Artificial Intelligence", "Annals of Statistics", "Anomaly detection", "ArXiv", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Bias\u2013variance dilemma", "Bias\u2013variance tradeoff", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "CiteSeerX", "Classification and regression tree", "Cluster analysis", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "Correlation", "Cross-validation (statistics)", "DBSCAN", "Data mining", "Decision tree", "Decision tree learning", "DeepDream", "Deep learning", "Digital object identifier", "Dimensionality reduction", "Donald Geman", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature (machine learning)", "Feature engineering", "Feature learning", "Gated recurrent unit", "Generalization error", "Gini impurity", "Glossary of artificial intelligence", "Gradient boosting", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "I.i.d.", "Independent component analysis", "Information gain", "International Conference on Machine Learning", "International Standard Book Number", "JSTOR", "Jerome H. Friedman", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbor algorithm", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kernel method", "Kernel methods", "Kernel random forest", "Learning to rank", "Lecture Notes in Computer Science", "Leo Breiman", "Linear discriminant analysis", "Linear regression", "Linear subspace", "Lipschitz", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Mathematical Reviews", "Mean-shift", "Mode (statistics)", "Multilayer perceptron", "Multinomial logistic regression", "Naive Bayes classifier", "Neural Computation (journal)", "Non-negative matrix factorization", "Non-parametric statistics", "OPTICS algorithm", "Occam learning", "Online machine learning", "Orange (software)", "Out-of-bag error", "Outline of machine learning", "Overfitting", "Partial permutation", "Perceptron", "Principal component analysis", "Probably approximately correct learning", "PubMed Central", "PubMed Identifier", "Q-learning", "R (programming language)", "R programming language", "Random forests", "Random subspace method", "Random tree", "Randomized algorithm", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Robert Tibshirani", "Sampling (statistics)", "Scikit-learn", "Self-organizing map", "Semi-supervised learning", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Test set", "Tin Kam Ho", "Trademark", "Trevor Hastie", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory", "Wikipedia"], "references": ["http://orbi.ulg.ac.be/bitstream/2268/9357/1/geurts-mlj-advance.pdf", "http://ect.bell-labs.com/who/tkh/publications/papers/compare.pdf", "http://ect.bell-labs.com/who/tkh/publications/papers/df.pdf", "http://ect.bell-labs.com/who/tkh/publications/papers/odt.pdf", "http://code.google.com/p/randomforest-matlab", "http://www.nature.com/modpathol/journal/v18/n4/full/3800322a.html", "http://oz.berkeley.edu/~breiman/some_theory2000.pdf", "http://www.stat.berkeley.edu/~breiman/RandomForests/cc_software.htm", "http://www.cis.jhu.edu/publications/papers_in_database/GEMAN/shape.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.9168", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.9168", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.6750", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.6069", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.698.2365", "http://www-stat.stanford.edu/~tibs/ElemStatLearn/", "http://sqp.upf.edu", "http://www-bcf.usc.edu/~gareth/ISL/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4760114", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5828645", "http://www.ncbi.nlm.nih.gov/pubmed/15529185", "http://www.ncbi.nlm.nih.gov/pubmed/20385727", "http://www.ncbi.nlm.nih.gov/pubmed/21576180", "http://www.ncbi.nlm.nih.gov/pubmed/26903687", "http://www.ncbi.nlm.nih.gov/pubmed/28114007", "http://www.ncbi.nlm.nih.gov/pubmed/29440440", "http://www.alglib.net/dataanalysis/decisionforest.php", "http://weka.sourceforge.net/doc.dev/weka/classifiers/trees/RandomForest.html", "http://www.ams.org/mathscinet-getitem?mr=1425956", "http://arxiv.org/abs/1402.4293", "http://arxiv.org/abs/1407.3939", "http://arxiv.org/abs/1502.03836", "http://arxiv.org/abs/1512.03444", "http://arxiv.org/archive/math.ST", "http://arxiv.org/archive/stat.ML", "http://doi.org/10.1007%2F978-3-319-26762-3_27", "http://doi.org/10.1007%2F978-3-319-46254-7_50", "http://doi.org/10.1007%2F978-3-540-74469-6_35", "http://doi.org/10.1007%2FBF01531079", "http://doi.org/10.1007%2Fs10994-006-6226-1", "http://doi.org/10.1016%2Fj.eswa.2007.01.029", "http://doi.org/10.1023%2FA:1010933404324", "http://doi.org/10.1038%2Fmodpathol.3800322", "http://doi.org/10.1073%2Fpnas.1800256115", "http://doi.org/10.1080%2F01621459.2015.1036994", "http://doi.org/10.1093%2Fbioinformatics%2Fbtq134", "http://doi.org/10.1093%2Fbioinformatics%2Fbtr300", "http://doi.org/10.1109%2F34.709601", "http://doi.org/10.1109%2Ftpami.2016.2636831", "http://doi.org/10.1145%2F2491055.2491063", "http://doi.org/10.1162%2Fneco.1997.9.7.1545", "http://doi.org/10.1198%2F016214505000001230", "http://doi.org/10.1198%2F106186006X94072", "http://doi.org/10.1214%2Faos%2F1032181157", "http://www.jstor.org/stable/27594168", "http://bioinformatics.oxfordjournals.org/content/27/14/1986.abstract", "http://bioinformatics.oxfordjournals.org/content/early/2010/04/12/bioinformatics.btq134.abstract", "http://cran.r-project.org/web/packages/party/index.html", "http://cran.r-project.org/web/packages/randomForest/index.html", "http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html", "https://github.com/imbs-hl/ranger", "https://epub.ub.uni-muenchen.de/1833/1/paper_464.pdf", "https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm", "https://www.researchgate.net/profile/Dirk_Van_den_Poel/publication/225175169_Random_Multiclass_Classification_Generalizing_Random_Forests_to_Random_MNL_and_Random_NB/links/02e7e5278a0a7b8e7f000000.pdf", "https://www.researchgate.net/profile/Houtao_Deng/publication/221079908_Bias_of_Importance_Measures_for_Multi-valued_Attributes_and_Solutions/links/0046351909faa8f0eb000000/Bias-of-Importance-Measures-for-Multi-valued-Attributes-and-Solutions.pdf", "https://dl.acm.org/citation.cfm?id=2491063", "https://web.archive.org/web/20160417030218/http://ect.bell-labs.com/who/tkh/publications/papers/odt.pdf", "https://arxiv.org/list/cs.LG/recent", "https://cran.r-project.org/doc/Rnews/Rnews_2002-3.pdf", "https://cran.r-project.org/web/packages/randomForest/randomForest.pdf", "https://pdfs.semanticscholar.org/8956/845b0701ec57094c7a8b4ab1f41386899aea.pdf", "https://pdfs.semanticscholar.org/faa4/c502a824a9d64bf3dc26eb90a2c32367921f.pdf"]}, "Taylor's law": {"categories": ["Biology laws", "Ecology", "Environmental statistics", "Statistical deviation and dispersion", "Statistical laws"], "title": "Taylor's law", "method": "Taylor's law", "url": "https://en.wikipedia.org/wiki/Taylor%27s_law", "summary": "Taylor's law (also known as Taylor's power law) is an empirical law in ecology that relates the variance of the number of individuals of a species per unit area of habitat to the corresponding mean by a power law relationship. It is named after the ecologist who first proposed it in 1961, Lionel Roy Taylor (1924\u20132007). Taylor's original name for this relationship was the law of the mean.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abscissa", "Absolute value", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli distribution", "Beta-binomial distribution", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Birth-death process", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chaos theory", "Chemometrics", "Chi-square distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convergence (mathematics)", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density-mass allometry", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Ecology", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "Extended truncated negative binomial", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Field (physics)", "First-hitting-time model", "Fish", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gamma distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric distribution", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "HIV", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Ilkka Hanski", "Index of dispersion", "Insect", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Intraclass correlation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Joel E. Cohen", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Katz family", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Leaf", "Lehmann\u2013Scheff\u00e9 theorem", "Leukemia", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logarithmic series distribution", "Logistic regression", "Lognormal distribution", "Loss function", "Lp space", "M-estimator", "M. S. Bartlet", "M. S. Bartlett", "Mann\u2013Whitney U test", "Markov process", "Maurice Tweedie", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "McNemar's test", "Mean", "Mean square error", "Median", "Median-unbiased estimator", "Medical statistics", "Mertens function", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mite", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Morisita's overlap index", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Number theory", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Osborne Reynolds", "Outline of statistics", "Overdispersion", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pascal distribution", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plant", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population density", "Population dynamics", "Population statistics", "Posterior probability", "Power (statistics)", "Power law", "Prediction interval", "Prime number", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quadrat", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R language", "Radar chart", "Random assignment", "Random matrix", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Richard Lewontin", "Robust regression", "Robust statistics", "Ronald Fisher", "Roy Taylor (ecologist)", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaling pattern of occupancy", "Scatter plot", "Scientific control", "Score test", "Sea", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sheep", "Sign test", "Simple linear regression", "Simultaneous equations model", "Single-nucleotide polymorphism", "Skewness", "Social statistics", "Soil", "Spatial analysis", "Spatial ecology", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical analysis", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical physics", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stopping rule", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Symphylid", "System identification", "Taylor Law", "Taylor rule", "Thermodynamic free energy", "Tick", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tweedie distributions", "Twin prime", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-mass allometry", "Vector autoregression", "Vilfredo Pareto", "Virus", "Wald test", "Watson's power law", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Worm", "Z-test", "Zooplankton"], "references": ["http://cc.oulu.fi/~jarioksa/softhelp/vegan/html/dispindmorisita.html", "http://apsjournals.apsnet.org/doi/pdf/10.1094/PHYTO-99-7-0833", "http://doi.org/10.1017%2FS0080456800012163", "http://doi.org/10.1038%2F189732a0", "http://doi.org/10.1094%2Fphyto-99-7-0833", "http://doi.org/10.2307%2F4285", "http://www.jstor.org/stable/4285", "http://www.worldcat.org/issn/0031-949X", "https://books.google.com/books?id=StwPAQAAMAAJ", "https://doi.org/10.1007%2FBF00469426", "https://doi.org/10.1007%2FBF02511568"]}, "Linear least squares (disambiguation)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2010", "Broad-concept articles", "Computational statistics", "Least squares", "Wikipedia articles needing page number citations from December 2010"], "title": "Linear least squares", "method": "Linear least squares (disambiguation)", "url": "https://en.wikipedia.org/wiki/Linear_least_squares", "summary": "Linear least squares is the least squares approximation of linear functions to data.\nIt is a set of formulations for solving statistical problems involved in linear regression, including variants for \nordinary (unweighted),\nweighted, and \ngeneralized (correlated) residuals.\nNumerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e3/Linear_least_squares2.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b0/Linear_least_squares_example2.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Analysis of covariance", "Analysis of variance", "Approximation theory", "Arithmetic mean", "B-spline", "Bayesian experimental design", "Bayesian linear regression", "Bayesian multivariate linear regression", "Beer-Lambert law", "Bias of an estimator", "Bibcode", "Binomial regression", "Calibration curve", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared distribution", "Closed-form expression", "Computational statistics", "Confounding", "Consistent estimator", "Constrained least squares", "Convex function", "Correlation and dependence", "Cumulative distribution function", "Curve fitting", "Data", "Data fitting", "Degrees of freedom (statistics)", "Dependent variable", "Descriptive statistics", "Design of experiments", "Digital object identifier", "Discrete choice", "Dominating decision rule", "Efficiency (statistics)", "Errors-in-variables models", "Errors and residuals in statistics", "Expected value", "Experiment", "Fixed effects model", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Gran plot", "Growth curve (statistics)", "Heteroscedasticity", "Homoscedasticity", "Ill-conditioned", "Independent variable", "Instrumental variables", "International Standard Book Number", "Isotonic regression", "Iterative method", "Iteratively reweighted least squares", "JSTOR", "James\u2013Stein estimator", "Kendall tau rank correlation coefficient", "Least-angle regression", "Least absolute deviations", "Least squares", "Least squares approximation", "Line-line intersection", "Line fitting", "Linear functions", "Linear least squares (mathematics)", "Linear regression", "List of statistics articles", "Local regression", "Logistic regression", "Mallows's Cp", "Mathematical model", "Mathematical optimization", "Mathematics", "Maxima and minima", "Maximum likelihood", "Mean and predicted response", "Mean squared error", "Minimum mean-square error", "Minimum mean square error", "Mixed logit", "Mixed model", "Model selection", "Moving least squares", "Multicollinearity", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate analysis of variance", "Non-linear least squares", "Non-negative least squares", "Nonlinear least squares", "Nonlinear regression", "Nonparametric regression", "Normal distribution", "Numerical analysis", "Numerical integration", "Numerical methods for linear least squares", "Numerical smoothing and differentiation", "Objective function", "Observational study", "Optimal design", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Outline of regression analysis", "Outline of statistics", "Overdetermined system", "Parameter", "Partial correlation", "Partial derivative", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson product-moment correlation coefficient", "Poisson regression", "Polynomial", "Polynomial regression", "Prediction", "Principal component regression", "Prior probability", "Probit model", "Proceedings of the National Academy of Sciences", "PubMed Central", "Quantile regression", "Random effects model", "Rank correlation", "Regression analysis", "Regression model validation", "Regularization (mathematics)", "Regularized least squares", "Residual (statistics)", "Residuals (statistics)", "Response surface methodology", "Ridge regression", "Robust regression", "Segmented regression", "Semiparametric regression", "Shrinkage estimator", "Simple linear regression", "Social Science Research Network", "Spearman's rank correlation coefficient", "Standard addition", "Statistical inference", "Statistical model", "Statistics", "Stein's phenomenon", "Stepwise regression", "Studentized residual", "System identification", "Tikhonov regularization", "Total least squares", "Vandermonde matrix", "Weighted least squares"], "references": ["http://ssrn.com/abstract=1406472", "http://mathworld.wolfram.com/LeastSquaresFitting.html", "http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html", "http://adsabs.harvard.edu/abs/1978PNAS...75.3034L", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC392707", "http://doi.org/10.1073%2Fpnas.75.7.3034", "http://doi.org/10.1137%2F1036055", "http://doi.org/10.1214%2Faos%2F1176345987", "http://doi.org/10.1214%2Fss%2F1177012408", "http://doi.org/10.2139%2Fssrn.1406472", "http://www.jstor.org/stable/2132463", "http://www.jstor.org/stable/2240725", "http://www.jstor.org/stable/2245853", "http://www.jstor.org/stable/2986237", "http://www.jstor.org/stable/68164"]}, "Hellin's law": {"categories": ["All stub articles", "Multiple births", "Statistical laws", "Statistics stubs", "Twin"], "title": "Hellin's law", "method": "Hellin's law", "url": "https://en.wikipedia.org/wiki/Hellin%27s_law", "summary": "Hellin's Law is the principle that one in about 80 natural pregnancies ends in the birth of twins, triplets once in 802 births, and quadruplets once in 803 births.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Australia", "Digital object identifier", "International Standard Serial Number", "Multiple birth", "Pregnancies", "PubMed Identifier", "Quadruplets", "Statistics", "Twin"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/19335190", "http://www.ncbi.nlm.nih.gov/pubmed/19335191", "http://doi.org/10.1375/twin.12.2.183", "http://doi.org/10.1375/twin.12.2.191", "http://www.worldcat.org/issn/1832-4274"]}, "Regression model validation": {"categories": ["All articles lacking sources", "Articles lacking sources from March 2010", "Regression diagnostics", "Validity (statistics)", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Regression validation", "method": "Regression model validation", "url": "https://en.wikipedia.org/wiki/Regression_validation", "summary": "In statistics, regression validation is the process of deciding whether the numerical results quantifying hypothesized relationships between variables, obtained from regression analysis, are acceptable as descriptions of the data. The validation process can involve analyzing the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates substantially when applied to data that were not used in model estimation.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Adjusted R-squared", "Anscombe's quartet", "Bayesian linear regression", "Bayesian multivariate linear regression", "Coefficient of determination", "Copyright status of work by the U.S. government", "Cross-validation (statistics)", "Data set", "Designed experiment", "Digital object identifier", "Discrete choice", "Durbin\u2013Watson statistic", "Errors-in-variables models", "Errors and residuals in statistics", "Explanatory variable", "F-test", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Heteroskedasticity", "Histogram", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Jan Kmenta", "Lag plot", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Mean and predicted response", "Mean squared error", "Mean squared prediction error", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "National Institute of Standards and Technology", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Normal probability plot", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "PubMed Identifier", "Quantile regression", "Random effects model", "Regression analysis", "Regression diagnostic", "Regression model validation", "Regularized least squares", "Residual (statistics)", "Robust regression", "Run chart", "Scatter plot", "Segmented regression", "Semiparametric regression", "Serial correlation", "Simple linear regression", "Specification (regression)", "Statistical graphics", "Statistical parameter", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Weighted least squares"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/28620945", "http://www.itl.nist.gov/div898/handbook/", "http://www.itl.nist.gov/div898/handbook/pmd/section4/pmd44.htm", "http://www.nist.gov", "http://doi.org/10.1002%2Fsim.7372", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5575530/pdf/SIM-36-3283.pdf"]}, "Probability metric": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from February 2012", "Articles needing additional references from February 2012", "Statistical distance"], "title": "Statistical distance", "method": "Probability metric", "url": "https://en.wikipedia.org/wiki/Statistical_distance", "summary": "In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.\nA distance between populations can be interpreted as measuring the distance between two probability distributions and hence they are essentially measures of distances between probability measures. Where statistical distance measures relate to the differences between random variables, these may have statistical dependence, and hence these distances are not directly related to measures of distances between probability measures. Again, a measure of distance between random variables may relate to the extent of dependence between them, rather than to their individual values.\nStatistical distance measures are mostly not metrics and they need not be symmetric. Some types of distance measures are referred to as (statistical) divergences.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bhattacharyya distance", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Dirac delta", "Distance correlation", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Earth mover's distance", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Energy distance", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-divergence", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Function (mathematics)", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hellinger distance", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Identity of indiscernibles", "Index of dispersion", "Information theory", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen\u2013Shannon divergence", "Johansen test", "Jonckheere's trend test", "Kantorovich metric", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kernel embedding of distributions", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kullback\u2013Leibler divergence", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "L\u00e9vy\u2013Prokhorov metric", "M-estimator", "Mahalanobis distance", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Metric (mathematics)", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-negative", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Positive-definite function", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probabilistic forecasting", "Probabilistic metric space", "Probability distribution", "Probability distribution function", "Probability measure", "Probability theory", "Proportional hazards model", "Pseudometric space", "Psychometrics", "Quality control", "Quasi-experiment", "Quasimetric", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Random variables", "Random vector", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real number", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "R\u00e9nyi divergence", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semimetric", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal-to-noise ratio", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Subadditivity", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Symmetric relation", "System identification", "Time domain", "Time series", "Tolerance interval", "Total variation distance", "Trend estimation", "Triangle inequality", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wasserstein metric", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "\u0141ukaszyk\u2013Karmowski metric"], "references": ["http://reference.wolfram.com/mathematica/guide/DistanceAndSimilarityMeasures.html"]}, "Total variation distance of probability measures": {"categories": ["All stub articles", "F-divergences", "Probability stubs", "Probability theory"], "title": "Total variation distance of probability measures", "method": "Total variation distance of probability measures", "url": "https://en.wikipedia.org/wiki/Total_variation_distance_of_probability_measures", "summary": "In probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric, and is sometimes called the statistical distance or variational distance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["Digital object identifier", "International Standard Book Number", "Kolmogorov\u2013Smirnov test", "Kullback\u2013Leibler divergence", "Pinsker's inequality", "Probability", "Probability distribution", "Probability measure", "Probability theory", "Sigma-algebra", "Statistical distance", "Subset", "Total variation", "Transportation theory (mathematics)", "Wasserstein metric"], "references": ["http://www.stat.berkeley.edu/~sourav/Lecture2.pdf", "http://doi.org/10.1007%2F978-3-540-71050-9", "https://link.springer.com/10.1007/978-3-540-71050-9", "https://web.archive.org/web/20080708205758/http://www.stat.berkeley.edu/~sourav/Lecture2.pdf"]}, "Gamma distribution": {"categories": ["All articles with incomplete citations", "All articles with unsourced statements", "Articles with incomplete citations from November 2012", "Articles with unsourced statements from September 2012", "Conjugate prior distributions", "Continuous distributions", "Exponential family distributions", "Factorial and binomial topics", "Infinitely divisible probability distributions", "Survival analysis", "Wikipedia articles needing clarification from July 2018"], "title": "Gamma distribution", "method": "Gamma distribution", "url": "https://en.wikipedia.org/wiki/Gamma_distribution", "summary": "In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are three different parametrizations in common use:\n\nWith a shape parameter k and a scale parameter \u03b8.\nWith a shape parameter \u03b1 = k and an inverse scale parameter \u03b2 = 1/\u03b8, called a rate parameter.\nWith a shape parameter k and a mean parameter \u03bc = k\u03b8 = \u03b1/\u03b2.In each of these three forms, both parameters are positive real numbers.\nThe gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and with respect to a 1/x base measure) for a random variable X for which E[X] = k\u03b8 = \u03b1/\u03b2 is fixed and greater than zero, and E[ln(X)] = \u03c8(k) + ln(\u03b8) = \u03c8(\u03b1) \u2212 ln(\u03b2) is fixed (\u03c8 is the digamma function).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8b/Gamma-KL-3D.png", "https://upload.wikimedia.org/wikipedia/commons/b/b1/Gamma-PDF-3D.png", "https://upload.wikimedia.org/wikipedia/commons/8/8d/Gamma_distribution_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e6/Gamma_distribution_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg"], "links": ["ARGUS distribution", "Accelerated life testing", "Arcsine distribution", "Asymmetric Laplace distribution", "Bacterial genetics", "Balding\u2013Nichols model", "Bates distribution", "Bayesian inference", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "ChIP-chip", "ChIP-seq", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "CiteSeerX", "Compound Poisson distribution", "Compound distribution", "Compound gamma distribution", "Conjugate prior", "Constitutively expressed", "Conway\u2013Maxwell\u2013Poisson distribution", "Copy number analysis", "Cumulative distribution function", "Dagum distribution", "David Blei", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Econometrics", "Elliptical distribution", "Encyclopedia of Mathematics", "Eric W. Weisstein", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential dispersion model", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma function", "Gamma process", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Gene expression", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized gamma distribution", "Generalized integer gamma distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Genomics", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Herman Rubin", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Incomplete gamma function", "Independent and identically-distributed random variables", "Independent and identically distributed random variables", "Infinite divisibility (probability)", "Information entropy", "Insurance policy", "Integer", "International Standard Book Number", "International Standard Serial Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse gamma distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "K-distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kullback\u2013Leibler divergence", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "Laplace transform", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "MathWorld", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Method of moments (statistics)", "Michiel Hazewinkel", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Natural parameters", "Natural statistics", "Negative binomial distribution", "Negative multinomial distribution", "Neuroscience", "Newton's method", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Parametrization", "Pareto distribution", "Peak calling", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poisson process", "Poisson regression", "Poly-Weibull distribution", "Polygamma function", "Prior probability", "Probability density function", "Probability distribution", "Probability theory", "Protein molecule", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rate parameter", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Rejection sampling", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Robert V. Hogg", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Statistics", "Student's t-distribution", "Support (mathematics)", "Temporal coding", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.wise.xmu.edu.cn/Master/Download/..%5C..%5CUploadFiles%5Cpaper-masterdownload%5C2009519932327055475115776.pdf", "http://www.biomedcentral.com/1471-2164/14/834", "http://www.epixanalytics.com/modelassist/AtRisk/Model_Assist.htm#Distributions/Continuous_distributions/Gamma.htm", "http://www.springerlink.com/content/u750hg4630387205/", "http://mathworld.wolfram.com/GammaDistribution.html", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.157.5540&rep=rep1&type=pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.93.3828", "http://www.stat.washington.edu/thompson/S341_10/Notes/week4.pdf", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm", "http://www.ams.org/journals/proc/1994-121-01/S0002-9939-1994-1195477-8/S0002-9939-1994-1195477-8.pdf", "http://luc.devroye.org/rnbookindex.html", "http://doi.org/10.1007%2FBF02293108", "http://doi.org/10.1007%2FBF02613934", "http://doi.org/10.1016%2Fj.jeconom.2008.12.014", "http://doi.org/10.1080%2F00401706.1969.10490731", "http://doi.org/10.1145%2F358315.358390", "http://doi.org/10.1145%2F358407.358414", "http://bioinformatics.oxfordjournals.org/content/24/3/396.full.pdf+html", "http://commons.wikimedia.org/wiki/File:Gamma-PDF-3D-by-Theta.png", "http://commons.wikimedia.org/wiki/File:Gamma-PDF-3D-by-k.png", "http://commons.wikimedia.org/wiki/File:Gamma-PDF-3D-by-x.png", "http://journals.tubitak.gov.tr/engineering/issues/muh-00-24-6/muh-24-6-7-9909-13.pdf", "https://tminka.github.io/papers/minka-gamma.pdf", "https://arxiv.org/pdf/1311.1704v3.pdf", "https://arxiv.org/pdf/math/0609442.pdf", "https://dx.doi.org/10.1016/0167-7152(86)90044-1", "https://www.encyclopediaofmath.org/index.php?title=p/g043300", "https://www.worldcat.org/search?fq=x0:jrnl&q=n2:0167-7152"]}, "Discrete time": {"categories": ["Dynamical systems", "Time"], "title": "Discrete time and continuous time", "method": "Discrete time", "url": "https://en.wikipedia.org/wiki/Discrete_time_and_continuous_time", "summary": "In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/88/Sampled.signal.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/88/20100706183722%21Sampled.signal.svg"], "links": ["Aliasing", "Analog signal", "Bernoulli process", "Calendar year", "Closed form solution", "Connected space", "Continuous function", "Continuous variable", "Continuum (set theory)", "Countable set", "Difference equation", "Differential equation", "Digital data", "Digital signal processing", "Discrete-time signal", "Discrete calculus", "Discrete system", "Discrete time", "Discrete variable", "Discretization", "Dynamical system", "Economic activity", "Empirical", "Excess demand", "Excess demand function", "First derivative", "Gross domestic product", "Horizontal axis", "Image processing", "Income", "Infinitesimal", "Infinity", "Integer", "International Standard Book Number", "Logistic map", "Mathematics", "Measurement", "Natural number", "Nonlinearity", "Normalized frequency (digital signal processing)", "Parameter", "Physics", "Price", "Quantity", "Quantization (signal processing)", "Real number", "Real number line", "Real numbers", "Regression analysis", "Sampling (signal processing)", "Sampling rate", "Scientific theory", "Sequence", "Signal (electrical engineering)", "Signal (information theory)", "Step function", "Time-scale calculus", "Time series", "Uncountable set", "Variable (mathematics)"], "references": []}, "H\u00e1jek\u2013Le Cam convolution theorem": {"categories": ["CS1 maint: Uses authors parameter", "Statistical theorems"], "title": "H\u00e1jek\u2013Le Cam convolution theorem", "method": "H\u00e1jek\u2013Le Cam convolution theorem", "url": "https://en.wikipedia.org/wiki/H%C3%A1jek%E2%80%93Le_Cam_convolution_theorem", "summary": "In statistics, the H\u00e1jek\u2013Le Cam convolution theorem states that any regular estimator in a parametric model is asymptotically equivalent to a sum of two independent random variables, one of which is normal with asymptotic variance equal to the inverse of Fisher information, and the other having arbitrary distribution.\nThe obvious corollary from this theorem is that the \u201cbest\u201d among regular estimators are those with the second component identically equal to zero. Such estimators are called efficient and are known to always exist for regular parametric models.\nThe theorem is named after Jaroslav H\u00e1jek and Lucien Le Cam.", "images": [], "links": ["Convergence in distribution", "Fisher information", "Independence (probability theory)", "International Standard Book Number", "Jaroslav H\u00e1jek", "Lucien Le Cam", "Matrix transpose", "Normal distribution", "Parametric model", "Regular estimator", "Score (statistics)", "Statistics"], "references": []}, "Almost surely": {"categories": ["Mathematical terminology", "Probability theory"], "title": "Almost surely", "method": "Almost surely", "url": "https://en.wikipedia.org/wiki/Almost_surely", "summary": "In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one. In other words, the set of possible exceptions may be non-empty, but it has probability zero. The concept is precisely the same as the concept of \"almost everywhere\" in measure theory.\nIn probability experiments on a finite sample space, there is often no difference between almost surely and surely. However, the distinction becomes important when the sample space is an infinite set, because an infinite set can have non-empty subsets of probability zero.\nSome examples of the use of this concept include the strong and uniform versions of the law of large numbers, and the continuity of the paths of Brownian motion.\nThe terms almost certainly (a.c.) and almost always (a.a.) are also used. Almost never describes the opposite of almost surely: an event that happens with probability zero happens almost never.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/3e/20180429195951%21Nuvola_apps_edu_mathematics_blue-p.svg"], "links": ["0 (number)", "Almost all", "Almost everywhere", "Asymptotic analysis", "Brownian motion", "Composite number", "Connectivity (graph theory)", "Convergence of random variables", "Degenerate distribution", "Erd\u0151s\u2013R\u00e9nyi model", "Event (probability theory)", "Independent and identically distributed random variables", "Infinite monkey theorem", "Infinite set", "International Standard Book Number", "International Standard Serial Number", "Law of large numbers", "Leonid Libkin", "Measure theory", "Null set", "Number theory", "Prasad V. Tetali", "Prime number theorem", "Probability 1", "Probability interpretations", "Probability space", "Probability theory", "Random graph", "Sample space"], "references": ["http://www.worldcat.org/issn/0065-9266", "https://books.google.com/books?id=u2c3LpjWs7EC&pg=PA4"]}, "Acceptance sampling": {"categories": ["Quality control tools", "Sampling (statistics)"], "title": "Acceptance sampling", "method": "Acceptance sampling", "url": "https://en.wikipedia.org/wiki/Acceptance_sampling", "summary": "Acceptance sampling uses statistical sampling to determine whether to accept or reject a production lot of material. It has been a common quality control technique used in industry. It is usually done as products leaves the factory, or in some cases even within the factory. Most often a producer supplies a consumer a number of items and a decision to accept or reject the items is made by determining the number of defective items in a sample from the lot. The lot is accepted if the number of defects falls below where the acceptance number or otherwise the lot is rejected.In general, acceptance sampling is employed when one or several of the following hold:\ntesting is destructive;\nthe cost of 100% inspection is very high; and\n100% inspection takes too long.A wide variety of acceptance sampling plans are available. For example, multiple sampling plans use more than two samples to reach a conclusion. A shorter examination period and smaller sample sizes are features of this type of plan. Although the samples are taken at random, the sampling procedure is still reliable.", "images": [], "links": ["ASTM", "Acceptable quality limit", "Acceptance testing", "HACCP", "Harold F. Dodge", "ISO 9000", "International Standard Book Number", "MIL-STD-105", "Operating characteristic curve", "Quality assurance", "Quality control", "Quality management system", "Sample size", "Sampling plan", "Six sigma", "Statistical process control", "Statistical sampling", "Technical specifications", "Technical standard", "Variables sampling plan", "Verifying"], "references": ["http://www.sqconline.com/"]}, "Rank correlation": {"categories": ["Covariance and correlation", "Nonparametric statistics", "Rankings"], "title": "Rank correlation", "method": "Rank correlation", "url": "https://en.wikipedia.org/wiki/Rank_correlation", "summary": "In statistics, a rank correlation is any of several statistics that measure an ordinal association\u2014the relationship between rankings of different ordinal variables or different rankings of the same variable, where a \"ranking\" is the assignment of the ordering labels \"first\", \"second\", \"third\", etc. to different observations of a particular variable. A rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess the significance of the relation between them. For example, two common nonparametric methods of significance that use rank correlation are the Mann\u2013Whitney U test and the Wilcoxon signed-rank test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodman and Kruskal's gamma", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall's tau rank correlation coefficient", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Metric (mathematics)", "Metric space", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal data", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Psychometrika", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank statistics", "Ranking", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Somers' D", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Symmetric group", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Kruskal", "Z-test"], "references": ["http://core.ecu.edu/psyc/wuenschk/docs30/Nonparametric-EffectSize.pdf", "http://doi.org/10.1007%2FBF02289138", "http://doi.org/10.1111%2Fj.1745-3984.1965.tb00396.x", "http://doi.org/10.2307%2F2281954", "http://doi.org/10.2466%2F11.IT.3.1", "http://www.jstor.org/stable/2281954"]}, "Volatility (finance)": {"categories": ["CS1 maint: Multiple names: authors list", "Mathematical finance", "Technical analysis", "Use dmy dates from August 2014"], "title": "Volatility (finance)", "method": "Volatility (finance)", "url": "https://en.wikipedia.org/wiki/Volatility_(finance)", "summary": "In finance, volatility (symbol \u03c3) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns.\nHistoric volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option).", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9b/VIX.png", "https://upload.wikimedia.org/wikipedia/commons/e/ed/Vix.png"], "links": ["Absolute deviation", "Accumulation/distribution index", "Advance\u2013decline line", "Adverse selection", "Algorithmic trading", "Alpha (finance)", "Arbitrage pricing theory", "Authorised capital", "Autoregressive conditional heteroskedasticity", "Average directional movement index", "Average true range", "Beno\u00eet Mandelbrot", "Beta (finance)", "Bid\u2013ask spread", "Black Scholes", "Black\u2013Scholes model", "Block trade", "Bollinger Bands", "Book value", "Bottom (technical analysis)", "Breadth of market", "Breakout (technical analysis)", "Broadening top", "Broker-dealer", "Bruno Dupire", "Bubble (economics)", "Buy and hold", "Candlestick chart", "Candlestick pattern", "Capital asset pricing model", "Capital market", "Capital market line", "Chart pattern", "Chris Brooks (academic)", "Commodity channel index", "Common stock", "Compound annual growth rate", "Contrarian investing", "Coppock curve", "Correlation", "Cross listing", "Cup and handle", "Dark pool", "Day trader", "Day trading", "Dead cat bounce", "Derivative (finance)", "Detrended price oscillator", "Digital object identifier", "Dividend", "Dividend discount model", "Dividend yield", "Doji", "Dollar cost averaging", "Donchian channel", "Double top and double bottom", "Dow theory", "DuPont analysis", "Dual-listed company", "Earnings per share", "Earnings yield", "Ease of movement", "Efficient-market hypothesis", "Efficient frontier", "Electronic communication network", "Elliott wave principle", "Emanuel Derman", "Fat tail", "Fibonacci retracement", "Finance", "Financial economics", "Financial law", "Financial market", "Financial regulation", "Flag and pennant patterns", "Flight-to-quality", "Floor broker", "Floor trader", "Force index", "Fourth market", "Fundamental analysis", "Gap (chart pattern)", "Gaussian", "Golden share", "Growth stock", "Haircut (finance)", "Hammer (candlestick pattern)", "Hanging man (candlestick pattern)", "Head and shoulders (chart pattern)", "Hikkake pattern", "IVX", "Ichimoku Kink\u014d Hy\u014d", "Implied volatility", "Initial public offering", "Instantaneous rate of return", "International Economic Review", "International Standard Serial Number", "Inverted hammer", "Investor", "Iraj Kani", "Island reversal", "Issued shares", "JSTOR", "Journal of Finance", "Journal of Financial Economics", "Journal of Portfolio Management", "Jules Regnault", "Jump-diffusion models", "Kagi chart", "Keltner channel", "Know sure thing oscillator", "Kurtosis", "Line chart", "Linear regression", "List of stock exchange trading hours", "List of stock exchanges", "Local volatility", "Logarithmic return", "Long (finance)", "L\u00e9vy distribution", "MACD", "Margin (finance)", "Mark Spitznagel", "Market anomaly", "Market capitalization", "Market depth", "Market maker", "Market manipulation", "Market microstructure", "Market timing", "Market trend", "Marubozu", "Mass index", "McClellan oscillator", "Mean reversion (finance)", "Modern portfolio theory", "Momentum (finance)", "Momentum investing", "Money flow index", "Morning star (candlestick pattern)", "Mosaic theory (investments)", "Moving average", "Multilateral trading facility", "Nassim Nicholas Taleb", "Nassim Taleb", "Negative volume index", "Nelson Saiers", "Net asset value", "Normal distribution", "On-balance volume", "Open-high-low-close chart", "Open outcry", "Option (finance)", "Over-the-counter (finance)", "Pairs trade", "Parabolic SAR", "Pivot point (stock market)", "Point and figure chart", "Poisson process", "Portfolio managers", "Position (finance)", "Post-modern portfolio theory", "Preferred stock", "Price channels", "Primary market", "Probability", "Proprietary trading", "Public float", "Public offering", "Put/call ratio", "Quantitative analyst", "Rally (stock market)", "Random walk", "Random walk hypothesis", "Rate of return", "Realized variance", "Relative strength index", "Restricted stock", "Returns-based style analysis", "Reverse stock split", "Risk", "Secondary market", "Sector rotation", "Security characteristic line", "Security market line", "Share capital", "Share repurchase", "Shares outstanding", "Shooting star (candlestick pattern)", "Short (finance)", "Slippage (finance)", "Smart money index", "Social Science Research Network", "Speculation", "Spinning top (candlestick pattern)", "Square root", "Stable distribution", "Standard deviation", "Stochastic oscillator", "Stochastic volatility", "Stock", "Stock dilution", "Stock exchange", "Stock market crash", "Stock market index", "Stock split", "Stock trader", "Stock valuation", "Straddle", "Style investing", "Support and resistance", "Swing trading", "T-model", "TRIN (finance)", "Taylor series", "Technical analysis", "Technical indicator", "Third market", "Three black crows", "Three white soldiers", "Time horizon", "Top (technical analysis)", "Tracking stock", "Trade (financial instrument)", "Trading strategy", "Treasury stock", "Trend following", "Trend line (technical analysis)", "Triangle (chart pattern)", "Triple top and triple bottom", "Trix (technical analysis)", "True strength index", "Ulcer index", "Ultimate oscillator", "Uptick rule", "VIX", "Value averaging", "Value investing", "Variance", "Variance swap", "Volatility arbitrage", "Volatility clustering", "Volatility smile", "Volatility swap", "Volatility tax", "Volume (finance)", "Volume\u2013price trend", "Vortex indicator", "Voting interest", "Wedge pattern", "Wiener process", "Williams %R", "Yield (finance)"], "references": ["http://www.ederman.com/new/docs/gs-volatility_smile.pdf", "http://www.iijournals.com/doi/abs/10.3905/JOT.2010.5.2.035", "http://www.investopedia.com/articles/optioninvestor/10/volatility-spikes-credit-spreads.asp", "http://www.lfrankcabrera.com/calc-hist-vol.pdf", "http://www.macroaxis.com/invest/market/GOOG--symbolVolatility", "http://www.readcube.com/articles/10.1002/wilm.10201?locale=en", "http://ssrn.com/abstract=2257549", "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=970480", "http://training.thomsonreuters.com/video/v.php?v=273", "http://www.wilmottwiki.com/wiki/index.php?title=Levy_distribution", "http://www.wilmottwiki.com/wiki/index.php?title=Volatility", "http://worldvolatility.com", "http://citeseer.ist.psu.edu/244698.html", "http://www.risk.net/hedge-funds-review/profile/2246892/interview-paul-britton-founder-ceo-capstone-holdings-group", "http://staff.science.uva.nl/~marvisse/volatility.html", "http://doi.org/10.1002/for.841", "http://doi.org/10.1111/j.1540-6261.1995.tb04793.x", "http://doi.org/10.1111/j.1540-6261.2012.01749.x", "http://doi.org/10.3905/jod.1993.407877", "http://www.jstor.org/stable/2329417", "http://www.jstor.org/stable/2527343", "http://www.worldcat.org/issn/1099-131X", "https://www.forbes.com/sites/steveschaefer/2013/02/14/blue-mountains-andrew-feldstein-three-ways-to-play-a-more-volatile-steel-industry", "https://www.nytimes.com/2011/03/18/business/global/18volatility.html", "https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2812353"]}, "Inverse Gaussian distribution": {"categories": ["Articles with example Java code", "Articles with example Python code", "Continuous distributions", "Exponential family distributions", "Pages using deprecated image syntax", "Pages with DOIs inactive since 2018"], "title": "Inverse Gaussian distribution", "method": "Inverse Gaussian distribution", "url": "https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution", "summary": "In probability theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions with support on (0,\u221e).\nIts probability density function is given by\n\n \n \n \n f\n (\n x\n ;\n \u03bc\n ,\n \u03bb\n )\n =\n \n \n [\n \n \n \u03bb\n \n 2\n \u03c0\n \n x\n \n 3\n \n \n \n \n \n ]\n \n \n 1\n \n /\n \n 2\n \n \n exp\n \u2061\n \n {\n \n \n \n \u2212\n \u03bb\n (\n x\n \u2212\n \u03bc\n \n )\n \n 2\n \n \n \n \n 2\n \n \u03bc\n \n 2\n \n \n x\n \n \n \n }\n \n \n \n {\\displaystyle f(x;\\mu ,\\lambda )=\\left[{\\frac {\\lambda }{2\\pi x^{3}}}\\right]^{1/2}\\exp \\left\\{{\\frac {-\\lambda (x-\\mu )^{2}}{2\\mu ^{2}x}}\\right\\}}\n for x > 0, where \n \n \n \n \u03bc\n >\n 0\n \n \n {\\displaystyle \\mu >0}\n is the mean and \n \n \n \n \u03bb\n >\n 0\n \n \n {\\displaystyle \\lambda >0}\n is the shape parameter.As \u03bb tends to infinity, the inverse Gaussian distribution becomes more like a normal (Gaussian) distribution. The inverse Gaussian distribution has several properties analogous to a Gaussian distribution. The name can be misleading: it is an \"inverse\" only in that, while the Gaussian describes a Brownian motion's level at a fixed time, the inverse Gaussian describes the distribution of the time a Brownian motion with positive drift takes to reach a fixed positive level.\nIts cumulant generating function (logarithm of the characteristic function) is the inverse of the cumulant generating function of a Gaussian random variable.\nTo indicate that a random variable X is inverse Gaussian-distributed with mean \u03bc and shape parameter \u03bb we write \n \n \n \n X\n \u223c\n IG\n \u2061\n (\n \u03bc\n ,\n \u03bb\n )\n \n \n \n \n {\\displaystyle X\\sim \\operatorname {IG} (\\mu ,\\lambda )\\,\\!}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a5/PDF_invGauss.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4f/Wald_Distribution_matplotlib.jpg"], "links": ["ARGUS distribution", "Abraham Wald", "ArXiv", "Arcsine distribution", "Arnljot H\u00f8yland", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Erwin Schr\u00f6dinger", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential dispersion model", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "First passage time", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Java (programming language)", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matplotlib", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maurice Tweedie", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Natural parameters", "Natural statistics", "Necessary and sufficient conditions", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Numpy", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Physikalische Zeitschrift", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "PubMed Central", "PubMed Identifier", "Python (programming language)", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "R programming language", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Stochastic process", "Stopping time", "Student's t-distribution", "Support (mathematics)", "The R Journal", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Tweedie distributions", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wiener process", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://mathworld.wolfram.com/InverseGaussianDistribution.html", "http://adsabs.harvard.edu/abs/2016arXiv160306687G", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3062635", "http://www.ncbi.nlm.nih.gov/pubmed/11816448", "http://www.ncbi.nlm.nih.gov/pubmed/21090905", "http://arxiv.org/abs/1603.06687", "http://doi.org/10.1037%2Fa0020747", "http://doi.org/10.2307%2F2683801", "http://doi.org/10.2307%2F2984691", "http://doi.org/10.3758%2Fbf03195403", "http://www.jstor.org/stable/2683801", "http://www.jstor.org/stable/2984691", "https://babel.hathitrust.org/cgi/pt?id=njp.32101054770928;view=1up;seq=337", "https://cran.r-project.org/web/packages/statmod/index.html", "https://journal.r-project.org/archive/2016-1"]}, "Xbar and R chart": {"categories": ["Quality control tools", "Statistical charts and diagrams"], "title": "X\u0305 and R chart", "method": "Xbar and R chart", "url": "https://en.wikipedia.org/wiki/X%CC%85_and_R_chart", "summary": "In statistical quality control, the \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n and R chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process.The chart is advantageous in the following situations:\nThe sample size is relatively small (say, n \u2264 10\u2014\n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n and s charts are typically used for larger sample sizes)\nThe sample size is constant\nHumans must perform the calculations for the chartThe \"chart\" actually consists of a pair of charts: One to monitor the process standard deviation (as approximated by the sample moving range) and another to monitor the process mean, as is done with the \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n and s and individuals control charts. The \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n and R chart plots the mean value for the quality characteristic across all units in the sample, \n \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n i\n \n \n \n \n {\\displaystyle {\\bar {x}}_{i}}\n , plus the range of the quality characteristic across all units in the sample as follows:\n\nR = xmax - xmin.The normal distribution is the basis for the charts and requires the following assumptions:\n\nThe quality characteristic to be monitored is adequately modeled by a normally distributed random variable\nThe parameters \u03bc and \u03c3 for the random variable are the same for each unit and each unit is independent of its predecessors or successors\nThe inspection procedure is same for each sample and is carried out consistently from sample to sampleThe control limits for this chart type are:\n\n \n \n \n \n D\n \n 3\n \n \n \n \n \n R\n \u00af\n \n \n \n \n \n {\\displaystyle D_{3}{\\bar {R}}}\n (lower) and \n \n \n \n \n D\n \n 4\n \n \n \n \n \n R\n \u00af\n \n \n \n \n \n {\\displaystyle D_{4}{\\bar {R}}}\n (upper) for monitoring the process variability\n\n \n \n \n \n \n \n x\n \u00af\n \n \n \n \u00b1\n \n A\n \n 2\n \n \n \n \n \n R\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}\\pm A_{2}{\\bar {R}}}\n for monitoring the process meanwhere \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n and \n \n \n \n \n \n \n R\n \u00af\n \n \n \n =\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n m\n \n \n \n (\n \n \n R\n \n m\n a\n x\n \n \n \u2212\n \n R\n \n m\n i\n n\n \n \n \n )\n \n \n m\n \n \n \n \n {\\displaystyle {\\bar {R}}={\\frac {\\sum _{i=1}^{m}\\left(R_{max}-R_{min}\\right)}{m}}}\n are the estimates of the long-term process mean and range established during control-chart setup and A2, D3, and D4 are sample size-specific anti-biasing constants. The anti-biasing constants are typically found in the appendices of textbooks on statistical process control.As with the \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n and s and individuals control charts, the \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n chart is only valid if the within-sample variability is constant. Thus, the R chart is examined before the \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n chart; if the R chart indicates the sample variability is in statistical control, then the \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n chart is examined to determine if the sample mean is also in statistical control. If on the other hand, the sample variability is not in statistical control, then the entire process is judged to be not in statistical control regardless of what the \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n chart indicates.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4e/R_chart_for_a_paired_xbar_and_R_chart.svg", "https://upload.wikimedia.org/wikipedia/commons/9/93/Xbar_chart_for_a_paired_xbar_and_R_chart.svg"], "links": ["Business process", "Control chart", "Hoboken, New Jersey", "International Standard Book Number", "John Wiley & Sons", "List of industrial processes", "National Institute of Standards and Technology", "Normal distribution", "OCLC", "Random variable", "Range (statistics)", "Shewhart individuals control chart", "Statistical process control", "Unbiased estimation of standard deviation", "Variable and attribute (research)", "Walter A. Shewhart", "Xbar and s chart"], "references": ["http://www.eas.asu.edu/~masmlab/montgomery/", "http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc321.htm", "http://www.worldcat.org/oclc/56729567"]}, "Statistical genetics": {"categories": ["Statistical genetics"], "title": "Statistical genetics", "method": "Statistical genetics", "url": "https://en.wikipedia.org/wiki/Statistical_genetics", "summary": "Statistical genetics is a scientific field concerned with the development of statistical methods for drawing inferences from genetic data. The term is most commonly used in the context of human genetics. Research in statistical genetics generally involves developing theory or methodology to support research in one of three related areas:\n\npopulation genetics - Study of evolutionary processes affecting genetic variation between organisms\ngenetic epidemiology - Studying effects of genes on diseases\nquantitative genetics - Studying the effects of genes on 'normal' phenotypesStatistical geneticists tend to collaborate closely with geneticists, molecular biologists, clinicians and bioinformaticians. Statistical genetics is a type of computational biology.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/archive/4/4a/20160405223351%21Commons-logo.svg"], "links": ["Bioinformatics", "Clinical genetics", "Computational biology", "Genetic epidemiology", "Genetics", "Human genetics", "Molecular biology", "Phenotypes", "Population genetics", "Quantitative genetics"], "references": []}, "Data point": {"categories": ["All stub articles", "Social research", "Statistical data types", "Statistics stubs"], "title": "Unit of observation", "method": "Data point", "url": "https://en.wikipedia.org/wiki/Unit_of_observation", "summary": "In statistics, a unit of observation is the unit described by the data that one analyzes. For example, in a study of the demand for money, the unit of observation might be chosen as the individual, with different observations (data points) for a given point in time differing as to which individual they refer to; or the unit of observation might be the country, with different observations differing only in regard to the country they refer to. A study may have a differing unit of observation and unit of analysis: for example, in community research, the research design may collect data at the individual level of observation but the level of analysis might be at the neighborhood level, drawing conclusions on neighborhood characteristics from data collected from individuals. Together, the unit of observation and the level of analysis define the population of a research enterprise.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Array data structure", "Boolean logic", "Category (mathematics)", "Community", "Computing", "Data", "Data collection system", "Data processing", "Datatype", "Demand for money", "Integer", "International Standard Book Number", "Level of measurement", "Money demand", "Real number", "Research design", "Sample population", "Statistical graphics", "Statistical inference", "Statistical sample", "Statistics", "Summary statistic", "Unit of analysis", "Units of measurement", "Vector space"], "references": []}, "Probability matching": {"categories": ["All articles lacking in-text citations", "All stub articles", "Articles lacking in-text citations from February 2015", "Cognitive science", "Decision-making", "Machine learning", "Statistical classification", "Statistics stubs"], "title": "Probability matching", "method": "Probability matching", "url": "https://en.wikipedia.org/wiki/Probability_matching", "summary": "Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, then the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of \"positive\" on 60% of instances, and a class label of \"negative\" on 40% of instances. \nThe optimal Bayesian decision strategy (to maximize the number of correct predictions, see Duda, Hart & Stork (2001)) in such a case is to always predict \"positive\" (i.e., predict the majority category in the absence of other information), which has 60% chance of winning rather than matching which has 52% of winning (where p is the probability of positive realization, the result of matching would be \n \n \n \n \n p\n \n 2\n \n \n +\n (\n 1\n \u2212\n p\n \n )\n \n 2\n \n \n \n \n {\\displaystyle p^{2}+(1-p)^{2}}\n , here \n \n \n \n .6\n \u00d7\n .6\n +\n .4\n \u00d7\n .4\n \n \n {\\displaystyle .6\\times .6+.4\\times .4}\n ). The probability-matching strategy is of psychological interest because it is frequently employed by human subjects in decision and classification studies (where it may be related to Thompson sampling).", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Base rates", "Bayesian decision theory", "Decision strategy", "New York City", "Statistics", "Thompson sampling"], "references": ["http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471056693.html"]}, "T-statistic": {"categories": ["All articles lacking sources", "All articles with unsourced statements", "Articles lacking sources from February 2011", "Articles with unsourced statements from February 2011", "Normal distribution", "Parametric statistics", "Statistical ratios", "Use dmy dates from November 2010"], "title": "T-statistic", "method": "T-statistic", "url": "https://en.wikipedia.org/wiki/T-statistic", "summary": "In statistics, the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is used in hypothesis testing via Student's t-test. For example, it is used in estimating the population mean from a sampling distribution of sample means if the population standard deviation is unknown.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Ancillary statistic", "Asymptotic normality", "Augmented Dickey\u2013Fuller test", "Brewery", "Confidence interval", "Consistent estimator", "Dublin, Ireland", "Errors and residuals in statistics", "Estimator", "F-test", "Guinness", "Homoscedasticity", "Hotelling's t-squared statistic", "Linear regression model", "Normal distribution", "Ordinary least squares", "Pen name", "Pivotal quantity", "Population mean", "Prediction interval", "Regression analysis", "Sample mean", "Sampling distribution", "Simple linear regression", "Standard deviation", "Standard error (statistics)", "Standard normal", "Standardized testing (statistics)", "Statistical hypothesis testing", "Statistical model", "Statistics", "Student's t-distribution", "Student's t-test", "Student's t test", "Studentized residual", "T-test", "Time series", "Unit root", "William Sealy Gosset", "Z-score", "Z-test"], "references": []}, "Sample (statistics)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2017", "Sampling (statistics)", "Wikipedia articles needing clarification from March 2018", "Wikipedia articles with GND identifiers"], "title": "Sample (statistics)", "method": "Sample (statistics)", "url": "https://en.wikipedia.org/wiki/Sample_(statistics)", "summary": "In statistics and quantitative research methodology, a data sample is a set of data collected and/or selected from a statistical population by a defined procedure. The elements of a sample are known as sample points, sampling units or observations.\nTypically, the population is very large, making a census or a complete enumeration of all the values in the population either impractical or impossible. The sample usually represents a subset of manageable size. Samples are collected and statistics are calculated from the samples, so that one can make inferences or extrapolations from the sample to the population. \nThe data sample may be drawn from a population without replacement (i.e. no element can be selected more than once in the same sample), in which case it is a subset of a population; or with replacement (i.e. an element may appear multiple times in the one sample), in which case it is a multisubset.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/b/bf/Simple_random_sampling.PNG"], "links": ["Census", "Cluster sampling", "Convenience sample", "Data", "Digital object identifier", "Enumeration", "Estimation theory", "Extrapolation", "Independent and identically-distributed random variables", "Inference", "Integrated Authority File", "International Standard Book Number", "Johan Strydom", "Judgment sample", "Lecture Notes in Computer Science", "Mathematical Reviews", "Non-probability sample", "Non-random sampling", "Probability distribution", "Purposive sample", "Quadrature node", "Quantitative research", "Quasi-Monte Carlo method", "Quota sample", "Random sample", "Replication (statistics)", "Roxy Peck", "Sample size determination", "Sampling (statistics)", "Samuel S. Wilks", "Simple random sample", "Snowball sampling", "Statistic", "Statistical independence", "Statistical population", "Statistical unit", "Statistics", "Stratified sampling", "Subset", "Survey sampling", "Systematic sampling", "William Gemmell Cochran", "Zentralblatt MATH"], "references": ["http://www-igm.univ-mlv.fr/~berstel/Articles/1993SturmianPatriceMFCS.pdf", "http://www.socialresearchmethods.net/kb/sampstat.php", "http://doi.org/10.1007%2F3-540-57182-5_20", "http://zbmath.org/?format=complete&q=an:0925.11026", "https://books.google.com/?id=2VkNiakfaUEC&printsec=frontcover&q=", "https://d-nb.info/gnd/4057502-0", "https://mathscinet.ams.org/mathscinet-getitem?mr=1326829", "https://www.wikidata.org/wiki/Q49906"]}, "Seasonal variation": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from November 2008", "Articles needing additional references from November 2010", "Articles with multiple maintenance issues", "Inventory", "Pages with citations having bare URLs", "Pages with citations lacking titles", "Seasonality", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Seasonality", "method": "Seasonal variation", "url": "https://en.wikipedia.org/wiki/Seasonality", "summary": "In time series data, seasonality is the presence of variations that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly. Seasonality may be caused by various factors, such as weather, vacation, and holidays and consists of periodic, repetitive, and generally regular and predictable patterns in the levels of a time series.\nSeasonal fluctuations in a time series can be contrasted with cyclical patterns. The latter occur when the data exhibits rises and falls that are not of a fixed period. Such non-seasonal fluctuations are usually due to economic conditions and are often related to the \"business cycle\"; their period usually extends beyond a single year, and the fluctuations are usually of at least two years.Organisations facing seasonal variations, such as ice-cream vendors, are often interested in knowing their performance relative to the normal seasonal variation. Seasonal variations in the labour market can be attributed to the entrance of school leavers into the job market as they aim to contribute to the workforce upon the completion of their schooling. These regular changes are of less interest to those who study employment data than the variations that occur due to the underlying state of the economy; their focus is on how unemployment in the workforce has changed, despite the impact of the regular seasonal variations.It is necessary for organisations to identify and measure seasonal variations within their market to help them plan for the future. This can prepare them for the temporary increases or decreases in labour requirements and inventory as demand for their product or service fluctuates over certain periods. This may require training, periodic maintenance, and so forth that can be organized in advance. Apart from these considerations, the organisations need to know if variation they have experienced has been more or less than the expected amount, beyond what the usual seasonal variations account for.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6a/Acfbeer.png", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/SeasonalplotUS.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARIMA", "Autocorrelation plot", "Box plot", "Copyright status of work by the U.S. government", "Cycle count", "Cyclostationary process", "Decomposition of time series", "Dependent variable", "Dummy variable (statistics)", "Frequency", "Graphical technique", "Independent variable", "International Standard Book Number", "Inventory", "Moving average", "National Institute of Standards and Technology", "Ordinary least squares", "Oscillation", "Periodic function", "Periodicity (disambiguation)", "Photoperiodism", "Regression analysis", "Run sequence plot", "Safety stock", "Seasonal adjustment", "Seasonal subseries plot", "Sine wave", "Sinusoidal model", "Spectral density estimation", "Time-series", "Time series", "Time series analysis", "Trend estimation", "X-12-ARIMA"], "references": ["http://www.allbusiness.com/barrons_dictionary/dictionary-seasonality-4946957-1.html", "http://www.businessdictionary.com/definition/seasonality.html", "http://stats.stackexchange.com/questions/16117/what-method-can-be-used-to-detect-seasonality-in-data", "http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc443.htm", "https://www.otexts.org/fpp/2/1", "https://www.otexts.org/fpp/6/1"]}, "Mean squared prediction error": {"categories": ["Accuracy disputes from May 2018", "All accuracy disputes", "All articles lacking sources", "All articles needing expert attention", "Articles lacking sources from December 2009", "Articles needing expert attention", "Loss functions", "Point estimation performance", "Statistical deviation and dispersion", "Statistics articles needing expert attention"], "title": "Mean squared prediction error", "method": "Mean squared prediction error", "url": "https://en.wikipedia.org/wiki/Mean_squared_prediction_error", "summary": "In statistics the mean squared prediction error or mean squared error of the predictions of a smoothing or curve fitting procedure is the expected value of the squared difference between the fitted values implied by the predictive function \n \n \n \n \n \n \n g\n ^\n \n \n \n \n \n {\\displaystyle {\\widehat {g}}}\n and the values of the (unobservable) function g. It is an inverse measure of the explanatory power of \n \n \n \n \n \n \n g\n ^\n \n \n \n ,\n \n \n {\\displaystyle {\\widehat {g}},}\n and can be used in the process of cross-validation of an estimated model.\nIf the smoothing or fitting procedure has projection matrix (i.e., hat matrix) L, which maps the observed values vector \n \n \n \n y\n \n \n {\\displaystyle y}\n to predicted values vector \n \n \n \n \n \n \n y\n ^\n \n \n \n \n \n {\\displaystyle {\\hat {y}}}\n via \n \n \n \n \n \n \n y\n ^\n \n \n \n =\n L\n y\n ,\n \n \n {\\displaystyle {\\hat {y}}=Ly,}\n then\n\n \n \n \n MSPE\n \u2061\n (\n L\n )\n =\n E\n \u2061\n \n [\n \n \n (\n \n g\n (\n \n x\n \n i\n \n \n )\n \u2212\n \n \n \n g\n ^\n \n \n \n (\n \n x\n \n i\n \n \n )\n \n )\n \n \n 2\n \n \n ]\n \n .\n \n \n {\\displaystyle \\operatorname {MSPE} (L)=\\operatorname {E} \\left[\\left(g(x_{i})-{\\widehat {g}}(x_{i})\\right)^{2}\\right].}\n The MSPE can be decomposed into two terms: the mean of squared biases of the fitted values and the mean of variances of the fitted values:\n\n \n \n \n n\n \u22c5\n MSPE\n \u2061\n (\n L\n )\n =\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n \n (\n \n E\n \u2061\n \n [\n \n \n \n \n g\n ^\n \n \n \n (\n \n x\n \n i\n \n \n )\n \n ]\n \n \u2212\n g\n (\n \n x\n \n i\n \n \n )\n \n )\n \n \n 2\n \n \n +\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n var\n \u2061\n \n [\n \n \n \n \n g\n ^\n \n \n \n (\n \n x\n \n i\n \n \n )\n \n ]\n \n .\n \n \n {\\displaystyle n\\cdot \\operatorname {MSPE} (L)=\\sum _{i=1}^{n}\\left(\\operatorname {E} \\left[{\\widehat {g}}(x_{i})\\right]-g(x_{i})\\right)^{2}+\\sum _{i=1}^{n}\\operatorname {var} \\left[{\\widehat {g}}(x_{i})\\right].}\n Knowledge of g is required in order to calculate the MSPE exactly; otherwise, it can be estimated.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/1/17/System-search.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Colin Mallows", "Cross-validation (statistics)", "Curve fitting", "Data analyst", "Errors and residuals in statistics", "Law of total variance", "Mallows's Cp", "Mean squared error", "Projection matrix", "Regression analysis", "Sample (statistics)", "Smoothing", "Statistical population", "Statistics"], "references": []}, "Sample-continuous process": {"categories": ["Stochastic processes"], "title": "Sample-continuous process", "method": "Sample-continuous process", "url": "https://en.wikipedia.org/wiki/Sample-continuous_process", "summary": "In mathematics, a sample-continuous process is a stochastic process whose sample paths are almost surely continuous functions.", "images": [], "links": ["Almost all", "Almost surely", "Brownian motion", "Continuous function", "Continuous function (topology)", "Continuous stochastic process", "Dimension", "Euclidean space", "Finite-dimensional distribution", "Index set", "International Standard Book Number", "Law (stochastic processes)", "Mathematics", "Probability space", "Real line", "Stochastic differential equation", "Stochastic process", "Topological space", "Wiener process"], "references": []}, "P\u2013P plot": {"categories": ["Statistical charts and diagrams", "Use dmy dates from August 2012"], "title": "P\u2013P plot", "method": "P\u2013P plot", "url": "https://en.wikipedia.org/wiki/P%E2%80%93P_plot", "summary": "In statistics, a P\u2013P plot (probability\u2013probability plot or percent\u2013percent plot or P value plot) is a probability plot for assessing how closely two data sets agree, which plots the two cumulative distribution functions against each other. P-P plots are vastly used to evaluate the skewness of a distribution.\nThe Q\u2013Q plot is more widely used, but they are both referred to as \"the\" probability plot, and are potentially confused.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6c/Probability-Probability_plot%2C_quality_characteristic_data.png"], "links": ["Biometrika", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Data set", "Digital object identifier", "Distribution fitting", "International Standard Book Number", "JSTOR", "Jean D. Gibbons", "L-moment", "MathWorks", "Median", "Normal probability plot", "Plotting position", "Probability plot", "Quantile", "Q\u2013Q plot", "R (programming language)", "Skewness", "Software", "StatSoft", "Variance-stabilizing transformation"], "references": ["http://doi.org/10.1111%2F1467-9957.00086", "http://doi.org/10.20982%2Ftqmp.12.1.p030", "https://books.google.com/books?id=gbegXB4SdosC", "https://books.google.com/books?id=gbegXB4SdosC&pg=PA31#PPA23,M1", "https://books.google.com/books?id=kJbVO2G6VicC", "https://books.google.com/books?id=kJbVO2G6VicC&pg=PA144#PPA145,M1", "https://dx.doi.org/10.1111/1467-9957.00086", "https://www.jstor.org/stable/2335939"]}, "Multivariate t-distribution": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from May 2012", "Articles with unsourced statements from April 2016", "Continuous distributions", "Multivariate continuous distributions"], "title": "Multivariate t-distribution", "method": "Multivariate t-distribution", "url": "https://en.wikipedia.org/wiki/Multivariate_t-distribution", "summary": "In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization to random vectors of the Student's t-distribution, which is a distribution applicable to univariate random variables. While the case of a random matrix could be treated within this structure, the matrix t-distribution is distinct and makes particular use of the matrix structure.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Copula (statistics)", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Euclidean norm", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Mahalanobis distance", "Marchenko\u2013Pastur distribution", "Marginal distribution", "Mathematical finance", "Matrix-exponential distribution", "Matrix (mathematics)", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Monte Carlo integration", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate probability distribution", "Multivariate stable distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Norm (mathematics)", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Pearson product-moment correlation coefficient", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Positive-definite matrix", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Random vector", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Statistics", "Student's t-distribution", "Student's t-test", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.mathworks.com/matlabcentral/fileexchange/53796", "http://www.statlect.com/mcdstu1.htm", "http://doi.org/10.1109%2FWSC.2015.7408180", "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7408180&isnumber=7408148", "https://www.springer.com/statistics/computational+statistics/book/978-3-642-01688-2", "https://web.archive.org/web/20061202010900/http://www.mth.kcl.ac.uk/~shaww/web_page/papers/MultiStudentc.pdf"]}, "Gambler's ruin": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2013", "Causal fallacies", "Gambling terminology", "Probability problems", "Variants of random walks"], "title": "Gambler's ruin", "method": "Gambler's ruin", "url": "https://en.wikipedia.org/wiki/Gambler%27s_ruin", "summary": "The term gambler's ruin is a statistical concept expressed in a variety of forms:\n\nThe original meaning is that a persistent gambler who raises his bet to a fixed fraction of bankroll when he wins, but does not reduce it when he loses, will eventually and inevitably go broke, even if he has a positive expected value on each bet.\nAnother common meaning is that a persistent gambler with finite wealth, playing a fair game (that is, each bet has expected value zero to both sides) will eventually and inevitably go broke against an opponent with infinite wealth. Such a situation can be modeled by a random walk on the real number line. In that context it is provable that the agent will return to his point of origin or go broke and is ruined an infinite number of times if the random walk continues forever.\nThe result above is a corollary of a general theorem by Christiaan Huygens which is also known as gambler's ruin. That theorem shows how to compute the probability of each player winning a series of bets that continues until one's entire initial stake is lost, given the initial stakes of the two players and the constant probability of winning. This is the oldest mathematical idea that goes by the name gambler's ruin, but not the first idea to which the name was applied.\nThe most common use of the term today is that a gambler playing a negative expected value game will eventually go broke, regardless of betting system. This is another corollary to Huygens' result.\nThe concept may be stated as an ironic paradox: Persistently taking beneficial chances is never beneficial at the end. This paradoxical form of gambler's ruin should not be confused with the gambler's fallacy, a different concept.The concept has specific relevance for gamblers; however it also leads to mathematical theorems with wide application and many related results in probability and statistics. Huygens' result in particular led to important advances in the mathematical theory of probability.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/3e/20180429195951%21Nuvola_apps_edu_mathematics_blue-p.svg"], "links": ["Blaise Pascal", "Christiaan Huygens", "Corollary", "Digital object identifier", "Expected value", "F. Thomas Bruss", "Fixed-odds betting", "Gambler's conceit", "Gambler's fallacy", "Gambling", "Impossibility of a gambling system", "International Standard Book Number", "Jan Gullberg", "Markov chain", "Martingale (betting system)", "Paradox", "Pierre Fermat", "Pierre de Carcavi", "Probability", "Problem of points", "Random walk", "Risk of ruin", "Statistics", "Stephen M. Stigler", "Theorem", "Wiener process"], "references": ["http://www.mathpages.com/home/kmath084/kmath084.htm", "http://demonstrations.wolfram.com/TheGamblersRuin/", "http://www.math.ucla.edu/~tom/", "http://math.ucsd.edu/~anistat/gamblers_ruin.html", "http://doi.org/10.1016%2F0315-0860(86)90028-5", "http://doi.org/10.2307%2F1402732"]}, "Experimentwise error rate": {"categories": ["All articles needing additional references", "All articles to be expanded", "All articles with empty sections", "All articles with unsourced statements", "Articles needing additional references from June 2016", "Articles to be expanded from February 2013", "Articles using small message boxes", "Articles with empty sections from February 2013", "Articles with unsourced statements from June 2016", "Multiple comparisons", "Rates", "Statistical hypothesis testing", "Wikipedia articles needing page number citations from June 2016"], "title": "Family-wise error rate", "method": "Experimentwise error rate", "url": "https://en.wikipedia.org/wiki/Family-wise_error_rate", "summary": "In statistics, family-wise error rate (FWER) is the probability of making one or more false discoveries, or type I errors when performing multiple hypotheses tests.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Alternative hypothesis", "American Journal of Public Health", "Annual Review of Psychology", "Biometrika", "Bonferroni correction", "Charles Dunnett", "CiteSeerX", "Classification of multiple hypothesis tests", "Closed testing procedure", "Data dredging", "Digital object identifier", "Dunnett's test", "Econometrica", "False coverage rate", "False discovery rate", "Holm\u2013Bonferroni method", "Homoscedasticity", "International Standard Book Number", "John Tukey", "Journal of the American Statistical Association", "Multiple comparisons", "Multiple testing correction", "Null hypothesis", "Pairwise comparison", "Post hoc analysis", "Probability", "PubMed Central", "PubMed Identifier", "Random variable", "Scheff\u00e9's method", "Statistical hypothesis testing", "Statistical power", "Statistics", "Student's t-test", "Studentized range", "Tukey's range test", "Type I and type II errors", "Yoav Benjamini", "\u0160id\u00e1k correction"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.198.2473", "http://www-stat.wharton.upenn.edu/~steele/Courses/956/Resource/MultipleComparision/Hochberg88.pdf", "http://digitalcommons.wayne.edu/jmasm/vol14/iss1/5", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1380484", "http://www.ncbi.nlm.nih.gov/pubmed/8629727", "http://doi.org/10.1093%2Fbiomet%2F75.4.800", "http://doi.org/10.1111%2Fj.1468-0262.2005.00615.x", "http://doi.org/10.1146%2Fannurev.ps.46.020195.003021", "http://doi.org/10.1198%2F016214504000000539", "http://doi.org/10.2105%2Fajph.86.5.726"]}, "Semiparametric model": {"categories": ["Mathematical and quantitative methods (economics)", "Semi-parametric models"], "title": "Semiparametric model", "method": "Semiparametric model", "url": "https://en.wikipedia.org/wiki/Semiparametric_model", "summary": "In statistics, a semiparametric model is a statistical model that has parametric and nonparametric components.\nA statistical model is a collection of distributions: \n \n \n \n {\n \n P\n \n \u03b8\n \n \n :\n \u03b8\n \u2208\n \u0398\n }\n \n \n {\\displaystyle \\{P_{\\theta }:\\theta \\in \\Theta \\}}\n indexed by a parameter \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n . \n\nA parametric model is one in which the indexing parameter is a finite-dimensional vector (in \n \n \n \n k\n \n \n {\\displaystyle k}\n -dimensional Euclidean space for some integer \n \n \n \n k\n \n \n {\\displaystyle k}\n ); i.e. the set of possible values for \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n is a subset of \n \n \n \n \n \n R\n \n \n k\n \n \n \n \n {\\displaystyle \\mathbb {R} ^{k}}\n , or \n \n \n \n \u0398\n \u2282\n \n \n R\n \n \n k\n \n \n \n \n {\\displaystyle \\Theta \\subset \\mathbb {R} ^{k}}\n . In this case we say that \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n is finite-dimensional.\nIn nonparametric models, the set of possible values of the parameter \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n is a subset of some space, not necessarily finite-dimensional. For example, we might consider the set of all distributions with mean 0. Such spaces are vector spaces with topological structure, but may not be finite-dimensional as vector spaces. Thus, \n \n \n \n \u0398\n \u2282\n \n F\n \n \n \n {\\displaystyle \\Theta \\subset \\mathbb {F} }\n for some possibly infinite-dimensional space \n \n \n \n \n F\n \n \n \n {\\displaystyle \\mathbb {F} }\n .\nIn semiparametric models, the parameter has both a finite-dimensional component and an infinite-dimensional component (often a real-valued function defined on the real line). Thus the parameter space \n \n \n \n \u0398\n \n \n {\\displaystyle \\Theta }\n in a semiparametric model satisfies \n \n \n \n \u0398\n \u2282\n \n \n R\n \n \n k\n \n \n \u00d7\n \n F\n \n \n \n {\\displaystyle \\Theta \\subset \\mathbb {R} ^{k}\\times \\mathbb {F} }\n , where \n \n \n \n \n F\n \n \n \n {\\displaystyle \\mathbb {F} }\n is an infinite-dimensional space.It may appear at first that semiparametric models include nonparametric models, since they have an infinite-dimensional as well as a finite-dimensional component. However, a semiparametric model is considered to be \"smaller\" than a completely nonparametric model because we are often interested only in the finite-dimensional component of \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n . That is, we are not interested in estimating the infinite-dimensional component. In nonparametric models, by contrast, the primary interest is in estimating the infinite-dimensional parameter. Thus the estimation task is statistically harder in nonparametric models.\nThese models often use smoothing or kernels.\n\n", "images": [], "links": ["International Standard Book Number", "Kernel (statistics)", "Non-parametric model", "Nonparametric", "Nuisance parameter", "Parametric model", "Parametric statistics", "Proportional hazards models", "Semiparametric regression", "Smoothing", "Statistical model", "Statistics"], "references": ["https://books.google.com/books?id=oP4ZJxBE1csC&pg=PA126"]}, "Shrinkage estimator": {"categories": ["Estimator"], "title": "Shrinkage estimator", "method": "Shrinkage estimator", "url": "https://en.wikipedia.org/wiki/Shrinkage_estimator", "summary": "In statistics, a shrinkage estimator is an estimator that, either explicitly or implicitly, incorporates the effects of shrinkage. In loose terms this means that a naive or raw estimate is improved by combining it with other information. The term relates to the notion that the improved estimate is made closer to the value supplied by the 'other information' than the raw estimate. In this sense, shrinkage is used to regularize ill-posed inference problems.", "images": [], "links": ["Bayesian inference", "Bessel's correction", "Bias of an estimator", "Dominating estimator", "Estimation of covariance matrices", "Estimator", "Excess kurtosis", "Ill-posed problem", "JSTOR", "James\u2013Stein estimator", "Journal of the Royal Statistical Society, Series B", "Journal of the Royal Statistical Society, Series C", "Least-squares estimation", "Mathematical Reviews", "Maximum likelihood", "Mean squared error", "Regression analysis", "Regularization (mathematics)", "Sample variance", "Shrinkage (statistics)", "Statistical inference", "Statistics", "Stein's example", "Tikhonov regularization", "Variance"], "references": ["http://jmlr.csail.mit.edu/papers/volume10/hausser09a/hausser09a.pdf", "http://www.ams.org/mathscinet-getitem?mr=0737642", "http://www.jstor.org/stable/2345402", "http://www.jstor.org/stable/2986235", "https://cran.r-project.org/web/packages/entropy/"]}, "Prais\u2013Winsten estimation": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "Estimation methods", "Regression with time series structure"], "title": "Prais\u2013Winsten estimation", "method": "Prais\u2013Winsten estimation", "url": "https://en.wikipedia.org/wiki/Prais%E2%80%93Winsten_estimation", "summary": "In econometrics, Prais\u2013Winsten estimation is a procedure meant to take care of the serial correlation of type AR(1) in a linear model. Conceived by Sigbert Prais and Christopher Winsten in 1954, it is a modification of Cochrane\u2013Orcutt estimation in the sense that it does not lose the first observation, which leads to more efficiency as a result and makes it a special case of feasible generalized least squares.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Autocorrelation", "Autoregressive model", "Christopher Winsten", "Cochrane\u2013Orcutt estimation", "Econometrica", "Econometrics", "Efficiency (statistics)", "Error term", "Errors and residuals in statistics", "Explanatory variable", "Feasible generalized least squares", "International Standard Book Number", "JSTOR", "Jan Kmenta", "John Johnston (econometrician)", "Linear model", "Ordinary least squares", "Serial correlation", "Sigbert Prais", "Time series", "Variance\u2013covariance matrix", "Vector (geometry)"], "references": ["http://cowles.econ.yale.edu/P/ccdp/st/s-0383.pdf", "http://www.jstor.org/stable/1909605", "https://books.google.com/books?id=aBOaAAAAIAAJ&pg=259"]}, "Testimator": {"categories": ["Estimator"], "title": "Testimator", "method": "Testimator", "url": "https://en.wikipedia.org/wiki/Testimator", "summary": "A testimator is an estimator whose value depends on the result of a test for statistical significance. In the simplest case the value of the final estimator is that of the basic estimator if the test result is significant, and otherwise the value is zero. However more general testimators are possible.", "images": [], "links": ["Annals of Statistics", "Communications in Statistics", "Estimator", "Statistical significance"], "references": ["http://www.informaworld.com/10.1080/03610928708829474", "http://www.journals.uchicago.edu/doi/abs/10.1086/519290", "https://dx.doi.org/10.1002/bimj.4710380706", "https://dx.doi.org/10.1214/009053607000000226"]}, "Ordered subset expectation maximization": {"categories": ["All stub articles", "Medical imaging", "Medical statistics", "Optimization algorithms and methods", "Statistics stubs"], "title": "Ordered subset expectation maximization", "method": "Ordered subset expectation maximization", "url": "https://en.wikipedia.org/wiki/Ordered_subset_expectation_maximization", "summary": "In mathematical optimization, the ordered subset expectation maximization (OSEM) method is an iterative method that is used in computed tomography.\nIn applications in medical imaging, the OSEM method is used for positron emission tomography, for single photon emission computed tomography, and for X-ray computed tomography.\nThe OSEM method is related to the expectation maximization (EM) method of statistics. The OSEM method is also related to methods of filtered back projection.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Computed tomography", "Digital object identifier", "Expectation maximization", "Filtered back projection", "Iterative method", "Mathematical optimization", "Medical imaging", "Osem (company)", "Positron emission tomography", "Single photon emission computed tomography", "Statistics"], "references": ["http://osem.s-pla.net", "https://doi.org/10.1007%2FBF00879671", "https://doi.org/10.1109%2F42.363108", "https://doi.org/10.1109%2F42.938248"]}, "Constant false alarm rate": {"categories": ["All articles needing additional references", "Articles needing additional references from December 2016", "Detection theory", "Radar signal processing"], "title": "Constant false alarm rate", "method": "Constant false alarm rate", "url": "https://en.wikipedia.org/wiki/Constant_false_alarm_rate", "summary": "Constant false alarm rate (CFAR) detection refers to a common form of adaptive algorithm used in radar systems to detect target returns against a background of noise, clutter and interference.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f0/Constant_false_alarm_rate.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Adaptive algorithm", "Addison Wesley", "Additive white Gaussian noise", "Antenna (radio)", "Clutter (radar)", "Detection theory", "Electric power", "Electromagnetic interference", "False alarm", "International Standard Book Number", "K-distribution", "Noise (radio)", "Periscopes", "Probability density function", "Pulse-Doppler signal processing", "Radar", "Receiver operating characteristic", "Sea clutter", "Signal-to-noise ratio", "Statistical Signal Processing", "Submarine"], "references": []}, "Rule of succession": {"categories": ["All articles needing additional references", "All articles with specifically marked weasel-worded phrases", "All articles with unsourced statements", "Articles needing additional references from February 2017", "Articles with specifically marked weasel-worded phrases from April 2013", "Articles with unsourced statements from April 2013", "Inductive reasoning", "Probability assessment"], "title": "Rule of succession", "method": "Rule of succession", "url": "https://en.wikipedia.org/wiki/Rule_of_succession", "summary": "In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem.The formula is still used, particularly to estimate underlying probabilities when there are few observations, or for events that have not been observed to occur at all in (finite) sample data. Assigning events a zero probability contravenes Cromwell's rule; such contravention can never be strictly justified in physical situations, albeit sometimes must be assumed in practice.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Additive smoothing", "Bayes' theorem", "Bayes estimator", "Bayes rule", "Bernoulli distribution", "Bernoulli trial", "Beta distribution", "Beta function", "Bound variable", "Conditional independence", "Conjugate prior", "Cromwell's rule", "Digital object identifier", "Dirichlet distribution", "Expected value", "Hypergeometric distribution", "Inductive reasoning", "JSTOR", "Krichevsky\u2013Trofimov estimator", "Laplace", "Laplace\u2013Bayes estimator", "Law of total probability", "Likelihood function", "Logarithm", "Multinomial distribution", "Natural logarithm", "New riddle of induction", "Normalizing constant", "Order of succession", "Pierre-Simon Laplace", "Principle of indifference", "Prior probability", "Probability density function", "Probability theory", "Pseudocount", "Random variable", "Rudolf Carnap", "Rule of succession", "Sunrise problem", "Zero probability"], "references": ["http://tu-dresden.de/die_tu_dresden/fakultaeten/philosophische_fakultaet/iph/thph/braeuer/lehre/induktion_projektion/CarnapOnInductiveLogic.pdf", "http://www.hss.caltech.edu/~franz/Confirmation%20and%20Induction/PDFs/Rudolf%20Carnap%20-%20On%20the%20Application%20of%20Inductive%20Logic.pdf", "http://bayes.wustl.edu/glb/book.pdf", "http://doi.org/10.1086%2F286851", "http://doi.org/10.2307%2F2102920", "http://www.jstor.org/stable/2102920", "http://www.stats.org.uk/priors/noninformative/Smith.pdf"]}, "Regression-kriging": {"categories": ["CS1 maint: Uses authors parameter", "Geostatistics", "Interpolation"], "title": "Regression-kriging", "method": "Regression-kriging", "url": "https://en.wikipedia.org/wiki/Regression-kriging", "summary": "In applied statistics, regression-kriging (RK) is a spatial prediction technique that combines a regression of the dependent variable on auxiliary variables (such as parameters derived from digital elevation modelling, remote sensing/imagery, and thematic maps) with kriging of the regression residuals. It is mathematically equivalent to the interpolation method variously called universal kriging and kriging with external drift, where auxiliary predictors are used directly to solve the kriging weights.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1e/A_generic_framework_for_spatial_prediction_of_soil_variables.png", "https://upload.wikimedia.org/wikipedia/commons/c/c3/Decision_tree_for_selecting_a_suitable_spatial_prediction_model.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/b7/Simulations_of_zinc_using_regression-kriging_model.png", "https://upload.wikimedia.org/wikipedia/commons/3/39/The_universal_model_of_spatial_variation.jpg"], "links": ["Advanced Spaceborne Thermal Emission and Reflection Radiometer", "Applied statistics", "Best linear unbiased prediction", "Deterministic system", "Digital Elevation Model", "Digital object identifier", "Downscaling", "Error propagation", "Generalized least squares", "International Standard Book Number", "JSTOR", "Kriging", "MODIS", "Ordinary least squares", "Regression analysis", "SPOT (satellite)", "Shuttle Radar Topographic Mission", "Stochastic process", "Universal kriging", "Universal model of spatial variation", "Variogram"], "references": ["http://leg.ufpr.br/geoR/", "http://glcf.umiacs.umd.edu/", "http://r-spatial.sourceforge.net/gallery/#fig07.R", "http://spatial-analyst.net/book/system/files/Hengl_2009_GEOSTATe2c1w.pdf", "http://doi.org/10.1016%2F0016-7061(95)00007-B", "http://doi.org/10.1016%2FS0924-2716(02)00124-7", "http://doi.org/10.1016%2Fj.cageo.2007.05.001", "http://doi.org/10.1016%2Fj.cageo.2008.01.005", "http://doi.org/10.1016%2Fj.geoderma.2003.08.018", "http://doi.org/10.1016%2Fj.geoderma.2007.04.028", "http://doi.org/10.1016%2Fj.isprsjprs.2006.02.003", "http://doi.org/10.1029%2FWR023i009p01717", "http://doi.org/10.1080%2F01621459.1962.10480665", "http://doi.org/10.1111%2Fj.1467-9671.2006.01015.x", "http://gstat.org", "http://www.jstor.org/stable/2281645", "http://r-project.org", "https://lpdaac.usgs.gov/get_data/data_pool"]}, "Common cause and special cause (statistics)": {"categories": ["All articles needing additional references", "All articles that may contain original research", "All articles with unsourced statements", "Applied mathematics", "Articles needing additional references from February 2013", "Articles that may contain original research from February 2013", "Articles with unsourced statements from February 2013", "Articles with unsourced statements from October 2010", "Philosophy of statistics", "Probability interpretations", "Risk analysis", "Statistical process control", "Use dmy dates from August 2012"], "title": "Common cause and special cause (statistics)", "method": "Common cause and special cause (statistics)", "url": "https://en.wikipedia.org/wiki/Common_cause_and_special_cause_(statistics)", "summary": "Common and special causes are the two distinct origins of variation in a process, as defined in the statistical thinking and methods of Walter A. Shewhart and W. Edwards Deming. Briefly, \"common causes\", also called natural patterns, are the usual, historical, quantifiable variation in a system, while \"special causes\" are unusual, not previously observed, non-quantifiable variation.\nThe distinction is fundamental in philosophy of statistics and philosophy of probability, with different treatment of these issues being a classic issue of probability interpretations, being recognised and discussed as early as 1703 by Gottfried Leibniz; various alternative names have been used over the years.\nThe distinction has been particularly important in the thinking of economists Frank Knight, John Maynard Keynes and G. L. S. Shackle.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["2011 T\u014dhoku earthquake and tsunami", "A Treatise on Probability", "Advanced Boiling Water Reactor", "Analytic and enumerative statistical studies", "Austrian School", "Bayesian probability", "Black swan theory", "Brian Randell", "Business process", "Calibration (probability)", "Classical liberalism", "Click fraud", "Containment building", "Control chart", "Corrective and preventive action", "Crash (computing)", "Electromagnetic interference", "Emergency Core Cooling System", "European Pressurized Reactor", "Expected utility", "Financial economics", "Frank Knight", "Free-market", "Frequency", "Frequency probability", "Fukushima Daiichi Nuclear Power Plant", "Full employment", "G. L. S. Shackle", "Gottfried Leibniz", "Harry Alpert", "Heuristic", "Indianapolis", "International Standard Book Number", "Ionizing radiation", "Jacob Bernoulli", "John Maynard Keynes", "Knightian uncertainty", "Ludwig von Mises", "Mathematics", "Measurement", "Mortality rate", "Nassim Nicholas Taleb", "Nuclear power", "Nuclear safety", "OCLC", "Patterns in nature", "Philosophy of probability", "Philosophy of statistics", "Population (statistics)", "Probabilistic risk assessment", "Probability", "Probability interpretations", "Probability theory", "Quality control", "RAID 1", "Redundancy (engineering)", "Response time (technology)", "Roulette", "Sampling (statistics)", "Sampling frame", "Sleeping while on duty", "Standard operating procedure", "Statistical Quality Control", "Statistical control", "Statistical process control", "Statistics", "Subset", "The General Theory of Employment, Interest and Money", "Voltage spike", "W. Edwards Deming", "Walter A. Shewhart", "Wear and tear", "Western Electric Company"], "references": ["http://www.anu.edu.au/nceph/surfstat/surfstat-home/5-1-2.html", "http://www.safetyinengineering.com/FileUploads/CMF%20in%20high-integrity%20C&I%20systems_1329414280_2.pdf", "http://hissa.nist.gov/chissa/SEI_Framework/framework_16.html", "http://www.worldcat.org/oclc/1045408", "http://www.worldcat.org/oclc/33858387", "https://web.archive.org/web/20061007055524/http://www.anu.edu.au/nceph/surfstat/surfstat-home/5-1-2.html"]}, "Computational statistics": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2009", "Computational fields of study", "Computational statistics", "Mathematics of computing", "Numerical analysis"], "title": "Computational statistics", "method": "Computational statistics", "url": "https://en.wikipedia.org/wiki/Computational_statistics", "summary": "Computational statistics, or statistical computing, is the interface between statistics and computer science. It is the area of computational science (or scientific computing) specific to the mathematical science of statistics. This area is also developing rapidly, leading to calls that a broader concept of computing should be taught as part of general statistical education.As in traditional statistics the goal is to transform raw data into knowledge, but the focus lies on computer intensive statistical methods, such as cases with very large sample size and non-homogeneous data sets.The terms 'computational statistics' and 'statistical computing' are often used interchangeably, although Carlo Lauro (a former president of the International Association for Statistical Computing) proposed making a distinction, defining 'statistical computing' as \"the application of computer science to statistics\",\nand 'computational statistics' as \"aiming at the design of algorithm for implementing\nstatistical methods on computers, including the ones unthinkable before the computer\nage (e.g. bootstrap, simulation), as well as to cope with analytically intractable problems\" [sic].The term 'Computational statistics' may also be used to refer to computationally intensive statistical methods including resampling methods, Markov chain Monte Carlo methods, local regression, kernel density estimation, artificial neural networks and generalized additive models.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/London_School_of_Economics_Statistics_Machine_Room_1964.jpg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Algorithms for statistical classification", "Artificial intelligence", "Artificial neural networks", "Bootstrapping (statistics)", "Communications in Statistics", "Computational Statistics", "Computational Statistics & Data Analysis", "Computational science", "Computer", "Computer lab", "Computer science", "Data science", "Data set", "Deborah A. Nolan", "Digital object identifier", "Edward Wegman", "Free statistical software", "Generalized additive model", "International Association for Statistical Computing", "International Standard Book Number", "Jennifer A. Hoeting", "Journal of Computational and Graphical Statistics", "Journal of Statistical Computation and Simulation", "Journal of Statistical Software", "Kernel density estimation", "Knowledge", "List of algorithms", "List of statistical packages", "Local regression", "London School of Economics", "Machine learning", "Markov chain Monte Carlo", "Monte Carlo simulation", "Raw data", "Resampling (statistics)", "Sample size determination", "Sic", "Statistical education", "Statistical methods", "Statistics", "Statistics and Computing", "The American Statistician", "The R Journal", "Wiley Interdisciplinary Reviews Computational Statistics"], "references": ["http://www.elsevier.com/wps/find/journaldescription.cws_home/505539/description", "http://www.informaworld.com/smpp/title~content=t713650378", "http://www.informaworld.com/smpp/title~db=all~content=t713597237", "http://www.sciencedirect.com/science/article/B6V8V-3SWT44Y-F/2/5320a35df36fb38ffba03483c73dc861", "http://www.amstat.org/publications/jcgs/", "http://doi.org/10.1016%2F0167-9473(96)88920-1", "http://doi.org/10.1198%2F0003130042872", "http://doi.org/10.1198%2F004017008000000460", "http://www.iasc-isi.org/", "http://stat-computing.org/", "http://www.washacadsci.org/journal/", "https://www.springer.com/statistics/computational/journal/11222", "https://www.jstor.org/stable/24536995"]}, "Martingale (probability theory)": {"categories": ["CS1 French-language sources (fr)", "Game theory", "Martingale theory", "Paul L\u00e9vy (mathematician)", "Stochastic processes", "Wikipedia articles with NDL identifiers"], "title": "Martingale (probability theory)", "method": "Martingale (probability theory)", "url": "https://en.wikipedia.org/wiki/Martingale_(probability_theory)", "summary": "In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time, the conditional expectation of the next value in the sequence, given all prior values, is equal to the present value.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/44/HittingTimes1.png", "https://upload.wikimedia.org/wikipedia/commons/9/96/Martingale1.svg"], "links": ["Abraham de Moivre", "Abstract Wiener space", "Actuarial mathematics", "Adapted process", "Almost surely", "Amoeba", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Azuma's inequality", "Bernoulli process", "Bessel process", "Betting strategy", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Classification of discontinuities", "Compound Poisson process", "Concave function", "Conditional expectation", "Conditional expected value", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Continuous time", "Convergence of random variables", "Convex function", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "David Williams (mathematician)", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob martingale", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Encyclopedia of Mathematics", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Exponential growth", "Extreme value theory", "Fair coin", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "France", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gambler", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Hagen Kleinert", "Harmonic function", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Index set", "Indicator function", "Infinitesimal generator (stochastic processes)", "Integrable function", "Interacting particle system", "International Standard Book Number", "Ising model", "Iterative method", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "It\u014d process", "Jensen's inequality", "Joseph Leo Doob", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Laplace operator", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Likelihood-ratio test", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "Lp space", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (betting system)", "Martingale central limit theorem", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Measurable function", "Michiel Hazewinkel", "Mixing (mathematics)", "Moran process", "Moving-average model", "National Diet Library", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Partial differential equation", "Paul L\u00e9vy (mathematician)", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Polya's urn", "Potential theory", "Potts model", "Predictable process", "Prefix", "Probability measure", "Probability space", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random sample", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sequence", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Square root", "Stable process", "Stationary process", "Statistical independence", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopped process", "Stopping time", "Stratonovich integral", "Subharmonic function", "Submartingale", "Superharmonic function", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Unified neutral theory of biodiversity and biogeography", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "Wald's martingale", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "Zentralblatt MATH"], "references": ["http://www.physik.fu-berlin.de/~kleinert/b5", "http://www.corelab.ece.ntua.gr/courses/rand-alg/slides/Martingales-Stopping_Times.pdf", "http://www.jehps.net/juin2009.html", "http://www.jehps.net/juin2009/Mansuy.pdf", "http://zbmath.org/?format=complete&q=an:0021.14601", "https://books.google.com/books?id=ETY7AQAAIAAJ", "https://id.ndl.go.jp/auth/ndlna/00567500", "https://web.archive.org/web/20120131103618/http://www.jehps.net/juin2009/Mansuy.pdf", "https://dx.doi.org/10.1090/S0002-9904-1939-07089-4", "https://www.encyclopediaofmath.org/index.php?title=p/m062570", "https://www.wikidata.org/wiki/Q534112"]}, "Increasing process": {"categories": ["All articles lacking sources", "All stub articles", "Articles lacking sources from June 2012", "Probability stubs", "Stochastic processes"], "title": "Increasing process", "method": "Increasing process", "url": "https://en.wikipedia.org/wiki/Increasing_process", "summary": "An increasing process is a stochastic process \n\n \n \n \n (\n \n X\n \n t\n \n \n \n )\n \n t\n \u2208\n M\n \n \n \n \n {\\displaystyle (X_{t})_{t\\in M}}\n where the random variables \n \n \n \n \n X\n \n t\n \n \n \n \n {\\displaystyle X_{t}}\n which make up the process are increasing almost surely and adapted:\n\n \n \n \n 0\n =\n \n X\n \n 0\n \n \n \u2264\n \n X\n \n \n t\n \n 1\n \n \n \n \n \u2264\n \u22ef\n .\n \n \n {\\displaystyle 0=X_{0}\\leq X_{t_{1}}\\leq \\cdots .}\n A continuous increasing process is such a process where the set \n \n \n \n M\n \n \n {\\displaystyle M}\n is continuous.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Adapted process", "Almost surely", "Probability", "Random variable", "Stochastic process"], "references": []}, "Tajima's D": {"categories": ["DNA", "Molecular evolution", "Statistical genetics", "Statistical tests"], "title": "Tajima's D", "method": "Tajima's D", "url": "https://en.wikipedia.org/wiki/Tajima%27s_D", "summary": "Tajima's D is a population genetic test statistic created by and named after the Japanese researcher Fumio Tajima. Tajima's D is computed as the difference between two measures of genetic diversity: the mean number of pairwise differences and the number of segregating sites, each scaled so that they are expected to be the same in a neutrally evolving population of constant size.\nThe purpose of Tajima's D test is to distinguish between a DNA sequence evolving randomly (\"neutrally\") and one evolving under a non-random process, including directional selection or balancing selection, demographic expansion or contraction, genetic hitchhiking, or introgression. A randomly evolving DNA sequence contains mutations with no effect on the fitness and survival of an organism. The randomly evolving mutations are called \"neutral\", while mutations under selection are \"non-neutral\". For example, you would expect to find that a mutation which causes prenatal death or severe disease to be under selection. When looking at the human population as a whole, we say that the population frequency of a neutral mutation fluctuates randomly (i.e. the percentage of people in the population with the mutation changes from one generation to the next, and this percentage is equally likely to go up or down) through genetic drift.\nThe strength of genetic drift depends on the population size. If a population is at a constant size with constant mutation rate, the population will reach an equilibrium of gene frequencies. This equilibrium has important properties, including the number of segregating sites \n \n \n \n S\n \n \n {\\displaystyle S}\n , and the number of nucleotide differences between pairs sampled (these are called pairwise differences). To standardize the pairwise differences, the mean or 'average' number of pairwise differences is used. This is simply the sum of the pairwise differences divided by the number of pairs, and is often symbolized by \n \n \n \n \u03c0\n \n \n {\\displaystyle \\pi }\n .\nThe purpose of Tajima's test is to identify sequences which do not fit the neutral theory model at equilibrium between mutation and genetic drift. In order to perform the test on a DNA sequence or gene, you need to sequence homologous DNA for at least 3 individuals. Tajima's statistic computes a standardized measure of the total number of segregating sites (these are DNA sites that are polymorphic) in the sampled DNA and the average number of mutations between pairs in the sample. The two quantities whose values are compared are both method of moments estimates of the population genetic parameter theta, and so are expected to equal the same value. If these two numbers only differ by as much as one could reasonably expect by chance, then the null hypothesis of neutrality cannot be rejected. Otherwise, the null hypothesis of neutrality is rejected.", "images": [], "links": ["Allele frequency", "Average", "Balancing selection", "Beta distribution", "BioPerl", "Combination", "Confidence interval", "DNA sequence", "Directional selection", "Disruptive selection", "Effective population size", "Expected value", "Fay and Wu's H", "Frequency", "Fumio Tajima", "Gene conversion", "Gene duplication", "Genetic drift", "Genetic hitchhiking", "Homology (biology)", "International Standard Book Number", "Introgression", "Ka/Ks ratio", "Models of DNA evolution", "Models of nucleotide substitution", "Molecular evolution", "Mutation", "Natural selection", "Negative selection (natural selection)", "Neutral mutation", "Nucleotide diversity", "Null hypothesis", "Polymorphism (biology)", "Process calculus", "PubMed Central", "PubMed Identifier", "Segregating site", "Selective sweep", "Silent mutation", "Single nucleotide polymorphism", "Stabilizing selection", "Standard deviation", "Statistical test", "Synonymous substitution", "Variance", "Watterson estimator"], "references": ["http://cmpg.unibe.ch/software/arlequin3/", "http://genome.ucsc.edu/cgi-bin/hgTracks?hgS_doLoadUrl=submit&hgS_loadUrlName=http://www.soe.ucsc.edu/~daryl/tajDsession.txt", "http://www.ub.es/dnasp/", "http://www.ub.es/softevol/variscan/", "http://wwwabi.snv.jussieu.fr/achaz/neutralitytest.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1203831", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1205353", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1206737", "http://www.ncbi.nlm.nih.gov/pubmed/2513255", "http://www.ncbi.nlm.nih.gov/pubmed/8454210", "http://www.ncbi.nlm.nih.gov/pubmed/8536987", "http://www.megasoftware.net/", "https://www.youtube.com/watch?v=wiyay4YMq2A", "https://metacpan.org/pod/Bio::PopGen::Statistics"]}, "Limited dependent variable": {"categories": ["All stub articles", "Design of experiments", "Econometrics stubs", "Regression analysis"], "title": "Limited dependent variable", "method": "Limited dependent variable", "url": "https://en.wikipedia.org/wiki/Limited_dependent_variable", "summary": "A limited dependent variable is a variable whose range of\npossible values is \"restricted in some important way.\" In econometrics, the term is often used when\nestimation of the relationship between the limited dependent variable\nof interest and other variables requires methods that take this\nrestriction into account. For example, this may arise when the variable\nof interest is constrained to lie between zero and one, as in\nthe case of a probability, or is constrained to be positive,\nas in the case of wages or hours worked.\nLimited dependent variable models include:\nCensoring, where for some individuals in a data set, some data are missing but other data are present;\nTruncation, where some individuals are systematically excluded from observation (failure to take this phenomenon into account can result in selection bias);\nDiscrete outcomes, such as binary decisions or qualitative data restricted to a small number of categories. Discrete choice models may have either unordered or ordered alternatives; ordered alternatives may take the form of count data or ordered rating responses (such as a Likert scale).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f3/Emblem-money.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg"], "links": ["Adam Smith", "Agricultural economics", "Alfred Marshall", "Applied economics", "Arthur Cecil Pigou", "Behavioral economics", "Business economics", "Censored regression model", "Computational economics", "Cultural economics", "David Ricardo", "Demographic economics", "Dependent variable", "Development economics", "Discrete choice", "Ecological economics", "Econometrics", "Economic geography", "Economic growth", "Economic history", "Economic methodology", "Economic planning", "Economic policy", "Economic sociology", "Economic statistics", "Economic system", "Economic theory", "Economics", "Economics of digitization", "Economist", "Education economics", "Engineering economics", "Environmental economics", "Evolutionary economics", "Expeditionary economics", "Experimental economics", "Financial economics", "Fran\u00e7ois Quesnay", "Game theory", "Glossary of economics", "Health economics", "Heterodox economics", "History of economic thought", "Index of economics articles", "Industrial organization", "Information economics", "Institutional economics", "International Standard Book Number", "International economics", "JEL classification codes", "John Maynard Keynes", "John Stuart Mill", "Karl Marx", "Knowledge economy", "Labour economics", "Law and economics", "Likert scale", "List of economics journals", "List of economists", "List of important publications in economics", "Logit", "Logit model", "L\u00e9on Walras", "Macroeconomics", "Mainstream economics", "Managerial economics", "Market (economics)", "Mathematical economics", "Microeconomics", "Monetary economics", "Multivariate probit", "National accounts", "Natural resource economics", "OCLC", "Operations research", "Ordered logit", "Ordered probit", "Organizational economics", "Outline of economics", "Paul Samuelson", "Personnel economics", "Political economy", "Probability", "Probit", "Probit model", "Public choice", "Public economics", "Regional economics", "Rural economics", "Schools of economic thought", "Selection bias", "Service economy", "Social choice theory", "Socioeconomics", "Thomas Robert Malthus", "Tobit model", "Truncated regression model", "Urban economics", "Welfare", "Welfare economics"], "references": ["http://www.worldcat.org/oclc/248704396", "http://www.worldcat.org/oclc/25207809", "http://www.worldcat.org/oclc/47521388"]}, "Observational error": {"categories": ["Accuracy and precision", "All articles needing additional references", "Articles needing additional references from September 2016", "Errors and residuals"], "title": "Observational error", "method": "Observational error", "url": "https://en.wikipedia.org/wiki/Observational_error", "summary": "Observational error (or measurement error) is the difference between a measured value of a quantity and its true value. In statistics, an error is not a \"mistake\". Variability is an inherent part of the results of measurements and of the measurement process.\nMeasurement errors can be divided into two components: random error and systematic error.Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by an inaccuracy (involving either the observation or measurement process) inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Accuracy and precision", "Ammeter", "Averaged", "Biophysical environment", "Calibration", "Causality", "Central limit theorem", "Coefficient of determination", "Computational mechanics", "Constant (mathematics)", "Correction for attenuation", "Dependent variable", "Diffraction grating", "Digital object identifier", "Distance", "Dynamic model", "Electromagnetic spectrum", "Error", "Errors-in-variables models", "Errors and residuals in statistics", "Experiment", "Fiducial marker", "Hypothesis test", "Independent variable", "Instrument error", "International Standard Book Number", "JSTOR", "Mathematical model", "Mean", "Measurement", "Measurement error", "Measurement in quantum mechanics", "Measurement uncertainty", "Metrology", "Multitrait-multimethod matrix", "Non-sampling error", "Normal distribution", "Observation", "Observations", "Oscillation frequency", "Pendulum", "Percentage error", "Physical law", "Physical quantity", "Probability theory", "Propagation of uncertainty", "Radar", "Random variable", "Regression dilution", "Replication (statistics)", "Ruler", "Science", "Sodium", "Speaking clock", "Spectrometer", "Standard deviation", "Statistical model", "Statistical theory", "Statistics", "Stochastic drift", "Stopwatch", "Surroundings", "System", "Systemic bias", "Test method", "Time-invariant", "Vernier scale", "Voltmeter", "Wavelength"], "references": ["http://www.merriam-webster.com/dictionary/systematic%20error", "http://sqp.upf.edu", "http://essedunet.nsd.uib.no/cms/topics/measurement/", "http://doi.org/10.1007%2Fs11205-015-1002-x", "http://doi.org/10.2307%2F1267450", "http://www.jstor.org/stable/1267450", "https://books.google.com/books?id=giFQcZub80oC&pg=PA94", "https://www.google.com/webhp?sourceid=chrome-instant&rlz=1CASMAG_enUS602US603&ion=1&espv=2&ie=UTF-8#q=systematic%20error%20definition"]}, "Arrival theorem": {"categories": ["Probability theorems", "Queueing theory"], "title": "Arrival theorem", "method": "Arrival theorem", "url": "https://en.wikipedia.org/wiki/Arrival_theorem", "summary": "In queueing theory, a discipline within the mathematical theory of probability, the arrival theorem (also referred to as the random observer property, ROP or job observer property) states that \"upon arrival at a station, a job observes the system as if in steady state at an arbitrary instant for the system without that job.\"The arrival theorem always holds in open product-form networks with unbounded queues at each node, but it also holds in more general networks. A necessary and sufficient condition for the arrival theorem to be satisfied in product-form networks is given in terms of Palm probabilities in Boucherie & Dijk, 1997. A similar result also holds in some closed networks. Examples of product-form networks where the arrival theorem does not hold include reversible Kingman networks and networks with a delay protocol.Mitrani offers the intuition that \"The state of node i as seen by an incoming job has a different distribution from the state seen by a random observer. For instance, an incoming job can never see all 'k jobs present at node i, because it itself cannot be among the jobs already present.\"", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Doubly stochastic Poisson process", "Erlang (unit)", "Erlang distribution", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell network", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "International Standard Book Number", "JSTOR", "Jackson's theorem (queueing theory)", "Jackson network", "John Kingman", "Journal of the ACM", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Palm probabilities", "Peter G. Harrison", "Pipeline (software)", "Poisson process", "Poisson processes", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations"], "references": ["http://doc.utwente.nl/70043/1/Doorn88conditional.pdf", "http://doi.org/10.1007/0-387-21525-5_4", "http://doi.org/10.1007/1-4020-3631-0_5", "http://doi.org/10.1016/0167-6377(88)90036-3", "http://doi.org/10.1016/0169-7552(93)90073-D", "http://doi.org/10.1016/S0166-5316(96)00045-4", "http://doi.org/10.1145/322186.322195", "http://doi.org/10.1145/322248.322257", "http://doi.org/10.1287/opre.30.2.223", "http://www.jstor.org/stable/3212273"]}, "Self-similar process": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "Articles with unsourced statements from June 2012", "Autocorrelation", "Teletraffic"], "title": "Self-similar process", "method": "Self-similar process", "url": "https://en.wikipedia.org/wiki/Self-similar_process", "summary": "Self-similar processes are types of stochastic processes that exhibit the phenomenon of self-similarity. A self-similar phenomenon behaves the same when viewed at different degrees of magnification, or different scales on a dimension (space or time). Self-similar processes can sometimes be described using heavy-tailed distributions, also known as long-tailed distributions. Example of such processes include traffic processes such as packet inter-arrival times and burst lengths. Self-similar processes can exhibit long-range dependency.", "images": [], "links": ["Asynchronous transfer mode", "Attractor", "Autocorrelation", "Beno\u00eet Mandelbrot", "Burst transmission", "Central limit theorem", "Convergence (mathematics)", "Cumulant", "Ethernet", "Exponential dispersion model", "Exponential family", "File Transfer Protocol", "Fractal", "Generalized linear model", "Heavy-tailed distribution", "International Standard Book Number", "Internet", "Long-range dependency", "Long-tail traffic", "Long-tailed distribution", "Mean", "Memorylessness", "Multifractal system", "Multiplexing", "Pareto distribution", "Pink noise", "Poisson distribution", "Poisson process", "Power law", "Probability density function", "Random variable", "Scale invariance", "Self-similarity", "Signaling System 7", "Stateless server", "Stochastic processes", "TELNET", "Taylor's law", "Telephony", "Transmission control protocol", "Tweedie distributions", "Variable bitrate", "Variance", "World wide web"], "references": ["http://www.cs.bu.edu/brite/user_manual/node42.html", "http://www.cs.bu.edu/pub/barford/ss_lrd.html", "http://www.columbia.edu/~ww2040/A12.html", "http://www.cs.kent.ac.uk/people/staff/pfl/presentations/longrange/"]}, "F-divergence": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2015", "F-divergences"], "title": "F-divergence", "method": "F-divergence", "url": "https://en.wikipedia.org/wiki/F-divergence", "summary": "In probability theory, an \u0192-divergence is a function Df\u2009(P\u2009\u2009||\u2009Q) that measures the difference between two probability distributions P and Q. It helps the intuition to think of the divergence as an average, weighted by the function f, of the odds ratio given by P and Q.\nThese divergences were introduced and studied independently by Csisz\u00e1r (1963), Morimoto (1963) and Ali & Silvey (1966) and are sometimes known as Csisz\u00e1r \u0192-divergences, Csisz\u00e1r-Morimoto divergences or Ali-Silvey distances.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Absolute continuity", "ArXiv", "Bibcode", "Convex function", "Digital object identifier", "Divergence (statistics)", "Hellinger distance", "IEEE Transactions on Information Theory", "Imre Csisz\u00e1r", "JSTOR", "Jensen\u2019s inequality", "Journal of the Royal Statistical Society", "KL-divergence", "Mathematical Reviews", "Odds ratio", "Probability density function", "Probability distributions", "Probability theory", "Sufficient statistic", "Total variation distance", "Transition probability"], "references": ["http://adsabs.harvard.edu/abs/1963JPSJ...18..328M", "http://adsabs.harvard.edu/abs/2014ISPL...21...10N", "http://www.renyi.hu/~csiszar/Publications/Information_Theory_and_Statistics:_A_Tutorial.pdf", "http://www.ams.org/mathscinet-getitem?mr=0196777", "http://arxiv.org/abs/1309.3029", "http://arxiv.org/abs/math/0604246", "http://doi.org/10.1109%2FLSP.2013.2288355", "http://doi.org/10.1109%2FTIT.2006.881731", "http://doi.org/10.1143%2FJPSJ.18.328", "http://doi.org/10.1561%2F0100000004", "http://www.jstor.org/stable/2984279"]}, "Barab\u00e1si\u2013Albert model": {"categories": ["Graph algorithms", "Random graphs", "Social networks"], "title": "Barab\u00e1si\u2013Albert model", "method": "Barab\u00e1si\u2013Albert model", "url": "https://en.wikipedia.org/wiki/Barab%C3%A1si%E2%80%93Albert_model", "summary": "The Barab\u00e1si\u2013Albert (BA) model is an algorithm for generating random scale-free networks using a preferential attachment mechanism. Several natural and human-made systems, including the Internet, the world wide web, citation networks, and some social networks are thought to be approximately scale-free and certainly contain few nodes (called hubs) with unusually high degree as compared to the other nodes of the network. The BA model tries to explain the existence of such nodes in real networks. The algorithm is named for its inventors Albert-L\u00e1szl\u00f3 Barab\u00e1si and R\u00e9ka Albert and is a special case of a more general model called Price's model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a8/Barabasi-albert_model_degree_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2e/Barabasi_Albert_generated_network.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/48/Barabasi_Albert_model.gif", "https://upload.wikimedia.org/wikipedia/commons/4/40/Barabasi_albert_graph.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e9/Data_collapse_m1.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/7b/ScaledDegreeDistribution-multiplot.jpg", "https://upload.wikimedia.org/wikipedia/commons/d/d2/Internet_map_1024.jpg"], "links": ["A. Korn", "A. Schubert", "A. Telcs", "Adjacency list", "Adjacency matrix", "Agent-based model", "Albert-L\u00e1szl\u00f3 Barab\u00e1si", "ArXiv", "Artificial neural network", "Assortativity", "Autocatalysis", "Average path length", "Balance theory", "Betweenness centrality", "Bianconi\u2013Barab\u00e1si model", "Bibcode", "Biological network", "Biometrika", "Bipartite graph", "Boolean network", "Centrality", "Chinese restaurant process", "Citation analysis", "CiteSeerX", "Clique (graph theory)", "Closeness (graph theory)", "Clustering coefficient", "Combinatorial optimization", "Community structure", "Complete graph", "Complex contagion", "Complex network", "Complex networks", "Computer network", "Connected component (graph theory)", "Cut (graph theory)", "Cycle (graph theory)", "Degree (graph theory)", "Degree distribution", "Dependency network", "Derek J. de Solla Price", "Digital object identifier", "Directed graph", "Distance (graph theory)", "Dynamic scaling", "Edge (graph theory)", "Efficiency (network science)", "Epidemic model", "Erd\u0151s\u2013R\u00e9nyi model", "Evolving networks", "Exponential random graph models", "Fitness model (network theory)", "Flow network", "Google", "Graph (abstract data type)", "Graph (discrete mathematics)", "Graph drawing", "H-index", "Handle System", "Herbert A. Simon", "Hierarchical network model", "Homophily", "Hyperbolic geometric graph", "Hypergraph", "Incidence list", "Incidence matrix", "Interdependent networks", "International Standard Serial Number", "Internet", "JSTOR", "Journal of the American Society for Information Science", "Lancichinetti\u2013Fortunato\u2013Radicchi benchmark", "Link analysis", "List of algorithms", "List of network scientists", "List of network theory topics", "Loop (graph theory)", "Matthew effect (sociology)", "Metrics (networking)", "Modularity (networks)", "Multigraph", "Neighbourhood (graph theory)", "Network controllability", "Network effect", "Network motif", "Network on a chip", "Network science", "Network theory", "PageRank", "Path (graph theory)", "Percolation theory", "Physical Review E", "Positive feedback", "Power law", "Preferential attachment", "Price's model", "PubMed Identifier", "Random geometric graph", "Random graph", "Reciprocity (network science)", "Reviews of Modern Physics", "Rich get richer", "R\u00e9ka Albert", "SIR model", "Scale-free network", "Scale-free networks", "Science (journal)", "Scientific collaboration network", "Semantic network", "Small-world network", "Social capital", "Social influence", "Social network", "Social network analysis software", "Social networks", "Spatial network", "Spectral properties", "Stochastic block model", "Telecommunications network", "Transitive relation", "Transport network", "Triadic closure", "Udny Yule", "Vertex (graph theory)", "Watts and Strogatz model", "Weighted network", "World wide web"], "references": ["http://www.hpl.hp.com/research/idl/papers/scalingcomment/", "http://www.popsci.com/science/article/2011-10/man-could-rule-world", "http://adsabs.harvard.edu/abs/1999Sci...286..509B", "http://adsabs.harvard.edu/abs/2001PhRvE..64b6704F", "http://adsabs.harvard.edu/abs/2002PhRvE..65e7102K", "http://adsabs.harvard.edu/abs/2002PhRvE..65f6122D", "http://adsabs.harvard.edu/abs/2002RvMP...74...47A", "http://adsabs.harvard.edu/abs/2003PhRvL..90e8701C", "http://adsabs.harvard.edu/abs/2009PhyA..388.2221K", "http://adsabs.harvard.edu/abs/2013EPJB...86..510F", "http://www.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/StatisticalMechanics_Rev%20of%20Modern%20Physics%2074,%2047%20(2002).pdf", "http://www.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/EmergenceRandom_Science%20286,%20509-512%20(1999).pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.114", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.176.6988", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.176.6988", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.242.4753", "http://www.ncbi.nlm.nih.gov/pubmed/10521342", "http://www.ncbi.nlm.nih.gov/pubmed/11497741", "http://www.ncbi.nlm.nih.gov/pubmed/12059755", "http://www.ncbi.nlm.nih.gov/pubmed/12188798", "http://www.ncbi.nlm.nih.gov/pubmed/12633404", "http://www.ncbi.nlm.nih.gov/pubmed/14683021", "http://hdl.handle.net/10261%2F15314", "http://hdl.handle.net/2047%2Fd20000692", "http://arxiv.org/abs/0809.0514", "http://arxiv.org/abs/1308.5169", "http://arxiv.org/abs/cond-mat/0102335", "http://arxiv.org/abs/cond-mat/0106096", "http://arxiv.org/abs/cond-mat/0107607", "http://arxiv.org/abs/cond-mat/0112143", "http://arxiv.org/abs/cond-mat/0205476", "http://arxiv.org/abs/cond-mat/0306255", "http://arxiv.org/abs/cond-mat/9910332", "http://doi.org/10.1002%2Fasi.4630270505", "http://doi.org/10.1016%2Fj.physa.2009.02.013", "http://doi.org/10.1093%2Fbiomet%2F42.3-4.425", "http://doi.org/10.1103%2FPhysRevE.64.026704", "http://doi.org/10.1103%2FPhysRevE.65.057102", "http://doi.org/10.1103%2FPhysRevE.65.066122", "http://doi.org/10.1103%2FPhysRevE.68.046126", "http://doi.org/10.1103%2FPhysRevLett.90.058701", "http://doi.org/10.1103%2FRevModPhys.74.47", "http://doi.org/10.1126%2Fscience.286.5439.509", "http://doi.org/10.1140%2Fepjb%2Fe2013-40920-6", "http://doi.org/10.2307%2F2341419", "http://www.e-publications.org/ims/submission/index.php/BEJ/user/submissionFile/10315?confirm=c40442a0", "http://www.jstor.org/stable/2341419", "http://www.worldcat.org/issn/0031-9007", "http://www.worldcat.org/issn/0034-6861", "https://github.com/alihadian/ROLL", "https://compuzzle.wordpress.com/2015/02/03/generating-barabasi-albert-model-graphs-in-clojure/", "https://web.archive.org/web/20120417112354/http://www.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/EmergenceRandom_Science%20286,%20509-512%20(1999).pdf", "https://web.archive.org/web/20150824235818/http://www3.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/StatisticalMechanics_Rev%20of%20Modern%20Physics%2074,%2047%20(2002).pdf", "https://dx.doi.org/10.1088/1751-8113/44/17/175101"]}, "Monte Carlo methods in finance": {"categories": ["CS1 maint: Multiple names: authors list", "Monte Carlo methods in finance", "Pages using citations with accessdate and no URL", "Pages using web citations with no URL", "Webarchive template wayback links"], "title": "Monte Carlo methods in finance", "method": "Monte Carlo methods in finance", "url": "https://en.wikipedia.org/wiki/Monte_Carlo_methods_in_finance", "summary": "Monte Carlo methods are used in finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the distribution of their value over the range of resultant outcomes. This is usually done by help of stochastic asset models. The advantage of Monte Carlo methods over other techniques increases as the dimensions (sources of uncertainty) of the problem increase.\nMonte Carlo methods were first introduced to finance in 1964 by David B. Hertz through his Harvard Business Review article, discussing their application in Corporate Finance. In 1977, Phelim Boyle pioneered the use of simulation in derivative valuation in his seminal Journal of Financial Economics paper.This article discusses typical financial problems in which Monte Carlo methods are used. It also touches on the use of so-called \"quasi-random\" methods such as the use of Sobol sequences.\n\n", "images": [], "links": ["401(k)", "Analytic solution", "Antithetic variates", "Asian options", "Aswath Damodaran", "Binomial options pricing model", "Black\u2013Scholes model", "Bond (finance)", "Bond option", "Bond valuation", "Brownian motion", "Bruno Dupire", "Capital investment", "Central limit theorem", "Chemistry", "Claremont Graduate University", "Collateralized mortgage obligation", "Columbia University", "Computer science", "Control variate", "Control variates", "Corporate Finance", "Corporate finance", "Correlation", "Damiano Brigo", "David B. Hertz", "Derivative (finance)", "Descriptive statistics", "Deterministic system (mathematics)", "Discount factor", "Discrete event simulation", "Exercise (options)", "Exotic derivatives", "Exotic option", "Expected value", "Fabio Mercurio", "Finance", "Financial analyst", "Financial economics", "Financial instrument", "Finite difference method", "Fixed income", "Frank J. Fabozzi", "Fundamental theorem of arbitrage-free pricing", "Greeks (finance)", "Harvard Business Review", "Histogram", "Historical simulation (finance)", "Importance sampling", "Integral", "Interest rate", "Interest rate derivative", "Interest rate derivatives", "International Standard Book Number", "Investment", "John C. Hull", "Journal of Financial Economics", "Lattice model (finance)", "Least squares", "Louisiana State University", "Low-discrepancy sequence", "L\u00e9vy process", "Mathematical finance", "Model validation", "Monte Carlo method", "Monte Carlo methods for option pricing", "Monte Carlo option model", "Net present value", "Norwegian School of Management", "Numerical integration", "Numerical method", "Oklahoma State University\u2013Stillwater", "Option (finance)", "Option style", "Option time value", "Partial differential equation", "Path dependence", "Personal financial planning", "Peter Jaeckel", "Phelim Boyle", "Physics", "Pontif\u00edcia Universidade Cat\u00f3lica do Rio de Janeiro", "Portfolio (finance)", "Present value", "Probabilistic", "Probability distribution", "Project finance", "Pure mathematics", "Quasi-Monte Carlo methods in finance", "Rational pricing", "Real options analysis", "Real options valuation", "Replicating portfolio", "Retirement", "Risk-neutral measure", "Risk neutrality", "Short-rate model", "Short rate model", "Simulating", "Simulation", "Sobol sequence", "Social Science Research Network", "Solvay Business School", "Stanford University", "Stern School of Business", "Stochastic", "Stochastic asset model", "Stock market simulator", "Stress testing", "Swap (finance)", "Swaption", "Uncertainty", "Underlying instruments", "Value at risk", "Variance reduction", "Volatility (finance)", "Wayback Machine", "Yield curve"], "references": ["http://www.simularsoft.com.ar/SimulAr1e.htm", "http://www.ulb.ac.be/cours/solvay/farber/Teaching%20Notes/Monte%20Carlo.pdf", "http://www.puc-rio.br/marco.ind/faq4.html", "http://www.puc-rio.br/marco.ind/monte-carlo.html", "http://www.analycorp.com/uncertainty/flawarticle.htm", "http://www.businessweek.com/2001/01_04/b3716156.htm", "http://www.crystalball.com/articles/download/charnes-options.pdf", "http://www.fea.com/resources/pdf/swaptions.pdf", "http://www.flexibleretirementplanner.com", "http://www.global-derivatives.com/index.php?option=com_content&task=view&id=21", "http://www.global-derivatives.com/maths/k-o.php", "http://knol.google.com/k/giancarlo-vercellino/pricing-using-monte-carlo-simulation/11d5i2rgd9gn5/3#", "http://www.investmentscience.com/Content/howtoArticles/simulation.pdf", "http://www.investopedia.com/articles/04/092904.asp", "http://www.kamakuraco.com/Blog/tabid/231/EntryId/347/Pitfalls-in-Asset-and-Liability-Management-One-Factor-Term-Structure-Models.aspx", "http://homepage.mac.com/j.norstad/finance/finplan.pdf", "http://www.palisade.com/risk/monte_carlo_simulation.asp", "http://www.prospercuity.com", "http://www.qfinance.com/financial-risk-management-best-practice/quantifying-corporate-financial-risk?full", "http://www.quantnotes.com/publications/papers/Fink-montecarlo.pdf", "http://www.retirementsimulation.com", "http://www.riskglossary.com/link/monte_carlo_method.htm", "http://www.riskglossary.com/link/monte_carlo_transformation.htm", "http://www.smartquant.com/references/MonteCarlo/mc6.pdf", "http://ssrn.com/abstract=265905", "http://www.vanguard.com/nesteggcalculator", "http://www.vertex42.com/ExcelArticles/mc/SalesForecast.html", "http://www.pjaeckel.webspace.virginmedia.com/eqf013_026.pdf", "http://www.columbia.edu/~mh2078/MCS04/MCS_framework_FEegs.pdf", "http://www.bus.lsu.edu/academics/finance/faculty/dchance/Instructional/TN96-03.pdf", "http://homepages.nyu.edu/~sl1544/articles.html", "http://www.math.nyu.edu/research/carrp/papers/pdf/hjm.pdf", "http://pages.stern.nyu.edu/~adamodar/pdfiles/papers/probabilistic.pdf", "http://spears.okstate.edu/home/tlk/legacy/fin5883/notes6_s05.doc", "http://spears.okstate.edu/home/tlk/legacy/fin5883/notes7_s05.doc", "http://finance-old.bi.no/~bernt/gcc_prog/recipes/recipes/node12.html", "http://repositories.cdlib.org/anderson/fin/1-01/", "http://hbr.org/product/risk-analysis-in-capital-investment-harvard-busine/an/79504-PDF-ENG", "http://ideas.repec.org/a/eee/insuma/v19y1996i1p19-30.html", "http://ideas.repec.org/a/eee/jfinec/v4y1977i3p323-338.html", "https://books.google.com/books?id=wF8yVzLI6EYC&pg=PA138&lpg=PA138&dq=cmo+valuation+fabozzi+simulation&source=bl&ots=zSvgwSKm2V&sig=lW48IuS6CEQAch0f-uGVyHdIg3A&hl=en&ei=tcfATqPPB8SKhQfGovGzBA&sa=X&oi=book_result&ct=result&resnum=4&ved=0CC4Q6AEwAw#v=onepage&q&f=false", "https://web.archive.org/web/20100716195259/http://www.puc-rio.br/marco.ind/faq4.html", "https://web.archive.org/web/20111207025740/http://www.analycorp.com/uncertainty/flawarticle.htm", "https://web.archive.org/web/20120105084424/http://www.columbia.edu/~mh2078/MCS04/MCS_framework_FEegs.pdf"]}, "Rasch model": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from January 2013", "Educational psychology", "Personality theories", "Psychometrics", "Statistical models"], "title": "Rasch model", "method": "Rasch model", "url": "https://en.wikipedia.org/wiki/Rasch_model", "summary": "The Rasch model, named after Georg Rasch, is a family of psychometric models for creating measurements from categorical data, such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between (a) the respondent's abilities, attitudes, or personality traits and (b) the item difficulty. For example, they may be used to estimate a student's reading ability or the extremity of a person's attitude to capital punishment from responses on a questionnaire. In addition to psychometrics and educational research, the Rasch model and its extensions are used in other areas, including the health profession and market research because of their general applicability.The mathematical theory underlying Rasch models is a special case of item response theory and, more generally, a special case of a generalized linear model. However, there are important differences in the interpretation of the model parameters and its philosophical implications that separate proponents of the Rasch model from the item response modeling tradition. A central aspect of this divide relates to the role of specific objectivity, a defining property of the Rasch model according to Georg Rasch, as a requirement for successful measurement.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/05/RaschICC.gif", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/7/75/ICCs_prog.png", "https://upload.wikimedia.org/wikipedia/en/a/a2/PersItm.PNG", "https://upload.wikimedia.org/wikipedia/en/6/6b/TCC.PNG"], "links": ["Acceleration", "Benjamin Drake Wright", "Categorical data", "David Andrich", "Difficulty of engagement", "Digital object identifier", "Educational Measurement: Issues and Practice", "Educational psychology", "Epistemology", "Erling Andersen", "Force", "Generalized linear model", "Georg Rasch", "Guttman scale", "Health profession", "Interactions", "Item Response Theory", "Item response theory", "L. L. Thurstone", "Law of comparative judgment", "Logistic function", "Logit", "Mass", "Maximum likelihood", "Mechanics", "Mokken scale", "Newton's second law", "Observations", "Odds", "Parameter", "Personality trait", "Physics", "Poisson distribution", "Polytomous Rasch model", "Psychometrics", "Random", "Rasch model estimation", "Reliability (statistics)", "Standard error of measurement", "Statistical", "Statistical estimation", "Statistical model", "Steve Blinkhorn", "Sufficient statistic", "Theory", "Thomas Kuhn", "Thurstone scale", "Units of measurement"], "references": ["http://www.edmeasurement.com.au/Learning.html", "http://www.education.uwa.edu.au/ppl", "http://www.rasch-analysis.com/", "http://www.sciencedirect.com/science/article/pii/S136403211630096X", "http://www.tandfonline.com/doi/abs/10.1080/15434303.2016.1160096?journalCode=hlaq20", "http://bearcenter.berkeley.edu", "http://raschmeas.info/", "http://www.apa.org/science/standards.html", "http://doi.org/10.1016%2Fj.rser.2016.04.063", "http://doi.org/10.1080%2F15434303.2016.1160096", "http://edres.org/irt/", "http://www.jampress.org", "http://www.jampress.org/JOM.htm", "http://www.ncme.org", "http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.bsmsp/1200512895&page=record", "http://www.rasch.org/memo41.htm", "http://www.rasch.org/memos.htm", "http://www.rasch.org/rmt/contents.htm", "http://www.rasch.org/software.htm", "https://springerplus.springeropen.com/track/pdf/10.1186/s40064-016-3418-4?site=springerplus.springeropen.com", "https://archive.is/20010627012405/http://work.psych.uiuc.edu/irt/", "https://web.archive.org/web/20061008012219/http://www.ncme.org/pubs/items.cfm", "https://www.jstor.org/stable/228678"]}, "Uncertainty coefficient": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2012", "Information theory", "Statistical ratios", "Statistics articles needing expert attention", "Summary statistics for contingency tables"], "title": "Uncertainty coefficient", "method": "Uncertainty coefficient", "url": "https://en.wikipedia.org/wiki/Uncertainty_coefficient", "summary": "In statistics, the uncertainty coefficient, also called proficiency, entropy coefficient or Theil's U, is a measure of nominal association. It was first introduced by Henri Theil and is based on the concept of information entropy.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["ArXiv", "Association (statistics)", "Binary classification", "Cluster analysis", "Conditional entropy", "Conditional probability distribution", "Density estimation", "Digital object identifier", "F1 score", "Henri Theil", "Information entropy", "Mutual information", "Precision and recall", "Rand index", "Statistics", "The Mathematical Theory of Communication", "Theil index"], "references": ["http://apps.nrbook.com/empanel/index.html#pg=761", "http://libagf.sourceforge.net", "http://peteysoft.users.sourceforge.net/TRES_A_507795.pdf", "http://arxiv.org/abs/1202.2194", "http://doi.org/10.1080/01431161.2010.507795", "http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf", "https://web.archive.org/web/20120426073755/http://peteysoft.users.sourceforge.net/TRES_A_507795.pdf"]}, "Goodness of fit": {"categories": ["All articles needing additional references", "Articles needing additional references from January 2018", "Statistical theory"], "title": "Goodness of fit", "method": "Goodness of fit", "url": "https://en.wikipedia.org/wiki/Goodness_of_fit", "summary": "The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov\u2013Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-squared test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Akaike information criterion", "Analysis of variance", "Anderson\u2013Darling test", "Bayesian linear regression", "Bayesian multivariate linear regression", "Categorical data", "Chi-squared distribution", "Chi-squared test", "Coefficient of determination", "Cram\u00e9r\u2013von Mises criterion", "Cumulative distribution function", "Degrees of freedom (statistics)", "Deviance (statistics)", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "Expected value", "F. James Rohlf", "Fixed effects model", "G-test", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Hosmer\u2013Lemeshow test", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Kolmogorov\u2013Smirnov", "Kolmogorov\u2013Smirnov test", "Kuiper's test", "Lack-of-fit sum of squares", "Least-angle regression", "Least absolute deviations", "Least squares", "Likelihood ratio test", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Maximum spacing estimation", "Mean and predicted response", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Natural logarithm", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Normality test", "Null hypothesis", "Ordered logit", "Ordered probit", "Ordinary least squares", "Overfitting", "Partial least squares regression", "Pearson's chi-squared test", "Poisson regression", "Polynomial regression", "Principal component regression", "Probability", "Probability distribution", "Probit model", "Quantile regression", "Random effects model", "Reduced chi-squared", "Regression analysis", "Regression model validation", "Regression validation", "Regularized least squares", "Robert R. Sokal", "Robust regression", "Segmented regression", "Semiparametric regression", "Shapiro\u2013Wilk test", "Simple linear regression", "Statistical hypothesis test", "Statistical hypothesis testing", "Statistical model", "Statistical significance", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Weighted least squares"], "references": ["http://anakena.dcc.uchile.cl/~mnmonsal/eso.pdf", "http://www.biostathandbook.com/gtestgof.html", "http://proceedings.mlr.press/v48/liub16.html"]}, "Directional statistics": {"categories": ["Directional statistics", "Statistical data types", "Statistical theory", "Types of probability distributions"], "title": "Directional statistics", "method": "Directional statistics", "url": "https://en.wikipedia.org/wiki/Directional_statistics", "summary": "Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Rn), axes (lines through the origin in Rn) or rotations in Rn. More generally, directional statistics deals with observations on compact Riemannian manifolds.\n\nThe fact that 0 degrees and 360 degrees are identical angles, so that for example 180 degrees is not a sensible mean of 2 degrees and 358 degrees, provides one illustration that special statistical methods are required for the analysis of some types of data (in this case, angular data). Other examples of data that may be regarded as directional include statistics involving temporal periods (e.g. time of day, week, month, year, etc.), compass directions, dihedral angles in molecules, orientations, rotations and so on.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ca/Point_sets_from_Kent_distributions_mapped_onto_a_sphere_-_journal.pcbi.0020131.g004.svg", "https://upload.wikimedia.org/wikipedia/en/4/42/Fb5_cover.jpg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Average", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bessel function", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bioinformatics", "Bivariate normal distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Cartesian Coordinate System", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Central limit theorem for directional statistics", "Chi-squared distribution", "Chi distribution", "Christopher Bingham", "Circular distribution", "Circular uniform distribution", "Complex normal distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Crystallography", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degree (angle)", "Delaporte distribution", "Digital object identifier", "Dihedral angle", "Dirac delta function", "Direction (geometry)", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geology", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Histogram", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kuiper's test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Line (geometry)", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Matrix von Mises\u2013Fisher distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean of circular quantities", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "N-sphere", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Protein", "PubMed Central", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quaternions", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Rayleigh test", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Riemannian manifold", "Rotation", "Rotation matrix", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Sphere", "Stable distribution", "Statistics", "Stiefel manifold", "Student's t-distribution", "Theta function", "Torus", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Two-dimensional sphere", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unit vector", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal", "Wrapped normal distribution", "Yamartino method", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2440424", "http://doi.org/10.1073%2Fpnas.0801715105", "http://doi.org/10.1093%2Fbiomet%2F59.3.665", "http://doi.org/10.1111%2Fj.1541-0420.2006.00682.x", "http://doi.org/10.1198%2F016214501750332974", "http://doi.org/10.1214%2Faos%2F1176342874", "http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.0020131", "https://books.google.com/books?id=sKqWMGqQXQkC&printsec=frontcover&dq=Jammalamadaka+Topics+in+circular&hl=en&ei=iJ3QTe77NKL00gGdyqHoDQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDcQ6AEwAA#v=onepage&q&f=false"]}, "Computer experiment": {"categories": ["Computational science", "Design of experiments", "Simulation"], "title": "Computer experiment", "method": "Computer experiment", "url": "https://en.wikipedia.org/wiki/Computer_experiment", "summary": "A computer experiment or simulation experiment is an experiment used to study a computer simulation, also referred to as an in silico system. This area includes computational physics, computational chemistry, computational biology and other similar disciplines.", "images": [], "links": ["Bayesian statistics", "Climate models", "Computational biology", "Computational chemistry", "Computational physics", "Computer model", "Computer simulation", "Covariance function", "Data assimilation", "Design of experiments", "Digital object identifier", "Discrete event simulation", "Finite element", "Forcing function (differential equations)", "Frequentist", "Gaussian process", "Gaussian process emulator", "Grey box completion and validation", "In silico", "Initial conditions", "International Standard Book Number", "Inverse problem", "Invertible matrix", "Latin hypercube sampling", "Low discrepancy sequences", "Matern covariance", "Monte Carlo method", "Optimal design", "Prior distribution", "Probabilities", "Simulation", "Statistics", "Surrogate model", "Systems design", "Uncertainty quantification"], "references": ["http://www.google.com/patents/WO2013055257A1?cl=en&hl=ru", "http://www.sciencedirect.com/science/article/pii/037837589090122B", "http://amstat.tandfonline.com/doi/abs/10.1198/TECH.2009.0015#.UbixC_nFWHQ", "http://www2.isye.gatech.edu/~jeffwu/publications/calibration-may1.pdf", "http://doi.org/10.3934%2FMath.2016.3.261", "https://wayback.archive-it.org/all/20120130182750/http://www.stat.wisc.edu/~zhiguang/Multistep_AOS.pdf", "https://web.archive.org/web/20170918022130/https://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ss/1177012413"]}, "Item tree analysis": {"categories": ["Data analysis", "Sampling (statistics)", "Types of polling"], "title": "Item tree analysis", "method": "Item tree analysis", "url": "https://en.wikipedia.org/wiki/Item_tree_analysis", "summary": "Item tree analysis (ITA) is a data analytical method which allows constructing a\nhierarchical structure on the items of a questionnaire or test from observed response\npatterns. Assume that we have a questionnaire with m items and that subjects can\nanswer positive (1) or negative (0) to each of these items, i.e. the items are\ndichotomous. If n subjects answer the items this results in a binary data matrix D\nwith m columns and n rows.\nTypical examples of this data format are test items which can be solved (1) or failed\n(0) by subjects. Other typical examples are questionnaires where the items are\nstatements to which subjects can agree (1) or disagree (0).\nDepending on the content of the items it is possible that the response of a subject to an\nitem j determines her or his responses to other items. It is, for example, possible that\neach subject who agrees to item j will also agree to item i. In this case we say that\nitem j implies item i (short \n \n \n \n i\n \u2192\n j\n \n \n {\\displaystyle i\\rightarrow j}\n ). The goal of an ITA is to uncover such\ndeterministic implications from the data set D.", "images": ["https://upload.wikimedia.org/wikipedia/en/a/ad/Results_of_ITA_for_ISSP_1995_question_4.jpg"], "links": ["Algebra", "Algorithm", "Binary numeral system", "Boolean analysis", "Boolean logic", "Concept inventory", "Data analysis", "Data set", "Determinism", "Dichotomy", "Exploratory data analysis", "Insight", "Item response theory", "Logical implication", "Logically consistent", "Mathematical proof", "Matrix (mathematics)", "Minority group", "National identity", "Quasi-order", "Questionnaire", "Reflexive relation", "Social studies", "Transitive relation", "Value system", "Western Germany"], "references": ["http://www.jstatsoft.org/v16/i10", "http://www.jstatsoft.org/v16/i10/paper"]}, "Exact test": {"categories": ["All articles needing expert attention", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Statistical tests", "Statistics articles needing expert attention"], "title": "Exact test", "method": "Exact test", "url": "https://en.wikipedia.org/wiki/Exact_test", "summary": "In statistics, an exact (significance) test is a test where all assumptions, upon which the derivation of the distribution of the test statistic is based, are met as opposed to an approximate test (in which the approximation may be made as close as desired by making the sample size big enough). This will result in a significance test that will have a false rejection rate always equal to the significance level of the test. For example an exact test at significance level 5% will in the long run reject true null hypotheses exactly 5% of the time.\nParametric tests, such as those described in exact statistics, are exact tests when the parametric assumptions are fully met, but in practice the use of the term exact (significance) test is reserved for those tests that do not rest on parametric assumptions \u2013 non-parametric tests. However, in practice most implementations of non-parametric test software use asymptotical algorithms for obtaining the significance value, which makes the implementation of the test non-exact.\nSo when the result of a statistical analysis is said to be an \u201cexact test\u201d or an \u201cexact p-value\u201d, it ought to imply that the test is defined without parametric assumptions and evaluated without using approximate algorithms. In principle however it could also mean that a parametric test has been employed in a situation where all parametric assumptions are fully met, but it is in most cases impossible to prove this completely in a real world situation. Exceptions when it is certain that parametric tests are exact include tests based on the binomial or Poisson distributions. Sometimes permutation test is used as a synonym for exact test, but although all permutation tests are exact tests, not all exact tests are permutation tests.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinatorics", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "E. J. G. Pitman", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Exact statistics", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's exact test", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Optimal discriminant analysis", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Significance test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Methods for Research Workers", "Statistical assumption", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1002%2F0470011815.b2a10019", "https://resources.cytel.com/sites/default/files/resources/exact-inference-for-categorical-data.pdf"]}, "Cumulative distribution function": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from March 2010", "Articles with short description", "Articles with unsourced statements from April 2012", "Functions related to probability distributions", "Wikipedia articles needing page number citations from June 2011"], "title": "Cumulative distribution function", "method": "Cumulative distribution function", "url": "https://en.wikipedia.org/wiki/Cumulative_distribution_function", "summary": "In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x.\nIn the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2e/Discrete_probability_distribution_illustration.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b5/Folded-cumulative-distribution-function.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/c/ca/Normal_Distribution_CDF.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Absolute continuity", "Almost everywhere", "Binomial distribution", "Central moment", "Characteristic function (probability theory)", "Combinant", "Continuous distribution", "Continuous function", "Continuous random variable", "Cumulant", "Cumulative frequency analysis", "C\u00e0dl\u00e0g", "Derivative", "Descriptive statistics", "Digital object identifier", "Discontinuity (mathematics)", "Discrete random variable", "Dispersion (statistics)", "Distribution fitting", "Empirical distribution function", "Engineering", "Expected value", "Hypothesis test", "International Standard Book Number", "Interval (mathematics)", "Inverse transform sampling", "JSTOR", "Kolmogorov\u2013Smirnov test", "Kuiper's test", "Kurtosis", "L-moment", "Lebesgue integral", "Markov's inequality", "Mean absolute deviation", "Median (statistics)", "Moment-generating function", "Monotone increasing", "Multivariate random variable", "Normal distribution", "Ogive (statistics)", "P-value", "Paul L\u00e9vy (mathematician)", "Poisson distribution", "Probability", "Probability-generating function", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Quantile function", "Random number generation", "Random variable", "Raw moment", "Right-continuous", "Skewness", "Springer Science+Business Media", "Standard deviation", "Statistical hypothesis test", "Statistics", "Survival analysis", "Survival function", "Test statistic", "Uniform distribution (continuous)", "Variance"], "references": ["http://doi.org/10.1016%2Fj.spl.2011.03.014", "http://doi.org/10.2307%2F2684570", "http://www.jstor.org/stable/2684570", "https://books.google.com/?id=m4r-KVxpLsAC&pg=PA348"]}, "Gumbel distribution": {"categories": ["Continuous distributions", "Extreme value data", "Location-scale family probability distributions", "Pages using deprecated image syntax"], "title": "Gumbel distribution", "method": "Gumbel distribution", "url": "https://en.wikipedia.org/wiki/Gumbel_distribution", "summary": "In probability theory and statistics, the Gumbel distribution (Generalized Extreme Value distribution Type-I) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur. The potential applicability of the Gumbel distribution to represent the distribution of maxima relates to extreme value theory, which indicates that it is likely to be useful if the distribution of the underlying sample data is of the normal or exponential type. The rest of this article refers to the Gumbel distribution to model the distribution of the maximum value. To model the minimum value, use the negative of the original values.\nThe Gumbel distribution is a particular case of the generalized extreme value distribution (also known as the Fisher-Tippett distribution). It is also known as the log-Weibull distribution and the double exponential distribution (a term that is alternatively sometimes used to refer to the Laplace distribution). It is related to the Gompertz distribution: when its density is first reflected about the origin and then restricted to the positive half line, a Gompertz function is obtained.\nIn the latent variable formulation of the multinomial logit model \u2014 common in discrete choice theory \u2014 the errors of the latent variables follow a Gumbel distribution. This is useful because the difference of two Gumbel-distributed random variables has a logistic distribution.\nThe Gumbel distribution is named after Emil Julius Gumbel (1891\u20131966), based on his original papers describing the distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9e/FitGumbelDistr.tif", "https://upload.wikimedia.org/wikipedia/commons/7/7d/Gumbel-Cumulative.svg", "https://upload.wikimedia.org/wikipedia/commons/3/32/Gumbel-Density.svg", "https://upload.wikimedia.org/wikipedia/commons/5/53/Gumbel_paper.JPG", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["ARGUS distribution", "Amazon Standard Identification Number", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Confidence band", "Conway\u2013Maxwell\u2013Poisson distribution", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Cumulative probability", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete choice", "Discrete phase-type distribution", "Discrete uniform distribution", "Distribution fitting", "Elliptical distribution", "Emil Julius Gumbel", "Erlang distribution", "Estimator", "Euler\u2013Mascheroni constant", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "Extreme value theory", "F-distribution", "Fisher's z-distribution", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized multivariate log-gamma distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gompertz function", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hydrology", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Latent variable", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Machine learning", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multinomial logit", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Number theory", "Order statistic", "Parabolic fractal distribution", "Pareto distribution", "Partition of an integer", "Pearson distribution", "Phase-type distribution", "Plotting position", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Prime constellations", "Prime gaps", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real numbers", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Unbiased estimator", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wikimedia Commons", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.amazon.com/dp/B0007DSHG4", "http://adsabs.harvard.edu/abs/2010JHyd..388..131B", "http://adsabs.harvard.edu/abs/2013arXiv1301.2242K", "http://lips.cs.princeton.edu/the-gumbel-max-trick-for-discrete-distributions/", "http://www.waterlog.info/pdf/freqtxt.pdf", "http://arxiv.org/abs/1301.2242", "http://doi.org/10.1016%2Fj.insmatheco.2006.07.003", "http://doi.org/10.1016%2Fj.jhydrol.2010.04.035", "http://doi.org/10.1215%2FS0012-7094-41-00826-8", "http://archive.numdam.org/article/AIHP_1935__5_2_115_0.pdf", "https://books.google.com/books/about/Statistical_theory_of_extreme_values_and.html?id=SNpJAAAAMAAJ", "https://www..waterlog.info/cumfreq.htm"]}, "68\u201395\u201399.7 rule": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from November 2016", "Normal distribution", "Rules of thumb", "Statistical approximations"], "title": "68\u201395\u201399.7 rule", "method": "68\u201395\u201399.7 rule", "url": "https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule", "summary": "In statistics, the 68\u201395\u201399.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within\na band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.\nIn mathematical notation, these facts can be expressed as follows, where X is an observation from a normally distributed random variable, \u03bc is the mean of the distribution, and \u03c3 is its standard deviation:\n\n \n \n \n \n \n \n \n Pr\n (\n \u03bc\n \u2212\n \n \n \u03c3\n \u2264\n X\n \u2264\n \u03bc\n +\n \n \n \u03c3\n )\n \n \n \n \u2248\n 0.6827\n \n \n \n \n Pr\n (\n \u03bc\n \u2212\n 2\n \u03c3\n \u2264\n X\n \u2264\n \u03bc\n +\n 2\n \u03c3\n )\n \n \n \n \u2248\n 0.9545\n \n \n \n \n Pr\n (\n \u03bc\n \u2212\n 3\n \u03c3\n \u2264\n X\n \u2264\n \u03bc\n +\n 3\n \u03c3\n )\n \n \n \n \u2248\n 0.9973\n \n \n \n \n \n \n {\\displaystyle {\\begin{aligned}\\Pr(\\mu -\\;\\,\\sigma \\leq X\\leq \\mu +\\;\\,\\sigma )&\\approx 0.6827\\\\\\Pr(\\mu -2\\sigma \\leq X\\leq \\mu +2\\sigma )&\\approx 0.9545\\\\\\Pr(\\mu -3\\sigma \\leq X\\leq \\mu +3\\sigma )&\\approx 0.9973\\end{aligned}}}\n In the empirical sciences the so-called three-sigma rule of thumb expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.\nThe usefulness of this heuristic depends significantly on the question under consideration. In the social sciences, a result may be considered \"significant\" if its confidence level is of the order of a two-sigma effect (95%), while in particle physics, there is a convention of a five-sigma effect (99.99994% confidence) being required to qualify as a discovery.\nThe \"three-sigma rule of thumb\" is related to a result also known as the three-sigma rule, which states that even for non-normally distributed variables, at least 88.8% of cases should fall within properly calculated three-sigma intervals. It follows from Chebyshev's Inequality. For unimodal distributions the probability of being within the interval is at least 95%. There may be certain assumptions for a distribution that force this probability to be at least 98%.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2b/Cumulative_distribution_function_for_normal_distribution%2C_mean_0_and_sd_1.png", "https://upload.wikimedia.org/wikipedia/commons/2/22/Empirical_rule_histogram.svg", "https://upload.wikimedia.org/wikipedia/commons/7/75/Standard_score_and_prediction_interval.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Belief revision", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Black Monday (1987)", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chebyshev's Inequality", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Confidence interval", "Confidence level", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Deviation (statistics)", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discovery (observation)", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Empirical science", "Erlang distribution", "Error function", "Errors and residuals in statistics", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "Extinction of dinosaurs", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gambler's fallacy", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "History of Earth", "Holtsmark distribution", "Homo (genus)", "Homo sapiens", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Nassim Nicholas Taleb", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normality test", "Null hypothesis", "Outliers", "P-value", "Parabolic fractal distribution", "Pareto distribution", "Particle physics", "Parts per billion", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Prior probability", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Sample size", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Six Sigma", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard deviation", "Standard score", "Standardizing", "Statistical hypothesis testing", "Statistics", "Stochastic volatility", "Student's t-distribution", "Studentized residual", "Studentizing", "T-statistic", "The Black Swan (Taleb book)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unimodality", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "X-axis", "Y-axis", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.wolframalpha.com/input/?i=erf(x/sqrt(2))", "http://www-stat.stanford.edu/~naras/jsm/NormalDensity/NormalDensity.html", "http://www.jstor.org/stable/2684253", "https://books.google.com/books?id=XvMJAQAAMAAJ", "https://books.google.com/books?id=gEpkYxwDbvgC&pg=PA342"]}, "Block design": {"categories": ["Combinatorics", "Design of experiments", "Design theory", "Set families"], "title": "Block design", "method": "Block design", "url": "https://en.wikipedia.org/wiki/Block_design", "summary": "In combinatorial mathematics, a block design is a set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties that are deemed useful for a particular application. These applications come from many areas, including experimental design, finite geometry, software testing, cryptography, and algebraic geometry. Many variations have been examined, but the most intensely studied are the balanced incomplete block designs (BIBDs or 2-designs) which historically were related to statistical issues in the design of experiments.A block design in which all the blocks have the same size is called uniform. The designs discussed in this article are all uniform. Pairwise balanced designs (PBDs) are examples of block designs that are not necessarily uniform.", "images": [], "links": ["15 schoolgirl problem", "Affine plane (incidence geometry)", "Algebraic geometry", "Analysis of covariance", "Analysis of variance", "Annals of Eugenics", "Annals of Mathematical Statistics", "Anne Penfold Street", "ArXiv", "Association scheme", "Bayesian experimental design", "Bayesian linear regression", "Bhat-Nayak Vasanti N.", "Binary relation", "Blind experiment", "Block code", "Blocking (statistics)", "Box\u2013Behnken design", "Bruck\u2013Ryser\u2013Chowla theorem", "Cambridge University Press", "Central composite design", "Cochran's theorem", "Combinatorial design", "Combinatorics", "Comparing means", "Completely randomized design", "Confounding", "Contrast (statistics)", "Covariate", "Crossover study", "Cryptography", "Damaraju Raghavarao", "Design of experiments", "Digital object identifier", "Digon", "Effect size", "Eric W. Weisstein", "Error correcting code", "Experiment", "Experimental design", "Experimental unit", "External validity", "Factorial experiment", "Family of sets", "Fano plane", "Finite geometry", "Fisher's inequality", "Fractional factorial design", "Generalized randomized block design", "Glossary of experimental design", "Graeco-Latin square", "H. J. Ryser", "Hadamard matrix", "Hierarchical Bayes model", "Hierarchical linear modeling", "Identity relation", "Incidence geometry", "Incidence matrix", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Journal of Combinatorial Theory", "Latin hypercube sampling", "Latin square", "Linear regression", "List of statistics articles", "MathWorld", "Mathematical Reviews", "Mathematics", "Mixed model", "Multiple comparison", "Multivariate analysis of variance", "M\u00f6bius plane", "Nuisance variable", "Optimal design", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Ovoid (projective geometry)", "Paley construction", "Paley digraph", "Partition of a set", "Peter Cameron (mathematician)", "Plackett-Burman design", "Polynomial and rational function modeling", "Projective linear group", "Projective plane", "Projective special linear group", "Pulse-position modulation", "Quadratic form", "Quadric (projective geometry)", "R", "R. C. Bose", "Random assignment", "Random effect", "Randomization", "Randomized block design", "Randomized controlled trial", "Raymond Paley", "Regular Hadamard matrix", "Repeated measures design", "Replication (statistics)", "Response surface methodology", "Restricted randomization", "Ronald Fisher", "S. S. Shrikhande", "Sample size", "Scientific control", "Scientific method", "Sequential analysis", "Sequential probability ratio test", "Set (mathematics)", "Software testing", "Statistical inference", "Statistical model", "Statistics", "Steiner system", "Taguchi methods", "Validity (statistics)"], "references": ["http://mathworld.wolfram.com/BlockDesign.html", "http://www.ams.org/mathscinet-getitem?mr=2384014", "http://arxiv.org/abs/1203.5378", "http://designtheory.org", "http://doi.org/10.1002%2Fjcd.20145", "http://doi.org/10.1016%2F0097-3165(71)90054-9", "http://doi.org/10.1016%2F0097-3165(78)90002-X", "http://doi.org/10.1080%2F01621459.1952.10501161", "http://doi.org/10.1109%2FLCOMM.2012.042512.120457", "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6205424", "http://www.neverendingbooks.org/DATA/biplanesingerman.pdf", "http://www.maths.qmul.ac.uk/~pjc/design/resources.html", "https://cran.r-project.org/package=agricolae"]}, "Irwin\u2013Hall distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax"], "title": "Irwin\u2013Hall distribution", "method": "Irwin\u2013Hall distribution", "url": "https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution", "summary": "In probability and statistics, the Irwin\u2013Hall distribution, named after Joseph Oscar Irwin and Philip Hall, is a probability distribution for a random variable defined as the sum of a number of independent random variables, each having a uniform distribution. For this reason it is also known as the uniform sum distribution.\nThe generation of pseudo-random numbers having an approximately normal distribution is sometimes accomplished by computing the sum of a number of pseudo-random numbers having a uniform distribution; usually for the sake of simplicity of programming. Rescaling the Irwin\u2013Hall distribution provides the exact distribution of the random variates being generated.\nThis distribution is sometimes confused with the Bates distribution, which is the mean (not sum) of n independent random variables uniformly distributed from 0 to 1.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/92/Irwin-hall-cdf.svg", "https://upload.wikimedia.org/wikipedia/en/2/23/Irwin-hall-pdf.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent and identically distributed", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Joseph Oscar Irwin", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Natural numbers", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "On-Line Encyclopedia of Integer Sequences", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Philip Hall", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability density function", "Probability distribution", "Pseudo-random number sampling", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Recurrence relation", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign function", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Spline (mathematics)", "Stable distribution", "Statistically independent", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["https://doi.org/10.1093%2Fbiomet%2F19.3-4.225", "https://doi.org/10.1093%2Fbiomet%2F19.3-4.240", "https://www.jstor.org/stable/2331960", "https://www.jstor.org/stable/2331961", "https://oeis.org/A188668", "https://oeis.org/A188816"]}, "Partial autocorrelation": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2011", "Covariance and correlation", "Time domain analysis", "Time series", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Partial autocorrelation function", "method": "Partial autocorrelation", "url": "https://en.wikipedia.org/wiki/Partial_autocorrelation_function", "summary": "In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a time series with its own lagged values, controlling for the values of the time series at all shorter lags. It contrasts with the autocorrelation function, which does not control for other lags.\nThis function plays an important role in data analysis aimed at identifying the extent of the lag in an autoregressive model. The use of this function was introduced as part of the Box\u2013Jenkins approach to time series modelling, whereby plotting the partial autocorrelative functions one could determine the appropriate lags p in an AR (p) model or in an extended ARIMA (p,d,q) model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autocorrelation function", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4463.htm"]}, "Experiment": {"categories": ["CS1 maint: Multiple names: authors list", "Causal inference", "Design of experiments", "Experiments", "Research", "Science experiments", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers"], "title": "Experiment", "method": "Experiment", "url": "https://en.wikipedia.org/wiki/Experiment", "summary": "An experiment is a procedure carried out to support, refute, or validate a hypothesis. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale, but always rely on repeatable procedure and logical analysis of the results. There also exists natural experimental studies.\nA child may carry out basic experiments to understand gravity, while teams of scientists may take years of systematic investigation to advance their understanding of a phenomenon. Experiments and other types of hands-on activities are very important to student learning in the science classroom. Experiments can raise test scores and help a student become more engaged and interested in the material they are learning, especially when used over time. Experiments can vary from personal and informal natural comparisons (e.g. tasting a range of chocolates to find a favorite), to highly controlled (e.g. tests requiring complex apparatus overseen by many scientists that hope to discover information about subatomic particles). Uses of experiments vary considerably between the natural and human sciences.\nExperiments typically include controls, which are designed to minimize the effects of variables other than the single independent variable. This increases the reliability of the results, often through a comparison between control measurements and the other measurements. Scientific controls are a part of the scientific method. Ideally, all variables in an experiment are controlled (accounted for by the control measurements) and none are uncontrolled. In such an experiment, if all controls work as expected, it is possible to conclude that the experiment works as intended, and that results are due to the effect of the tested variable.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/35/Blackbox3D-obs.png", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/6/60/Mirror_baby.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/2/27/Snow-cholera-map-1.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Ad hoc", "Agriculture", "Akaike information criterion", "Allegiance bias", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Antoine Lavoisier", "Arithmetic mean", "Assay", "Astronomy", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average treatment effect", "Baconian method", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Biochemistry", "Bioinformatics", "Biostatistics", "Biplot", "Black box", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Branches of science", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Causality", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemistry", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster (epidemiology)", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Colorimetry (chemical method)", "Combustion", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Concept development and experimentation", "Confidence interval", "Confounding", "Conservation of mass", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Control group", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Counterexample", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "David A. Freedman", "Decomposition of time series", "Deductive reasoning", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Ecology", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical research", "Engineering", "Engineering statistics", "English Renaissance", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment (disambiguation)", "Experimental", "Experimental economics", "Experimental music", "Experimental physics", "Experimental unit", "Experimentum crucis", "Explanatory variables", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feedback", "Field experiment", "First-hitting-time model", "Food and Drug Administration", "Forest plot", "Fourier analysis", "Fractional factorial design", "Francis Bacon", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Galileo Galilei", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geology", "Geometric mean", "Geostatistics", "Germ theory of disease", "Gertrude Mary Cox", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "History of experiments", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human experimentation", "Human subject research", "Hypotheses", "Hypothesis", "Ibn al-Haytham", "Independent variable", "Index of dispersion", "Informed consent", "Integrated Authority File", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "John Snow (physician)", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laboratory", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Library of Congress Control Number", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of experiments", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Long-term experiment", "Loss function", "Louis Pasteur", "Lp space", "M-estimator", "Manhattan Project", "Mann\u2013Whitney U test", "Markov's inequality", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement", "Median", "Median-unbiased estimator", "Medical statistics", "Meta-analysis", "Meteorology", "Method of moments (statistics)", "Methods engineering", "Microbiology", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National accounts", "Natural experiment", "Natural science", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Null hypothesis", "Number", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "Paleontology", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Philosophy", "Philosophy of science", "Pie chart", "Pivotal quantity", "Placebo", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Political science", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Propensity score matching", "Proportional hazards model", "Protein", "Psychology", "Psychometrics", "Ptolemy", "Quality control", "Quasi-experiment", "Quasi-experiments", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replicate (statistics)", "Replication (statistics)", "Resampling (statistics)", "Research ethics", "Research subject", "Response surface methodology", "Response variable", "Restricted randomization", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Science", "Scientific control", "Scientific method", "Scientific models", "Scientific theory", "Scientist", "Score test", "Seasonal adjustment", "Selection bias", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social science", "Social sciences", "Social statistics", "Solution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spectrophotometer", "Spontaneous generation", "Standard curve", "Standard deviation", "Standard error", "Stanford Encyclopedia of Philosophy", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stimulation", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System", "System identification", "Systematic review", "Taguchi methods", "Test method", "Test statistic", "Time domain", "Time series", "Tolerance interval", "Treatment group", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variable (mathematics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Gemmell Cochran", "Z-test"], "references": ["http://plato.stanford.edu/entries/physics-experiment/", "http://psychology.ucdavis.edu/SommerB/sommerdemo/experiment/types.htm", "http://depts.washington.edu/methods/readings/Shadish.pdf", "http://openbookproject.net/electricCircuits/Exper/index.html", "http://doi.org/10.1002%2F(SICI)1098-2736(199601)33:1%3C101::AID-TEA6%3E3.0.CO;2-Z", "http://doi.org/10.2307%2F2289064", "http://www.jstor.org/stable/2289064", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Experiment", "https://id.loc.gov/authorities/subjects/sh85046449", "https://d-nb.info/gnd/4015999-1", "https://id.ndl.go.jp/auth/ndlna/00574737", "https://web.archive.org/web/20141219220204/http://psychology.ucdavis.edu/faculty_sites/sommerb/sommerdemo/experiment/types.htm", "https://www.wikidata.org/wiki/Q101965"]}, "Minimax estimator": {"categories": ["Decision theory", "Estimator"], "title": "Minimax estimator", "method": "Minimax estimator", "url": "https://en.wikipedia.org/wiki/Minimax_estimator", "summary": "In statistical decision theory, where we are faced with the problem of estimating a deterministic parameter (vector) \n \n \n \n \u03b8\n \u2208\n \u0398\n \n \n {\\displaystyle \\theta \\in \\Theta }\n from observations \n \n \n \n x\n \u2208\n \n \n X\n \n \n ,\n \n \n {\\displaystyle x\\in {\\mathcal {X}},}\n an estimator (estimation rule) \n \n \n \n \n \u03b4\n \n M\n \n \n \n \n \n \n {\\displaystyle \\delta ^{M}\\,\\!}\n is called minimax if its maximal risk is minimal among all estimators of \n \n \n \n \u03b8\n \n \n \n \n {\\displaystyle \\theta \\,\\!}\n . In a sense this means that \n \n \n \n \n \u03b4\n \n M\n \n \n \n \n \n \n {\\displaystyle \\delta ^{M}\\,\\!}\n is an estimator which performs best in the worst possible case allowed in the problem.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/06/MSE_of_ML_vs_JS.png", "https://upload.wikimedia.org/wikipedia/commons/7/7f/Riskset_minimax_smaller.svg"], "links": ["Admissible decision rule", "Annals of Statistics", "Bayes estimator", "Bessel function", "Beta distribution", "Binomial distribution", "Charles Stein (statistician)", "Conditional probability distribution", "Decision theory", "Digital object identifier", "Estimator", "Expected value", "Fair coin", "International Standard Book Number", "James\u2013Stein estimator", "Loss function", "Mathematical Reviews", "Maximum likelihood", "Mean squared error", "Metric entropy number", "Minimax", "Minimum mean square error", "Normal distribution", "Randomised decision rule", "Risk function", "Robust optimization", "Sphere", "Uniform distribution (continuous)", "Zentralblatt MATH"], "references": ["http://www.shaker.eu/shop/978-3-8440-0332-1", "http://www.ams.org/mathscinet-getitem?mr=0630098", "http://doi.org/10.1214%2Faos%2F1176345632", "http://zbmath.org/?format=complete&q=an:0476.62035"]}, "Quota sampling": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2010", "Quotas", "Sampling techniques"], "title": "Quota sampling", "method": "Quota sampling", "url": "https://en.wikipedia.org/wiki/Quota_sampling", "summary": "Quota sampling is a method for selecting survey participants that is a non-probabilistic version of stratified sampling.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Accidental sampling", "Bias (statistics)", "Coefficient of variation", "International Standard Book Number", "Mutually exclusive", "Random sample", "Reliability (statistics)", "Sampling frame", "Standard deviation", "Stratified sampling"], "references": ["http://www.fao.org/docrep/W3241E/w3241e08.htm#quota%20sampling"]}, "Seven-number summary": {"categories": ["Summary statistics"], "title": "Seven-number summary", "method": "Seven-number summary", "url": "https://en.wikipedia.org/wiki/Seven-number_summary", "summary": "In descriptive statistics, the seven-number summary is a collection of seven summary statistics, and is an extension of the five-number summary. There are two similar, common forms.\nAs with the five-number summary, it can be represented by a modified box plot, adding hatch-marks on the \"whiskers\" for two of the additional numbers.", "images": [], "links": ["Arthur Bowley", "Box plot", "Decile", "Descriptive statistics", "Five-number summary", "Interdecile range", "Median", "Midsummary", "Non-parametric statistics", "Normal distribution", "Percentile", "Quartile", "Sample maximum", "Sample minimum", "Skewness", "Stanine", "Summary statistics", "Three-point estimation"], "references": []}, "Biostatistics": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "All pages needing cleanup", "Articles needing additional references from December 2016", "Articles needing cleanup from March 2016", "Articles with sections that need to be turned into prose from March 2016", "Articles with unsourced statements from December 2016", "Bioinformatics", "Biostatistics", "CS1: Julian\u2013Gregorian uncertainty", "CS1 maint: Explicit use of et al.", "Commons category link from Wikidata", "Demography", "Public health"], "title": "Biostatistics", "method": "Biostatistics", "url": "https://en.wikipedia.org/wiki/Biostatistics", "summary": "Biostatistics are the application of statistics to a wide range of topics in biology. It encompasses the design of biological experiments, especially in medicine, pharmacy, agriculture and fishery; the collection, summarization, and analysis of data from those experiments; and the interpretation of, and inference from, the results. A major branch is medical biostatistics, which is exclusively concerned with medicine and health.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/34/Correlation_coefficient.png", "https://upload.wikimedia.org/wikipedia/commons/1/1d/Example_histogram.png", "https://upload.wikimedia.org/wikipedia/commons/1/15/Examples_of_descriptive_tools.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ANOVA", "ASReml", "Abhaya Indrayan", "Abiogenesis", "Accelerated failure time model", "Accuracy and precision", "Actuarial science", "Agriculture", "Akaike information criterion", "Allele", "Alternative hypothesis", "Alternatives to Darwinism", "Analysis of covariance", "Analysis of variance", "Anatomy", "Anderson\u2013Darling test", "Animal breeding", "ArXiv", "Arabidopsis thaliana", "Arithmetic mean", "Arthur Dukinfield Darbishire", "Artificial neural network", "Association rule learning", "Astrobiology", "Asymptomatic carrier", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Auxology", "Bachelor of Science in Public Health", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavior change (public health)", "Behavioural change theories", "Bias of an estimator", "Bibcode", "Binomial regression", "Biochemistry", "Bioconductor", "Biogeography", "Biohistory", "Bioinformatics", "Biological classification", "Biological database", "Biological hazard", "Biology", "Biomechanics", "Biometrics", "Biometrics (journal)", "Biophysics", "Biostatistics (journal)", "Biplot", "Blocking (statistics)", "Bonferroni correction", "Bootstrapping (statistics)", "Botany", "Box plot", "Box\u2013Jenkins method", "Brazil", "Breusch\u2013Godfrey test", "Caltech", "Canonical correlation", "Carl Rogers Darnall", "Cartography", "Case\u2013control", "Case\u2013control study", "Categorical variable", "Cell biology", "Cells", "Cellular microbiology", "Census", "Centers for Disease Control and Prevention", "Central limit theorem", "Central tendency", "Charles Davenport", "Chart", "Chemical biology", "Chemometrics", "Chi-squared test", "Chief Medical Officer", "Child mortality", "Chronobiology", "Clinical research", "Clinical studies", "Clinical study design", "Clinical trial", "Clinical trials", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort (statistics)", "Cointegration", "Community health", "Completely randomized design", "Completeness (statistics)", "Computational biology", "Confidence interval", "Confidence intervals", "Confounding", "Conservation biology", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Council on Education for Public Health", "Count data", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Cultural competence in health care", "Cytogenetics", "D'Arcy Thompson", "DNA microarray", "DNA sequencing", "Daniel Bernoulli", "Data analysis", "Data collection", "Data mining", "DbSNP", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive Statistics", "Descriptive statistics", "Design of experiments", "Developmental biology", "Deviance (sociology)", "Dickey\u2013Fuller test", "Diffusion of innovations", "Digital object identifier", "Disease surveillance", "Divergence (statistics)", "Doctor of Public Health", "Durbin\u2013Watson statistic", "Ecological forecasting", "Ecology", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Embryology", "Emergency sanitation", "Empirical distribution function", "Engineering statistics", "Environment (systems)", "Environmental health", "Environmental statistics", "Epidemic", "Epidemiological method", "Epidemiological studies", "Epidemiology", "Epigenetics", "Equivalence (measure theory)", "Errors and residuals in statistics", "Estimating equations", "Estimation theory", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Evolution", "Evolutionary biology", "Exon", "Experiment", "Experimental design", "Experimental designs", "Exponential family", "Exponential smoothing", "F-statistics", "F-test", "Factor analysis", "Factorial designs", "Factorial experiment", "Failure rate", "False discovery rate", "False positives and false negatives", "Family-wise error rate", "Family planning", "Fan chart (statistics)", "Fecal\u2013oral route", "First-hitting-time model", "Fisheries", "Fisheries science", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Forest plot", "Fourier analysis", "Francis Galton", "Frequency", "Frequency distribution", "Frequency domain", "Frequentist inference", "Freshwater biology", "Friden, Inc.", "Friedman test", "G-test", "Gene", "Gene Set Enrichment Analysis", "Gene expression", "Gene map", "Gene ontology", "General linear model", "Generalized linear model", "Genetically modified food", "Genetics", "Genome", "Genome-wide association study", "Genomics", "Genotype", "Geobiology", "Geographic information system", "Geometric mean", "Geostatistics", "Germ theory of disease", "GitHub", "Global health", "Globalization and disease", "Good agricultural practice", "Good manufacturing practice", "Goodness of fit", "Granger causality", "Graphical model", "Gregor Mendel", "Group size measures", "Grouped data", "HACCP", "Hand washing", "Harmonic mean", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health indicator", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health services research", "Health system", "Heteroscedasticity", "Histogram", "Histology", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human biology", "Human factors and ergonomics", "Human genetics", "Human nutrition", "Hygiene", "Hypothesis", "ISO 22000", "Immunology", "Inbreeding coefficient", "Index of dispersion", "Individuals", "Infant mortality", "Infection control", "Inference", "Inferiority", "Injury prevention", "Interaction (statistics)", "International Nucleotide Sequence Database Collaboration", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "J. B. S. Haldane", "JAK-STAT signaling pathway", "Jackknife resampling", "James Lind", "Jarque\u2013Bera test", "Java (programming language)", "Jean d\u2019Alembert", "Johansen test", "John Arbuthnot", "John Snow (physician)", "Jonckheere's trend test", "Joseph Lister", "K-means clustering", "KEGG", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lattice model (physics)", "Lehmann\u2013Scheff\u00e9 theorem", "Life science", "Life sciences", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line graph", "Linear discriminant analysis", "Linear regression", "Linkage disequilibrium", "List of epidemics", "List of fields of application of statistics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "List of statistics articles", "List of statistics journals", "Literature review", "Livestock", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Louis Denis Jules Gavarret", "Lp space", "M-estimator", "Machine learning", "Machine learning in bioinformatics", "Mann\u2013Whitney U test", "Margaret Sanger", "Marine biology", "Marker-assisted selection", "Mary Mallon", "Mass spectrometers", "Maternal health", "Mathematical and theoretical biology", "Mathematical biology", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement", "Median", "Median-unbiased estimator", "Medical anthropology", "Medical sociology", "Medical statistics", "Medicine", "Mental health", "Metabolism", "Method of moments (statistics)", "Methods engineering", "Metric measure", "Microarray", "Microarrays", "Microbiology", "Microorganisms", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Ministry of Health and Family Welfare", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Molecular biology", "Molecular marker", "Moment (mathematics)", "Monotone likelihood ratio", "Multicollinearity", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Mycology", "National accounts", "Natural experiment", "Negative binomial distribution", "Nelson\u2013Aalen estimator", "Neontology", "Neuroscience", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Notifiable disease", "Null hypothesis", "Nutrition", "OCLC", "Observational study", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Official statistics", "One- and two-tailed tests", "Open defecation", "Operon", "Opinion poll", "Optimal decision", "Optimal design", "Oral hygiene", "Orange (software)", "Order statistic", "Ordinary least squares", "Organisms", "Outlier", "Outline of statistics", "P-value", "PRECEDE-PROCEED model", "Paleontology", "Parametric statistics", "Parasitology", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pathology", "Patient safety", "Patient safety organization", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pharmaceutical policy", "Pharmacology", "Pharmacovigilance", "Pharmacy", "Phenotype", "Phylogenetics", "Physiology", "Pie chart", "Pierre-Charles-Alexandre Louis", "Pivotal quantity", "Placer mining", "Plant breeding", "Plants", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population", "Population (statistics)", "Population dynamics", "Population genetics", "Population health", "Population statistics", "Positive deviance", "Posterior probability", "Postgraduate", "Power (statistics)", "Prediction interval", "Preventive healthcare", "Preventive nutrition", "Primordial soup", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Professional degrees of public health", "Proportional hazards model", "Proteomics", "Psychometrics", "PubMed", "PubMed Central", "PubMed Identifier", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quadrat", "Qualitative data", "Quality control", "Quantitative data", "Quantitative trait locus", "Quantum biology", "Quarantine", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "RNA-Seq", "ROC curve", "R (programming language)", "Race and health", "Radar chart", "Random assignment", "Random forests", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Re-sampling (statistics)", "Real-time polymerase chain reaction", "Recombinant inbred strain", "Regression analysis", "Regression model validation", "Relative risk", "Reliability engineering", "Replication (statistics)", "Reproductive health", "Resampling (statistics)", "Restricted maximum likelihood", "Robust regression", "Robust statistics", "Ronald Fisher", "Rothamsted Research", "Run chart", "S", "SAS (software)", "SAS Institute", "SAS language", "SNP genotyping", "Safe sex", "Sample (statistics)", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scale parameter", "Scatter plot", "Scientific community", "Scientific control", "Scientific question", "Score test", "Seasonal adjustment", "Selective breeding", "Self-organizing map", "Semiparametric regression", "Sequence analysis", "Sewall G. Wright", "Sexually transmitted infection", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Single-nucleotide polymorphism", "Size", "Skewness", "Smallpox", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Social statistics", "Sociobiology", "Sociology of health and illness", "Spatial analysis", "Spearman's rank correlation coefficient", "Species", "Spectral density estimation", "Split plot", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Methods for Research Workers", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical genetics", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistical variability", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural biology", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Superior (hierarchy)", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Systematics", "Systems biology", "Systems medicine", "Table (information)", "Teratology", "Test statistic", "The Genetical Theory of Natural Selection", "Theory of planned behavior", "Thomas Hunt Morgan", "Time domain", "Time series", "Tolerance interval", "Toxicology", "Transtheoretical model", "Treatment group", "Trend estimation", "Tropical disease", "Type II error", "Type I error", "U-statistic", "Uniformly most powerful test", "United States Public Health Service", "Unsupervised learning", "V-statistic", "Vaccination", "Vaccine trial", "Variance", "Vector autoregression", "Vector control", "Virology", "Virophysics", "Wald test", "Walter Weldon", "Waterborne diseases", "Wavelet", "Weka (machine learning)", "Whittle likelihood", "Wilcoxon signed-rank test", "Wilhelm Johannsen", "William Bateson", "World Health Organization", "World Toilet Organization", "Z-test", "Zika virus", "Zoology"], "references": ["http://tabnet.datasus.gov.br/cgi/deftohtm.exe?sinasc/cnv/nvuf.def", "http://www.biostatsresearch.com/repository/", "http://www.medpagetoday.com/lib/content/Medpage-Guide-to-Biostatistics.pdf", "http://journals.sagepub.com/home/smm", "http://thescipub.com/journals/ajbs", "http://www.tilsonfunds.com/MungerUCSBspeech.pdf", "http://adsabs.harvard.edu/abs/1895RSPTA.186..343P", "http://adsabs.harvard.edu/abs/2005PNAS..10215545S", "http://adsabs.harvard.edu/abs/2008Natur.456..719G", "http://adsabs.harvard.edu/abs/2016Natur.531..151B", "http://phytozome.jgi.doe.gov/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1239896", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3750305", "http://www.ncbi.nlm.nih.gov/pubmed/15881678", "http://www.ncbi.nlm.nih.gov/pubmed/17654500", "http://www.ncbi.nlm.nih.gov/pubmed/18042950", "http://www.ncbi.nlm.nih.gov/pubmed/21176179", "http://www.ncbi.nlm.nih.gov/pubmed/23876160", "http://www.ncbi.nlm.nih.gov/pubmed/26961635", "http://www.ncbi.nlm.nih.gov/pubmed/28965742", "http://arxiv.org/abs/0808.0572", "http://doi.org/10.1002%2F0470011815.b2a17065", "http://doi.org/10.1002%2Fjcp.21218", "http://doi.org/10.1007%2Fs10709-004-2705-0", "http://doi.org/10.1016%2Fj.tplants.2017.08.011", "http://doi.org/10.1038%2F456719a", "http://doi.org/10.1038%2Femm.2017.290", "http://doi.org/10.1038%2Fnature.2016.19503", "http://doi.org/10.1038%2Fnj7384-263a", "http://doi.org/10.1046%2Fj.1525-139X.2002.00085.x", "http://doi.org/10.1053%2Fj.jvca.2017.04.020", "http://doi.org/10.1073%2Fpnas.0506580102", "http://doi.org/10.1098%2Frsta.1895.0010", "http://doi.org/10.1111%2Fj.1753-6405.2009.00372.x", "http://doi.org/10.1177%2F0115426507022006629", "http://doi.org/10.1186%2F1746-4811-9-29", "http://doi.org/10.1186%2Fgb-2010-11-12-220", "http://doi.org/10.1214%2F07-STS236", "http://doi.org/10.2134%2Fagronj15.0144", "http://doi.org/10.3835%2Fplantgenome2008.02.0089", "http://dx.doi.org/10.1111/j.1753-6405.2009.00372.x", "http://insdc.org", "http://rsta.royalsocietypublishing.org/content/186/343", "http://www.worldcat.org/issn/0264-3820", "http://www.worldcat.org/issn/1326-0200", "http://www.worldcat.org/oclc/30301196", "http://www.worldcat.org/oclc/56568530", "http://agrobiol.sggw.waw.pl/cbcs/", "http://www.vsni.co.uk/", "https://www.degruyter.com/view/j/ijb", "https://www.degruyter.com/view/j/sagmb", "https://www.jscimedcentral.com/Biometrics/editors.php", "https://academic.oup.com/biomet", "https://academic.oup.com/biostatistics", "https://publons.com/journal/36965/american-journal-of-biostatistics", "https://www.sangakoo.com/en/unit/absolute-relative-cumulative-frequency-and-statistical-tables", "https://www.statlect.com/glossary/null-hypothesis", "https://onlinelibrary.wiley.com/doi/pdf/10.1002/1098-240X(200006)23:3%3C246::AID-NUR9%3E3.0.CO;2-H", "https://onlinelibrary.wiley.com/journal/10970258", "https://onlinelibrary.wiley.com/journal/15214036", "https://onlinelibrary.wiley.com/journal/15391612", "https://onlinelibrary.wiley.com/journal/15410420", "https://www.ncbi.nlm.nih.gov/", "https://www.ncbi.nlm.nih.gov/labs/journals/j-epidemiol-biostat/", "https://ebph.it/", "https://www.ddbj.nig.ac.jp/index-e.html", "https://www.arabidopsis.org/", "https://web.archive.org/web/20150402180351/http://www.biostat.katerynakon.in.ua/en/", "https://www.biometricsociety.org/", "https://cran.r-project.org/", "https://www.worldcat.org/oclc/30301196", "https://www.worldcat.org/oclc/56568530", "https://www.ebi.ac.uk/", "https://www.vsni.co.uk/", "https://www.vsni.co.uk/software/cycdesign/"]}, "Computational formula for the variance": {"categories": ["Statistical deviation and dispersion"], "title": "Algebraic formula for the variance", "method": "Computational formula for the variance", "url": "https://en.wikipedia.org/wiki/Algebraic_formula_for_the_variance", "summary": "In probability theory and statistics, there are several algebraic formulae for the variance available for deriving the variance of a random variable. The usefulness of these depends on what is already known about the random variable; for example a random variable may be defined in terms of its probability density function or by construction from other random variables. The context here is that of deriving algebraic expressions for the theoretical variance of a random variable, in contrast to questions of estimating the variance of a population from sample data for which there are special considerations in implementing computational algorithms.", "images": [], "links": ["Algorithms for calculating variance", "Bias (statistics)", "Christiaan Huygens", "Covariance", "Covariance matrix", "Cross-covariance", "Digital object identifier", "Donald E. Knuth", "Expected value", "International Standard Book Number", "Jakob Steiner", "Johann Samuel K\u00f6nig", "Loss of significance", "Probability density function", "Probability theory", "Random variable", "Random vector", "Standard deviation", "Statistical population", "Statistics", "The Art of Computer Programming", "Variance"], "references": ["http://dl.acm.org/citation.cfm?id=3221269.3223036", "http://doi.org/10.1145/3221269.3223036", "https://books.google.com/books?id=Hiw25tqvScsC&pg=PA50"]}, "Mean absolute error": {"categories": ["Errors and residuals", "Point estimation performance", "Statistical deviation and dispersion", "Time series"], "title": "Mean absolute error", "method": "Mean absolute error", "url": "https://en.wikipedia.org/wiki/Mean_absolute_error", "summary": "In statistics, mean absolute error (MAE) is a measure of difference between two continuous variables. Assume X and Y are variables of paired observations that express the same phenomenon. Examples of Y versus X include comparisons of predicted versus observed, subsequent time versus initial time, and one technique of measurement versus an alternative technique of measurement. Consider a scatter plot of n points, where point i has coordinates (xi, yi)... Mean Absolute Error (MAE) is the average vertical distance between each point and the identity line. MAE is also the average horizontal distance between each point and the identity line.\nThe Mean Absolute Error is given by:\n\n \n \n \n \n M\n A\n E\n \n =\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n |\n \n \n y\n \n i\n \n \n \u2212\n \n x\n \n i\n \n \n \n |\n \n \n n\n \n \n =\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n |\n \n e\n \n i\n \n \n |\n \n \n n\n \n \n .\n \n \n {\\displaystyle \\mathrm {MAE} ={\\frac {\\sum _{i=1}^{n}\\left|y_{i}-x_{i}\\right|}{n}}={\\frac {\\sum _{i=1}^{n}\\left|e_{i}\\right|}{n}}.}\n It is possible to express MAE as the sum of two components: Quantity Disagreement and Allocation Disagreement. Quantity Disagreement is the absolute value of the Mean Error. Allocation Disagreement is MAE minus Quantity Disagreement. The Mean Error is given by:\n\n \n \n \n \n M\n E\n \n =\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n y\n \n i\n \n \n \u2212\n \n x\n \n i\n \n \n \n n\n \n \n .\n \n \n {\\displaystyle \\mathrm {ME} ={\\frac {\\sum _{i=1}^{n}y_{i}-x_{i}}{n}}.}\n It is also possible to identify the types of difference by looking at an \n \n \n \n (\n x\n ,\n y\n )\n \n \n {\\displaystyle (x,y)}\n plot. Allocation difference exists if and only if points reside on both sides of the identity line. Quantity difference exists when the average of the X values does not equal the average of the Y values.\nMAE has a clear interpretation as the average absolute difference between yi and xi. Many researchers want to know this average difference because its interpretation is clear, but researchers frequently compute and misinterpret the Root Mean Squared Error (RMSE), which is not the average absolute error. \nAs the name suggests, the mean absolute error is an average of the absolute errors \n \n \n \n \n |\n \n \n e\n \n i\n \n \n \n |\n \n =\n \n |\n \n \n y\n \n i\n \n \n \u2212\n \n x\n \n i\n \n \n \n |\n \n \n \n {\\displaystyle |e_{i}|=|y_{i}-x_{i}|}\n , where \n \n \n \n \n y\n \n i\n \n \n \n \n {\\displaystyle y_{i}}\n is the prediction and \n \n \n \n \n x\n \n i\n \n \n \n \n {\\displaystyle x_{i}}\n the true value. Note that alternative formulations may include relative frequencies as weight factors. The mean absolute error uses the same scale as the data being measured. This is known as a scale-dependent accuracy measure and therefore cannot be used to make comparisons between series using different scales. The mean absolute error is a common measure of forecast error in time series analysis, where the terms \"mean absolute deviation\" is sometimes used in confusion with the more standard definition of mean absolute deviation. The same confusion exists more generally.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/5/55/MAE_example.png", "https://upload.wikimedia.org/wikipedia/en/archive/5/55/20170507184243%21MAE_example.png"], "links": ["Average absolute deviation", "Digital object identifier", "Forecast error", "Identity line", "International Standard Book Number", "K-medians clustering", "Least absolute deviations", "Least squares", "Mean absolute deviation", "Mean absolute difference", "Mean absolute percentage error", "Mean absolute scaled error", "Mean percentage error", "Mean signed difference", "Mean squared error", "Multivariate median", "Random variable", "Root Mean Squared Error", "Spatial median", "Statistics", "Symmetric mean absolute percentage error", "Time series analysis"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.154.9771&rep=rep1&type=pdf", "http://doi.org/10.1007/s10651-007-0043-y", "http://doi.org/10.1080/13658810500286976", "http://doi.org/10.3354/cr030079", "https://www.otexts.org/fpp/2/5"]}, "JMulTi": {"categories": ["All articles needing additional references", "All articles with topics of unclear notability", "Articles needing additional references from October 2014", "Articles with multiple maintenance issues", "Articles with topics of unclear notability from October 2014", "Free econometrics software", "Free software programmed in Java (programming language)", "Pages using deprecated image syntax", "Products articles with topics of unclear notability", "Time series software"], "title": "JMulTi", "method": "JMulTi", "url": "https://en.wikipedia.org/wiki/JMulTi", "summary": "JMulTi is an open-source interactive software for econometric analysis, specialised in univariate and multivariate time series analysis. It has a Java graphical user interface.\nThe motivation for its designed was to provide the means by which some time-series econometric procedures that were difficult or unavailable in other packages could be undertaken. Such procedures include Impulse Response Analysis with bootstrapped confidence intervals for VAR/VEC modelling.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/3/31/Free_and_open-source_software_logo_%282009%29.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c7/JMulTi_icon.gif", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ADMB", "Analyse-it", "BMDP", "BV4.1 (software)", "CSPro", "Commercial software", "Comparison of statistical packages", "Computing platform", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "EViews", "Econometric analysis", "Econometrics software", "Epi Info", "Freeware", "GAUSS (software)", "GNU General Public License", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Graphical user interface", "Gretl", "H2O (software)", "JASP", "JMP (statistical software)", "Java (programming language)", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Linux", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Open-source", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "Time series", "UNISTAT", "VECM", "Vector autoregression", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://scholar.google.com/scholar?q=%22JMulTi%22", "http://www.google.com/search?&q=%22JMulTi%22+site:news.google.com/newspapers&source=newspapers", "http://www.google.com/search?as_eq=wikipedia&q=%22JMulTi%22&num=50", "http://www.google.com/search?tbm=nws&q=%22JMulTi%22+-wikipedia", "http://www.google.com/search?tbs=bks:1&q=%22JMulTi%22+-wikipedia", "http://www.jmulti.com/", "https://sourceforge.net/projects/jmulti/", "https://www.jstor.org/action/doBasicSearch?Query=%22JMulTi%22&acc=on&wc=on"]}, "G-network": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from February 2012", "Queueing theory"], "title": "G-network", "method": "G-network", "url": "https://en.wikipedia.org/wiki/G-network", "summary": "In queueing theory, a discipline within the mathematical theory of probability, a G-network (generalized queueing network or Gelenbe network) is an open network of G-queues first introduced by Erol Gelenbe as a model for queueing systems with specific control functions, such as traffic re-routing or traffic destruction, as well as a model for neural networks. A G-queue is a network of queues with several types of novel and useful customers:\n\npositive customers, which arrive from other queues or arrive externally as Poisson arrivals, and obey standard service and routing disciplines as in conventional network models,\nnegative customers, which arrive from another queue, or which arrive externally as Poisson arrivals, and remove (or 'kill') customers in a non-empty queue, representing the need to remove traffic when the network is congested, including the removal of \"batches\" of customers \n\"triggers\", which arrive from other queues or from outside the network, and which displace customers and move them to other queuesA product form solution superficially similar in form to Jackson's theorem, but which requires the solution of a system of non-linear equations for the traffic flows, exists for the stationary distribution of G-networks while the traffic equations of a G-network are in fact surprisingly non-linear, and the model does not obey partial balance. This broke previous assumptions that partial balance was a necessary condition for a product form solution. A powerful property of G-networks is that they are universal approximators for continuous and bounded functions, so that they can be used to approximate quite general input-output behaviours.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["802.11g", "Abstract Wiener space", "Actuarial mathematics", "Adversarial queueing network", "Arrival theorem", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "BCMP network", "Balance equation", "Bene\u0161 method", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burke's theorem", "Burkholder\u2013Davis\u2013Gundy inequalities", "Buzen's algorithm", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time Markov chain", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Erlang (unit)", "Erlang distribution", "Erol Gelenbe", "Exchangeable random variables", "Extreme value theory", "FIFO (computing and electronics)", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "First come first served", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "Fractional Brownian motion", "G/G/1 queue", "G/M/1 queue", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Gordon\u2013Newell theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heavy traffic approximation", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Information system", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "JSTOR", "Jackson's theorem (queueing theory)", "Jackson network", "Jump diffusion", "Jump process", "Kelly network", "Kendall's notation", "Kingman's formula", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "LIFO (computing)", "Laplace transform", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Layered queueing network", "Lindley equation", "List of inequalities", "List of stochastic processes topics", "Little's law", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "Loss network", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Markovian arrival process", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Matrix analytic method", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mean field theory", "Mean value analysis", "Message queue", "Mixing (mathematics)", "Moran process", "Moving-average model", "Network congestion", "Network scheduler", "Neural networks", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Peter G. Harrison", "Piecewise deterministic Markov process", "Pipeline (software)", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Poisson processes", "Pollaczek\u2013Khinchine formula", "Polling system", "Potts model", "Predictable process", "Probability theory", "Processor sharing", "Product-form solution", "Product form solution", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Quality of service", "Quasireversibility", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Rational arrival process", "Reflected Brownian motion", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Retrial queue", "Risk process", "Round-robin scheduling", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Scheduling (computing)", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Shortest job first", "Shortest remaining time", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Teletraffic engineering", "The Computer Journal", "Time reversibility", "Time series", "Time series analysis", "Traffic equations", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://doi.org/10.1016%2FS0166-5316(02)00127-X", "http://doi.org/10.1016%2FS0377-2217(99)00476-2", "http://doi.org/10.1017%2Fs0269964800002953", "http://doi.org/10.1093%2Fcomjnl%2Fbxp021", "http://doi.org/10.1109%2F72.737488", "http://doi.org/10.2307%2F3214499", "http://doi.org/10.2307%2F3214524", "http://doi.org/10.2307%2F3214781", "http://www.jstor.org/stable/3214499", "http://www.jstor.org/stable/3214524", "http://www.jstor.org/stable/3214781", "https://books.google.com/books?id=ClU2XG64UOIC&lpg=PA9&ots=RXnZw1Oo94&pg=PA9"]}, "Large deviations theory": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2011", "Asymptotic analysis", "Asymptotic theory (statistics)", "Large deviations theory", "Use dmy dates from June 2011"], "title": "Large deviations theory", "method": "Large deviations theory", "url": "https://en.wikipedia.org/wiki/Large_deviations_theory", "summary": "In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. While some basic ideas of the theory can be traced to Laplace, the formalization started with insurance mathematics, namely ruin theory with Cram\u00e9r and Lundberg. A unified formalization of large deviation theory was developed in 1966, in a paper by Varadhan. Large deviations theory formalizes the heuristic ideas of concentration of measures and widely generalizes the notion of convergence of probability measures.\nRoughly speaking, large deviations theory concerns itself with the exponential decline of the probability measures of certain kinds of extreme or tail events.", "images": [], "links": ["Aleksei Zinovyevich Petrov", "ArXiv", "Asymptotic equipartition property", "Bernoulli distribution", "Bernoulli entropy", "Bernoulli trial", "Bibcode", "Binomial coefficient", "Borel algebra", "Brownian motion", "Central limit theorem", "Chernoff's inequality", "Closure (topology)", "Communications on Pure and Applied Mathematics", "Contraction principle (large deviations theory)", "Convergence of measures", "Cram\u00e9r's large deviation theorem", "Cram\u00e9r's theorem (large deviations)", "Cumulant generating function", "D. Ruelle", "Digital object identifier", "Entropy", "Extreme value theory", "Filip Lundberg", "Freidlin\u2013Wentzell theorem", "Gromov\u2013Hausdorff convergence", "Harald Cram\u00e9r", "I.i.d.", "Information theory", "Interior (topology)", "International Standard Book Number", "It\u014d diffusion", "Kullback\u2013Leibler divergence", "Laplace's method", "Laplace principle (large deviations theory)", "Large deviation principle", "Large deviations of Gaussian random functions", "Law of large numbers", "Legendre\u2013Fenchel transformation", "Lower semicontinuous", "Mark Freidlin", "Markov chain", "Mathematical expectation", "Measurable set", "Normal distribution", "Oscar Lanford", "Pierre-Simon Laplace", "Polish space", "Power series", "Probability theory", "Pushforward measure", "Random variable", "Rate function", "Risk management", "Ruin theory", "S.R.S. Varadhan", "S. R. Srinivasa Varadhan", "Sanov's theorem", "Schilder's theorem", "Statistical mechanics", "Stirling approximation", "Thermodynamics", "Toshikazu Sunada", "Varadhan's lemma"], "references": ["http://adsabs.harvard.edu/abs/2009PhR...478....1T", "http://www.nps.edu/Academics/Schools/GSEAS/SRI/R37.pdf", "http://www.nps.edu/Academics/Schools/GSEAS/SRI/R41.pdf", "http://math.nyu.edu/faculty/varadhan/Spring2012/Chapters1-2.pdf", "http://arxiv.org/abs/0804.0327", "http://doi.org/10.1016%2Fj.physrep.2009.05.002", "http://www.cl.cam.ac.uk/Research/SRG/netos/old-projects/measure/tutorial/rev-tutorial.ps.gz", "https://math.nyu.edu/faculty/varadhan/wald.pdf", "https://arxiv.org/abs/0804.2330v1", "https://doi.org/10.1214%2F07-AOP348"]}, "Parallel coordinates": {"categories": ["CS1 maint: Multiple names: authors list", "CS1 maint: Uses editors parameter", "Data visualization", "Multi-dimensional geometry", "Statistical charts and diagrams"], "title": "Parallel coordinates", "method": "Parallel coordinates", "url": "https://en.wikipedia.org/wiki/Parallel_coordinates", "summary": "Parallel coordinates are a common way of visualizing high-dimensional geometry and analyzing multivariate data.\nTo show a set of points in an n-dimensional space, a backdrop is drawn consisting of n parallel lines, typically vertical and equally spaced. A point in n-dimensional space is represented as a polyline with vertices on the parallel axes; the position of the vertex on the i-th axis corresponds to the i-th coordinate of the point.\nThis visualization is closely related to time series visualization, except that it is applied to data where the axes do not correspond to points in time, and therefore do not have a natural order. Therefore, different axis arrangements may be of interest.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/89/Ggobi-flea2.png", "https://upload.wikimedia.org/wikipedia/commons/5/5c/Parallel_coordinates-sample.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/ParCorFisherIris.png"], "links": ["Air traffic control", "Alfred Inselberg", "Andrews plot", "Computer vision", "Coordinate", "D3.js", "Data mining", "Digital object identifier", "Dimensions", "ELKI", "Edinburgh", "Euclidian space", "GGobi", "GPL", "Geometry", "Hans-Peter Kriegel", "High-dimensional", "International Standard Book Number", "Intrusion detection system", "JSTOR", "Macrofocus High-D", "Matplotlib", "Minimum spanning tree", "Mondrian data analysis", "Multivariate data", "N-dimensional space", "Napier University", "Orange (software)", "Pandas (software)", "Parallel (geometry)", "Philbert Maurice d'Ocagne", "Point (geometry)", "Polar coordinates", "Polyline", "Process control", "Projective space", "Protovis.js", "Python (programming language)", "ROOT", "R (programming language)", "Radar chart", "SIGMOD", "Time series", "Traffic collision avoidance system", "UK", "University of Newcastle upon Tyne", "Vertex (geometry)"], "references": ["http://www.davidrumsey.com/luna/servlet/detail/RUMSEY~8~1~32803~1152181:General-summary,-showing-the-rank-o?sort=Pub_Date,Pub_List_No_InitialSort&qvq=q:List_No%3D'4521.152'%22%2B;sort:Pub_Date,Pub_List_No_InitialSort;lc:RUMSEY~8~1&mi=0&trs=1", "http://exposedata.com/parallel/", "http://www.high-d.com/", "http://www.ichrome.com/grapheme", "http://www.r-statistics.com/2010/06/clustergram-visualization-and-diagnostics-for-cluster-analysis-r-code/", "http://www.sliversoftware.com/", "http://forums.visokio.com/discussion/2136/radar-view-2.8-#parallel_coordinates", "http://herakles.zcu.cz/seminars/docs/infovis/papers/Moustafa_generalized_parallel_coordinates.pdf", "http://davis.wpi.edu/xmdv/vis_parcoord.html", "http://davis.wpi.edu/~xmdv/docs/tr0313_osf.pdf", "http://cda.ornl.gov/projects/eden/", "http://www.cs.tau.ac.il/~aiisreal", "http://doi.org/10.1007%2FBF01898350", "http://doi.org/10.1145%2F2463676.2463696", "http://eagereyes.org/techniques/parallel-coordinates", "http://www.ggobi.org/docs/parallel-coordinates//", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=636793", "http://www.jstor.org/stable/2528964", "http://bl.ocks.org/1341281", "http://bl.ocks.org/syntagmatic", "http://pandas.pydata.org/pandas-docs/version/0.13.1/visualization.html#parallel-coordinates", "http://www.xdat.org/", "http://www.agocg.ac.uk/reports/visual/casestud/brunsdon/abstract.htm", "http://www.dcs.napier.ac.uk/~marting/parCoord/GrahamKennedyParallelCurvesIV03.pdf", "https://mbostock.github.com/d3/talk/20111116/iris-parallel.html", "https://mbostock.github.com/protovis/ex/cars.html", "https://syntagmatic.github.com/parallel-coordinates/", "https://archive.org/details/coordonnesparal00ocaggoog", "https://web.archive.org/web/20131224111246/http://herakles.zcu.cz/seminars/docs/infovis/papers/Moustafa_generalized_parallel_coordinates.pdf", "https://diglib.eg.org/handle/10.2312/conf.EG2013.stars.095-116", "https://cran.r-project.org/web/packages/GGally/index.html"]}, "High-dimensional statistics": {"categories": ["Functional analysis", "Multivariate statistics", "Probability theory"], "title": "High-dimensional statistics", "method": "High-dimensional statistics", "url": "https://en.wikipedia.org/wiki/High-dimensional_statistics", "summary": "In statistical theory, the field of high-dimensional statistics studies data whose dimension is larger than dimensions considered in classical multivariate analysis. High-dimensional statistics relies on the theory of random vectors. In many applications, the dimension of the data vectors may be larger than the sample size.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Consistency (statistics)", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random element", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sara van de Geer", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "To How Many Simultaneous Hypothesis Tests Can Normal, Student's t or Bootstrap Calibration Be Applied", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "\u0160id\u00e1k correction for t-test"], "references": ["http://onlinelibrary.wiley.com/doi/10.1002/sim.6418/abstract", "http://arxiv.org/abs/math/0701003", "http://doi.org/10.1002%2Fsim.6418", "http://doi.org/10.1198%2F016214507000000969", "http://hd-stat.narod.ru"]}, "Percentage point": {"categories": ["Mathematical terminology", "Probability assessment", "Units of measurement"], "title": "Percentage point", "method": "Percentage point", "url": "https://en.wikipedia.org/wiki/Percentage_point", "summary": "A percentage point or percent point is the unit for the arithmetic difference of two percentages. For example, moving up from 40% to 44% is a 4 percentage point increase, but is an actual 10 percent increase in what is being measured. In the literature, the percentage point unit is usually either written out, or abbreviated as pp or p.p. to avoid ambiguity. After the first occurrence, some writers abbreviate by using just \"point\" or \"points\".\nConsider the following hypothetical example: In 1980, 50 percent of the population smoked, and in 1990 only 40 percent smoked. One can thus say that from 1980 to 1990, the prevalence of smoking decreased by 10 percentage points although smoking did not decrease by 10 percent (it decreased by 20 percent) \u2013 percentages indicate ratios, not differences.\nPercentage-point differences are one way to express a risk or probability. Consider a drug that cures a given disease in 70 percent of all cases, while without the drug, the disease heals spontaneously in only 50 percent of cases. The drug reduces absolute risk by 20 percentage points. Alternatives may be more meaningful to consumers of statistics, such as the reciprocal, also known as the number needed to treat (NNT). In this case, the reciprocal transform of the percentage-point difference would be 1/(20pp) = 1/0.20 = 5. Thus if 5 patients are treated with the drug, one could expect to heal one more case of the disease than would have occurred in the absence of the drug.\nFor measurements involving percentages as a unit, such as, growth, yield, or ejection fraction, statistical deviations and related descriptive statistics, including the standard deviation and root-mean-square error, the result should be expressed in units of percentage points instead of percentage. Mistakenly using percentage as the unit for the standard deviation is confusing, since percentage is also used as a unit for the relative standard deviation, i.e. standard deviation divided by average value (coefficient of variation).", "images": [], "links": ["Baker percentage", "Basis point", "Coefficient of variation", "Descriptive statistics", "Difference (mathematics)", "Ejection fraction", "International Standard Book Number", "Multiplicative inverse", "Number needed to treat", "Parts-per notation", "Percent point", "Percent point function", "Percentage", "Permille", "Probabilities", "Relative standard deviation", "Root-mean-square error", "Standard deviation", "Statistical deviation", "Unit (measurement)", "Yield (finance)"], "references": ["https://books.google.com/?id=RYtYmMD2ReAC&lpg=PP1&dq=textbook%20mathematics%20%22percentage%20points%22&pg=PA30#v=onepage&q=points&f=false", "https://books.google.com/?id=jSsHAAAAQBAJ&lpg=PA190&dq=percentage%20points&pg=PA190#v=onepage&q=percentage%20points&f=false", "https://web.archive.org/web/20150518123538/https://books.google.co.uk/books?id=RYtYmMD2ReAC&lpg=PP1&dq=textbook%20mathematics%20%22percentage%20points%22&hl=no&pg=PA30#v=onepage&q=points&f=false", "https://web.archive.org/web/20150518123546/https://books.google.co.uk/books?id=jSsHAAAAQBAJ&lpg=PA190&dq=percentage%20points&hl=no&pg=PA190#v=onepage&q=percentage%20points&f=false"]}, "Sliced inverse regression": {"categories": ["All articles with style issues", "Dimension reduction", "Regression analysis", "Wikipedia articles with style issues from December 2009"], "title": "Sliced inverse regression", "method": "Sliced inverse regression", "url": "https://en.wikipedia.org/wiki/Sliced_inverse_regression", "summary": "Sliced inverse regression (SIR) is a tool for dimension reduction in the field of multivariate statistics.\nIn statistics, regression analysis is a popular way of studying the relationship between a response variable y and its explanatory variable \n \n \n \n \n \n x\n _\n \n \n \n \n {\\displaystyle {\\underline {x}}}\n , which is a p-dimensional vector. There are several approaches which come under the term of regression. For example parametric methods include multiple linear regression; non-parametric techniques include local smoothing.\nWith high-dimensional data (as p grows), the number of observations needed to use local smoothing methods escalates exponentially. Reducing the number of dimensions makes the operation computable. Dimension reduction aims to show only the most important directions of the data. SIR uses the inverse regression curve, \n \n \n \n E\n (\n \n \n x\n _\n \n \n \n \n |\n \n \n y\n )\n \n \n {\\displaystyle E({\\underline {x}}\\,|\\,y)}\n to perform a weighted principal component analysis, with which one identifies the effective dimension reducing directions.\nThis article first introduces the reader to the subject of dimension reduction and how it is performed using the model here. There is then a short review on inverse regression, which later brings these pieces together.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Curse of dimensionality", "Dimension reduction", "International Standard Book Number", "Journal of the American Statistical Association", "Local smoothing", "Multivariate statistics", "Regression analysis", "Statistics"], "references": ["http://teachwiki.wiwi.hu-berlin.de/index.php/Basic_Linear_Algebra_and_Gram-Schmidt_Orthogonalization%7CBasic", "https://www.jstor.org/stable/2290563", "https://www.jstor.org/stable/2290564"]}, "Morisita's overlap index": {"categories": ["All articles with unsourced statements", "All stub articles", "Articles with unsourced statements from February 2012", "Ecological metrics", "Population ecology", "Statistics stubs"], "title": "Morisita's overlap index", "method": "Morisita's overlap index", "url": "https://en.wikipedia.org/wiki/Morisita%27s_overlap_index", "summary": "Morisita's overlap index, named after Masaaki Morisita, is a statistical measure of dispersion of individuals in a population. It is used to compare overlap among samples (Morisita 1959). This formula is based on the assumption that increasing the size of the samples will increase the diversity because it will include different habitats (i.e. different faunas).\nFormula:\n\n \n \n \n \n C\n \n D\n \n \n =\n \n \n \n 2\n \n \u2211\n \n i\n =\n 1\n \n \n S\n \n \n \n x\n \n i\n \n \n \n y\n \n i\n \n \n \n \n (\n \n D\n \n x\n \n \n +\n \n D\n \n y\n \n \n )\n X\n Y\n \n \n \n \n \n {\\displaystyle C_{D}={\\frac {2\\sum _{i=1}^{S}x_{i}y_{i}}{(D_{x}+D_{y})XY}}}\n xi is the number of times species i is represented in the total X from one sample.\nyi is the number of times species i is represented in the total Y from another sample.\nDx and Dy are the Simpson's index values for the x and y samples respectively.\nS is the number of unique speciesCD = 0 if the two samples do not overlap in terms of species, and CD = 1 if the species occur in the same proportions in both samples.Horn's modification of the index is (Horn 1966):\n\n \n \n \n \n C\n \n H\n \n \n =\n \n \n \n 2\n \n \u2211\n \n i\n =\n 1\n \n \n S\n \n \n \n x\n \n i\n \n \n \n y\n \n i\n \n \n \n \n \n (\n \n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n S\n \n \n \n x\n \n i\n \n \n 2\n \n \n \n \n X\n \n 2\n \n \n \n \n +\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n S\n \n \n \n y\n \n i\n \n \n 2\n \n \n \n \n Y\n \n 2\n \n \n \n \n \n )\n \n X\n Y\n \n \n \n \n .\n \n \n {\\displaystyle C_{H}={\\frac {2\\sum _{i=1}^{S}x_{i}y_{i}}{\\left({\\sum _{i=1}^{S}x_{i}^{2} \\over X^{2}}+{\\sum _{i=1}^{S}y_{i}^{2} \\over Y^{2}}\\right)XY}}\\,.}", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Dispersion (statistics)", "JSTOR", "Kyushu University", "Sample (statistics)", "Simpson's index", "Statistics"], "references": ["http://www.morisita.or.jp", "https://web.archive.org/web/20100324130601/http://www.tnstate.edu/ganter/B412%20Ch%2015&16%20CommMetric.html", "https://www.jstor.org/stable/1936817", "https://www.jstor.org/stable/2424587", "https://www.jstor.org/stable/2459242", "https://www.jstor.org/stable/4045"]}, "Logistic function": {"categories": ["Articles containing Ancient Greek-language text", "Articles containing French-language text", "Curves", "Differential equations", "Logistic regression", "Population", "Population ecology", "Special functions"], "title": "Logistic function", "method": "Logistic function", "url": "https://en.wikipedia.org/wiki/Logistic_function", "summary": "A logistic function or logistic curve is a common \"S\" shape (sigmoid curve), with equation:\n\n \n \n \n f\n (\n x\n )\n =\n \n \n L\n \n 1\n +\n \n e\n \n \u2212\n k\n (\n x\n \u2212\n \n x\n \n 0\n \n \n )\n \n \n \n \n \n \n \n {\\displaystyle f(x)={\\frac {L}{1+e^{-k(x-x_{0})}}}}\n where\n\ne = the natural logarithm base (also known as Euler's number),\nx0 = the x-value of the sigmoid's midpoint,\nL = the curve's maximum value, and\nk = the logistic growth rate or steepness of the curve.For values of x in the domain of real numbers from \u2212\u221e to +\u221e, the S-curve shown on the right is obtained, with the graph of f approaching L as x approaches +\u221e and approaching zero as x approaches \u2212\u221e.\nThe logistic function finds applications in a range of fields, including artificial neural networks, biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, and statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/05/Barley_S-curve.png", "https://upload.wikimedia.org/wikipedia/commons/8/84/Courbe_logistique%2C_Verhulst%2C_1845.png", "https://upload.wikimedia.org/wikipedia/commons/8/88/Logistic-curve.svg", "https://upload.wikimedia.org/wikipedia/commons/0/04/Pierre_Francois_Verhulst.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/9a/Sugarcane_S-curve.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Alfred J. Lotka", "An Essay on the Principle of Population", "Ancient Greek language", "Anderson Gray McKendrick", "Antiderivative", "ArXiv", "Arithmetic", "Arithmetic growth", "Artificial neural network", "Artificial neuron", "Autocatalysis", "Backpropagation", "Bernoulli differential equation", "Bibcode", "Biological life cycle", "Biology", "Biomathematics", "Boundary condition", "Carrying capacity", "Cars", "Chemistry", "Constant of integration", "Continuum (theory)", "Cross fluid", "Cumulative distribution function", "Demography", "Derivative", "Differential equation", "Diffusion bonding", "Diffusion of innovations", "Digital object identifier", "Dimensional analysis", "E (mathematical constant)", "Ecology", "Economics", "Electrification", "Elo rating system", "Eric W. Weisstein", "Even function", "Explanatory variables", "Exponential curve", "Exponential function", "Exponential growth", "Fermi function", "French language", "Gabriel Tarde", "Generalised logistic curve", "Generalized logistic curve", "Geometric growth", "Geoscience", "Gompertz curve", "Greek mathematics", "Heaviside step function", "Hubbert curve", "Hyperbolic tangent", "IIASA", "Integration by substitution", "International Standard Book Number", "Item response theory", "Johns Hopkins University", "Kondratiev wave", "Language change", "Linear combination", "Linguistics", "Log-likelihood ratio", "Log-linear model", "Logarithmic curve", "Logistic distribution", "Logistic map", "Logistic regression", "Logistics", "Logit", "Louis Charles Karpinski", "Lowell Reed", "Machine learning", "Malthusian growth model", "MathWorld", "Mathematical psychology", "Maximum likelihood", "Multinomial logistic regression", "Natural logarithm", "Natural selection", "Neural network", "Nonlinearity", "Odd function", "Odd functions", "Odds", "Ordinary differential equation", "PRIMUS (journal)", "Parabola", "Perceptron", "Phase line (mathematics)", "Pierre Fran\u00e7ois Verhulst", "Political science", "Population dynamics", "Population growth", "Population growth rate", "Probability", "Proceedings of the National Academy of Sciences of the United States of America", "Pythagoras", "R/K selection theory", "Ramp function", "Range (mathematics)", "Rasch model", "Raymond Pearl", "Real number", "Rectifier (neural networks)", "Robert Ayres (scientist)", "Romanization of Ancient Greek", "Segmented regression", "Shifted Gompertz distribution", "Sigmoid function", "Sociology", "Softmax activation function", "Softplus", "Soil salinity", "Species", "Star model", "Statistics", "Thomas Malthus", "Tipping point (sociology)", "Water table"], "references": ["http://www.iiasa.ac.at/Admin/PUB/Documents/RR-89-001.pdf", "http://www.iiasa.ac.at/Admin/PUB/Documents/XB-90-704.pdf", "http://yann.lecun.com/exdb/publis/pdf/lecun-98b.pdf", "http://www.sciencecodex.com/seeing_the_scurve_in_everything", "http://mathworld.wolfram.com/LogisticEquation.html", "http://mathworld.wolfram.com/SigmoidFunction.html", "http://page.mi.fu-berlin.de/rojas/neural/chapter/K11.pdf", "http://jsxgraph.uni-bayreuth.de/wiki/index.php/Logistic_process", "http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN129323640_0018&DMDID=dmdlog7", "http://math.bu.edu/people/mak/MA565/Pearl_Reed_PNAS_1920.pdf", "http://adsabs.harvard.edu/abs/2009PhyD..238.1752Y", "http://jeffreyfreeman.me/restricted-logarithmic-growth-with-injection/", "http://www.agci.org/dB/PDFs/03S2_CMarchetti_Cyclotymic.pdf", "http://arxiv.org/abs/0901.4714", "http://www.cesaremarchetti.org/archive/scan/MARCHETTI-037.pdf", "http://doi.org/10.1016%2Fj.physd.2009.05.011", "http://doi.org/10.1017%2FS0370164600025426", "http://doi.org/10.1080%2F10511979808965879", "http://www.inside-r.org/packages/cran/clusterPower/docs/expit", "http://rasch.org/rmt/rmt64k.htm", "https://books.google.com/?id=8GsEAAAAYAAJ", "https://www.sciencedaily.com/releases/2011/07/110720151541.htm", "https://gdz.sub.uni-goettingen.de/id/PPN129323640_0018?tify=%7B%22pages%22:%5B21%5D,%22view%22:%22info%22%7D", "https://gdz.sub.uni-goettingen.de/id/PPN129323640_0018?tify=%7B%22pages%22:%5B54%5D,%22panX%22:0.487,%22panY%22:0.616,%22view%22:%22info%22,%22zoom%22:0.592%7D", "https://gdz.sub.uni-goettingen.de/id/PPN129323640_0018?tify=%7B%22pages%22:%5B14%5D,%22view%22:%22info%22%7D", "https://www.waterlog.info/croptol.htm", "https://www.waterlog.info/cropwat.htm", "https://www.waterlog.info/segreg.htm", "https://www.waterlog.info/sigmoid.htm", "https://www.researchgate.net/publication/233238354_Math-alive_using_original_sources_to_teach_mathematics_in_social_context", "https://web.archive.org/web/20060914155939/http://luna.cas.usf.edu/~mbrannic/files/regression/Logistic.html", "https://arxiv.org/pdf/0901.4714", "https://babel.hathitrust.org/cgi/pt?id=mdp.39015005675411", "https://www.webcitation.org/68z5VsD7L?url=http://www.agci.org/dB/PDFs/03S2_CMarchetti_Cyclotymic.pdf"]}, "Box\u2013Cox transformation": {"categories": ["Normal distribution", "Statistical data transformation"], "title": "Power transform", "method": "Box\u2013Cox transformation", "url": "https://en.wikipedia.org/wiki/Power_transform", "summary": "In statistics, a power transform is a family of functions that are applied to create a monotonic transformation of data using power functions. This is a useful data transformation technique used to stabilize variance, make the data more normal distribution-like, improve the validity of measures of association such as the Pearson correlation between variables and for other data stabilization procedures.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/e/e1/BUPA_BoxCox.JPG"], "links": ["Alanine transaminase", "ArXiv", "Biometrika", "Box\u2013Cox distribution", "Cobb\u2013Douglas", "Confidence interval", "Consistency (statistics)", "Continuous function", "Cram\u00e9r\u2013Rao bound", "Data transformation (statistics)", "David Cox (statistician)", "Derivative", "Digital object identifier", "Dimensional analysis", "Econometrics", "Encyclopedia of Mathematics", "Epidemiology", "Errors and residuals in statistics", "Gamma-glutamyl transpeptidase", "Geometric mean", "George E. P. Box", "Histogram", "Homogeneous function", "International Standard Book Number", "JSTOR", "John Johnston (econometrician)", "Journal of the Royal Statistical Society", "Journal of the Royal Statistical Society, Series B", "Likelihood-ratio test", "Likelihood function", "Local asymptotic normality", "Mathematical Reviews", "Maximum likelihood", "Michiel Hazewinkel", "Monotonic function", "Morris H. DeGroot", "Normal distribution", "Pearson product-moment correlation coefficient", "Peter J. Bickel", "Power (mathematics)", "Power function", "Profile likelihood", "Q-Q plot", "Regression analysis", "Robust regression", "SOCR", "Scatterplot", "Sign function", "Statistics", "Time-series", "Truncated distribution", "Truncated normal distribution"], "references": ["http:ftp://ftp.ics.uci.edu/pub/machine-learning-databases/liver-disorders", "http://www.ime.usp.br/~abe/lista/pdfm9cJKUmFZp.pdf", "http://www.springerlink.com/content/mt81u60813077641/", "http://www.springerlink.com/content/y25q020x24602701/", "http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_PowerTransformFamily_Graphs", "http://wiki.stat.ucla.edu/socr/uploads/b/b8/PowerTransformFamily_Biometrica609.pdf", "http://portal.acm.org/citation.cfm?id=1172964.1173292&coll=&dl=acm&CFID=15151515&CFTOKEN=6184618", "http://www.ams.org/mathscinet-getitem?mr=0192611", "http://arxiv.org/abs/cond-mat/0606104", "http://doi.org/10.1007%2FBF01043245", "http://doi.org/10.1007%2Fs10910-005-9003-7", "http://doi.org/10.1080%2F01621459.1981.10477649", "http://doi.org/10.1111%2Fj.1467-9876.2005.00476.x", "http://doi.org/10.1214%2Fss%2F1177013223", "http://doi.org/10.2307%2F2348250", "http://www.encyclopediaofmath.org/index.php/Box%E2%80%93Cox_transformation", "http://www.jstor.org/stable/2348250", "http://www.jstor.org/stable/2673623", "http://www.jstor.org/stable/2984418", "https://www.stat.umn.edu/arc/yjpower.pdf", "https://www.encyclopediaofmath.org/index.php?title=B/b110790"]}, "Independent and identically distributed random variables": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from December 2009", "Articles with unsourced statements from February 2016", "Independence (probability theory)", "Statistical theory"], "title": "Independent and identically distributed random variables", "method": "Independent and identically distributed random variables", "url": "https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables", "summary": "In probability theory and statistics, a sequence or collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent. Identically distributed, on its own, is often abbreviated ID. For uniformity, as both are discussed\u2014and in widespread use\u2014this article uses the visually cleaner IID in preference to the more prevalent convention i.i.d.\nThe annotation IID is particularly common in statistics, where observations in a sample are often assumed to be effectively IID for the purposes of statistical inference. The assumption (or requirement) that observations be IID tends to simplify the underlying mathematics of many statistical methods (see mathematical statistics and statistical theory). However, in practical applications of statistical modeling the assumption may or may not be realistic. To test how realistic the assumption is on a given data set, the autocorrelation can be computed, lag plots drawn or turning point test performed.\nThe generalization of exchangeable random variables is often sufficient and more easily met.\nThe assumption is important in the classical form of the central limit theorem, which states that the probability distribution of the sum (or average) of IID variables with finite variance approaches a normal distribution.\nOften the IID assumption arises in the context of sequences of random variables. Then \"independent and identically distributed\" in part implies that an element in the sequence is independent of the random variables that came before it. In this way, an IID sequence is different from a Markov sequence, where the probability distribution for the nth random variable is a function of the previous random variable in the sequence (for a first order Markov sequence). An IID sequence does not imply the probabilities for all elements of the sample space or event space must be the same. For example, repeated throws of loaded dice will produce a sequence that is IID, despite the outcomes being biased.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bayesian statistics", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bruno de Finetti", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "De Finetti's theorem", "Deconvolution", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Discrete time", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "EPFL Press", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gambler's fallacy", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "IID", "IID (disambiguation)", "Iff", "Image processing", "Independence (probability theory)", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Joint probability distribution", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Lag plot", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Markov sequence", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mean", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Normal distribution", "Null hypothesis", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Permutation", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Roulette", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sample space", "Sampling without replacement", "Sanov's theorem", "Santa Fe Institute", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sequence", "Sigma-martingale", "Signal processing", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistical inference", "Statistical modeling", "Statistical sample", "Statistical theory", "Statistics", "Stochastic analysis", "Stochastic calculus", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "Symmetric group", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Turning point test", "Uniform integrability", "Usual hypotheses", "Variance", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "Z-test"], "references": ["http://infoscience.epfl.ch/record/146812/files/perfPublisherVersion.pdf", "http://tuvalu.santafe.edu/~aaronc/courses/7000/csci7000-001_2011_L0.pdf"]}, "Taguchi loss function": {"categories": ["Loss functions"], "title": "Taguchi loss function", "method": "Taguchi loss function", "url": "https://en.wikipedia.org/wiki/Taguchi_loss_function", "summary": "The Taguchi loss function is graphical depiction of loss developed by the Japanese business statistician Genichi Taguchi to describe a phenomenon affecting the value of products produced by a company. Praised by Dr. W. Edwards Deming (the business guru of the 1980s American quality movement), it made clear the concept that quality does not suddenly plummet when, for instance, a machinist exceeds a rigid blueprint tolerance. Instead 'loss' in value progressively increases as variation increases from the intended condition. This was considered a breakthrough in describing quality, and helped fuel the continuous improvement movement that since has become known as lean manufacturing.\nThe concept of Taguchi's quality loss function was in contrast with the American concept of quality, popularly known as goal post philosophy, the concept given by American quality guru Phil Crosby. Goal post philosophy emphasizes that if a product feature doesn't meet the designed specifications it is termed as a product of poor quality (rejected), irrespective of amount of deviation from the target value (mean value of tolerance zone). This concept has similarity with the concept of scoring a 'goal' in the game of football or hockey, because a goal is counted 'one' irrespective of the location of strike of the ball in the 'goal post', whether it is in the center or towards the corner. This means that if the product dimension goes out of the tolerance limit the quality of the product drops suddenly. \nThrough his concept of the quality loss function, Taguchi explained that from the customer's point of view this drop of quality is not sudden. The customer experiences a loss of quality the moment product specification deviates from the 'target value'. This 'loss' is depicted by a quality loss function and it follows a parabolic curve mathematically given by L = k(y\u2013m)2, where m is the theoretical 'target value' or 'mean value' and y is the actual size of the product, k is a constant and L is the loss. This means that if the difference between 'actual size' and 'target value' i.e. (y\u2013m) is large, loss would be more, irrespective of tolerance specifications. In Taguchi's view tolerance specifications are given by engineers and not by customers; what the customer experiences is 'loss'. This equation is true for a single product; if 'loss' is to be calculated for multiple products the loss function is given by L = k[S2 + (\n \n \n \n \n \n \n y\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {y}}}\n \u2013 m)2], where S2 is the 'variance of product size' and \n \n \n \n \n \n \n y\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {y}}}\n is the average product size.", "images": [], "links": ["Continuous improvement", "Genichi Taguchi", "International Standard Book Number", "Lean manufacturing", "Loss function", "Philip B. Crosby", "Quality (business)", "Taguchi methods", "W. Edwards Deming"], "references": []}, "Systematic sampling": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2012", "Sampling techniques"], "title": "Systematic sampling", "method": "Systematic sampling", "url": "https://en.wikipedia.org/wiki/Systematic_sampling", "summary": "Systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equiprobability method. In this approach, progression through the list is treated circularly, with a return to the top once the end of the list is passed. The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, the sampling interval (sometimes known as the skip): this is calculated as:\n\n \n \n \n k\n =\n \n \n N\n n\n \n \n \n \n {\\displaystyle k={\\frac {N}{n}}}\n where n is the sample size, and N is the population size.\nUsing this procedure each element in the population has a known and equal probability of selection. This makes systematic sampling functionally similar to simple random sampling (SRS). However it is not the same as SRS because not every possible sample of a certain size has an equal chance of being chosen (e.g. samples with at least two elements adjacent to each other will never be chosen by systematic sampling). It is however, much more efficient (if variance within systematic sample is more than variance of population).Systematic sampling is to be applied only if the given population is logically homogeneous, because systematic sample units are uniformly distributed over the population. The researcher must ensure that the chosen sampling interval does not hide a pattern. Any pattern would threaten randomness. \nExample: Suppose a supermarket wants to study buying habits of their customers, then using systematic sampling they can choose every 10th or 15th customer entering the supermarket and conduct the study on this sample.\nThis is random sampling with a system. From the sampling frame, a starting point is chosen at random, and choices thereafter are at regular intervals. For example, suppose you want to sample 8 houses from a street of 120 houses. 120/8=15, so every 15th house is chosen after a random starting point between 1 and 15. If the random starting point is 11, then the houses selected are 11, 26, 41, 56, 71, 86, 101, and 116. As an aside, if every 15th house was a \"corner house\" then this corner pattern could destroy the randomness of the sample. \nIf, as more frequently, the population is not evenly divisible (suppose you want to sample 8 houses out of 125, where 125/8=15.625), should you take every 15th house or every 16th house? If you take every 16th house, 8*16=128, so there is a risk that the last house chosen does not exist. On the other hand, if you take every 15th house, 8*15=120, so the last five houses will never be selected. The random starting point should instead be selected as a non integer between 0 and 15.625 (inclusive on one endpoint only) to ensure that every house has equal chance of being selected; the interval should now be non integral (15.625); and each non integer selected should be rounded up to the next integer. If the random starting point is 3.6, then the houses selected are 4, 20, 35, 50, 66, 82, 98, and 113, where there are 3 cyclic intervals of 15 and 4 intervals of 16.\nTo illustrate the danger of systematic skip concealing a pattern, suppose we were to sample a planned neighborhood where each street has ten houses on each block. This places houses No. 1, 10, 11, 20, 21, 30... on block corners; corner blocks may be less valuable, since more of their area is taken up by street front etc. that is unavailable for building purposes. If we then sample every 10th household, our sample will either be made up only of corner houses (if we start at 1 or 10) or have no corner houses (any other start); either way, it will not be representative.\nSystematic sampling may also be used with non-equal selection probabilities. In this case, rather than simply counting through elements of the population and selecting every kth unit, we allocate each element a space along a number line according to its selection probability. We then generate a random start from a uniform distribution between 0 and 1, and move along the number line in steps of 1.\nExample: We have a population of 5 units (A to E). We want to give unit A a 20% probability of selection, unit B a 40% probability, and so on up to unit E (100%). Assuming we maintain alphabetical order, we allocate each unit to the following interval:\n\nA: 0 to 0.2\nB: 0.2 to 0.6 (= 0.2 + 0.4)\nC: 0.6 to 1.2 (= 0.6 + 0.6)\nD: 1.2 to 2.0 (= 1.2 + 0.8)\nE: 2.0 to 3.0 (= 2.0 + 1.0)\n\nIf our random start was 0.156, we would first select the unit whose interval contains this number (i.e. A). Next, we would select the interval containing 1.156 (element C), then 2.156 (element E). If instead our random start was 0.350, we would select from points 0.350 (B), 1.350 (D), and 2.350 (E).\n\n", "images": [], "links": ["Equiprobability", "International Standard Book Number", "Number line", "Sampling frame", "Simple random sampling", "Statistical population", "Statistics"], "references": ["http://www.juliantrubin.com/encyclopedia/mathematics/dictionary_statistics.html", "http://trsl.sourceforge.net/"]}, "Variance": {"categories": ["All articles lacking in-text citations", "All articles with incomplete citations", "All articles with unsourced statements", "Articles containing proofs", "Articles lacking in-text citations from November 2018", "Articles with excessive see also sections from May 2017", "Articles with incomplete citations from March 2013", "Articles with inconsistent citation formats", "Articles with unsourced statements from February 2012", "Articles with unsourced statements from June 2015", "Articles with unsourced statements from September 2016", "CS1 maint: Uses authors parameter", "Moment (mathematics)", "Statistical deviation and dispersion", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Variance", "method": "Variance", "url": "https://en.wikipedia.org/wiki/Variance", "summary": "In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of (random) numbers are spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n {\\displaystyle \\sigma ^{2}}\n , \n \n \n \n \n s\n \n 2\n \n \n \n \n {\\displaystyle s^{2}}\n , or \n \n \n \n Var\n \u2061\n (\n X\n )\n \n \n {\\displaystyle \\operatorname {Var} (X)}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Comparison_standard_deviations.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/6/60/Scaled_chi_squared.svg", "https://upload.wikimedia.org/wikipedia/commons/9/97/Scaled_chi_squared_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/6/64/Variance_visualisation.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algebraic formula for the variance", "Algorithms for calculating variance", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average absolute deviation", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bessel's correction", "Bhatia\u2013Davis inequality", "Bias of an estimator", "Biased estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biometry", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box test", "Box\u2013Anderson test", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cantor distribution", "Capon test", "Cartography", "Catastrophic cancellation", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central moment", "Central tendency", "Characteristic function (probability theory)", "Chebyshev's inequality", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi square test", "CiteSeerX", "Classical mechanics", "Classical test theory", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinant", "Common-method variance", "Completeness (statistics)", "Complex conjugate", "Complex number", "Concave function", "Conditional expectation", "Conditional variance", "Confidence interval", "Confounding", "Conjugate transpose", "Consistent estimator", "Contingency table", "Continuous distribution", "Continuous probability distribution", "Continuous random variable", "Control chart", "Correlated", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Covariance matrix", "Credible interval", "Crime statistics", "Cronbach's alpha", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulative distribution function", "Data collection", "Data set", "Decomposition of time series", "Definite integral", "Degrees of freedom (statistics)", "Delta method", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Deviation (statistics)", "Dice", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete probability distribution", "Discrete random variable", "Distance variance", "Divergence (statistics)", "Downside risk", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation of covariance matrices", "Estimation theory", "Estimator", "Euclidean distance", "Excess kurtosis", "Expected value", "Experiment", "Explained variance", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "F test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Floating point arithmetic", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heavy-tailed distribution", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis testing", "Independence (probability theory)", "Index of dispersion", "Integrated Authority File", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Invariant (mathematics)", "Investment", "Ir\u00e9n\u00e9e-Jules Bienaym\u00e9", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen's inequality", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Klotz test", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Law of total variance", "Lehmann test", "Lehmann\u2013Scheff\u00e9 theorem", "Leo Goodman", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean absolute difference", "Mean absolute error", "Mean preserving spread", "Mean square error", "Mean squared error", "Measurement error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michel Lo\u00e8ve", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment-generating function", "Moment (mathematics)", "Moment (physics)", "Moment of inertia", "Moment of inertia tensor", "Monotone likelihood ratio", "Monte Carlo method", "Mood test", "Moses test", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Observations", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Pareto distribution", "Pareto index", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Pooled variance", "Popoviciu's inequality on variances", "Population (statistics)", "Population statistics", "Positive definite matrix", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability-generating function", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Proportional hazards model", "Psychometrics", "Qualitative variation", "Quality control", "Quantile function", "Quasi-experiment", "Quasi-variance", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raw moment", "Reduced chi-squared", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Root mean square deviation", "Run chart", "Sample (statistics)", "Sample covariance", "Sample mean", "Sample mean and covariance", "Sample median", "Sample size determination", "Sample standard deviation", "Sampling (statistics)", "Sampling distribution", "Samuelson's inequality", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Semivariance", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shrinkage estimator", "Sigma", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spearman\u2013Brown prediction formula", "Spectral density estimation", "Square root", "Squared deviations", "Standard deviation", "Standard error", "Standard error (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sukhatme test", "Sum of normally distributed random variables", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taylor's law", "Taylor expansion", "Taylor expansions for the moments of functions of random variables", "The Correlation Between Relatives on the Supposition of Mendelian Inheritance", "Time domain", "Time series", "Tolerance interval", "Trace (linear algebra)", "Transpose", "Trend estimation", "U-statistic", "Unbiased estimation of standard deviation", "Uncorrelated", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-covariance matrix", "Variance (disambiguation)", "Vector autoregression", "Vector space", "Wald test", "Wavelet", "Weighted mean", "Weighted variance", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15097/1/9.pdf", "http://www.mathstatica.com/book/Mathematical_Statistics_with_Mathematica.pdf", "http://mathworld.wolfram.com/SampleVarianceDistribution.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.551.9397", "http://www.ijpam.eu/contents/2005-21-3/10/10.pdf", "http://www.ijpam.eu/contents/2009-52-1/5/5.pdf", "http://gallica.bnf.fr/ark:/12148/bpt6k16411c/f166.image.n19", "http://visualiseur.bnf.fr/CadresFenetre?O=NUMM-2994&I=313", "http://sites.mathdoc.fr/JMPA/PDF/JMPA_1867_2_12_A10_0.pdf", "http://krishikosh.egranth.ac.in/bitstream/1/2025521/1/G2257.pdf", "http://doi.org/10.1006%2Fjmaa.1999.6688", "http://doi.org/10.1016%2FS0167-7152(98)00041-8", "http://doi.org/10.1080%2F01621459.1968.10480944", "http://doi.org/10.2307%2F2281592", "http://doi.org/10.7153%2Fjmi-02-11", "http://www.jstor.org/stable/2281592", "http://www.jstor.org/stable/2285901", "https://d-nb.info/gnd/4078739-4", "https://id.ndl.go.jp/auth/ndlna/00561029", "https://www.wikidata.org/wiki/Q175199"]}, "Semi-Markov process": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2012", "Markov processes"], "title": "Markov renewal process", "method": "Semi-Markov process", "url": "https://en.wikipedia.org/wiki/Markov_renewal_process", "summary": "In probability and statistics a Markov renewal process is a random process that generalizes the notion of Markov jump processes. Other random processes like Markov chain, Poisson process, and renewal process can be derived as a special case of an MRP (Markov renewal process).", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4a/Marked_point_process.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["CTMC", "Continuous-time Markov process", "DTMC", "Exponential distribution", "Hidden semi-Markov model", "International Standard Book Number", "Markov chain", "Markov process", "Markov property", "Poisson process", "Probability and statistics", "Renewal process", "Renewal theory", "Stochastic process", "Tuple", "Variable-order Markov model"], "references": []}, "Urn problem": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from June 2011", "Articles needing additional references from June 2011", "Probability problems", "Thought experiments"], "title": "Urn problem", "method": "Urn problem", "url": "https://en.wikipedia.org/wiki/Urn_problem", "summary": "In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawing one color or another, \nor some other properties. A number of important variations are described below.\nAn urn model is either a set of probabilities that describe events within an urn problem, or it is a probability distribution, or a family of such distributions, of random variables associated with urn problems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abraham de Moivre", "Ars Conjectandi", "Ballot box", "Ballots", "Balls into bins", "Beta-binomial model", "Binomial distribution", "Coin-tossing problem", "Coupon collector's problem", "Dirichlet-multinomial distribution", "Doge of Venice", "Election", "Ellsberg paradox", "Games of chance", "Geometric distribution", "Hoppe urn", "Hypergeometric distribution", "International Standard Book Number", "Inverse probability", "Italian language", "Jacob Bernoulli", "Latin", "Lottery", "Multinomial distribution", "Negative binomial distribution", "Noncentral hypergeometric distributions", "Probability", "Probability distribution", "Probability theory", "P\u00f3lya urn model", "Random variable", "Sortition", "Statistical physics", "Statistics", "Thomas Bayes", "Thought experiment", "Urn", "Venice"], "references": ["http://www.hpl.hp.com/techreports/2007/HPL-2007-28R1.html", "http://probabilityandstats.wordpress.com/2010/03/27/the-occupancy-problem/"]}, "Analysis of variance": {"categories": ["All articles with incomplete citations", "All articles with unsourced statements", "All pages needing factual verification", "Analysis of variance", "Articles with incomplete citations from November 2012", "Articles with unsourced statements from August 2011", "Articles with unsourced statements from May 2011", "Articles with unsourced statements from October 2013", "Commons category link is on Wikidata", "Design of experiments", "Parametric statistics", "Statistical tests", "Use dmy dates from June 2013", "Webarchive template wayback links", "Wikipedia articles needing factual verification from December 2014", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from November 2014"], "title": "Analysis of variance", "method": "Analysis of variance", "url": "https://en.wikipedia.org/wiki/Analysis_of_variance", "summary": "Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the \"variation\" among and between groups) used to analyze the differences among group means in a sample. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher. In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether the population means of several groups are equal, and therefore generalizes the t-test to more than two groups. ANOVA is useful for comparing (testing) three or more group means for statistical significance. It is conceptually similar to multiple two-sample t-tests, but is more conservative, resulting in fewer type I errors, and is therefore suited to a wide range of practical problems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/80/ANOVA_fair_fit.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/af/ANOVA_very_good_fit.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/4b/Anova%2C_no_fit..png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["AMOVA", "ANORVA", "ANOVA-simultaneous component analysis", "ANOVA on ranks", "A priori and a posteriori", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Anderson\u2013Darling test", "ArXiv", "Arithmetic mean", "Asymptomatic carrier", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Auxology", "Bachelor of Science in Public Health", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavior change (public health)", "Behavioural change theories", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biological hazard", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Carl Friedrich Gauss", "Carl Rogers Darnall", "Cartography", "Case\u2013control study", "Categorical variable", "Census", "Centers for Disease Control and Prevention", "Central composite design", "Central limit theorem", "Central tendency", "Charles Sanders Peirce", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chief Medical Officer", "Child mortality", "CiteSeerX", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coding (social sciences)", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Community health", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contraposition", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Council on Education for Public Health", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Cultural competence in health care", "Data collection", "David A. Freedman (statistician)", "David R. Cox", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Deviance (sociology)", "Dickey\u2013Fuller test", "Diffusion of innovations", "Digital object identifier", "Disease surveillance", "Divergence (statistics)", "Doctor of Public Health", "Dunnett's test", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Emergency sanitation", "Empirical distribution function", "Engineering statistics", "Environmental health", "Environmental statistics", "Epidemic", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Evolutionary biology", "Experiment", "Experimental design", "Experimental unit", "Explained variation", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "External validity", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Falsificationism", "Family planning", "Fan chart (statistics)", "Fecal\u2013oral route", "First-hitting-time model", "Fixed effects model", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Forest plot", "Fourier analysis", "Fractional factorial design", "Francis J. Anscombe", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Functional equation", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Genetically modified food", "Geographic information system", "Geometric mean", "George E. P. Box", "Geostatistics", "Germ theory of disease", "Global health", "Globalization and disease", "Glossary of experimental design", "Good agricultural practice", "Good manufacturing practice", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "HACCP", "Hand washing", "Handle System", "Harmonic mean", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human factors and ergonomics", "Human nutrition", "Hygiene", "ISO 22000", "Index of dispersion", "Infant mortality", "Infection control", "Injury prevention", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Iowa State University", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "John Snow (physician)", "Jonckheere's trend test", "Joseph Lister", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kruskal\u2013Wallis test", "Kurtosis", "L-moment", "Lack-of-fit sum of squares", "Latin hypercube sampling", "Latin square", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear model", "Linear regression", "Linear trend estimation", "List of epidemics", "List of fields of application of statistics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logarithm", "Logistic regression", "Longitudinal study", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Margaret Sanger", "Mary Mallon", "Maternal health", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical anthropology", "Medical sociology", "Medical statistics", "Mental health", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Ministry of Health and Family Welfare", "Missing data", "Mixed-design analysis of variance", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multiple comparisons problem", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Nancy M. Reid", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Notifiable disease", "Nuisance variable", "Null hypothesis", "Observational study", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Official statistics", "One- and two-tailed tests", "One-hot", "One-way ANOVA", "One-way analysis of variance", "Open defecation", "Opinion poll", "Optimal decision", "Optimal design", "Oral hygiene", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "P-value", "PRECEDE-PROCEED model", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Patient safety", "Patient safety organization", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Permutational analysis of variance", "Personal equation", "Pharmaceutical policy", "Pharmacovigilance", "Pie chart", "Pierre-Simon Laplace", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population health", "Population statistics", "Positive deviance", "Post-hoc analysis", "Posterior probability", "Power (statistics)", "Prediction interval", "Preventive healthcare", "Preventive nutrition", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Professional degrees of public health", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quality control", "Quarantine", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "ROC curve", "Race and health", "Radar chart", "Random assignment", "Random effect", "Random effects model", "Random variable", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative risk", "Reliability engineering", "Repeated measures", "Repeated measures design", "Replication (statistics)", "Reproductive health", "Resampling (statistics)", "Residual (statistics)", "Response surface methodology", "Response variable", "Restricted randomization", "Robust regression", "Robust statistics", "Ronald Fisher", "Rosemary A. Bailey", "Rothamsted Experimental Station", "Run chart", "SOCR", "Safe sex", "Sample (statistics)", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Sexually transmitted infection", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Social statistics", "Sociology of health and illness", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Methods for Research Workers", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical test", "Statistical theory", "Statistician", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sum of squares (statistics)", "Survey methodology", "Survey sampling", "Survival analysis", "Survival function", "System identification", "T-test", "Taguchi methods", "The Correlation Between Relatives on the Supposition of Mendelian Inheritance", "Theory of planned behavior", "Time domain", "Time series", "Tolerance interval", "Transtheoretical model", "Trend estimation", "Tropical disease", "Tukey's range test", "Tukey's test of additivity", "Two-way analysis of variance", "Type II errors", "Type I errors", "U-statistic", "Uniformly most powerful test", "United States Public Health Service", "V-statistic", "Vaccination", "Vaccine trial", "Validity (statistics)", "Variance", "Variance decomposition", "Vector autoregression", "Vector control", "Wald test", "Waterborne diseases", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "World Health Organization", "World Toilet Organization", "Z-test"], "references": ["http://www.library.adelaide.edu.au/digitised/fisher/15.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.120.4818", "http://www.socr.ucla.edu/htmls/ana/ANOVA1Way_Analysis.html", "http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_ANOVA_1Way", "http://www.ncbi.nlm.nih.gov/pubmed/19565683", "http://www.itl.nist.gov/div898/handbook/pmd/section3/pmd31.htm", "http://www.itl.nist.gov/div898/handbook/prc/section4/prc43.htm", "http://www.itl.nist.gov/div898/handbook/pri/section7/pri7.htm", "http://www.biomedicalstatistics.info/en/multiplegroups/one-way-anova.html", "http://hdl.handle.net/2440%2F15170", "http://www.ams.org/mathscinet-getitem?mr=0030181", "http://www.ams.org/mathscinet-getitem?mr=1604954", "http://www.ams.org/mathscinet-getitem?mr=2283455", "http://arxiv.org/abs/math/0504499", "http://doi.org/10.1017%2FS0021859600003750", "http://doi.org/10.1037%2F0003-066X.54.8.594", "http://doi.org/10.1037%2F0033-2909.112.1.155", "http://doi.org/10.1093%2Fbiomet%2F40.3-4.318", "http://doi.org/10.1093%2Fbiomet%2F6.1.1", "http://doi.org/10.1214%2F009053604000001048", "http://doi.org/10.1214%2Faoms%2F1177728717", "http://doi.org/10.1214%2Faoms%2F1177728786", "http://doi.org/10.2307%2F2984159", "http://www.jstor.org/stable/2333350", "http://www.jstor.org/stable/2984159", "http://www.maths.qmul.ac.uk/~rab/DOEbook", "http://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm", "https://getcalc.com/statistics-anova-calculator.htm", "https://web.archive.org/web/20010612211752/http://www.library.adelaide.edu.au/digitised/fisher/15.pdf", "https://web.archive.org/web/20141107211953/http://www.biomedicalstatistics.info/en/multiplegroups/one-way-anova.html", "https://web.archive.org/web/20150405053021/http://biostat.katerynakon.in.ua/en/multiplegroups/anova.html", "https://www.openintro.org/stat/textbook.php"]}, "Folded normal distribution": {"categories": ["Continuous distributions", "Normal distribution", "Pages using deprecated image syntax"], "title": "Folded normal distribution", "method": "Folded normal distribution", "url": "https://en.wikipedia.org/wiki/Folded_normal_distribution", "summary": "The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed random variable X with mean \u03bc and variance \u03c32, the random variable Y = |X| has a folded normal distribution. Such a case may be encountered if only the magnitude of some variable is recorded, but not its sign. The distribution is called \"folded\" because probability mass to the left of the x = 0 is folded over by taking the absolute value. In the physics of heat conduction, the folded normal distribution is a fundamental solution of the heat equation on the upper plane (i.e. a heat kernel).\nThe probability density function (PDF) is given by\n\n \n \n \n \n f\n \n Y\n \n \n (\n x\n ;\n \u03bc\n ,\n \n \u03c3\n \n 2\n \n \n )\n =\n \n \n 1\n \n 2\n \u03c0\n \n \u03c3\n \n 2\n \n \n \n \n \n \n \n e\n \n \u2212\n \n \n \n (\n x\n \u2212\n \u03bc\n \n )\n \n 2\n \n \n \n \n 2\n \n \u03c3\n \n 2\n \n \n \n \n \n \n \n +\n \n \n 1\n \n 2\n \u03c0\n \n \u03c3\n \n 2\n \n \n \n \n \n \n \n e\n \n \u2212\n \n \n \n (\n x\n +\n \u03bc\n \n )\n \n 2\n \n \n \n \n 2\n \n \u03c3\n \n 2\n \n \n \n \n \n \n \n \n \n {\\displaystyle f_{Y}(x;\\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}\\,e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}+{\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}\\,e^{-{\\frac {(x+\\mu )^{2}}{2\\sigma ^{2}}}}}\n for x\u22650, and 0 everywhere else. An alternative formulation is given by\n\n \n \n \n f\n \n (\n x\n )\n \n =\n \n \n \n 2\n \n \u03c0\n \n \u03c3\n \n 2\n \n \n \n \n \n \n \n e\n \n \u2212\n \n \n \n (\n \n \n x\n \n 2\n \n \n +\n \n \u03bc\n \n 2\n \n \n \n )\n \n \n 2\n \n \u03c3\n \n 2\n \n \n \n \n \n \n \n cosh\n \u2061\n \n \n (\n \n \n \n \u03bc\n x\n \n \n \u03c3\n \n 2\n \n \n \n \n )\n \n \n \n \n {\\displaystyle f\\left(x\\right)={\\sqrt {\\frac {2}{\\pi \\sigma ^{2}}}}e^{-{\\frac {\\left(x^{2}+\\mu ^{2}\\right)}{2\\sigma ^{2}}}}\\cosh {\\left({\\frac {\\mu x}{\\sigma ^{2}}}\\right)}}\n ,\nwhere cosh is the cosine Hyperbolic function. It follows that the cumulative distribution function (CDF) is given by:\n\n \n \n \n \n F\n \n Y\n \n \n (\n x\n ;\n \u03bc\n ,\n \n \u03c3\n \n 2\n \n \n )\n =\n \n \n 1\n 2\n \n \n \n [\n \n \n \n erf\n \n \n \n (\n \n \n \n x\n +\n \u03bc\n \n \n 2\n \n \u03c3\n \n 2\n \n \n \n \n \n )\n \n +\n \n \n erf\n \n \n \n (\n \n \n \n x\n \u2212\n \u03bc\n \n \n 2\n \n \u03c3\n \n 2\n \n \n \n \n \n )\n \n \n ]\n \n \n \n {\\displaystyle F_{Y}(x;\\mu ,\\sigma ^{2})={\\frac {1}{2}}\\left[{\\mbox{erf}}\\left({\\frac {x+\\mu }{\\sqrt {2\\sigma ^{2}}}}\\right)+{\\mbox{erf}}\\left({\\frac {x-\\mu }{\\sqrt {2\\sigma ^{2}}}}\\right)\\right]}\n for x\u22650, where erf() is the error function. This expression reduces to the CDF of the half-normal distribution when \u03bc = 0.\nThe mean of the folded distribution is then\n\n \n \n \n \n \u03bc\n \n Y\n \n \n =\n \u03c3\n \n \n \n 2\n \u03c0\n \n \n \n \n \n exp\n \u2061\n \n (\n \n \n \n \u2212\n \n \u03bc\n \n 2\n \n \n \n \n 2\n \n \u03c3\n \n 2\n \n \n \n \n \n )\n \n +\n \u03bc\n \n \n \n erf\n \n \n \n (\n \n \n \u03bc\n \n 2\n \n \u03c3\n \n 2\n \n \n \n \n \n )\n \n \n \n {\\displaystyle \\mu _{Y}=\\sigma {\\sqrt {\\frac {2}{\\pi }}}\\,\\,\\exp \\left({\\frac {-\\mu ^{2}}{2\\sigma ^{2}}}\\right)+\\mu \\,{\\mbox{erf}}\\left({\\frac {\\mu }{\\sqrt {2\\sigma ^{2}}}}\\right)}\n or\n\n \n \n \n \n \u03bc\n \n Y\n \n \n =\n \n \n \n 2\n \u03c0\n \n \n \n \u03c3\n \n e\n \n \u2212\n \n \n \n \u03bc\n \n 2\n \n \n \n 2\n \n \u03c3\n \n 2\n \n \n \n \n \n \n \n +\n \u03bc\n \n [\n \n 1\n \u2212\n 2\n \u03a6\n \n (\n \n \u2212\n \n \n \u03bc\n \u03c3\n \n \n \n )\n \n \n ]\n \n \n \n {\\displaystyle \\mu _{Y}={\\sqrt {\\frac {2}{\\pi }}}\\sigma e^{-{\\frac {\\mu ^{2}}{2\\sigma ^{2}}}}+\\mu \\left[1-2\\Phi \\left(-{\\frac {\\mu }{\\sigma }}\\right)\\right]}\n where \n \n \n \n \u03a6\n \n \n {\\displaystyle \\Phi }\n is the normal cumulative distribution function:\n\n \n \n \n \u03a6\n (\n x\n )\n \n =\n \n \n \n 1\n 2\n \n \n \n [\n \n 1\n +\n erf\n \u2061\n \n (\n \n \n x\n \n 2\n \n \n \n )\n \n \n ]\n \n .\n \n \n {\\displaystyle \\Phi (x)\\;=\\;{\\frac {1}{2}}\\left[1+\\operatorname {erf} \\left({\\frac {x}{\\sqrt {2}}}\\right)\\right].}\n The variance then is expressed easily in terms of the mean:\n\n \n \n \n \n \u03c3\n \n Y\n \n \n 2\n \n \n =\n \n \u03bc\n \n 2\n \n \n +\n \n \u03c3\n \n 2\n \n \n \u2212\n \n \u03bc\n \n Y\n \n \n 2\n \n \n .\n \n \n {\\displaystyle \\sigma _{Y}^{2}=\\mu ^{2}+\\sigma ^{2}-\\mu _{Y}^{2}.}\n Both the mean (\u03bc) and variance (\u03c32) of X in the original normal distribution can be interpreted as the location and scale parameters of Y in the folded distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Folded_normal_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/0/02/Folded_normal_pdf.svg"], "links": ["ARGUS distribution", "Absolute value", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Error function", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded-t distribution", "Folded cumulative distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heat conduction", "Heat equation", "Heat kernel", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic function", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal cumulative distribution function", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "R (programming language)", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://doi.org/10.1007%2Fs00170-003-2043-x", "http://doi.org/10.2307%2F1266560", "http://doi.org/10.2307%2F1266561", "http://doi.org/10.2307%2F1266622", "http://www.jstor.org/stable/1266560", "http://www.jstor.org/stable/1266561", "http://www.jstor.org/stable/1266622", "http://www.randomservices.org/random/special/FoldedNormal.html"]}, "Generalized expected utility": {"categories": ["All stub articles", "Economics and finance stubs", "Expected utility", "Motivation", "Optimal decisions"], "title": "Generalized expected utility", "method": "Generalized expected utility", "url": "https://en.wikipedia.org/wiki/Generalized_expected_utility", "summary": "Generalized expected utility is a decision-making metric based on any of a variety of theories that attempt to resolve some discrepancies between expected utility theory and empirical observations, concerning choice under risky (probabilistic) circumstances.\nThe expected utility model developed by John von Neumann and Oskar Morgenstern dominated decision theory from its formulation in 1944 until the late 1970s, not only as a prescriptive, but also as a descriptive model, despite powerful criticism from Maurice Allais and Daniel Ellsberg who showed that, in certain choice problems, decisions were usually inconsistent with the axioms of expected utility theory. These problems are usually referred to as the Allais paradox and Ellsberg paradox.\nBeginning in 1979 with the publication of the prospect theory of Daniel Kahneman and Amos Tversky, a range of generalized expected utility models were developed with the aim of resolving the Allais and Ellsberg paradoxes, while maintaining many of the attractive properties of expected utility theory.\nImportant examples were anticipated utility theory, later referred to as rank-dependent utility theory, weighted utility (Chew 1982), and expected uncertain utility theory. A general representation, using the concept of the local utility function was presented by Mark J. Machina. Since then, generalizations of expected utility theory have proliferated, but the probably most frequently used model is nowadays cumulative prospect theory, a rank-dependent development of prospect theory, introduced in 1992 by Daniel Kahneman and Amos Tversky.\nGiven its motivations and approach, generalized expected utility theory may properly be regarded as a subfield of behavioral economics, but it is more frequently located within mainstream economic theory.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/29/ThreeCoins.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/2/29/20180705065644%21ThreeCoins.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/2/29/20081006162233%21ThreeCoins.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/2/29/20081006161859%21ThreeCoins.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/2/29/20081006153702%21ThreeCoins.svg"], "links": ["Allais paradox", "Amos Tversky", "Behavioral economics", "Cumulative prospect theory", "Daniel Ellsberg", "Daniel Kahneman", "Decision theory", "Descriptive", "Digital object identifier", "Econometrica", "Economic theory", "Economics", "Ellsberg paradox", "Empirical observation", "Expected utility theory", "JSTOR", "John Quiggin", "John von Neumann", "Mark J. Machina", "Maurice Allais", "Oskar Morgenstern", "Prescriptive", "Prospect theory", "Rank-dependent expected utility", "Risk (statistics)"], "references": ["http://www.dklevine.com/archive/refs4122247000000002185.pdf", "http://doi.org/10.1016%2F0167-2681(82)90008-7", "http://www.jstor.org/stable/1912631"]}, "Predictive inference": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from November 2011", "Statistical inference"], "title": "Predictive inference", "method": "Predictive inference", "url": "https://en.wikipedia.org/wiki/Predictive_inference", "summary": "Predictive inference is an approach to statistical inference that emphasizes the prediction of future observations based on past observations.\nInitially, predictive inference was based on observable parameters and it was the main purpose of studying probability, but it fell out of favor in the 20th century due to a new parametric approach pioneered by Bruno de Finetti. The approach modeled phenomena as a physical system observed with error (e.g., celestial mechanics). De Finetti's idea of exchangeability\u2014that future observations should behave like past observations\u2014came to the attention of the English-speaking world with the 1974 translation from French of his 1937 paper, and has since been propounded by such statisticians as Seymour Geisser.", "images": [], "links": ["Bruno de Finetti", "Celestial mechanics", "Digital object identifier", "Exchangeability", "International Standard Book Number", "International Standard Serial Number", "Prediction", "Prediction interval", "Predictive analytics", "Probability", "Seymour Geisser", "Statistical inference"], "references": ["http://doi.org/10.1007%2F978-1-4612-0919-5_10", "http://www.worldcat.org/issn/0365-320X", "https://books.google.com/books?id=wfdlBZ_iwZoC"]}, "Watterson estimator": {"categories": ["All Wikipedia articles needing context", "All pages needing cleanup", "Population genetics", "Statistical genetics", "Wikipedia articles needing context from October 2009", "Wikipedia introduction cleanup from October 2009"], "title": "Watterson estimator", "method": "Watterson estimator", "url": "https://en.wikipedia.org/wiki/Watterson_estimator", "summary": "In population genetics, the Watterson estimator is a method for describing the genetic diversity in a population. It is estimated by counting the number of polymorphic sites. It is a measure of the \"population mutation rate\" (the product of the effective population size and the neutral mutation rate) from the observed nucleotide diversity of a population. \n \n \n \n \u03b8\n =\n 4\n \n N\n \n e\n \n \n \u03bc\n \n \n {\\displaystyle \\theta =4N_{e}\\mu }\n , where \n \n \n \n \n N\n \n e\n \n \n \n \n {\\displaystyle N_{e}}\n is the effective population size and \n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n is the per-generation mutation rate of the population of interest (Watterson (1975) ). The assumptions made are that there is a sample of \n \n \n \n n\n \n \n {\\displaystyle n}\n haploid individuals from the population of interest, that there are infinitely many sites capable of varying (so that mutations never overlay or reverse one another), and that \n \n \n \n n\n \u226a\n \n N\n \n e\n \n \n \n \n {\\displaystyle n\\ll N_{e}}\n .\nBecause the number of segregating sites counted will increase with the number of sequences looked at, the correction factor \n \n \n \n \n a\n \n n\n \n \n \n \n {\\displaystyle a_{n}}\n is used.\nThe estimate of \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n , often denoted as \n \n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n w\n \n \n \n \n \n {\\displaystyle {{\\hat {\\theta }}_{w}}}\n , is\n\n \n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n w\n \n \n \n =\n \n \n K\n \n a\n \n n\n \n \n \n \n ,\n \n \n {\\displaystyle {{\\hat {\\theta }}_{w}}={K \\over a_{n}},}\n where \n \n \n \n K\n \n \n {\\displaystyle K}\n is the number of segregating sites (an example of a segregating site would be a single-nucleotide polymorphism) in the sample and \n\n \n \n \n \n a\n \n n\n \n \n =\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \u2212\n 1\n \n \n \n \n 1\n i\n \n \n \n \n {\\displaystyle a_{n}=\\sum _{i=1}^{n-1}{1 \\over i}}\n is the \n \n \n \n (\n n\n \u2212\n 1\n )\n \n \n {\\displaystyle (n-1)}\n th harmonic number.\nThis estimate is based on coalescent theory. Watterson's estimator is commonly used for its simplicity. When its assumptions are met, the estimator is unbiased and the variance of the estimator decreases with increasing sample size or recombination rate. However, the estimator can be biased by population structure. For example, \n \n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n w\n \n \n \n \n \n {\\displaystyle {{\\hat {\\theta }}_{w}}}\n is downwardly biased in an exponentially growing population. It can also be biased by violation of the infinite-sites mutational model; if multiple mutations can overwrite one another, Watterson's estimator will be biased downward.\nComparing the value of the Watterson's estimator, to nucleotide diversity is the basis of Tajima's D which allows inference of the evolutionary regime of a given locus.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Bias of an estimator", "Coalescent theory", "Coupon collector's problem", "Digital object identifier", "Effective population size", "Ewens sampling formula", "Exponential growth", "Genetic diversity", "Haploid", "Harmonic number", "Mutation rate", "Population genetics", "PubMed Identifier", "Single-nucleotide polymorphism", "Tajima's D", "Variance"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/1145509", "http://doi.org/10.1016/0040-5809(75)90020-9"]}, "Relevance vector machine": {"categories": ["Classification algorithms", "Kernel methods for machine learning", "Nonparametric Bayesian statistics"], "title": "Relevance vector machine", "method": "Relevance vector machine", "url": "https://en.wikipedia.org/wiki/Relevance_vector_machine", "summary": "In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification.\nThe RVM has an identical functional form to the support vector machine, but provides probabilistic classification.\nIt is actually equivalent to a Gaussian process model with covariance function:\n\n \n \n \n k\n (\n \n x\n \n ,\n \n \n x\n \u2032\n \n \n )\n =\n \n \u2211\n \n j\n =\n 1\n \n \n N\n \n \n \n \n 1\n \n \u03b1\n \n j\n \n \n \n \n \u03c6\n (\n \n x\n \n ,\n \n \n x\n \n \n j\n \n \n )\n \u03c6\n (\n \n \n x\n \n \u2032\n \n ,\n \n \n x\n \n \n j\n \n \n )\n \n \n {\\displaystyle k(\\mathbf {x} ,\\mathbf {x'} )=\\sum _{j=1}^{N}{\\frac {1}{\\alpha _{j}}}\\varphi (\\mathbf {x} ,\\mathbf {x} _{j})\\varphi (\\mathbf {x} ',\\mathbf {x} _{j})}\n where \n \n \n \n \u03c6\n \n \n {\\displaystyle \\varphi }\n is the kernel function (usually Gaussian), \n \n \n \n \n \u03b1\n \n j\n \n \n \n \n {\\displaystyle \\alpha _{j}}\n are the variances of the prior on the weight vector\n\n \n \n \n w\n \u223c\n N\n (\n 0\n ,\n \n \u03b1\n \n \u2212\n 1\n \n \n I\n )\n \n \n {\\displaystyle w\\sim N(0,\\alpha ^{-1}I)}\n , and \n \n \n \n \n \n x\n \n \n 1\n \n \n ,\n \u2026\n ,\n \n \n x\n \n \n N\n \n \n \n \n {\\displaystyle \\mathbf {x} _{1},\\ldots ,\\mathbf {x} _{N}}\n are the input vectors of the training set.Compared to that of support vector machines (SVM), the Bayesian formulation of the RVM avoids the set of free parameters of the SVM (that usually require cross-validation-based post-optimizations). However RVMs use an expectation maximization (EM)-like learning method and are therefore at risk of local minima. This is unlike the standard sequential minimal optimization (SMO)-based algorithms employed by SVMs, which are guaranteed to find a global optimum (of the convex problem).\nThe relevance vector machine is patented in the United States by Microsoft.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian inference", "Bayesian network", "Bias-variance dilemma", "Boosting (machine learning)", "Bootstrap aggregating", "C++", "CURE data clustering algorithm", "Canonical correlation analysis", "Cluster analysis", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "Covariance function", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Dimensionality reduction", "Empirical risk minimization", "Ensemble learning", "Expectation maximization", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature engineering", "Feature learning", "Gated recurrent unit", "Gaussian process", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "Independent component analysis", "International Conference on Machine Learning", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kernel function", "Kernel trick", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Mathematics", "Mean-shift", "Microsoft", "Multilayer perceptron", "Naive Bayes classifier", "Non-negative matrix factorization", "OPTICS algorithm", "Occam's razor", "Occam learning", "Online machine learning", "Outline of machine learning", "Perceptron", "Platt scaling", "Principal component analysis", "Probabilistic classification", "Probably approximately correct learning", "Q-learning", "R (programming language)", "Random forest", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Restricted Boltzmann machine", "Self-organizing map", "Semi-supervised learning", "Sequential minimal optimization", "Software patents under United States patent law", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Training set", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory"], "references": ["http://www.relevancevector.com", "http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3237/pdf/imm3237.pdf", "http://jmlr.csail.mit.edu/papers/v1/tipping01a.html", "http://dlib.net", "http://www.terborg.net/research/kml/", "http://www.maths.bris.ac.uk/R/web/packages/rvmbinary/index.html", "https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US6633857", "https://github.com/AmazaspShumik/sklearn-bayes/blob/master/skbayes/rvm_ard_models/fast_rvm.py", "https://github.com/AmazaspShumik/sklearn-bayes/blob/master/ipython_notebooks_tutorials/rvm_ard/rvm_demo.ipynb", "https://github.com/JamesRitchie/scikit-rvm", "https://www.quora.com/Why-is-it-that-RVMs-are-not-as-popular-as-SVMs", "https://web.archive.org/web/20111005202038/http://www.tristanfletcher.co.uk/RVM%20Explained.pdf", "https://arxiv.org/list/cs.LG/recent"]}, "Markov process": {"categories": ["All accuracy disputes", "All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from February 2012", "Articles that may be too long from February 2017", "Articles with disputed statements from March 2015", "Articles with unsourced statements from March 2009", "Articles with unsourced statements from March 2012", "CS1 maint: Archived copy as title", "CS1 maint: Extra text: authors list", "CS1 maint: Multiple names: authors list", "Graph theory", "Markov models", "Markov processes", "Webarchive template wayback links", "Wikipedia articles with GND identifiers", "Wikipedia articles with content forks"], "title": "Markov chain", "method": "Markov process", "url": "https://en.wikipedia.org/wiki/Markov_chain", "summary": "A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.In probability theory and related fields, a Markov process, named after the Russian mathematician Andrey Markov, is a stochastic process that satisfies the Markov property (sometimes characterized as \"memorylessness\"). Roughly speaking, a process satisfies the Markov property if one can make predictions for the future of the process based solely on its present state just as well as one could knowing the process's full history, hence independently from such history; i.e., conditional on the present state of the system, its future and past states are independent.\nA Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless of the nature of time), but it is also common to define a Markov chain as having discrete time in either countable or continuous state space (thus regardless of the state space).Markov studied Markov processes in the early 20th century, publishing his first paper on the topic in 1906. Random walks based on integers and the gambler's ruin problem are examples of Markov processes. Some variations of these processes were studied hundreds of years earlier in the context of independent variables. Two important examples of Markov processes are the Wiener process, also known as the Brownian motion process, and the Poisson process, which are considered the most important and central stochastic processes in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after 1906, in various settings. These two processes are Markov processes in continuous time, while random walks on the integers and the gambler's ruin problem are examples of Markov processes in discrete time.Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, exchange rates of currencies, storage systems such as dams, and population growths of certain animal species. The algorithm known as PageRank, which was originally proposed for the internet search engine Google, is based on a Markov process.Markov processes are the basis for general stochastic simulation methods known as Gibbs sampling and Markov chain Monte Carlo. Furthermore, they are used for simulating random objects with specific probability distributions, and have found extensive application in Bayesian statistics.The adjective Markovian is used to describe something that is related to a Markov process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/70/AAMarkov.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/9/95/Finance_Markov_chain_example_state_space.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a6/Financial_Markov_process.svg", "https://upload.wikimedia.org/wikipedia/commons/0/07/Intensities_vs_transition_probabilities.svg", "https://upload.wikimedia.org/wikipedia/commons/d/da/Markov_Chains_prediction_on_50_discrete_steps..png", "https://upload.wikimedia.org/wikipedia/commons/8/86/Markov_Chains_prediction_on_n%3D3..png", "https://upload.wikimedia.org/wikipedia/commons/f/f3/Markov_chain_extremly_simple1.png", "https://upload.wikimedia.org/wikipedia/commons/2/2b/Markovkate_01.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0b/Mchain_simple_corrected_C1.png", "https://upload.wikimedia.org/wikipedia/commons/5/5b/Mvchain_approx_C2.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9a/Transition_graph_pac-man.png", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["A Mathematical Theory of Communication", "Absorbing Markov chain", "Abstract Wiener space", "Actuarial mathematics", "Agner Krarup Erlang", "Alexander Pushkin", "Algorithmic composition", "Andrei Kolmogorov", "Andrey Markov", "Arithmetic coding", "AstroTurf", "Authoritarian", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Base stealing", "Bayesian inference", "Bayesian statistics", "Bear market", "Bernoulli process", "Bernoulli scheme", "Bessel process", "Biased random walk on a graph", "Bibcode", "Bioinformatics", "Bipartite graph", "Birth-death process", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Bull market", "Bunt (baseball)", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Capitalism", "Cauchy process", "Central limit theorem", "Chapman\u2013Kolmogorov equation", "Chen model", "Chinese restaurant process", "CiteSeerX", "Classical Wiener space", "Claude Shannon", "Compound Poisson process", "Conditional probability", "Conditional probability distribution", "Connected component (graph theory)", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time Markov process", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous or discrete variable", "Continuous stochastic process", "Convergence of random variables", "Copolymer", "Countable set", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Credit rating agency", "Cruise control", "Csound", "C\u00e0dl\u00e0g", "Dam", "Das Kapital", "Data compression", "Defective matrix", "Democratic regime", "Detailed balance", "Diagonal matrix", "Diffusion equation", "Diffusion process", "Digital object identifier", "Directed acyclic graph", "Directed graph", "Dirichlet process", "Discrete-time stochastic process", "Dissociated press", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynamics of Markovian particles", "Dynkin's formula", "Econometrics", "Economic development", "Edmund F. Robertson", "Eigendecomposition", "Eigenvalue", "Eigenvector", "Element (mathematics)", "Empirical process", "Encyclopedia of Mathematics", "Entropy encoding", "Epithelial cell", "Equivalence class", "Equivalence relation", "Ergodic", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Eugene Dynkin", "Eugene Onegin", "Examples of Markov chains", "Exchange rate", "Exchangeable random variables", "Expected value", "Exponent", "Exponential distribution", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Finite-state machine", "Finite group", "Finite set", "First-order differential equation", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Forward equation", "Fractional Brownian motion", "Francis Galton", "Frobenius norm", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gambler's ruin", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "General equilibrium", "Genetic drift", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Google", "Google search engine", "Greatest common divisor", "Harris chain", "Heath\u2013Jarrow\u2013Morton framework", "Henry William Watson", "Hertz", "Heston model", "Hi Ho! Cherry-O", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Identity matrix", "If and only if", "In silico", "Independence (probability theory)", "Independent and identically distributed random variables", "Indexed family", "Infinitesimal generator (stochastic processes)", "Information entropy", "Information theory", "Inner product space", "Integers", "Integrated Authority File", "Interacting particle system", "International Standard Book Number", "International Standard Serial Number", "Invariant measure", "Ion channel", "Ir\u00e9n\u00e9e-Jules Bienaym\u00e9", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Iverson bracket", "J. L. Doob", "J. Laurie Snell", "JSTOR", "James D. Hamilton", "James R. Norris", "John G. Kemeny", "John J. O'Connor (mathematician)", "Jordan normal form", "Joseph O'Rourke (professor)", "Journal of Econometrics", "Jump diffusion", "Jump process", "Karl Marx", "Kelly's lemma", "Kolmogorov's criterion", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kronecker delta", "Kunita\u2013Watanabe inequality", "LIBOR market model", "LZ77 and LZ78", "Large deviation principle", "Large deviations theory", "Lattice QCD", "Laurent E. Calvet", "Law of large numbers", "Law of the iterated logarithm", "Lempel\u2013Ziv\u2013Markov chain algorithm", "Leslie matrix", "List of inequalities", "List of stochastic processes topics", "Little-o notation", "Local martingale", "Local time (mathematics)", "Locally interacting Markov chains", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "MIDI", "MacTutor History of Mathematics archive", "Machine learning", "Main diagonal", "Malliavin calculus", "Marginal distribution", "Mark V. Shaney", "Markov additive process", "Markov blanket", "Markov chain Monte Carlo", "Markov chain approximation method", "Markov chain geostatistics", "Markov chain mixing time", "Markov chains on a measurable state space", "Markov decision process", "Markov information source", "Markov model", "Markov process", "Markov property", "Markov random field", "Markov switching multifractal", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical Reviews", "Mathematical finance", "Mathematical statistics", "Matrix (mathematics)", "Matrix exponential", "Maurice Fr\u00e9chet", "Max (software)", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Memorylessness", "Michaelis-Menten kinetics", "Michaelis\u2013Menten kinetics", "Michiel Hazewinkel", "Middle class", "Mixing (mathematics)", "Moran process", "Motoo Kimura", "Motor vehicle", "Moving-average model", "Natural language generation", "Natural numbers", "Non-homogeneous Poisson process", "Norbert Wiener", "Norm (mathematics)", "Number line", "OCLC", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Oxford English Dictionary", "PageRank", "Parody generator", "Path-dependent", "Pattern recognition", "Paul Ehrenfest", "Pavel Nekrasov", "Percolation theory", "Periodic function", "Perron\u2013Frobenius theorem", "Phase-type distribution", "Phrase (music)", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Political", "Population dynamics", "Population genetics", "Population process", "Posterior distribution", "Potts model", "Predictable process", "Probability theory", "Probability vector", "Progressively measurable process", "Prokhorov's theorem", "PubMed Central", "PubMed Identifier", "Quadratic variation", "Quantum Markov chain", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Reinforcement learning", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Right stochastic matrix", "Risk process", "Ruin theory", "Russia", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semi-Markov process", "Semigroup", "Semimartingale", "Sequence", "Serial dependence", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snakes and Ladders", "Snell envelope", "Society for Industrial and Applied Mathematics", "Software", "Sparre\u2013Anderson model", "Speech recognition", "Stable process", "Standard simplex", "State diagram", "State estimation", "State space", "State transition", "Stationary probability distribution", "Stationary process", "Statistical mechanics", "Statistical model", "Statistics", "Steric effects", 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sausage", "Wiener space", "Wilkie investment model", "William Feller", "YouTube", "Zero matrix"], "references": ["http://probability.ca/MT/BOOK.pdf", "http://bbs.cenet.org.cn/uploadImages/200352118122167693.pdf", "http://www.google.com/patents/US6285999", "http://oed.com/search?searchType=dictionary&q=Markovian", "http://www.oxforddnb.com/help/subscribe#public", "http://www.pankin.com/markov/intro.htm", "http://www.pankin.com/markov/theory.htm", "http://rarlindseysmash.com/posts/2009-11-21-making-sense-and-nonsense-of-markov-chains", "http://www.alpha60.de/research/markov/DavidLink_AnExampleOfStatistical_MarkovTrans_2007.pdf", "http://www.columbia.edu/~ww2040/4106S11/MC_BondRating.pdf", "http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf", "http://adsabs.harvard.edu/abs/2005AmJPh..73..395B", "http://adsabs.harvard.edu/abs/2006Natur.442.1038G", "http://adsabs.harvard.edu/abs/2009PLSCB...5E0532G", 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interference exists. Knowledge of the distributions can be used to determine the likelihood that one parameter exceeds another, and by how much.\nThis technique can be used for dimensioning of mechanical parts, determining when an applied load exceeds the strength of a structure, and in many other situations. This type of analysis can also be used to estimate the probability of failure or the frequency of failure.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/fe/Interference.jpg", "https://upload.wikimedia.org/wikipedia/en/1/1b/Interference_Forces.jpg"], "links": ["Arithmetic mean", "Interference fit", "International Standard Book Number", "Joint probability distribution", "Log-normal distribution", "Monte Carlo method", "Normal distribution", "Probabilistic design", "Probability distribution", "Process capability", "Reliability engineering", "Specification", "Standard deviation", "Statistical inference", "Tolerance (engineering)", "Variance"], "references": ["http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA365683", "http://www.fpl.fs.fed.us/documnts/fplrp/fplrp302.pdf"]}, "Newey\u2013West estimator": {"categories": ["Estimator", "Regression with time series structure"], "title": "Newey\u2013West estimator", "method": "Newey\u2013West estimator", "url": "https://en.wikipedia.org/wiki/Newey%E2%80%93West_estimator", "summary": "A Newey\u2013West estimator is used in statistics and econometrics to provide an estimate of the covariance matrix of the parameters of a regression-type model when this model is applied in situations where the standard assumptions of regression analysis do not apply. It was devised by Whitney K. Newey and Kenneth D. West in 1987, although there are a number of later variants. The estimator is used to try to overcome autocorrelation (also called serial correlation), and heteroskedasticity in the error terms in the models, often for regressions applied to time series data.\nThe problem in autocorrelation, often found in time series data, is that the error terms are correlated over time. This can be demonstrated in \n \n \n \n \n Q\n \n \u2217\n \n \n \n \n {\\displaystyle Q^{*}}\n , a matrix of sums of squares and cross products that involves \n \n \n \n \n \u03c3\n \n (\n i\n j\n )\n \n \n \n \n {\\displaystyle \\sigma _{(ij)}}\n and the rows of \n \n \n \n X\n \n \n {\\displaystyle X}\n . The least squares estimator \n \n \n \n b\n \n \n {\\displaystyle b}\n is a consistent estimator of \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n . This implies that the least squares residuals \n \n \n \n \n e\n \n i\n \n \n \n \n {\\displaystyle e_{i}}\n are \"point-wise\" consistent estimators of their population counterparts \n \n \n \n \n E\n \n i\n \n \n \n \n {\\displaystyle E_{i}}\n . The general approach, then, will be to use \n \n \n \n X\n \n \n {\\displaystyle X}\n and \n \n \n \n e\n \n \n {\\displaystyle e}\n to devise an estimator of \n \n \n \n \n Q\n \n \u2217\n \n \n \n \n {\\displaystyle Q^{*}}\n . This means that as the time between error terms increases, the correlation between the error terms decreases. The estimator thus can be used to improve the ordinary least squares (OLS) regression when the residuals are heteroskedastic and/or autocorrelated.\n\n \n \n \n \n Q\n \n \u2217\n \n \n =\n \n \n 1\n T\n \n \n \n \u2211\n \n t\n =\n 1\n \n \n T\n \n \n \n e\n \n t\n \n \n 2\n \n \n \n x\n \n t\n \n \n \n x\n \n t\n \n \u2032\n \n +\n \n \n 1\n T\n \n \n \n \u2211\n \n \u2113\n =\n 1\n \n \n L\n \n \n \n \u2211\n \n t\n =\n \u2113\n +\n 1\n \n \n T\n \n \n \n w\n \n \u2113\n \n \n \n e\n \n t\n \n \n \n e\n \n t\n \u2212\n \u2113\n \n \n (\n \n x\n \n t\n \n \n \n x\n \n t\n \u2212\n \u2113\n \n \u2032\n \n +\n \n x\n \n t\n \u2212\n \u2113\n \n \n \n x\n \n t\n \n \u2032\n \n )\n \n \n {\\displaystyle Q^{*}={\\frac {1}{T}}\\sum _{t=1}^{T}e_{t}^{2}x_{t}x'_{t}+{\\frac {1}{T}}\\sum _{\\ell =1}^{L}\\sum _{t=\\ell +1}^{T}w_{\\ell }e_{t}e_{t-\\ell }(x_{t}x'_{t-\\ell }+x_{t-\\ell }x'_{t})}\n \n \n \n \n \n w\n \n \u2113\n \n \n =\n 1\n \u2212\n \n \n \u2113\n \n L\n +\n 1\n \n \n \n \n \n {\\displaystyle w_{\\ell }=1-{\\frac {\\ell }{L+1}}}\n \n \n \n \n \n w\n \n \u2113\n \n \n \n \n {\\displaystyle w_{\\ell }}\n can be thought of as a `weight'. Disturbances that are farther apart from each other are given lower weight, while those with equal subscripts are given a weight of 1. This ensures that second term converges (in some appropriate sense) to a finite matrix.", "images": [], "links": ["Autocorrelation", "Consistent estimator", "Covariance matrix", "Digital object identifier", "Donald Andrews", "Econometrics", "Error term", "Errors and residuals in statistics", "Fumio Hayashi", "Heteroscedasticity-consistent standard errors", "Heteroskedasticity", "International Standard Book Number", "JSTOR", "James D. Hamilton", "James H. Stock", "Kenneth D. West", "Least squares", "Linear regression", "MATLAB", "Mark Watson (economist)", "Ordinary least squares", "Python (programming language)", "R (programming language)", "Regression analysis", "Stata", "Statistics", "Time series", "Whitney K. Newey"], "references": ["http://www.mathfinance.cn/newey-west-estimator/", "http://doi.org/10.1017%2FS0266466605050103", "http://doi.org/10.2307%2F1913610", "http://doi.org/10.2307%2F2297912", "http://doi.org/10.2307%2F2938229", "http://www.jstatsoft.org/v11/i10/paper", "http://www.jstor.org/stable/1913610", "http://www.jstor.org/stable/2297912", "http://www.jstor.org/stable/2938229", "http://www.statsmodels.org/dev/stats.html", "https://books.google.com/books?id=B8_1UBmqVUoC&pg=PA279", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA408", "https://www.mathworks.com/help/econ/hac.html", "https://www.stata.com/manuals14/tsnewey.pdf", "https://cran.r-project.org/package=plm", "https://cran.r-project.org/package=sandwich"]}, "Fisher consistency": {"categories": ["Estimation theory"], "title": "Fisher consistency", "method": "Fisher consistency", "url": "https://en.wikipedia.org/wiki/Fisher_consistency", "summary": "In statistics, Fisher consistency, named after Ronald Fisher, is a desirable property of an estimator asserting that if the estimator were calculated using the entire population rather than a sample, the true value of the estimated parameter would be obtained.", "images": [], "links": ["Arithmetic mean", "Bias of an estimator", "Consistent estimator", "Cumulative distribution function", "Digital object identifier", "Empirical distribution function", "Estimation theory", "Exchangeable random variables", "Expected value", "Functional (mathematics)", "Indicator function", "International Standard Book Number", "JSTOR", "Jahrbuch \u00fcber die Fortschritte der Mathematik", "Jana Jure\u010dkov\u00e1", "Parameter", "Ronald Fisher", "Sample (statistics)", "Statistical population", "Statistics", "Strong law of large numbers", "Uniform distribution (continuous)"], "references": ["http://digital.library.adelaide.edu.au/dspace/handle/2440/15172", "http://economics.about.com/library/glossary/bldef-fisher-consistency.htm", "http://www.stat.osu.edu/~yklee/881/consistency.pdf", "http://doi.org/10.1098%2Frsta.1922.0009", "http://www.jstor.org/stable/91208", "http://zbmath.org/?format=complete&q=an:48.1280.02"]}, "Median polish": {"categories": ["Exploratory data analysis"], "title": "Median polish", "method": "Median polish", "url": "https://en.wikipedia.org/wiki/Median_polish", "summary": "The median polish is an exploratory data analysis procedure proposed by the statistician John Tukey. It finds an additively-fit model for data in a two-way layout table (usually, results from a factorial experiment) of the form row effect + column effect + overall median.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Addison-Wesley", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brian D. Ripley", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frederick Mosteller", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Tukey", "John Wiley & Sons", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New York City", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Reading, MA", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.stats.ox.ac.uk/pub/MASS4/VR4stat.pdf"]}, "Pedometric mapping": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2012", "CS1 maint: Extra text: authors list", "Cartography", "Geostatistics", "Pedology"], "title": "Pedometric mapping", "method": "Pedometric mapping", "url": "https://en.wikipedia.org/wiki/Pedometric_mapping", "summary": "Pedometric mapping, or statistical soil mapping, is data-driven generation of soil property and class maps that is based on use of statistical methods. The main objective of pedometric mapping is to predict values of some soil variable at unobserved locations and access the uncertainty of that estimate using statistical inference i.e. statistically optimal approaches. From the application point of view, the main objective of soil mapping is to accurately predict response of a soil-plant ecosystem to various soil management strategies. In other words, the main objective of pedometric mapping is to generate maps of soil properties and soil classes that can be used to feed other environmental models or for decision making. Pedometric mapping is largely based on applying geostatistics in soil science and other statistical methods used in pedometrics.\nAlthough pedometric mapping is mainly data-driven, it can also largely be based on use of expert knowledge. The expert knowledge, however, needs to be plugged-in into a pedometric computational framework so that it can be used to produce more accurate prediction models. For example, data assimilation techniques, such as the space\u2013time Kalman filter, can be used to integrate pedogenetic knowledge and field observations.In the information theory context, the objective of pedometric mapping is to describe the spatial complexity of soils (information content of soil variables over a geographical area), then represent this complexity using maps, summary measures, mathematical models and simulations. Simulations are a preferred way of visualizing soil patterns as they represent both the deterministic pattern due to the landscape, geographic hot-spots and short range variability (see image below).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d8/Logo_pedometrics_RGB.png", "https://upload.wikimedia.org/wikipedia/commons/9/95/Soil_profile.png", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Symbol_information_vote.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a5/Traditional_soil_map_vs_pedometric_map.png", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["1938 USDA soil taxonomy", "AASHTO Soil Classification System", "Acrisol", "Advanced Spaceborne Thermal Emission and Reflection Radiometer", "Agricultural science", "Agricultural soil science", "Agroecology", "Agrology", "Alfisol", "Alisols", "Alkali soil", "Andisol", "Andosol", "Anthrosol", "Archaeology", "Aridisol", "Australian Society of Soil Science Incorporated", "Australian Soil Classification", "Automated mapping", "BLUP", "Biogeography", "Calcisol", "Cambisol", "Canadian Society of Soil Science", "Canadian system of soil classification", "Chernozem", "Clorpt", "Crust (geology)", "Cryosols", "Data assimilation", "Digital elevation model", "Digital object identifier", "Digital soil mapping", "Durisol", "Earth materials", "Edaphology", "Entisol", "Environmental soil science", "Erosion control", "FAO soil classification", "Ferralsols", "Fluvisol", "Gelisol", "Geochemistry", "Geology", "Geomorphology", "Georges Matheron", "Geostatistics", "Geotechnical engineering", "Gleysol", "Groundwater", "Gypsisols", "Hans Jenny (pedologist)", "Histosol", "Hydrogeology", "Hydrology", "Impervious surface", "Inceptisol", "Index of soil-related articles", "Infiltration (hydrology)", "Information theory", "International Standard Book Number", "International Union of Soil Sciences", "International Year of Soil", "Kalman filter", "Kastanozems", "Kriging", "Land conversion", "Land management", "Land use", "Landsat", "Leptosol", "LiDAR", "Liming (soil)", "List of U.S. state soils", "List of soil scientists", "List of vineyard soil types", "Lixisol", "Luvisol", "MODIS", "Mollisol", "National Society of Consulting Soil Scientists", "Nitisol", "Oxisol", "Pedodiversity", "Pedogenesis", "Pedology", "Pedometrics", "Pedosphere", "Petrology", "Phaeozem", "Planosol", "Plinthosol", "Podzol", "Polish Soil Classification", "Pore space in soil", "Pore water pressure", "Precision agriculture", "Psamment", "Regosol", "Regression-kriging", "Remote sensing", "Reproducible research", "Retisol", "R\u00e9f\u00e9rentiel p\u00e9dologique", "SRTM", "Soil", "Soil Moisture and Ocean Salinity satellite", "Soil Science Society of America", "Soil acidification", "Soil and Water Conservation Society", "Soil biodiversity", "Soil biology", "Soil biomantle", "Soil carbon", "Soil chemistry", "Soil classification", "Soil color", "Soil compaction", "Soil compaction (agriculture)", "Soil conservation", "Soil contamination", "Soil crust", "Soil ecology", "Soil erosion", "Soil fertility", "Soil gas", "Soil governance", "Soil guideline value", "Soil health", "Soil horizon", "Soil life", "Soil management", "Soil map", "Soil mapping", "Soil mechanics", "Soil moisture", "Soil morphology", "Soil organic matter", "Soil pH", "Soil physics", "Soil policy", "Soil policy (Victoria, Australia)", "Soil quality", "Soil resilience", "Soil respiration", "Soil retrogression and degradation", "Soil salinity", "Soil salinity control", "Soil science", "Soil spectroscopy", "Soil structure", "Soil survey", "Soil taxonomy", "Soil test", "Soil texture", "Soil type", "Soil value", "Soil water (retention)", "Soil zoology", "Solonchak", "Solonetz", "Stagnosol", "Statistical inference", "Surface runoff", "Technosol", "USDA soil taxonomy", "Ultisol", "Umbrisol", "Unified Soil Classification System", "Vegetation", "Vertisol", "World Congress of Soil Science", "World Reference Base for Soil Resources"], "references": ["http://casoilresource.lawr.ucdavis.edu", "http://r-spatial.sourceforge.net/gallery/#fig07.R", "http://doi.org/10.1002/jpln.200521962", "http://doi.org/10.1016/S0016-7061(01)00025-8", "http://doi.org/10.1016/S0016-7061(03)00223-4", "http://doi.org/10.1016/j.jag.2012.02.005", "http://doi.org/10.1111/j.1365-2389.2010.01232.x", "http://geomorphometry.org", "http://www.isric.org", "http://pedometrics.org", "http://www.pedometrics.org"]}, "Kuder\u2013Richardson Formula 20": {"categories": ["Comparison of assessments", "Educational psychology research methods", "Psychometrics", "Use dmy dates from August 2012"], "title": "Kuder\u2013Richardson Formula 20", "method": "Kuder\u2013Richardson Formula 20", "url": "https://en.wikipedia.org/wiki/Kuder%E2%80%93Richardson_Formula_20", "summary": "In psychometrics, the Kuder\u2013Richardson Formula 20 (KR-20), first published in 1937, is a measure of internal consistency reliability for measures with dichotomous choices. It is a special case of Cronbach's \u03b1, computed for dichotomous scores. It is often claimed that a high KR-20 coefficient (e.g., > 0.90) indicates a homogeneous test. However, like Cronbach's \u03b1, homogeneity (that is, unidimensionality) is actually an assumption, not a conclusion, of reliability coefficients. It is possible, for example, to have a high KR-20 with a multidimensional scale, especially with a large number of items. \nValues can range from 0.00 to 1.00 (sometimes expressed as 0 to 100), with high values indicating that the examination is likely to correlate with alternate forms (a desirable characteristic). The KR-20 may be affected by difficulty of the test, the spread in scores and the length of the examination.\nIn the case when scores are not tau-equivalent (for example when there is not homogeneous but rather examination items of increasing difficulty) then the KR-20 is an indication of the lower bound of internal consistency (reliability).\nThe formula for KR-20 for a test with K test items numbered i=1 to K is \n\n \n \n \n r\n =\n \n \n K\n \n K\n \u2212\n 1\n \n \n \n \n [\n \n 1\n \u2212\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n K\n \n \n \n p\n \n i\n \n \n \n q\n \n i\n \n \n \n \n \u03c3\n \n X\n \n \n 2\n \n \n \n \n \n ]\n \n \n \n {\\displaystyle r={\\frac {K}{K-1}}\\left[1-{\\frac {\\sum _{i=1}^{K}p_{i}q_{i}}{\\sigma _{X}^{2}}}\\right]}\n where pi is the proportion of correct responses to test item i, qi is the proportion of incorrect responses to test item i (so that pi + qi = 1), and the variance for the denominator is \n\n \n \n \n \n \u03c3\n \n X\n \n \n 2\n \n \n =\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n (\n \n X\n \n i\n \n \n \u2212\n \n \n \n X\n \u00af\n \n \n \n \n )\n \n 2\n \n \n \n \n\n \n \n n\n \n \n .\n \n \n {\\displaystyle \\sigma _{X}^{2}={\\frac {\\sum _{i=1}^{n}(X_{i}-{\\bar {X}})^{2}\\,{}}{n}}.}\n where n is the total sample size.\nIf it is important to use unbiased operators then the sum of squares should be divided by degrees of freedom (n \u2212 1) and the probabilities are multiplied by \n\n \n \n \n \n \n n\n \n n\n \u2212\n 1\n \n \n \n \n \n {\\displaystyle {\\frac {n}{n-1}}}\n \n\n", "images": [], "links": ["Cronbach's alpha", "Dichotomous", "Psychometrics", "Reliability (statistics)", "Test (student assessment)"], "references": ["http://www.hr-survey.com/WpAssessmentHandbook.htm", "http://eric.ed.gov/?id=ED526237"]}, "Statgraphics": {"categories": ["All articles needing additional references", "All articles needing expert attention", "All articles that are too technical", "Articles needing additional references from September 2017", "Articles needing expert attention from September 2017", "Articles with multiple maintenance issues", "Articles with specifically marked weasel-worded phrases from January 2016", "CS1 maint: Archived copy as title", "Science software for Windows", "Statistical software", "Wikipedia articles needing clarification from January 2016", "Wikipedia articles that are too technical from September 2017"], "title": "Statgraphics", "method": "Statgraphics", "url": "https://en.wikipedia.org/wiki/Statgraphics", "summary": "Statgraphics is a statistics package that performs and explains basic and advanced statistical functions. The software was created in 1980 by Dr. Neil Polhemus while working as a professor of statistics at Princeton university. The current version of the program, Statgraphics Centurion XVII, was released in fall 2014. Version XVII, available in both 32-bit and 64-bit editions, is available in five languages: English, French, Spanish, German and Italian.\nStatgraphics is distributed by Statpoint Technologies, Inc., a privately held company based in Warrenton, Virginia.\nStatgraphics is frequently used with Six Sigma process improvement. The program has also been used in various health and nutrition-related studies.During spring 2006, Statgraphics Mobile was released as the first sophisticated statistical program designed to run on hand-held computers (Pocket PC, Pocket PC Phone Edition, or compatible device running Windows Mobile 5 or Windows Pocket PC 2003).\nIn September 2008 the Statgraphics Online version was released. Statgraphics Online is a statistical package that runs within a web browser. Users can enter data directly into the data editor or import data from text files, Excel files, or other formats. The calculations are performed remotely on a web server and the results returned to the user's browser as HTML with embedded graphics images.\nIn July 2012 Statgraphics Sigma express was released. It is an add-in for Microsoft Excel that enables users to perform various calculations required when learning or applying Six Sigma. It adds a menu selection to Excel containing sections for each item of the DMAIC paradigm (Define, Measure, Analyze, Improve and Control) plus additional menu items for Tools and Help. The program is designed to meet the needs of Six Sigma yellow belts, green belts and most black belts. Sigma express is available in English and French.\nIn October 2014 Statpoint Technologies Incorporated released Centurion XVII, the companies flagship software. Centurion XVII included 32 new statistical procedures. With Centurion XVII the company placed a new emphases on data visualization.\nFollowing extensive development, Statgraphics released its cloud based \"Stratus\" in June 2015. Billed as one of the first cloud analytic tools on the market, it is designed to work either as a stand-alone program or in conjunction with Centurion XVII.\nStratus was designed by Statpoint Technologies Incorporated to work on PCs, Macs, tablets and handheld devices.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Cloud Analytics", "Comparison of statistical packages", "Data visualization", "Digital object identifier", "List of information graphics software", "List of statistical packages", "Microsoft Windows", "Operating system", "Proprietary software", "Six Sigma", "Software categories", "Software developer", "Software license", "Software release life cycle", "Statistical", "Warrenton, Virginia"], "references": ["http://journals.lww.com/pidj/pages/articleviewer.aspx?year=2008&issue=11000&article=00004&type=abstract", "http://www.saspen.com/2001/educational.htm", "http://statgraphics.com/", "http://www.statgraphics.com", "http://www.statgraphics.com/statpoint.htm", "http://pt.wkhealth.com/pt/re/bjon/abstract.00002375-200407000-00006.htm;jsessionid=KJsMcG759pWFtDx7TX8bZ5QhGQhj03lYywMtrkww5hxQkLyQcq1W!1864410514!181195629!8091!-1", "http://doi.org/10.1097%2FINF.0b013e31817acfaa", "https://archive.is/20120912041117/http://www.thefreelibrary.com/Statistical+Software+with+Six+Sigma-a01073757206", "https://web.archive.org/web/20080907071937/http://www.saspen.com/2001/educational.htm"]}, "Lift (data mining)": {"categories": ["Data mining"], "title": "Lift (data mining)", "method": "Lift (data mining)", "url": "https://en.wikipedia.org/wiki/Lift_(data_mining)", "summary": "In data mining and association rule learning, lift is a measure of the performance of a targeting model (association rule) at predicting or classifying cases as having an enhanced response (with respect to the population as a whole), measured against a random choice targeting model. A targeting model is doing a good job if the response within the target is much better than the average for the population as a whole. Lift is simply the ratio of these values: target response divided by average response.\nFor example, suppose a population has an average response rate of 5%, but a certain model (or rule) has identified a segment with a response rate of 20%. Then that segment would have a lift of 4.0 (20%/5%).\nTypically, the modeller seeks to divide the population into quantiles, and rank the quantiles by lift. Organizations can then consider each quantile, and by weighing the predicted response rate (and associated financial benefit) against the cost, they can decide whether to market to that quantile or not.\nLift is analogous to information retrieval's average precision metric, if one treats the precision (fraction of the positives that are true positives) as the target response probability.\nThe lift curve can also be considered a variation on the receiver operating characteristic (ROC) curve, and is also known in econometrics as the Lorenz or power curve.\n \n \n \n l\n i\n f\n t\n =\n \n \n \n P\n (\n A\n \u2229\n B\n )\n \n \n P\n (\n A\n )\n \u2217\n P\n (\n B\n )\n \n \n \n \n \n {\\displaystyle lift={\\frac {P(A\\cap B)}{P(A)*P(B)}}}", "images": [], "links": ["Association rule learning", "Correlation and dependence", "Data mining", "Information retrieval", "Lift (disambiguation)", "Lorenz curve", "Model (abstract)", "Quantile", "Receiver operating characteristic", "Uplift modelling"], "references": ["http://www.information-management.com/news/5329-1.html"]}, "Linnik distribution": {"categories": ["Continuous distributions", "Geometric stable distributions", "Probability distributions with non-finite variance"], "title": "Geometric stable distribution", "method": "Linnik distribution", "url": "https://en.wikipedia.org/wiki/Geometric_stable_distribution", "summary": "A geometric stable distribution or geo-stable distribution is a type of leptokurtic probability distribution. Geometric stable distributions were introduced in Klebanov, L. B., Maniya, G. M., and Melamed, I. A. (1985). A problem of Zolotarev and analogs of infinitely divisible and stable distributions in a scheme for summing a random number of random variables. These distributions are analogues for stable distributions for the case when the number of summands is random, independent of the distribution of summand, and having geometric distribution. The geometric stable distribution may be symmetric or asymmetric. A symmetric geometric stable distribution is also referred to as a Linnik distribution. The Laplace distribution and asymmetric Laplace distribution are special cases of the geometric stable distribution. The Laplace distribution is also a special case of a Linnik distribution. The Mittag-Leffler distribution is also a special case of a geometric stable distribution.The geometric stable distribution has applications in finance theory.", "images": [], "links": ["ARGUS distribution", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent and identically distributed random variables", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Leptokurtic", "Limit (mathematics)", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Standardized moment", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.math.bas.bg/serdica/1999/1999-241-256.pdf", "http://www.m-hikari.com/ijcms-password/ijcms-password1-4-2006/kozubowskiIJCMS1-4-2006.pdf", "http://www.sciencedirect.com/science/article/pii/S0378375810001837", "http://www.sciencedirect.com/science/article/pii/S0895717799001077", "http://www.mathematik.uni-dortmund.de/lsiv/scheffler/ctrw1.pdf", "http://ecommons.cornell.edu/bitstream/1813/9075/1/TR001191.pdf", "http://faculty.wcas.northwestern.edu/~mea405/laplace.pdf", "http://arxiv.org/abs/1410.4093", "http://doi.org/10.1007%2Fs00362-011-0367-4", "http://doi.org/10.1016%2FS0895-7177(99)00107-7", "http://th-www.if.uj.edu.pl/~acta/vol39/pdf/v39p1043.pdf", "https://web.archive.org/web/20110629133648/http://th-www.if.uj.edu.pl/~acta/vol39/pdf/v39p1043.pdf", "https://web.archive.org/web/20110719101917/http://www.mathematik.uni-dortmund.de/lsiv/scheffler/ctrw1.pdf"]}, "Lack-of-fit sum of squares": {"categories": ["Analysis of variance", "Design of experiments", "Least squares", "Statistical hypothesis testing"], "title": "Lack-of-fit sum of squares", "method": "Lack-of-fit sum of squares", "url": "https://en.wikipedia.org/wiki/Lack-of-fit_sum_of_squares", "summary": "In statistics, a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well. The other component is the pure-error sum of squares.\nThe pure-error sum of squares is the sum of squared deviations of each value of the dependent variable from the average value over all observations sharing its independent variable value(s). These are errors that could never be avoided by any predictive equation that assigned a predicted value for the dependent variable as a function of the value(s) of the independent variable(s). The remainder of the residual sum of squares is attributed to lack of fit of the model since it would be mathematically possible to eliminate these errors entirely.", "images": [], "links": ["Analysis of variance", "CRC Press", "Chi-squared distribution", "Confidence level", "Cumulative distribution function", "Degrees of freedom (statistics)", "Dependent variable", "Errors and residuals in statistics", "Expected value", "F-distribution", "F-test", "F distribution", "Goodness of fit", "Independence (probability theory)", "Independent variable", "International Standard Book Number", "Least squares", "Likelihood-ratio test", "Linear regression", "Non-central F-distribution", "Noncentral chi-squared distribution", "Normal distribution", "Null hypothesis", "Numerator", "Replication (statistics)", "Residual sum of squares", "Response variable", "Statistical independence", "Statistics", "Stochastic order", "Sum of squares (statistics)", "Variance"], "references": ["http://www.danielsoper.com/statcalc3", "http://vassarstats.net/textbook/apx_d.html"]}, "Stochastic rounding": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Arithmetic", "Articles needing additional references from October 2017", "Articles with unsourced statements from July 2009", "Articles with unsourced statements from June 2017", "CS1 maint: Uses editors parameter", "Computer arithmetic", "Statistical data transformation", "Theory of computation", "Webarchive template wayback links", "Wikipedia articles needing clarification from September 2017"], "title": "Rounding", "method": "Stochastic rounding", "url": "https://en.wikipedia.org/wiki/Rounding", "summary": "Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing $23.4476 with $23.45, or the fraction 312/941 with 1/3, or the expression \u221a2 with 1.414.\nRounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement or estimate; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is better stated as \"about 123,500\".\nOn the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting many computations \u2013 especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating-point representation with a fixed number of significant digits. In a sequence of calculations, these rounding errors generally accumulate, and in certain ill-conditioned cases they may make the result meaningless.\nAccurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as \"the table-maker's dilemma\".\nRounding has many similarities to the quantization that occurs when physical quantities must be encoded by numbers or digital signals.\nA wavy equals sign (\u2248: approximately equal to) is sometimes used to indicate rounding of exact numbers, e.g., 0.75 \u2248 1. This sign was introduced by Alfred George Greenhill in 1892.Ideal characteristics of rounding methods include:\n\nRounding should be done by a function. This way, when the same input is rounded in different instances, the output is unchanged.\nCalculations done with rounding should be close to those done without rounding.\nAs a result of (1) and (2), the output from rounding should be close to its input, often as close as possible by some metric.\nTo be considered rounding, the range will be a subset of the domain. Additionally, the range will have cardinality \n \n \n \n \n \u2135\n \n 0\n \n \n \n \n {\\displaystyle \\aleph _{0}}\n or less. The classical range is the integers, Z\nRounding should preserve symmetries that already exist between the domain and range. With finite precision (or a discrete domain) this translates to removing bias.\nA rounding method should have utility in computer science or human arithmetic where finite precision is used, and speed is a consideration.But, because it is not usually possible for a method to satisfy all ideal characteristics, many methods exist.\nAs a general rule, rounding is idempotent, i.e., once a number has been rounded, rounding it again will not change its value. In practice, rounding functions are also monotonic.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8a/Comparison_rounding_graphs_SMIL.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["2's complement", "ABCC index", "ASTM", "Accuracy and precision", "Age heaping", "Alfred George Greenhill", "Anne Schilling", "ArXiv", "Arithmetic overflow", "Array data type", "Base 60", "Bias (statistics)", "Binary number", "Birkh\u00e4user", "Bruno Nachtergaele", "C (programming language)", "Cardinality", "Cascading Style Sheets", "Celsius", "Churchill Eisenhart", "CiteSeerX", "Clay tablet", "Communicate", "Computable number", "Continued fraction", "Continuous signal", "Decimal number", "Digital object identifier", "Digital signal (signal processing)", "Discrete mathematics", "Discrete uniform distribution", "Dithering", "Document Object Model", "Domain of a function", "Double precision floating-point format", "ECMAScript", "ENS Lyon", "Equals sign", "Eric W. Weisstein", "Error diffusion", "Estimate", "Expectation (mathematics)", "Extended real number line", "FORTRAN", "Farey sequence", "Fixed-point arithmetic", "Floating-point arithmetic", "Floor and ceiling functions", "Floyd\u2013Steinberg dithering", "Function (mathematics)", "Fused multiply\u2013add", "Gal's accurate tables", "Gelfond\u2013Schneider theorem", "Goldbach's conjecture", "Halting problem", "Human computer", "IBM", "IEEE 754", "IEEE 754-2008", "IEEE floating point", "ISO 80000-1", "Idempotence", "Ill-conditioned", "Integer", "Integer (computing)", "Interface description language", "International Standard Book Number", "Interval arithmetic", "JavaScript", "J\u00f6rg Baten", "Kahan summation algorithm", "Kilobyte", "Library (computing)", "Library of Congress Control Number", "Lindemann\u2013Weierstrass theorem", "Literacy", "Logarithm", "Lumber", "MPFR", "Machine learning", "MathWorld", "Measurement", "Megabyte", "Mesopotamia", "Meteorology", "Metric (mathematics)", "Monotonic function", "Monte Carlo method", "Multiplicative inverse", "Nearest integer function", "Number system", "Numeracy", "Numerical value", "Overprecision", "PHP", "Physical quantity", "Pi", "Power (mathematics)", "Preferred number", "Preferred value", "Printf", "Programming language", "Propagation of uncertainty", "Pulse-width modulation", "Quantization (signal processing)", "Random seed", "Random walk", "Range (mathematics)", "Rational number", "Report", "Robert Simpson Woodward", "Round-off error", "Rounding (disambiguation)", "Scalable Vector Graphics", "Sign function", "Signed-digit representation", "Signed zero", "Significant digit", "Significant figure", "Significant figures", "Sine", "Slide rule", "Square root", "Stern\u2013Brocot tree", "Stochastic", "Stock index", "Stock price", "Strictfp", "Sun Microsystems", "Swedish rounding", "Symmetry in mathematics", "Transcendental function", "Transcendental number", "Truncation", "Unit in the last place", "United States", "Unprovable", "Vancouver Stock Exchange", "Variable (programming)", "Wayback Machine", "William Kahan", "X87", "\u2248"], "references": ["http://www.clivemaxfield.com/diycalculator/popup-m-round.shtml", "http://electronicdesign.com/article/components/excel-formula-calculates-standard-1-resistor-value.aspx", "http://www.kennethkuhn.com/students/ee431/text/voltage_regulators_zeners.pdf", "http://support.microsoft.com/kb/196652", "http://docs.oracle.com/javase/8/docs/api/java/math/RoundingMode.html#HALF_UP", "http://www.sciencedirect.com/science/article/pii/S0731708515300753", "http://mathworld.wolfram.com/Rounding.html", "http://www.cs.berkeley.edu/~wkahan/LOG10HAF.TXT", "http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=05170001&view=50&frames=0&seq=48", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.43.3309", "http://it.stlawu.edu/~dmelvill/mesomath/tablets/YBC7289.html", "http://web.cs.ucla.edu/~stott/mca/CSD-970014.ps.gz", "http://www.math.utah.edu/cgi-bin/man2html.cgi?/usr/local/man/man3/libultim.3", "http://www.math.utah.edu/cgi-bin/man2html.cgi?/usr/local/man/man3/libmcr.3", "http://www.cs.utexas.edu/users/moore/publications/divide_paper.pdf", "http://ec.europa.eu/economy_finance/publications/publication1224_en.pdf", "http://lipforge.ens-lyon.fr/www/crlibm/", "http://lccn.loc.gov/2009939668", "http://www.ofcm.gov/fmh-1/fmh1.htm", "http://portal.acm.org/citation.cfm?id=221332.221334", "http://arxiv.org/abs/1502.02551", "http://doi.org/10.1007%2F978-0-8176-4705-6", "http://doi.org/10.1016%2Fj.jpba.2015.07.021", "http://doi.org/10.1109%2F12.713311", "http://doi.org/10.1109%2FTC.1977.1674893", "http://doi.org/10.1109%2FTC.2007.70819", "http://doi.org/10.1145%2F221332.221334", "http://www.ecma-international.org/publications/files/ECMA-ST/ECMA-262.pdf", "http://www.open-std.org/JTC1/SC22/JSG/docs/m3/docs/jsgn326.pdf", "http://stellafane.org/tm/atm/test/tester-3.html", "http://upload.wikimedia.org/wikipedia/commons/8/8a/Comparison_rounding_graphs_SMIL.svg", "https://hal.inria.fr/inria-00080427v2/document", "https://archive.org/details/selectedtechniqu00colu", "https://web.archive.org/web/19990420051036/http://www.ofcm.gov/fmh-1/fmh1.htm", "https://web.archive.org/web/20150603082624/http://mscweb.gsfc.nasa.gov/543web/files/GSFC-X-673-64-1F.pdf", "https://web.archive.org/web/20161027224938/http://lipforge.ens-lyon.fr/www/crlibm", "https://doi.org/10.1109/TC.1977.1674893", "https://gcc.gnu.org/bugzilla/show_bug.cgi?id=21718#c25", "https://docs.python.org/3/library/decimal.html#rounding-modes", "https://upload.wikimedia.org/wikipedia/commons/8/8a/Comparison_rounding_graphs_SMIL.svg"]}, "Logistic distribution": {"categories": ["Commons category link from Wikidata", "Continuous distributions", "Location-scale family probability distributions", "Pages using deprecated image syntax"], "title": "Logistic distribution", "method": "Logistic distribution", "url": "https://en.wikipedia.org/wiki/Logistic_distribution", "summary": "In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/08/FitLogisticdistr.tif", "https://upload.wikimedia.org/wikipedia/commons/1/1a/Logistic_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/6/66/Logisticpdfunction.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["ARGUS distribution", "Applied Probability Trust", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli number", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Central limit theorem", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Confidence belt", "Continuous variable", "Conway\u2013Maxwell\u2013Poisson distribution", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dependent variable", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete choice", "Discrete phase-type distribution", "Discrete uniform distribution", "Distribution fitting", "Elliptical distribution", "Elo rating system", "Erlang distribution", "Error variable", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Feedforward neural network", "Fermi function", "Fermi level", "Fermi\u2013Dirac statistics", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized logistic distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heavy-tailed distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hydrology", "Hyper-Erlang distribution", "Hyperbolic function", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse function", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "Latent variable", "Linear regression", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic function", "Logistic regression", "Logit", "Logit-normal distribution", "Logit function", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "On-Line Encyclopedia of Integer Sequences", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Plotting position", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Probit regression", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Robust statistics", "Scale parameter", "Scaled inverse chi-squared distribution", "Sech distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sigmoid function", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard deviation", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "United States Chess Federation", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.waterlog.info/pdf/freqtxt.pdf", "http://doi.org/10.2307%2F2684541"]}, "Projection pursuit regression": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "Regression analysis"], "title": "Projection pursuit regression", "method": "Projection pursuit regression", "url": "https://en.wikipedia.org/wiki/Projection_pursuit_regression", "summary": "In statistics, projection pursuit regression (PPR) is a statistical model developed by Jerome H. Friedman and Werner Stuetzle which is an extension of additive models. This model adapts the additive models in that it first projects the data matrix of explanatory variables in the optimal direction before applying smoothing functions to these explanatory variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Additive model", "Alternating optimization", "Backfitting algorithm", "Cross-validation (statistics)", "Curse of dimensionality", "Data matrix (multivariate statistics)", "Design matrix", "Explanatory variable", "Gauss-Newton algorithm", "Generalized additive model", "Heikki Mannila", "International Standard Book Number", "Jerome H. Friedman", "K-nearest neighbors", "Linear combination", "Link function", "Mean absolute deviation", "Neural networks", "Ordinary least squares", "Projection pursuit", "Statistical model", "Statistics", "Taylor series", "Weighted least squares", "Werner Stuetzle"], "references": ["https://web.archive.org/web/20150126123924/http://statweb.stanford.edu/~tibs/ElemStatLearn/"]}, "False positive paradox": {"categories": ["Behavioral finance", "CS1 maint: Extra text: editors list", "Cognitive biases", "Probability fallacies", "Relevance fallacies", "Statistical paradoxes"], "title": "Base rate fallacy", "method": "False positive paradox", "url": "https://en.wikipedia.org/wiki/Base_rate_fallacy", "summary": "The base rate fallacy, also called base rate neglect or base rate bias, is a formal fallacy. If presented with related base rate information (i.e. generic, general information) and specific information (information pertaining only to a certain case), the mind tends to ignore the former and focus on the latter.Base rate neglect is a specific form of the more general extension neglect.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/cd/Socrates.png", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["Ad hominem", "Ad nauseam", "Amos Tversky", "Appeal to accomplishment", "Appeal to consequences", "Appeal to emotion", "Appeal to fear", "Appeal to flattery", "Appeal to motive", "Appeal to nature", "Appeal to novelty", "Appeal to pity", "Appeal to ridicule", "Appeal to spite", "Appeal to the stone", "Appeal to tradition", "Argument from authority", "Argument from ignorance", "Argument from silence", "Argument to moderation", "Argumentum ad baculum", "Argumentum ad crumenam", "Argumentum ad lazarum", "Argumentum ad populum", "Association fallacy", "Attributional bias", "Base rate", "Bayes' theorem", "Bayes's theorem", "Bayesian probability", "Breathalyzer", "Bulverism", "Chronological snobbery", "Clich\u00e9", "Cochrane Collaboration", "College admissions", "Daniel Kahneman", "Data dredging", "Digital object identifier", "Dispositional attribution", "Etymological fallacy", "Expected value", "Extension neglect", "Fallacy", "False positive", "False positive paradox", "Formal fallacy", "Fundamental attribution error", "Genetic fallacy", "Godwin's law", "Grade point average", "Heuristics in judgment and decision making", "I'm entitled to my opinion", "In-group favoritism", "Inductive argument", "International Standard Book Number", "Invented here", "Invincible ignorance fallacy", "Ipse dixit", "Irrelevant conclusion", "Island mentality", "Law of total probability", "List of cognitive biases", "List of fallacies", "List of paradoxes", "Misleading vividness", "Moralistic fallacy", "NASA", "Naturalistic fallacy", "Not invented here", "Parade of horribles", "Poisoning the well", "Population (statistics)", "Posterior probability", "Prevention paradox", "Prior probability", "Proof by assertion", "Prosecutor's fallacy", "Psychologist", "PubMed Central", "PubMed Identifier", "Rationalization (psychology)", "Red-baiting", "Red herring", "Reductio ad Hitlerum", "Reference class problem", "Representativeness heuristic", "Richard Nisbett", "Rule of thumb", "Simpson's paradox", "Special pleading", "Stereotype", "Steroids", "Straw man", "Think of the children", "Tone policing", "True positive", "Tu quoque", "Two wrongs make a right", "Whataboutism", "Wisdom of repugnance", "Wishful thinking"], "references": ["http://ipdas.ohri.ca/IPDAS-Chapter-C.pdf", "http://www.eeps.com/riskicon/", "http://findarticles.com/p/articles/mi_qa4089/is_200305/ai_n9252796/pg_2/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1122766", "http://www.ncbi.nlm.nih.gov/pubmed/11124351", "http://www.ncbi.nlm.nih.gov/pubmed/11188724", "http://www.ncbi.nlm.nih.gov/pubmed/11934777", "http://www.ncbi.nlm.nih.gov/pubmed/12044739", "http://www.ncbi.nlm.nih.gov/pubmed/17835457", "http://www.ncbi.nlm.nih.gov/pubmed/17963533", "http://doi.org/10.1002%2F14651858.CD006776.pub2", "http://doi.org/10.1002%2Facp.1460", "http://doi.org/10.1007%2F978-1-4612-4308-3_27", "http://doi.org/10.1016%2F0001-6918(80)90046-3", "http://doi.org/10.1016%2F0010-0277(95)00664-8", "http://doi.org/10.1016%2FS0010-0277(00)00133-5", "http://doi.org/10.1016%2FS0010-0277(02)00050-1", "http://doi.org/10.1017%2FS0140525X00041157", "http://doi.org/10.1017%2FS0140525X07001653", "http://doi.org/10.1037%2F0033-295X.102.4.684", "http://doi.org/10.1037%2F0033-295X.106.2.425", "http://doi.org/10.1037%2F0096-3445.130.3.380", "http://doi.org/10.1037%2Fh0034747", "http://doi.org/10.1126%2Fscience.185.4157.1124", "http://doi.org/10.1126%2Fscience.290.5500.2261", "http://doi.org/10.1136%2Fbmj.324.7341.827", "http://www.fallacyfiles.org/baserate.html", "https://books.google.com/books?id=5gQz0akjYcwC&pg=113#v=onepage&q&f=false", "https://www.youtube.com/watch?v=D8VZqxcu0I0", "https://www.cia.gov/library/center-for-the-study-of-intelligence/csi-publications/books-and-monographs/psychology-of-intelligence-analysis/art15.html#ft145", "https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980045313_1998119122.pdf"]}, "Regression estimation": {"categories": ["Actuarial science", "All articles with unsourced statements", "Articles with unsourced statements from February 2010", "Articles with unsourced statements from March 2011", "Commons category link is on Wikidata", "Estimation theory", "Regression analysis", "Wikipedia articles with BNF identifiers", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers"], "title": "Regression analysis", "method": "Regression estimation", "url": "https://en.wikipedia.org/wiki/Regression_analysis", "summary": "In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors'). More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.\nMost commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables \u2013 that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, a function of the independent variables called the regression function is to be estimated. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the prediction of the regression function using a probability distribution. A related but distinct approach is Necessary Condition Analysis (NCA), which estimates the maximum (rather than average) value of the dependent variable for a given value of the independent variable (ceiling line rather than central line) in order to identify what value of the independent variable is necessary but not sufficient for a given value of the dependent variable.\nRegression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable.\nMany techniques for carrying out regression analysis have been developed. Familiar methods such as linear regression and ordinary least squares regression are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional.\nThe performance of regression analysis methods in practice depends on the form of the data generating process, and how it relates to the regression approach being used. Since the true form of the data-generating process is generally not known, regression analysis often depends to some extent on making assumptions about this process. These assumptions are sometimes testable if a sufficient quantity of data is available. Regression models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally. However, in many applications, especially with small effects or questions of causality based on observational data, regression methods can give misleading results.In a narrower sense, regression may refer specifically to the estimation of continuous response (dependent) variables, as opposed to the discrete response variables used in classification. The case of a continuous dependent variable may be more specifically referred to as metric regression to distinguish it from related problems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c7/CurveWeightHeight.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Adrien-Marie Legendre", "Adrien Marie Legendre", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anomaly detection", "Approximation theory", "Arithmetic mean", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Asymptomatic carrier", "Asymptotic theory (statistics)", "Autocorrelation", "Autoencoder", "Automated machine learning", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Auxology", "Average value", "BIRCH", "Bachelor of Science in Public Health", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian method", "Bayesian multivariate linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Behavior change (public health)", "Behavioural change theories", "Bias-variance dilemma", "Bias of an estimator", "Biblioth\u00e8que nationale de France", "Binomial regression", "Bioinformatics", "Biological hazard", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Boosting (machine learning)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "CURE data clustering algorithm", "Calibration curve", "Canonical correlation", "Canonical correlation analysis", "Carl Friedrich Gauss", "Carl Rogers Darnall", "Cartography", "Case\u2013control study", "Categorical variable", "Causality", "Censored regression model", "Census", "Centers for Disease Control and Prevention", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Chief Medical Officer", "Child mortality", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Community health", "Completeness (statistics)", "Computational learning theory", "Computational statistics", "Conditional distribution", "Conditional expectation", "Conditional random field", "Conference on Neural Information Processing Systems", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Convolutional neural network", "Correlation and dependence", "Correlogram", "Council on Education for Public Health", "Count data", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cultural competence in health care", "Curve fitting", "D.V. Lindley", "DBSCAN", "Data", "Data collection", "Data mining", "Decision tree learning", "Decomposition of time series", "DeepDream", "Deep learning", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Dependent variable", "Descriptive statistics", "Design of experiments", "Deviance (sociology)", "Diagonal matrix", "Dickey\u2013Fuller test", "Diffusion of innovations", "Digital object identifier", "Dimension", "Dimensionality reduction", "Discrete choice", "Disease surveillance", "Divergence (statistics)", "Doctor of Public Health", "Durbin\u2013Watson statistic", "Econometric model", "Econometrics", "Edinburgh", "Effect size", "Efficiency (statistics)", "Efficient (statistics)", "Elliptical distribution", "Emergency sanitation", "Empirical distribution function", "Empirical risk minimization", "Encyclopedia of Mathematics", "Engineering statistics", "Ensemble learning", "Environmental health", "Environmental statistics", "Epidemic", "Epidemiology", "Errors-in-variables model", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Estimation Theory", "Estimation theory", "Euclidean vector", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Expectation\u2013maximization algorithm", "Experiment", "Exponential family", "Exponential smoothing", "Extrapolation", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Family planning", "Fan chart (statistics)", "Feature engineering", "Feature learning", "Fecal\u2013oral route", "First-hitting-time model", "Fixed effects model", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Forecasting", "Forest plot", "Fourier analysis", "Fraction of variance unexplained", "Francis Galton", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Function (mathematics)", "Function approximation", "G-test", "G. Udny Yule", "Gated recurrent unit", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Generalized linear models", "Genetically modified food", "Geographic information system", "Geometric mean", "Geostatistics", "Germ theory of disease", "Global health", "Globalization and disease", "Glossary of artificial intelligence", "Good agricultural practice", "Good manufacturing practice", "Goodness of fit", "Grammar induction", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "HACCP", "Hand washing", "Harmonic mean", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Heckman correction", "Heteroscedasticity", "Hidden Markov model", "Hierarchical clustering", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human factors and ergonomics", "Human nutrition", "Hygiene", "Hypothesis test", "ISO 22000", "Independent component analysis", "Independent variable", "Index of dispersion", "Infant mortality", "Infection control", "Injury prevention", "Integrated Authority File", "Interaction (statistics)", "International Conference on Machine Learning", "International Standard Book Number", "Interpolation", "Interquartile range", "Interval estimation", "Invertible matrix", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Snow (physician)", "Joint distribution", "Jonckheere's trend test", "Joseph Lister", "Journal of Machine Learning Research", "Judith Tanur", "Julian C. Stanley", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Learning to rank", "Least-angle regression", "Least absolute deviations", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Library of Congress Control Number", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Limited dependent variable", "Linear combination", "Linear discriminant analysis", "Linear least squares", "Linear least squares (mathematics)", "Linear probability model", "Linear regression", "Linearly independent", "List of datasets for machine-learning research", "List of epidemics", "List of fields of application of statistics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Local outlier factor", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Long short-term memory", "Loss function", "Lp space", "M-estimator", "Machine Learning (journal)", "Machine learning", "Mallows's Cp", "Mann\u2013Whitney U test", "Margaret Sanger", "Mary Mallon", "Maternal health", "Maximum a posteriori estimation", "Maximum likelihood", "McGraw Hill", "McNemar's test", "Mean", "Mean-shift", "Mean and predicted response", "Mean square error", "Median", "Median-unbiased estimator", "Medical anthropology", "Medical sociology", "Medical statistics", "Mental health", "Method of least squares", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Ministry of Health and Family Welfare", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Modifiable areal unit problem", "Moment (mathematics)", "Monotone likelihood ratio", "Moving average", "Moving least squares", "Multilayer perceptron", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate probit", "Multivariate statistics", "Naive Bayes classifier", "National Diet Library", "National accounts", "Natural experiment", "Necessity and sufficiency", "Negative binomial", "Nelson\u2013Aalen estimator", "New Palgrave: A Dictionary of Economics", "Non-linear least squares", "Non-negative least squares", "Non-negative matrix factorization", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Notifiable disease", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "OPTICS algorithm", "Observational study", "Occam learning", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Official statistics", "One- and two-tailed tests", "Online machine learning", "Open defecation", "Opinion poll", "Optimal decision", "Optimal design", "Oral hygiene", "Order statistic", "Ordered logit", "Ordered probit", "Ordinal regression", "Ordinal variable", "Ordinary least squares", "Orthogonal polynomials", "Outline of machine learning", "Outline of statistics", "Overdetermined system", "PRECEDE-PROCEED model", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Patient safety", "Patient safety organization", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perceptron", "Permutation test", "Pharmaceutical policy", "Pharmacovigilance", "Phillip Good", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polychoric correlation", "Polynomial regression", "Population (statistics)", "Population health", "Population parameter", "Population statistics", "Positive deviance", "Posterior probability", "Power (statistics)", "Prediction", "Prediction interval", "Preventive healthcare", "Preventive nutrition", "Principal component analysis", "Principal component regression", "Prior probability", "Probabilistic design", "Probability distribution", "Probably approximately correct learning", "Probit model", "Professional degrees of public health", "Proportional hazards model", "Psychometrics", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Q-learning", "Quality control", "Quantile", "Quantile regression", "Quarantine", "Quasi-experiment", "Quasi-variance", "Questionnaire", "Q\u2013Q plot", "R-squared", "ROC curve", "Race and health", "Radar chart", "Random assignment", "Random effects model", "Random forest", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recurrent neural network", "Regression analysis", "Regression diagnostics", "Regression intercept", "Regression model validation", "Regression toward the mean", "Regression validation", "Regressor", "Regularized least squares", "Reinforcement learning", "Relative risk", "Relevance vector machine", "Reliability engineering", "Replication (statistics)", "Reproductive health", "Resampling (statistics)", "Residual sum of squares", "Response surface methodology", "Restricted Boltzmann machine", "Ridge regression", "Robust regression", "Robust statistics", "Ronald A. Fisher", "Run chart", "Safe sex", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scalar (physics)", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Self-organizing map", "Semi-supervised learning", "Semiparametric regression", "Sexually transmitted infection", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal processing", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smoking cessation", "Social Science Research Network", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Social statistics", "Sociology of health and illness", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spreadsheet", "Standard deviation", "Standard error", "Standard error (statistics)", "State\u2013action\u2013reward\u2013state\u2013action", "Stationary process", "Statistic", "Statistical assumption", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Structured prediction", "Student's t-test", "Studentized residual", "Sufficient statistic", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-distributed stochastic neighbor embedding", "T-test", "Temporal difference learning", "Theory of planned behavior", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Transtheoretical model", "Trend analysis", "Trend estimation", "Tropical disease", "U-Net", "U-statistic", "Udny Yule", "Uncorrelated", "Uniformly most powerful test", "United States Public Health Service", "Unsupervised learning", "V-statistic", "Vaccination", "Vaccine trial", "Vapnik\u2013Chervonenkis theory", "Variance", "Vector autoregression", "Vector control", "Wald test", "Waterborne diseases", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "William Kruskal", "World Health Organization", "World Toilet Organization", "Yadolah Dodge", "Z-test"], "references": ["http://psychclassics.yorku.ca/Fisher/Methods/", "http://ssrn.com/abstract=1406472", "http://jeff560.tripod.com/r.html", "http://onlinelibrary.wiley.com/doi/10.1002/for.3980140502/abstract", "http://pages.cs.wisc.edu/~huangyz/caip09_Long.pdf", "http://data.bnf.fr/ark:/12148/cb119445648", "http://www.incertitudes.fr/book.pdf", "http://www.erim.eur.nl/centres/necessary-condition-analysis/", "http://doi.org/10.1016%2Fj.patrec.2007.07.019", "http://doi.org/10.1068%2Fa231025", "http://doi.org/10.1093%2Fbiomet%2F2.2.211", "http://doi.org/10.1214%2F088342305000000331", "http://doi.org/10.1214%2Fss%2F1177012581", "http://doi.org/10.2139%2Fssrn.1406472", "http://doi.org/10.2307%2F2341124", "http://doi.org/10.2307%2F2979746", "http://www.imf.org/external/pubs/ft/fandd/2006/03/basics.htm", "http://www.jstor.org/stable/20061201", "http://www.jstor.org/stable/2245330", "http://www.jstor.org/stable/2331683", "http://www.jstor.org/stable/2341124", "http://www.jstor.org/stable/2979746", "http://www.vias.org/simulations/simusoft_regrot.html", "https://books.google.com/books?id=BuPNIbaN5v4C&lpg=PA274&dq=regression%20extrapolation&pg=PA274#v=onepage&q=regression%20extrapolation&f=false", "https://books.google.com/books?id=FRcOAAAAQAAJ", "https://books.google.com/books?id=ZQ8OAAAAQAAJ&printsec=frontcover&dq=Theoria+combinationis+observationum+erroribus+minimis+obnoxiae&as_brr=3#v=onepage&q=&f=false", "https://catalogue.bnf.fr/ark:/12148/cb119445648", "https://id.loc.gov/authorities/subjects/sh85112392", "https://d-nb.info/gnd/4129903-6", "https://id.ndl.go.jp/auth/ndlna/00564579", "https://web.archive.org/web/20100108055346/http://pages.cs.wisc.edu/~huangyz/caip09_Long.pdf", "https://arxiv.org/list/cs.LG/recent", "https://www.encyclopediaofmath.org/index.php?title=p/r080620", "https://www.jstor.org/stable/270724", "https://www.wikidata.org/wiki/Q208042"]}, "Univariate": {"categories": ["All articles lacking sources", "All stub articles", "Articles lacking sources from November 2009", "Mathematical terminology", "Mathematics stubs", "Theory of probability distributions"], "title": "Univariate", "method": "Univariate", "url": "https://en.wikipedia.org/wiki/Univariate", "summary": "In mathematics, univariate refers to an expression, equation, function or polynomial of only one variable. Objects of any of these types involving more than one variable may be called multivariate. In some cases the distinction between the univariate and multivariate cases is fundamental; for example, the fundamental theorem of algebra and Euclid's algorithm for polynomials are fundamental properties of univariate polynomials that cannot be generalized to multivariate polynomials.\nThe term is commonly used in statistics to distinguish a distribution of one variable from a distribution of several variables, although it can be applied in other ways as well. For example, univariate data are composed of a single scalar component. In time series analysis, the term is applied with a whole time series as the object referred to: thus a univariate time series refers to the set of values over time of a single quantity. Correspondingly, a \"multivariate time series\" refers to the changing values over time of several quantities. Thus there is a minor conflict of terminology since the values within a univariate time series may be treated using certain types of multivariate statistical analyses and may be represented using multivariate distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/35/E-to-the-i-pi.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bivariate (disambiguation)", "Equation", "Euclid's algorithm for polynomials", "Expression (mathematics)", "Frequency distribution", "Function (mathematics)", "Fundamental theorem of algebra", "Joint distributions", "Multivariate statistics", "Polynomial", "Scalar (mathematics)", "Statistics", "Time series analysis", "Univariate analysis", "Univariate binary model", "Univariate distribution", "Univariate time series", "Variable (mathematics)"], "references": []}, "Kendall's W": {"categories": ["Inter-rater reliability", "Nonparametric statistics"], "title": "Kendall's W", "method": "Kendall's W", "url": "https://en.wikipedia.org/wiki/Kendall%27s_W", "summary": "Kendall's W (also known as Kendall's coefficient of concordance) is a non-parametric statistic. It is a normalization of the statistic of the Friedman test, and can be used for assessing agreement among raters. Kendall's W ranges from 0 (no agreement) to 1 (complete agreement).\nSuppose, for instance, that a number of people have been asked to rank a list of political concerns, from most important to least important. Kendall's W can be calculated from these data. If the test statistic W is 1, then all the survey respondents have been unanimous, and each respondent has assigned the same order to the list of concerns. If W is 0, then there is no overall trend of agreement among the respondents, and their responses may be regarded as essentially random. Intermediate values of W indicate a greater or lesser degree of unanimity among the various responses.\nWhile tests using the standard Pearson correlation coefficient assume normally distributed values and compare two sequences of outcomes at a time, Kendall's W makes no assumptions regarding the nature of the probability distribution and can handle any number of distinct outcomes.\nW is linearly related to the mean value of the Spearman's rank correlation coefficients between all pairs of the rankings over which it is calculated.\n\n", "images": [], "links": ["Block design", "Copula (probability theory)", "Digital object identifier", "Friedman test", "International Standard Book Number", "JSTOR", "Kendall's tau", "Maurice Kendall", "Non-parametric statistic", "Normally distributed", "Pearson correlation coefficient", "Probability distribution", "Significance test", "Spearman's rank correlation coefficient", "Yadolah Dodge"], "references": ["http://www.bio.umontreal.ca/legendre/reprints/Kendall_W_paper.pdf", "http://doi.org/10.1080%2F00949655.2013.766189", "http://doi.org/10.1214%2Faoms%2F1177732186", "http://www.jstor.org/stable/2235668", "https://dx.doi.org/10.1080/00949655.2013.766189"]}, "Multivariate probit model": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2017", "Regression models"], "title": "Multivariate probit model", "method": "Multivariate probit model", "url": "https://en.wikipedia.org/wiki/Multivariate_probit_model", "summary": "In statistics and econometrics, the multivariate probit model is a generalization of the probit model used to estimate several correlated binary outcomes jointly. For example, if it is believed that the decisions of sending at least one child to public school and that of voting in favor of a school budget are correlated (both decisions are binary), then the multivariate probit model would be appropriate for jointly predicting these two choices on an individual-specific basis. This approach was initially developed by Siddhartha Chib and Edward Greenberg.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Bivariate normal distribution", "Cumulative distribution function", "Digital object identifier", "Discrete choice", "Econometrics", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "GHK algorithm", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Isotonic regression", "Iteratively reweighted least squares", "Latent variable", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Maximum likelihood", "Mean and predicted response", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Weighted least squares"], "references": ["http://doi.org/10.1007%2Fs10994-017-5652-6", "https://academic.oup.com/biomet/article-abstract/85/2/347/298820", "https://link.springer.com/content/pdf/10.1007%2Fs10994-017-5652-6.pdf"]}, "Comparison of general and generalized linear models": {"categories": ["All articles needing additional references", "All stub articles", "Articles needing additional references from September 2014", "Generalized linear models", "Statistics stubs"], "title": "Comparison of general and generalized linear models", "method": "Comparison of general and generalized linear models", "url": "https://en.wikipedia.org/wiki/Comparison_of_general_and_generalized_linear_models", "summary": "", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ANCOVA", "ANOVA", "Bayesian probability", "Best linear unbiased prediction", "EViews", "General linear model", "Generalized linear model", "International Standard Book Number", "John Nelder", "Least squares", "Linear regression", "Logistic regression", "MANCOVA", "MANOVA", "Mathematica", "Matlab (programming language)", "Maximum likelihood", "Mixed model", "Peter McCullagh", "Poisson regression", "R (programming language)", "SAS System", "SPSS", "Stata", "Statistics", "Wolfram Language"], "references": ["http://www.eviews.com/help/helpintro.html#page/content/commandcmd-ls.html", "http://www.eviews.com/help/helpintro.html#page/content/commandcmd-glm.html", "http://reference.wolfram.com/language/ref/GeneralizedLinearModelFit.html", "http://reference.wolfram.com/language/ref/LinearModelFit.html"]}, "Excess risk": {"categories": ["Epidemiology", "Medical statistics"], "title": "Risk difference", "method": "Excess risk", "url": "https://en.wikipedia.org/wiki/Risk_difference", "summary": "In epidemiology, risk difference (RD) or excess risk is the difference between the risk of an outcome in the exposed group and the unexposed group. It is computed as \n \n \n \n \n I\n \n e\n \n \n \u2212\n \n I\n \n u\n \n \n \n \n {\\displaystyle I_{e}-I_{u}}\n , where \n \n \n \n \n I\n \n e\n \n \n \n \n {\\displaystyle I_{e}}\n is the incidence in the exposed group, and \n \n \n \n \n I\n \n u\n \n \n \n \n {\\displaystyle I_{u}}\n is the incidence in the unexposed group. If the risk of an outcome is increased by the exposure, the term absolute risk increase (ARI) is used, and computed as \n \n \n \n \n I\n \n e\n \n \n \u2212\n \n I\n \n u\n \n \n \n \n {\\displaystyle I_{e}-I_{u}}\n . Equivalently, If the risk of an outcome is decreased by the exposure, the term absolute risk reduction (ARR) is used, and computed as \n \n \n \n \n I\n \n u\n \n \n \u2212\n \n I\n \n e\n \n \n \n \n {\\displaystyle I_{u}-I_{e}}\n .The inverse of the absolute risk reduction is the number needed to treat, and the inverse of the absolute risk increase is the number needed to harm.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5d/Illustration_of_risk_reduction.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/5/5d/20180916192654%21Illustration_of_risk_reduction.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/5/5d/20180916173618%21Illustration_of_risk_reduction.svg"], "links": ["Abbreviation", "Absolute risk reduction", "Academic clinical trials", "Adaptive clinical trial", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Ben Goldacre", "Blind experiment", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Colon cancer", "Contingency table", "Control event rate", "Correlation does not imply causation", "Cross-sectional study", "Cumulative incidence", "Design of experiments", "Digital object identifier", "Ecological study", "Epidemiological methods", "Epidemiology", "Evidence-based medicine", "Experiment", "Experimental event rate", "First-in-man study", "Glossary of clinical research", "Hazard ratio", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Intention-to-treat analysis", "International Standard Book Number", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "Natural number", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "OCLC", "Observational study", "Odds ratio", "Open-label trial", "Period prevalence", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk", "Risk ratio", "Risk\u2013benefit ratio", "Scientific control", "Seeding trial", "Selection bias", "Specificity and sensitivity", "Standard score", "Statistical significance", "Survivorship bias", "Systematic review", "Vaccine trial", "Virulence"], "references": ["http://www.oxfordreference.com/view/10.1093/acref/9780199976720.001.0001/acref-9780199976720", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2844943", "http://www.ncbi.nlm.nih.gov/pubmed/20332511", "http://doi.org/10.1093%2Facref%2F9780199976720.001.0001", "http://doi.org/10.1136%2Fbmj.c869", "http://www.worldcat.org/oclc/750986180", "https://www.academia.edu/16420844/Measuring_Effectiveness", "https://www.worldcat.org/oclc/750986180"]}, "Quality control": {"categories": ["CS1 errors: external links", "CS1 maint: Multiple names: authors list", "Design for X", "Pages using citations with accessdate and no URL", "Quality control", "Quality management", "Statistical process control", "Use dmy dates from September 2010", "Wikipedia articles incorporating text from MIL-STD-188", "Wikipedia articles incorporating text from the Federal Standard 1037C", "Wikipedia articles with NDL identifiers"], "title": "Quality control", "method": "Quality control", "url": "https://en.wikipedia.org/wiki/Quality_control", "summary": "Quality control (QC) is a process by which entities review the quality of all factors involved in production. ISO 9000 defines quality control as \"A part of quality management focused on fulfilling quality requirements\".This approach places an emphasis on three aspects (enshrined in standards such as ISO 9001):\n\nElements such as controls, job management, defined and well managed processes, performance and integrity criteria, and identification of records\nCompetence, such as knowledge, skills, experience, and qualifications\nSoft elements, such as personnel, integrity, confidence, organizational culture, motivation, team spirit, and quality relationships.Inspection is a major component of quality control, where physical product is examined visually (or the end results of a service are analyzed). Product inspectors will be provided with lists and descriptions of unacceptable product defects such as cracks or surface blemishes for example.The quality of the outputs is at risk if any of these three aspects is deficient in any way.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cc/Fotothek_df_n-04_0000019.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Acceptance sampling", "Actuarial science", "Akaike information criterion", "American Society for Quality", "Analysis of covariance", "Analysis of variance", "Analytical quality control", "Anderson\u2013Darling test", "Anvil", "Arithmetic mean", "Armand V. Feigenbaum", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Cambridge, Massachusetts", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Cincinnati", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Control system", "Copyright status of work by the U.S. government", "Corrective and preventative action", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "East Germany", "Econometrics", "Effect size", "Efficiency (statistics)", "Eight dimensions of quality", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Englewood Cliffs, New Jersey", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "First article inspection", "Forest plot", "Fourier analysis", "Fracture", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General Services Administration", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Go/no go", "Good Automated Manufacturing Practice", "Good manufacturing practice", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Harvard Business Review", "Harvard University Press", "Heteroscedasticity", "Histogram", "History of technology", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "ISO 9000", "Index of dispersion", "Indianapolis, Indiana", "Inspection", "Integrity", "Interaction (statistics)", "Interchangeable parts", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Joseph M. Juran", "Kaoru Ishikawa", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lean Six Sigma", "Lean enterprise", "Lean manufacturing", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MIL-STD-188", "Mann\u2013Whitney U test", "Mass production", "Maximum a posteriori estimation", "Maximum likelihood", "McGraw-Hill", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Milwaukee", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Motivation", "Motorola", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New York City", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "OCLC", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Organizational culture", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Plug gauge", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Prentice-Hall", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Product (business)", "Product defect", "Project management", "Proportional hazards model", "Psychometrics", "QA/QC", "Quality Control Music", "Quality assurance", "Quality control (disambiguation)", "Quality management framework", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Ring gauge", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Schaumburg, Illinois", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Six Sigma", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard operating procedure", "Stationary process", "Statistic", "Statistical Quality Control", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stone tools", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Team spirit", "Test method", "Time domain", "Time series", "Tolerance interval", "Total Quality Management", "Trend estimation", "U-statistic", "Uniformly most powerful test", "United States Department of Defense", "V-statistic", "Variance", "Vector autoregression", "Volkseigener Betrieb", "Wald test", "Walter A. Shewhart", "Waste", "Wavelet", "Western Electric Company", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.motorolasolutions.com", "http://www.motorolasolutions.com/web/Business/_Moto_University/_Documents/_Static_Files/What_is_SixSigma.pdf", "http://www.pmhut.com/quality-control-in-project-management", "http://www.praxiom.com/iso-9001.htm", "http://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm", "http://www.opm.gov/fedclass/gs1910.pdf", "http://www.astm.org/Standards/quality-control-standards.html", "http://www.nationalcallcenters.org/images/stories/InQueue/Vol2No22.pdf", "http://www.nationalcallcenters.org/images/stories/InQueue/vol2no21.pdf", "http://www.worldcat.org/issn/0017-8012", "http://www.worldcat.org/oclc/1045408", "http://www.worldcat.org/oclc/11467749", "http://www.worldcat.org/oclc/1220529", "http://www.worldcat.org/oclc/1701274", "http://www.worldcat.org/oclc/1751795", "http://www.worldcat.org/oclc/32394752", "http://www.worldcat.org/oclc/33858387", "http://www.worldcat.org/oclc/38475486", "http://www.worldcat.org/oclc/567344", "https://id.ndl.go.jp/auth/ndlna/00563228", "https://archive.org/details/controlofquality00radf", "https://archive.org/stream/CAT10502416#page/2/mode/2up", "https://web.archive.org/web/20131203031507/http://www.motorolasolutions.com/web/Business/_Moto_University/_Documents/_Static_Files/What_is_SixSigma.pdf", "https://www.wikidata.org/wiki/Q827792"]}, "Simpson's paradox": {"categories": ["1951 introductions", "All articles with unsourced statements", "Articles with short description", "Articles with unsourced statements from August 2017", "Causal inference", "Commons category link is on Wikidata", "Probability theory paradoxes", "Statistical paradoxes"], "title": "Simpson's paradox", "method": "Simpson's paradox", "url": "https://en.wikipedia.org/wiki/Simpson%27s_paradox", "summary": "Simpson's paradox, or the Yule\u2013Simpson effect, is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined. It is sometimes given the descriptive title reversal paradox or amalgamation paradox.This result is often encountered in social-science and medical-science statistics and is particularly problematic when frequency data is unduly given causal interpretations. The paradoxical elements disappear when causal relations are brought into consideration. It has been used to try to inform the non-specialist or public audience about the kind of misleading results mis-applied statistics can generate. Martin Gardner wrote a popular account of Simpson's paradox in his March 1976 Mathematical Games column in Scientific American.Edward H. Simpson first described this phenomenon in a technical paper in 1951, but the statisticians Karl Pearson et al., in 1899, and Udny Yule, in 1903, had mentioned similar effects earlier. The name Simpson's paradox was introduced by Colin R. Blyth in 1972.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9b/Simpson_paradox_balances.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cd/Simpson_paradox_vectors.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/4/47/Simpson%27s_paradox_continuous.svg"], "links": ["Alexander Bogomolny", "Anscombe's quartet", "BMJ", "Baseball-Reference.com", "Batting average", "Bayesian Networks", "Bayesian networks", "Berkson's paradox", "Biometrika", "Br Med J (Clin Res Ed)", "Causal", "Chemistry", "Confounding", "Coralie Colmez", "Correlation", "David A. Freedman", "David Justice", "Derek Jeter", "Digital object identifier", "Ecological correlation", "Ecological fallacy", "Edoardo Airoldi", "Edward H. Simpson", "Engineering", "Graduate school", "I. J. Good", "International Standard Book Number", "International Standard Serial Number", "Intuition", "JSTOR", "John Wiley and Sons", "Journal of the Royal Statistical Society", "Judea Pearl", "Karl Pearson", "Kidney stone", "Leila Schneps", "Low birth-weight paradox", "Martin Gardner", "Mathematical Games column", "Mathematics Magazine", "Mind", "MinutePhysics", "Modifiable areal unit problem", "PDF", "Parallelogram rule", "Path analysis (statistics)", "Percutaneous nephrolithotomy", "Peter J. Bickel", "Philosopher", "Philosophical Transactions of the Royal Society A", "Probability", "Probability calculus", "Professional baseball", "Prosecutor's fallacy", "PubMed Central", "PubMed Identifier", "Sample size", "Science (journal)", "Scientific American", "Significance (magazine)", "Slope", "Stanford Encyclopedia of Philosophy", "Statistical significance", "Statistics", "Sure-thing principle", "The American Statistician", "The Annals of Statistics", "Udny Yule", "University of California, Berkeley", "Vector (geometry)", "Vector space", "W. W. Norton & Company"], "references": ["http://bmj.bmjjournals.com/cgi/content/full/309/6967/1480", "http://stats.stackexchange.com/questions/78255/how-to-resolve-simpsons-paradox", "http://ed.ted.com/lessons/how-statistics-can-be-misleading-mark-liddell", "http://jeff560.tripod.com/s.html", "http://flowcytometry.sysbio.med.harvard.edu/files/flowcytometryhms/files/herzenbergfacshistory.pdf#129", "http://www.math.siu.edu/kocik/papers/simpson2.pdf", "http://plato.stanford.edu/entries/paradox-simpson/", "http://cits.tamiu.edu/kock/pubs/journals/2015JournalIJeC/Kock_2015_IJeC_SimpPdox.pdf", "http://cits.tamiu.edu/kock/pubs/journals/2016JournalIJANS_ModJCveNetCorrp/Kock_Gaskins_2016_IJANS_SimpPdox.pdf", "http://bayes.cs.ucla.edu/LECTURE/lecture_sec1.htm", "http://bayes.cs.ucla.edu/R264.pdf", "http://ftp.cs.ucla.edu/pub/stat_ser/r414.pdf", "http://ftp.cs.ucla.edu/pub/stat_ser/r466.pdf", "http://homepage.stat.uiowa.edu/~mbognar/1030/Bickel-Berkeley.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1339981", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2541623", "http://www.ncbi.nlm.nih.gov/pubmed/17835295", "http://www.ncbi.nlm.nih.gov/pubmed/3083922", "http://www.ncbi.nlm.nih.gov/pubmed/7804052", "http://jco.ascopubs.org/content/34/9/1016.1.full", "http://www.cut-the-knot.org/Curriculum/Algebra/SimpsonParadox.shtml", "http://www.cut-the-knot.org/blue/Mediant.shtml", "http://doi.org/10.1093%2Fbiomet%2F2.2.121", "http://doi.org/10.1098%2Frsta.1899.0006", "http://doi.org/10.1126%2Fscience.187.4175.398", "http://doi.org/10.1136%2Fbmj.292.6524.879", "http://doi.org/10.1136%2Fbmj.309.6967.1480", "http://doi.org/10.1198%2Ftast.2009.09007", "http://doi.org/10.1214%2Faos%2F1176350369", "http://doi.org/10.1371%2Fjournal.pcbi.1005535", "http://doi.org/10.2307%2F2284382", "http://doi.org/10.2307%2F2684093", "http://doi.org/10.2307%2F2691038", "http://www.jstor.org/stable/2241334", "http://www.jstor.org/stable/2284382", "http://www.jstor.org/stable/2684093", "http://www.worldcat.org/issn/0090-5364", "http://www.worldcat.org/issn/1553-7358", "http://www.statslife.org.uk/the-statistics-dictionary/2012-simpson-s-paradox-a-cautionary-tale-in-advanced-analytics", "https://www.baseball-reference.com/j/jeterde01.shtml", "https://www.baseball-reference.com/j/justida01.shtml", "https://www.wsj.com/articles/SB125970744553071829", "https://www.youtube.com/watch?v=ebEkn-BiW5k", "https://www.youtube.com/watch?v=s7x5P1yiYks&list=PL0FfKwFuQb2Trlr06KCyfdGZyE5Et-Pgj&index=1"]}, "Test for structural change": {"categories": ["Business cycle", "Change", "Wikipedia articles with GND identifiers"], "title": "Structural change", "method": "Test for structural change", "url": "https://en.wikipedia.org/wiki/Structural_change", "summary": "In economics, structural change is a shift or change in the basic ways a market or economy functions or operates.Such change can be caused by such factors as economic development, global shifts in capital and labor, changes in resource availability due to war or natural disaster or discovery or depletion of natural resources, or a change in political system. For example, a subsistence economy may be transformed into a manufacturing economy, or a regulated mixed economy may be liberalized. A current driver of structural change in the world economy is globalization. Structural change is possible because of the dynamic nature of the economic system.Patterns and changes in sectoral employment drive demand shifts through the income elasticity. Shifting demand for both locally sourced goods and for imported products is a fundamental part of development. The structural changes that move countries through the development process are often viewed in terms of shifts from primary, to secondary and finally, to tertiary production. Technical progress is seen as crucial in the process of structural change as it involves the obsolescence of skills, vocations, and permanent changes in spending and production resulting in structural unemployment.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/b/ba/US_employment_by_sectors%2C_both_genders.png"], "links": ["Agriculture", "Allan George Barnard Fisher", "Chow test", "Coal and steel industry", "Data set", "Digital object identifier", "Division of Korea", "Dortmund", "Econometrics", "Economic development", "Economic system", "Germany", "Globalization", "IT", "Income elasticity", "Integrated Authority File", "International Standard Book Number", "Korea under Japanese rule", "Logistics", "Manufacturing", "Micro systems technology", "Mixed economy", "Obsolescence", "Primary sector", "Replication (statistics)", "Revolutions of 1989", "Ruhr", "Samsung", "Service (economics)", "Signal Iduna", "South Korea", "Sovereign state", "Statistical hypothesis testing", "Structural break", "Structural fix", "Structural unemployment", "Subsistence economy", "Tertiary sector", "Wilo", "World War II"], "references": ["http://www.investopedia.com/terms/s/structural_change.asp", "http://ssrn.com/abstract=1449085", "http://doi.org/10.1016%2F0016-3287(80)90091-9", "https://d-nb.info/gnd/4058136-6", "https://web.archive.org/web/20141117072912/http://www.bluenomics.com/data#!data/national_accounts_gdp/gdp_production_approach/structure_of_gross_value_added_by_sectors_gva_/structure_of_gross_value_added_by_sectors_gva_annual_of_gdp%7Cchart/line$countries=usa&sorting=list//title", "https://www.wikidata.org/wiki/Q1969120"]}, "Contingency table": {"categories": ["CS1 errors: dates", "Commons category link is on Wikidata", "Contingency table", "Frequency distribution", "Infographics"], "title": "Contingency table", "method": "Contingency table", "url": "https://en.wikipedia.org/wiki/Contingency_table", "summary": "In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering and scientific research. They provide a basic picture of the interrelation between two variables and can help find interactions between them. The term contingency table was first used by Karl Pearson in \"On the Theory of Contingency and Its Relation to Association and Normal Correlation\", part of the Drapers' Company Research Memoirs Biometric Series I published in 1904.\nA crucial problem of multivariate statistics is finding the (direct-)dependence structure underlying the variables contained in high-dimensional contingency tables. If some of the conditional independences are revealed, then even the storage of the data can be done in a smarter way (see Lauritzen (2002)). In order to do this one can use information theory concepts, which gain the information only from the distribution of probability, which can be expressed easily from the contingency table by the relative frequencies.\nA pivot table is a way to create contingency tables using spreadsheet software.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Barnard's test", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional independence", "Confidence interval", "Confounding", "Confusion matrix", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Cram\u00e9r's V", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Drapers' Company", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's exact test", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gamma test (statistics)", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodman and Kruskal's gamma", "Goodman and Kruskall's lambda", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Handedness", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "If and only if", "Index of dispersion", "Information theory", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iterative proportional fitting", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kendall tau", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Main diagonal", "Mann\u2013Whitney U test", "Marginal total", "Mathematical Reviews", "Matrix (mathematics)", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal variable", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phi coefficient", "Pie chart", "Pivot table", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polychoric correlation", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Solomon Kullback", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Steffen L. Lauritzen", "Stem-and-leaf display", "Stephen Fienberg", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "TPL Tables", "Table (information)", "Tau b", "Tau c", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uncertainty coefficient", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Yvonne Bishop", "Z-test"], "references": ["http:ftp://ftp.cdc.gov/pub/Software/epi_info/EIHAT_WEB/Lesson5AnalysisCreatingStatistics.pdf", "http://www.custominsight.com/articles/crosstab-sample.asp", "http://people.revoledu.com/kardi/tutorial/Questionnaire/ContingencyTable.html", "http://www.andrews.edu/~calkins/math/edrm611/edrm13.htm", "http://www.physics.csbsju.edu/stats/contingency.html", "http://webarchive.loc.gov/all/20011127081700/http://www2.chass.ncsu.edu/garson/pa765/assocnominal.htm", "http://www.ams.org/mathscinet-getitem?mr=0381130", "http://www.ams.org/mathscinet-getitem?mr=1633357", "http://statpages.org/ctab2x2.html", "http://www.stats.ox.ac.uk/~steffen/papers/cont.pdf", "https://archive.org/details/cu31924003064833", "https://web.archive.org/web/20050113063235/http://www.csupomona.edu/~jlkorey/POWERMUTT/Topics/displaying_categorical_data.html", "https://web.archive.org/web/20110717190345/http://www.childrensmercy.org/stats/journal/oddsratio.asp"]}, "Law of total probability": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from September 2010", "Probability theorems", "Statistical laws"], "title": "Law of total probability", "method": "Law of total probability", "url": "https://en.wikipedia.org/wiki/Law_of_total_probability", "summary": "In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events\u2014hence the name.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png"], "links": ["Bayes' theorem", "Boole's inequality", "Complementary event", "Conditional independence", "Conditional probabilities", "Conditional probability", "Countable set", "Discrete random variable", "Dominic Welsh", "Elementary event", "Event (probability theory)", "Geoffrey Grimmett", "Independence (probability theory)", "International Standard Book Number", "Joint probability distribution", "Law of large numbers", "Law of total cumulance", "Law of total expectation", "Law of total variance", "Light bulb", "Marginal distribution", "Marginal probability", "Measurable set", "Pairwise disjoint", "Partition of a set", "Probability axioms", "Probability measure", "Probability space", "Probability theory", "Proposition", "Random variable", "Sample space", "Statistics", "Tree diagram (probability theory)", "Union (set theory)", "Venn diagram", "Weighted average"], "references": ["https://books.google.com/books?id=Kglc9g5IPf4C&pg=PA179", "https://books.google.com/books?id=Vj3NZ59ZcnoC&pg=PA58", "https://books.google.com/books?id=_mayRBczVRwC&pg=PA47"]}, "Fleming\u2013Viot process": {"categories": ["All stub articles", "Markov processes", "Martingale theory", "Probability stubs", "Statistical genetics"], "title": "Fleming\u2013Viot process", "method": "Fleming\u2013Viot process", "url": "https://en.wikipedia.org/wiki/Fleming%E2%80%93Viot_process", "summary": "In probability theory, a Fleming\u2013Viot process (F\u2013V process) is a member of a particular subset of probability measure-valued Markov processes on compact metric spaces, as defined in the 1979 paper by Wendell Helms Fleming and Michel Viot. Such processes are martingales and diffusions.\nThe Fleming\u2013Viot processes have proved to be important to the development of a mathematical basis for the theories behind allele drift.\nThey are generalisations of the Wright\u2013Fisher process and arise as infinite population limits of suitably rescaled variants of Moran processes.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "ArXiv", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Coalescent theory", "Compact space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Genetic drift", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Metric space", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability", "Probability measure", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "Voter model", "Wendell Fleming", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://www.iumj.indiana.edu/IUMJ/FTDLOAD/1979/28/28058/pdf", "http://www.lorentzcenter.nl/lc/web/2006/189/ferrari2.pdf", "http://arxiv.org/abs/0904.3039", "http://doi.org/10.1239%2Fjap%2F1308662630"]}, "Stationary subspace analysis": {"categories": ["All Wikipedia articles needing context", "All articles needing additional references", "All pages needing cleanup", "Articles created via the Article Wizard", "Articles needing additional references from November 2010", "Articles with multiple maintenance issues", "Multivariate time series", "Wikipedia articles needing context from November 2010", "Wikipedia introduction cleanup from November 2010"], "title": "Stationary subspace analysis", "method": "Stationary subspace analysis", "url": "https://en.wikipedia.org/wiki/Stationary_subspace_analysis", "summary": "Stationary Subspace Analysis (SSA) is a blind source separation algorithm which factorizes a multivariate time series into stationary and non-stationary components.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Algorithm", "Blind signal separation", "Blind source separation", "Brain-computer interface", "Cointegration", "Computer vision", "EEG", "Factor analysis", "Independent component analysis", "International Standard Book Number", "Non-stationary", "Stationary process", "Time series"], "references": ["https://www.ncbi.nlm.nih.gov/pubmed/21096218", "https://dx.doi.org/10.1007/978-3-642-17537-4_52", "https://dx.doi.org/10.1103/PhysRevLett.103.214101", "https://dx.doi.org/10.1109/ICCVW.2009.5457715"]}, "Nuisance variable": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2009", "Latent variable models", "Stochastic processes"], "title": "Nuisance variable", "method": "Nuisance variable", "url": "https://en.wikipedia.org/wiki/Nuisance_variable", "summary": "In the theory of stochastic processes in probability theory and statistics, a nuisance variable is a random variable that is fundamental to the probabilistic model, but that is of no particular interest in itself or is no longer of interest: one such usage arises for the Chapman\u2013Kolmogorov equation. For example, a model for a stochastic process may be defined conceptually using intermediate variables that are not observed in practice. If the problem is to derive the theoretical properties, such as the mean, variance and covariances of quantities that would be observed, then the intermediate variables are nuisance variables.The related term nuisance factor has been used in the context of block experiments, where the terms in the model representing block-means, often called \"factors\", are of no interest. Many approaches to the analysis of such experiments, particularly where the experimental design is subject to randomization, treat these factors as random variables. More recently, \"nuisance variable\" has been used in the same context.\"Nuisance variable\" has been used in the context of statistical surveys to refer information that is not of direct interest but which needs to be taken into account in an analysis.In the context of stochastic models, the treatment of nuisance variables does not necessarily involve working with the full joint distribution of all the random variables involved, although this is one approach. Instead, an analysis may proceed directly to the quantities of interest.\nThe term nuisance variable is sometimes also used in more general contexts, simply to designate those variables that are marginalised over when finding a marginal distribution. In particular, the term may sometimes be used in the context of Bayesian analysis as an alternative to nuisance parameter, given that Bayesian statistics allows parameters to be treated as having probability distributions. However this is usually avoided as the term nuisance parameter has a specific meaning in statistical theory.", "images": [], "links": ["Bayesian analysis", "Bayesian statistics", "Chapman\u2013Kolmogorov equation", "Digital object identifier", "Experimental design", "International Standard Book Number", "Marginal distribution", "Nuisance parameter", "Probabilistic model", "Probability theory", "PubMed Central", "PubMed Identifier", "Random variable", "Randomized block design", "Sean Eddy", "Statistics", "Stochastic process", "Stochastic processes"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2396288", "http://www.ncbi.nlm.nih.gov/pubmed/16731313", "http://www.ncbi.nlm.nih.gov/pubmed/18516236", "http://doi.org/10.1016%2Fj.pec.2006.04.002", "http://doi.org/10.1371%2Fjournal.pcbi.1000069"]}, "Sufficient statistic": {"categories": ["Articles containing proofs", "Statistical principles", "Statistical theory"], "title": "Sufficient statistic", "method": "Sufficient statistic", "url": "https://en.wikipedia.org/wiki/Sufficient_statistic", "summary": "In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if \"no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter\". In particular, a statistic is sufficient for a family of probability distributions if the sample from which it is calculated gives no additional information than does the statistic, as to which of those probability distributions is that of the population from which the sample was taken.\nA related concept is that of linear sufficiency, which is weaker than sufficiency but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic.\nThe concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted 1973 that the concept of sufficiency had fallen out of favor in descriptive statistics because of the strong dependence on an assumption of the distributional form (see Pitman\u2013Koopman\u2013Darmois theorem below), but remained very important in theoretical work.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Adrian Smith (academic)", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Ancillary statistic", "Anderson\u2013Darling test", "Annals of Statistics", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Basu's theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli trial", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional probability distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "David Blackwell", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Euclidean vector", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fair coin", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gamma distribution", "Gaussian distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "German tank problem", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "If and only if", "Independent identically distributed", "Index of dispersion", "Indicator function", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jacobian matrix and determinant", "Jahrbuch \u00fcber die Fortschritte der Mathematik", "Jarque\u2013Bera test", "Johansen test", "Joint distribution", "Joint probability distribution", "Jonckheere's trend test", "Jos\u00e9-Miguel Bernardo", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov structure function", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimator", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameter", "Parametric family", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample (statistics)", "Sample maximum", "Sample mean", "Sample median", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistically independent", "Statistics", "Stem-and-leaf display", "Stephen Stigler", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient dimension reduction", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "Zentralblatt MATH"], "references": ["http://digital.library.adelaide.edu.au/dspace/handle/2440/15172", "http://www.ams.org/mathscinet-getitem?mr=0326872", "http://www.ams.org/mathscinet-getitem?mr=0663456", "http://www.ams.org/mathscinet-getitem?mr=1731351", "http://cnx.org/content/m11480/1.6/", "http://doi.org/10.1016%2FS0167-7152(99)00089-9", "http://doi.org/10.1093%2Fbiomet%2F60.3.439", "http://doi.org/10.1098%2Frsta.1922.0009", "http://doi.org/10.1214%2Faos%2F1176345895", "http://doi.org/10.2143%2Fast.17.1.2014984", "http://www.jstor.org/stable/2334992", "http://www.jstor.org/stable/2345978", "http://www.jstor.org/stable/2984375", "http://www.jstor.org/stable/91208", "http://zbmath.org/?format=complete&q=an:0485.62004", "http://zbmath.org/?format=complete&q=an:0964.62003", "http://zbmath.org/?format=complete&q=an:48.1280.02", "https://www.encyclopediaofmath.org/index.php?title=S/s091070"]}, "Weighted covariance matrix": {"categories": ["All articles needing additional references", "All articles needing expert attention", "All articles that are too technical", "Articles needing additional references from February 2008", "Articles needing expert attention from June 2014", "Articles with multiple maintenance issues", "Covariance and correlation", "Estimation methods", "Matrices", "Summary statistics", "U-statistics", "Wikipedia articles that are too technical from June 2014"], "title": "Sample mean and covariance", "method": "Weighted covariance matrix", "url": "https://en.wikipedia.org/wiki/Sample_mean_and_covariance", "summary": "The sample mean or empirical mean and the sample covariance are statistics computed from a collection (the sample) of data on one or more random variables.\nThe sample mean and sample covariance are estimators of the population mean and population covariance, where the term population refers to the set from which the sample was taken.\nThe sample mean is a vector each of whose elements is the sample mean of one of the random variables \u2013 that is, each of whose elements is the arithmetic average of the observed values of one of the variables. The sample covariance matrix is a square matrix whose i, j element is the sample covariance (an estimate of the population covariance) between the sets of observed values of two of the variables and whose i, i element is the sample variance of the observed values of one of the variables. If only one variable has had values observed, then the sample mean is a single number (the arithmetic average of the observed values of that variable) and the sample covariance matrix is also simply a single value (a 1x1 matrix containing a single number, the sample variance of the observed values of that variable).\nDue to their ease of calculation and other desirable characteristics, the sample mean and sample covariance are widely used in statistics and applications to numerically represent the location and dispersion, respectively, of a distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Arithmetic average", "Arithmetic mean", "Bart Kosko", "Bessel's correction", "Bias of an estimator", "Covariance", "Covariance matrix", "Estimation of covariance matrices", "Estimator", "Estimators", "Gaussian distribution", "International Standard Book Number", "Interquartile range", "Location parameter", "Matrix (mathematics)", "Maximum likelihood", "Mean", "Multivariate random variable", "Normalizing constant", "Outliers", "Positive semi-definite matrix", "Probability distribution", "Quantile", "Random variable", "Random variables", "Random vector", "Realization (probability)", "Robust statistics", "Sample (statistics)", "Sample median", "Sample variance", "Scatter matrix", "Standard error of the mean", "Statistic", "Statistical dispersion", "Statistical population", "Trimmed estimator", "Trimmed mean", "Unbiased estimation of standard deviation", "Vector (mathematics)", "Weighted mean", "Winsorising", "Winsorized mean"], "references": ["http://www.edge.org/q2008/q08_16.html#kosko", "https://books.google.com/books?id=gFWcQgAACAAJ", "https://www.gnu.org/software/gsl/manual", "https://www.gnu.org/software/gsl/manual/html_node/Weighted-Samples.html"]}, "Projection pursuit": {"categories": ["Exploratory data analysis", "Multivariate statistics"], "title": "Projection pursuit", "method": "Projection pursuit", "url": "https://en.wikipedia.org/wiki/Projection_pursuit", "summary": "Projection pursuit (PP) is a type of statistical technique which involves finding the most \"interesting\" possible projections in multidimensional data. Often, projections which deviate more from a normal distribution are considered to be more interesting. As each projection is found, the data are reduced by removing the component along that projection, and the process is repeated to find new projections; this is the \"pursuit\" aspect that motivated the technique known as matching pursuit.The idea of projection pursuit is to locate the projection or projections from high-dimensional space to low-dimensional space that reveal the most details about the structure of the data set. Once an interesting set of projections has been found, existing structures (clusters, surfaces, etc.) can be extracted and analyzed separately.\nProjection pursuit has been widely used for blind source separation, so it is very important in independent component analysis. Projection pursuit seeks one projection at a time such that the extracted signal is as non-Gaussian as possible.", "images": [], "links": ["Blind source separation", "Digital object identifier", "Discriminant analysis", "Factor analysis", "High-dimensional space", "Independent component analysis", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Jerome H. Friedman", "John Tukey", "Matching pursuit", "Normal distribution", "Principal component analysis", "Projection (linear algebra)", "Projection pursuit regression", "Targeted projection pursuit"], "references": ["http://www.stat.rutgers.edu/~rebecka/Stat687/huber.pdf", "http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-1312.pdf", "http://doi.org/10.1109%2FT-C.1974.224051", "http://doi.org/10.1214%2Faos%2F1176349519", "http://doi.org/10.2307%2F2981662", "http://www.jstor.org/stable/2981662", "http://www.worldcat.org/issn/0018-9340"]}, "Kalman filter": {"categories": ["All Wikipedia articles written in American English", "All articles needing additional references", "All articles to be expanded", "All articles with unsourced statements", "Articles needing additional references from April 2016", "Articles needing additional references from December 2010", "Articles to be expanded from August 2011", "Articles using small message boxes", "Articles with unsourced statements from December 2010", "CS1 maint: Multiple names: authors list", "CS1 maint: Uses authors parameter", "Control theory", "Hungarian inventions", "Linear filters", "Markov models", "Nonlinear filters", "Robot control", "Signal estimation", "Stochastic differential equations", "Use American English from March 2018", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers", "Wikipedia external links cleanup from June 2015", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from June 2015"], "title": "Kalman filter", "method": "Kalman filter", "url": "https://en.wikipedia.org/wiki/Kalman_filter", "summary": "In statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. K\u00e1lm\u00e1n, one of the primary developers of its theory.\nThe Kalman filter has numerous applications in technology. A common application is for guidance, navigation, and control of vehicles, particularly aircraft and spacecraft. Furthermore, the Kalman filter is a widely applied concept in time series analysis used in fields such as signal processing and econometrics. Kalman filters also are one of the main topics in the field of robotic motion planning and control, and they are sometimes included in trajectory optimization. The Kalman filter also works for modeling the central nervous system's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedback, use of the Kalman filter supports a realistic model for making estimates of the current state of the motor system and issuing updated commands.The algorithm works in a two-step process. In the prediction step, the Kalman filter produces estimates of the current state variables, along with their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some amount of error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. The algorithm is recursive. It can run in real time, using only the present input measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.\nUsing a Kalman filter does not assume that the errors are Gaussian. However, the filter yields the exact conditional probability estimate in the special case that all errors are Gaussian.\nExtensions and generalizations to the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The underlying model is similar to a hidden Markov model except that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a5/Basic_concept_of_Kalman_filtering.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/8/81/HMM_Kalman_Filter_Derivation.svg", "https://upload.wikimedia.org/wikipedia/commons/d/da/Kalman.png", "https://upload.wikimedia.org/wikipedia/commons/a/a0/Kalman_filter_model_2.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["3D modeling", "AGM-86 ALCM", "A posteriori", "Academic Press", "Accuracy and precision", "Adaptive control", "Algorithm", "Ali H. Sayed", "Alpha beta filter", "ArXiv", "Arithmetic underflow", "Artificial neural networks", "Attitude and heading reference systems", "Attitude dynamics and control", "Autocovariance", "Automation and Remote Control", "Autopilot", "Babak Hassibi", "Ballistic missile submarine", "Bayesian model comparison", "BeiDou Navigation Satellite System", "Belief filter", "Bibcode", "Block diagram", "Bode plot", "Brain-computer interface", "C. Johan Masreliez", "Chain rule (probability)", "Charged particles", "Cholesky decomposition", "Cholesky factorization", "Closed-loop controller", "Closed-loop transfer function", "Coefficient diagram method", "Compressed sensing", "Computer vision", "Condition number", "Control Theory", "Control reconfiguration", "Control system", "Control theory", "Controllability", "Covariance", "Covariance intersection", "Covariance matrix", "DORIS (geodesy)", "Data fusion", "Dead reckoning", "Degrees of freedom (physics and chemistry)", "Dempster\u2013Shafer theory", "Density estimation", "Differentiable function", "Digital control", "Digital object identifier", "Digital signal processing", "Discrete-time signal", "Discrete time", "Distributed Control System", "Distributed parameter systems", "Drift (telecommunication)", "Dynamic Bayesian network", "Dynamic positioning", "Econometric", "Econometrics", "Economics", "Electric motors", "Electronics", "Embedded system", "Energy-shaping control", "Engineering", "Ensemble Kalman filter", "Estimator", "European Geostationary Navigation Overlay Service", "Expectation-maximization algorithm", "Expected value", "Extended Kalman filter", "Fast Kalman filter", "Filtering problem (stochastic processes)", "Fisher information", "Fisher information matrix", "Fourier transform", "Fractional-order control", "Frequency modulation", "Frequency response", "Fuzzy control", "Fuzzy logic", "GLONASS", "GNSS augmentation", "GNSS reflectometry", "GNU General Public License", "GNU Octave", "GPS", "GPS Aided GEO Augmented Navigation", "GPS\u00b7C", "Gain (electronics)", "Galileo (satellite navigation)", "Generalized filtering", "Generative model", "Global Positioning System", "Guidance, navigation, and control", "H-infinity loop-shaping", "Hankel singular value", "Hidden Markov model", "Human sensorimotor processing", "Hybrid computer", "Indian Regional Navigation Satellite System", "Industrial Control Systems", "Inertial guidance system", "Infinite impulse response", "Innovation (signal processing)", "Integrated Authority File", "Intelligent control", "International Space Station", "International Standard Book Number", "International Standard Serial Number", "Invariant extended Kalman filter", "Invertible matrix", "JSTOR", "Jacobian matrix", "John Wiley & Sons", "Johns Hopkins University", "Joint Precision Approach and Landing System", "Joint probability distribution", "Kalman filter", "Kalman\u2013Bucy filter", "Kernel adaptive filter", "Kevin Warwick", "Krener's theorem", "LAPACK", "LDL decomposition", "Laplace transform", "Latent variable", "Lead-lag compensator", "Least squares", "Linear-quadratic regulator", "Linear belief function", "Linear dynamical system", "Linear operator", "Linear\u2013quadratic\u2013Gaussian control", "Local Area Augmentation System", "Lyapunov stability", "MTSAT Satellite Augmentation System", "Macroeconomics", "Marginal likelihood", "Markov chain", "Markov process", "Masreliez's theorem", "Mathematician", "Matlab", "Matrix (mathematics)", "Matrix calculus", "Maximum likelihood", "Mechatronics", "Minimum mean-square error", "Minimum mean square error", "Minor loop feedback", "Model predictive control", "Monte Carlo sampling", "Motion control", "Moving horizon estimation", "Multivariable", "Multivariate normal distribution", "NASA", "NASA Ames Research Center", "National Diet Library", "Navigation system", "Negative feedback", "Networked Transport of RTCM via Internet Protocol", "Neural", "Newton's laws of motion", "Noise", "Noise (physics)", "Nonlinear control", "Nonlinear filter", "Normal distribution", "Nova Science Publishers, Inc.", "Nuclear medicine", "Numerical control", "Numerical stability", "Observability", "Optimal control", "Orbit Determination", "Orthogonalization", "Oxford University Press", "PID controller", "Particle detector", "Particle filter", "Perceptual control theory", "Performance", "Peter Swerling", "Phase-locked loop", "Pivot element", "Positive-definite matrix", "Positive-semidefinite matrix", "Positive feedback", "Predictor\u2013corrector method", "Prentice Hall", "Probability density function", "Process Control", "Programmable logic controller", "Project Apollo", "PubMed Identifier", "Quantization (signal processing)", "Quasi-Zenith Satellite System", "Radar", "Radar tracker", "Real-time Control System", "Real-time computing", "Real-time control", "Real number", "Recursive Bayesian estimation", "Recursive filter", "Recursive least squares filter", "Residuals (statistics)", "Reusable launch vehicle", "Riccati equation", "Robotics", "Robust control", "Root Locus", "Rudolf E. K\u00e1lm\u00e1n", "Ruslan Stratonovich", "SCADA", "Sample (statistics)", "Satellite communications", "Satellite navigation", "Satellite navigation system", "Schmidt\u2013Kalman filter", "Seismology", "Sensor fusion", "Separation principle", "Servomechanism", "Signal-flow graph", "Signal processing", "Simultaneous localization and mapping", "Sliding mode control", "Society for Industrial and Applied Mathematics", "Sparse signal", "Speech enhancement", "Springer Science+Business Media", "Square root", "Square root of a matrix", "Stability theory", "Stanley F. Schmidt", "StarFire (navigation system)", "State observer", "State space (controls)", "State space representation", "Statistical independence", "Statistical noise", "Statistics", "Steady State", "Steffen Lauritzen", "Stochastic control", "Stochastic differential equation", "Structural health monitoring", "Switching Kalman filter", "System Dynamics", "System identification", "Taylor series", "Thomas Kailath", "Thorvald Nicolai Thiele", "Timation", "Time series", "Time series analysis", "Tomahawk missile", "Trace (matrix)", "Trajectory optimization", "Transfer function", "Transit (satellite)", "Triangular matrix", "Truman Bewley", "Tsiklon (satellite)", "U.S. Air Force", "U.S. Navy", "Unit triangular matrix", "University of Southern California", "Unscented Kalman filter", "Unscented transform", "Variable-frequency drive", "Vector control (motor)", "Vector space", "Velocity", "Visual odometry", "Wavelet", "Weather forecasting", "Weighted mean", "White noise", "Wide Area Augmentation System", "Wiener filter", "YouTube", "Z Transform", "Zoubin Ghahramani"], "references": ["http:ftp://ftp.econ.au.dk/creates/rp/08/rp08_33.pdf", "http://www.lara.unb.br/~gaborges/disciplinas/efe/papers/wan2000.pdf", "http://www.elo.utfsm.cl/~ipd481/Papers%20varios/kalman1960.pdf", "http://www.mathfinance.cn/kalman-filter-finance-revisited/", "http://blog.sciencenet.cn/home.php?mod=space&uid=1565&do=blog&id=851754", "http://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/", "http://www.informaworld.com/index/779885789.pdf", "http://www.intechopen.com/books/smoothing-filtering-and-prediction-estimating-the-past-present-and-future", "http://www.mathworks.com/discovery/kalman-filter.html", "http://www.mathworks.com/matlabcentral/fileexchange/32537", "http://www.frc.ri.cmu.edu/~alonzo/pubs/reports/kalman_V2.pdf", "http://academic.csuohio.edu/simond/estimation/", "http://adsabs.harvard.edu/abs/1965AIAAJ...3.1445.", "http://adsabs.harvard.edu/abs/1977fmds.book.....B", "http://adsabs.harvard.edu/abs/1987NIMPA.262..444F", "http://adsabs.harvard.edu/abs/1997SPIE.3068..182J", "http://adsabs.harvard.edu/abs/2006ITSP...54.1069E", "http://adsabs.harvard.edu/abs/2007ITSP...55.1543E", "http://adsabs.harvard.edu/abs/2007JPS...174...30V", "http://adsabs.harvard.edu/abs/2008AGUFM.G43B..01B", "http://adsabs.harvard.edu/abs/2010ITSP...58.2405C", "http://adsabs.harvard.edu/abs/2012ITSP...60..545G", "http://adsabs.harvard.edu/abs/2012ITSP...60.4967Z", "http://adsabs.harvard.edu/abs/2014ISPL...21.1467E", "http://www.princeton.edu/~stengel/OptConEst.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.361.6851", "http://www.cs.unc.edu/~tracker/media/pdf/SIGGRAPH2001_CoursePack_08.pdf", "http://www.cs.unc.edu/~welch/kalman/", "http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html", "http://www.cs.unc.edu/~welch/kalman/media/pdf/Julier1997_SPIE_KF.pdf", "http://www.cs.unc.edu/~welch/kalman/media/pdf/maybeck_ch1.pdf", "http://www.cs.unc.edu/~welch/media/pdf/scaat.pdf", "http://jbrwww.che.wisc.edu/software/als/", "http://jbrwww.che.wisc.edu/theses/rajamani.pdf", "http://eia.udg.es/~qsalvi/Slam.zip", "http://www.ncbi.nlm.nih.gov/pubmed/11127840", "http://www.ncbi.nlm.nih.gov/pubmed/12662535", "http://www.ncbi.nlm.nih.gov/pubmed/18218487", "http://www.ncbi.nlm.nih.gov/pubmed/9950734", "http://www.eng.tau.ac.il/~liptser/lectures1/lect6.pdf", "http://www.dtic.mil/dtic/tr/fulltext/u2/a282853.pdf", "http://www.data-assimilation.net/Tools/AssimDemo/?method=KF", "http://pubs.acs.org/doi/abs/10.1021/ie9018116", "http://arxiv.org/abs/1206.2496", "http://doi.org/10.1007%2Fs10614-008-9160-4", "http://doi.org/10.1016%2F0005-1098(95)00069-9", "http://doi.org/10.1016%2F0168-9002(87)90887-4", "http://doi.org/10.1016%2FS0893-6080(96)00035-4", "http://doi.org/10.1016%2Fj.automatica.2008.05.032", "http://doi.org/10.1016%2Fj.automatica.2014.12.044", "http://doi.org/10.1016%2Fj.enconman.2007.05.017", "http://doi.org/10.1016%2Fj.jpowsour.2007.04.011", "http://doi.org/10.1021%2Fie034308l", "http://doi.org/10.1021%2Fie9018116", "http://doi.org/10.1038%2F81497", "http://doi.org/10.1080%2F00207178708933989", "http://doi.org/10.1109%2F42.276148", "http://doi.org/10.1109%2FASSPCC.2000.882463", "http://doi.org/10.1109%2FICIP.2008.4711899", "http://doi.org/10.1109%2FLSP.2014.2341641", "http://doi.org/10.1109%2FMCS.2008.929281", "http://doi.org/10.1109%2FTAC.1968.1099025", "http://doi.org/10.1109%2FTAC.1977.1101538", "http://doi.org/10.1109%2FTAC.2003.821415", "http://doi.org/10.1109%2FTAC.2006.878741", "http://doi.org/10.1109%2FTAC.2014.2309282", "http://doi.org/10.1109%2FTSP.2005.863042", "http://doi.org/10.1109%2FTSP.2006.889402", "http://doi.org/10.1109%2FTSP.2009.2038959", "http://doi.org/10.1109%2FTSP.2012.2203813", "http://doi.org/10.1109%2Ftac.2015.2404511", "http://doi.org/10.1109%2Ftsp.2011.2172431", "http://doi.org/10.1115%2F1.3662552", "http://doi.org/10.1117%2F12.280797", "http://doi.org/10.1134%2FS2075108711020076", "http://doi.org/10.1145%2F258734.258876", "http://doi.org/10.1162%2F089976699300016674", "http://doi.org/10.2307%2F1402616", "http://doi.org/10.2514%2F3.3166", "http://doi.org/10.2514%2F6.2003-5445", "http://doi.org/10.3182%2F20090706-3-FR-2004.00061", "http://doi.org/10.3182%2F20120711-3-BE-2027.00011", "http://doi.org/10.3390%2Fs110808164", "http://doi.org/10.5281%2Fzenodo.44386", "http://ieeexplore.ieee.org/abstract/document/6916211/,", "http://ieeexplore.ieee.org/document/7042740/", "http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1101538", "http://ieeecss.org/CSM/library/2010/june10/11-HistoricalPerspectives.pdf", "http://www.jstor.org/stable/1402616", "http://netlib.org/a/esl.tgz", "http://www.siam.org/pdf/news/362.pdf", "http://www.trs-80.org/interview-jack-crenshaw/", "http://www.worldcat.org/issn/0018-9286", "http://www.riksbank.se/en/Press-and-published/Published-from-the-Riksbank/Other-reports/Working-Paper-Series/2008/No-224-Block-Kalman-filtering-for-large-scale-DSGE-models/", "http://www.robots.ox.ac.uk/~ian/Teaching/Estimation/LectureNotes2.pdf", "https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python", "https://github.com/sbitzer/UKF-exposed", "https://books.google.com/books?id=AQxRAAAAMAAJ", "https://books.google.com/books?id=irugmNUwuG4C&q=kalman#v=snippet&q=kalman&f=false", "https://link.springer.com/content/pdf/10.1134%2FS2075108711020076.pdf", "https://www.youtube.com/watch?v=d0D3VwBh5UQ", "https://cse.sc.edu/~terejanu/files/tutorialKF.pdf", "https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770005172_1977005172.pdf", "https://d-nb.info/gnd/4130759-8", "https://id.ndl.go.jp/auth/ndlna/001096900", "https://www.researchgate.net/publication/216411106_Methods_for_Estimating_State_and_Measurement_Noise_Covariance_Matrices_Aspects_and_Comparison", "https://web.archive.org/web/20080529105724/http://www.elo.utfsm.cl/~ipd481/Papers%20varios/kalman1960.pdf", "https://web.archive.org/web/20160304042652/http://www.cnel.ufl.edu/~weifeng/publication.htm", "https://www.wikidata.org/wiki/Q846780"]}, "Statistical arbitrage": {"categories": ["Arbitrage", "Articles with specifically marked weasel-worded phrases from June 2011", "Investment", "Mathematical finance"], "title": "Statistical arbitrage", "method": "Statistical arbitrage", "url": "https://en.wikipedia.org/wiki/Statistical_arbitrage", "summary": "In finance, statistical arbitrage (often abbreviated as Stat Arb or StatArb) is a class of short-term financial trading strategies that employ mean reversion models involving broadly diversified portfolios of securities (hundreds to thousands) held for short periods of time (generally seconds to days). These strategies are supported by substantial mathematical, computational, and trading platforms.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9f/Chicklet-currency.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f8/Statistical_Arbitrage.png"], "links": ["A Demon Of Our Own Design", "Activist shareholder", "Algorithmic trading", "Alpha (investment)", "Arbitrage", "Arbitrage pricing theory", "Assets under management", "Beta (finance)", "Black\u2013Scholes model", "Bond market", "Capital asset pricing model", "Capital structure", "Cointegration", "Commodity market", "Commodity trading advisor", "Convergence trade", "Convertible arbitrage", "Copula (probability theory)", "Correlation", "Courant Institute of Mathematical Sciences", "Currency correlation", "Data mining", "Day trading", "Default (finance)", "Delta neutral", "Derivative (finance)", "Digital object identifier", "Distressed securities", "Ed Thorp", "Event-driven investing", "Family office", "Finance", "Financial endowment", "Fixed-income relative-value investing", "Fixed income arbitrage", "Foreign exchange market", "Fourier-related transforms", "Fund governance", "Fund of funds", "Fundamental analysis", "Global macro", "Greeks (finance)", "Hedge (finance)", "Hedge Fund Standards Board", "Hedge fund", "High-frequency trading", "High-net-worth individual", "Institutional investor", "Insurance", "International Standard Book Number", "International Standard Serial Number", "Investment banking", "Long/short equity", "Long (finance)", "MSCI", "Machine learning", "Managed futures account", "Margin call", "Market maker", "Market neutral", "Mean reversion (finance)", "Merchant bank", "Mergers and acquisitions", "Model risk", "Momentum (finance)", "Money market", "Morgan Stanley", "Multi-manager investment", "Pairs trade", "Pension fund", "Prime brokerage", "Program trading", "Proprietary trading", "Relative value (economics)", "Risk arbitrage", "Securitization", "Security characteristic line", "Short (finance)", "Sovereign wealth fund", "Special situation", "Stock market", "Stocks", "Structured finance", "Taxation of private equity and hedge funds", "Technical analysis", "Time series", "Trend following", "Volatility arbitrage", "Vulture fund", "When Genius Failed: The Rise and Fall of Long-Term Capital Management", "Wilmott"], "references": ["http://www.apt.com", "http://www.axioma.com/", "http://www.derivativesstrategy.com/magazine/archive/1998/0298fea2.asp", "http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/statisticalarbitrage4.doc.doc", "http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/statisticalarbitrage5.doc.doc", "http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/statisticalarbitrage6.doc.doc", "http://www.northinfo.com", "http://www.riskinfotech.com", "http://ssrn.com/abstract=1371903", "http://ssrn.com/abstract=1505073", "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1288988", "http://media.wiley.com/product_data/excerpt/11/04700235/0470023511.pdf", "http://www.wilmott.com/pdfs/080617_thorp.pdf", "http://www.wilmott.com/pdfs/080630_thorp.pdf", "http://www.wilmott.com/pdfs/080709_thorp.pdf", "http://faculty.baruch.cuny.edu/lwu/papers/StatArb.pdf", "http://www.stat.fsu.edu/~jfrade/PAPERS/Statistical%20Arbitrage/faj.v63.n5.pdf", "http://web.mit.edu/alo/www/Papers/august07.pdf", "http://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf", "http://www.math.nyu.edu/faculty/avellane/Lecture8Risk2011.pdf", "http://press.princeton.edu/titles/9177.html", "http://doi.org/10.1002%2Fwilm.10167", "http://doi.org/10.1002%2Fwilm.10201", "http://doi.org/10.1002%2Fwilm.10252", "http://doi.org/10.1080%2F14697688.2016.1164337", "http://www.worldcat.org/issn/1469-7688", "https://www.wsj.com/articles/SB10001424052748704509704575019032416477138#articleTabs=article", "https://dx.doi.org/10.1080/14697688.2016.1164337"]}, "Optimal decision": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2018", "Optimal decisions"], "title": "Optimal decision", "method": "Optimal decision", "url": "https://en.wikipedia.org/wiki/Optimal_decision", "summary": "An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory. In order to compare the different decision outcomes, one commonly assigns a utility value to each of them. If there is uncertainty as to what the outcome will be, then under the von Neumann\u2013Morgenstern axioms the optimal decision maximizes the expected utility (a probability\u2013weighted average of utility over all possible outcomes of a decision).\nSometimes, the equivalent problem of minimizing the expected value of loss is considered, where loss is (\u20131) times utility.\n\"Utility\" is only an arbitrary term for quantifying the desirability of a particular decision outcome and not necessarily related to \"usefulness.\" For example, it may well be the optimal decision for someone to buy a sports car rather than a station wagon, if the outcome in terms of another criterion (e.g., effect on personal image) is more desirable, even given the higher cost and lack of versatility of the sports car.\nThe problem of finding the optimal decision is a mathematical optimization problem. In practice, few people verify that their decisions are optimal, but instead use heuristics to make decisions that are \"good enough\"\u2014that is, they engage in satisficing. \nA more formal approach may be used when the decision is important enough to motivate the time it takes to analyze it, or when it is too complex to solve with more simple intuitive approaches, such as with a large number of available decision options and a complex decision\u2013outcome relationship.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional probability distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decision-making", "Decision-making software", "Decision theory", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected utility hypothesis", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Heuristics", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical optimization", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monty Hall problem", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Satisficing", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Two-alternative forced choice", "U-statistic", "Uniformly most powerful test", "Utility", "V-statistic", "Variance", "Vector autoregression", "Von Neumann\u2013Morgenstern axioms", "Wald test", "Wavelet", "Weighted average", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Dagum distribution": {"categories": ["All articles needing additional references", "Articles needing additional references from June 2011", "Continuous distributions", "Income inequality metrics", "Pages using deprecated image syntax"], "title": "Dagum distribution", "method": "Dagum distribution", "url": "https://en.wikipedia.org/wiki/Dagum_distribution", "summary": "The Dagum distribution is a continuous probability distribution defined over positive real numbers. It is named after Camilo Dagum, who proposed it in a series of papers in the 1970s. The Dagum distribution arose from several variants of a new model on the size distribution of personal income and is mostly associated with the study of income distribution. There is both a three-parameter specification (Type I) and a four-parameter specification (Type II) of the Dagum distribution; a summary of the genesis of this distribution can be found in \"A Guide to the Dagum Distributions\". A general source on statistical size distributions often cited in work using the Dagum distribution is Statistical Size Distributions in Economics and Actuarial Sciences.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/DagumCDF.png", "https://upload.wikimedia.org/wikipedia/commons/f/fc/DagumPDF.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized beta distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gini coefficient", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Income distribution", "International Statistical Institute", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Positive real numbers", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singh-Maddala distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://aix1.uottawa.ca/~gxgcb/Dagum_engl.htm"]}, "Alignments of random points": {"categories": ["Astronomy", "Combinatorics", "Computer vision", "Euclidean geometry", "Spatial data analysis", "Statistical randomness"], "title": "Alignments of random points", "method": "Alignments of random points", "url": "https://en.wikipedia.org/wiki/Alignments_of_random_points", "summary": "Alignments of random points in the plane can be demonstrated by statistics to be counter-intuitively easy to find when a large number of random points are marked on a bounded flat surface. This has been put forward as a demonstration that ley lines and other similar mysterious alignments believed by some to be phenomena of deep significance might exist solely due to chance alone, as opposed to the supernatural or anthropological explanations put forward by their proponents. The topic has also been studied in the fields of computer vision and astronomy.\nA number of studies have examined the mathematics of alignment of random points on the plane. In all of these, the width of the line - the allowed displacement of the positions of the points from a perfect straight line - is important. It allows the fact that real-world features are not mathematical points, and that their positions need not line up exactly for them to be considered in alignment. Alfred Watkins, in his classic work on ley lines The Old Straight Track, used the width of a pencil line on a map as the threshold for the tolerance of what might be regarded as an alignment. For example, using a 1 mm pencil line to draw alignments on a 1:50,000 Ordnance Survey map, the corresponding width on the ground would be 50 m.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/7e/Ley_lines.svg", "https://upload.wikimedia.org/wikipedia/commons/4/49/Leylines.png"], "links": ["Alfred Watkins", "Apophenia", "Astronomy", "Binomial coefficient", "Clustering illusion", "Coincidence", "Collinearity", "Combination", "Combinatorial explosion", "Complete spatial randomness", "Computer simulation", "Computer vision", "Contrary to intuition", "Counter-intuitively", "Factorial", "General position", "Geodesic", "Great circle", "International Standard Book Number", "Ley line", "Manifold", "Ordnance Survey", "Pattern recognition", "Procrustes analysis", "Ramsey theory", "Randomness", "Statistical shape analysis", "Statistics", "Straight line", "The Old Straight Track"], "references": ["http://www.engr.mun.ca/~ggeorge/astron/thesis.html", "http://hal.inria.fr/docs/00/95/65/96/PDF/point-alignement-detection.pdf", "https://www.jstor.org/stable/1426603"]}, "Working\u2013Hotelling procedure": {"categories": ["Multiple comparisons", "Regression analysis"], "title": "Working\u2013Hotelling procedure", "method": "Working\u2013Hotelling procedure", "url": "https://en.wikipedia.org/wiki/Working%E2%80%93Hotelling_procedure", "summary": "In statistics, particularly regression analysis, the Working\u2013Hotelling procedure, named after Holbrook Working and Harold Hotelling, is a method of simultaneous estimation in linear regression models. One of the first developments in simultaneous inference, it was devised by Working and Hotelling for the simple linear regression model in 1929. It provides a confidence region for multiple mean responses, that is, it gives the upper and lower bounds of more than one value of a dependent variable at several levels of the independent variables at a certain confidence level. The resulting confidence bands are known as the Working\u2013Hotelling\u2013Scheff\u00e9 confidence bands.\nLike the closely related Scheff\u00e9's method in the analysis of variance, which considers all possible contrasts, the Working\u2013Hotelling procedure considers all possible values of the independent variables; that is, in a particular regression model, the probability that all the Working\u2013Hotelling confidence intervals cover the true value of the mean response is the confidence coefficient. As such, when only a small subset of the possible values of the independent variable is considered, it is more conservative and yields wider intervals than competitors like the Bonferroni correction at the same level of confidence. It outperforms the Bonferroni correction as more values are considered.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a5/Heightmass-bonf_%281%29.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Heightmass-wh.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Analysis of covariance", "Analysis of variance", "Approximation theory", "Bayesian experimental design", "Bayesian linear regression", "Bayesian multivariate linear regression", "Binomial regression", "Bonferroni correction", "Calibration curve", "Chebyshev nodes", "Chebyshev polynomials", "Computational statistics", "Confidence band", "Confidence coefficient", "Confidence level", "Confidence region", "Confounding", "Contrast (statistics)", "Correlation and dependence", "Curve fitting", "Degrees of freedom (statistics)", "Dependent variable", "Design of experiments", "Digital object identifier", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "F-distribution", "Fixed effects model", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Growth curve (statistics)", "Harold Hotelling", "Holbrook Working", "Hyperbola", "Independent variable", "International Standard Book Number", "International Standard Serial Number", "Isotonic regression", "Iteratively reweighted least squares", "Kendall tau rank correlation coefficient", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "List of statistics articles", "Local regression", "Logistic regression", "Mallows's Cp", "Mean and predicted response", "Mean squared error", "Minimum mean-square error", "Mixed logit", "Mixed model", "Model selection", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate analysis of variance", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Normal distribution", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Optimal design", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson product-moment correlation coefficient", "Percentile", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Rank correlation", "Regression analysis", "Regression model validation", "Regularized least squares", "Response surface methodology", "Ridge regression", "Robust regression", "Scheff\u00e9's method", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Simultaneous inference", "Spearman's rank correlation coefficient", "Statistical model", "Statistics", "Stepwise regression", "Student's t-distribution", "Studentized residual", "System identification", "Tikhonov regularization", "Total least squares", "Weighted least squares"], "references": ["http://www.tandfonline.com/doi/abs/10.1080/01621459.1967.10482917", "http://onlinelibrary.wiley.com/book/10.1002/0471667196;jsessionid=52A4434648CAAFAC4B5CF6F525F38E57.f04t04", "http://doi.org/10.1002%2F0471667196", "http://doi.org/10.1080%2F01621459.1929.10506274", "http://doi.org/10.1080%2F01621459.1967.10482917", "http://www.worldcat.org/issn/0162-1459", "https://dx.doi.org/10.1080/01621459.1929.10506274"]}, "Averaged one-dependence estimators": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2011", "Bayesian estimation", "Classification algorithms", "Statistical classification"], "title": "Averaged one-dependence estimators", "method": "Averaged one-dependence estimators", "url": "https://en.wikipedia.org/wiki/Averaged_one-dependence_estimators", "summary": "Averaged one-dependence estimators (AODE) is a probabilistic classification learning technique. It was developed to address the attribute-independence problem of the popular naive Bayes classifier. It frequently develops substantially more accurate classifiers than naive Bayes at the cost of a modest increase in the amount of computation.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Classifier (mathematics)", "Cluster-weighted modeling", "Digital object identifier", "Naive Bayes classifier", "Weka (machine learning)"], "references": ["http://www.springerlink.com/content/u8w306673m1p866k/", "https://doi.org/10.1007%2Fs10994-005-4258-6"]}, "Robbins lemma": {"categories": ["Lemmas", "Poisson distribution", "Statistical theorems"], "title": "Robbins lemma", "method": "Robbins lemma", "url": "https://en.wikipedia.org/wiki/Robbins_lemma", "summary": "In statistics, the Robbins lemma, named after Herbert Robbins, states that if X is a random variable having a Poisson distribution with parameter \u03bb, and f is any function for which the expected value E(f(X)) exists, then\n\n \n \n \n E\n \u2061\n (\n X\n f\n (\n X\n \u2212\n 1\n )\n )\n =\n \u03bb\n E\n \u2061\n (\n f\n (\n X\n )\n )\n .\n \n \n {\\displaystyle \\operatorname {E} (Xf(X-1))=\\lambda \\operatorname {E} (f(X)).}\n Robbins introduced this proposition while developing empirical Bayes methods.\n\n", "images": [], "links": ["Empirical Bayes method", "Expected value", "Herbert Robbins", "International Standard Book Number", "Poisson distribution", "Random variable", "Statistics"], "references": ["https://books.google.com/books?id=v1HSBQAAQBAJ&pg=PA118"]}, "Chauvenet's criterion": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from July 2013", "Articles with unsourced statements from July 2013", "Statistical outliers", "Statistical tests"], "title": "Chauvenet's criterion", "method": "Chauvenet's criterion", "url": "https://en.wikipedia.org/wiki/Chauvenet%27s_criterion", "summary": "In statistical theory, Chauvenet's criterion (named for William Chauvenet) is a means of assessing whether one piece of experimental data \u2014 an outlier \u2014 from a set of observations, is likely to be spurious.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Grubbs' test for outliers", "International Standard Book Number", "Mean", "Normal distribution", "Outlier", "Peirce's criterion", "Probability", "Standard deviation", "William Chauvenet"], "references": ["http://newton.newhaven.edu/sross/piercescriterion.pdf"]}, "Beta negative binomial distribution": {"categories": ["Compound probability distributions", "Discrete distributions", "Factorial and binomial topics"], "title": "Beta negative binomial distribution", "method": "Beta negative binomial distribution", "url": "https://en.wikipedia.org/wiki/Beta_negative_binomial_distribution", "summary": "In probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable X equal to the number of failures needed to get r successes in a sequence of independent Bernoulli trials where the probability p of success on each trial is constant within any given experiment but is itself a random variable following a beta distribution, varying between different experiments. Thus the distribution is a compound probability distribution.\nThis distribution has also been called both the inverse Markov-P\u00f3lya distribution and the generalized Waring distribution. A shifted form of the distribution has been called the beta-Pascal distribution.If parameters of the beta distribution are \u03b1 and \u03b2, and if\n\n \n \n \n X\n \u2223\n p\n \u223c\n \n N\n B\n \n (\n r\n ,\n p\n )\n ,\n \n \n {\\displaystyle X\\mid p\\sim \\mathrm {NB} (r,p),}\n where\n\n \n \n \n p\n \u223c\n \n \n B\n \n \n (\n \u03b1\n ,\n \u03b2\n )\n ,\n \n \n {\\displaystyle p\\sim {\\textrm {B}}(\\alpha ,\\beta ),}\n then the marginal distribution of X is a beta negative binomial distribution:\n\n \n \n \n X\n \u223c\n \n B\n N\n B\n \n (\n r\n ,\n \u03b1\n ,\n \u03b2\n )\n .\n \n \n {\\displaystyle X\\sim \\mathrm {BNB} (r,\\alpha ,\\beta ).}\n In the above, NB(r, p) is the negative binomial distribution and B(\u03b1, \u03b2) is the beta distribution.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli trial", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Compound probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heavy tail distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypergeometric function", "Hypoexponential distribution", "Independence (probability theory)", "Integer", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the Royal Statistical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Pochammer symbol", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Probability mass function", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Stirling's approximation", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.math.wm.edu/~leemis/chart/UDR/UDR.html", "https://doi.org/10.1016%2Fj.jspi.2010.09.020"]}, "Partial least squares": {"categories": ["Articles prone to spam from November 2017", "Articles with example pseudocode", "Latent variable models", "Least squares", "Wikipedia articles with GND identifiers"], "title": "Partial least squares regression", "method": "Partial least squares", "url": "https://en.wikipedia.org/wiki/Partial_least_squares_regression", "summary": "Partial least squares regression (PLS regression) is a statistical method that bears some relation to principal components regression; instead of finding hyperplanes of maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable variables to a new space. Because both the X and Y data are projected to new spaces, the PLS family of methods are known as bilinear factor models. Partial least squares Discriminant Analysis (PLS-DA) is a variant used when the Y is categorical.\nPLS is used to find the fundamental relations between two matrices (X and Y), i.e. a latent variable approach to modeling the covariance structures in these two spaces. A PLS model will try to find the multidimensional direction in the X space that explains the maximum multidimensional variance direction in the Y space. PLS regression is particularly suited when the matrix of predictors has more variables than observations, and when there is multicollinearity among X values. By contrast, standard regression will fail in these cases (unless it is regularized).\nPartial least squares was introduced by the Swedish statistician Herman O. A. Wold, who then developed it with his son, Svante Wold. An alternative term for PLS (and more correct according to Svante Wold) is projection to latent structures, but the term partial least squares is still dominant in many areas. Although the original applications were in the social sciences, PLS regression is today most widely used in chemometrics and related areas. It is also used in bioinformatics, sensometrics, neuroscience and anthropology.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Canonical correlation", "Chemometrics", "Covariance", "Data mining", "Deming regression", "Digital object identifier", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "Feature extraction", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Herman Wold", "Hyperplane", "Integrated Authority File", "International Standard Book Number", "International Standard Serial Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society", "Latent variable", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Machine learning", "Matrix (mathematics)", "Mean and predicted response", "Mixed logit", "Mixed model", "Multicollinearity", "Multilevel model", "Multilinear subspace learning", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Observable variable", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthonormal matrix", "Partial least squares path modeling", "Poisson regression", "Polynomial regression", "Predicted variable", "Principal component analysis", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Total sum of squares", "Variance", "Weighted least squares"], "references": ["http://www.sciencedirect.com/science/article/pii/S0169743901001551", "http://www.sciencedirect.com/science/article/pii/S0304407615000354", "http://amstat.tandfonline.com/doi/full/10.1080/00401706.1993.10485033", "http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1099-128X(199701)11:1%3C73::AID-CEM435%3E3.0.CO;2-%23/abstract", "http://onlinelibrary.wiley.com/doi/10.1002/cem.1180070104/abstract", "http://onlinelibrary.wiley.com/doi/10.1002/cem.1180080204/abstract", "http://onlinelibrary.wiley.com/doi/10.1002/cem.1180080208/abstract", "http://onlinelibrary.wiley.com/doi/10.1111/jofi.12060/abstract", "http://www.utd.edu/~herve/Abdi-PLSR2007-pretty.pdf", "http://doi.org/10.1002%2F(SICI)1099-128X(199701)11:1%3C73::AID-CEM435%3E3.0.CO;2-%23", "http://doi.org/10.1002%2Fcem.1180070104", "http://doi.org/10.1002%2Fcem.1180080204", "http://doi.org/10.1002%2Fcem.1180080208", "http://doi.org/10.1002%2Fcem.695", "http://doi.org/10.1002%2Fwics.51", "http://doi.org/10.1016%2F0169-7439(93)85002-X", "http://doi.org/10.1016%2FS0169-7439(01)00155-1", "http://doi.org/10.1016%2Fj.chemolab.2007.10.006", "http://doi.org/10.1016%2Fj.jeconom.2015.02.011", "http://doi.org/10.1080%2F00401706.1993.10485033", "http://doi.org/10.1080%2F01621459.1994.10476452", "http://doi.org/10.1111%2F1467-9469.00201", "http://doi.org/10.1111%2Fjofi.12060", "http://doi.org/10.1137%2F0905052", "http://doi.org/10.1207%2Fs15328031us0304_4", "http://www.jstor.org/stable/2291207", "http://www.jstor.org/stable/2345437", "http://www.jstor.org/stable/4616159", "http://www.worldcat.org/issn/1540-6261", "https://d-nb.info/gnd/4591652-4", "https://archive.is/20130203091137/http://amstat.tandfonline.com/doi/full/10.1080/00401706.1993.10485033", "https://www.wikidata.org/wiki/Q422009"]}, "Explained sum of squares": {"categories": ["All articles lacking in-text citations", "All articles needing expert attention", "Articles lacking in-text citations from December 2010", "Articles needing expert attention from September 2009", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Least squares", "Statistics articles needing expert attention"], "title": "Explained sum of squares", "method": "Explained sum of squares", "url": "https://en.wikipedia.org/wiki/Explained_sum_of_squares", "summary": "In statistics, the explained sum of squares (ESS), alternatively known as the model sum of squares or sum of squares due to regression (\"SSR\" \u2013 not to be confused with the residual sum of squares RSS or sum of squares of errors), is a quantity used in describing how well a model, often a regression model, represents the data being modelled. In particular, the explained sum of squares measures how much variation there is in the modelled values and this is compared to the total sum of squares, which measures how much variation there is in the observed data, and to the residual sum of squares, which measures the variation in the modelling errors.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Coefficient", "Error term", "Explanatory variable", "Fraction of variance unexplained", "International Standard Book Number", "Lack-of-fit sum of squares", "Ordinary least squares", "Regression analysis", "Regression model", "Residual sum of squares", "Response variable", "Simple linear regression", "Statistics", "Sum of squares (statistics)", "Total sum of squares"], "references": []}, "Fisher information metric": {"categories": ["Differential geometry", "Information geometry", "Statistical distance"], "title": "Fisher information metric", "method": "Fisher information metric", "url": "https://en.wikipedia.org/wiki/Fisher_information_metric", "summary": "In information geometry, the Fisher information metric is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability measures defined on a common probability space. It can be used to calculate the informational difference between measurements.\nThe metric is interesting in several respects. By Chentsov\u2019s theorem, the Fisher information metric on statistical models is the only Riemannian metric (up to rescaling) that is invariant under sufficient statistics.It can also be understood to be the infinitesimal form of the relative entropy (i.e., the Kullback\u2013Leibler divergence); specifically, it is the Hessian of the divergence. Alternately, it can be understood as the metric induced by the flat space Euclidean metric, after appropriate changes of variable. When extended to complex projective Hilbert space, it becomes the Fubini\u2013Study metric; when written in terms of mixed states, it is the quantum Bures metric.\nConsidered purely as a matrix, it is known as the Fisher information matrix. Considered as a measurement technique, where it is used to estimate hidden parameters in terms of observed random variables, it is known as the observed information.", "images": [], "links": ["1-form", "2-form", "Abuse of notation", "Action (physics)", "Berry phase", "Bra\u2013ket notation", "Bures metric", "Category-theoretic", "Cauchy sequence", "Cauchy\u2013Schwarz inequality", "Chemical industry", "Chentsov\u2019s theorem", "Cotangent space", "Cram\u00e9r\u2013Rao bound", "Curve length", "Digital object identifier", "Discrete probability space", "Entropy", "Euclidean metric", "Expectation value", "Exponential map (Riemannian geometry)", "Fisher information", "Fisher information matrix", "Fr\u00e9chet space", "Fubini\u2013Study metric", "Geodesic", "Geometric phase", "Gibbs measure", "Hellinger distance", "Helstrom metric", "Hessian matrix", "Hilbert space", "Information geometry", "Information theory", "Inner product", "International Standard Serial Number", "Jensen\u2013Shannon divergence", "Kullback\u2013Leibler divergence", "Lagrange multiplier", "Markovian process", "Measure space", "Measure theory", "Mikhail Gromov (mathematician)", "Mixed state (physics)", "Observed information", "Orientable manifold", "Parallel transport", "Partition function (mathematics)", "Polar coordinate", "Probability amplitude", "Probability measure", "Probability space", "Processing industry", "Projective Hilbert space", "Pure state", "Radon\u2013Nikodym derivative", "Radon\u2013Nikodym property", "Radon\u2013Nikodym theorem", "Random variable", "Riemannian manifold", "Riemannian metric", "Ruppeiner metric", "Shun'ichi Amari", "Sigma algebra", "Simplex", "Smooth manifold", "Square-integrable", "Statistical manifold", "Submanifold", "Sufficient statistic", "Symplectic form", "Tangent space", "Thermodynamic limit", "Weak topology", "Weinhold metric"], "references": ["http://www.sciencedirect.com/science/article/pii/S0926224507001027", "http://threeplusone.com/Feng2009.pdf", "http://www.ihes.fr/~gromov/PDF/structre-serch-entropy-july5-2012.pdf", "http://doi.org/10.1007%2Fs41884-018-0006-4", "http://www.worldcat.org/issn/2511-2481", "https://link.springer.com/article/10.1007%2Fs41884-018-0006-4", "https://arxiv.org/abs/0706.0559", "https://arxiv.org/abs/1009.5219", "https://dx.doi.org/10.1016/j.difgeo.2007.11.027"]}, "Scatter matrix": {"categories": ["All articles lacking sources", "All stub articles", "Articles lacking sources from September 2010", "Covariance and correlation", "Matrices", "Statistics stubs"], "title": "Scatter matrix", "method": "Scatter matrix", "url": "https://en.wikipedia.org/wiki/Scatter_matrix", "summary": "For the notion in quantum mechanics, see scattering matrix.In multivariate statistics and probability theory, the scatter matrix is a statistic that is used to make estimates of the covariance matrix, for instance of the multivariate normal distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Centering matrix", "Covariance matrix", "Estimation of covariance matrices", "Gram matrix", "Matrix transpose", "Maximum likelihood", "Multivariate normal distribution", "Multivariate statistics", "Outer product", "Positive definite matrix", "Probability theory", "Sample covariance matrix", "Sample mean", "Scattering matrix", "Statistic", "Statistics", "Wishart distribution"], "references": []}, "Sequential probability ratio test": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2015", "Mathematical psychology", "Psychometrics", "Sequential methods", "Statistical tests"], "title": "Sequential probability ratio test", "method": "Sequential probability ratio test", "url": "https://en.wikipedia.org/wiki/Sequential_probability_ratio_test", "summary": "The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald and later proven to be optimal by Wald and Jacob Wolfowitz. Neyman and Pearson's 1933 result inspired Wald to reformulate it as a sequential analysis problem. The Neyman-Pearson lemma, by contrast, offers a rule of thumb for when all the data is collected (and its likelihood ratio known).\nWhile originally developed for use in quality control studies in the realm of manufacturing, SPRT has been formulated for use in the computerized testing of human examinees as a termination criterion.\n\n", "images": [], "links": ["Abraham Wald", "Addison-Wesley", "Alternative hypothesis", "Bhaskar Kumar Ghosh", "CUSUM", "Classical test theory", "Computerized classification test", "David Spiegelhalter", "Digital object identifier", "Exponential distribution", "Harold Shipman", "High-stakes testing", "Hypothesis testing", "International Standard Book Number", "Item response theory", "JSTOR", "Jacob Wolfowitz", "Likelihood-ratio test", "Neyman\u2013Pearson lemma", "Null hypothesis", "Parallel lines", "Parameter estimation", "Probability distribution function", "Quality control", "Resistance thermometer", "Rule of thumb", "SPRT", "Sampling frequency", "Sequential analysis", "Slope", "Standard-setting study", "Stopping rule", "Type I and type II errors", "Wald test"], "references": ["http://www.tandfonline.com/doi/full/10.1080/07474946.2011.539924", "http://eric.ed.gov/ERICWebPortal/custom/portlets/recordDetails/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=ED034406&ERICExtSearch_SearchType_0=no&accno=ED034406", "http://doi.org/10.1080%2F07474946.2011.539924", "http://doi.org/10.1177%2F01466219922031365", "http://doi.org/10.1214%2Faoms%2F1177731118", "http://www.jstor.org/stable/2235638", "http://www.jstor.org/stable/2235829", "http://intqhc.oxfordjournals.org/content/15/1/7.full.pdf", "https://cran.r-project.org/web/packages/SPRT/SPRT.pdf"]}, "Multiple testing correction": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2012", "Articles with unsourced statements from January 2012", "Articles with unsourced statements from June 2016", "CS1 maint: Multiple names: authors list", "Multiple comparisons", "Statistical hypothesis testing"], "title": "Multiple comparisons problem", "method": "Multiple testing correction", "url": "https://en.wikipedia.org/wiki/Multiple_comparisons_problem", "summary": "In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or infers a subset of parameters selected based on the observed values. In certain fields it is known as the look-elsewhere effect.\nThe more inferences are made, the more likely erroneous inferences are to occur. Several statistical techniques have been developed to prevent this from happening, allowing significance levels for single and multiple comparisons to be directly compared. These techniques generally require a stricter significance threshold for individual comparisons, so as to compensate for the number of inferences being made.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/6/66/Quantile_meta_test.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a7/Split-arrows.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0c/Spurious_correlations_-_spelling_bee_spiders.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bonferroni bound", "Bonferroni correction", "Boole's inequality", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Closed testing procedure", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Coverage probability", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "DNA microarray", "Data collection", "Data dredging", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Eli Upfal", "Elliptical distribution", "Empirical distribution function", "Empirical research", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected number", "Experiment", "Experimental unit", "Experimentwise error rate", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "False coverage rate", "False discovery rate", "False positive", "False positive rate", "Family-wise error rate", "Familywise error rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Genetic association", "Genomics", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Holm\u2013Bonferroni method", "Homoscedasticity", "Index of dispersion", "Information technology", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Israel", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Neter", "Jonckheere's trend test", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society, Series B", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Look-elsewhere effect", "Loss function", "Lp space", "M-estimator", "MANOVA", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michael Mitzenmacher", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo simulation", "Multiple comparison", "Multiple comparisons", "Multiple testing correction", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Null hypothesis", "Observational study", "Official statistics", "Omnibus test", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pharmacology", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Post-hoc analysis", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Q-Q plot", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Random variable", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling error", "Scale parameter", "Scatter plot", "Scheff\u00e9", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard score", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Test statistic", "Testing hypotheses suggested by the data", "Texas sharpshooter fallacy", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tukey", "Tukey's range test", "Type I and type II errors", "Type I error", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Voxel", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "\u0160id\u00e1k correction"], "references": ["http://www.nature.com/nbt/journal/v27/n12/full/nbt1209-1135.html", "http://www.tylervigen.com/spurious-correlations", "http://adsabs.harvard.edu/abs/2003PNAS..100.9440S", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1124898", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1380484", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC170937", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2907892", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3270946", "http://www.ncbi.nlm.nih.gov/pubmed/12493654", "http://www.ncbi.nlm.nih.gov/pubmed/12883005", "http://www.ncbi.nlm.nih.gov/pubmed/15110000", "http://www.ncbi.nlm.nih.gov/pubmed/18064589", "http://www.ncbi.nlm.nih.gov/pubmed/20010596", "http://www.ncbi.nlm.nih.gov/pubmed/2081237", "http://www.ncbi.nlm.nih.gov/pubmed/20926032", "http://www.ncbi.nlm.nih.gov/pubmed/21154895", "http://www.ncbi.nlm.nih.gov/pubmed/8629727", "http://arxiv.org/abs/1002.1104", "http://doi.org/10.1002%2Fbimj.200900299", "http://doi.org/10.1002%2Fhbm.20471", "http://doi.org/10.1016%2Fj.neuroimage.2003.12.047", "http://doi.org/10.1038%2Fnbt1209-1135", "http://doi.org/10.1073%2Fpnas.1530509100", "http://doi.org/10.1097%2F00001648-199001000-00010", "http://doi.org/10.1136%2Fbmj.325.7378.1437", "http://doi.org/10.1145%2F2220357.2220359", "http://doi.org/10.1198%2F016214501753382129", "http://doi.org/10.2105%2Fajph.86.5.726", "http://www.jstor.org/stable/20065622", "http://www.jstor.org/stable/2346101", "http://www.jstor.org/stable/3085878", "http://www.jstor.org/stable/3144228", "http://www.mcp-conference.org", "http://www.niss.org/sites/default/files/Young%20Karr%20Obs%20Study%20Problem.pdf", "http://www.worldcat.org/issn/0147-958X", "http://www.worldcat.org/issn/1087-0156", "https://doi.org/10.2202%2F1544-6155.1585"]}, "Truncated normal distribution": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from June 2010", "Continuous distributions", "Normal distribution"], "title": "Truncated normal distribution", "method": "Truncated normal distribution", "url": "https://en.wikipedia.org/wiki/Truncated_normal_distribution", "summary": "In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above (or both). The truncated normal distribution has wide applications in statistics and econometrics. For example, it is used to model the probabilities of the binary outcomes in the probit model and to model censored data in the Tobit model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/8/8d/TnormCDF.svg", "https://upload.wikimedia.org/wikipedia/en/d/df/TnormPDF.png"], "links": ["ARGUS distribution", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital Object Identifier", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Econometrics", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "First-order stochastic dominance", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gibbs sampling", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Instituto Superior T\u00e9cnico", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverse transform method", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Loss of significance", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean-preserving contraction", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normally distributed", "PERT distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probit model", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "R (programming language)", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard normal distribution", "Student's t-distribution", "Support (mathematics)", "Tobit model", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.smp.uq.edu.au/people/YoniNazarathy/teaching_projects/studentWork/EricOrjebin_TruncatedNormalMoments.pdf", "http://www.mathworks.com/matlabcentral/fileexchange/53180-truncated-normal-generator", "http://www.christophlassner.de/blog/2013/08/12/Generation-of-Truncated-Gaussian-Samples/", "http://eudl.eu/doi/10.4108/eai.25-10-2016.2266879", "http://www.crest.fr/ckfinder/userfiles/files/Pageperso/chopin/truncnorm_20120618.tgz", "http://miv.u-strasbg.fr/mazet/rtnorm/rtnormCpp.zip", "http://miv.u-strasbg.fr/mazet/rtnorm/rtnormM.zip", "http://arxiv.org/abs/0907.4010", "http://arxiv.org/abs/1603.04166", "http://doi.org/10.1007%2FBF00143942", "http://doi.org/10.1016%2Fj.spl.2008.09.006", "http://doi.org/10.1080%2F00031305.1999.10474490", "http://doi.org/10.1111%2Frssb.12162", "http://doi.org/10.1198%2F10618600152627906", "http://doi.org/10.2307%2F1266749", "http://doi.org/10.4108%2Feai.25-10-2016.2266879", "http://web.ist.utl.pt/~ist11038/compute/qc/,truncG/lecture4k.pdf", "https://github.com/cossio/TruncatedNormal.jl", "https://www.springer.com/social+sciences/book/978-0-387-71264-2", "https://people.sc.fsu.edu/~jburkardt/presentations/truncated_normal.pdf", "https://web.archive.org/web/20120208134826/http://rss.acs.unt.edu/Rdoc/library/msm/html/tnorm.html", "https://arxiv.org/abs/1201.6140", "https://dx.doi.org/10.1007/s11222-009-9168-1", "https://cran.r-project.org/web/packages/TruncatedNormal", "https://cran.r-project.org/web/packages/msm/index.html", "https://cran.r-project.org/web/packages/truncnorm/"]}, "Therapeutic effect": {"categories": ["Medical statistics", "Medical treatments"], "title": "Therapeutic effect", "method": "Therapeutic effect", "url": "https://en.wikipedia.org/wiki/Therapeutic_effect", "summary": "Therapeutic effect refers to the responses(s) after a treatment of any kind, the results of which are judged to be useful or favorable. This is true whether the result was expected, unexpected, or even an unintended consequence. An adverse effect (including nocebo) is the converse and refers to harmful or undesired responses(s). What constitutes a therapeutic effect versus a side effect is a matter of both the nature of the situation and the goals of treatment. No inherent difference separates therapeutic and undesired side effects; both responses are behavioral/physiologic changes that occur as a response to the treatment strategy or agent.", "images": [], "links": ["Adjunctive", "Adverse effect", "Aerobic exercise", "Aloe vera", "Antidiabetic", "Antimicrobial", "Antioxidant", "Antitumor", "Autoimmune disorder", "Behavioral", "Botulinum toxin", "Cancer", "Depression (mood)", "Digital object identifier", "Erectile dysfunction", "Extracorporeal shockwave therapy", "Hypoglycemic", "Hypolipidemic", "In vitro", "International Standard Serial Number", "Irradiation", "Irritable bowel syndrome", "Low level laser therapy", "Mental illness", "Mindfulness", "Myasthenia gravis", "Nocebo", "Nutraceuticals", "Paroxysms", "Physiologic", "Probiotics", "Resistance exercise", "Rituximab", "Stem cell therapy", "Stress reduction", "Therapeutic", "Trigeminal neuralgia", "Unintended consequence", "Wound healing"], "references": ["http://doi.org/10.1007%2Fs00415-014-7532-3", "http://doi.org/10.1007%2Fs10103-015-1730-9", "http://doi.org/10.1007%2Fs12015-014-9545-9", "http://doi.org/10.1016%2Fj.cpr.2015.01.006", "http://doi.org/10.1016%2Fj.eururo.2016.05.050", "http://doi.org/10.1016%2Fj.jtcme.2014.10.006", "http://doi.org/10.1038%2Fnchembio817", "http://doi.org/10.1136%2Fbjsports-2017-098285", "http://doi.org/10.1176%2Fappi.ajp.2016.15091228", "http://doi.org/10.1186%2Fs10194-016-0651-8", "http://doi.org/10.3748%2Fwjg.v21.i10.3072", "http://www.worldcat.org/issn/0002-953X", "http://www.worldcat.org/issn/0268-8921", "http://www.worldcat.org/issn/0272-7358", "http://www.worldcat.org/issn/0302-2838", "http://www.worldcat.org/issn/0306-3674", "http://www.worldcat.org/issn/0340-5354", "http://www.worldcat.org/issn/1007-9327", "http://www.worldcat.org/issn/1129-2369", "http://www.worldcat.org/issn/1550-8943", "http://www.worldcat.org/issn/1552-4450", "http://www.worldcat.org/issn/2225-4110", "https://www.medscape.com/viewarticle/448250", "https://www.merriam-webster.com/dictionary/therapeutic", "https://www.pharmacorama.com/en/Sections/Pharmacology-Definitions.php"]}, "Coefficient of variation": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from February 2018", "Articles with unsourced statements from September 2016", "CS1 errors: dates", "Statistical deviation and dispersion", "Statistical ratios", "Use dmy dates from October 2017", "Webarchive template wayback links"], "title": "Coefficient of variation", "method": "Coefficient of variation", "url": "https://en.wikipedia.org/wiki/Coefficient_of_variation", "summary": "In probability theory and statistics, the coefficient of variation (CV), also known as relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage, and is defined as the ratio of the standard deviation \n \n \n \n \n \u03c3\n \n \n {\\displaystyle \\ \\sigma }\n to the mean \n \n \n \n \n \u03bc\n \n \n {\\displaystyle \\ \\mu }\n (or its absolute value, \n \n \n \n \n |\n \n \u03bc\n \n |\n \n \n \n {\\displaystyle |\\mu |}\n ). \nThe CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R. In addition, CV is utilized by economists and investors in economic models and in determining the volatility of a security.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA gauge R&R", "Absolute error", "Absolute value", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Analytical chemistry", "Anderson\u2013Darling test", "Arithmetic mean", "Assay", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Biased estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Celsius", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimensionless number", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Economic model", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Fahrenheit", "Failure rate", "Fan chart (statistics)", "Fano factor", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Gini coefficient", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hyper-exponential distribution", "Hypothesis test", "Image processing", "Income inequality metrics", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Interval scale", "Intraclass correlation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kelvin", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-normal", "Log-normal distribution", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McKay's approximation for the coefficient of variation", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Midhinge", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiplicative inverse", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural log", "Nelson\u2013Aalen estimator", "Non-central t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normalization (statistics)", "Normally distributed", "Observational study", "Official statistics", "Omega ratio", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Physics", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quartile coefficient of dispersion", "Quasi-experiment", "Questionnaire", "Queueing theory", "Q\u2013Q plot", "RMSD", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rankine scale", "Rao\u2013Blackwell theorem", "Ratio scale", "Regression analysis", "Regression model validation", "Reliability engineering", "Reliability theory", "Renewal theory", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Security (finance)", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal-to-noise ratio (imaging)", "Signal processing", "Signal to noise ratio", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Standardized (statistics)", "Standardized moment", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-to-mean ratio", "Vector autoregression", "Volatility (finance)", "Wald test", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.graphpad.com/faq/viewfaq.cfm?faq=1089", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC130103", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4112421", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4478151", "http://www.ncbi.nlm.nih.gov/pubmed/10709801", "http://www.ncbi.nlm.nih.gov/pubmed/12414755", "http://www.ncbi.nlm.nih.gov/pubmed/1601532", "http://www.ncbi.nlm.nih.gov/pubmed/24728329", "http://www.ncbi.nlm.nih.gov/pubmed/25757675", "http://www.ncbi.nlm.nih.gov/pubmed/25987306", "http://www.ncbi.nlm.nih.gov/pubmed/27581804", "http://www.ncbi.nlm.nih.gov/pubmed/4370388", "http://doi.org/10.1002%2F(SICI)1097-0258(19960330)15:6%3C647::AID-SIM184%3E3.0.CO;2-P", "http://doi.org/10.1002%2Fajhb.22690", "http://doi.org/10.1007%2Fs00180-013-0445-2", "http://doi.org/10.1080%2F00031305.1996.10473537", "http://doi.org/10.1080%2F03610920802187448", "http://doi.org/10.1081%2FBIP-100101013", "http://doi.org/10.1093%2Fbiomet%2F51.1-2.25", "http://doi.org/10.1093%2Fije%2Fdyw191", "http://doi.org/10.1128%2FCDLI.9.6.1235-1239.2002", "http://doi.org/10.1136%2Fannrheumdis-2014-205228", "http://doi.org/10.1214%2Faoms%2F1177732503", "http://doi.org/10.1641%2F0006-3568(2001)051%5B0341:LNDATS%5D2.0.CO;2", "http://doi.org/10.2307%2F1267363", "http://doi.org/10.3758%2Fs13428-015-0600-5", "http://www.fao.org/docs/up/easypol/448/simple_inequality_mesures_080en.pdf", "http://www.jstor.org/stable/1267363", "http://www.jstor.org/stable/2530139", "http://www.jstor.org/stable/2685039", "http://www.jstor.org/stable/2957564", "http://ije.oxfordjournals.org/content/early/2016/08/30/ije.dyw191.extract", "http://pharmasug.org/proceedings/2011/PO/PharmaSUG-2011-PO08.pdf", "http://www.worldcat.org/issn/0300-5771", "http://www.worldcat.org/issn/1554-3528", "http://pub.epsilon.slu.se/4489/1/forkman_j_110214.pdf", "https://books.google.com/?id=qd4PAQAAMAAJ&q=%22unitized+risk%22", "https://scholarworks.gsu.edu/math_theses/124", "https://www.powderprocess.net/Measuring_Degree_Mixing.html", "https://web.archive.org/web/20081215175508/http://graphpad.com/faq/viewfaq.cfm?faq=1089", "https://web.archive.org/web/20110824094357/http://pharmasug.org/proceedings/2011/PO/PharmaSUG-2011-PO08.pdf", "https://web.archive.org/web/20131206021229/http://pub.epsilon.slu.se/4489/1/forkman_j_110214.pdf", "https://web.archive.org/web/20140301102042/http://scholarworks.gsu.edu/cgi/viewcontent.cgi?article=1116&context=math_theses", "https://web.archive.org/web/20160805101141/http://www.fao.org/docs/up/easypol/448/simple_inequality_mesures_080en.pdf", "https://web.archive.org/web/20171114145327/https://www.powderprocess.net/Measuring_Degree_Mixing.html", "https://cran.r-project.org/package=cvequality"]}, "Negative predictive value": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2012", "Biostatistics", "Categorical data", "Statistical ratios", "Summary statistics for contingency tables"], "title": "Positive and negative predictive values", "method": "Negative predictive value", "url": "https://en.wikipedia.org/wiki/Positive_and_negative_predictive_values", "summary": "The positive and negative predictive values (PPV and NPV respectively) are the proportions of positive and negative results in statistics and diagnostic tests that are true positive and true negative results, respectively. The PPV and NPV describe the performance of a diagnostic test or other statistical measure. A high result can be interpreted as indicating the accuracy of such a statistic. The PPV and NPV are not intrinsic to the test; they depend also on the prevalence. The PPV can be derived using Bayes' theorem.\nAlthough sometimes used synonymously, a positive predictive value generally refers to what is established by control groups, while a post-test probability refers to a probability for an individual. Still, if the individual's pre-test probability of the target condition is the same as the prevalence in the control group used to establish the positive predictive value, the two are numerically equal.\nIn information retrieval, the PPV statistic is often called the precision.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Accuracy and precision", "Bayes' theorem", "Binary classification", "Bowel cancer", "Case-control study", "Cross-sectional study", "Diagnostic odds ratio", "Diagnostic test", "Digital object identifier", "Endoscopy", "F1 score", "False discovery rate", "False negative", "False negative rate", "False omission rate", "False positive", "False positive rate", "Fecal occult blood", "Information retrieval", "International Standard Book Number", "Likelihood ratios in diagnostic testing", "Negative likelihood ratio", "Negative predictive value", "Positive likelihood ratio", "Positive predictive value", "Post-test probabilities", "Pre- and post-test probability", "Pre-test probability", "Precision (information retrieval)", "Precision and recall", "Prevalence", "PubMed Central", "PubMed Identifier", "Recall (information retrieval)", "Receiver-operator characteristic", "Relevance (information retrieval)", "Sensitivity (tests)", "Sensitivity and specificity", "Sensitivity index", "Specificity (tests)", "Statistical population", "Statistical power", "Statistics", "True negative", "True negative rate", "True positive", "True positive rate", "Type II error", "Type I error"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2540558", "http://www.ncbi.nlm.nih.gov/pubmed/12111911", "http://www.ncbi.nlm.nih.gov/pubmed/21274995", "http://www.ncbi.nlm.nih.gov/pubmed/26873279", "http://www.ncbi.nlm.nih.gov/pubmed/8038641", "http://doi.org/10.1002%2Fjmri.22466", "http://doi.org/10.1002%2Fsim.1119", "http://doi.org/10.1016%2Fj.ijid.2016.02.002", "http://doi.org/10.1136%2Fbmj.309.6947.102", "http://www.infovoice.se/fou/epv", "http://science-network.tv/epv-calculator/"]}, "Odds ratio": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2012", "Articles with unsourced statements from March 2015", "Bayesian statistics", "Epidemiology", "Medical statistics", "Wikipedia articles needing page number citations from September 2018"], "title": "Odds ratio", "method": "Odds ratio", "url": "https://en.wikipedia.org/wiki/Odds_ratio", "summary": "The odds ratio (OR) is a statistic defined as the ratio of the odds of A in the presence of B and the odds of A without the presence of B. This statistic attempts to quantify the strength of the association between A and B. \nIf the OR is greater than 1, then A is considered to be associated with B in the sense that, compared to the absence of B, the presence of B raises the odds of A. Note that this does not establish that B causes A. Often the odds ratio is used to compare the occurrence of some outcome (A) in the presence of some exposure (B), with the occurrence of the outcome (A) in the absence of a particular exposure (absence of B).Two similar statistics that are often used to quantify associations are the risk ratio (RR) and the absolute risk reduction (ARR). Often, the parameter of greatest interest is actually the RR, which is the ratio of the probabilities analogous to the odds used in the OR. However, available data frequently do not allow for the computation of the RR or the ARR but do allow for the computation of the OR, as in case-control studies, as explained below. On the other hand, if one of the properties (A or B) is sufficiently rare (in epidemiology this is called the rare disease assumption), then the OR is approximately equal to the corresponding RR.\nThe OR plays an important role in logistic regression.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/9/96/Odds_ratio_map.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7d/Odds_ratio_minsig.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d6/WHO_Rod.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abbreviation", "Absolute risk reduction", "Academic clinical trials", "Accelerated failure time model", "Accidental sampling", "Actuarial science", "Adaptive clinical trial", "Akaike information criterion", "Analysis of clinical trials", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Animal testing", "Animal testing on non-human primates", "Arithmetic mean", "Association (statistics)", "Asymptotic theory (statistics)", "Attributable fraction among the exposed", "Attributable fraction for the population", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias (statistics)", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Boston University School of Public Health", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Case-control studies", "Case-control study", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran\u2013Mantel\u2013Haenszel statistics", "Coefficient of determination", "Coefficient of variation", "Cohen's h", "Cohen's kappa", "Cohort study", "Cointegration", "Completeness (statistics)", "Conditional probabilities", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Control event rate", "Control group", "Correlation and dependence", "Correlation does not imply causation", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-sectional study", "Cross-validation (statistics)", "Cumulative incidence", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Diagnostic odds ratio", "Dichotomy", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Ecological study", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiological methods", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Evidence-based medicine", "Experiment", "Experimental event rate", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "First-in-man study", "Fisher's exact test", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of clinical research", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hazard ratio", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "In vitro", "In vivo", "Incidence (epidemiology)", "Index of dispersion", "Infectivity", "Intention-to-treat analysis", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratios in diagnostic testing", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of clinical research topics", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Logit", "Longitudinal study", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Meta-analysis", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Morbidity", "Mortality rate", "Multicenter trial", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural logarithm", "Natural logarithms", "Nelson\u2013Aalen estimator", "Nested case\u2013control study", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds", "Official statistics", "One- and two-tailed tests", "Open-label trial", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Period prevalence", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Point prevalence", "Poisson regression", "Population (statistics)", "Population Impact Measures", "Population statistics", "Posterior probability", "Power (statistics)", "Pre- and post-test probability", "Prediction interval", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Proportional hazards model", "Prospective cohort study", "Protocol (science)", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random sampling", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rare disease assumption", "Rate ratio", "Regression analysis", "Regression model validation", "Relative risk", "Relative risk reduction", "Reliability engineering", "Replication (statistics)", "Reproducibility", "Resampling (statistics)", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Seeding trial", "Selection bias", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Specificity and sensitivity", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Standard normal random variable", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survey research", "Survival analysis", "Survival function", "Survivorship bias", "Symmetry", "System identification", "Systematic review", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Unit (statistics)", "V-statistic", "Vaccine trial", "Variance", "Vector autoregression", "Virulence", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.OpenEpi.com", "http://sph.bu.edu/otlt/MPH-Modules/EP/EP713_AnalyticOverview/EP713_AnalyticOverview5.html#", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1112884", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2545775", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3289830", "http://www.ncbi.nlm.nih.gov/pubmed/12377421", "http://www.ncbi.nlm.nih.gov/pubmed/15655138", "http://www.ncbi.nlm.nih.gov/pubmed/18580722", "http://www.ncbi.nlm.nih.gov/pubmed/20842279", "http://www.ncbi.nlm.nih.gov/pubmed/22429441", "http://www.ncbi.nlm.nih.gov/pubmed/3133061", "http://www.ncbi.nlm.nih.gov/pubmed/8549701", "http://www.ncbi.nlm.nih.gov/pubmed/9832001", "http://www.hutchon.net/ConfidOR.htm", "http://doi.org/10.1001%2Farchderm.141.1.19", "http://doi.org/10.1001%2Fjama.280.19.1690", "http://doi.org/10.1007%2FBF01721219", "http://doi.org/10.1016%2FS0029-7844(01)01488-0", "http://doi.org/10.1016%2FS1047-2797(01)00278-2", "http://doi.org/10.1097%2FSMJ.0b013e31817a7ee4", "http://doi.org/10.1136%2Fbmj.296.6632.1313", "http://doi.org/10.1136%2Fbmj.316.7136.989", "http://doi.org/10.3399%2Fbjgp12X630223", "http://statpages.org/ctab2x2.html", "http://www.worldcat.org/issn/1719-8429", "https://www.bmj.com/rapid-response/2011/10/27/use-misuse-and-interpretation-odds-ratios", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757/"]}, "Gravity model of trade": {"categories": ["Econometric models", "International trade theory", "Mathematical economics"], "title": "Gravity model of trade", "method": "Gravity model of trade", "url": "https://en.wikipedia.org/wiki/Gravity_model_of_trade", "summary": "The gravity model of international trade in international economics is a model that, in its traditional form, predicts bilateral trade flows based on the economic sizes (often using GDP measurements) and distance between two units.\nThe model was first introduced in economics world by Walter Isard in 1954. The basic model for trade between two countries (i and j) takes the form of\n\n \n \n \n \n F\n \n i\n j\n \n \n =\n G\n \u2217\n \n M\n \n i\n \n \n \u2217\n \n M\n \n j\n \n \n \n /\n \n \n \n D\n \n i\n j\n \n \n \n \n \n {\\displaystyle F_{ij}=G*M_{i}*M_{j}/{D_{ij}}}\n In this formula G is the constant, F stands for trade flow, D stands for the distance and M stands for the economic dimensions of the countries that are being measured. The equation can be changed into a linear form for the purpose of econometric analyses by employing logarithms. The model has been used by economists to analyse the determinants of bilateral trade flows such as common borders, common languages, common legal systems, common currencies, common colonial legacies, and it has been used to test the effectiveness of trade agreements and organizations such as the North American Free Trade Agreement (NAFTA) and the World Trade Organization (WTO) (Head and Mayer 2014). The model has also been used in international relations to evaluate the impact of treaties and alliances on trade (Head and Mayer).\nThe model has also been applied to other bilateral flow data (also 'dyadic' data) such as migration, traffic, remittances and foreign direct investment.", "images": [], "links": ["Alan Deardorff", "Bertil Ohlin", "Data migration", "Differentiation (marketing)", "Digital object identifier", "Econometric", "Economy of Germany", "Economy of United States", "Elhanan Helpman", "Exports", "Factor of production", "Foreign direct investment", "GDP", "Gravity model of migration", "Heckscher\u2013Ohlin model", "Home bias in trade puzzle", "Home market effect", "International economics", "Internationalization", "Intra-industry trade", "JSTOR", "James E. Anderson", "Jeffrey Bergstrand", "Jeffrey Frankel", "Least squares", "Leontief paradox", "Linder hypothesis", "North American Free Trade Agreement", "Paul Krugman", "Radiation law for human mobility", "Reciprocal dumping", "Remittances", "Social Science Research Network", "Staffan Linder", "Trade costs", "Trade flows", "United States", "Walter Isard", "Wassily Leontief", "World Integrated Trade Solution", "World Trade Organization"], "references": ["http://www.bepress.com/peps/vol9/iss2/1/", "http://linkinghub.elsevier.com/retrieve/pii/S0022199608001062", "http://www.ingentaconnect.com/content/aea/aer/2003/00000093/00000001/art00009", "http://www.sciencedirect.com/science/article/pii/S0165176511001741", "http://www.springerlink.com/content/b9wq4batxqpmbdya/", "http://ssrn.com/abstract=2249536", "http://mpra.ub.uni-muenchen.de/9453/1/MPRA_paper_9453.pdf", "http://www.macalester.edu/research/economics/PAGE/HAVEMAN/Trade.Resources/TradeData.html", "http://doi.org/10.1007%2Fs001680200105", "http://doi.org/10.1016%2Fj.econlet.2011.05.008", "http://doi.org/10.1016%2Fj.jinteco.2008.10.004", "http://doi.org/10.11130%2Fjei.2007.22.4.780", "http://doi.org/10.1162%2Frest.88.4.641", "http://doi.org/10.1257%2F000282803321455214", "http://doi.org/10.2202%2F1554-8597.1061", "http://doi.org/10.2307%2F1884452", "http://doi.org/10.2307%2F1925976", "http://doi.org/10.2307%2F1928068", "http://www.jstor.org/stable/1884452", "http://www.jstor.org/stable/1925976", "http://www.jstor.org/stable/1928068", "http://www.jstor.org/stable/3131862", "http://www.mitpressjournals.org/doi/pdfplus/10.1162/rest.88.4.641", "http://www.unescap.org/tid/artnet/research_institution.asp", "http://info.worldbank.org/etools/BSPAN/PresentationView.asp?PID=416&EID=217", "http://web.worldbank.org/servlets/ECR?contentMDK=20103741&contTypePK=217180&folderPK=214577&sitePK=239055", "http://wits.worldbank.org/WITS/docs/GSIMMethodology.pdf", "http://wits.worldbank.org/simulationtool.html", "http://www.cefir.ru/papers/WP200.pdf", "http://personal.lse.ac.uk/tenreyro/LGW.html", "https://rd.springer.com/article/10.1057/s41308-016-0001-5", "https://gravity.usitc.gov", "https://web.archive.org/web/20060529203229/http://www.econ.unt.edu/research/pdf/00-09MATlinder1.PDF", "https://www.nber.org/chapters/c7818.pdf"]}, "Statistical probability": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2012", "Probability interpretations", "Use dmy dates from January 2011"], "title": "Frequentist probability", "method": "Statistical probability", "url": "https://en.wikipedia.org/wiki/Frequentist_probability", "summary": "Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in a large number of trials. This interpretation supports the statistical needs of experimental scientists and pollsters; probabilities can be found (in principle) by a repeatable objective process (and are thus ideally devoid of opinion). It does not support all needs; gamblers typically require estimates of the odds without experiments.\nThe development of the frequentist account was motivated by the problems and paradoxes of the previously dominant viewpoint, the classical interpretation. In the classical interpretation, probability was defined in terms of the principle of indifference, based on the natural symmetry of a problem, so, e.g. the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube. This classical interpretation stumbled at any statistical problem that has no natural symmetry for reasoning.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/03/John_Venn.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrey Kolmogorov", "Antoine Augustin Cournot", "Aristotle", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Carl Friedrich Gauss", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Classical definition of probability", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dutch book", "Econometrics", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Event (probability theory)", "Experiment", "Experiment (probability theory)", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George Boole", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "History of probability", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Inductive reasoning", "Interaction (statistics)", "International Standard Book Number", "Interpretation of probability", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jacob Bernoulli", "Jakob Friedrich Fries", "Jarque\u2013Bera test", "Jeffreys\u2013Lindley paradox", "Jerzy Neyman", "Johansen test", "John Maynard Keynes", "John Stuart Mill", "John Venn", "Jonckheere's trend test", "Joseph Louis Fran\u00e7ois Bertrand", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Limit of a sequence", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maurice Kendall", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Oxford English Dictionary", "P-values", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pierre-Simon Laplace", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principle of indifference", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Probability interpretations", "Probability theory", "Propensity probability", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative frequency", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rhetoric (Aristotle)", "Richard von Mises", "Robert Leslie Ellis", "Robust regression", "Robust statistics", "Ronald Aylmer Fisher", "Run chart", "Sample median", "Sample size determination", "Sample space", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Sim\u00e9on Denis Poisson", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Probabilities", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical probability", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Subset", "Sufficient statistic", "Sunrise problem", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Feller", "Z-test"], "references": ["http://plato.stanford.edu/archives/win2012/entries/probability-interpret/", "http://www.ma.utexas.edu/~friedman/freq.ps", "http://www.leidenuniv.nl/fsw/verduin/stathist/1stword.htm", "http://doi.org/10.1006%2Faama.1999.0653", "http://doi.org/10.1093%2Fbiomet%2F36.1-2.101", "http://doi.org/10.1098%2Frsta.1937.0005", "http://doi.org/10.1214%2Fss%2F1177011360", "http://www.jstor.org/stable/2332534", "http://rsta.royalsocietypublishing.org/content/roypta/236/767/333.full.pdf", "https://archive.org/details/expositiondelat00courgoog", "https://archive.org/details/logicofchance029416mbp"]}, "Confirmation bias": {"categories": ["Articles with short description", "Barriers to critical thinking", "Cognitive inertia", "Design of experiments", "Error", "Fallacies", "Featured articles", "Ignorance", "Inductive fallacies", "Memory biases", "Misuse of statistics", "Psychological concepts", "Psychology"], "title": "Confirmation bias", "method": "Confirmation bias", "url": "https://en.wikipedia.org/wiki/Confirmation_bias", "summary": "Confirmation bias, also called confirmatory bias or myside bias, is the tendency to search for, interpret, favor, and recall information in a way that confirms one's preexisting beliefs or hypotheses. It is a type of cognitive bias and a systematic error of inductive reasoning. People display this bias when they gather or remember information selectively, or when they interpret it in a biased way. The effect is stronger for emotionally charged issues and for deeply entrenched beliefs. Confirmation bias is a variation of the more general tendency of apophenia.\nPeople also tend to interpret ambiguous evidence as supporting their existing position. Biased search, interpretation and memory have been invoked to explain attitude polarization (when a disagreement becomes more extreme even though the different parties are exposed to the same evidence), belief perseverance (when beliefs persist after the evidence for them is shown to be false), the irrational primacy effect (a greater reliance on information encountered early in a series) and illusory correlation (when people falsely perceive an association between two events or situations).\nA series of psychological experiments in the 1960s suggested that people are biased toward confirming their existing beliefs. Later work re-interpreted these results as a tendency to test ideas in a one-sided way, focusing on one possibility and ignoring alternatives. In certain situations, this tendency can bias people's conclusions. Explanations for the observed biases include wishful thinking and the limited human capacity to process information. Another explanation is that people show confirmation bias because they are weighing up the costs of being wrong, rather than investigating in a neutral, scientific way. However, even scientists can be prone to confirmation bias.Confirmation biases contribute to overconfidence in personal beliefs and can maintain or strengthen beliefs in the face of contrary evidence. Poor decisions due to these biases have been found in political and organizational contexts.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Fred_Barnard07.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/bb/Klayman_Ha1.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2a/Klayman_Ha2.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Klayman_ha3_annotations.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7c/Logic_portal.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ee/MRI-Philips.JPG", "https://upload.wikimedia.org/wikipedia/commons/7/73/Nicolas_P._Rougier%27s_rendering_of_the_human_brain.png", "https://upload.wikimedia.org/wikipedia/commons/6/6c/Psi2.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5c/Somer_Francis_Bacon.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/5/53/Witness_impeachment.jpg", "https://upload.wikimedia.org/wikipedia/en/e/e7/Cscr-featured.svg"], "links": ["Aaron T. Beck", "Academic bias", "Acquiescence bias", "Adversarial system", "Affirmative action", "Alternative medicine", "Anchoring", "Anecdotal evidence", "Apophenia", "Argument", "Arthur Schopenhauer", "Attack on Pearl Harbor", "Attentional bias", "Attitude change", "Attitude polarization", "Attribution bias", "Authority bias", "Automation bias", "Availability heuristic", "Barbara W. Tuchman", "Bayesian probability", "Behavioral confirmation", "Belief", "Belief bias", "Belief perseverance", "Ben Goldacre", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Bibcode", "Boomerang effect (psychology)", "Brady Campaign", "Brendan Nyhan", "Charles Dickens", "Cherry picking", "Choice-supportive bias", "Circular source", "CiteSeerX", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Cognitive dissonance", "Cognitive inertia", "Cognitive miser", "Cognitive therapy", "Cold reading", "Confidence", "Conflict of interest", "Congruence bias", "Consistency", "Contemporary Educational Psychology", "Cordelia Fine", "Correlation", "Cost-benefit analysis", "Cultural bias", "Cultural tracking", "Dante Alighieri", "David Perkins (geneticist)", "Debiasing", "Decision making", "Democracy", "Denial", "Denialism", "Depression (mood)", "Design of experiments", "Desire (emotion)", "Deterrence (psychology)", "Digital object identifier", "Distinction bias", "Divine Comedy", "Dunning\u2013Kruger effect", "Echo chamber (media)", "Edzard Ernst", "Egocentric bias", "Eisegesis", "Election stock market", "Emotion", "Emotional bias", "Empathic", "Evidence", "Evolutionary psychology", "Experimental psychology", "Exploratory thought", "Extrasensory perception", "Extrinsic incentives bias", "Extroversion and introversion", "FUTON bias", "Fading affect bias", "False consensus effect", "Falsificationism", "Filter bubble", "Forecast bias", "Francis Bacon", "Fundamental attribution error", "Funding bias", "George W. Bush", "Great Pyramid of Giza", "Gun politics", "Halo effect", "Healthy user bias", "Heuristics in judgment and decision-making", "Heuristics in judgment and decision making", "Hindsight bias", "History of medicine", "History of science", "History of the Peloponnesian War", "Horn effect", "Hostile attribution bias", "Hostile media effect", "Husband E. Kimmel", "Hypochondria", "Hypocrisy", "Ibn Khaldun", "Id\u00e9e fixe (psychology)", "Illusory correlation", "Impact bias", "In-group favoritism", "Inductive bias", "Inductive reasoning", "Information bias (epidemiology)", "Information processing theory", "Information theory", "Infrastructure bias", "Inherent bias", "Inquisitorial system", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "James Randi", "Jennifer Lerner", "Job performance", "John Kerry", "Lead time bias", "Length time bias", "Leo Tolstoy", "List of biases in judgment and decision making", "List of cognitive biases", "List of memory biases", "Magnetic resonance imaging", "Material conditional", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Michael Shermer", "Mock trial", "Muqaddimah", "National Rifle Association", "Negativity bias", "Net bias", "Normalcy bias", "Novum Organum", "O.J. Simpson", "OCLC", "Observer-expectancy effect", "Odd number", "Omission bias", "Omitted-variable bias", "Optimism bias", "Outcome bias", "Overconfidence effect", "Overton window", "Parapsychology", "Participation bias", "Peer review", "Peter Cathcart Wason", "Philip E. Tetlock", "Philip Tetlock", "Phobias", "Political Behavior (journal)", "Pollyanna principle", "Precision bias", "Pro-innovation bias", "Psychic", "PubMed Central", "PubMed Identifier", "Publication bias", "Pyramidology", "Randomized controlled trial", "Raymond S. Nickerson", "Recall bias", "Reinforcement theory", "Reporting bias", "Response bias", "Restraint bias", "Risk aversion", "Robert MacCoun", "Rorschach inkblot test", "SAT", "Sampling bias", "Schema (psychology)", "Science", "Scientific evidence", "Scott Plous", "Selection bias", "Selective exposure theory", "Selective perception", "Self-enhancement", "Self-fulfilling prophecy", "Self-image", "Self-monitoring", "Self-selection bias", "Self-serving bias", "Self-verification", "Semmelweis reflex", "Serial position effect", "Simon Singh", "Social Science Research Network", "Social comparison bias", "Social desirability bias", "Social media", "Social norms", "Social skills", "Spectrum bias", "St. Thomas Aquinas", "Stanford University", "Status quo bias", "Steven James Bartlett", "Stuart Sutherland", "Survivorship bias", "Systematic error", "Systematic review", "Systemic bias", "The Skeptic's Dictionary", "The World as Will and Representation", "Thucydides", "Time-saving bias", "Trait ascription bias", "Trick or Treatment?: Alternative Medicine on Trial", "Truth", "U.S. Navy", "U.S. state", "United States news media and the Vietnam War", "United States presidential election, 2004", "Uriah Heep", "Verification bias", "Von Restorff effect", "Wason selection task", "Wet bias", "What Is Art?", "White hat bias", "Wishful thinking", "Woozle effect", "Zero-risk bias", "Ziva Kunda"], "references": ["http://hosted.xamai.ca/confbias/", "http://www.boston.com/bostonglobe/ideas/articles/2010/07/11/how_facts_backfire/?page=full", "http://www.magonlinelibrary.com/doi/abs/10.12968/hmed.2017.78.6.350?url_ver=Z39.88-2003&rfr_id=ori:rid:crossref.org&rfr_dat=cr_pub%3Dpubmed", "http://www.scientificamerican.com/article.cfm?id=the-political-brain", "http://skepdic.com/confirmbias.html", "http://www.skepdic.com/backfireeffect.html", "http://ssrn.com/abstract=1619124", "http://ssrn.com/abstract=2819073", "http://youarenotsosmart.com/2010/06/23/confirmation-bias/", "http://faculty.babson.edu/krollag/org_site/soc_psych/lord_death_pen.html", "http://socrates.berkeley.edu/~maccoun/MacCoun_AnnualReview98.pdf", "http://www.dartmouth.edu/~nyhan/nyhan-reifler.pdf", "http://adsabs.harvard.edu/abs/1974Sci...185.1124T", "http://adsabs.harvard.edu/abs/1996PNAS...93.2895R", "http://adsabs.harvard.edu/abs/2006SciAm.295a..36S", "http://think.psy.muohio.edu/home/WolfePublications/Wolfe_Locus_My%20Side%20Bias_2008.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.372.1743", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.472.7064", "http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0200:book=4:chapter=108:section=4", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1120670", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC39730", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4803283", "http://www.ncbi.nlm.nih.gov/pubmed/1142062", "http://www.ncbi.nlm.nih.gov/pubmed/11440947", "http://www.ncbi.nlm.nih.gov/pubmed/1185517", "http://www.ncbi.nlm.nih.gov/pubmed/15012470", "http://www.ncbi.nlm.nih.gov/pubmed/15536240", "http://www.ncbi.nlm.nih.gov/pubmed/17069484", "http://www.ncbi.nlm.nih.gov/pubmed/21098355", "http://www.ncbi.nlm.nih.gov/pubmed/2213492", "http://www.ncbi.nlm.nih.gov/pubmed/2304222", "http://www.ncbi.nlm.nih.gov/pubmed/2810025", "http://www.ncbi.nlm.nih.gov/pubmed/28614014", "http://www.ncbi.nlm.nih.gov/pubmed/5683766", "http://www.ncbi.nlm.nih.gov/pubmed/8350746", "http://www.ncbi.nlm.nih.gov/pubmed/8483985", "http://www.cjr.org/behind_the_news/the_backfire_effect.php", "http://www.devpsy.org/teaching/method/confirmation_bias.html", "http://doi.org/10.1001%2Farchinternmed.2010.406", "http://doi.org/10.1001%2Fjama.263.10.1438", "http://doi.org/10.1002%2Fasi.22784", "http://doi.org/10.1006%2Fjesp.1993.1004", "http://doi.org/10.1006%2Fobhd.1993.1044", "http://doi.org/10.1007%2FBF01173636", "http://doi.org/10.1007%2FBF01186796", "http://doi.org/10.1007%2Fs11109-010-9112-2", 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"http://doi.org/10.1177%2F014616702236869", "http://doi.org/10.1177%2F0146167204271180", "http://doi.org/10.1177%2F014616728061012", "http://doi.org/10.1177%2F01461672952111011", "http://doi.org/10.1177%2F0146167298241004", "http://doi.org/10.1177%2F0963721413480174", "http://doi.org/10.1207%2FS15327760JPFM0201_4", "http://doi.org/10.12968%2Fhmed.2017.78.6.350", "http://doi.org/10.2139%2Fssrn.2819073", "http://doi.org/10.3758%2Fbf03197186", "http://www.gutenberg.org/etext/4602", "http://www.jstor.org/stable/2094423", "http://www.worldcat.org/issn/0022-0167", "http://www.worldcat.org/issn/0022-1031", "http://www.worldcat.org/issn/0022-3514", "http://www.worldcat.org/issn/0033-295X", "http://www.worldcat.org/issn/0036-8733", "http://www.worldcat.org/issn/0092-5853", "http://www.worldcat.org/issn/1089-2680", "http://www.worldcat.org/issn/1542-7579", "http://www.worldcat.org/issn/1552-7433", "http://www.worldcat.org/issn/1556-5068", "http://www.worldcat.org/issn/1747-0226", "http://www.worldcat.org/issn/1939-1315", "http://www.worldcat.org/oclc/259713114", "http://www.worldcat.org/oclc/26359284", "http://www.worldcat.org/oclc/26931106", "http://www.worldcat.org/oclc/277205993", "http://www.worldcat.org/oclc/316403966", "http://www.worldcat.org/oclc/318365881", "http://www.worldcat.org/oclc/319499491", "http://www.worldcat.org/oclc/32699443", "http://www.worldcat.org/oclc/33832963", "http://www.worldcat.org/oclc/34731629", "http://www.worldcat.org/oclc/35025826", "http://www.worldcat.org/oclc/37180929", "http://www.worldcat.org/oclc/39002877", "http://www.worldcat.org/oclc/40618974", "http://www.worldcat.org/oclc/42823720", "http://www.worldcat.org/oclc/44683470", "http://www.worldcat.org/oclc/469971634", "http://www.worldcat.org/oclc/474568621", "http://www.worldcat.org/oclc/55078722", "http://www.worldcat.org/oclc/55124398", "http://www.worldcat.org/oclc/56825108", "http://www.worldcat.org/oclc/602015097", "http://www.worldcat.org/oclc/60668289", "http://www.worldcat.org/oclc/61864118", "http://www.worldcat.org/oclc/63297791", "http://www.worldcat.org/oclc/69423179", "http://www.worldcat.org/oclc/72151566", "http://www.worldcat.org/oclc/7578020", "http://www.worldcat.org/oclc/86117725", "http://www.stats.org.uk/statistical-inference/KlaymanHa1987.pdf", "https://books.google.com/books?id=0SYVAAAAYAAJ&pg=PA124&vq=falsity&dq=tolstoy+%2B+%22what+is+art%22&output=html&source=gbs_search_r&cad=1", "https://www.newstatesman.com/science-tech/social-media/2016/11/forget-fake-news-facebook-real-filter-bubble-you", "https://educationblog.oup.com/theory-of-knowledge/facts-matter-after-all-rejecting-the-backfire-effect", "https://www.ted.com/talks/eli_pariser_beware_online_filter_bubbles", "https://www.wired.com/2015/05/did-facebooks-big-study-kill-my-filter-bubble-thesis/", "https://www.wsj.com/articles/SB10001424052748703811604574533680037778184", "https://web.archive.org/web/20120417061049/http://web.mac.com/kstanovich/Site/YUP_Reviews_files/TICS_review.pdf", "https://www.poynter.org/news/fact-checking-doesnt-backfire-new-study-suggests"]}, "Fan chart (time series)": {"categories": ["CS1 maint: Multiple names: authors list", "Statistical charts and diagrams", "Statistical forecasting", "Use dmy dates from March 2011"], "title": "Fan chart (time series)", "method": "Fan chart (time series)", "url": "https://en.wikipedia.org/wiki/Fan_chart_(time_series)", "summary": "In time series analysis, a fan chart is a chart that joins a simple line chart for observed past data, by showing ranges for possible values of future data together with a line showing a central estimate or most likely value for the future outcomes. As predictions become increasingly uncertain the further into the future one goes, these forecast ranges spread out, creating distinctive wedge or \"fan\" shapes, hence the term. Alternative forms of the chart can also include uncertainty for past data, such as preliminary data that is subject to revision.\nThe term \"fan chart\" was coined by the Bank of England, which has been using these charts and this term since 1997 in its \"Inflation Report\" to describe its best prevision of future inflation to the general public. Fan charts have been used extensively in finance and monetary policy, for instance to represent forecasts of inflation.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/83/FanChartInfl.jpg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/83/20110310210012%21FanChartInfl.jpg"], "links": ["Bank of England", "Confidence interval", "Digital object identifier", "Finance", "Inflation", "Inflation targeting", "Line chart", "Median", "Mode (statistics)", "Monetary policy", "Normal distribution", "R (programming language)", "Split normal distribution", "Student's t distribution", "Time series"], "references": ["http://www.banrep.gov.co/docum/ftp/borra468.pdf", "http://www.informaworld.com/10.1080/03610928208828279", "http://www.mathworks.com/matlabcentral/fileexchange/27702-fan-chart", "http://www.riksbank.com/SiteSeeker/Find.aspx?id=26726&quicksearchquery=Uncertainty+Bands+for+Inflation+Forecasts+&defl=2", "http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471584959.html", "http://mpra.ub.uni-muenchen.de/29141/1/HDPFanChartDataRev.pdf", "http://doi.org/10.1080%2F03610928208828279", "http://www.bankofengland.co.uk/publications/Pages/inflationreport/default.aspx", "http://www.bankofengland.co.uk/publications/inflationreport/irfanch.htm", "http://www.bankofengland.co.uk/publications/quarterlybulletin/qb9801.pdf", "https://sites.google.com/site/jmjulioroman/documents/FanChartGdpGrowth.xls?attredirects=0&d=1", "https://web.archive.org/web/20110715184916/http://www.riksbank.com/SiteSeeker/Find.aspx?id=26726&quicksearchquery=Uncertainty+Bands+for+Inflation+Forecasts+&defl=2", "https://cran.r-project.org/web/packages/fanplot/index.html", "https://ideas.repec.org/p/col/000094/004294.html"]}, "Gaussian measure": {"categories": ["All articles lacking sources", "Articles lacking sources from December 2009", "Measures (measure theory)", "Stochastic processes"], "title": "Gaussian measure", "method": "Gaussian measure", "url": "https://en.wikipedia.org/wiki/Gaussian_measure", "summary": "In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space Rn, closely related to the normal distribution in statistics. There is also a generalization to infinite-dimensional spaces. Gaussian measures are named after the German mathematician Carl Friedrich Gauss. One reason why Gaussian measures are so ubiquitous in probability theory is the Central Limit Theorem. Loosely speaking, it states that if a random variable\nX is obtained by summing a large number N of independent random variables of order 1, then X is of order \n \n \n \n \n \n N\n \n \n \n \n {\\displaystyle {\\sqrt {N}}}\n and its law is\napproximately Gaussian.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Absolute continuity", "Abstract Wiener space", "Banach space", "Besov measure", "Borel measure", "Borel sigma algebra", "Cameron\u2013Martin theorem", "Carl Friedrich Gauss", "Central Limit Theorem", "Classical Wiener space", "Complete measure", "Continuous function", "Derivative", "Dirac measure", "Equivalence (measure theory)", "Euclidean space", "Germany", "Inner regular measure", "Invariant (mathematics)", "Lebesgue measure", "Linear functional", "Locally finite measure", "Mathematician", "Mathematics", "Mean", "Normal distribution", "Open set", "Path (topology)", "Probability distribution", "Probability measure", "Push-forward measure", "Pushforward measure", "Radon measure", "Radon\u2013Nikodym derivative", "Separable space", "Statistics", "Strictly positive measure", "Support (measure theory)", "There is no infinite-dimensional Lebesgue measure", "Translation (geometry)", "Variance", "Vector space", "Weak convergence of measures"], "references": []}, "data collection": {"categories": ["All articles needing additional references", "Articles needing additional references from April 2017", "Data collection", "Design of experiments", "Survey methodology"], "title": "Data collection", "method": "data collection", "url": "https://en.wikipedia.org/wiki/Data_collection", "summary": "Data collection is the process of gathering and measuring information on targeted variables in an established system, which then enables one to answer relevant questions and evaluate outcomes. Data collection is a component of research in all fields of study including physical and social sciences, humanities, and business. While methods vary by discipline, the emphasis on ensuring accurate and honest collection remains the same. The goal for all data collection is to capture quality evidence that allows analysis to lead to the formulation of convincing and credible answers to the questions that have been posed.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/54/Automated_weighbridge_for_Ad%C3%A9lie_penguins_-_journal.pone.0085291.g002.png", "https://upload.wikimedia.org/wikipedia/commons/f/f3/Emblem-money.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8b/Nuvola_apps_kalzium.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5a/Wikipedia%27s_W.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d2/Internet_map_1024.jpg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Ad\u00e9lie penguin", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Business", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection system", "Data curation", "Data management", "Data validation", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Humanities", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Physical science", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Prentice Hall", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Public policy", "Qualitative method", "Quality control", "Quantitative method", "Quantitative methods in criminology", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific data archiving", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social science", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical survey", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey data collection", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighbridge", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3906005", "http://www.ncbi.nlm.nih.gov/pubmed/24489657", "http://www.statisticsguyana.gov.gy/", "http://doi.org/10.1038%2Fsdata.2018.188", "http://doi.org/10.1371%2Fjournal.pone.0085291", "https://www.nature.com/articles/sdata2018188"]}, "Total survey error": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from June 2015", "Survey methodology"], "title": "Total survey error", "method": "Total survey error", "url": "https://en.wikipedia.org/wiki/Total_survey_error", "summary": "In survey sampling, total survey error includes all forms of survey error including sampling variability, interviewer effects, frame errors, response bias, and non-response bias. Total survey error is discussed in detail in many sources including Salant and Dillman.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["International Standard Book Number", "Interviewer effect", "JSTOR", "Measurement error", "Non-response bias", "Nonsampling error", "Public Opinion Quarterly", "Response bias", "Sampling error", "Sampling frame", "Specification error", "Survey sampling"], "references": ["http://www.press.uchicago.edu/ucp/books/book/chicago/T/bo3619292.html", "http://poq.oxfordjournals.org/content/74/5.toc", "https://www.jstor.org/stable/3203346"]}, "Martingale difference sequence": {"categories": ["All stub articles", "Martingale theory", "Probability stubs"], "title": "Martingale difference sequence", "method": "Martingale difference sequence", "url": "https://en.wikipedia.org/wiki/Martingale_difference_sequence", "summary": "In probability theory, a martingale difference sequence (MDS) is related to the concept of the martingale. A stochastic series X is an MDS if its expectation with respect to the past is zero. Formally, consider an adapted sequence \n \n \n \n {\n \n X\n \n t\n \n \n ,\n \n \n \n F\n \n \n \n t\n \n \n \n }\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n \n \n {\\displaystyle \\{X_{t},{\\mathcal {F}}_{t}\\}_{-\\infty }^{\\infty }}\n on a probability space \n \n \n \n (\n \u03a9\n ,\n \n \n F\n \n \n ,\n \n P\n \n )\n \n \n {\\displaystyle (\\Omega ,{\\mathcal {F}},\\mathbb {P} )}\n . \n \n \n \n \n X\n \n t\n \n \n \n \n {\\displaystyle X_{t}}\n is an MDS if it satisfies the following two conditions:\n\n \n \n \n \n E\n \n \n |\n \n X\n \n t\n \n \n |\n \n <\n \u221e\n \n \n {\\displaystyle \\mathbb {E} \\left|X_{t}\\right|<\\infty }\n , and\n \n \n \n \n E\n \n \n [\n \n \n X\n \n t\n \n \n \n |\n \n \n \n \n F\n \n \n \n t\n \u2212\n 1\n \n \n \n ]\n \n =\n 0\n ,\n a\n .\n s\n .\n \n \n {\\displaystyle \\mathbb {E} \\left[X_{t}|{\\mathcal {F}}_{t-1}\\right]=0,a.s.}\n ,for all \n \n \n \n t\n \n \n {\\displaystyle t}\n . By construction, this implies that if \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n is a martingale, then \n \n \n \n \n X\n \n t\n \n \n =\n \n Y\n \n t\n \n \n \u2212\n \n Y\n \n t\n \u2212\n 1\n \n \n \n \n {\\displaystyle X_{t}=Y_{t}-Y_{t-1}}\n will be an MDS\u2014hence the name.\nThe MDS is an extremely useful construct in modern probability theory because it implies much milder restrictions on the memory of the sequence than independence, yet most limit theorems that hold for an independent sequence will also hold for an MDS.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Expected value", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independence (probability theory)", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability", "Probability space", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": []}, "State space representation": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from May 2009", "Classical control theory", "Mathematical modeling", "Time domain analysis", "Time series models"], "title": "State-space representation", "method": "State space representation", "url": "https://en.wikipedia.org/wiki/State-space_representation", "summary": "In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve through time in a way that depends on the values they have at any given time and also depends on the externally imposed values of input variables. Output variables\u2019 values depend on the values of the state variables.\nThe \"state space\" is the Euclidean space in which the variables on the axes are the state variables. The state of the system can be represented as a vector within that space.\nTo abstract from the number of inputs, outputs and states, these variables are expressed as vectors. Additionally, if the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.\nThe state-space method is characterized by significant algebraization of general system theory, which makes it possible to use Kronecker vector-matrix structures. The capacity of these structures can be efficiently applied to research systems with modulation or without it. \nThe state-space representation (also known as the \"time-domain approach\") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With \n \n \n \n p\n \n \n {\\displaystyle p}\n inputs and \n \n \n \n q\n \n \n {\\displaystyle q}\n outputs, we would otherwise have to write down \n \n \n \n q\n \u00d7\n p\n \n \n {\\displaystyle q\\times p}\n Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state-space representation is not limited to systems with linear components and zero initial conditions. The state-space model is used in many different areas. In econometrics, the state-space model can be used for forecasting stock prices and numerous other variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/1/12/Typical_State_Space_model.png", "https://upload.wikimedia.org/wikipedia/commons/d/d9/Typical_State_Space_model_with_feedback.png", "https://upload.wikimedia.org/wikipedia/commons/6/66/Typical_State_Space_model_with_feedback_and_input.png"], "links": ["Algebraic equation", "BIBO stability", "Capacitor", "Characteristic polynomial", "Complex pole", "Control engineering", "Control theory", "Controllability", "Determinant", "Difference equation", "Differential equation", "Discretization", "Dynamical system", "Econometrics", "Eigenvalue", "Eigenvalues", "Euclidean space", "Exponential stability", "Frequency domain", "Hybrid system", "Identity matrix", "Iff", "Inductor", "International Standard Book Number", "Kalman filter", "LTI system", "Laplace domain", "Laplace transform", "Lyapunov stability", "Marginal stability", "Mathematical singularity", "Matrix (mathematics)", "Mechanical equilibrium", "Minimum phase", "Negative feedback", "Newton's laws of motion", "Observability", "PDF", "Pendulum", "Phase space", "Proper transfer function", "Rank (linear algebra)", "Realization (systems)", "Removable singularity", "Rosenbrock system matrix", "Row and column vectors", "State observer", "State space", "State space (physics)", "State variable", "Stationary point", "Stock price", "Strictly proper", "System theory", "Time-domain", "Transfer function", "Wolfram language", "Z-domain"], "references": ["http://reference.wolfram.com/language/ref/AffineStateSpaceModel.html", "http://reference.wolfram.com/language/ref/NonlinearStateSpaceModel.html", "http://reference.wolfram.com/language/ref/StateSpaceModel.html", "http://www.math.rutgers.edu/~sontag/FTPDIR/sontag_mathematical_control_theory_springer98.pdf", "http://ntv.ifmo.ru/en/article/13866/modelirovanie_dinamicheskih_sistem_s_modulyacieys_ispolzovaniem_kronekerovskih_vektorno-matrichnyhpredstavleniy.htm", "https://books.google.com/books?id=-w7rbl1QKVsC&pg=PA254", "https://books.google.com/books?id=Jgtwi3o-mmUC&pg=PA25", "https://books.google.com.hk/books?hl=en&lr=&id=xyneCwAAQBAJ&oi=fnd&pg=PA57&dq=%22Rita+yi+man+li%22&ots=7YTLXxGi5z&sig=1j-NKyZu1yGUbzUv_O84z2bysTc&redir_esc=y#v=onepage&q=%22Rita%20yi%20man%20li%22&f=false"]}, "Bose\u2013Mesner algebra": {"categories": ["Algebra", "Algebraic combinatorics", "All articles lacking in-text citations", "Analysis of variance", "Articles lacking in-text citations from September 2010", "Design of experiments", "Representation theory"], "title": "Bose\u2013Mesner algebra", "method": "Bose\u2013Mesner algebra", "url": "https://en.wikipedia.org/wiki/Bose%E2%80%93Mesner_algebra", "summary": "In mathematics, a Bose\u2013Mesner algebra is a special set of matrices which arise from a combinatorial structure known as an association scheme, together with the usual set of rules for combining (forming the products of) those matrices, such that they form an associative algebra, or, more precisely, a unitary commutative algebra. Among these rules are:\n\nthe result of a product is also within the set of matrices,\nthere is an identity matrix in the set, and\ntaking products is commutative.Bose\u2013Mesner algebras have applications in physics to spin models, and in statistics to the design of experiments. They are named for R. C. Bose and Dale Marsh Mesner.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Abelian variety", "Adjacency matrix", "Analysis of covariance", "Analysis of variance", "Annals of Mathematical Statistics", "Association scheme", "Associative algebra", "Bayesian experimental design", "Bayesian linear regression", "Blind experiment", "Blocking (statistics)", "Box\u2013Behnken design", "Cartesian power", "Central composite design", "Cochran's theorem", "Code", "Commutative algebra", "Commutativity", "Comparing means", "Complete graph", "Completely randomized design", "Complex number", "Confounding", "Contrast (statistics)", "Covariate", "Crossover study", "Design of experiments", "Diagonal matrix", "Digital object identifier", "Effect size", "Eigenvalue", "Eigenvalues", "Experiment", "Experimental unit", "Extension field", "External validity", "Factorial experiment", "Finite field", "Fractional factorial design", "Generalized randomized block design", "Glossary of experimental design", "Graeco-Latin square", "Graphs and Combinatorics", "Hamming scheme", "Hierarchical Bayes model", "Hierarchical linear modeling", "Idempotent matrix", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "JSTOR", "Kronecker's theorem", "Kronecker product", "Latin hypercube sampling", "Latin square", "Linear independence", "Linear regression", "List of statistics articles", "Mathematical Reviews", "Mathematics", "Matrix (mathematics)", "Mixed model", "Multiple comparison", "Multivariate analysis of variance", "Neil J. A. Sloane", "Nuisance variable", "Optimal design", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Paul Camion", "Physics", "Plackett-Burman design", "Polynomial and rational function modeling", "Polynomial ring", "R. C. Bose", "Random assignment", "Random effect", "Randomization", "Randomized block design", "Randomized controlled trial", "Repeated measures design", "Replication (statistics)", "Response surface methodology", "Restricted randomization", "Rosemary A. Bailey", "Sample size", "Scientific control", "Scientific method", "Sequential analysis", "Sequential probability ratio test", "Spin model", "Statistical inference", "Statistical model", "Statistics", "Subgroup", "Symmetric matrix", "Taguchi methods", "Unital algebra", "Validity (statistics)", "Vector space", "Vera Pless", "Vladimir Levenshtein"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0102157", "http://www.ams.org/mathscinet-getitem?mr=0882540", "http://www.ams.org/mathscinet-getitem?mr=2047311", "http://doi.org/10.1007/PL00007251", "http://doi.org/10.1023/A:1008644201287", "http://doi.org/10.1109/18.720545", "http://doi.org/10.1214/aoms/1177706356", "http://www.jstor.org/stable/2237117", "http://projecteuclid.org/euclid.aoms/1177706356", "http://www.maths.qmul.ac.uk/~rab/Asbook"]}, "ANOVA on ranks": {"categories": ["All articles with unsourced statements", "Analysis of variance", "Articles with unsourced statements from November 2018", "Nonparametric statistics"], "title": "ANOVA on ranks", "method": "ANOVA on ranks", "url": "https://en.wikipedia.org/wiki/ANOVA_on_ranks", "summary": "In statistics, one purpose for the analysis of variance (ANOVA) is to analyze differences in means between groups. The test statistic, F, assumes independence of observations, homogeneous variances, and population normality. ANOVA on ranks is a statistic designed for situations when the normality assumption has been violated.", "images": [], "links": ["Analysis of variance", "Anova", "Digital object identifier", "Hotelling's T-square distribution", "Independence (probability theory)", "International Standard Book Number", "JSTOR", "Kruskal\u2013Wallis one-way analysis of variance", "Mann\u2013Whitney U", "Mathematical Reviews", "Mean", "Monte Carlo method", "Normal distribution", "Null hypothesis", "Statistical power", "Statistical software", "Statistics", "T-test", "Type I error", "Wilcoxon rank-sum"], "references": ["http://is.ba.ttu.edu/conover/Dr.Conover.htm", "http://www.ams.org/mathscinet-getitem?mr=1604954", "http://doi.org/10.1080%2F01621459.1989.10478773", "http://doi.org/10.1093%2Fbiomet%2F78.3.697", "http://doi.org/10.2307%2F1165018", "http://doi.org/10.2307%2F2683975", "http://doi.org/10.2307%2F3314695", "http://doi.org/10.3102%2F00346543060001091", "http://doi.org/10.3102%2F10769986010004368", "http://www.jstor.org/stable/1165018", "http://www.jstor.org/stable/2683975", "http://www.jstor.org/stable/3314695", "https://web.archive.org/web/20110302030459/http://is.ba.ttu.edu/conover/Dr.Conover.htm"]}, "Stochastic approximation": {"categories": ["All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from June 2012", "Statistical approximations", "Stochastic optimization", "Wikipedia articles that are too technical from June 2012"], "title": "Stochastic approximation", "method": "Stochastic approximation", "url": "https://en.wikipedia.org/wiki/Stochastic_approximation", "summary": "Stochastic approximation algorithms are recursive update rules that can be used, among other things, to solve optimization problems and fixed point equations (including standard linear systems) when the collected data is subject to noise. In engineering, optimization problems are often of this type, when you do not have a mathematical model of the system (which can be too complex) but still would like to optimize its behavior by adjusting certain parameters.\nFor this purpose, you can do experiments or run simulations to evaluate the performance of the system at given values of the parameters. Stochastic approximation algorithms have also been used in the social sciences to describe collective dynamics: fictitious play in learning theory and consensus algorithms can be studied using their theoryStochastic approximation methods are a family of iterative stochastic optimization algorithms that attempt to find zeroes or extrema of functions which cannot be computed directly, but only estimated via noisy observations. This situation is common, for instance, when taking noisy measurements of empirical data, or when computing parameters of a statistical model.\nMathematically, the goal of these algorithms is to understand properties of a function\n\nwhich is the expected value of a function depending on a random variable \n \n \n \n \u03be\n \n \n {\\textstyle \\xi }\n , but to do so without evaluating \n \n \n \n f\n \n \n {\\textstyle f}\n directly. Instead, the algorithms use random samples of \n \n \n \n F\n (\n \u03b8\n ,\n \u03be\n )\n \n \n {\\textstyle F(\\theta ,\\xi )}\n to efficiently approximate properties of \n \n \n \n f\n \n \n {\\textstyle f}\n such as zeros or extrema.\nThe earliest, and prototypical, algorithms of this kind are the Robbins-Monro and Kiefer-Wolfowitz algorithms introduced respectively in 1951 and 1952.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Algorithm", "Arkadi Nemirovski", "Aryeh Dvoretzky", "C. Johan Masreliez", "Control theory", "Convergence of random variables", "Digital object identifier", "Estimation", "Extremum", "Harold J. Kushner", "Herbert Robbins", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Jack Kiefer (statistician)", "Jacob Wolfowitz", "Optimization problem", "R. Douglas Martin", "Random variable", "Robust statistics", "Simultaneous perturbation stochastic approximation", "Statistical model", "Stochastic gradient descent", "Stochastic optimization"], "references": ["http://www.professeurs.polymtl.ca/jerome.le-ny/teaching/DP_fall09/notes/lec11_SA.pdf", "http://doi.org/10.1007%2F978-1-4899-2696-8", "http://doi.org/10.1007%2FBF00536178", "http://doi.org/10.1109%2FTAC.2000.880982", "http://doi.org/10.1109%2FTIT.1975.1055386", "http://doi.org/10.1137%2F0330046", "http://doi.org/10.1137%2F070704277", "http://doi.org/10.1214%2Faoms%2F1177698258", "http://doi.org/10.1214%2Faoms%2F1177706619", "http://doi.org/10.1214%2Faoms%2F1177728716", "http://doi.org/10.1214%2Faoms%2F1177728794", "http://doi.org/10.1214%2Faoms%2F1177729392", "http://doi.org/10.1214%2Faoms%2F1177729586", "http://doi.org/10.1214%2Faos%2F1176344840", "http://www.jstor.org/stable/2237335", "http://projecteuclid.org/euclid.aoms/1177698258", "http://projecteuclid.org/euclid.aoms/1177728716", "http://projecteuclid.org/euclid.aoms/1177728794", "http://projecteuclid.org/euclid.aos/1176344840", "http://projecteuclid.org/euclid.bsmsp/1200501645", "http://www.worldcat.org/issn/0003-4851", "http://www.worldcat.org/issn/0044-3719", "http://www.worldcat.org/issn/0090-5364", "https://books.google.com/books?id=9MLL2RN40asC&printsec=frontcover#v=onepage&q&f=false", "https://link.springer.com/article/10.1007/BF00536178", "https://www.springer.com/us/book/9780387008943", "https://www.researchgate.net/publication/236736759_New_stochastic_approximation_type_procedures_In_Russian", "https://www.researchgate.net/publication/242608650_Efficient_estimators_from_a_slowly_converging_robbins-monro_process"]}, "Orthogonality": {"categories": ["Abstract algebra", "All articles with unsourced statements", "Articles containing Ancient Greek-language text", "Articles with unsourced statements from April 2011", "Articles with unsourced statements from February 2012", "Linear algebra"], "title": "Orthogonality", "method": "Orthogonality", "url": "https://en.wikipedia.org/wiki/Orthogonality", "summary": "In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form B are orthogonal when B(u, v) = 0. Depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors. In the case of function spaces, families of orthogonal functions are used to form a basis.\nBy extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in other fields including art and chemistry.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2f/Linear_subspaces_with_shading.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5e/Orthogonality_and_rotation.svg", "https://upload.wikimedia.org/wikipedia/commons/8/84/Perpendicular-coloured.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikibooks-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["802.11", "ADSL", "A Greek\u2013English Lexicon", "Abstract algebra", "Addressing mode", "Adriaan van Wijngaarden", "Algol 68", "Analytical chemistry", "Ancient Greek", "Angle", "Basic Linear Algebra Subprograms", "Basis (linear algebra)", "Basis function", "Bilinear form", "Bioorthogonal chemistry", "Bivector", "Block matrix", "Burgoyne Diller", "Chebyshev polynomials", "Chess", "Column space", "Combinatorics", "Comparison of linear algebra libraries", "Comparison of numerical analysis software", "Confluence (term rewriting)", "Coquaternion", "Correlation", "Cramer's rule", "Cross product", "DNA", "DVB-T", "Dependent and independent variables", "Digital object identifier", "Dirac notation", "Direct sum of modules", "Dot product", "Dual space", "Econometrics", "Eigenstates", "Eigenvalues and eigenvectors", "Euclidean space", "Euclidean vector", "Expected value", "Exponential distribution", "Exterior algebra", "Floating point", "Fourier series", "Function (mathematics)", "Function space", "Functional group", "G.hn", "Gamma distribution", "Gaussian distribution", "Gaussian elimination", "Generalized Method of Moments", "Geometric algebra", "Geometry", "Go (game)", "Gram\u2013Schmidt process", "Greg Egan", "Hermite polynomials", "Hermitian operator", "Hyperbolic angle", "Hyperbolic orthogonality", "Hyperplane", "ITU-T", "If and only if", "Imaginary number", "Information Hiding", "Inner product", "Inner product space", "Instruction set", "Integral calculus", "International Standard Book Number", "Invertible matrix", "Isogonal (disambiguation)", "Isogonal trajectory", "Kernel (linear algebra)", "Kronecker delta", "Laguerre polynomials", "Latin squares", "Legendre polynomials", "Line (geometry)", "Linear algebra", "Linear combination", "Linear independence", "Linear map", "Linear span", "Linear subspace", "MATLAB", "Mathematician", "Mathematics", "Matrix (mathematics)", "Matrix decomposition", "Matrix multiplication", "Maximum likelihood", "Minkowski spacetime", "Minor (linear algebra)", "Module (mathematics)", "Multilinear algebra", "Multiple regression", "Multivector", "Natural pairing", "Neuroscience", "New drug application", "Non-covalent", "Norm (mathematics)", "Numerical linear algebra", "Numerical stability", "Ordinary Least Squares", "Organic synthesis", "Orthogonal", "Orthogonal (novel)", "Orthogonal complement", "Orthogonal frequency-division multiplexing", "Orthogonal functions", "Orthogonal group", "Orthogonal instruction set", "Orthogonal ligand-protein pair", "Orthogonal matrix", "Orthogonal polynomials", "Orthogonal transform", "Orthogonality (term rewriting)", "Orthogonalization", "Orthonormal basis", "Orthonormality", "Outer product", "Outline of linear algebra", "Oxford English Dictionary", "Perpendicular", "Perpendicularity", "Perspective (graphical)", "Piet Mondrian", "Plane (mathematics)", "Probability", "Processor register", "Projection (linear algebra)", "Protecting group", "Pseudo-Euclidean space", "PubMed Central", "PubMed Identifier", "Quantum mechanics", "Quotient space (linear algebra)", "Radian", "Rank (linear algebra)", "Rectangle", "Riemann integration", "Right angle", "Right triangle", "Row space", "Scalar (mathematics)", "Scalar multiplication", "Schr\u00f6dinger equation", "Separation of concerns", "Seven-dimensional cross product", "Simple linear regression", "Sparse matrix", "Statistics", "Sturm\u2013Liouville theory", "Subcarrier", "Superimposition", "Supramolecular chemistry", "Surface normal", "System of linear equations", "Taxonomy (general)", "Tensor product", "Term rewriting system", "The Art of Unix Programming", "The Road to Reality", "Thyssen-Bornemisza Museum", "Time division multiple access", "Transformation matrix", "Transpose", "Triple product", "Uniform distribution (continuous)", "Unit vector", "Vanishing point", "Vector algebra", "Vector projection", "Vector space", "Web site", "Weight function", "Wi-Fi", "WiMAX", "Wigner semicircle distribution", "Worldline"], "references": ["http://mathworld.wolfram.com/Orthogonal.html", "http://www.perseus.tufts.edu/hopper/morph?l=gwni/a&la=greek#lexicon", "http://www.perseus.tufts.edu/hopper/morph?l=o)rqog/wnion&la=greek#lexicon", "http://www.perseus.tufts.edu/hopper/morph?l=o)rqos&la=greek#lexicon", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3304098", "http://www.ncbi.nlm.nih.gov/pubmed/22162316", "http://www.chessvariants.org/misc.dir/coreglossary.html#orthogonal_direction", "http://doi.org/10.1002%2Fanie.201104389", "http://www.faqs.org/docs/artu/ch04s02.html", "http://www.museothyssen.org/thyssen_ing/coleccion/obras_ficha_texto_print497.html", "https://books.google.com/books?id=HrUYlIbI2mEC&pg=PA168", "https://books.google.com/books?id=QGPHAl9GE-IC&pg=PA257", "https://books.google.com/books?id=bj-Lu6zjWbEC&pg=PA13", "https://www.youtube.com/watch?v=umu37m0qUiE"]}, "Maxwell's theorem": {"categories": ["James Clerk Maxwell", "Probability theorems"], "title": "Maxwell's theorem", "method": "Maxwell's theorem", "url": "https://en.wikipedia.org/wiki/Maxwell%27s_theorem", "summary": "In probability theory, Maxwell's theorem, named in honor of James Clerk Maxwell, states that if the probability distribution of a vector-valued random variable X = ( X1, ..., Xn )T is the same as the distribution of GX for every n\u00d7n orthogonal matrix G and the components are independent, then the components X1, ..., Xn are normally distributed with expected value 0, all have the same variance, and all are independent. This theorem is one of many characterizations of the normal distribution.\nSince a multiplication by an orthogonal matrix is a rotation, the theorem says that if the probability distribution of a random vector is unchanged by rotations and if the components are independent, then the components are identically distributed and normally distributed. In other words, the only rotationally invariant probability distributions on Rn that have independent components are multivariate normal distributions with expected value 0 and variance \u03c32In, (where In = the n\u00d7n identity matrix), for some positive number \u03c32.", "images": [], "links": ["Characterization (mathematics)", "Expected value", "James Clerk Maxwell", "Multivariate normal distribution", "Normal distribution", "Orthogonal matrix", "Philosophical Magazine", "Probability distribution", "Probability theory", "Random variable", "Statistical independence", "Variance", "Vector space", "William Feller"], "references": []}, "Ergodic theory": {"categories": ["Articles containing Ancient Greek-language text", "CS1 maint: Multiple names: authors list", "Ergodic theory", "Use dmy dates from July 2013", "Wikipedia articles incorporating text from PlanetMath", "Wikipedia articles needing clarification from January 2017", "Wikipedia articles with NDL identifiers"], "title": "Ergodic theory", "method": "Ergodic theory", "url": "https://en.wikipedia.org/wiki/Ergodic_theory", "summary": "Ergodic theory (Greek: \u03ad\u03c1\u03b3\u03bf\u03bd ergon \"work\", \u03cc\u03b4\u03bf\u03c2 hodos \"way\") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics.\nA central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincar\u00e9 recurrence theorem, which claims that almost all points in any subset of the phase space eventually revisit the set. More precise information is provided by various ergodic theorems which assert that, under certain conditions, the time average of a function along the trajectories exists almost everywhere and is related to the space average. Two of the most important theorems are those of Birkhoff (1931) and von Neumann which assert the existence of a time average along each trajectory. For the special class of ergodic systems, this time average is the same for almost all initial points: statistically speaking, the system that evolves for a long time \"forgets\" its initial state. Stronger properties, such as mixing and equidistribution, have also been extensively studied.\nThe problem of metric classification of systems is another important part of the abstract ergodic theory. An outstanding role in ergodic theory and its applications to stochastic processes is played by the various notions of entropy for dynamical systems.\nThe concepts of ergodicity and the ergodic hypothesis are central to applications of ergodic theory. The underlying idea is that for certain systems the time average of their properties is equal to the average over the entire space. Applications of ergodic theory to other parts of mathematics usually involve establishing ergodicity properties for systems of special kind. In geometry, methods of ergodic theory have been used to study the geodesic flow on Riemannian manifolds, starting with the results of Eberhard Hopf for Riemann surfaces of negative curvature. Markov chains form a common context for applications in probability theory. Ergodic theory has fruitful connections with harmonic analysis, Lie theory (representation theory, lattices in algebraic groups), and number theory (the theory of diophantine approximations, L-functions).", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f7/Hamiltonian_flow_classical.gif", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg"], "links": ["Abelian group", "Albert Shiryaev", "Algebraic group", "Almost all", "Almost everywhere", "Almost surely", "Ancient Greek", "Anosov flow", "Artin billiard", "Bernoulli shift", "Bibcode", "Calvin C. Moore", "Chaos theory", "Character (mathematics)", "Circle group", "Compact group", "Compact space", "Conditional expectation", "Continuous dynamical system", "D. V. Anosov", "Digital object identifier", "Diophantine approximations", "Dynamical system", "Eberhard Hopf", "Eigenvalue", "Elon Lindenstrauss", "Encyclopedia of Mathematics", "Equidistribution", "Equidistribution theorem", "Ergodic hypothesis", "Ergodic process", "Ergodicity", "Fields medal", "Friederich Ignaz Mautner", "G. A. Hedlund", "Gaussian curvature", "Geodesic flow", "Geometry", "George David Birkhoff", "Grigory Margulis", "Group action", "Group automorphism", "Haar measure", "Hadamard's billiards", "Hamiltonian system", "Harmonic analysis", "Hilbert space", "Hillel Furstenberg", "Homogeneous space", "Hyperbolic manifold", "Hyperbolic space", "I. M. Gelfand", "I.i.d. random variables", "Indicator function", "Integrable system", "International Standard Book Number", "Invariant measure", "Irrational number", "Irrational rotation", "Israel Gelfand", "JSTOR", "John von Neumann", "Kingman's subadditive ergodic theorem", "Kolmogorov's zero\u2013one law", "L-functions", "Lattice (discrete subgroup)", "Lebesgue measure", "Lie group", "Lie theory", "Lindy effect", "Liouville's theorem (Hamiltonian)", "Lyapunov time", "Marina Ratner", "Markov chain", "Mathematics", "Maximal ergodic theorem", "Mean sojourn time", "Measure-preserving transformation", "Measure-theoretic entropy", "Measure space", "Michiel Hazewinkel", "Minimal dynamical system", "Mixing (mathematics)", "National Diet Library", "Number theory", "One-parameter group", "One-parameter semigroup", "Ornstein isomorphism theorem", "Orthogonal projection", "Phase space", "PlanetMath", "Poincar\u00e9 recurrence theorem", "Pontryagin dual", "Predictability", "Probability theory", "PubMed Central", "PubMed Identifier", "Ratner's theorems", "Representation theory", "Riemann surface", "Riemannian manifolds", "Riemannian symmetric space", "Rigidity (mathematics)", "Root of unity", "S. V. Fomin", "SL2(R)", "SO(n,1)", "Sectional curvature", "Semisimple Lie group", "Sergei Fomin", "Shift map", "Springer-Verlag", "Stationary process", "Statistical mechanics", "Statistical physics", "Stochastic process", "Strong operator topology", "Symbolic dynamics", "Telescoping series", "Torus group", "Trivial character", "Unimodular matrix", "Unique ergodicity", "Unit interval", "Unitary operator", "Velocity", "Vladimir Igorevich Arnol'd", "Weak operator topology", "Ya. G. Sinai", "Zentralblatt MATH"], "references": ["http://physicsworld.com/cws/article/news/47559", "http://adsabs.harvard.edu/abs/1931PNAS...17..656B", "http://adsabs.harvard.edu/abs/1932PNAS...18...70N", "http://adsabs.harvard.edu/abs/1932PNAS...18..263N", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076138", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076162", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076204", "http://www.ncbi.nlm.nih.gov/pubmed/16577406", "http://www.ncbi.nlm.nih.gov/pubmed/16577432", "http://www.ncbi.nlm.nih.gov/pubmed/16587674", "http://bactra.org/notebooks/ergodic-theory.html", "http://doi.org/10.1006%2Fhmat.2001.2338", "http://doi.org/10.1073%2Fpnas.17.12.656", "http://doi.org/10.1073%2Fpnas.18.1.70", "http://doi.org/10.1073%2Fpnas.18.3.263", "http://doi.org/10.2307%2F1970054", "http://doi.org/10.2307%2F2303229", "http://doi.org/10.2307%2F2373052", "http://www.jstor.org/stable/1970054", "http://www.jstor.org/stable/2303229", "http://www.jstor.org/stable/2373052", "http://www.jstor.org/stable/86260", "http://www.pnas.org/cgi/reprint/17/12/656", "http://zbmath.org/?format=complete&q=an:0475.28009", "https://id.ndl.go.jp/auth/ndlna/00562040", "https://www.encyclopediaofmath.org/index.php?title=e/e036150", "https://www.wikidata.org/wiki/Q5498822"]}, "Population statistics": {"categories": ["All articles lacking sources", "Articles lacking sources from July 2012", "Population statistics"], "title": "Demographic statistics", "method": "Population statistics", "url": "https://en.wikipedia.org/wiki/Demographic_statistics", "summary": "Demographic statistics are measures of the characteristics of, or changes to, a population. Records of births, deaths, marriages, immigration and emigration and a regular census of population provide information that is key to making sound decisions about national policy.\nA useful summary of such data is the population pyramid. It provides data about the sex and age distribution of the population in an accessible graphical format.\nAnother summary is called the life table. For a cohort of persons born in the same year, it traces and projects their life experiences from birth to death. For a given cohort, the proportion expected to survive each year (or decade in an abridged life table) is presented in tabular or graphical form.\nThe ratio of males to females by age indicates the consequences of differing mortality rates on the sexes. Thus, while values above one are common for newborns, the ratio dwindles until it is well below one for the older population.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bloomberg Innovation Index", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Census Bureau", "Census block", "Census block group", "Census tract", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic economics", "Demographic window", "Demographics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Divorce demography", "Durbin\u2013Watson statistic", "Econometrics", "Education Index", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Health", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human Development Index", "Human Poverty Index", "Index of dispersion", "Innovation Union Scoreboard", "Interaction (statistics)", "Intercensal estimate", "International Innovation Index", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Life table", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Linguistic diversity index", "List of African countries by population", "List of Arab countries by population", "List of Asian countries by population", "List of Caribbean countries by population", "List of Eurasian countries by population", "List of European Union member states by population", "List of European countries by population", "List of Latin American countries by population", "List of Middle Eastern countries by population", "List of North American countries by population", "List of Oceanian countries by population", "List of South American countries by population", "List of cities proper by population", "List of continents by population", "List of countries and dependencies by population", "List of countries and dependencies by population density", "List of countries by HIV/AIDS adult prevalence rate", "List of countries by Human Development Index", "List of countries by Official Development Assistance received", "List of countries by Sen social welfare function", "List of countries by age at first marriage", "List of countries by age structure", "List of countries by body mass index", "List of countries by dependency ratio", "List of countries by employment rate", "List of countries by future population (United Nations, medium fertility variant)", "List of countries by health expenditure covered by government", "List of countries by imports", "List of countries by income equality", "List of countries by inequality-adjusted HDI", "List of countries by infant and under-five mortality rates", "List of countries by irrigated land area", "List of countries by labour force", "List of countries by life expectancy", "List of countries by literacy rate", "List of countries by maternal mortality rate", "List of countries by median age", "List of countries by natural increase", "List of countries by net migration rate", "List of countries by number of households", "List of countries by past and future population", "List of countries by past life expectancy", "List of countries by past population (United Nations, estimates)", "List of countries by percentage of population living in poverty", "List of countries by percentage of population suffering from undernourishment", "List of countries by population (United Nations)", "List of countries by population growth rate", "List of countries by population in 1000", "List of countries by population in 1500", "List of countries by population in 1600", "List of countries by population in 1700", "List of countries by population in 1800", "List of countries by population in 1900", "List of countries by population in 1907", "List of countries by population in 1939", "List of countries by population in 1989", "List of countries by population in 2000", "List of countries by population in 2005", "List of countries by population in 2010", "List of countries by public sector", "List of countries by real population density based on food growing capacity", "List of countries by sex ratio", "List of countries by student skills", "List of countries by suicide rate", "List of countries by tertiary education attainment", "List of countries by the number of billionaires", "List of countries by total health expenditure per capita", "List of countries by unemployment rate", "List of countries by urban population", "List of countries by women's average years in school", "List of countries in the Americas by population", "List of countries ranked by ethnic and cultural diversity level", "List of development aid country donors", "List of fields of application of statistics", "List of international rankings", "List of islands by population", "List of member states of the Commonwealth of Nations by population", "List of metropolitan areas by population", "List of national capitals by population", "List of population milestones by country", "List of sovereign states and dependencies by total fertility rate", "List of sovereign states and dependent territories by birth rate", "List of sovereign states and dependent territories by immigrant population", "List of sovereign states and dependent territories by mortality rate", "List of states by population in 1 CE", "List of statistics articles", "List of top international rankings by country", "List of urban areas by population", "Lists by country", "Lists of countries and territories", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Megacity", "Megalopolis", "Metadata", "Method of moments (statistics)", "Methods engineering", "Millionaire", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Overcount", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population density", "Population projection", "Population pyramid", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Programme for the International Assessment of Adult Competencies", "Progress in International Reading Literacy Study", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stockpiling antiviral medications for pandemic influenza", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Trends in International Mathematics and Science Study", "U-statistic", "Undercount", "Uniformly most powerful test", "Urbanization by country", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "World Intellectual Property Indicators", "World population", "Z-test"], "references": ["http://www.geohive.com/"]}, "Species discovery curve": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2013", "Community ecology", "Population ecology"], "title": "Species discovery curve", "method": "Species discovery curve", "url": "https://en.wikipedia.org/wiki/Species_discovery_curve", "summary": "In ecology, the species discovery curve or species accumulation curve is a graph recording the cumulative number of species of living things recorded in a particular environment as a function of the cumulative effort expended searching for them (usually measured in person-hours). It is related to, but not identical with, the species-area curve. \nThe species discovery curve will necessarily be increasing, and will normally be negatively accelerated (that is, its rate of increase will slow down). Plotting the curve gives a way of estimating the number of additional species that will be discovered with further effort. This is usually done by fitting some kind of functional form to the curve, either by eye or by using non-linear regression techniques. Commonly used functional forms include the logarithmic function and the negative exponential function. The advantage of the negative exponential function is that it tends to an asymptote which equals the number of species that would be discovered if infinite effort is expended. However, some theoretical approaches imply that the logarithmic curve may be more appropriate, implying that though species discovery will slow down with increasing effort, it will never entirely cease, so there is no asymptote, and if infinite effort was expended, an infinite number of species would be discovered.The first theoretical investigation of the species-discovery process was in a classic paper by Fisher, Corbet and Williams (1943), which was based on a large collection of butterflies made in Malaya. Theoretical statistical work on the problem continues, see for example the recent paper by Chao and Shen (2004). The theory is linked to that of Zipf's law.\nThe same approach is used in many other fields. For example, in ethology, it can be applied to the number of distinct fixed action patterns that will be discovered as a function of cumulative effort studying the behaviour of a species of animal; in molecular genetics it is now being applied to the number of distinct genes that are discovered; and in literary studies, it can be used to estimate the total vocabulary of a writer from the given sample of his or her recorded works (see Efron & Thisted, 1976).", "images": [], "links": ["Anne Chao", "Asymptote", "British Malaya", "Butterfly", "Ecology", "Ethology", "Exponential function", "Fixed action pattern", "Gene", "Logarithm", "Molecular genetics", "Regression analysis", "Species", "Species-area curve", "Vocabulary", "Zipf's law"], "references": []}, "Schilder's theorem": {"categories": ["Asymptotic analysis", "Large deviations theory", "Theorems regarding stochastic processes"], "title": "Schilder's theorem", "method": "Schilder's theorem", "url": "https://en.wikipedia.org/wiki/Schilder%27s_theorem", "summary": "In mathematics, Schilder's theorem is a result in the large deviations theory of stochastic processes. Roughly speaking, Schilder's theorem gives an estimate for the probability that a (scaled-down) sample path of Brownian motion will stray far from the mean path (which is constant with value 0). This statement is made precise using rate functions. Schilder's theorem is generalized by the Freidlin\u2013Wentzell theorem for It\u014d diffusions.", "images": [], "links": ["Absolutely continuous", "Banach space", "Brownian motion", "Closed set", "Dimension", "Euclidean space", "Freidlin\u2013Wentzell theorem", "Infimum", "International Standard Book Number", "It\u014d diffusion", "Large deviations theory", "Law (stochastic processes)", "Mathematical Reviews", "Mathematics", "Open ball", "Open set", "Probability measure", "Rate function", "Stochastic process", "Supremum norm", "Wiener measure"], "references": ["http://www.ams.org/mathscinet-getitem?mr=1619036"]}, "Bootstrapping (statistics)": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from June 2012", "Articles with unsourced statements from April 2009", "Articles with unsourced statements from August 2015", "Articles with unsourced statements from January 2010", "Articles with unsourced statements from June 2012", "Articles with unsourced statements from March 2012", "Computational statistics", "Resampling (statistics)", "Webarchive template archiveis links"], "title": "Bootstrapping (statistics)", "method": "Bootstrapping (statistics)", "url": "https://en.wikipedia.org/wiki/Bootstrapping_(statistics)", "summary": "In statistics, bootstrapping is any test or metric that relies on random sampling with replacement. Bootstrapping allows assigning measures of accuracy (defined in terms of bias, variance, confidence intervals, prediction error or some other such measure) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Generally, it falls in the broader class of resampling methods.\nBootstrapping is the practice of estimating properties of an estimator (such as its variance) by measuring those properties when sampling from an approximating distribution. One standard choice for an approximating distribution is the empirical distribution function of the observed data. In the case where a set of observations can be assumed to be from an independent and identically distributed population, this can be implemented by constructing a number of resamples with replacement, of the observed dataset (and of equal size to the observed dataset).\nIt may also be used for constructing hypothesis tests. It is often used as an alternative to statistical inference based on the assumption of a parametric model when that assumption is in doubt, or where parametric inference is impossible or requires complicated formulas for the calculation of standard errors.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/93/MedianHists.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a6/SpeedOfLightScale.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["A. Colin Cameron", "Absolute value", "Accelerated failure time model", "Accuracy and precision", "Actuarial science", "Ad\u00e8r, H. J.", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Statistics", "Anthony C. Davison", "Archive.is", "Arithmetic mean", "Asymptotic theory", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian estimator", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias (statistics)", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrap aggregating", "Bootstrapping", "Box plot", "Box\u2013Jenkins method", "Bradley Efron", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Consistency (statistics)", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Data set", "David S. Moore", "David V. Hinkley", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical likelihood", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Explanatory variable", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian processes", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Gideon J. Mellenbergh", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heavy-tailed distribution", "Heteroscedasticity", "Heteroskedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Imputation (statistics)", "Independent and identically distributed", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kernel density", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Median absolute deviation", "Medical statistics", "Meta-algorithm", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo simulation", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance parameter", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Persi Diaconis", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Point estimator", "Poisson regression", "Population (statistics)", "Population mean", "Population parameter", "Population statistics", "Posterior distribution", "Posterior probability", "Power (statistics)", "Power law distribution", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Rademacher distribution", "Random assignment", "Random number generation", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real number", "Regression analysis", "Regression model validation", "Reliability (statistics)", "Reliability engineering", "Replication (statistics)", "Reproducibility", "Resampling (statistics)", "Review of Economics and Statistics", "Robert Tibshirani", "Robust regression", "Robust statistics", "Run chart", "Sam Scheiner", "Sample mean", "Sample median", "Sample size", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific American", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simon Newcomb", "Simple linear regression", "Simple random sample", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Speed of light", "Standard deviation", "Standard error", "Standard error (statistics)", "Standard normal distribution", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-statistic", "Student's t-test", "Studentization", "Studentized residuals", "Sufficient statistic", "Support (measure theory)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The Annals of Statistics", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "UMVU", "U statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://statwww.epfl.ch/davison/BMA/library.html", "http://www.burns-stat.com/pages/Tutor/bootstrap_resampling.html", "http://excelandfinance.com/simulation-of-stock-prices/bootstrap/", "http://www.insightful.com/Hesterberg/bootstrap", "http://people.revoledu.com/kardi/tutorial/Bootstrap/index.html", "http://jeff560.tripod.com/b.html", "http://bcs.whfreeman.com/ips5e/content/cat_080/pdf/moore14.pdf", "http://mathworld.wolfram.com/BootstrapMethods.html", "http://lib.stat.cmu.edu/S/bootstrap.funs", "http://www.stat.columbia.edu/~gelman/book/data/", "http://www.statistics101.net/", "http://doi.org/10.1080%2F01621459.1994.10476870", "http://doi.org/10.1093%2Fbiomet%2F68.3.589", "http://doi.org/10.1162%2Frest.90.3.414", "http://doi.org/10.1214%2Faos%2F1176344552", "http://doi.org/10.1214%2Faos%2F1176347265", "http://doi.org/10.1214%2Faos%2F1176349025", "http://doi.org/10.1214%2Faos%2F1176350142", "http://doi.org/10.2307%2F2289144", "http://www.jstor.org/stable/2289144", "http://www.economics.soton.ac.uk/staff/aldrich/Mathematical%20Words.htm#boots", "https://math.mit.edu/~dav/05.dir/class24-prep-a.pdf", "https://statistics.stanford.edu/sites/default/files/BIO%2083.pdf", "https://archive.is/20120712124533/http://lib.stat.cmu.edu/S/bootstrap.funs", "https://web.archive.org/web/20060215221403/http://bcs.whfreeman.com/ips5e/content/cat_080/pdf/moore14.pdf", "https://projecteuclid.org/download/pdf_1/euclid.aos/1176350371", "https://cran.r-project.org/package=animation"]}, "Secular variation": {"categories": ["Articles with short description", "Geomagnetism", "Time series"], "title": "Secular variation", "method": "Secular variation", "url": "https://en.wikipedia.org/wiki/Secular_variation", "summary": "The secular variation of a time series is its long-term non-periodic variation (see Decomposition of time series). Whether something is perceived as a secular variation or not depends on the available timescale: a secular variation over a time scale of centuries may be part of a periodic variation over a time scale of millions of years. Natural quantities often have both periodic and secular variations. Secular variation is sometimes called secular trend or secular drift when the emphasis is on a linear long-term trend.\nThe term secular variation is used wherever time series are applicable in economics, operations research, biological anthropology, astronomy (particularly celestial mechanics) such as VSOP (planets) etc.", "images": [], "links": ["Academic Press", "Annals of Human Biology", "Astronomy", "Astronomy & Astrophysics", "Axial precession (astronomy)", "Bibcode", "Biological anthropology", "CRC Press", "Cambridge University Press", "Celestial mechanics", "Century", "Chaos theory", "Climate", "Decomposition of time series", "Digital object identifier", "Dynamical system", "Earth's magnetic field", "Economics", "Emission spectrum", "Ephemeris", "Equinox", "Extinction event", "Galactic habitable zone", "Galactic plane", "Galaxies", "Geomagnetic jerk", "Geomagnetic reversals", "Geomagnetic secular variation", "Gravitation", "International Standard Book Number", "Ionosphere", "Kepler's laws of planetary motion", "Linear trend", "Magnetosphere", "Many-body system", "Market trends", "Menarche", "Mercury (planet)", "Milankovitch cycles", "Natural satellite", "Neptune", "Numerical model", "Operations research", "Outer core", "Periodic variation", "Perturbation theory", "Plane of the ecliptic", "Planet", "Planetary migration", "Planets", "PubMed Central", "PubMed Identifier", "Puberty", "Secular acceleration of the Moon", "Secularity", "Solar System", "Solar wind", "Spacecraft", "Star", "Sun", "Technical analysis", "Tidal force", "Time series", "VSOP (planets)", "Variations S\u00e9culaires des Orbites Plan\u00e9taires", "Westward drift"], "references": ["http://www.oed.com/view/Entry/174620?redirectedFrom=secular", "http://adsabs.harvard.edu/abs/1982A&A...114..278B", "http://adsabs.harvard.edu/abs/2001jsrs.meet..119K", "http://adsabs.harvard.edu/abs/2001jsrs.meet..231K", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3575631", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4460992", "http://www.ncbi.nlm.nih.gov/pubmed/10421080", "http://www.ncbi.nlm.nih.gov/pubmed/11201332", "http://www.ncbi.nlm.nih.gov/pubmed/20465526", "http://www.ncbi.nlm.nih.gov/pubmed/20696727", "http://pediatrics.aappublications.org/content/121/Supplement_3/S172.abstract", "http://doi.org/10.1080%2F03014460150201896", "http://doi.org/10.1542%2Fpeds.2009-3079", "http://doi.org/10.3109%2F03014461003727606", "https://www.etymonline.com/word/secular#etymonline_v_23091"]}, "Lorenz curve": {"categories": ["Commons category link is on Wikidata", "Economics curves", "Income inequality metrics", "Statistical charts and diagrams", "Welfare economics"], "title": "Lorenz curve", "method": "Lorenz curve", "url": "https://en.wikipedia.org/wiki/Lorenz_curve", "summary": "In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution.\nThe curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution, where it shows for the bottom x% of households, what percentage (y%) of the total income they have. The percentage of households is plotted on the x-axis, the percentage of income on the y-axis. It can also be used to show distribution of assets. In such use, many economists consider it to be a measure of social inequality.\nThe concept is useful in describing inequality among the size of individuals in ecology and in studies of biodiversity, where the cumulative proportion of species is plotted against the cumulative proportion of individuals. It is also useful in business modeling: e.g., in consumer finance, to measure the actual percentage y% of delinquencies attributable to the x% of people with worst risk scores.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/57/Lorenz_curve_of_Denmark%2C_Hungary%2C_and_Namibia.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/5/59/Economics_Gini_coefficient2.svg"], "links": ["Asset (economics)", "Bibcode", "Biodiversity", "Business modeling", "Christian Damgaard", "Consumer finance", "Continuous function", "Credit score", "Cumulative distribution function", "Debt", "Digital object identifier", "Distribution (economics)", "Distribution of income", "Distribution of wealth", "Ecology", "Economic inequality", "Economics", "Gini coefficient", "Graph of a function", "Hoover index", "Income distribution", "Income inequality metrics", "Increasing function", "Infimum", "International Standard Book Number", "JSTOR", "Lorenz asymmetry coefficient", "Lua programming language", "Mathematica", "Max O. Lorenz", "Mean absolute deviation", "Mean deviation (disambiguation)", "Nature (journal)", "Net worth", "Pareto distribution", "Percentage", "Piecewise linear function", "Probability density function", "Probability mass function", "PubMed Identifier", "Python (programming language)", "ROC analysis", "Social inequality", "Social welfare (political science)", "Stata", "WIDER", "Wealth", "Wealth distribution", "Welfare economics", "Zipf's law"], "references": ["http://dasp.ecn.ulaval.ca/", "http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=19968", "http://pure.au.dk/portal/en/cfd@dmu.dk", "http://adsabs.harvard.edu/abs/1905PAmSA...9..209L", "http://adsabs.harvard.edu/abs/2009Natur.458..623W", "http://www.wider.unu.edu/research/Database/en_GB/database/", "http://www.ncbi.nlm.nih.gov/pubmed/19270679", "http://luaforge.net/project/showfiles.php?group_id=49", "http://doi.org/10.1038%2Fnature07840", "http://doi.org/10.1890%2F0012-9658(2000)081%5B1139:DIIPSO%5D2.0.CO;2", "http://doi.org/10.2307%2F1937992", "http://doi.org/10.2307%2F2276207", "http://www.jstor.org/stable/1937992", "http://www.jstor.org/stable/2276207", "http://www.r-project.org/", "http://www.poorcity.richcity.org/calculator.htm", "https://docs.google.com/Doc?docid=0AXe2E1Mm09WIZGhzazhxaDRfMjUzZ25nMjdkZzY&hl=en", "https://docs.google.com/uc?id=0B3e2E1Mm09WIMzQ1ODg5MDgtZjgwNi00NmU1LTgyNmMtZDRhZTYyMTRiYzlk&export=download&hl=en", "https://archive.is/20121204174230/http://www.wessa.net/co.wasp", "https://ideas.repec.org/c/boc/bocode/s366302.html"]}, "Latin square": {"categories": ["CS1 errors: external links", "CS1 maint: Multiple names: authors list", "Design of experiments", "Error detection and correction", "Latin squares", "Non-associative algebra", "Webarchive template wayback links", "Wikipedia articles with BNF identifiers", "Wikipedia articles with GND identifiers", "Wikipedia articles with SUDOC identifiers"], "title": "Latin square", "method": "Latin square", "url": "https://en.wikipedia.org/wiki/Latin_square", "summary": "In combinatorics and in experimental design, a Latin square is an n \u00d7 n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3x3 Latin square is:\n\nThe name \"Latin square\" was inspired by mathematical papers by Leonhard Euler (1707\u20131783), who used Latin characters as symbols, but any set of symbols can be used: in the above example, the alphabetic sequence A, B, C can be replaced by the integer sequence 1, 2, 3.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/Fisher-stainedglass-gonville-caius.jpg", "https://upload.wikimedia.org/wikipedia/commons/e/e4/Magicsquareexample.svg"], "links": ["A. W. F. Edwards", "Algebra", "Alphamagic square", "Analysis of covariance", "Analysis of variance", "Anne Penfold Street", "Antimagic square", "Bayesian experimental design", "Bayesian linear regression", "Biblioth\u00e8que nationale de France", "Binary numeral system", "Blazon", "Blind experiment", "Block design", "Blocking (statistics)", "Box\u2013Behnken design", "C. R. Rao", "Cayley table", "Central composite design", "Charles Colbourn", "Cochran's theorem", "Combinatorial design", "Combinatorics", "Comparing means", "Completely randomized design", "Confounding", "Contrast (statistics)", "Covariate", "Crossover study", "Cyclic group", "Damaraju Raghavarao", "Design of experiments", "Digital object identifier", "Discrete Mathematics (journal)", "Donald Knuth", "Effect size", "Eight queens puzzle", "Encyclopaedia of Mathematics", "Equivalence relation", "Eric W. Weisstein", "Error correcting codes", "Experiment", "Experimental unit", "External validity", "Factorial experiment", "Fractional factorial design", "Futoshiki", "Generalized randomized block design", "Geometric magic square", "Glossary of experimental design", "Gonville and Caius College, Cambridge", "Graeco-Latin square", "Graph coloring", "Group theory", "Heterosquare", "Hierarchical Bayes model", "Hierarchical linear modeling", "Integrated Authority File", "Interaction (statistics)", "Internal validity", "International Biometric Society", "International Standard Book Number", "Kamisado", "KenKen", "Klein four-group", "Latin characters", "Latin hypercube sampling", "Latin square property", "Leonhard Euler", "Linear regression", "List of statistics articles", "Loop (algebra)", "Magic circle (mathematics)", "Magic constant", "Magic cube", "Magic cube classes", "Magic graph", "Magic hexagon", "Magic hexagram", "Magic hyperbeam", "Magic hypercube", "Magic polygon", "Magic series", "Magic square", "Magic star", "Magic triangle (mathematics)", "Main class", "Main class isotopic", "MathWorld", "Mathematical Reviews", "Mathematics of Sudoku", "Matrix (mathematics)", "Mixed model", "Multiple comparison", "Multiplication table", "Multivariate analysis of variance", "NP-complete", "Nuisance variable", "Number Scrabble", "On-Line Encyclopedia of Integer Sequences", "Optimal design", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "Pandiagonal magic square", "Parastrophe", "Paratopy", "Paul Erd\u0151s", "Permanent (mathematics)", "Permute", "Plackett-Burman design", "Polynomial and rational function modeling", "Problems in Latin squares", "Quasigroup", "Random assignment", "Random effect", "Randomization", "Randomized block design", "Randomized controlled trial", "Repeated measures design", "Replication (statistics)", "Response surface methodology", "Restricted randomization", "Richard M. Wilson", "Ronald Fisher", "Rook's graph", "Rosemary A. Bailey", "Sample size", "Sator Square", "Scientific control", "Scientific method", "Sequential analysis", "Sequential probability ratio test", "Small Latin squares and quasigroups", "Stained glass", "Statistical Society of Canada", "Statistical inference", "Statistical model", "Sudoku", "Syst\u00e8me universitaire de documentation", "Taguchi methods", "The Art of Computer Programming", "Validity (statistics)", "Vedic square", "Wayback Machine", "White noise", "Word square"], "references": ["http://www.ssc.ca/archive/main/about/history/arms_e.html", "http://ac.els-cdn.com/0012365X9290722R/1-s2.0-0012365X9290722R-main.pdf?_tid=27cfba60-574b-11e5-8983-00000aacb362&acdnat=1441841780_a90f541979c332007154c0577042d668", "http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470385510.html", "http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471551775.html", "http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471727563.html", "http://mathworld.wolfram.com/LatinSquare.html", "http://eom.springer.de/L/l057620.htm", "http://data.bnf.fr/ark:/12148/cb119596221", "http://www.ams.org/mathscinet-getitem?mr=0351850", "http://www.ams.org/mathscinet-getitem?mr=0908490", "http://www.ams.org/mathscinet-getitem?mr=1016151", "http://www.ams.org/mathscinet-getitem?mr=1096296", "http://www.ams.org/mathscinet-getitem?mr=1102899", "http://www.ams.org/mathscinet-getitem?mr=1492586", "http://www.ams.org/mathscinet-getitem?mr=1644242", "http://www.ams.org/mathscinet-getitem?mr=2129060", "http://www.ams.org/mathscinet-getitem?mr=2363107", "http://www.ams.org/mathscinet-getitem?mr=2422352", "http://doi.org/10.1002%2F(sici)1520-6610(1996)4:6%3C405::aid-jcd3%3E3.0.co;2-j", "http://doi.org/10.1016%2F0012-365x(92)90722-r", "http://doi.org/10.1016%2F0166-218X(84)90075-1", "http://doi.org/10.1098%2Frsta.2006.1885", "http://doi.org/10.1109%2Ftit.2004.828150", "http://www.tibs.org", "http://joas.agrif.bg.ac.rs/archive/article/59", "http://www.maths.qmul.ac.uk/~rab/DOEbook", "https://books.google.com/books?id=GiYc5nRVKf8C", "https://books.google.com/books?id=PTbb7x-mI5gC&pg=PA212", "https://books.google.com/books?id=T3wWj2kVYZgC&printsec=frontcover&cad=4_0", "https://books.google.com/books?id=T3wWj2kVYZgC&printsec=frontcover", "https://www.springer.com/series/694", "https://catalogue.bnf.fr/ark:/12148/cb119596221", "https://www.idref.fr/027588483", "https://d-nb.info/gnd/4166852-2", "https://web.archive.org/web/20050507083541/http://www.tibs.org/", "https://web.archive.org/web/20130521075715/http://www.ssc.ca/archive/main/about/history/arms_e.html", "https://www.wikidata.org/wiki/Q679367"]}, "Covariance": {"categories": ["Algebra of random variables", "All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from December 2010", "Articles needing additional references from December 2010", "CS1 errors: dates", "CS1 maint: Uses authors parameter", "Covariance and correlation"], "title": "Covariance", "method": "Covariance", "url": "https://en.wikipedia.org/wiki/Covariance", "summary": "In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values, (i.e., the variables tend to show similar behavior), the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, (i.e., the variables tend to show opposite behavior), the covariance is negative. The sign of the covariance therefore shows the tendency in the linear relationship between the variables. The magnitude of the covariance is not easy to interpret because it is not normalized and hence depends on the magnitudes of the variables. The normalized version of the covariance, the correlation coefficient, however, shows by its magnitude the strength of the linear relation.\nA distinction must be made between (1) the covariance of two random variables, which is a population parameter that can be seen as a property of the joint probability distribution, and (2) the sample covariance, which in addition to serving as a descriptor of the sample, also serves as an estimated value of the population parameter.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algorithms for calculating variance", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autocovariance", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bilinear operator", "Binomial regression", "Bioinformatics", "Biology", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Capital asset pricing model", "Cartography", "Catastrophic cancellation", "Categorical variable", "Cauchy\u2013Schwarz inequality", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Covariance (disambiguation)", "Covariance and correlation", "Covariance function", "Covariance matrix", "Covariance operator", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cross covariance", "DNA", "Data collection", "Decomposition of time series", "Definite bilinear form", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimensionless number", "Distance covariance", "Divergence (statistics)", "Diversification (finance)", "Donald E. Knuth", "Durbin\u2013Watson statistic", "Econometrics", "Eddy covariance", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Financial economics", "First-hitting-time model", "Floating point", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Inner product", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Joint distribution", "Joint probability distribution", "Jonckheere's trend test", "Kalman filtering", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of total covariance", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear algebra", "Linear dependence", "Linear discriminant analysis", "Linear regression", "Linear relationship", "Linear transformation", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marginal distribution", "MathWorld", "Matrix (mathematics)", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "MicroRNA", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Modern portfolio theory", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Noncoding RNA", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normally distributed and uncorrelated does not imply independent", "Normative economics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Positive economics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Propagation of uncertainty", "Proportional hazards model", "Protein", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Quotient space (linear algebra)", "Q\u2013Q plot", "RNA", "Radar chart", "Random assignment", "Random variable", "Random vector", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real number", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample mean and sample covariance", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Second moment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "State estimation", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical estimation", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The Art of Computer Programming", "Time domain", "Time series", "Tolerance interval", "Transpose", "Trend estimation", "U-statistic", "Uncorrelated", "Uniformly most powerful test", "Unit of measurement", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whitening transformation", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://itfeature.com/probability/covariance-and-correlation", "http://www.r-tutor.com/elementary-statistics/numerical-measures/covariance", "http://www.sciencedirect.com/science/article/pii/S1051200415003140", "http://mathworld.wolfram.com/Covariance.html", "http://www.math.uah.edu/stat/expect/Covariance.html", "http://doi.org/10.1016%2Fj.dsp.2015.10.011", "https://onlinecourses.science.psu.edu/stat414/node/109", "https://www.encyclopediaofmath.org/index.php?title=p/c026800"]}, "Tukey's range test": {"categories": ["Analysis of variance", "Multiple comparisons", "Statistical tests"], "title": "Tukey's range test", "method": "Tukey's range test", "url": "https://en.wikipedia.org/wiki/Tukey%27s_range_test", "summary": "Tukey's range test, also known as the Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, is a single-step multiple comparison procedure and statistical test. It can be used on raw data or in conjunction with an ANOVA (post-hoc analysis) to find means that are significantly different from each other. Named after John Tukey, it compares all possible pairs of means, and is based on a studentized range distribution (q) (this distribution is similar to the distribution of t from the t-test. See below). The Tukey HSD tests should not be confused with the Tukey Mean Difference tests (also known as the Bland\u2013Altman diagram).\nTukey's test compares the means of every treatment to the means of every other treatment; that is, it applies simultaneously to the set of all pairwise comparisons\n\n \n \n \n \n \u03bc\n \n i\n \n \n \u2212\n \n \u03bc\n \n j\n \n \n \n \n \n {\\displaystyle \\mu _{i}-\\mu _{j}\\,}\n and identifies any difference between two means that is greater than the expected standard error. The confidence coefficient for the set, when all sample sizes are equal, is exactly \n \n \n \n 1\n \u2212\n \u03b1\n \n \n {\\displaystyle 1-\\alpha }\n for any \n \n \n \n 0\n \u2264\n \u03b1\n \u2264\n 1\n \n \n {\\displaystyle 0\\leq \\alpha \\leq 1}\n . For unequal sample sizes, the confidence coefficient is greater than 1 \u2212 \u03b1. In other words, the Tukey method is conservative when there are unequal sample sizes.", "images": [], "links": ["ANOVA", "Biometrics (journal)", "Bland\u2013Altman plot", "Central limit theorem", "Clyde Kramer", "Confidence coefficient", "Confidence interval", "Cumulative distribution function", "Digital object identifier", "Family-wise error rate", "Familywise error rate", "Homoscedasticity", "JSTOR", "John Tukey", "Multiple comparison", "Newman\u2013Keuls method", "Normal distribution", "Null hypothesis", "Post-hoc analysis", "Quantile function", "R (programming language)", "Sample mean", "Set (mathematics)", "Standard error", "Standard error (statistics)", "Statistical independence", "Statistical test", "Student's t-distribution", "Studentized range", "Studentized range distribution", "T-test", "Type I error"], "references": ["http://faculty.vassar.edu/lowry/ch14pt2.html", "http://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm", "http://doi.org/10.1016%2Fj.jns.2013.01.016", "http://www.jstor.org/stable/3001913", "https://web.archive.org/web/20081017161620/http://faculty.vassar.edu/lowry/ch14pt2.html"]}, "Variational message passing": {"categories": ["Bayesian networks"], "title": "Variational message passing", "method": "Variational message passing", "url": "https://en.wikipedia.org/wiki/Variational_message_passing", "summary": "Variational message passing (VMP) is an approximate inference technique for continuous- or discrete-valued Bayesian networks, with conjugate-exponential parents, developed by John Winn. VMP was developed as a means of generalizing the approximate variational methods used by such techniques as Latent Dirichlet allocation and works by updating an approximate distribution at each node through messages in the node's Markov blanket.", "images": [], "links": ["Approximate inference", "Bayesian networks", "Conjugate exponents", "Conjugate prior", "Dirichlet distribution", "Exponential distribution", "Exponential family", "Gamma distribution", "Gaussian distribution", "Graphical models", "Latent Dirichlet allocation", "Markov blanket", "Mean", "Natural parameter", "Normalization factor", "Poisson distribution", "Relative entropy", "Sufficient statistic", "Variational Bayesian methods"], "references": ["http://research.microsoft.com/infernet", "http://www.cs.toronto.edu/~beal/thesis/beal03.pdf", "http://vibes.sourceforge.net", "http://www.johnwinn.org/Publications/papers/VMP2004.pdf", "http://dimple.probprog.org", "https://web.archive.org/web/20050428173705/http://www.cs.toronto.edu/~beal/thesis/beal03.pdf"]}, "Drift rate": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2010", "Mathematical finance", "Time series"], "title": "Stochastic drift", "method": "Drift rate", "url": "https://en.wikipedia.org/wiki/Stochastic_drift", "summary": "In probability theory, stochastic drift is the change of the average value of a stochastic (random) process. A related concept is the drift rate, which is the rate at which the average changes. For example, a process that counts the number of heads in a series of \n \n \n \n n\n \n \n {\\displaystyle n}\n fair coin tosses has a drift rate of 1/2 per toss. This is in contrast to the random fluctuations about this average value. The stochastic mean of that coin-toss process is 1/2 and the drift rate of the stochastic mean is 0, assuming 1=heads and 0=tails.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Autocorrelation", "Coin toss", "Decomposition of time series", "First difference", "Fourier series", "Genetic drift", "Gross domestic product", "Longitudinal studies", "Monetary policy", "Natural selection", "Polynomial", "Population genetics", "Price level", "Probability theory", "Secular variation", "Speciation", "Stationary process", "Stochastic process", "Stock price", "Time series analysis", "Trend stationary", "Unit root", "White noise"], "references": ["http://www.visualstatistics.net/Readings/Secular%20Trends/Secular%20Trends.asp"]}, "Population process": {"categories": ["All articles lacking sources", "Articles lacking sources from March 2008", "Markov models", "Population"], "title": "Population process", "method": "Population process", "url": "https://en.wikipedia.org/wiki/Population_process", "summary": "In applied probability, a population process is a Markov chain in which the state of the chain is analogous to the number of individuals in a population (0, 1, 2, etc.), and changes to the state are analogous to the addition or removal of individuals from the population. \nAlthough named by analogy to biological populations from population dynamics, population processes find application in a much wider range of fields than just ecology and other biological sciences. These other applications include telecommunications and queueing theory, chemical kinetics and financial mathematics, and hence the 'population' could be of packets in a computer network, of molecules in a chemical reaction, or even of units in a financial index. \nPopulation processes are typically characterized by processes of birth and immigration, and of death, emigration and catastrophe, which correspond to the basic demographic processes and broad environmental effects to which a population is subject. However, population processes are also often equivalent to other processes that may typically be characterised under other paradigms (in the literal sense of 'patterns'). Queues, for example, are often characterised by an arrivals process, a service process, and the number of servers. In appropriate circumstances, however, arrivals at a queue are functionally equivalent to births or immigration and the service of waiting 'customers' is equivalent to death or emigration. \nTypical population processes include birth-death processes and birth, death and catastrophe processes.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Applied probability", "Biology", "Birth, death and catastrophe process", "Birth-death process", "Chemical kinetics", "Chemical reaction", "Computer network", "Demography", "Ecology", "Financial mathematics", "Markov chain", "Molecule", "Moran process", "Natural environment", "Packet switching", "Paradigm", "Population dynamics", "Queueing theory", "Stock market index", "Telecommunication"], "references": []}, "SETAR (model)": {"categories": ["Nonlinear systems", "Time series models"], "title": "SETAR (model)", "method": "SETAR (model)", "url": "https://en.wikipedia.org/wiki/SETAR_(model)", "summary": "In statistics, Self-Exciting Threshold AutoRegressive (SETAR) models are typically applied to time series data as an extension of autoregressive models, in order to allow for higher degree of flexibility in model parameters through a regime switching behaviour.\nGiven a time series of data xt, the SETAR model is a tool for understanding and, perhaps, predicting future values in this series, assuming that the behaviour of the series changes once the series enters a different regime. The switch from one regime to another depends on the past values of the x series (hence the Self-Exciting portion of the name).\nThe model consists of k autoregressive (AR) parts, each for a different regime. The model is usually referred to as the SETAR(k, p) model where k is the number of regimes and p is the order of the autoregressive part (since those can differ between regimes, the p portion is sometimes dropped and models are denoted simply as SETAR(k).", "images": [], "links": ["Autoregressive", "Exogenous", "Journal of the Royal Statistical Society", "Star model", "Statistics", "Time series", "Variance", "White noise"], "references": ["http://lx2.saas.hku.hk/research/research-report-471.pdf", "https://www.ssc.wisc.edu/~bhansen/papers/saii_11.pdf", "https://web.archive.org/web/20110530064724/http://www.intlpress.com/SII/SII-BrowseJournal.php"]}, "Non-sampling error": {"categories": ["All stub articles", "Auditing terms", "Errors and residuals", "Statistics stubs", "Survey methodology"], "title": "Non-sampling error", "method": "Non-sampling error", "url": "https://en.wikipedia.org/wiki/Non-sampling_error", "summary": "In statistics, non-sampling error is a catch-all term for the deviations of estimates from their true values that are not a function of the sample chosen, including various systematic errors and random errors that are not due to sampling. Non-sampling errors are much harder to quantify than sampling errors.Non-sampling errors in survey estimates can arise from:\nCoverage errors, such as failure to accurately represent all population units in the sample, or the inability to obtain information about all sample cases;\nResponse errors by respondents due for example to definitional differences, misunderstandings, or deliberate misreporting;\nMistakes in recording the data or coding it to standard classifications;\nPseudo-opinions given by respondents when they have no opinion, but do not wish to say so (see: Metallic Metals Act)\nOther errors of collection, nonresponse, processing, or imputation of values for missing or inconsistent data.An excellent discussion of issues pertaining to non-sampling error can be found in several sources such as Kalton (1983) and Salant and Dillman (1995),", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Coverage error", "Errors and residuals in statistics", "Imputation (statistics)", "International Standard Book Number", "Metallic Metals Act", "Random error", "Respondent error", "Sampling error", "Statistics", "Systematic error"], "references": ["http://www2.census.gov/econ/qfr/pubs/qfr11q4.pdf", "http://www.amstat.org/sections/srms/pamphlet.pdf"]}, "Error function": {"categories": ["All articles with unsourced statements", "Analytic functions", "Articles with unsourced statements from August 2011", "CS1 German-language sources (de)", "Functions related to probability distributions", "Gaussian function", "Special hypergeometric functions", "Use dmy dates from July 2013", "Wikipedia articles needing clarification from May 2012", "Wikipedia articles with NDL identifiers"], "title": "Error function", "method": "Error function", "url": "https://en.wikipedia.org/wiki/Error_function", "summary": "In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion. It is defined as:\n\n \n \n \n \n \n \n \n erf\n \u2061\n (\n x\n )\n \n \n \n =\n \n \n 1\n \n \u03c0\n \n \n \n \n \u222b\n \n \u2212\n x\n \n \n x\n \n \n \n e\n \n \u2212\n \n t\n \n 2\n \n \n \n \n \n d\n t\n \n \n \n \n \n \n =\n \n \n 2\n \n \u03c0\n \n \n \n \n \u222b\n \n 0\n \n \n x\n \n \n \n e\n \n \u2212\n \n t\n \n 2\n \n \n \n \n \n d\n t\n .\n \n \n \n \n \n \n {\\displaystyle {\\begin{aligned}\\operatorname {erf} (x)&={\\frac {1}{\\sqrt {\\pi }}}\\int _{-x}^{x}e^{-t^{2}}\\,dt\\\\[5pt]&={\\frac {2}{\\sqrt {\\pi }}}\\int _{0}^{x}e^{-t^{2}}\\,dt.\\end{aligned}}}\n In statistics, for nonnegative values of x, the error function has the following interpretation: for a random variable Y that is normally distributed with mean 0 and variance 1/2, erf(x) describes the probability of Y falling in the range [\u2212x, x].", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/0/00/ComplexErf.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/18/ComplexEx2.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/2f/Error_Function.svg", "https://upload.wikimedia.org/wikipedia/commons/0/02/Error_Function_Generalised.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ec/Mplwp_erf_inv.svg"], "links": ["68\u201395\u201399.7 rule", "ACM Trans. Math. Softw.", "Abramowitz and Stegun", "Antiderivative", "Arithmetic overflow", "Arithmetic underflow", "Asymptotic expansion", "Bit error rate", "Boundary condition", "Closed-form expression", "Complex conjugate", "Complex number", "Confluent hypergeometric function", "Continued fraction", "Coverage probability", "Dawson function", "Digital Library of Mathematical Functions", "Digital object identifier", "Double factorial", "Elementary function", "Elementary function (differential algebra)", "Entire function", "Eric W. Weisstein", "Errors and residuals", "Even and odd functions", "Even function", "Expected value", "Factorial series", "Faddeeva function", "Frank W. J. Olver", "Fresnel integral", "Gamma function", "Gaussian function", "Gaussian integral", "Goodwin\u2013Staton integral", "Hans Heinrich B\u00fcrmann", "Heat equation", "Heaviside step function", "Hermite polynomials", "Horatio Scott Carslaw", "Incomplete gamma function", "Integrand", "Integration by parts", "International Standard Book Number", "Interval estimation", "Inverse function", "Irene Stegun", "James Whitbread Lee Glaisher", "John Conrad Jaeger", "Landau notation", "Library of Congress Control Number", "Maclaurin series", "Mathematical Reviews", "Mathematics", "Milton Abramowitz", "Mittag-Leffler function", "Monthly Notices of the Royal Astronomical Society", "National Diet Library", "Newton's method", "Normal cumulative distribution function", "Normal distribution", "OEIS", "On-Line Encyclopedia of Integer Sequences", "Oscar Schl\u00f6milch", "Partial differential equation", "Probability", "Probability density", "Probit", "Q-function", "Quantile function", "Random variable", "Regularized gamma function", "Rising factorial", "Sigmoid function", "Sign function", "Special function", "Standard deviation", "Statistics", "Stirling number of the first kind", "Taylor expansion", "With high probability"], "references": ["http://www.math.sfu.ca/~cbm/aands/page_297.htm", "http://sites.google.com/site/winitzki/sergei-winitzkis-files/erf-approx.pdf", "http://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/", "http://apps.nrbook.com/empanel/index.html#pg=259", "http://mathworld.wolfram.com/BuermannsTheorem.html", "http://mathworld.wolfram.com/Erf.html", "http://wsl.stanford.edu/~ee359/craig.pdf", "http://www.stat.wisc.edu/courses/st771-newton/papers/p22-cody.pdf", "http://lccn.loc.gov/64-60036", "http://dlmf.nist.gov/7", "http://nvlpubs.nist.gov/nistpubs/jres/73B/jresv73Bn1p1_A1b.pdf", "http://users.auth.gr/users/9/3/028239/public_html/pdf/Q_Approxim.pdf", "http://campus.unibo.it/85943/1/mcddmsTranWIR2003.pdf", "http://www.ams.org/mathscinet-getitem?mr=0167642", "http://www.ams.org/mathscinet-getitem?mr=2723248", "http://doi.org/10.1109%2FTCOMM.2011.072011.100049", "http://doi.org/10.1109%2FTWC.2003.814350", "http://doi.org/10.1111%2Fj.1365-2966.2006.11377.x", "http://doi.org/10.1145%2F151271.151273", "http://escholarship.org/uc/item/6hw4v7pg", "http://mnras.oxfordjournals.org/content/375/3/1043", "https://books.google.com/books?id=2CAqsF-RebgC&pg=PA110#v=onepage&q&f=false", "https://books.google.com/books?id=8Po7AQAAMAAJ&pg=RA1-PA294", "https://books.google.com/books?id=yJ1YAAAAcAAJ&pg=PA421", "https://lccn.loc.gov/65012253", "https://id.ndl.go.jp/auth/ndlna/00562553", "https://archive.org/details/handbuchgamma00nielrich", "https://archive.org/details/zeitschriftfrma09runggoog", "https://arxiv.org/pdf/math/0604627.pdf", "https://www.wikidata.org/wiki/Q579262"]}, "Engineering statistics": {"categories": ["CS1 maint: Multiple names: authors list", "CS1 maint: Uses authors parameter", "Engineering", "Engineering statistics"], "title": "Engineering statistics", "method": "Engineering statistics", "url": "https://en.wikipedia.org/wiki/Engineering_statistics", "summary": "Engineering statistics combines engineering and statistics using scientific methods for analyzing data. Engineering statistics involves data concerning manufacturing processes such as: component dimensions, tolerances, type of material, and fabrication process control. There are many methods used in engineering analysis and they are often displayed as histograms to give a visual of the data as opposed to being just numerical. Examples of methods are:\nDesign of Experiments (DOE) is a methodology for formulating scientific and engineering problems using statistical models. The protocol specifies a randomization procedure for the experiment and specifies the primary data-analysis, particularly in hypothesis testing. In a secondary analysis, the statistical analyst further examines the data to suggest other questions and to help plan future experiments. In engineering applications, the goal is often to optimize a process or product, rather than to subject a scientific hypothesis to test of its predictive adequacy. The use of optimal (or near optimal) designs reduces the cost of experimentation.\nQuality control and process control use statistics as a tool to manage conformance to specifications of manufacturing processes and their products.\nTime and methods engineering use statistics to study repetitive operations in manufacturing in order to set standards and find optimum (in some sense) manufacturing procedures.\nReliability engineering which measures the ability of a system to perform for its intended function (and time) and has tools for improving performance.\nProbabilistic design involving the use of probability in product and system design\nSystem identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data for fitting such models.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abacus", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Charles Babbage", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of Experiments", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dynamical system", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering", "Engineering tolerance", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George E. P. Box", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Harvard University", "Harvard mark I", "Heteroscedasticity", "Histogram", "Histograms", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "IBM", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Manufacturing", "Mathematical Reviews", "Mathematical model", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Process control", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Richard E. Barlow", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific methods", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Slide Rule", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical method", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time and methods engineering", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ams.org/mathscinet-getitem?mr=1621421", "http://www.lse.ac.uk/collections/cats/People/HenryPage.htm", "https://www.britannica.com/science/slide-rule#ref81001", "https://books.google.com/books?id=oIHsrw6NBmoC"]}, "Rao\u2013Blackwell theorem": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2014", "CS1 maint: Uses authors parameter", "Estimation theory", "Statistical theorems"], "title": "Rao\u2013Blackwell theorem", "method": "Rao\u2013Blackwell theorem", "url": "https://en.wikipedia.org/wiki/Rao%E2%80%93Blackwell_theorem", "summary": "In statistics, the Rao\u2013Blackwell theorem, sometimes referred to as the Rao\u2013Blackwell\u2013Kolmogorov theorem, is a result which characterizes the transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria.\nThe Rao\u2013Blackwell theorem states that if g(X) is any kind of estimator of a parameter \u03b8, then the conditional expectation of g(X) given T(X), where T is a sufficient statistic, is typically a better estimator of \u03b8, and is never worse. Sometimes one can very easily construct a very crude estimator g(X), and then evaluate that conditional expected value to get an estimator that is in various senses optimal.\nThe theorem is named after Calyampudi Radhakrishna Rao and David Blackwell. The process of transforming an estimator using the Rao\u2013Blackwell theorem is sometimes called Rao\u2013Blackwellization. The transformed estimator is called the Rao\u2013Blackwell estimator.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrey Kolmogorov", "Annals of Mathematical Statistics", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Basu's theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "C. R. Rao", "Calyampudi Radhakrishna Rao", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional expectation", "Conditional probability", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convex function", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "David Blackwell", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Idempotent", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen's inequality", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of total expectation", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean squared error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson process", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Risk function", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficiency (statistics)", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "Zentralblatt MATH"], "references": ["http://www.tandfonline.com/doi/abs/10.1080/00031305.2015.1100683?journalCode=utas20", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4960505", "http://www.ncbi.nlm.nih.gov/pubmed/27499547", "http://www.ams.org/mathscinet-getitem?mr=0019903", "http://www.ams.org/mathscinet-getitem?mr=0036479", "http://doi.org/10.1080%2F00031305.2015.1100683", "http://doi.org/10.1080%2F00031305.2017.1419145", "http://doi.org/10.1214%2Faoms%2F1177730497", "http://zbmath.org/?format=complete&q=an:0033.07603", "https://www.encyclopediaofmath.org/index.php?title=R/r077550"]}, "Fixed effects estimator": {"categories": ["All articles needing additional references", "All articles to be merged", "Analysis of variance", "Articles needing additional references from September 2009", "Articles to be merged from October 2017", "Articles with multiple maintenance issues", "Regression models"], "title": "Fixed effects model", "method": "Fixed effects estimator", "url": "https://en.wikipedia.org/wiki/Fixed_effects_model", "summary": "In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities. This is in contrast to random effects models and mixed models in which all or some of the model parameters are considered as random variables. In many applications including econometrics and biostatistics a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a random effects model in which the group means are a random sample from a population. Generally, data can be grouped according to several observed factors. The group means could be modeled as fixed or random effects for each grouping. In a fixed effects model each group mean is a group-specific fixed quantity.\nIn panel data where longitudinal observations exist for the same subject, fixed effects represent the subject-specific means. In panel data analysis the term fixed effects estimator (also known as the within estimator) is used to refer to an estimator for the coefficients in the regression model including those fixed effects (one time-invariant intercept for each subject).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ArXiv", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bibcode", "Biometrics (journal)", "Biostatistics", "Chamberlain's approach to unobserved effects models", "Coefficient", "Consistent estimator", "Control variable", "Digital object identifier", "Discrete choice", "Durbin\u2013Wu\u2013Hausman test", "Dynamic unobserved effects model", "Econometrics", "Efficiency (statistics)", "Endogeneity (econometrics)", "Errors-in-variables models", "Errors and residuals in statistics", "Estimator", "First-Difference Estimator", "First difference", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Marc Nerlove", "Mean and predicted response", "Mixed logit", "Mixed model", "Multicollinearity", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Panel data", "Parameter", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistical model", "Statistics", "Statistics in Medicine (journal)", "Studentized residual", "Tikhonov regularization", "Total least squares", "Variance-covariance matrix", "Weighted least squares"], "references": ["http://adsabs.harvard.edu/abs/2018ApJ...857L...9R", "http://pmrc.uga.edu/TR2000-7.pdf", "http://teaching.sociology.ul.ie/DCW/confront/node45.html", "http://arxiv.org/abs/1803.06776", "http://doi.org/10.1002%2Fsim.3478", "http://doi.org/10.3847%2F2041-8213%2Faab7f5", "http://www.jstor.org/stable/2529876", "http://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm", "https://books.google.com/books?id=2eZpoAZnu9UC&pg=PA36", "https://books.google.com/books?id=Zf0gCwxC9ocC&pg=PA717", "https://books.google.com/books?id=i9iPG7C3EP4C&pg=PA95"]}, "Geometric stable distribution": {"categories": ["Continuous distributions", "Geometric stable distributions", "Probability distributions with non-finite variance"], "title": "Geometric stable distribution", "method": "Geometric stable distribution", "url": "https://en.wikipedia.org/wiki/Geometric_stable_distribution", "summary": "A geometric stable distribution or geo-stable distribution is a type of leptokurtic probability distribution. Geometric stable distributions were introduced in Klebanov, L. B., Maniya, G. M., and Melamed, I. A. (1985). A problem of Zolotarev and analogs of infinitely divisible and stable distributions in a scheme for summing a random number of random variables. These distributions are analogues for stable distributions for the case when the number of summands is random, independent of the distribution of summand, and having geometric distribution. The geometric stable distribution may be symmetric or asymmetric. A symmetric geometric stable distribution is also referred to as a Linnik distribution. The Laplace distribution and asymmetric Laplace distribution are special cases of the geometric stable distribution. The Laplace distribution is also a special case of a Linnik distribution. The Mittag-Leffler distribution is also a special case of a geometric stable distribution.The geometric stable distribution has applications in finance theory.", "images": [], "links": ["ARGUS distribution", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent and identically distributed random variables", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Leptokurtic", "Limit (mathematics)", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Standardized moment", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.math.bas.bg/serdica/1999/1999-241-256.pdf", "http://www.m-hikari.com/ijcms-password/ijcms-password1-4-2006/kozubowskiIJCMS1-4-2006.pdf", "http://www.sciencedirect.com/science/article/pii/S0378375810001837", "http://www.sciencedirect.com/science/article/pii/S0895717799001077", "http://www.mathematik.uni-dortmund.de/lsiv/scheffler/ctrw1.pdf", "http://ecommons.cornell.edu/bitstream/1813/9075/1/TR001191.pdf", "http://faculty.wcas.northwestern.edu/~mea405/laplace.pdf", "http://arxiv.org/abs/1410.4093", "http://doi.org/10.1007%2Fs00362-011-0367-4", "http://doi.org/10.1016%2FS0895-7177(99)00107-7", "http://th-www.if.uj.edu.pl/~acta/vol39/pdf/v39p1043.pdf", "https://web.archive.org/web/20110629133648/http://th-www.if.uj.edu.pl/~acta/vol39/pdf/v39p1043.pdf", "https://web.archive.org/web/20110719101917/http://www.mathematik.uni-dortmund.de/lsiv/scheffler/ctrw1.pdf"]}, "M-separation": {"categories": ["Graphical models"], "title": "M-separation", "method": "M-separation", "url": "https://en.wikipedia.org/wiki/M-separation", "summary": "In statistics, m-separation is a measure of disconnectedness in ancestral graphs and a generalization of d-separation for directed acyclic graphs. It is the opposite of m-connectedness.\nSuppose G is an ancestral graph. For given source and target nodes s and t and a set Z of nodes in G\\{s, t}, m-connectedness can be defined as follows. Consider a path from s to t. An intermediate node on the path is called a collider if both edges on the path touching it are directed toward the node. The path is said to m-connect the nodes s and t, given Z, if and only if:\n\nevery non-collider on the path is outside Z, and\nfor each collider c on the path, either c is in Z or there is a directed path from c to an element of Z.If s and t cannot be m-connected by any path satisfying the above conditions, then the nodes are said to be m-separated.\nThe definition can be extended to node sets S and T. Specifically, S and T are m-connected if each node in S can be m-connected to any node in T, and are m-separated otherwise.", "images": [], "links": ["Ancestral graph", "D-separation", "Directed acyclic graph", "Path (graph theory)", "Statistics"], "references": ["http://www.stat.washington.edu/www/research/reports/2003/tr437.pdf"]}, "Likelihood function": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2016", "Bayesian statistics", "Maximum likelihood estimation"], "title": "Likelihood function", "method": "Likelihood function", "url": "https://en.wikipedia.org/wiki/Likelihood_function", "summary": "In frequentist inference, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, given specific observed data. Likelihood functions play a key role in frequentist inference, especially methods of estimating a parameter from a set of statistics. In informal contexts, \"likelihood\" is often used as a synonym for \"probability\". In mathematical statistics, the two terms have different meanings. Probability in this mathematical context describes the plausibility of a random outcome, given a model parameter value, without reference to any observed data. Likelihood describes the plausibility of a model parameter value, given specific observed data.\nIn Bayesian inference, although one can speak about the likelihood of any proposition or random variable given another random variable: for example the likelihood of a parameter value or of a statistical model (see marginal likelihood), given specified data or other evidence, the likelihood function remains the same entity, with the additional interpretations of (i) a conditional density of the data given the parameter (since it is then a random variable) and (ii) a measure or amount of information brought by the data about the parameter value or even the model. Due to the introduction of a probability structure on the parameter space or on the collection of models, it is a possible occurrence that a parameter value or a statistical model have a large likelihood value for a given specified observed data, and yet have a low probability, or vice versa. This is often the case in medical contexts. Following Bayes' Rule, the likelihood when seen as a conditional density can be multiplied by the prior probability density of the parameter and then normalized, to give a posterior probability density.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5a/LikelihoodFunctionAfterHH.png", "https://upload.wikimedia.org/wikipedia/commons/2/20/LikelihoodFunctionAfterHHT.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["A. W. F. Edwards", "Accelerated failure time model", "Actuarial science", "Akaike Information Criterion", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anders Hald", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes' Rule", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Bioinformatics (journal)", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Cambridge University Press", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chapman & Hall", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional entropy", "Conditional probability", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Counting measure", "Coverage probability", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "David Cox (statistician)", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Derivative", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Divergent series", "Donald A. S. Fraser", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical likelihood", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "Exponentiation", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's exact test", "Forest plot", "Fourier analysis", "Francis Ysidro Edgeworth", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Function (mathematics)", "Fundamental theorem of calculus", "G-test", "Gamma distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "German tank problem", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Harvard University Press", "Heteroscedasticity", "Histogram", "History of probability", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypergeometric distribution", "IID", "Identifiability analysis", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval (mathematics)", "Interval estimate", "Interval estimation", "Inverse probability", "Isotonic regression", "Iverson bracket", "JSTOR", "Jackknife resampling", "Jahrbuch \u00fcber die Fortschritte der Mathematik", "Jarque\u2013Bera test", "Johansen test", "John W. Pratt", "John Wiley & Sons", "Johns Hopkins University Press", "Jonckheere's trend test", "Journal of the Royal Statistical Society, Series A", "Journal of the Royal Statistical Society, Series B", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L'H\u00f4pital's rule", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood interval", "Likelihood principle", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marginal likelihood", "Mathematical Reviews", "Mathematical statistics", "Maximum", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimate", "Maximum likelihood estimation", "McNemar's test", "Mean", "Mean value", "Median", "Median-unbiased estimator", "Medical statistics", "Method of maximum likelihood", "Method of moments (statistics)", "Methods engineering", "Middle English", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural logarithm", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Nuisance parameter", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameterized family", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial derivative", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Philosophical Transactions of the Royal Society", "Phylogenetics", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principle of maximum entropy", "Prior probability", "Probabilistic design", "Probability", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Proportional hazards model", "Prosecutor's fallacy", "Pseudolikelihood", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Radon\u2013Nikodym theorem", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Residual maximum likelihood", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score (statistics)", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shorter Oxford English Dictionary", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Stationary process", "Statistic", "Statistical Science", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistically independent", "Statistics", "Stem-and-leaf display", "Stephen Stigler", "Stratified sampling", "Strictly increasing", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The Annals of Statistics", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tunghai University", "U-statistic", "Uncertainty analysis", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://digital.library.adelaide.edu.au/dspace/handle/2440/15172", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3324512", "http://www.ncbi.nlm.nih.gov/pubmed/19505944", "http://www.ncbi.nlm.nih.gov/pubmed/22355081", "http://www.ams.org/mathscinet-getitem?mr=0400509", "http://doi.org/10.1002/9781118341544", "http://doi.org/10.1007%2Fs00362-007-0056-5", "http://doi.org/10.1093%2Fbioinformatics%2Fbtp358", "http://doi.org/10.1093%2Fbioinformatics%2Fbts088", "http://doi.org/10.1093%2Fbiomet%2F62.2.269", "http://doi.org/10.1098%2Frsta.1922.0009", "http://doi.org/10.1214%2Faos%2F1176343457", "http://doi.org/10.1214%2Fss%2F1009212248", "http://doi.org/10.1214%2Fss%2F1030037905", "http://doi.org/10.2307%2F2344804", "http://www.jstor.org/stable/2344804", "http://www.jstor.org/stable/2676741", "http://www.jstor.org/stable/2958222", "http://www.jstor.org/stable/91208", "http://bioinformatics.oxfordjournals.org/content/28/8/1130.long", "http://planetmath.org/likelihoodfunction", "http://projecteuclid.org/download/pdf_1/euclid.ss/1009212248", "http://zbmath.org/?format=complete&q=an:48.1280.02", "http://www.math.uni.wroc.pl/~pms/files/15/Article/15.21.pdf", "http://web.thu.edu.tw/wenwei/www/glmpdfmargin.htm", "https://academic.oup.com/bioinformatics/article/25/15/1923/213246", "https://projecteuclid.org/euclid.ss/1030037905", "https://books.google.co.uk/books?id=hyN6gXHvSo0C"]}, "Time\u2013frequency analysis": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2010", "Signal processing", "Time\u2013frequency analysis", "Wikipedia articles needing clarification from January 2011"], "title": "Time\u2013frequency analysis", "method": "Time\u2013frequency analysis", "url": "https://en.wikipedia.org/wiki/Time%E2%80%93frequency_analysis", "summary": "In signal processing, time\u2013frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time\u2013frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time\u2013frequency analysis studies a two-dimensional signal \u2013 a function whose domain is the two-dimensional real plane, obtained from the signal via a time\u2013frequency transform.The mathematical motivation for this study is that functions and their transform representation are often tightly connected, and they can be understood better by studying them jointly, as a two-dimensional object, rather than separately. A simple example is that the 4-fold periodicity of the Fourier transform \u2013 and the fact that two-fold Fourier transform reverses direction \u2013 can be interpreted by considering the Fourier transform as a 90\u00b0 rotation in the associated time\u2013frequency plane: 4 such rotations yield the identity, and 2 such rotations simply reverse direction (reflection through the origin).\nThe practical motivation for time\u2013frequency analysis is that classical Fourier analysis assumes that signals are infinite in time or periodic, while many signals in practice are of short duration, and change substantially over their duration. For example, traditional musical instruments do not produce infinite duration sinusoids, but instead begin with an attack, then gradually decay. This is poorly represented by traditional methods, which motivates time\u2013frequency analysis.\nOne of the most basic forms of time\u2013frequency analysis is the short-time Fourier transform (STFT), but more sophisticated techniques have been developed, notably wavelets.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/59/Filter_fractional.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/72/Filter_tf.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/23/Mul_mod.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/b1/Sampling.jpg"], "links": ["Alfr\u00e9d Haar", "Aliasing", "Ambiguity function", "Balian\u2013Low theorem", "Bilinear time\u2013frequency distribution", "Cone-shape distribution function", "Dennis Gabor", "Digital object identifier", "Electrocardiogram", "Electroencephalography", "Electromyography", "Fourier analysis", "Fourier transform", "Fractional Fourier transform", "Fresnel diffraction", "Gabor atom", "Gabor limit", "Gabor transform", "Gabor\u2013Wigner transform", "Haar wavelet", "Heisenberg uncertainty principle", "History of wavelets", "Instantaneous frequency", "Instantaneous phase", "International Standard Book Number", "International Standard Serial Number", "Light", "Linear canonical transform", "Linear canonical transformation", "Locally integrable", "Modified Wigner distribution function", "Modulation", "Multiplexing", "Nyquist\u2013Shannon sampling theorem", "Otoacoustic emissions", "Quantum mechanics", "Reflection through the origin", "Short-time Fourier transform", "Signal processing", "Spectral density estimation", "Symplectic geometry", "Tempered distributions", "Time\u2013frequency analysis for music signal", "Time\u2013frequency representation", "Transient (acoustics)", "Wavelet", "Wavelet transform", "Wigner distribution function", "Wigner\u2013Ville distribution"], "references": ["http://doi.org/10.1155%2F2009%2F673539", "http://www.worldcat.org/issn/1687-6180", "https://link.springer.com/article/10.1155/2009/673539"]}, "Kurtosis": {"categories": ["All articles to be expanded", "Articles containing Greek-language text", "Articles to be expanded from December 2009", "Articles using small message boxes", "CS1 errors: dates", "Commons category link is on Wikidata", "Moment (mathematics)", "Statistical deviation and dispersion"], "title": "Kurtosis", "method": "Kurtosis", "url": "https://en.wikipedia.org/wiki/Kurtosis", "summary": "In probability theory and statistics, kurtosis (from Greek: \u03ba\u03c5\u03c1\u03c4\u03cc\u03c2, kyrtos or kurtos, meaning \"curved, arching\") is a measure of the \"tailedness\" of the probability distribution of a real-valued random variable. In a similar way to the concept of skewness, kurtosis is a descriptor of the shape of a probability distribution and, just as for skewness, there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. Depending on the particular measure of kurtosis that is used, there are various interpretations of kurtosis, and of how particular measures should be interpreted.\nThe standard measure of kurtosis, originating with Karl Pearson, is based on a scaled version of the fourth moment of the data or population. This number is related to the tails of the distribution, not its peak; hence, the sometimes-seen characterization as \"peakedness\" is mistaken. For this measure, higher kurtosis is the result of infrequent extreme deviations (or outliers), as opposed to frequent modestly sized deviations.\nThe kurtosis of any univariate normal distribution is 3. It is common to compare the kurtosis of a distribution to this value. Distributions with kurtosis less than 3 are said to be platykurtic, although this does not imply the distribution is \"flat-topped\" as sometimes reported. Rather, it means the distribution produces fewer and less extreme outliers than does the normal distribution. An example of a platykurtic distribution is the uniform distribution, which does not produce outliers. Distributions with kurtosis greater than 3 are said to be leptokurtic. An example of a leptokurtic distribution is the Laplace distribution, which has tails that asymptotically approach zero more slowly than a Gaussian, and therefore produces more outliers than the normal distribution. It is also common practice to use an adjusted version of Pearson's kurtosis, the excess kurtosis, which is the kurtosis minus 3, to provide the comparison to the normal distribution. Some authors use \"kurtosis\" by itself to refer to the excess kurtosis. For the reason of clarity and generality, however, this article follows the non-excess convention and explicitly indicates where excess kurtosis is meant.\nAlternative measures of kurtosis are: the L-kurtosis, which is a scaled version of the fourth L-moment; measures based on four population or sample quantiles. These are analogous to the alternative measures of skewness that are not based on ordinary moments.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/dd/1909_US_Penny.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/96/Pearson_type_VII_distribution_PDF.png", "https://upload.wikimedia.org/wikipedia/commons/7/78/Pearson_type_VII_distribution_log-PDF.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e6/Standard_symmetric_pdfs.png", "https://upload.wikimedia.org/wikipedia/commons/0/0b/Standard_symmetric_pdfs_logscale.png", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": 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"Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Coin toss", "Cointegration", "Cokurtosis", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous uniform distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "D'Agostino's K-squared test", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Deviation (statistics)", "Dickey\u2013Fuller test", "Digital image", "Digital object identifier", "Discrete uniform distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expectation operator", "Expected value", "Experiment", "Exponential distribution", "Exponential family", "Exponential power distribution", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fat-tailed distribution", "First-hitting-time model", "Forensic analysis", "Forest plot", "Fourier analysis", "Fourth moment", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness-of-fit", "Goodness of fit", "Granger causality", "Graphical model", "Greek language", "Grouped data", 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analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Negative number", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normality test", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabola", "Parameter", "Parametric family", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population statistics", "Positive number", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability mass", "Probability theory", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quantiles", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Raised cosine distribution", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Real line", "Real number", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample mean", "Sample median", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shoulders of a distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standardized data", "Standardized moment", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Studia Mathematica", "Sufficient statistic", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Tensor", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Turbulence", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Z-test", "Zentralblatt MATH"], "references": ["http://www.fxsolver.com/solve/share/RMqwaVp85T_5rbacksPD4g==/", "http://medical-dictionary.thefreedictionary.com/lepto-", "http://jeff560.tripod.com/k.html", "http://jeff560.tripod.com/mathword.html", "http://www.yourdictionary.com/platy-prefix", "http://www.cs.albany.edu/~lsw/homepage/PUBLICATIONS_files/ICCP.pdf", "http://faculty.etsu.edu/seier/doc/Kurtosis100years.doc", "http://adsabs.harvard.edu/abs/1959JFM.....6..221S", "http://adsabs.harvard.edu/abs/2013arXiv1309.2896S", "http://weber.ucsd.edu/~hwhite/pub_files/hwcv-092.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4321753", "http://www.ncbi.nlm.nih.gov/pubmed/25678714", "http://www.ams.org/mathscinet-getitem?mr=3452232", "http://arxiv.org/abs/1309.2896", "http://doi.org/10.1007%2FBF01087176", "http://doi.org/10.1016%2FS1544-6123(03)00003-5", "http://doi.org/10.1016%2Fj.jspi.2004.06.004", "http://doi.org/10.1017%2FS0022112059000581", "http://doi.org/10.1080%2F00031305.1970.10478885", "http://doi.org/10.1080%2F00031305.1986.10475415", "http://doi.org/10.1080%2F00031305.2014.917055", "http://doi.org/10.1093%2Fbiomet%2F21.1-4.361", "http://doi.org/10.1109%2Ftac.1980.1102343", "http://doi.org/10.1111%2F1467-9884.00122", "http://doi.org/10.1216%2FRMJ-2015-45-5-1639", "http://doi.org/10.2307%2F2684482", "http://doi.org/10.2307%2F2685210", "http://dx.doi.org/10.1109/tac.1980.1102343", "http://escholarship.org/uc/item/7b52v07p", "http://www.jstor.org/stable/2684482", "http://www.jstor.org/stable/2685210", "http://www.worldcat.org/issn/0018-9286", "http://www.worldcat.org/issn/0039-3223", "http://zbmath.org/?format=complete&q=an:1355.60028", "https://archive.is/20121208231710/http://www.wessa.net/skewkurt.wasp", "https://www.encyclopediaofmath.org/index.php?title=p/e036800", "https://eudml.org/doc/216962"]}, "Geographic information system": {"categories": ["All articles with unsourced statements", "Articles prone to spam from December 2015", "Articles with short description", "Articles with unsourced statements from August 2014", "Articles with unsourced statements from November 2016", "CS1 maint: Archived copy as title", "Computational fields of study", "Geographic information systems", "Webarchive template wayback links", "Wikipedia articles needing clarification from August 2014", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers"], "title": "Geographic information system", "method": "Geographic information system", "url": "https://en.wikipedia.org/wiki/Geographic_information_system", "summary": "A geographic information system (GIS) is a system designed to capture, store, manipulate, analyze, manage, and present spatial or geographic data. GIS applications are tools that allow users to create interactive queries (user-created searches), analyze spatial information, edit data in maps, and present the results of all these operations. GIS (more commonly GIScience) sometimes refers to geographic information science (GIScience), the science underlying geographic concepts, applications, and systems.GIS can refer to a number of different technologies, processes, and methods. It is attached to many operations and has many applications related to engineering, planning, management, transport/logistics, insurance, telecommunications, and business. For that reason, GIS and location intelligence applications can be the foundation for many location-enabled services that rely on analysis and visualization.\nGIS can relate unrelated information by using location as the key index variable. Locations or extents in the Earth space\u2013time may be recorded as dates/times of occurrence, and x, y, and z coordinates representing, longitude, latitude, and elevation, respectively. All Earth-based spatial\u2013temporal location and extent references should be relatable to one another and ultimately to a \"real\" physical location or extent. This key characteristic of GIS has begun to open new avenues of scientific inquiry.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/45/Dem.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/80/Field-Map_birdie.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/25/Geoservices_server_with_apps.png", "https://upload.wikimedia.org/wikipedia/commons/0/0e/Gislayers.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c7/Snow-cholera-map.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/95/World_map_green.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/3/3b/GeaBiosOpenLaszloSatelliteMappingApplication2.PNG", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["AJAX", "AM/FM/GIS", "Adobe Flash", "Advanced very-high-resolution radiometer", "Aerial photography", "Aeryon Scout", "Agricultural geography", "Allsopp Helikite", "Altitude", "Anaglyph 3D", "Analytic geometry", "Application programming interface", "ArcGIS", "Archaeology", "Aspect (geography)", "At-location mapping", "Atmospheric science", "Automotive navigation system", "Barry Smith (academic and ontologist)", "Behavioral geography", "Bibcode", "Bing Maps", "Biogeography", "Business", "Business intelligence", "California", "Canada Geographic Information System", "Canada Land Inventory", "Cartographic relief depiction", "Cartography", "Catchment area (human geography)", "Censorship", "Cholera", "Climatology", "Coastal geography", "Collaborative mapping", "Commonwealth Scientific and Industrial Research Organisation", "Comparison of GIS software", "Computer-aided design", "Computer hardware", "Contour line", "Coordinate", "Copyright", "Correlation", "Counter-mapping", "Crime mapping", "Crowdsourcing", "Cultural geography", "Current Science", "CyberGIS", "DHTML", "DOS", "Dana Tomlin", "Data integration", "Data mining", "Data set", "Datum (geodesy)", "David William Rhind", "Decision support system", "Defense (military)", "Development geography", "Digital Elevation Model", "Digital elevation model", "Digital geologic mapping", "Digital object identifier", "Digitizer", "Digitizing", "Directed edge", "Distributed GIS", "Draughtsman", "E. 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"University of Barcelona", "Unmanned aerial vehicle", "Urban geography", "Vector graphics", "Venn diagram", "Virtual globe", "Water power", "Waterfowl", "Wayback Machine", "Web Feature Service", "Web Map Server", "Web Map Service", "Web mapping", "Weighted moving average", "Wetlands", "World Geodetic System", "World Wide Web", "World Wide Web Consortium", "ZIP Code", "Zoogeography"], "references": ["http://funk.on.br/esantos/doutorado/GEO/igce/DBMS.pdf", "http://www.inf.ufpr.br/carmem/oficinaBD/artigos1s2014/dist-clustering.pdf", "http://www.aeryon.com/news/pressreleases/248-softwareversion5.html", "http://continuingeducation.construction.com/article.php?L=5&C=879", "http://www.esri.com/industries/localgov/open-government", "http://www.esri.com/news/arcnews/fall12articles/the-fiftieth-anniversary-of-gis.html", "http://www.esri.com/news/arcnews/spring09articles/integrating-gis.html", "http://www.geospatialtoday.com", "http://gisgeography.com/history-of-gis", "http://www.gisplanning.com/", "http://www.gisplanning.com/Products/zoomprospector-enterprise.html", "http://www.mdpi.com/2220-9964/6/12/397", "http://www.palgrave-journals.com/udi/journal/v16/n1/abs/udi201025a.html", "http://pasitesearch.com/", "http://safecitygis.com/", "http://www.spatialanalysisonline.com", "http://reference.wolfram.com/language/guide/Geodesy.html", "http://adsabs.harvard.edu/abs/1998CG.....24..315J", "http://adsabs.harvard.edu/abs/2011ISenJ..11..641M", "http://www.gis.dce.harvard.edu/fisher/HTFisher.htm", "http://lib.dr.iastate.edu/scm_pubs/6/", "http://muse.jhu.edu/journals/journal_of_latin_american_geography/", "http://www.personal.psu.edu/faculty/f/u/fuf1/Fonseca-Sheth.pdf", "http://www.geog.ucsb.edu/~good/papers/261.pdf", "http://knoesis.wright.edu/library/download/ACM-GIS_06_Perry.pdf", "http://gallica.bnf.fr/ark:/12148/bpt6k842918/f353.image", "http://www.fgdc.gov/standards/projects/FGDC-standards-projects/accuracy/part3/chapter3", "http://sweet.jpl.nasa.gov/ontology/", "http://www.nasa.gov/topics/earth/features/seaicemin09.html", "http://www.ncbi.nlm.nih.gov/pubmed/22795180", "http://www.ncbi.nlm.nih.gov/pubmed/24827070", "http://www.currentscience.ac.in/Downloads/article_id_094_05_0568_0569_0.pdf", "http://hdl.handle.net/10803/400097", "http://www.broward.org/library/bienes/lii14009.htm", "http://doi.org/10.1007%2F978-4-431-55519-3", "http://doi.org/10.1007%2F978-94-007-2120-3", "http://doi.org/10.1016%2FS0098-3004(98)00032-6", "http://doi.org/10.1016%2Fj.apergo.2012.04.013", "http://doi.org/10.1016%2Fj.jasrep.2017.07.004", "http://doi.org/10.1016%2Fj.trc.2014.10.007", "http://doi.org/10.1023%2FA:1024986003350", "http://doi.org/10.1057%2Fudi.2010.25", "http://doi.org/10.1080%2F00140139.2014.909950", "http://doi.org/10.1080%2F02693798908941519", "http://doi.org/10.1109%2FJSEN.2010.2056916", "http://doi.org/10.1111%2F0033-3352.00028", "http://doi.org/10.1111%2Fj.1538-4632.1997.tb00944.x", "http://doi.org/10.1214%2F088342305000000241", "http://doi.org/10.1353%2Flag.2010.0027", "http://doi.org/10.2752%2F175630613x13584367984947", "http://doi.org/10.3390%2Fijgi6120397", "http://doi.org/10.5311%2FJOSIS.2010.1.2", "http://www.geosco.org/", "http://www.jstor.org/stable/20061176", "http://www.opengeospatial.org/ogc/members", "http://wiki.osgeo.org/wiki/Open_Source_GIS_History", "http://philpapers.org/archive/WINMKI.pdf", "http://ucgis.org/ucgis-fellow/roger-tomlinson", "http://www.urisa.org/node/395", "http://www.w3.org/2005/Incubator/geo/", "http://www.worldcat.org/issn/1540-6210", "http://www.worldcat.org/oclc/70866933", "http://www.worldcat.org/oclc/733249695", "http://www.worldcat.org/oclc/885014629", "http://www.worldcat.org/oclc/900306594", "http://dergipark.gov.tr/rigeo/issue/11187/133647", "http://www.ordnancesurvey.co.uk/oswebsite/ontology/", "http://www.ordnancesurvey.co.uk/oswebsite/partnerships/research/research/terracognita.html", "https://www.crcpress.com/Strategic-GIS-Planning-and-Management-in-Local-Government/Holdstock/p/book/9781466556508", "https://books.google.com/books?id=M-ksAQAAMAAJ", "https://www.academia.edu/2180165/Toward_renewable_energy_geo-information_infrastructures_Applications_of_GIScience_and_remote_sensing_that_build_institutional_capacity", "https://id.loc.gov/authorities/subjects/sh2003007733", "https://d-nb.info/gnd/4261642-6", "https://id.ndl.go.jp/auth/ndlna/00933031", "https://web.archive.org/web/20070518054232/http://www.ordnancesurvey.co.uk/oswebsite/partnerships/research/research/terracognita.html", "https://web.archive.org/web/20070521025424/http://www.ordnancesurvey.co.uk/oswebsite/ontology/", "https://web.archive.org/web/20070529200940/http://sweet.jpl.nasa.gov/ontology/", "https://web.archive.org/web/20070604194024/http://www.broward.org/library/bienes/lii14009.htm", "https://web.archive.org/web/20070714083049/http://www.urisa.org/node/395", "https://web.archive.org/web/20071213234339/http://www.gis.dce.harvard.edu/fisher/HTFisher.htm", "https://web.archive.org/web/20091022085822/http://www.esri.com/news/arcnews/spring09articles/integrating-gis.html", "https://web.archive.org/web/20110424091317/http://funk.on.br/esantos/doutorado/GEO/igce/DBMS.pdf", "https://web.archive.org/web/20120308044542/http://continuingeducation.construction.com/article.php?L=5&C=879", "https://web.archive.org/web/20151217012639/http://ucgis.org/ucgis-fellow/roger-tomlinson", "https://www.wikidata.org/wiki/Q483130", "https://dspace.lboro.ac.uk/2134/10350", "https://dspace.lboro.ac.uk/2134/11589", "https://dspace.lboro.ac.uk/dspace-jspui/bitstream/2134/23845/3/Parker,%20May,%20Mitchell%20-%202014%20-%20User-centred%20design%20of%20neogeography%20the%20impact%20of%20volunteered%20geographic%20information%20on%20users'%20perception.pdf", "https://njgin.state.nj.us/NJ_NJGINExplorer/IW.jsp"]}, "Margin of error": {"categories": ["Error", "Measurement", "Sampling (statistics)", "Statistical deviation and dispersion", "Webarchive template wayback links"], "title": "Margin of error", "method": "Margin of error", "url": "https://en.wikipedia.org/wiki/Margin_of_error", "summary": "The margin of error is a statistic expressing the amount of random sampling error in a survey's results. The larger the margin of error, the less confidence one should have that the poll's reported results are close to the \"true\" figures; that is, the figures for the whole population. Margin of error is positive whenever a population is incompletely sampled and the outcome measure has positive variance (that is, it varies).\nThe term \"margin of error\" is often used in non-survey contexts to indicate observational error in reporting measured quantities.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1d/Marginoferror95.PNG", "https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg"], "links": ["Bayesian inference", "Bayesian probability", "Bias (statistics)", "Binomial proportion confidence interval", "Confidence", "Confidence interval", "Correlation", "Dick Cheney", "Digital object identifier", "Encyclopedia of Mathematics", "Engineering tolerance", "Eric W. Weisstein", "Factor of safety", "Finite population correction", "Formula", "George W. Bush", "International Standard Book Number", "JSTOR", "John Edwards", "John Kerry", "Key relevance", "Line segment", "Linearization", "Margin for error (film)", "MathWorld", "Mean", "Measurement uncertainty", "Michiel Hazewinkel", "Newsweek", "Normal distribution", "Observational error", "Percentage", "Peter Camejo", "Plurality voting system", "Plus-minus sign", "Probability density function", "Questionnaire construction", "Ralph Nader", "Random error", "Random sample", "Random variable", "Resampling (statistics)", "Response rate (survey)", "Sample size", "Sampling (statistics)", "Sampling error", "Sampling fraction", "Simple random sample", "Standard deviation", "Standard error (statistics)", "Statistic", "Statistical population", "Statistical significance", "Statistical survey", "Tolerance (engineering)", "U.S. presidential election, 2004", "Upper bound", "Variance", "Wayback Machine"], "references": ["http://www.msnbc.msn.com/id/6159637/site/newsweek/", "http://www.prnewswire.com/cgi-bin/micro_stories.pl?ACCT=617800&TICK=NEWS&STORY=/www/story/10-02-2004/0002263797&EDATE=Oct+2,+20", "http://www.washingtonmonthly.com/archives/individual/2004_08/004536.php", "http://mathworld.wolfram.com/MarginofError.html", "http://www.researchsolutions.co.nz/sample_sizes.htm", "http://doi.org/10.2307%2F2340569", "http://www.jstor.org/stable/2340569", "https://www.census.gov/hhes/www/income/medincsizeandstate.html", "https://web.archive.org/web/20120121114200/http://www.researchsolutions.co.nz/sample_sizes.htm", "https://www.encyclopediaofmath.org/index.php?title=p/e036240"]}, "Expected utility hypothesis": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2008", "Articles with unsourced statements from February 2011", "Articles with unsourced statements from June 2010", "Articles with unsourced statements from September 2016", "Articles with unsourced statements from September 2018", "Belief revision", "CS1 maint: Archived copy as title", "CS1 maint: BOT: original-url status unknown", "Expected utility", "Game theory", "Motivational theories", "Optimal decisions", "Webarchive template wayback links"], "title": "Expected utility hypothesis", "method": "Expected utility hypothesis", "url": "https://en.wikipedia.org/wiki/Expected_utility_hypothesis", "summary": "In economics, game theory, and decision theory the expected utility hypothesis, concerning people's preferences with regard to choices that have uncertain outcomes (gambles), states that the subjective value associated with an individual's gamble is the statistical expectation of that individual's valuations of the outcomes of that gamble, where these valuations may differ from the dollar value of those outcomes.\nInitiated by Daniel Bernoulli in 1738, this hypothesis has proven useful to explain some popular choices that seem to contradict the expected value criterion (which takes into account only the sizes of the payouts and the probabilities of occurrence), such as occur in the contexts of gambling and insurance. Until the mid-twentieth century, the standard term for the expected utility was the moral expectation, contrasted with \"mathematical expectation\" for the expected value.The von Neumann\u2013Morgenstern utility theorem provides necessary and sufficient conditions under which the expected utility hypothesis holds. From relatively early on, it was accepted that some of these conditions would be violated by real decision-makers in practice but that the conditions could be interpreted nonetheless as 'axioms' of rational choice.", "images": [], "links": ["AFM Smith", "Affine transformation", "Aggregation problem", "Allais paradox", "Ambiguity aversion", "American Economic Review", "Amos Tversky", "Average cost", "Axiom", "Bayes's rule", "Bayesian probability", "Behavioral economics", "Behavioral finance", "Belief revision", "Bilateral monopoly", "Bruno de Finetti", "Budget set", "Business economics", "Cardinal utility", "Certainty equivalent", "Charles Sanders Peirce", "Choice", "Competition (economics)", "Completeness (order theory)", "Computational economics", "Concave function", "Conditional probability", "Constant absolute risk aversion", "Constant relative risk aversion", "Consumer choice", "Convexity in economics", "Cost\u2013benefit analysis", "Cumulative prospect theory", "Daniel Bernoulli", "Daniel Kahneman", "Deadweight loss", "Decision theory", "Digital object identifier", "Discrete and continuous variables", "Distribution (economics)", "Donald Davidson (philosopher)", "Duopoly", "Econometrics", "Economic cost", "Economic equilibrium", "Economic profit", "Economic rent", "Economic surplus", "Economics", "Economies of scale", "Economies of scope", "Elasticity (economics)", "Elliptical distribution", "Engineering Economics", "Entropic risk measure", "Expected utility", "Expected value", "Experimental economics", "Externality", "Family economics", "Frank P. Ramsey", "Gabriel Cramer", "Game theory", "General equilibrium theory", "Generalized expected utility", "Hyperprior", "Income\u2013consumption curve", "Independence of irrelevant alternatives", "Indifference curve", "Indifference price", "Industrial organization", "Information economics", "International Standard Book Number", "International Standard Serial Number", "Intertemporal choice", "JSTOR", "Joseph Jastrow", "Knightian uncertainty", "Labor economics", "Long-tailed distribution", "Loss function", "Lottery (probability)", "Managerial economics", "Marginal cost", "Marginal utility", "Market (economics)", "Market failure", "Market structure", "Martin Shubik", "Mathematical economics", "Mathematical model", "Mathematical optimization", "Microeconomics", "Microfoundations", "Minimax", "Minimax regret", "Modern portfolio theory", "Monopolistic competition", "Monopoly", "Monopsony", "Monty Hall problem", "Multilevel model", "Nicolas Bernoulli", "Non-convexity (economics)", "Normal distribution", "Oligopoly", "Oligopsony", "Operations research", "Opportunity cost", "Ordinal utility", "Oskar Morgenstern", "Pareto efficiency", "Patrick Suppes", "Paul Slovic", "Perfect competition", "Preference (economics)", "Price", "Probability density function", "Production set", "Prospect theory", "Public good", "Rank-dependent expected utility", "Rational choice theory", "Rationality", "Rationing", "Returns to scale", "Risk", "Risk (statistics)", "Risk attitude", "Risk aversion", "Risk aversion (Economics)", "Risk premium", "Robust decision", "SP/A theory", "Scarcity", "Scenario analysis", "Scott Plous", "Sensitivity analysis", "Set theory", "Shortage", "Sidney Siegel", "Social choice theory", "Social cost", "St. Petersburg paradox", "Stanford University Press", "Statistical decision theory", "Subjective expected utility", "Subjective theory of value", "Substitution effect", "Sunk cost", "Supply and demand", "Theory of the firm", "Trade", "Transaction cost", "Transitive relation", "Two-moment decision models", "Uncertainty", "Utility", "Variance", "Von Neumann\u2013Morgenstern utility theorem", "Wage", "Wayback Machine", "Welfare economics", "William Stanley Jevons"], "references": ["http://psychclassics.yorku.ca/Peirce/small-diffs.htm", "http://www.google.com/search?q=SP/A+theory", "http://jeff560.tripod.com/m.html", "http://cerebro.xu.edu/math/Sources/NBernoulli/correspondence_petersburg_game.pdf", "http://psycnet.apa.org/journals/xge/89/1/46/", "http://doi.org/10.1016%2F0022-0531(83)90129-1", "http://doi.org/10.1037%2Fh0031207", "http://doi.org/10.1287%2Fmnsc.34.12.1416", "http://doi.org/10.2307%2F1909829", "http://doi.org/10.2307%2F1913738", "http://doi.org/10.2307%2F2296336", "http://doi.org/10.2307%2F2328079", "http://www.jstor.org/stable/1808708", "http://www.jstor.org/stable/1813367", "http://www.jstor.org/stable/1909829", "http://www.jstor.org/stable/1913738", "http://www.jstor.org/stable/2296336", "http://www.jstor.org/stable/2328079", "http://www.numdam.org/item?id=AIHP_1937__7_1_1_0", "http://www.worldcat.org/issn/0096-3445", "https://web.archive.org/web/20061014122843/http://cepa.newschool.edu/het/texts/ramsey/ramsess.pdf", "https://web.archive.org/web/20110511132124/http://jeff560.tripod.com/m.html", "https://web.archive.org/web/20140316004831/http://math.fau.edu/richman/Ideas/daniel.htm", "https://web.archive.org/web/20150501234331/http://cerebro.xu.edu/math/Sources/NBernoulli/correspondence_petersburg_game.pdf"]}, "Marginal variable": {"categories": ["Theory of probability distributions"], "title": "Marginal distribution", "method": "Marginal variable", "url": "https://en.wikipedia.org/wiki/Marginal_distribution", "summary": "In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables.\nMarginal variables are those variables in the subset of variables being retained. These concepts are \"marginal\" because they can be found by summing values in a table along rows or columns, and writing the sum in the margins of the table. The distribution of the marginal variables (the marginal distribution) is obtained by marginalizing \u2013 that is, focusing on the sums in the margin \u2013 over the distribution of the variables being discarded, and the discarded variables are said to have been marginalized out.\nThe context here is that the theoretical studies being undertaken, or the data analysis being done, involves a wider set of random variables but that attention is being limited to a reduced number of those variables. In many applications, an analysis may start with a given collection of random variables, then first extend the set by defining new ones (such as the sum of the original random variables) and finally reduce the number by placing interest in the marginal distribution of a subset (such as the sum). Several different analyses may be done, each treating a different subset of variables as the marginal variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8e/MultivariateNormal.png", "https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png"], "links": ["Bayes' theorem", "Boole's inequality", "Complementary event", "Compound probability distribution", "Conditional distribution", "Conditional independence", "Conditional probability", "Continuous random variable", "Data analysis", "Discrete random variable", "Elementary event", "Event (probability theory)", "Expected value", "Frequency distribution", "Independence (probability theory)", "Indexed family", "International Standard Book Number", "Joint distribution", "Joint probability", "Joint probability distribution", "Law of large numbers", "Law of the unconscious statistician", "Law of total probability", "Multivariate distribution", "Mutual information", "Probability axioms", "Probability density function", "Probability distribution", "Probability mass function", "Probability measure", "Probability space", "Probability theory", "Random variable", "Sample space", "Statistics", "Subset", "Tree diagram (probability theory)", "Venn diagram", "Wasserstein metric"], "references": []}, "Factor regression model": {"categories": ["All Wikipedia articles needing context", "All pages needing cleanup", "Factor analysis", "Latent variable models", "Regression models", "Wikipedia articles needing context from July 2012", "Wikipedia introduction cleanup from July 2012"], "title": "Factor regression model", "method": "Factor regression model", "url": "https://en.wikipedia.org/wiki/Factor_regression_model", "summary": "The factor regression model, or hybrid factor model, is a special multivariate model with the following form:\n\n \n \n \n \n \n y\n \n \n n\n \n \n =\n \n A\n \n \n \n x\n \n \n n\n \n \n +\n \n B\n \n \n \n z\n \n \n n\n \n \n +\n \n c\n \n +\n \n \n e\n \n \n n\n \n \n \n \n {\\displaystyle \\mathbf {y} _{n}=\\mathbf {A} \\mathbf {x} _{n}+\\mathbf {B} \\mathbf {z} _{n}+\\mathbf {c} +\\mathbf {e} _{n}}\n where,\n\n \n \n \n \n \n y\n \n \n n\n \n \n \n \n {\\displaystyle \\mathbf {y} _{n}}\n is the \n \n \n \n n\n \n \n {\\displaystyle n}\n -th \n \n \n \n G\n \u00d7\n 1\n \n \n {\\displaystyle G\\times 1}\n (known) observation.\n \n \n \n \n \n x\n \n \n n\n \n \n \n \n {\\displaystyle \\mathbf {x} _{n}}\n is the \n \n \n \n n\n \n \n {\\displaystyle n}\n -th sample \n \n \n \n \n L\n \n x\n \n \n \n \n {\\displaystyle L_{x}}\n (unknown) hidden factors.\n \n \n \n \n A\n \n \n \n {\\displaystyle \\mathbf {A} }\n is the (unknown) loading matrix of the hidden factors.\n \n \n \n \n \n z\n \n \n n\n \n \n \n \n {\\displaystyle \\mathbf {z} _{n}}\n is the \n \n \n \n n\n \n \n {\\displaystyle n}\n -th sample \n \n \n \n \n L\n \n z\n \n \n \n \n {\\displaystyle L_{z}}\n (known) design factors.\n \n \n \n \n B\n \n \n \n {\\displaystyle \\mathbf {B} }\n is the (unknown) regression coefficients of the design factors.\n \n \n \n \n c\n \n \n \n {\\displaystyle \\mathbf {c} }\n is a vector of (unknown) constant term or intercept.\n \n \n \n \n \n e\n \n \n n\n \n \n \n \n {\\displaystyle \\mathbf {e} _{n}}\n is a vector of (unknown) errors, often white Gaussian noise.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Constant term", "Digital object identifier", "Factor analysis", "Mathematical model", "Multivariate normal distribution", "Observation", "PubMed Central", "Regression model", "Software", "Vector (mathematics and physics)", "White Gaussian noise"], "references": ["http://www.cmsworldwide.com/ICASSP2011/Papers/ViewPapers.asp?PaperNum=4439", "http://www.isds.duke.edu/research/software/west/bfrm/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3017385", "http://doi.org/10.1198/016214508000000869", "https://web.archive.org/web/20111003195637/http://www.isds.duke.edu/research/software/west/bfrm/", "https://web.archive.org/web/20111123144133/http://www.cmsworldwide.com/ICASSP2011/Papers/ViewPapers.asp?PaperNum=4439"]}, "Bayesian (disambiguation)": {"categories": ["Lists of things named after mathematicians"], "title": "List of things named after Thomas Bayes", "method": "Bayesian (disambiguation)", "url": "https://en.wikipedia.org/wiki/List_of_things_named_after_Thomas_Bayes", "summary": "Thomas Bayes (/be\u026az/; c. 1701 \u2013 1761) was an English statistician, philosopher, and Presbyterian minister. \nBayesian (/\u02c8be\u026azi\u0259n/) refers to a range of concepts and approaches that are ultimately based on Bayes' theorem, of which the most important are:\n\nBayesian probability, the degree-of-belief interpretation of probability, also known as Bayesianism\nBayesian inferenceOther things named after Thomas Bayes include:", "images": [], "links": ["Approximate Bayesian computation", "Bayes' theorem", "Bayes error rate", "Bayes estimator", "Bayes factor", "Bayes linear statistics", "Bayes prior", "Bayesian Filtering Library", "Bayesian approaches to brain function", "Bayesian average", "Bayesian econometrics", "Bayesian efficiency", "Bayesian experimental design", "Bayesian game", "Bayesian inference", "Bayesian inference in phylogeny", "Bayesian information criterion", "Bayesian linear regression", "Bayesian model selection", "Bayesian multivariate linear regression", "Bayesian network", "Bayesian poisoning", "Bayesian probability", "Bayesian programming", "Bayesian search theory", "Bayesian spam filtering", "Bayesian statistics", "Bayesian tool for methylation analysis", "Bayesian vector autoregression", "Dynamic Bayesian network", "Empirical Bayes method", "Evidence under Bayes theorem", "Hierarchical Bayes model", "International Society for Bayesian Analysis", "Laplace\u2013Bayes estimator", "Naive Bayes classifier", "Quantum Bayesianism", "Random naive Bayes", "Recursive Bayesian estimation", "Robust Bayesian analysis", "Thomas Bayes", "Variable-order Bayesian network", "Variational Bayesian methods"], "references": []}, "Stochastic drift": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2010", "Mathematical finance", "Time series"], "title": "Stochastic drift", "method": "Stochastic drift", "url": "https://en.wikipedia.org/wiki/Stochastic_drift", "summary": "In probability theory, stochastic drift is the change of the average value of a stochastic (random) process. A related concept is the drift rate, which is the rate at which the average changes. For example, a process that counts the number of heads in a series of \n \n \n \n n\n \n \n {\\displaystyle n}\n fair coin tosses has a drift rate of 1/2 per toss. This is in contrast to the random fluctuations about this average value. The stochastic mean of that coin-toss process is 1/2 and the drift rate of the stochastic mean is 0, assuming 1=heads and 0=tails.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Autocorrelation", "Coin toss", "Decomposition of time series", "First difference", "Fourier series", "Genetic drift", "Gross domestic product", "Longitudinal studies", "Monetary policy", "Natural selection", "Polynomial", "Population genetics", "Price level", "Probability theory", "Secular variation", "Speciation", "Stationary process", "Stochastic process", "Stock price", "Time series analysis", "Trend stationary", "Unit root", "White noise"], "references": ["http://www.visualstatistics.net/Readings/Secular%20Trends/Secular%20Trends.asp"]}, "Chapman\u2013Kolmogorov equation": {"categories": ["Equations", "Markov processes", "Stochastic calculus"], "title": "Chapman\u2013Kolmogorov equation", "method": "Chapman\u2013Kolmogorov equation", "url": "https://en.wikipedia.org/wiki/Chapman%E2%80%93Kolmogorov_equation", "summary": "In mathematics, specifically in the theory of Markovian stochastic processes in probability theory, the Chapman\u2013Kolmogorov equation is an identity relating the joint probability distributions of different sets of coordinates on a stochastic process. The equation was derived independently by both the British mathematician Sydney Chapman and the Russian mathematician Andrey Kolmogorov.\n\n", "images": [], "links": ["Andrey Kolmogorov", "Eric W. Weisstein", "Examples of Markov chains", "Fokker\u2013Planck equation", "International Standard Book Number", "Joint probability distribution", "Kolmogorov backward equation", "Marginalization (probability)", "Markov chain", "Markov property", "Master equation", "MathWorld", "Mathematics", "Matrix multiplication", "Nuisance variable", "Probability theory", "Stochastic process", "Sydney Chapman (mathematician)", "Transition probability"], "references": ["http://mathworld.wolfram.com/Chapman-KolmogorovEquation.html"]}, "Mixing (mathematics)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2008", "Ergodic theory"], "title": "Mixing (mathematics)", "method": "Mixing (mathematics)", "url": "https://en.wikipedia.org/wiki/Mixing_(mathematics)", "summary": "In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, etc.\nThe concept appears in ergodic theory\u2014the study of stochastic processes and measure-preserving dynamical systems. Several different definitions for mixing exist, including strong mixing, weak mixing and topological mixing, with the last not requiring a measure to be defined. Some of the different definitions of mixing can be arranged in a hierarchical order; thus, strong mixing implies weak mixing. Furthermore, weak mixing (and thus also strong mixing) implies ergodicity: that is, every system that is weakly mixing is also ergodic (and so one says that mixing is a \"stronger\" notion than ergodicity).", "images": [], "links": ["Arnold's cat map", "Borel sigma algebra", "Bounded linear operator", "Ces\u00e0ro mean", "Complete metric space", "Continuous (topology)", "Continuous map", "Cylinder set", "Decomposition of spectrum (functional analysis)", "Dense set", "Digital object identifier", "Dyadic map", "Eigenfunction", "Ergodic theory", "Ergodicity", "Flow (mathematics)", "Generalized function", "Harris chain", "Horseshoe map", "Hypercyclic operator", "Hypercyclic vector", "International Standard Book Number", "Irrational rotation", "Isolated point", "Iterated function", "Kolmogorov automorphism", "Markov process", "Mathematics", "Measure-preserving dynamical system", "Measure (mathematics)", "Metric space", "Mixing (physics)", "Open set", "Operator theory", "Physics", "Product topology", "Random variable", "Shift operator", "Sigma-algebra", "Sigma algebra", "Square-integrable", "Statistical independence", "Stochastic process", "Thermodynamic process", "Topological vector space", "Topology", "Wandering set"], "references": ["http://doi.org/10.1016%2Fj.jeconom.2009.10.001"]}, "Kirkwood approximation": {"categories": ["Discrete distributions", "Statistical approximations"], "title": "Kirkwood approximation", "method": "Kirkwood approximation", "url": "https://en.wikipedia.org/wiki/Kirkwood_approximation", "summary": "The Kirkwood superposition approximation was introduced in 1935 by John G. Kirkwood as a means of representing a discrete probability distribution. The Kirkwood approximation for a discrete probability density function \n \n \n \n P\n (\n \n x\n \n 1\n \n \n ,\n \n x\n \n 2\n \n \n ,\n \u2026\n ,\n \n x\n \n n\n \n \n )\n \n \n {\\displaystyle P(x_{1},x_{2},\\ldots ,x_{n})}\n is given by\n\n \n \n \n \n P\n \n \u2032\n \n \n (\n \n x\n \n 1\n \n \n ,\n \n x\n \n 2\n \n \n ,\n \u2026\n ,\n \n x\n \n n\n \n \n )\n =\n \n \n \n \n \n \n \u220f\n \n \n \n \n T\n \n \n \n n\n \u2212\n 1\n \n \n \u2286\n \n \n V\n \n \n \n \n p\n (\n \n \n \n T\n \n \n \n n\n \u2212\n 1\n \n \n )\n \n \n \n \u220f\n \n \n \n \n T\n \n \n \n n\n \u2212\n 2\n \n \n \u2286\n \n \n V\n \n \n \n \n p\n (\n \n \n \n T\n \n \n \n n\n \u2212\n 2\n \n \n )\n \n \n \u22ee\n \n \n \n \u220f\n \n \n \n \n T\n \n \n \n 1\n \n \n \u2286\n \n \n V\n \n \n \n \n p\n (\n \n \n \n T\n \n \n \n 1\n \n \n )\n \n \n \n \n \n {\\displaystyle P^{\\prime }(x_{1},x_{2},\\ldots ,x_{n})={\\frac {\\frac {\\frac {\\prod _{{\\mathcal {T}}_{n-1}\\subseteq {\\mathcal {V}}}p({\\mathcal {T}}_{n-1})}{\\prod _{{\\mathcal {T}}_{n-2}\\subseteq {\\mathcal {V}}}p({\\mathcal {T}}_{n-2})}}{\\vdots }}{\\prod _{{\\mathcal {T}}_{1}\\subseteq {\\mathcal {V}}}p({\\mathcal {T}}_{1})}}}\n where\n\n \n \n \n \n \u220f\n \n \n \n \n T\n \n \n \n i\n \n \n \u2286\n \n \n V\n \n \n \n \n p\n (\n \n \n \n T\n \n \n \n i\n \n \n )\n \n \n {\\displaystyle \\prod _{{\\mathcal {T}}_{i}\\subseteq {\\mathcal {V}}}p({\\mathcal {T}}_{i})}\n is the product of probabilities over all subsets of variables of size i in variable set \n \n \n \n \n \n \n V\n \n \n \n \n \n {\\displaystyle \\scriptstyle {\\mathcal {V}}}\n . This kind of formula has been considered by Watanabe (1960) and, according to Watanabe, also by Robert Fano. For the three-variable case, it reduces to simply\n\n \n \n \n \n P\n \n \u2032\n \n \n (\n \n x\n \n 1\n \n \n ,\n \n x\n \n 2\n \n \n ,\n \n x\n \n 3\n \n \n )\n =\n \n \n \n p\n (\n \n x\n \n 1\n \n \n ,\n \n x\n \n 2\n \n \n )\n p\n (\n \n x\n \n 2\n \n \n ,\n \n x\n \n 3\n \n \n )\n p\n (\n \n x\n \n 1\n \n \n ,\n \n x\n \n 3\n \n \n )\n \n \n p\n (\n \n x\n \n 1\n \n \n )\n p\n (\n \n x\n \n 2\n \n \n )\n p\n (\n \n x\n \n 3\n \n \n )\n \n \n \n \n \n {\\displaystyle P^{\\prime }(x_{1},x_{2},x_{3})={\\frac {p(x_{1},x_{2})p(x_{2},x_{3})p(x_{1},x_{3})}{p(x_{1})p(x_{2})p(x_{3})}}}\n The Kirkwood approximation does not generally produce a valid probability distribution (the normalization condition is violated). Watanabe claims that for this reason informational expressions of this type are not meaningful, and indeed there has been very little written about the properties of this measure. The Kirkwood approximation is the probabilistic counterpart of the interaction information.\nJudea Pearl (1988 \u00a73.2.4) indicates that an expression of this type can be exact in the case of a decomposable model, that is, a probability distribution that admits a graph structure whose cliques form a tree. In such cases, the numerator contains the product of the intra-clique joint distributions and the denominator contains the product of the clique intersection distributions.", "images": [], "links": ["Clique (graph theory)", "Discrete probability distribution", "Graph (discrete mathematics)", "Interaction information", "J. Chem. Phys.", "John Gamble Kirkwood", "Judea Pearl", "Probability density function", "Tree (graph theory)"], "references": []}, "Gauss\u2013Newton algorithm": {"categories": ["Least squares", "Optimization algorithms and methods", "Statistical algorithms"], "title": "Gauss\u2013Newton algorithm", "method": "Gauss\u2013Newton algorithm", "url": "https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm", "summary": "The Gauss\u2013Newton algorithm is used to solve non-linear least squares problems. It is a modification of Newton's method for finding a minimum of a function. Unlike Newton's method, the Gauss\u2013Newton algorithm can only be used to minimize a sum of squared function values, but it has the advantage that second derivatives, which can be challenging to compute, are not required.\nNon-linear least squares problems arise, for instance, in non-linear regression, where parameters in a model are sought such that the model is in good agreement with available observations.\nThe method is named after the mathematicians Carl Friedrich Gauss and Isaac Newton, and first appeared in Gauss' 1809 work Theoria motus corporum coelestium in sectionibus conicis solem ambientum.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5e/Gauss_Newton_illustration.png", "https://upload.wikimedia.org/wikipedia/commons/7/72/Max_paraboloid.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a8/Regression_pic_assymetrique.gif"], "links": ["Abraham de Moivre", "Absolute space and time", "Absolute theory", "Affine scaling", "An Historical Account of Two Notable Corruptions of Scripture", "Analysis of covariance", "Analysis of variance", "Approximation algorithm", "Approximation theory", "ArXiv", "Arithmetica Universalis", "Augmented Lagrangian method", "BFGS method", "Barrier function", "Bayesian experimental design", "Bellman\u2013Ford algorithm", "Benjamin Pulleyn", "Berndt\u2013Hall\u2013Hall\u2013Hausman algorithm", "Binomial regression", "Bor\u016fvka's algorithm", "Branch and bound", "Branch and cut", "Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm", "Bucket argument", "Calculus", "Calibration curve", "Carl Friedrich Gauss", "Catherine Barton", "Chebyshev nodes", "Chebyshev polynomials", "Cholesky decomposition", "Classical mechanics", "Column vectors", "Combinatorial optimization", "Comparison of optimization software", "Computational statistics", "Confounding", "Conjugate gradient", "Conjugate gradient method", "Convex minimization", "Convex optimization", "Copernican Revolution", "Corpuscular theory of light", "Correlation and dependence", "Cranbury Park", "Criss-cross algorithm", "Curve fitting", "Cutting-plane method", "Davidon\u2013Fletcher\u2013Powell formula", "De analysi per aequationes numero terminorum infinitas", "De motu corporum in gyrum", "Descent direction", "Design of experiments", "Difference quotient", "Digital object identifier", "Dijkstra's algorithm", "Dinic's algorithm", "Direction (geometry, geography)", "Dynamic programming", "Dynamics (mechanics)", "Early life of Isaac Newton", "Edmonds\u2013Karp algorithm", "Elements of the Philosophy of Newton", "Ellipsoid method", "Errors and residuals in statistics", "Evolutionary algorithm", "Exchange algorithm", "Finite difference", "Flow network", "Floyd\u2013Warshall algorithm", "Fluxion", "Ford\u2013Fulkerson algorithm", "Frank\u2013Wolfe algorithm", "Function (mathematics)", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General Scholium", "General linear model", "Generalized Gauss\u2013Newton method", "Generalized least squares", "Generalized linear model", "Golden-section search", "Goodness of fit", "Gradient", "Gradient descent", "Graph algorithm", "Gravitational constant", "Greedy algorithm", "Growth curve (statistics)", "Hessian matrix", "Heuristic algorithm", "Hill climbing", "Hypotheses non fingo", "Ill-conditioned", "Impact depth", "Inertia", "Integer programming", "International Standard Book Number", "Isaac Barrow", "Isaac Newton", "Isaac Newton's occult studies", "Isaac Newton Group of Telescopes", "Isaac Newton Institute", "Isaac Newton Medal", "Isaac Newton S/O Philipose", "Isaac Newton Telescope", "Isaac Newton in popular culture", "Isotonic regression", "Iterative method", "Iteratively reweighted least squares", "Jacobian matrix", "John Conduitt", "John Keill", "John Wiley & Sons", "Johnson's algorithm", "Karmarkar's algorithm", "Kendall tau rank correlation coefficient", "Kepler's laws of planetary motion", "Kissing number problem", "Kruskal's algorithm", "Later life of Isaac Newton", "Least squares", "Leibniz\u2013Newton calculus controversy", "Lemke's algorithm", "Levenberg\u2013Marquardt algorithm", "Limited-memory BFGS", "Line search", "Linear approximation", "Linear least squares (mathematics)", "Linear programming", "Linear regression", "List of statistics articles", "List of things named after Isaac Newton", "Local convergence", "Local regression", "Local search (optimization)", "Logistic regression", "Mallows's Cp", "Mathematical optimization", "Matrix transpose", "Matroid", "Maxima and minima", "Mean and predicted response", "Metaheuristic", "Method of Fluxions", "Minimum mean-square error", "Minimum spanning tree", "Model selection", "Moore\u2013Penrose pseudoinverse", "Moving least squares", "Multivariate analysis of variance", "Nelder\u2013Mead method", "Newton's cannonball", "Newton's cradle", "Newton's identities", "Newton's inequalities", "Newton's law of cooling", "Newton's law of universal gravitation", "Newton's laws of motion", "Newton's metal", "Newton's method", "Newton's method in optimization", "Newton's notation", "Newton's reflector", "Newton's rings", "Newton's theorem about ovals", "Newton's theorem of revolving orbits", "Newton (Blake)", "Newton (Paolozzi)", "Newton (unit)", "Newton disc", "Newton fractal", "Newton polygon", "Newton polynomial", "Newton scale", "Newtonian dynamics", "Newtonian fluid", "Newtonian potential", "Newtonian telescope", "Newtonianism", "Newton\u2013Cartan theory", "Newton\u2013Cotes formulas", "Newton\u2013Euler equations", "Newton\u2013Okounkov body", "Newton\u2013Pepys problem", "Non-linear least squares", "Non-linear regression", "Nonlinear conjugate gradient method", "Nonlinear programming", "Nonlinear regression", "Nonparametric regression", "Notes on the Jewish Temple", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Opticks", "Optimal design", "Optimization algorithm", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Parallel computing", "Parallelogram of force", "Parameterized post-Newtonian formalism", "Partial correlation", "Partial least squares", "Partition of sums of squares", "Pearson product-moment correlation coefficient", "Penalty method", "Philosophi\u00e6 Naturalis Principia Mathematica", "Poisson regression", "Polynomial regression", "Post-Newtonian expansion", "Powell's method", "Power number", "Problem of Apollonius", "Puiseux series", "Push\u2013relabel maximum flow algorithm", "QR factorization", "Quadratic programming", "Quaestiones quaedam philosophicae", "Quantile regression", "Quasi-Newton method", "Rank correlation", "Rate of convergence", "Regression analysis", "Regression model validation", "Religious views of Isaac Newton", "Residual (statistics)", "Response surface methodology", "Revised simplex method", "Ridge regression", "Robust regression", "Rotating spheres", "Schr\u00f6dinger\u2013Newton equation", "Scientific revolution", "Segmented regression", "Semiparametric regression", "Sequential quadratic programming", "Sextant", "Simple linear regression", "Simplex algorithm", "Simulated annealing", "Solar mass", "Sparse matrix", "Spearman's rank correlation coefficient", "Spectrum", "Standing on the shoulders of giants", "Stationary point", "Statistical model", "Steepest descent", "Stepwise regression", "Structural coloration", "Studentized residual", "Subgradient method", "Subroutine", "Successive linear programming", "Successive parabolic interpolation", "Symmetric rank-one", "System identification", "Table of Newtonian series", "Tabu search", "Taylor's theorem", "The Chronology of Ancient Kingdoms Amended", "The Mysteryes of Nature and Art", "The Queries", "Total least squares", "Truncated Newton method", "Trust region", "Weighted least squares", "William Clarke (apothecary)", "William Jones (mathematician)", "William Stukeley", "Wolfe conditions", "Woolsthorpe Manor", "Writing of Principia Mathematica"], "references": ["http://arxiv.org/abs/1309.7922", "http://doi.org/10.1007%2Fs10107-013-0720-6", "http://www.henley.ac.uk/web/FILES/maths/09-04.pdf", "https://www.artelys.com/en/optimization-tools/knitro"]}, "Generalizability theory": {"categories": ["All articles lacking in-text citations", "All articles needing expert attention", "Articles lacking in-text citations from August 2012", "Articles needing expert attention from February 2017", "Articles needing expert attention with no reason or talk parameter", "Statistical theory", "Statistics articles needing expert attention"], "title": "Generalizability theory", "method": "Generalizability theory", "url": "https://en.wikipedia.org/wiki/Generalizability_theory", "summary": "Generalizability theory, or G theory, is a statistical framework for conceptualizing, investigating, and designing reliable observations. It is used to determine the reliability (i.e., reproducibility) of measurements under specific conditions. It is particularly useful for assessing the reliability of performance assessments. It was originally introduced in Cronbach, L.J., Nageswari, R., & Gleser, G.C. (1963).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Analysis of variance", "Classical test theory", "Lee Cronbach", "Observation", "Reliability (statistics)"], "references": ["http://www.rasch.org/rmt/rmt71h.htm", "https://web.archive.org/web/20010627112737/http://www.psychology.sdsu.edu/faculty/matt/Pubs/GThtml/GTheory_GEMatt.html"]}, "Maximum entropy method": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2008", "Bayesian statistics", "CS1 maint: Extra text: editors list", "Entropy and information", "Mathematical principles", "Probability assessment", "Statistical principles"], "title": "Principle of maximum entropy", "method": "Maximum entropy method", "url": "https://en.wikipedia.org/wiki/Principle_of_maximum_entropy", "summary": "The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information).\nAnother way of stating this: Take precisely stated prior data or testable information about a probability distribution function. Consider the set of all trial probability distributions that would encode the prior data. According to this principle, the distribution with maximal information entropy is the best choice.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Admissible decision rule", "Akaike information criterion", "Approximate Bayesian computation", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernstein\u2013von Mises theorem", "Bibcode", "Bounded interval", "Brian Skyrms", "Channel coding", "Closed form solution", "Conjugate prior", "Conserved quantities", "Continuous distribution", "Convex optimization", "Credible interval", "Cromwell's rule", "Cross entropy", "Differential entropy", "Digital object identifier", "Dissipation", "E. T. Jaynes", "Edwin Thompson Jaynes", "Empirical Bayes method", "Empirical likelihood", "Entropy", "Entropy (information theory)", "Entropy maximization", "Ergodic", "Expected value", "Exponentially tilted empirical likelihood", "Gibbs distribution", "Gibbs measure", "Graham Wallis", "H. K. Kesavan", "Hyperparameter", "Hyperprior", "Inference", "Info-metrics", "Information entropy", "Information theory", "International Standard Book Number", "Interval (mathematics)", "JSTOR", "Journal of Econometrics", "Journal of the American Statistical Association", "Kinetic theory of gases", "Kullback\u2013Leibler divergence", "Lagrange multiplier", "Likelihood function", "Limiting density of discrete points", "Logical inference", "Logistic regression", "Machine learning", "Marginalization (probability)", "Markov chain Monte Carlo", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum entropy (disambiguation)", "Maximum entropy classifier", "Maximum entropy probability distribution", "Maximum entropy spectral estimation", "Maximum entropy thermodynamics", "Maxwell\u2013Boltzmann statistics", "Molecular chaos", "Multinomial distribution", "Mutually exclusive", "Natural language processing", "Numerical analysis", "Partition function (mathematics)", "Pitman\u2013Koopman theorem", "Posterior predictive distribution", "Posterior probability", "Principle of indifference", "Principle of maximum caliber", "Principle of transformation groups", "Prior information", "Prior probability", "Probability distribution", "Probability interpretations", "Probability kinematics", "Proposition", "PubMed Identifier", "Quadratic programming", "Radical probabilism", "Real numbers", "Relative entropy", "Richard Jeffrey", "Schwarz criterion", "Statistical ensemble", "Statistical mechanics", "Statistical thermodynamics", "Statistics", "Stirling's approximation", "Sufficiency (statistics)", "Support vector machine", "Symmetries", "Symmetry groups", "Thermodynamic equilibrium", "Uniform distribution (discrete)"], "references": ["http://www.sciencedirect.com/science/article/pii/S1566253512000139", "http://www.cs.cmu.edu/~./aberger/maxent.html", "http://adsabs.harvard.edu/abs/1957PhRv..106..620J", "http://adsabs.harvard.edu/abs/1957PhRv..108..171J", "http://adsabs.harvard.edu/abs/2001Entrp...3..191H", "http://adsabs.harvard.edu/abs/2017Entrp..19..381C", "http://repository.upenn.edu/cgi/viewcontent.cgi?article=1083&context=ircs_reports", "http://bayes.wustl.edu/etj/articles/brandeis.pdf", "http://bayes.wustl.edu/etj/articles/brandeis.ps.gz", "http://bayes.wustl.edu/etj/articles/cmonkeys.pdf", "http://bayes.wustl.edu/etj/articles/relationship.pdf", "http://bayes.wustl.edu/etj/articles/theory.1.pdf", "http://bayes.wustl.edu/etj/articles/theory.2.pdf", "http://bayes.wustl.edu/etj/node1.html", "http://cowles.econ.yale.edu/P/cd/d15b/d1569.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/18184793", "http://www.ams.org/mathscinet-getitem?mr=0087305", "http://www.ams.org/mathscinet-getitem?mr=0096414", "http://www.ams.org/mathscinet-getitem?mr=1825292", "http://doi.org/10.1007%2Fbf03023004", "http://doi.org/10.1007%2Fs00362-008-0149-9", "http://doi.org/10.1007%2Fs11009-007-9057-z", "http://doi.org/10.1007%2Fs11009-009-9133-7", "http://doi.org/10.1016%2Fj.inffus.2012.01.012", "http://doi.org/10.1016%2Fj.jeconom.2006.05.003", "http://doi.org/10.1080%2F10556799208230532", "http://doi.org/10.1093%2Fbiomet%2F90.2.319", "http://doi.org/10.1093%2Fbiomet%2F92.1.31", "http://doi.org/10.1103%2FPhysRev.106.620", "http://doi.org/10.1103%2FPhysRev.108.171", "http://doi.org/10.1109%2FTSSC.1968.300117", "http://doi.org/10.1523%2FJNEUROSCI.3359-07.2008", "http://doi.org/10.2307%2F2669786", "http://doi.org/10.3390%2Fe19080381", "http://doi.org/10.3390%2Fe3030191", "http://www.jstor.org/stable/2669786", "http://przyrbwn.icm.edu.pl/APP/PDF/117/a117z602.pdf", "http://homepages.inf.ed.ac.uk/s0450736/maxent.html", "https://link.springer.com/article/10.1007/s11009-007-9057-z", "https://link.springer.com/article/10.1007/s11009-009-9133-7", "https://web.archive.org/web/20060603144738/http://www.phys.uu.nl/~wwwgrnsl/jos/mepabst/mep.pdf", "https://arxiv.org/abs/0708.1593"]}, "Similarity matrix": {"categories": ["Clustering criteria", "Similarity and distance measures", "Statistical classification", "Statistical distance"], "title": "Similarity measure", "method": "Similarity matrix", "url": "https://en.wikipedia.org/wiki/Similarity_measure", "summary": "In statistics and related fields, a similarity measure or similarity function is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity measure exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. For example, if two pieces of data have close x, y coordinates, then their \u201csimilarity\u201d score, the likelihood that they are similar, will be much higher than two data points with more space between them. In the context of cluster analysis, Frey and Dueck suggest defining a similarity measure\n\n \n \n \n s\n (\n x\n ,\n y\n )\n =\n \u2212\n \u2016\n x\n \u2212\n y\n \n \u2016\n \n 2\n \n \n 2\n \n \n \n \n {\\displaystyle s(x,y)=-\\|x-y\\|_{2}^{2}}\n where \n \n \n \n \u2016\n x\n \u2212\n y\n \n \u2016\n \n 2\n \n \n 2\n \n \n \n \n {\\displaystyle \\|x-y\\|_{2}^{2}}\n is the squared Euclidean distance.Cosine similarity is a commonly used similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions.", "images": [], "links": ["Adenine", "Affinity propagation", "Amino acid", "BLOSUM", "Bernhard Sch\u00f6lkopf", "Cluster analysis", "Cosine similarity", "Cytosine", "DNA", "Digital object identifier", "Euclidean distance", "Genetic code", "Guanine", "Information retrieval", "Kernel trick", "Machine learning", "Margaret Oakley Dayhoff", "Matrix similarity", "Metric (mathematics)", "Nucleic acid", "Nucleotide", "Point accepted mutation", "Protein", "PubMed Identifier", "Purine", "Pyrimidine", "Radial basis function kernel", "Real-valued function", "Recurrence plot", "Science (journal)", "Self-similarity matrix", "Semantic similarity", "Sequence alignment", "Similarity matrix", "Spectral clustering", "Statistics", "String metric", "Symmetric matrix", "Thymine", "Vector space model"], "references": ["http://books.nips.cc/papers/files/nips14/AA35.pdf", "http://www.eecis.udel.edu/~lliao/cis841s06/primer_on_kernel_methods_vert.pdf", "http://informatics.umdnj.edu/bioinformatics/courses/5020/notes/BLOSUM62%20primer.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/15286655", "http://www.ncbi.nlm.nih.gov/pubmed/17218491", "http://doi.org/10.1016%2FS1046-2023(05)80165-3", "http://doi.org/10.1016%2Fj.neucom.2012.06.023", "http://doi.org/10.1038%2Fnbt0804-1035", "http://doi.org/10.1126%2Fscience.1136800", "http://doi.org/10.4249%2Fscholarpedia.4116", "https://web.archive.org/web/20060903191751/http://informatics.umdnj.edu/bioinformatics/courses/5020/notes/BLOSUM62%20primer.pdf", "https://deepai.org/machine-learning-glossary-and-terms/affinity-matrix", "https://dx.doi.org/10.1016/j.neucom.2012.06.023"]}, "Partition of sums of squares": {"categories": ["All articles needing expert attention", "Analysis of variance", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Least squares", "Statistics articles needing expert attention"], "title": "Partition of sums of squares", "method": "Partition of sums of squares", "url": "https://en.wikipedia.org/wiki/Partition_of_sums_of_squares", "summary": "The partition of sums of squares is a concept that permeates much of inferential statistics and descriptive statistics. More properly, it is the partitioning of sums of squared deviations or errors. Mathematically, the sum of squared deviations is an unscaled, or unadjusted measure of dispersion (also called variability). When scaled for the number of degrees of freedom, it estimates the variance, or spread of the observations about their mean value. Partitioning of the sum of squared deviations into various components allows the overall variability in a dataset to be ascribed to different types or sources of variability, with the relative importance of each being quantified by the size of each component of the overall sum of squares.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["Analysis of variance", "Degrees of freedom (statistics)", "Descriptive statistics", "Euclidean space", "Explained sum of squares", "Hilbert space", "Inferential statistics", "Inner-product space", "International Standard Book Number", "Lack-of-fit sum of squares", "Least squares", "Linear regression model", "Mean squared error", "Orthogonal complement", "Orthogonal projection", "Orthogonality", "Orthomodular lattice", "Orthonormal basis", "Peter Whittle (mathematician)", "Pythagorean theorem", "Residual sum of squares", "Rosemary A. Bailey", "Squared deviations", "Standard deviation", "Statistical dispersion", "Statistical variability", "Sum of squares (disambiguation)", "Total sum of squares", "Variance", "Variance decomposition", "Variance partitioning"], "references": ["http://www.maths.qmul.ac.uk/~rab/DOEbook"]}, "Quasi-maximum likelihood": {"categories": ["Maximum likelihood estimation"], "title": "Quasi-maximum likelihood estimate", "method": "Quasi-maximum likelihood", "url": "https://en.wikipedia.org/wiki/Quasi-maximum_likelihood_estimate", "summary": "A quasi-maximum likelihood estimate (QMLE, also known as a pseudo-likelihood estimate or a composite likelihood estimate) is an estimate of a parameter \u03b8 in a statistical model that is formed by maximizing a function that is related to the logarithm of the likelihood function, but is not equal to it. In contrast, the maximum likelihood estimate maximizes the actual log likelihood function for the data and model. The function that is maximized to form a QMLE is often a simplified form of the actual log likelihood function. A common way to form such a simplified function is to use the log-likelihood function of a misspecified model that treats certain data values as being independent, even when in actuality they may not be. This removes any parameters from the model that are used to characterize these dependencies. Doing this only makes sense if the dependency structure is a nuisance parameter with respect to the goals of the analysis.\nAs long as the quasi-likelihood function that is maximized is not oversimplified, the QMLE (or composite likelihood estimate) is consistent and asymptotically normal. It is less efficient than the maximum likelihood estimate, but may only be slightly less efficient if the quasi-likelihood is constructed so as to minimize the loss of information relative to the actual likelihood. Standard approaches to statistical inference that are used with maximum likelihood estimates, such as the formation of confidence intervals, and statistics for model comparison, can be generalized to the quasi-maximum likelihood setting.", "images": [], "links": ["Consistent estimator", "Digital object identifier", "Efficiency (statistics)", "Fixed-effect Poisson model", "Fixed effects", "International Standard Book Number", "Likelihood function", "Mathematical Reviews", "Maximum likelihood", "Normal distribution", "Nuisance parameter", "Parameter", "Poisson distribution", "Quasi-likelihood", "Random effects", "Statistical model", "Unobserved effects", "Unobserved heterogeneity"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0999014", "http://doi.org/10.1090%2Fconm%2F080%2F999014", "http://doi.org/10.1093%2Fbiomet%2F91.3.729", "http://doi.org/10.1093%2Fbiomet%2F92.3.519"]}, "Pitman closeness criterion": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from March 2018", "Point estimation performance", "Statistical distance"], "title": "Pitman closeness criterion", "method": "Pitman closeness criterion", "url": "https://en.wikipedia.org/wiki/Pitman_closeness_criterion", "summary": "In statistical theory, the Pitman closeness criterion, named after E. J. G. Pitman, is a way of comparing two candidate estimators for the same parameter. Under this criterion, estimator A is preferred to estimator B if the probability that estimator A is closer to the true value than estimator B is greater than one half. Here the meaning of closer is determined by the absolute difference in the case of a scalar parameter, or by the Mahalanobis distance for a vector parameter.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Biometrika", "Digital object identifier", "E. J. G. Pitman", "Estimator", "International Standard Book Number", "JSTOR", "Journal of the American Statistical Association", "Mahalanobis distance", "Sankhya (journal)", "Statistical theory"], "references": ["https://doi.org/10.1016%2F0378-3758(90)90046-W", "https://doi.org/10.1017%2FS0305004100019563", "https://doi.org/10.1080%2F03610929108830721", "https://www.jstor.org/stable/2290692", "https://www.jstor.org/stable/2332381", "https://www.jstor.org/stable/25052351"]}, "Common-method variance": {"categories": ["All stub articles", "Latent variable models", "Psychometrics", "Statistical deviation and dispersion", "Statistics stubs"], "title": "Common-method variance", "method": "Common-method variance", "url": "https://en.wikipedia.org/wiki/Common-method_variance", "summary": "In applied statistics, (e.g., applied to the social sciences and psychometrics), common-method variance (CMV) is the spurious \"variance that is attributable to the measurement method rather than to the constructs the measures are assumed to represent\" or equivalently as \"systematic error variance shared among variables measured with and introduced as a function of the same method and/or source\". For example, an electronic survey method might influence results for those who might be unfamiliar with an electronic survey interface differently than for those who might be familiar. If measures are affected by CMV or common-method bias, the intercorrelations among them can be inflated or deflated depending upon several factors. Although it is sometimes assumed that CMV affects all variables, evidence suggests that whether or not the correlation between two variables is affected by CMV is a function of both the method and the particular constructs being measured.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Applied statistics", "Confirmatory factor analysis", "Construct (philosophy of science)", "Digital object identifier", "Ex ante", "Ex post", "Measurement", "Psychometrics", "PubMed Identifier", "Social science", "Statistics"], "references": ["http://www.palgrave-journals.com/jibs/journal/v41/n2/abs/jibs200988a.html", "http://orm.sagepub.com/content/12/4/762.short", "http://orm.sagepub.com/content/13/3/477.short", "http://www.scriptwarp.com/warppls/pubs/Kock_Lynn_2012.pdf", "http://www.personal.psu.edu/jxb14/M554/articles/Podsakoffetal2003.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/14516251", "http://doi.org/10.1006/obhd.1994.1011", "http://doi.org/10.1037/0021-9010.86.1.114", "http://doi.org/10.1037/0021-9010.88.5.879", "http://doi.org/10.1057/jibs.2009.88", "http://doi.org/10.1177/1094428105284955", "http://doi.org/10.1177/1094428109332834", "http://doi.org/10.1177/1094428110366036", "https://drive.google.com/file/d/0B76EXfrQqs3hYlZhTWdWcXRockU/view", "https://www.researchgate.net/profile/Michael_Lindell/publication/12032562_Accounting_for_common_method_variance_in_cross-sectional_research_designs/links/0046352250fcb6bb24000000.pdf"]}, "Ecological study": {"categories": ["Design of experiments", "Epidemiology"], "title": "Ecological study", "method": "Ecological study", "url": "https://en.wikipedia.org/wiki/Ecological_study", "summary": "Ecological studies are studies of risk-modifying factors on health or other outcomes based on populations defined either geographically or temporally. Both risk-modifying factors and outcomes are averaged for the populations in each geographical or temporal unit and then compared using standard statistical methods.\nEcological studies have often found links between risk-modifying factors and health outcomes well in advance of other epidemiological or laboratory approaches.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["1854 Broad Street cholera outbreak", "Academic clinical trials", "Adaptive clinical trial", "Alzheimer\u2019s disease", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Blind experiment", "Bradford Hill criteria", "Calcifediol", "Cancer", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Colon cancer", "Correlation does not imply causation", "Cross-sectional study", "Cumulative incidence", "Design of experiments", "Digital object identifier", "Ecological fallacy", "Epidemiological methods", "Epidemiological study", "Evidence-based medicine", "Experiment", "First-in-man study", "Frank C. Garland", "Glossary of clinical research", "Hazard ratio", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Influenza", "Intention-to-treat analysis", "John Cannell", "John Snow (physician)", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "Period prevalence", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Robert Koch", "Scientific control", "Seasonality", "Seeding trial", "Selection bias", "Specificity and sensitivity", "Survivorship bias", "Systematic review", "Ultraviolet", "Vaccine trial", "Virulence"], "references": ["http://www.mdpi.com/2072", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870528", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3820056", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3916854", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4149254", "http://www.ncbi.nlm.nih.gov/pubmed/1140864", "http://www.ncbi.nlm.nih.gov/pubmed/16112578", "http://www.ncbi.nlm.nih.gov/pubmed/16959053", "http://www.ncbi.nlm.nih.gov/pubmed/20219962", "http://www.ncbi.nlm.nih.gov/pubmed/22836187", "http://www.ncbi.nlm.nih.gov/pubmed/24037034", "http://www.ncbi.nlm.nih.gov/pubmed/24084056", "http://www.ncbi.nlm.nih.gov/pubmed/24379012", "http://www.ncbi.nlm.nih.gov/pubmed/7440046", "http://www.ncbi.nlm.nih.gov/pubmed/9209011", "http://doi.org/10.1002/(sici)1097-0215(1997)10+%3C2::aid-ijc2%3E3.3.co;2-0", "http://doi.org/10.1002/ijc.2910150411", "http://doi.org/10.1016/j.tim.2005.08.003", "http://doi.org/10.1017/S0950268806007175", "http://doi.org/10.1093/ije/9.3.227", "http://doi.org/10.3233/JAD-130719", "http://doi.org/10.3233/JAD-2012-129041", "http://doi.org/10.3390/nu5103993", "http://doi.org/10.3390/nu6010163", "http://doi.org/10.3945/ajcn.2009.29094", "http://www.sunarc.org/JAD97.pdf"]}, "Felsenstein's tree-pruning algorithm": {"categories": ["All stub articles", "Genetics stubs", "Statistical genetics", "Statistics stubs"], "title": "Felsenstein's tree-pruning algorithm", "method": "Felsenstein's tree-pruning algorithm", "url": "https://en.wikipedia.org/wiki/Felsenstein%27s_tree-pruning_algorithm", "summary": "In statistical genetics, Felsenstein's tree-pruning algorithm (or Felsenstein's tree-peeling algorithm), attributed to Joseph Felsenstein, is an algorithm for computing the likelihood of an evolutionary tree from nucleic acid sequence data. The algorithm is often used as a subroutine in a search for a maximum likelihood estimate for an evolutionary tree. Further, it can be used in a hypothesis test for whether evolutionary rates are constant (by using likelihood ratio tests). It can also be used to provide error estimates for the parameters describing an evolutionary tree.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cf/Plain_DNA_icon.svg"], "links": ["Algorithm", "Digital object identifier", "Evolutionary tree", "Genetics", "Joe Felsenstein", "Joseph Felsenstein", "Likelihood", "Likelihood ratio test", "Maximum likelihood", "Nucleic acid", "PubMed Identifier", "Statistical genetics", "Statistics"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/7288891", "http://doi.org/10.1007/BF01734359", "http://doi.org/10.1093/sysbio/22.3.240"]}, "Rademacher distribution": {"categories": ["Discrete distributions"], "title": "Rademacher distribution", "method": "Rademacher distribution", "url": "https://en.wikipedia.org/wiki/Rademacher_distribution", "summary": "In probability theory and statistics, the Rademacher distribution (which is named after Hans Rademacher) is a discrete probability distribution where a random variate X has a 50% chance of being +1 and a 50% chance of being -1.A series of Rademacher distributed variables can be regarded as a simple symmetrical random walk where the step size is 1.", "images": [], "links": ["ARGUS distribution", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Banach space", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Bootstrapping (statistics)", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Concentration inequality", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Euclidean norm", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hans Rademacher", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hutchinson trace estimator", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Khintchine inequality", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mathematische Zeitschrift", "Matrix-exponential distribution", "Matrix (mathematics)", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normally distributed and uncorrelated does not imply independent", "Numerical optimization", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Probability mass function", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Raised cosine distribution", "Random matrix", "Random variate", "Random walk", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Series (mathematics)", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Simultaneous perturbation stochastic approximation", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Stochastic approximation", "Student's t-distribution", "Support (mathematics)", "Trace (linear algebra)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Vapnik\u2013Chervonenkis theory", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://adsabs.harvard.edu/abs/2011arXiv1112.4988V", "http://arxiv.org/abs/1112.4988", "http://doi.org/10.1007%2F978-1-4612-0253-0_2", "http://doi.org/10.1007%2FBF01192399", "http://doi.org/10.1090%2FS0002-9939-1990-1013975-0", "http://doi.org/10.1145%2F1944345.1944349", "http://www.jstor.org/stable/2244710"]}, "Pairwise comparison": {"categories": ["Psychometrics"], "title": "Pairwise comparison", "method": "Pairwise comparison", "url": "https://en.wikipedia.org/wiki/Pairwise_comparison", "summary": "Pairwise comparison generally is any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some quantitative property, or whether or not the two entities are identical. The method of pairwise comparison is used in the scientific study of preferences, attitudes, voting systems, social choice, public choice, requirements engineering and multiagent AI systems. In psychology literature, it is often referred to as paired comparison.\nProminent psychometrician L. L. Thurstone first introduced a scientific approach to using pairwise comparisons for measurement in 1927, which he referred to as the law of comparative judgment. Thurstone linked this approach to psychophysical theory developed by Ernst Heinrich Weber and Gustav Fechner. Thurstone demonstrated that the method can be used to order items along a dimension such as preference or importance using an interval-type scale.", "images": [], "links": ["Analytic Hierarchy Process", "Bradley\u2013Terry model", "Digital object identifier", "Equivalence relation", "Ernst Heinrich Weber", "Gustav Fechner", "International Standard Book Number", "Just noticeable difference", "L. L. Thurstone", "Law of comparative judgment", "Logistic function", "Logit", "Multiagent AI system", "Neil Sloane", "Ogive (statistics)", "On-Line Encyclopedia of Integer Sequences", "PROMETHEE", "Paired difference test", "Potentially all pairwise rankings of all possible alternatives", "Preference", "Preference (economics)", "Psychology", "Psychometrician", "Public choice", "Quantitative property", "Rasch model", "Requirements engineering", "Social choice", "Spanish Royal Academy of Sciences", "Stirling number of the second kind", "Strict weak order", "Strict weak ordering", "Thomas L. Saaty", "Thurstone scale", "Total preorder", "Voting systems", "XOR"], "references": ["http://www.danko-nikolic.com/wp-content/uploads/2011/09/Nikolic-Transitivity-2007.pdf", "http://resolver.sub.uni-goettingen.de/purl?GDZPPN002370808", "http://www.rac.es/ficheros/doc/00576.PDF", "http://doi.org/10.1007%2Fbf03191825", "https://oeis.org/A000142", "https://oeis.org/A000670"]}, "Innovations vector": {"categories": ["Statistical signal processing"], "title": "Innovation (signal processing)", "method": "Innovations vector", "url": "https://en.wikipedia.org/wiki/Innovation_(signal_processing)", "summary": "In time series analysis (or forecasting) \u2014 as conducted in statistics, signal processing, and many other fields \u2014 the innovation is the difference between the observed value of a variable at time t and the optimal forecast of that value based on information available prior to time t. If the forecasting method is working correctly, successive innovations are uncorrelated with each other, i.e., constitute a white noise time series. Thus it can be said that the innovation time series is obtained from the measurement time series by a process of 'whitening', or removing the predictable component. The use of the term innovation in the sense described here is due to Hendrik Bode and Claude Shannon (1950) in their discussion of the Wiener filter problem, although the notion was already implicit in the work of Kolmogorov.", "images": [], "links": ["Claude Shannon", "Errors and residuals in statistics", "Filtering problem (stochastic processes)", "Hendrik Bode", "Innovation butterfly", "International Standard Book Number", "Kalman filter", "Kolmogorov", "Signal processing", "Statistics", "Time series analysis", "White noise", "Wiener filter"], "references": []}, "Cartogram": {"categories": ["All articles lacking in-text citations", "All articles to be expanded", "Articles lacking in-text citations from November 2014", "Articles to be expanded from August 2011", "Articles using small message boxes", "Commons category link is on Wikidata", "Diagrams", "Statistical charts and diagrams"], "title": "Cartogram", "method": "Cartogram", "url": "https://en.wikipedia.org/wiki/Cartogram", "summary": "A cartogram is a map in which some thematic mapping variable \u2013 such as travel time, population, or GNP \u2013 is substituted for land area or distance. The geometry or space of the map is distorted, sometimes extremely, in order to convey the information of this alternate variable. They are primarily used to display emphasis and for analysis as nomographs.Two common types of cartograms are area and distance cartograms. Cartograms have a fairly long history, with examples from the mid-1800s.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/47/Cartlinearlarge.png", "https://upload.wikimedia.org/wikipedia/commons/d/df/EU_net_budget_2007-2013_per_capita_cartogram.png", "https://upload.wikimedia.org/wikipedia/commons/3/30/Germany-population-cartogram.png", "https://upload.wikimedia.org/wikipedia/commons/d/d1/PaullHennig2016WorldMap.OAha.CC-BY-4.0.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ArXiv", "ArcGIS", "Atlas", "B. S. Daya Sagar", "Bettina Speckmann", "Bibcode", "Cartography", "Choropleth map", "Contour line", "Countries of the world", "County (United States)", "Daniel A. Keim", "Danny Dorling", "Digital object identifier", "Early world maps", "Environmental Systems Research Institute", "European Union", "Eurostat", "GIS software", "Geography", "Geologic map", "Germany", "Gross National Product", "Herbert Edelsbrunner", "History of cartography", "JSTOR", "Linguistic map", "List of cartographers", "Map", "Map projection", "National Center for Geographic Information and Analysis", "Nautical chart", "Nomography", "Open Europe", "Organic farming", "Pictorial map", "Population", "PubMed Central", "PubMed Identifier", "R (programming language)", "Thematic map", "Topographic map", "Topography", "United States", "United States presidential election, 2004", "University of California, Santa Barbara", "University of Michigan", "University of Sheffield", "Visual geography", "Waldo R. Tobler", "Waldo Tobler", "Weather map"], "references": ["http://www.math.yorku.ca/SCS/Gallery/bright-ideas.html", "http://scapetoad.choros.ch/", "http://www.arcgis.com/home/item.html?id=d348614c97264ae19b0311019a5f2276", "http://www.esri.com/news/arcuser/0110/cartograms.html", "http://indiemaps.com/blog/2008/12/early-cartograms/", "http://indiemaps.com/blog/2011/02/noncontiguous-cartograms-in-openlayers-and-polymaps/", "http://www.tandfonline.com/doi/abs/10.1080/00330124.2011.639613", "http://www.tandfonline.com/doi/abs/10.1080/13658816.2012.709247", "http://graphics.wsj.com/elections/2016/2016-electoral-college-map-predictions/", "http://adsabs.harvard.edu/abs/2004PNAS..101.7499G", "http://www.viz.tamu.edu/faculty/house/cartograms/Vis98.PDF", "http://www.geog.ucsb.edu/~kclarke/G232/ToblerCartograms.pdf", "http://www.ncgia.ucsb.edu/projects/Cartogram_Central/index.html", "http://www-personal.umich.edu/~mejn/cart/", "http://www.comeetie.fr/map_lbc.php", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC419634", "http://www.ncbi.nlm.nih.gov/pubmed/15136719", "http://sunsp.net/portfolio.html", "http://www.grida.no/prog/global/cgiar/awpack/morph.htm#", "http://artofsoftware.org/2012/02/08/cartogram-crash-course/", "http://arxiv.org/abs/1802.07625", "http://arxiv.org/abs/physics/0401102", "http://www.dannydorling.org/?page_id=1448", "http://doi.org/10.1007%2F978-3-540-30140-0_64", "http://doi.org/10.1073%2Fpnas.0400280101", "http://doi.org/10.1073%2Fpnas.1712674115", "http://doi.org/10.1080%2F00330124.2011.639613", "http://doi.org/10.1080%2F13658816.2012.709247", "http://doi.org/10.1109%2FINFVIS.2004.57", "http://doi.org/10.1109%2FMCG.2005.64", "http://doi.org/10.1109%2FTVCG.2004.1260761", "http://doi.org/10.1111%2Fj.1467-8306.2004.09401004.x", "http://www.jstor.org/stable/3694068", "http://www.pnas.org/content/101/20/7499.full", "https://projects.fivethirtyeight.com/2016-election-forecast/?ex_cid=rrpromo#plus&electoral-map", "https://www.nytimes.com/interactive/2008/11/02/opinion/20081102_OPCHART.html", "https://www.academia.edu/25648267/Atlas_of_Organics_Four_maps_of_the_world_of_organic_agriculture", "https://florencioq.github.io/cartogram-brazil/", "https://web.archive.org/web/20070929083558/http://www.grida.no/prog/global/cgiar/awpack/morph.htm#", "https://doi.org/10.1073/pnas.1712674115", "https://dx.doi.org/10.1007/978-3-642-34848-8", "https://cran.r-project.org/package=recmap", "https://worldmapper.org/"]}, "N of 1 trial": {"categories": ["Clinical trials", "Design of experiments"], "title": "N of 1 trial", "method": "N of 1 trial", "url": "https://en.wikipedia.org/wiki/N_of_1_trial", "summary": "An N of 1 trial is a clinical trial in which a single patient is the entire trial, a single case study. A trial in which random allocation can be used to determine the order in which an experimental and a control intervention are given to a patient is an N of 1 randomized controlled trial. The order of experimental and control interventions can also be fixed by the researcher.\nThis type of study has enabled practitioners to achieve experimental progress without the overwhelming work of designing a group comparison study. It can be very effective in confirming causality. This can be achieved in many ways. One of the most common procedures is the ABA withdrawal experimental design, where the patient problem is measured before a treatment is introduced (baseline) and then measured again during the treatment and finally when the treatment has terminated. If the problem vanished during the treatment it can be established that the treatment was effective. But the N=1 study can also be executed in an AB quasi experimental way; this means that causality cannot be definitively demonstrated. Another variation is non-concurrent experimental design where different points in time are compared with one another. This experimental design also has a problem with causality.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["Applied behavior analysis", "Attention deficit hyperactivity disorder", "B. F. Skinner", "Causality", "Clinical trial", "Digital object identifier", "Group comparison study", "Journal of General Internal Medicine", "Osteoarthritis", "Pediatrics (journal)", "Peripheral neuropathy", "PubMed Central", "PubMed Identifier", "Quantified Self", "Quasi-experiment", "Random allocation", "Randomized controlled trial", "Researcher", "Seth Roberts", "Single-subject design", "The Shangri-La Diet"], "references": ["http://iospress.metapress.com/content/t51wg3207328hv38/?genre=article&issn=1387-2877&volume=21&issue=3&spage=967", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2917656", "http://www.ncbi.nlm.nih.gov/pubmed/15673992", "http://www.ncbi.nlm.nih.gov/pubmed/15911473", "http://www.ncbi.nlm.nih.gov/pubmed/16740846", "http://www.ncbi.nlm.nih.gov/pubmed/20386995", "http://www.ncbi.nlm.nih.gov/pubmed/2297206", "http://doi.org/10.1007/s11606-010-1352-7", "http://doi.org/10.1016/j.cct.2005.02.004", "http://doi.org/10.1089/acm.2004.10.979", "http://doi.org/10.1542/peds.2005-1328", "http://doi.org/10.7326/0003-4819-112-4-293", "https://www.liebertpub.com/doi/pdfplus/10.1089/big.2012.0002", "https://archive.is/20130923221601/http://iospress.metapress.com/content/t51wg3207328hv38/?genre=article&issn=1387-2877&volume=21&issue=3&spage=967"]}, "Analysis of molecular variance": {"categories": ["All stub articles", "Analysis of variance", "Genetics", "Molecular biology", "Population genetics", "Statistics stubs"], "title": "Analysis of molecular variance", "method": "Analysis of molecular variance", "url": "https://en.wikipedia.org/wiki/Analysis_of_molecular_variance", "summary": "Analysis of molecular variance (AMOVA), is a statistical model for the molecular variation in a single species, typically biological. The name and model are inspired by ANOVA. The method was developed by Laurent Excoffier, Peter Smouse and Joseph Quattro at Rutgers University in 1992.\nSince developing AMOVA, Excoffier has written a program for running such analyses. This program, which runs on Windows is called Arlequin, and is freely available on Excoffier's website. There is also an implementation by Sandrine Pavoine in R language in the ade4 package available on CRAN (Comprehensive R Archive Network). Another implementation is in Info-Gen, which also runs on Windows. The student version is free and fully functional. Native language of the application is Spanish but an English version is also available.\nAn additional free statistical package, GenAlEx, is geared toward teaching as well as research and allows for complex genetic analyses to be employed and compared within the commonly used Microsoft Excel interface. This software allows for calculation of analyses such as AMOVA, as well as comparisons with other types of closely related statistics including F-statistics and Shannon's index, and more.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["ANOVA", "Arlequin", "Balding\u2013Nichols model", "Biology", "Coalescent theory", "Coefficient of relationship", "Computer program", "Ecological selection", "Evolution", "Evolutionary game theory", "Fisher's fundamental theorem of natural selection", "Fitness (biology)", "Fitness landscape", "Founder effect", "Genetic drift", "Genetic genealogy", "Genetic hitchhiking", "Genetic linkage", "Hardy\u2013Weinberg principle", "Heritability", "Identity by descent", "Index of evolutionary biology articles", "Info-Gen", "International Standard Serial Number", "J. B. S. Haldane", "Joseph Quattro", "Laurent Excoffier", "Linkage disequilibrium", "Microevolution", "Microsoft Windows", "Natural selection", "Negative selection (natural selection)", "Neutral theory of molecular evolution", "Peter Smouse", "Population bottleneck", "Population genetics", "Price equation", "PubMed Central", "PubMed Identifier", "Quantitative genetics", "R language", "Ronald Fisher", "Rutgers University", "Selective breeding", "Sewall Wright", "Sexual selection", "Shifting balance theory", "Small population size", "Species", "Statistical model", "Statistics"], "references": ["http://www.info-gen.com.ar/", "http://biology.anu.edu.au/GenAlEx/Welcome.html", "http://cmpg.unibe.ch/software/arlequin3/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1205020", "http://www.ncbi.nlm.nih.gov/pubmed/1644282", "http://www.worldcat.org/issn/0016-6731", "http://www.yhrd.org/pages/tools/amova"]}, "Manhattan plot": {"categories": ["All stub articles", "Genetic epidemiology", "Single-nucleotide polymorphisms", "Statistical charts and diagrams", "Statistics stubs"], "title": "Manhattan plot", "method": "Manhattan plot", "url": "https://en.wikipedia.org/wiki/Manhattan_plot", "summary": "A Manhattan plot is a type of scatter plot, usually used to display data with a large number of data-points - many of non-zero amplitude, and with a distribution of higher-magnitude values, for instance in genome-wide association studies (GWAS). In GWAS Manhattan plots, genomic coordinates are displayed along the X-axis, with the negative logarithm of the association P-value for each single nucleotide polymorphism (SNP) displayed on the Y-axis, meaning that each dot on the Manhattan plot signifies a SNP. Because the strongest associations have the smallest P-values (e.g., 10\u221215), their negative logarithms will be the greatest (e.g., 15).\nIt gains its name from the similarity of such a plot to the Manhattan skyline: a profile of skyscrapers towering above the lower level \"buildings\" which vary around a lower height.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/1/12/Manhattan_Plot.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Digital object identifier", "Genome-wide association study", "Logarithm", "Manhattan", "P-value", "PubMed Identifier", "Scatter plot", "Single nucleotide polymorphism", "Skyline", "Skyscrapers", "Statistics"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/20581876", "http://doi.org/10.1038%2Fng0710-558"]}, "Cross tabulation": {"categories": ["CS1 errors: dates", "Commons category link is on Wikidata", "Contingency table", "Frequency distribution", "Infographics"], "title": "Contingency table", "method": "Cross tabulation", "url": "https://en.wikipedia.org/wiki/Contingency_table", "summary": "In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering and scientific research. They provide a basic picture of the interrelation between two variables and can help find interactions between them. The term contingency table was first used by Karl Pearson in \"On the Theory of Contingency and Its Relation to Association and Normal Correlation\", part of the Drapers' Company Research Memoirs Biometric Series I published in 1904.\nA crucial problem of multivariate statistics is finding the (direct-)dependence structure underlying the variables contained in high-dimensional contingency tables. If some of the conditional independences are revealed, then even the storage of the data can be done in a smarter way (see Lauritzen (2002)). In order to do this one can use information theory concepts, which gain the information only from the distribution of probability, which can be expressed easily from the contingency table by the relative frequencies.\nA pivot table is a way to create contingency tables using spreadsheet software.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Barnard's test", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional independence", "Confidence interval", "Confounding", "Confusion matrix", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Cram\u00e9r's V", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Drapers' Company", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's exact test", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gamma test (statistics)", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodman and Kruskal's gamma", "Goodman and Kruskall's lambda", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Handedness", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "If and only if", "Index of dispersion", "Information theory", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iterative proportional fitting", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kendall tau", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Main diagonal", "Mann\u2013Whitney U test", "Marginal total", "Mathematical Reviews", "Matrix (mathematics)", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal variable", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phi coefficient", "Pie chart", "Pivot table", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polychoric correlation", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Solomon Kullback", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Steffen L. Lauritzen", "Stem-and-leaf display", "Stephen Fienberg", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "TPL Tables", "Table (information)", "Tau b", "Tau c", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uncertainty coefficient", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Yvonne Bishop", "Z-test"], "references": ["http:ftp://ftp.cdc.gov/pub/Software/epi_info/EIHAT_WEB/Lesson5AnalysisCreatingStatistics.pdf", "http://www.custominsight.com/articles/crosstab-sample.asp", "http://people.revoledu.com/kardi/tutorial/Questionnaire/ContingencyTable.html", "http://www.andrews.edu/~calkins/math/edrm611/edrm13.htm", "http://www.physics.csbsju.edu/stats/contingency.html", "http://webarchive.loc.gov/all/20011127081700/http://www2.chass.ncsu.edu/garson/pa765/assocnominal.htm", "http://www.ams.org/mathscinet-getitem?mr=0381130", "http://www.ams.org/mathscinet-getitem?mr=1633357", "http://statpages.org/ctab2x2.html", "http://www.stats.ox.ac.uk/~steffen/papers/cont.pdf", "https://archive.org/details/cu31924003064833", "https://web.archive.org/web/20050113063235/http://www.csupomona.edu/~jlkorey/POWERMUTT/Topics/displaying_categorical_data.html", "https://web.archive.org/web/20110717190345/http://www.childrensmercy.org/stats/journal/oddsratio.asp"]}, "Geospatial predictive modeling": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from June 2009", "Geographic information systems", "Spatial data analysis"], "title": "Geospatial predictive modeling", "method": "Geospatial predictive modeling", "url": "https://en.wikipedia.org/wiki/Geospatial_predictive_modeling", "summary": "Geospatial predictive modeling is conceptually rooted in the principle that the occurrences of\nevents being modeled are limited in distribution. Occurrences of events are neither uniform\nnor random in distribution \u2013 there are spatial environment factors (infrastructure, sociocultural,\ntopographic, etc.) that constrain and influence where the locations of events occur.\nGeospatial predictive modeling attempts to describe those constraints and influences by\nspatially correlating occurrences of historical geospatial locations with environmental factors\nthat represent those constraints and influences. Geospatial predictive modeling is a process\nfor analyzing events through a geographic filter in order to make statements of likelihood for\nevent occurrence or emergence.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e5/Signature_Analyst_Assessment_of_DC.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Predictive Analysis", "Predictive modelling", "Suitability analysis"], "references": ["http://www.springerlink.com/content/9k5tqr6xtb1br393/", "http://www.natureserve.org/prodServices/pdf/EDM_white_paper_2.0.pdf"]}, "Kappa statistic": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2012", "Categorical variable interactions", "Inter-rater reliability", "Nonparametric statistics", "Wikipedia articles needing page number citations from April 2012"], "title": "Cohen's kappa", "method": "Kappa statistic", "url": "https://en.wikipedia.org/wiki/Cohen%27s_kappa", "summary": "Cohen's kappa coefficient (\u03ba) is a statistic which measures inter-rater agreement for qualitative (categorical) items. It is generally thought to be a more robust measure than simple percent agreement calculation, as \u03ba takes into account the possibility of the agreement occurring by chance. There is controversy surrounding Cohen\u2019s kappa due to the difficulty in interpreting indices of agreement. Some researchers have suggested that it is conceptually simpler to evaluate disagreement between items. See the Limitations section for more detail.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/1/1d/Kappa_example.png", "https://upload.wikimedia.org/wikipedia/en/9/92/Kappa_vs_accuracy.png", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Accuracy and precision", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bangdiwala's B", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Evaluation of binary classifiers", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finger Prints (book)", "First-hitting-time model", "Fleiss' kappa", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Informedness", "Inter-rater agreement", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Intraclass correlation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jacob Cohen (statistician)", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Joseph L. Fleiss", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Machine learning", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean absolute error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Scott's Pi", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Youden's J statistic", "Z-test"], "references": ["http://agreestat.com/research_papers/inter_rater_reliability_dependency.pdf", "http://www.agreestat.com/", "http://www.agreestat.com/book4/", "http://www.agreestat.com/research_papers.html", "http://www.agreestat.com/research_papers/bjmsp2008_interrater.pdf", "http://www.agreestat.com/research_papers/psychometrika2008_irr_random_raters.pdf", "http://www.agreestat.com/research_papers/wiley_encyclopedia2008_eoct631.pdf", "http://dl.dropbox.com/u/27743223/201209-eacl2012-Kappa.pdf", "http://www.john-uebersax.com/stat/kappa.htm#procon", "http://akcora.wordpress.com/2011/05/30/weighted-kappa-example-in-php/", "http://www.clarku.edu/~rpontius/", "http://www.gsu.edu/~psyrab/ComKappa2.zip", "http://www.glue.umd.edu/~dchoy/thesis/Kappa/", "http://www.ncbi.nlm.nih.gov/pubmed/15733050", "http://www.ncbi.nlm.nih.gov/pubmed/18482474", "http://www.ncbi.nlm.nih.gov/pubmed/19673146", "http://www.ncbi.nlm.nih.gov/pubmed/843571", "http://justus.randolph.name/kappa", "http://doi.org/10.1007%2Fs11336-007-9054-8", "http://doi.org/10.1016%2Fj.compedu.2005.04.002", "http://doi.org/10.1037%2F0033-2909.101.1.140", "http://doi.org/10.1037%2F1082-989X.2.4.357", "http://doi.org/10.1037%2Fh0026256", "http://doi.org/10.1037%2Fh0028106", "http://doi.org/10.1037%2Fh0031619", "http://doi.org/10.1086%2F266577", "http://doi.org/10.1093%2Fptj%2F85.3.257", "http://doi.org/10.1177%2F001316446002000104", "http://doi.org/10.1177%2F001316447303300309", "http://doi.org/10.1177%2F001316448104100307", "http://doi.org/10.1177%2F001316448904900407", "http://doi.org/10.1348%2F000711006X126600", "http://doi.org/10.2307%2F2529310", "http://doi.org/10.2307%2F3315487", "http://doi.org/10.3758%2FBF03209495", "http://www.jstor.org/stable/2529310", "http://www.jstor.org/stable/2531300", "http://www.jstor.org/stable/3315487", "http://www.na-mic.org/Wiki/images/d/df/Kapp_and_decision_making_models.pdf", "http://www.worldcat.org/issn/1538-6724", "https://services.niwa.co.nz/services/statistical/kappa", "https://web.archive.org/web/20140201193356/https://mlnl.net/jg/software/ira/", "https://arquivo.pt/wayback/20160518183306/http://dl.dropbox.com/u/27743223/201209-eacl2012-Kappa.pdf"]}, "Robust measures of scale": {"categories": ["All articles to be expanded", "Articles to be expanded from October 2013", "Articles using small message boxes", "Robust statistics", "Scale statistics", "Statistical deviation and dispersion"], "title": "Robust measures of scale", "method": "Robust measures of scale", "url": "https://en.wikipedia.org/wiki/Robust_measures_of_scale", "summary": "In statistics, a robust measure of scale is a robust statistic that quantifies the statistical dispersion in a set of numerical data. The most common such statistics are the interquartile range (IQR) and the median absolute deviation (MAD). These are contrasted with conventional measures of scale, such as sample variance or sample standard deviation, which are non-robust, meaning greatly influenced by outliers.\nThese robust statistics are particularly used as estimators of a scale parameter, and have the advantages of both robustness and superior efficiency on contaminated data, at the cost of inferior efficiency on clean data from distributions such as the normal distribution. To illustrate robustness, the standard deviation can be made arbitrarily large by increasing exactly one observation (it has a breakdown point of 0, as it can be contaminated by a single point), a defect that is not shared by robust statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128143823%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128140726%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110427033551%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110424212543%21Wiki_letter_w_cropped.svg"], "links": ["Breakdown point", "Cauchy distribution", "Consistent estimator", "Data", "Digital object identifier", "Efficiency (statistics)", "Estimator", "Expected value", "Gaussian distribution", "Heavy-tailed distribution", "Indicator function", "Interdecile range", "Interquartile range", "Interval scale", "JSTOR", "L-estimator", "Location parameter", "Median", "Median absolute deviation", "Mixture distribution", "Normal distribution", "Outlier", "Parameter estimation", "Percentile", "Peter Rousseeuw", "Population variance", "Range (statistics)", "Robust statistics", "Scale factor", "Scale parameter", "Skewness", "Standard deviation", "Statistical dispersion", "Statistics", "Trimmed estimator", "Unbiased estimator", "Variance"], "references": ["http://doi.org/10.1198/016214504000001312", "http://doi.org/10.2307/2291267", "http://www.jstor.org/stable/2291267"]}, "Sexual dimorphism measures": {"categories": ["Applied sciences", "Sex", "Sexual dimorphism", "Social statistics"], "title": "Sexual dimorphism measures", "method": "Sexual dimorphism measures", "url": "https://en.wikipedia.org/wiki/Sexual_dimorphism_measures", "summary": "Although the subject of sexual dimorphism is not in itself controversial, the measures by which it is assessed differ widely. Most of the measures are used on the assumption that a random variable is considered so that probability distributions should be taken into account. In this review, a series of sexual dimorphism measures are discussed concerning both their definition and the probability law on which they are based. Most of them are sample functions, or statistics, which account for only partial characteristics, for example the mean or expected value, of the distribution involved. Further, the most widely used measure fails to incorporate an inferential support.", "images": ["https://upload.wikimedia.org/wikipedia/en/7/7f/Overlapmix.jpg", "https://upload.wikimedia.org/wikipedia/en/a/a4/Overlapnorm.jpg"], "links": ["Arithmetic mean", "Bateman's principle", "Bayesian inference", "Binomial distribution", "Central limit theorem", "Digit ratio", "Estimator", "Expectation-maximization algorithm", "Expected value", "Gender differences", "Geoffrey McLachlan", "Inferential statistics", "Kaye Basford", "Kolmogorov-Smirnov test", "Markov chain Monte Carlo", "Mean", "Measure (mathematics)", "Method of moments (statistics)", "Mixture model", "Monogamy", "Normal distribution", "Null hypothesis", "Parameter", "Polygyny", "Probability density function", "Probability distribution", "Random variable", "Sexual dimorphism", "Statistics", "Student's t-distribution", "Variance"], "references": []}, "Glivenko\u2013Cantelli theorem": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from February 2010", "Articles needing additional references from November 2008", "Articles with multiple maintenance issues", "Asymptotic theory (statistics)", "Empirical process", "Probability theorems", "Statistical theorems"], "title": "Glivenko\u2013Cantelli theorem", "method": "Glivenko\u2013Cantelli theorem", "url": "https://en.wikipedia.org/wiki/Glivenko%E2%80%93Cantelli_theorem", "summary": "In the theory of probability, the Glivenko\u2013Cantelli theorem, named after Valery Ivanovich Glivenko and Francesco Paolo Cantelli, determines the asymptotic behaviour of the empirical distribution function as the number of independent and identically distributed observations grows. The uniform convergence of more general empirical measures becomes an important property of the Glivenko\u2013Cantelli classes of functions or sets. The Glivenko\u2013Cantelli classes arise in Vapnik\u2013Chervonenkis theory, with applications to machine learning. Applications can be found in econometrics making use of M-estimators.\nAssume that \n \n \n \n \n X\n \n 1\n \n \n ,\n \n X\n \n 2\n \n \n ,\n \u2026\n \n \n {\\displaystyle X_{1},X_{2},\\dots }\n are independent and identically-distributed random variables in \n \n \n \n \n R\n \n \n \n {\\displaystyle \\mathbb {R} }\n with common cumulative distribution function \n \n \n \n F\n (\n x\n )\n \n \n {\\displaystyle F(x)}\n . The empirical distribution function for \n \n \n \n \n X\n \n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n \n \n {\\displaystyle X_{1},\\dots ,X_{n}}\n is defined by\n\n \n \n \n \n F\n \n n\n \n \n (\n x\n )\n =\n \n \n 1\n n\n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n I\n \n [\n \n X\n \n i\n \n \n ,\n \u221e\n )\n \n \n (\n x\n )\n \n \n {\\displaystyle F_{n}(x)={\\frac {1}{n}}\\sum _{i=1}^{n}I_{[X_{i},\\infty )}(x)}\n where \n \n \n \n \n I\n \n C\n \n \n \n \n {\\displaystyle I_{C}}\n is the indicator function of the set \n \n \n \n C\n \n \n {\\displaystyle C}\n . For every (fixed) \n \n \n \n x\n \n \n {\\displaystyle x}\n , \n \n \n \n \n F\n \n n\n \n \n (\n x\n )\n \n \n {\\displaystyle F_{n}(x)}\n is a sequence of random variables which converge to \n \n \n \n F\n (\n x\n )\n \n \n {\\displaystyle F(x)}\n almost surely by the strong law of large numbers, that is, \n \n \n \n \n F\n \n n\n \n \n \n \n {\\displaystyle F_{n}}\n converges to \n \n \n \n F\n \n \n {\\displaystyle F}\n pointwise. Glivenko and Cantelli strengthened this result by proving uniform convergence of \n \n \n \n \n F\n \n n\n \n \n \n \n {\\displaystyle F_{n}}\n to \n \n \n \n F\n \n \n {\\displaystyle F}\n .\nTheorem\n\n \n \n \n \u2016\n \n F\n \n n\n \n \n \u2212\n F\n \n \u2016\n \n \u221e\n \n \n =\n \n sup\n \n x\n \u2208\n \n R\n \n \n \n \n |\n \n \n F\n \n n\n \n \n (\n x\n )\n \u2212\n F\n (\n x\n )\n \n |\n \n \u27f6\n 0\n \n \n {\\displaystyle \\|F_{n}-F\\|_{\\infty }=\\sup _{x\\in \\mathbb {R} }|F_{n}(x)-F(x)|\\longrightarrow 0}\n almost surely.This theorem originates with Valery Glivenko, and Francesco Cantelli, in 1933.\nRemarks\n\nIf \n \n \n \n \n X\n \n n\n \n \n \n \n {\\displaystyle X_{n}}\n is a stationary ergodic process, then \n \n \n \n \n F\n \n n\n \n \n (\n x\n )\n \n \n {\\displaystyle F_{n}(x)}\n converges almost surely to \n \n \n \n F\n (\n x\n )\n =\n E\n (\n \n 1\n \n \n X\n \n 1\n \n \n \u2264\n x\n \n \n )\n \n \n {\\displaystyle F(x)=E(1_{X_{1}\\leq x})}\n . The Glivenko\u2013Cantelli theorem gives a stronger mode of convergence than this in the iid case.\nAn even stronger uniform convergence result for the empirical distribution function is available in the form of an extended type of law of the iterated logarithm. See asymptotic properties of the empirical distribution function for this and related results.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Aad van der Vaart", "Atom (measure theory)", "Borel set", "Chervonenkis", "Convergence of random variables", "Cumulative distribution function", "Digital object identifier", "Donsker's theorem", "Dvoretzky\u2013Kiefer\u2013Wolfowitz inequality", "Econometrics", "Empirical distribution function", "Empirical measure", "Ergodic process", "Francesco Paolo Cantelli", "Iid", "Independent and identically-distributed random variables", "Independent and identically distributed random variables", "Indicator function", "International Standard Book Number", "Kolmogorov-Smirnov test", "Law of large numbers", "Law of the iterated logarithm", "M-estimator", "Machine learning", "Pointwise convergence", "Probability measure", "Richard M. Dudley", "Shattering (machine learning)", "Theory of probability", "Uniform convergence", "Valery Ivanovich Glivenko", "Vapnik", "Vapnik\u2013Chervonenkis theory"], "references": ["http://doi.org/10.1137%2F1116025", "http://doi.org/10.1214%2Faoms%2F1177706212", "https://www.jstor.org/discover/10.2307/2237422?uid=3738256&uid=2&uid=4&sid=21102589085583"]}, "Covariate": {"categories": ["Design of experiments", "Independence (probability theory)", "Mathematical terminology", "Regression analysis", "Webarchive template wayback links"], "title": "Dependent and independent variables", "method": "Covariate", "url": "https://en.wikipedia.org/wiki/Dependent_and_independent_variables", "summary": "In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables. The dependent variables represent the output or outcome whose variation is being studied. The independent variables, also known in a statistical context as regressors, represent inputs or causes, that is, potential reasons for variation. In an experiment, any variable that the experimenter manipulates can be called an independent variable. Models and experiments test the effects that the independent variables have on the dependent variables. Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential confounding effect.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f8/Polynomialdeg2.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg"], "links": ["Abscissa", "Bias (statistics)", "Blocking (statistics)", "Calculus", "Cartesian product", "Confounding", "Control variable", "Covariance", "Data mining", "Dependent variable", "Design of experiments", "Digital object identifier", "Econometrics", "Errors and residuals", "Experimental science", "Feature (machine learning)", "Function (mathematics)", "Goodness of fit", "Graph of a function", "Horizontal axis", "Hypothesis", "Independence (probability theory)", "International Standard Book Number", "Linear model", "Machine learning", "Manifold (mathematics)", "Mathematical modeling", "Medical statistics", "Multivariable calculus", "Multivariate statistics", "Omitted variable bias", "Ordinate", "Pattern recognition", "Prediction", "RapidMiner", "Reliability theory", "Risk factor", "Set (mathematics)", "Set theory", "Simulation", "Statistical model", "Stochastic", "Subset", "Supervised learning", "Test data", "Variable and attribute (research)", "Vector-valued functions", "Vertical axis", "Wayback Machine"], "references": ["http://1xltkxylmzx3z8gd647akcdvov.wpengine.netdna-cdn.com/wp-content/uploads/2013/10/rapidminer-5.0-manual-english_v1.0.pdf", "http://onlinestatbook.com/2/introduction/variables.html", "http://doi.org/10.1080%2F15210608709379549", "https://web.archive.org/web/20140210002634/http://1xltkxylmzx3z8gd647akcdvov.wpengine.netdna-cdn.com/wp-content/uploads/2013/10/rapidminer-5.0-manual-english_v1.0.pdf"]}, "Pareto interpolation": {"categories": ["Estimation methods", "Income inequality metrics", "Parametric statistics", "Theory of probability distributions", "Vilfredo Pareto"], "title": "Pareto interpolation", "method": "Pareto interpolation", "url": "https://en.wikipedia.org/wiki/Pareto_interpolation", "summary": "Pareto interpolation is a method of estimating the median and other properties of a population that follows a Pareto distribution. It is used in economics when analysing the distribution of incomes in a population, when one must base estimates on a relatively small random sample taken from the population.\nThe family of Pareto distributions is parameterized by\n\na positive number \u03ba that is the smallest value that a random variable with a Pareto distribution can take. As applied to distribution of incomes, \u03ba is the lowest income of any person in the population; and\na positive number \u03b8 the \"Pareto index\"; as this increases, the tail of the distribution gets thinner. As applied to distribution of incomes, this means that the larger the value of the Pareto index \u03b8 the smaller the proportion of incomes many times as big as the smallest incomes.Pareto interpolation can be used when the available information includes the proportion of the sample that falls below each of two specified numbers a < b. For example, it may be observed that 45% of individuals in the sample have incomes below a = $35,000 per year, and 55% have incomes below b = $40,000 per year.\nLet\n\nPa = proportion of the sample that lies below a;Pb = proportion of the sample that lies below b.Then the estimates of \u03ba and \u03b8 are\n\n \n \n \n \n \n \n \u03ba\n ^\n \n \n \n =\n \n \n (\n \n \n \n \n P\n \n b\n \n \n \u2212\n \n P\n \n a\n \n \n \n \n \n (\n \n 1\n \n /\n \n \n a\n \n \n \n \u03b8\n ^\n \n \n \n \n \n )\n \n \u2212\n \n (\n \n 1\n \n /\n \n \n b\n \n \n \n \u03b8\n ^\n \n \n \n \n \n )\n \n \n \n \n )\n \n \n 1\n \n /\n \n \n \n \n \u03b8\n ^\n \n \n \n \n \n \n \n {\\displaystyle {\\widehat {\\kappa }}=\\left({\\frac {P_{b}-P_{a}}{\\left(1/a^{\\widehat {\\theta }}\\right)-\\left(1/b^{\\widehat {\\theta }}\\right)}}\\right)^{1/{\\widehat {\\theta }}}}\n and\n\n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n =\n \n \n \n \n log\n \u2061\n (\n 1\n \u2212\n \n P\n \n a\n \n \n )\n \u2212\n log\n \u2061\n (\n 1\n \u2212\n \n P\n \n b\n \n \n )\n \n \n log\n \u2061\n (\n b\n )\n \u2212\n log\n \u2061\n (\n a\n )\n \n \n \n .\n \n \n {\\displaystyle {\\widehat {\\theta }}\\;=\\;{\\frac {\\log(1-P_{a})-\\log(1-P_{b})}{\\log(b)-\\log(a)}}.}\n The estimate of the median would then be\n\n \n \n \n \n \n estimated median\n \n \n =\n \n \n \n \u03ba\n ^\n \n \n \n \u22c5\n \n 2\n \n 1\n \n /\n \n \n \n \n \u03b8\n ^\n \n \n \n \n \n ,\n \n \n \n {\\displaystyle {\\mbox{estimated median}}={\\widehat {\\kappa }}\\cdot 2^{1/{\\widehat {\\theta }}},\\,}\n since the actual population median is\n\n \n \n \n \n \n median\n \n \n =\n \u03ba\n \n \n 2\n \n 1\n \n /\n \n \u03b8\n \n \n .\n \n \n \n {\\displaystyle {\\mbox{median}}=\\kappa \\,2^{1/\\theta }.\\,}", "images": [], "links": ["Economics", "Estimator", "Median", "Pareto distribution", "Random variable"], "references": ["http://mumford.albany.edu/census/CityProfiles/Profiles/MHHINote.htm", "https://web.archive.org/web/20060825221627/http://www.sipp.census.gov/sipp/sourceac/S&A01_20060323_Long(S&A-3).pdf"]}, "Residual sum of squares": {"categories": ["All articles needing additional references", "Articles needing additional references from April 2013", "Errors and residuals", "Least squares"], "title": "Residual sum of squares", "method": "Residual sum of squares", "url": "https://en.wikipedia.org/wiki/Residual_sum_of_squares", "summary": "In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data). It is a measure of the discrepancy between the data and an estimation model. A small RSS indicates a tight fit of the model to the data. It is used as an optimality criterion in parameter selection and model selection.\nIn general, total sum of squares = explained sum of squares + residual sum of squares. For a proof of this in the multivariate ordinary least squares (OLS) case, see partitioning in the general OLS model.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Chi-squared distribution", "Coefficient", "Degrees of freedom (statistics)", "Errors and residuals in statistics", "Estimator", "Explained sum of squares", "Hat matrix", "International Standard Book Number", "Lack-of-fit sum of squares", "Least squares", "Model selection", "Optimality criterion", "Ordinary least squares", "Pearson correlation coefficient", "Regressand", "Regression model", "Regressor", "Square (arithmetic)", "Squared deviations", "Statistics", "Sum of squares (statistics)", "Summation", "Total sum of squares", "Vector norm"], "references": []}, "Forecast bias": {"categories": ["Bias", "Statistical forecasting", "Supply chain analytics"], "title": "Forecast bias", "method": "Forecast bias", "url": "https://en.wikipedia.org/wiki/Forecast_bias", "summary": "A forecast bias occurs when there are consistent differences between actual outcomes and previously generated forecasts of those quantities; that is: forecasts may have a general tendency to be too high or too low. A normal property of a good forecast is that it is not biased.As a quantitative measure, the \"forecast bias\" can be specified as a probabilistic or statistical property of the forecast error. A typical measure of bias of forecasting procedure is the arithmetic mean or expected value of the forecast errors, but other measures of bias are possible. For example, a median-unbiased forecast would be one where half of the forecasts are too low and half too high: see Bias of an estimator.\nIn contexts where forecasts are being produced on a repetitive basis, the performance of the forecasting system may be monitored using a tracking signal, which provides an automatically maintained summary of the forecasts produced up to any given time. This can be used to monitor for deteriorating performance of the system.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8b/Nuvola_apps_kalzium.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7a/Nuvola_apps_kcmsystem.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Academic bias", "Acquiescence bias", "Anchoring", "Arithmetic mean", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "Belief bias", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Calculating demand forecast accuracy", "Choice-supportive bias", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Confirmation bias", "Congruence bias", "Consensus forecast", "Cultural bias", "Debiasing", "Demand forecasting", "Distinction bias", "Dunning\u2013Kruger effect", "Egocentric bias", "Emotional bias", "Expected value", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Forecast error", "Forecast skill", "Fundamental attribution error", "Funding bias", "Halo effect", "Healthy user bias", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "Impact bias", "In-group favoritism", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "Lead time bias", "Length time bias", "List of cognitive biases", "List of memory biases", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Negativity bias", "Net bias", "Normalcy bias", "Omission bias", "Omitted-variable bias", "Optimism bias", "Outcome bias", "Overton window", "Participation bias", "Precision bias", "Pro-innovation bias", "Publication bias", "Recall bias", "Reporting bias", "Response bias", "Restraint bias", "Sampling bias", "Selection bias", "Self-selection bias", "Self-serving bias", "Social comparison bias", "Social desirability bias", "Spectrum bias", "Status quo bias", "Survivorship bias", "Systematic error", "Systemic bias", "Time-saving bias", "Tracking signal", "Trait ascription bias", "United States news media and the Vietnam War", "Verification bias", "Von Restorff effect", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://www.apics.org/Resources/APICSDictionary.htm"]}, "Doubly stochastic model": {"categories": ["Hidden stochastic models", "Latent variable models"], "title": "Doubly stochastic model", "method": "Doubly stochastic model", "url": "https://en.wikipedia.org/wiki/Doubly_stochastic_model", "summary": "In statistics, a doubly stochastic model is a type of model that can arise in many contexts, but in particular in modelling time-series and stochastic processes. \nThe basic idea for a doubly stochastic model is that an observed random variable is modelled in two stages. In one stage, the distribution of the observed outcome is represented in a fairly standard way using one or more parameters. At a second stage, some of these parameters (often only one) are treated as being themselves random variables. In a univariate context this is essentially the same as the well-known concept of compounded distributions. For the more general case of doubly stochastic models, there is the idea that many values in a time-series or stochastic model are simultaneously affected by the underlying parameters, either by using a single parameter affecting many outcome variates, or by treating the underlying parameter as a time-series or stochastic process in its own right.\nThe basic idea here is essentially similar to that broadly used in latent variable models except that here the quantities playing the role of latent variables usually have an underlying dependence structure related to the time-series or spatial context.\nAn example of a doubly stochastic model is the following. The observed values in a point process might be modelled as a Poisson process in which the rate (the relevant underlying parameter) is treated as being the exponential of a Gaussian process.", "images": [], "links": ["Compound probability distribution", "Cox process", "Digital object identifier", "Gaussian process", "International Standard Book Number", "Latent variable", "Latent variable model", "Poisson process", "Stochastic processes", "Time-series"], "references": ["http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9892.1986.tb00485.x/abstract", "http://doi.org/10.1111%2Fj.1467-9892.1986.tb00485.x"]}, "Constant elasticity of substitution": {"categories": ["Econometric modeling", "Elasticity (economics)", "Production economics", "Utility function types"], "title": "Constant elasticity of substitution", "method": "Constant elasticity of substitution", "url": "https://en.wikipedia.org/wiki/Constant_elasticity_of_substitution", "summary": "Constant elasticity of substitution (CES), in economics, is a property of some production functions and utility functions.\nSpecifically, it arises in a particular type of aggregator function which combines two or more types of consumption goods, or two or more types of production inputs into an aggregate quantity. This aggregator function exhibits constant elasticity of substitution.", "images": [], "links": ["American Economic Review", "Avinash Dixit", "Bagicha Singh Minhas", "Capital (economics)", "Cardinal utility", "Cobb\u2013Douglas production function", "Consumer theory", "Demand function", "Digital object identifier", "Economics", "Elasticity of substitution", "Expenditure function", "General equilibrium", "Hal Varian", "Hirofumi Uzawa", "Hollis B. Chenery", "Homothetic preferences", "Indirect utility function", "International Standard Book Number", "Isoelastic utility", "JSTOR", "Joseph Stiglitz", "Kenneth Arrow", "Leontief production function", "Linear utility", "Manual labour", "Marginal rate of technical substitution", "Monopolistic competition", "Neoclassical economics", "Ordinal utility", "Partial equilibrium", "Paul Armington", "Production function", "Robert Solow", "Total factor productivity", "Utility function"], "references": ["http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2354226", "http://www2.hawaii.edu/~fuleky/anatomy/anatomy2.html", "http://www.econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/elasticity%20of%20substitutionrevised.tex.pdf", "http://doi.org/10.1111%2Fj.1540-5915.2001.tb00965.x", "http://doi.org/10.1162%2Frest.89.1.183", "http://doi.org/10.2307%2F1884513", "http://doi.org/10.2307%2F1927286", "http://doi.org/10.2307%2F2296305", "http://doi.org/10.2307%2F3866403", "http://www.jstor.org/stable/1831401", "http://www.jstor.org/stable/1927286"]}, "Law of large numbers": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2015", "Asymptotic theory (statistics)", "Mathematical proofs", "Probability theorems", "Statistical theorems", "Wikipedia articles needing clarification from November 2016", "Wikipedia articles needing clarification from October 2018"], "title": "Law of large numbers", "method": "Law of large numbers", "url": "https://en.wikipedia.org/wiki/Law_of_large_numbers", "summary": "In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.\nThe LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the law only applies (as the name indicates) when a large number of observations is considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be \"balanced\" by the others (see the gambler's fallacy).", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4d/DiffusionMicroMacro.gif", "https://upload.wikimedia.org/wikipedia/commons/c/c9/Lawoflargenumbers.svg", "https://upload.wikimedia.org/wikipedia/commons/4/49/Lawoflargenumbersanimation2.gif", "https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Absolute difference", "Absolutely continuous", "Aleksandr Khinchin", "Almost everywhere", "Almost sure convergence", "Almost surely", "Andrey Kolmogorov", "Andrey Markov", "ArXiv", "Ars Conjectandi", "Asymptotic", "Asymptotic equipartition property", "Average", "Bayes' theorem", "Bernoulli's principle", "Bernoulli random variable", "Bernoulli trial", "Boole's inequality", "Business Insider", "Cauchy distribution", "Central limit theorem", "Characteristic function (probability theory)", "Chebyshev's inequality", "Chemistry", "Complementary event", "Complex function", "Conditional independence", "Conditional probability", "Convergence in distribution", "Convergence in probability", "Convergence of random variables", "Daniel Bernoulli", "Daniel McFadden", "Dice", "Digital object identifier", "Dirichlet integral", "Dominated convergence theorem", "Elementary event", "Empirical probability", "Encyclopedia of Mathematics", "Ergodic theory", "Eric W. Weisstein", "Event (probability theory)", "Expected value", "Exponential distribution", "Extremum estimator", "Fair coin", "Fick's law", "Francesco Paolo Cantelli", "Function (mathematics)", "Gambler's fallacy", "Gaussian distribution", "Geometric distribution", "Gerolamo Cardano", "I.i.d.", "Independence (probability theory)", "Independent and identically distributed random variables", "Infinite monkey theorem", "International Standard Book Number", "JSTOR", "Jacob Bernoulli", "Joint probability distribution", "Law of averages", "Law of the iterated logarithm", "Law of total probability", "Lebesgue integration", "Lebesgue measure", "Limit of a sequence", "Lindy effect", "L\u00e9vy continuity theorem", "Marginal distribution", "MathWorld", "Median", "Michiel Hazewinkel", "Molecular diffusion", "Pafnuty Chebyshev", "Pairwise independence", "Probability", "Probability axioms", "Probability measure", "Probability space", "Probability theory", "R (programming language)", "Random variable", "Real number", "Regression toward the mean", "Riemann integral", "Roulette", "Sample mean", "Sample space", "Series (mathematics)", "Sim\u00e9on Denis Poisson", "Solution", "Sortition", "Statistics", "Taylor's theorem", "Theorem", "Tree diagram (probability theory)", "Variance", "Venn diagram", "Yuri Vasilyevich Prokhorov", "\u00c9mile Borel"], "references": ["http://www.businessinsider.com/law-of-large-numbers-tim-cook-2015-2", "http://math.stackexchange.com/questions/266870/weak-law-of-large-numbers-proof-using-characteristic-functions-vs-proof-using-t", "http://mathworld.wolfram.com/StrongLawofLargeNumbers.html", "http://mathworld.wolfram.com/WeakLawofLargeNumbers.html", "http://terrytao.wordpress.com/2008/06/18/the-strong-law-of-large-numbers/", "http://www.isds.duke.edu/courses/Fall09/sta205/lec/lln.pdf", "http://www.stat.umn.edu/geyer/8112/notes/weaklaw.pdf", "http://www.mathnet.or.kr/mathnet/kms_tex/31810.pdf", "http://arxiv.org/abs/1309.6488", "http://doi.org/10.1007%2FBF01013465", "http://doi.org/10.1214%2Faoms%2F1177697731", "http://doi.org/10.1515%2Fcrll.1846.33.259", "http://doi.org/10.3150%2F12-BEJSP12", "https://books.google.com/?id=K6t5qn-SEp8C&pg=PA432&lpg=PA432&q=%22even%20if%20the%20mean%20does%20not%20exist%22", "https://books.google.com/books?id=uovoFE3gt2EC&pg=PA7#v=onepage", "https://web.archive.org/web/20081110071309/http://animation.yihui.name/prob:law_of_large_numbers", "https://web.archive.org/web/20130309032810/http://www.isds.duke.edu/courses/Fall09/sta205/lec/lln.pdf", "https://www.encyclopediaofmath.org/index.php/Law_of_large_numbers", "https://www.encyclopediaofmath.org/index.php/Strong_law_of_large_numbers", "https://www.encyclopediaofmath.org/index.php?title=p/l057720", "https://www.jstor.org/discover/10.2307/2323947?uid=3738032&uid=2&uid=4&sid=21103621939777", "https://www.jstor.org/stable/2709176", "https://projecteuclid.org/euclid.bj/1377612845", "https://cran.r-project.org/package=animation"]}, "Lists of people": {"categories": ["Lists of lists", "Lists of people", "Use dmy dates from May 2013"], "title": "Lists of people", "method": "Lists of people", "url": "https://en.wikipedia.org/wiki/Lists_of_people", "summary": "Lists of people by characteristics include:", "images": ["https://upload.wikimedia.org/wikipedia/en/6/69/P_vip.svg"], "links": ["Disney Legends", "Kidney stone formers", "Library of Congress Classification", "List of Apollo astronauts", "List of Arab scientists and scholars", "List of Brookings Institution scholars", "List of Dewey Decimal classes", "List of HIV-positive people", "List of Muslim Christianity scholars", "List of Muslim scholars", "List of Nobel laureates", "List of Titanic passengers", "List of YouTubers", "List of bankrupts", "List of brain tumor patients", "List of celebrities on The Simpsons", "List of centuries", "List of computer scientists", "List of conservationists", "List of deaf people", "List of decades", "List of historical anniversaries", "List of hunger strikes", "List of ice hockey players who died during their playing career", "List of individuals", "List of individuals (disambiguation)", "List of literary dunces", "List of mummies", "List of nonviolence scholars and leaders", "List of one-word stage names", "List of paraplegic people", "List of people believed to have been affected by bipolar disorder", "List of people diagnosed with pancreatic cancer", "List of people diagnosed with ulcerative colitis", "List of people educated at Westminster School", "List of people known as The Great", "List of people on multiple governing boards", "List of people on stamps", "List of people who died in road accidents", "List of people who disappeared mysteriously", "List of people who have declined a British honour", "List of people who have lit the Olympic Cauldron", "List of people who have suffered from depression", "List of people who were beheaded", "List of people who were executed", "List of people with Crohn's disease", "List of people with dyslexia", "List of people with epilepsy", "List of polio survivors", "List of premature obituaries", "List of pseudonyms", "List of serial killers before 1900", "List of serial killers by country", "List of serial killers by number of victims", "List of serial killers in the United States", "List of sportspeople", "List of stage names", "List of the 100 wealthiest people", "List of the heaviest people", "List of timelines", "List of transgender people", "List of tuberculosis victims", "Lists of authors", "Lists of countries and territories", "Lists of men", "Lists of office-holders", "Lists of people by belief", "Lists of people by cause of death", "Lists of people by nationality", "Lists of people by occupation", "Lists of presidents", "Lists of women", "November 15", "Outline of academic disciplines", "People"], "references": []}, "Paired difference test": {"categories": ["Statistical hypothesis testing"], "title": "Paired difference test", "method": "Paired difference test", "url": "https://en.wikipedia.org/wiki/Paired_difference_test", "summary": "In statistics, a paired difference test is a type of location test that is used when comparing two sets of measurements to assess whether their population means differ. A paired difference test uses additional information about the sample that is not present in an ordinary unpaired testing situation, either to increase the statistical power, or to reduce the effects of confounders.\nSpecific methods for carrying out paired difference tests are, for normally distributed difference t-test (where the population standard deviation of difference is not known) and the paired Z-test (where the population standard deviation of the difference is known), and for differences that may not be normally distributed the Wilcoxon signed-rank test.The most familiar example of a paired difference test occurs when subjects are measured before and after a treatment. Such a \"repeated measures\" test compares these measurements within subjects, rather than across subjects, and will generally have greater power than an unpaired test. Another example comes from matching cases of a disease with comparable controls.", "images": [], "links": ["Average", "Blocking (statistics)", "Conditional logistic regression", "Confounder", "Correlation", "Cumulative distribution function", "Digital object identifier", "Expected value", "JSTOR", "Location test", "Matching (statistics)", "Normal distribution", "Null hypothesis", "Observational study", "Pairwise comparison", "PubMed Identifier", "Random effect", "Sample (statistics)", "Sign test", "Statistical power", "Statistical significance", "Statistics", "T-test", "Two-tailed test", "Type I and type II errors", "Variance", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://deseng.ryerson.ca/~fil/t/pwisecomp.html", "http://compbio.berkeley.edu/people/ed/SeqCompEval/", "http://www.rac.es/ficheros/doc/00576.PDF", "http://www.ncbi.nlm.nih.gov/pubmed/7272415", "http://doi.org/10.2307/2529684", "http://doi.org/10.2307/2530417", "http://www.jstor.org/stable/2529684", "http://www.jstor.org/stable/2530417", "http://www.jstor.org/stable/4615774", "http://www.stat-d.si/mz/Articles.html"]}, "Fisher\u2013Tippett\u2013Gnedenko theorem": {"categories": ["All articles lacking sources", "All stub articles", "Articles lacking sources from March 2011", "Extreme value data", "Statistical theorems", "Statistics stubs", "Tails of probability distributions"], "title": "Fisher\u2013Tippett\u2013Gnedenko theorem", "method": "Fisher\u2013Tippett\u2013Gnedenko theorem", "url": "https://en.wikipedia.org/wiki/Fisher%E2%80%93Tippett%E2%80%93Gnedenko_theorem", "summary": "In statistics, the Fisher\u2013Tippett\u2013Gnedenko theorem (also the Fisher\u2013Tippett theorem or the extreme value theorem) is a general result in extreme value theory regarding asymptotic distribution of extreme order statistics. The maximum of a sample of iid random variables after proper renormalization can only converge in distribution to one of 3 possible distributions, the Gumbel distribution, the Fr\u00e9chet distribution, or the Weibull distribution. Credit for the extreme value theorem (or convergence to types theorem) is given to Gnedenko (1948), previous versions were stated by Ronald Fisher and Leonard Henry Caleb Tippett in 1928 and Fr\u00e9chet in 1927.\nThe role of the extremal types theorem for maxima is similar to that of central limit theorem for averages, except that the central limit theorem applies to the average of a sample from any distribution with finite variance, while the Fisher-Tippet-Gnedenko theorem only states that if the distribution of a normalized maximum converges, then the limit has to be one of a particular class of distributions. It does not state that the distribution of the normalized maximum does converge.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/a/aa/Youngronaldfisher2.JPG", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Central limit theorem", "Convergence of random variables", "Converges in distribution", "Extreme value theorem", "Extreme value theory", "Fr\u00e9chet", "Fr\u00e9chet distribution", "Generalized extreme value distribution", "Gnedenko", "Gumbel distribution", "Iid", "Independent and identically-distributed random variables", "Leonard Henry Caleb Tippett", "Location-scale family", "Order statistic", "Pickands\u2013Balkema\u2013de Haan theorem", "Random variable", "Ronald Fisher", "Statistics", "Weibull distribution"], "references": []}, "Maxwell\u2013Boltzmann distribution": {"categories": ["Continuous distributions", "Gases", "James Clerk Maxwell", "Normal distribution", "Pages using deprecated image syntax", "Particle distributions", "Wikipedia articles needing clarification from June 2018"], "title": "Maxwell\u2013Boltzmann distribution", "method": "Maxwell\u2013Boltzmann distribution", "url": "https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution", "summary": "In physics (in particular in statistical mechanics), the Maxwell\u2013Boltzmann distribution is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. \nIt was first defined and used for describing particle speeds in idealized gases, where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment. \nThe term \"particle\" in this context refers to gaseous particles only (atoms or molecules), and the system of particles is assumed to have reached thermodynamic equilibrium.\nThe energies of such particles follow what is known as Maxwell-Boltzmann statistics, and the statistical distribution of speeds is derived by equating particle energies with kinetic energy.\nMathematically, the Maxwell\u2013Boltzmann distribution is the chi distribution with three degrees of freedom (the components of the velocity vector in Euclidean space), with a scale parameter measuring speeds in units proportional to the square root of \n \n \n \n T\n \n /\n \n m\n \n \n {\\displaystyle T/m}\n (the ratio of temperature and particle mass).The Maxwell\u2013Boltzmann distribution is a result of the kinetic theory of gases, which provides a simplified explanation of many fundamental gaseous properties, including pressure and diffusion. \nThe Maxwell\u2013Boltzmann distribution applies fundamentally to particle velocities in three dimensions, but turns out to depend only on the speed (the magnitude of the velocity) of the particles. \nA particle speed probability distribution indicates which speeds are more likely: a particle will have a speed selected randomly from the distribution, and is more likely to be within one range of speeds than another.\nThe kinetic theory of gases applies to the classical ideal gas, which is an idealization of real gases. In real gases, there are various effects (e.g., van der Waals interactions, vortical flow, relativistic speed limits, and quantum exchange interactions) that can make their speed distribution different from the Maxwell\u2013Boltzmann form. \nHowever, rarefied gases at ordinary temperatures behave very nearly like an ideal gas and the Maxwell speed distribution is an excellent approximation for such gases. \nIdeal plasmas, which are ionized gases of sufficiently low density, frequently also have particle distributions that are partially or entirely Maxwellian.The distribution was first derived by Maxwell in 1860 on heuristic grounds. \nBoltzmann later, in the 1870s, carried out significant investigations into the physical origins of this distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/98/Maxwell-Boltzmann_distribution_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/1/19/Maxwell-Boltzmann_distribution_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/0/01/MaxwellBoltzmann-en.svg"], "links": ["ARGUS distribution", "Adiabatic index", "Air", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Atmospheric chemistry", "Atoms", "Avogadro constant", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Boltzmann's constant", "Boltzmann constant", "Boltzmann distribution", "Boltzmann factor", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Collision", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Darwin\u2013Fowler method", "Davis distribution", "Degenerate distribution", "Degrees of freedom", "Delaporte distribution", "Derivative", "Diffusion", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Equipartition theorem", "Erlang distribution", "Error function", "Euclidean space", "Ewens's sampling formula", "Excess kurtosis", "Exchange interaction", "Expectation value", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gas constant", "Gas in a box", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "H-theorem", "Half-logistic distribution", "Half-normal distribution", "Harald J. W. Mueller-Kirsten", "Heat capacity", "Helium", "Holtsmark distribution", "Hotelling's T-squared distribution", "Humidity", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Ideal gas", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "James Clerk Maxwell", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kinetic energy", "Kinetic theory of gases", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Ludwig Boltzmann", "L\u00e9vy distribution", "Magnitude (mathematics)", "Marchenko\u2013Pastur distribution", "Mathworld", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell-Boltzmann statistics", "Maxwell\u2013Boltzmann statistics", "Maxwell\u2013J\u00fcttner distribution", "Microstate (statistical mechanics)", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Molecule", "Molecules", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noble gas", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normalizing constant", "Ordinary differential equation", "Oxygen", "Parabolic fractal distribution", "Pareto distribution", "Partition function (statistical mechanics)", "Pearson distribution", "Phase-type distribution", "Physics", "Plasma (physics)", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Pressure", "Probability density function", "Probability distribution", "Proportionality (mathematics)", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantum Boltzmann equation", "Quantum mechanics", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rarefied", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Room temperature", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Special relativity", "Specific heat", "Speed", "Speed of sound", "Spherical coordinate system", "Spherical coordinates", "Stable distribution", "Statistical mechanics", "Statistical thermodynamics", "Student's t-distribution", "Support (mathematics)", "Thermodynamic equilibrium", "Thermodynamic temperature", "Tracy\u2013Widom distribution", "Translation (physics)", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Van der Waals interaction", "Variance", "Variance-gamma distribution", "Velocity", "Voigt profile", "Volume element", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Vortex", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "World Scientific", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://demonstrations.wolfram.com/TheMaxwellSpeedDistribution/", "http://adsabs.harvard.edu/abs/2017SHPMP..57...53G", "http://arxiv.org/abs/1702.01411", "http://doi.org/10.1016%2Fj.shpsb.2017.01.001", "https://books.google.com/books?id=6C0R1qpAk7EC&pg=SA2-PA278", "https://books.google.com/books?id=HLxV-IKYO5IC&pg=PA352", "https://books.google.com/books?id=QF6iMewh4KMC", "https://books.google.com/books?id=QF6iMewh4KMC&pg=PA434", "https://www.biodiversitylibrary.org/item/20012#page/37/mode/1up", "https://www.biodiversitylibrary.org/item/53795#page/33/mode/1up"]}, "Simple random sample": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2012", "Articles needing additional references from November 2011", "Sampling techniques"], "title": "Simple random sample", "method": "Simple random sample", "url": "https://en.wikipedia.org/wiki/Simple_random_sample", "summary": "In statistics, a simple random sample is a subset of individuals (a sample) chosen from a larger set (a population). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals. This process and technique is known as simple random sampling, and should not be confused with systematic random sampling. A simple random sample is an unbiased surveying technique.\nSimple random sampling is a basic type of sampling, since it can be a component of other more complex sampling methods. The principle of simple random sampling is that every object has the same probability of being chosen. For example, suppose N college students want to get a ticket for a basketball game, but there are only X < N tickets for them, so they decide to have a fair way to see who gets to go. Then, everybody is given a number in the range from 0 to N-1, and random numbers are generated, either electronically or from a table of random numbers. Numbers outside the range from 0 to N-1 are ignored, as are any numbers previously selected. The first X numbers would identify the lucky ticket winners.\nIn small populations and often in large ones, such sampling is typically done \"without replacement\", i.e., one deliberately avoids choosing any member of the population more than once. Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement.\nSampling done without replacement is no longer independent, but still satisfies exchangeability, hence many results still hold. Further, for a small sample from a large population, sampling without replacement is approximately the same as sampling with replacement, since the odds of choosing the same individual twice is low.\nAn unbiased random selection of individuals is important so that if a large number of samples were drawn, the average sample would accurately represent the population. However, this does not guarantee that a particular sample is a perfect representation of the population. Simple random sampling merely allows one to draw externally valid conclusions about the entire population based on the sample.\nConceptually, simple random sampling is the simplest of the probability sampling techniques. It requires a complete sampling frame, which may not be available or feasible to construct for large populations. Even if a complete frame is available, more efficient approaches may be possible if other useful information is available about the units in the population.\nAdvantages are that it is free of classification error, and it requires minimum advance knowledge of the population other than the frame. Its simplicity also makes it relatively easy to interpret data collected in this manner. For these reasons, simple random sampling best suits situations where not much information is available about the population and data collection can be efficiently conducted on randomly distributed items, or where the cost of sampling is small enough to make efficiency less important than simplicity. If these conditions do not hold, stratified sampling or cluster sampling may be a better choice.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Binomial distribution", "Cluster sampling", "Digital object identifier", "Exchangeable random variables", "Hypergeometric distribution", "Individuals", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Multistage sampling", "Nonprobability sampling", "Opinion poll", "Probability", "Quantitative marketing research", "Randomization", "Reservoir sampling", "Sample (statistics)", "Sampling frame", "Set (mathematics)", "Statistical population", "Statistics", "Stratified sampling", "Subset", "Systematic sampling", "W.H. Freeman"], "references": ["http://www.tandfonline.com/doi/abs/10.1080/01621459.1962.10480667", "http://doi.acm.org/10.1145/3147.3165", "http://doi.org/10.1007/0-387-34240-0", "http://doi.org/10.1080/01621459.1962.10480667", "http://doi.org/10.1145/3147.3165", "http://doi.org/10.2307/2346966", "http://jmlr.org/proceedings/papers/v28/meng13a.pdf", "http://www.jstor.org/stable/10.2307/2346966", "http://www.worldcat.org/issn/0098-3500", "http://www.worldcat.org/issn/0162-1459", "https://link.springer.com/10.1007/0-387-34240-0", "https://erikerlandson.github.io/blog/2014/09/11/faster-random-samples-with-gap-sampling/"]}, "Simple random sampling": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2012", "Articles needing additional references from November 2011", "Sampling techniques"], "title": "Simple random sample", "method": "Simple random sampling", "url": "https://en.wikipedia.org/wiki/Simple_random_sample", "summary": "In statistics, a simple random sample is a subset of individuals (a sample) chosen from a larger set (a population). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals. This process and technique is known as simple random sampling, and should not be confused with systematic random sampling. A simple random sample is an unbiased surveying technique.\nSimple random sampling is a basic type of sampling, since it can be a component of other more complex sampling methods. The principle of simple random sampling is that every object has the same probability of being chosen. For example, suppose N college students want to get a ticket for a basketball game, but there are only X < N tickets for them, so they decide to have a fair way to see who gets to go. Then, everybody is given a number in the range from 0 to N-1, and random numbers are generated, either electronically or from a table of random numbers. Numbers outside the range from 0 to N-1 are ignored, as are any numbers previously selected. The first X numbers would identify the lucky ticket winners.\nIn small populations and often in large ones, such sampling is typically done \"without replacement\", i.e., one deliberately avoids choosing any member of the population more than once. Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement.\nSampling done without replacement is no longer independent, but still satisfies exchangeability, hence many results still hold. Further, for a small sample from a large population, sampling without replacement is approximately the same as sampling with replacement, since the odds of choosing the same individual twice is low.\nAn unbiased random selection of individuals is important so that if a large number of samples were drawn, the average sample would accurately represent the population. However, this does not guarantee that a particular sample is a perfect representation of the population. Simple random sampling merely allows one to draw externally valid conclusions about the entire population based on the sample.\nConceptually, simple random sampling is the simplest of the probability sampling techniques. It requires a complete sampling frame, which may not be available or feasible to construct for large populations. Even if a complete frame is available, more efficient approaches may be possible if other useful information is available about the units in the population.\nAdvantages are that it is free of classification error, and it requires minimum advance knowledge of the population other than the frame. Its simplicity also makes it relatively easy to interpret data collected in this manner. For these reasons, simple random sampling best suits situations where not much information is available about the population and data collection can be efficiently conducted on randomly distributed items, or where the cost of sampling is small enough to make efficiency less important than simplicity. If these conditions do not hold, stratified sampling or cluster sampling may be a better choice.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Binomial distribution", "Cluster sampling", "Digital object identifier", "Exchangeable random variables", "Hypergeometric distribution", "Individuals", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Multistage sampling", "Nonprobability sampling", "Opinion poll", "Probability", "Quantitative marketing research", "Randomization", "Reservoir sampling", "Sample (statistics)", "Sampling frame", "Set (mathematics)", "Statistical population", "Statistics", "Stratified sampling", "Subset", "Systematic sampling", "W.H. Freeman"], "references": ["http://www.tandfonline.com/doi/abs/10.1080/01621459.1962.10480667", "http://doi.acm.org/10.1145/3147.3165", "http://doi.org/10.1007/0-387-34240-0", "http://doi.org/10.1080/01621459.1962.10480667", "http://doi.org/10.1145/3147.3165", "http://doi.org/10.2307/2346966", "http://jmlr.org/proceedings/papers/v28/meng13a.pdf", "http://www.jstor.org/stable/10.2307/2346966", "http://www.worldcat.org/issn/0098-3500", "http://www.worldcat.org/issn/0162-1459", "https://link.springer.com/10.1007/0-387-34240-0", "https://erikerlandson.github.io/blog/2014/09/11/faster-random-samples-with-gap-sampling/"]}, "Sampling risk": {"categories": ["Actuarial science", "All articles needing additional references", "Articles needing additional references from March 2013", "Auditing terms", "Sampling (statistics)"], "title": "Sampling risk", "method": "Sampling risk", "url": "https://en.wikipedia.org/wiki/Sampling_risk", "summary": "Sampling risk is one of the many types of risks an auditor may face when performing the necessary procedure of audit sampling. Audit sampling exists because of the impractical and costly effects of examining all or 100% of a client's records or books. As a result, a \"sample\" of a client's accounts are examined.\nDue to the negative effects produced by sampling risk, an auditor may have to perform additional procedures which in turn can impact the overall efficiency of the audit.Sampling risk represents the possibility that an auditor's conclusion based on a sample is different from that reached if the entire population were subject to audit procedure. The auditor may conclude that material misstatements exist, when in fact they do not; or material misstatements do not exist but in fact they do exist. Auditors can lower the sampling risk by increasing the sampling size.\nAlthough there are many types of risks associated with the audit process, each type primarily has an effect on the overall audit engagement. The effects produced by sampling risk generally can increase audit risk, the risk that an entity's financial statements will contain a material misstatement, though given an unqualified ('clean') audit report. Sampling risk can also increase detection risk which suggests the possibility that an auditor will not find material misstatements relating to the financial statements through substantive tests and analysis.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Audit", "Auditor", "Population", "Sample (statistics)", "Sample size"], "references": ["http://www.investopedia.com/terms/d/detection-risk.asp#axzz2Dp909dYp", "http://pakaccountants.com/what-is-sampling-risk-in-auditing/", "http://www.resourcemanagement.com/audit_sampling.html", "http://www.aicpa.org/Research/Standards/AuditAttest/DownloadableDocuments/AU-00350.pdf"]}, "Trimean": {"categories": ["Exploratory data analysis", "Means", "Robust statistics", "Summary statistics"], "title": "Trimean", "method": "Trimean", "url": "https://en.wikipedia.org/wiki/Trimean", "summary": "In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles:\n\n \n \n \n T\n M\n =\n \n \n \n \n Q\n \n 1\n \n \n +\n 2\n \n Q\n \n 2\n \n \n +\n \n Q\n \n 3\n \n \n \n 4\n \n \n \n \n {\\displaystyle TM={\\frac {Q_{1}+2Q_{2}+Q_{3}}{4}}}\n This is equivalent to the average of the median and the midhinge:\n\n \n \n \n T\n M\n =\n \n \n 1\n 2\n \n \n \n (\n \n \n Q\n \n 2\n \n \n +\n \n \n \n \n Q\n \n 1\n \n \n +\n \n Q\n \n 3\n \n \n \n 2\n \n \n \n )\n \n \n \n {\\displaystyle TM={\\frac {1}{2}}\\left(Q_{2}+{\\frac {Q_{1}+Q_{3}}{2}}\\right)}\n The foundations of the trimean were part of Arthur Bowley's teachings, and later popularized by statistician John Tukey in his 1977 book which has given its name to a set of techniques called exploratory data analysis.\nLike the median and the midhinge, but unlike the sample mean, it is a statistically resistant L-estimator with a breakdown point of 25%. This beneficial property has been described as follows:\n\nAn advantage of the trimean as a measure of the center (of a distribution) is that it combines the median's emphasis on center values with the midhinge's attention to the extremes.\n\n", "images": [], "links": ["Arthur Bowley", "Average", "Efficiency (statistics)", "Exploratory data analysis", "International Standard Book Number", "Interquartile mean", "John Tukey", "L-estimator", "MathWorld", "Median", "Midhinge", "Midsummary", "Probability distribution", "Quartiles", "Robust statistics", "Sample mean", "Statistically resistant", "Statistics", "Truncated mean", "Weighted average"], "references": ["http://mathworld.wolfram.com/Trimean.html", "https://books.google.com/books?id=tPw6b1VXfkoC&pg=PA39&ots=XMd1BObzZr&dq=trimean&sig=WMtwB-23lw44mmnnrrvz4lPHFKQ#PPA39,M1", "https://archive.org/details/atomicnucleus032805mbp", "https://archive.org/stream/atomicnucleus032805mbp#page/n925/mode/2up"]}, "Generalized beta distribution": {"categories": ["All articles lacking reliable references", "Articles lacking reliable references from April 2013", "Continuous distributions"], "title": "Generalized beta distribution", "method": "Generalized beta distribution", "url": "https://en.wikipedia.org/wiki/Generalized_beta_distribution", "summary": "In probability and statistics, the generalized beta distribution is a continuous probability distribution with five parameters, including more than thirty named distributions as limiting or special cases. It has been used in the modeling of income distribution, stock returns, as well as in regression analysis. The exponential generalized Beta (EGB) distribution follows directly from the GB and generalizes other common distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6e/Egbtree.jpg", "https://upload.wikimedia.org/wikipedia/commons/6/62/GBtree.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/88/Hazardshape.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded-t and half-t distributions", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized beta prime distribution", "Generalized extreme value distribution", "Generalized gamma distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gini index", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hazard function", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypergeometric series", "Hypoexponential distribution", "Income distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverted Dirichlet distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Limiting case (mathematics)", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lognormal", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability and statistics", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Special case", "Stable distribution", "Student's t-distribution", "Theil index", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "Type I extreme value distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["https://doi.org/10.1016%2F0304-4076(94)01612-4", "https://doi.org/10.1016%2F0378-3758(87)90089-9", "https://doi.org/10.1080%2F01621459.1980.10477530", "https://www.jstor.org/stable/2237889"]}, "Quasi-variance": {"categories": ["Statistical deviation and dispersion"], "title": "Quasi-variance", "method": "Quasi-variance", "url": "https://en.wikipedia.org/wiki/Quasi-variance", "summary": "Quasi-variance (qv) estimates are a statistical approach that is suitable for communicating the effects of a categorical explanatory variable within a statistical model. In standard statistical models the effects of a categorical explanatory variable are assessed by comparing one category (or level) that is set as a benchmark against which all other categories are compared. The benchmark category is usually referred to as the 'reference' or 'base' category. In order for comparisons to be made the reference category is arbitrarily fixed to zero. Statistical data analysis software usually undertakes formal comparisons of whether or not each level of the categorical variable differs from the reference category. These comparisons generate the well known \u2018significance values\u2019 of parameter estimates (i.e., coefficients). Whilst it is straightforward to compare any one category with the reference category, it is more difficult to formally compare two other categories (or levels) of an explanatory variable with each other when neither is the reference category. This is known as the reference category problem.\nQuasi-variances are approximations of variances. Quasi-variances are statistics associated with the parameter estimates (coefficients) of the different levels of categorical explanatory variables within statistical models. Quasi-variances can be presented alongside parameter estimates to enable readers to assess differences between any combinations of parameter estimates for a categorical explanatory variable. The approach is beneficial because such comparisons are not usually possible without access to the full variance-covariance matrix for the estimates. \nUsing quasi-variance estimates addresses the reference category problem. The underlying idea was first proposed by Ridout but the technique was set out by Professor David Firth. The suitability of this technique for social science data analysis has been demonstrated. An on-line tool for the calculation of quasi-variance estimates is available and a short technical description of the methodology is provided.\nQuasi-variances can be calculated in Stata using the QV module and can also be calculated in R using the package qvcalc.", "images": [], "links": ["Categorical variable", "David Firth (statistician)", "Digital object identifier", "Estimation", "Explanatory variable", "Generalized linear model", "International Standard Serial Number", "Parameter estimate", "R (programming language)", "Regression model", "SPSS", "Stata", "Statistical model", "Variance"], "references": ["http://journals.sagepub.com/doi/10.1111/j.0081-1750.2003.t01-1-00125.x", "http://journals.sagepub.com/doi/abs/10.1177/0038038507084830", "http://doi.org/10.1111/j.0081-1750.2003.t01-1-00125.x", "http://doi.org/10.1177/0038038507084830", "http://econpapers.repec.org/software/bocbocode/s457831.htm", "http://www.worldcat.org/issn/0038-0385", "http://www.restore.ac.uk/Longitudinal/qv/", "http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research/firth/software/qvcalc", "http://www2.warwick.ac.uk/fac/sci/statistics/staff/academic-research/firth/software/qvcalc/qv_doc.pdf", "https://oup.silverchair-cdn.com/oup/backfile/Content_public/Journal/biomet/91/1/10.1093/biomet/91.1.65/2/910065.pdf?Expires=1490132691&Signature=JkxQT3GX8GLSp3zwpc5kfrBDzzYHPKmcYkk08apMVw0Fk1QNsgfa5itP4r3lXPPA9LPWiVmdXC1EfbLd928uuFxIM0f2zTHrXAjUmN4vVgn~W3Ra0J~SGBNymLiETEZo3ntVlWJVyb81p4gJhK89Gs2127h~cznqFbKgQYjkscQ0oIvaJalQW6u~Cme8AS6ZDChsKql8ls~9kAmxZc4NVC5rbzLxwOB4vcslPZtmYtfRpNXqyOMh1E~HRMN4YkxNJ2BdtGXEJZJj3XZAK111afM7WNrwWwnBVZTm6VwPFn1jTbvvL04jth2TyEbrjId1V08sgzKKjBXPx173XY6Cig__&Key-Pair-Id=APKAIUCZBIA4LVPAVW3Q", "https://cran.r-project.org/web/packages/qvcalc/index.html"]}, "Data mining": {"categories": ["All articles with unsourced statements", "Articles to be expanded from September 2011", "Articles with Curlie links", "Articles with unsourced statements from April 2014", "CS1 maint: Multiple names: authors list", "Commons category link is on Wikidata", "Data mining", "Formal sciences", "Webarchive template wayback links", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Data mining", "method": "Data mining", "url": "https://en.wikipedia.org/wiki/Data_mining", "summary": "Data mining is the process of discovering patterns in large data sets involving methods at the intersection of machine learning, statistics, and database systems. Data mining is an interdisciplinary subfield of computer science with an overall goal to extract information (with intelligent methods) from a data set and transform the information into a comprehensible structure for further use. Data mining is the analysis step of the \"knowledge discovery in databases\" process, or KDD. Aside from the raw analysis step, it also involves database and data management aspects, data pre-processing, model and inference considerations, interestingness metrics, complexity considerations, post-processing of discovered structures, visualization, and online updating.The term \"data mining\" is in fact a misnomer, because the goal is the extraction of patterns and knowledge from large amounts of data, not the extraction (mining) of data itself. It also is a buzzword and is frequently applied to any form of large-scale data or information processing (collection, extraction, warehousing, analysis, and statistics) as well as any application of computer decision support system, including artificial intelligence (e.g., machine learning) and business intelligence. The book Data mining: Practical machine learning tools and techniques with Java (which covers mostly machine learning material) was originally to be named just Practical machine learning, and the term data mining was only added for marketing reasons. Often the more general terms (large scale) data analysis and analytics \u2013 or, when referring to actual methods, artificial intelligence and machine learning \u2013 are more appropriate.\nThe actual data mining task is the semi-automatic or automatic analysis of large quantities of data to extract previously unknown, interesting patterns such as groups of data records (cluster analysis), unusual records (anomaly detection), and dependencies (association rule mining, sequential pattern mining). This usually involves using database techniques such as spatial indices. These patterns can then be seen as a kind of summary of the input data, and may be used in further analysis or, for example, in machine learning and predictive analytics. For example, the data mining step might identify multiple groups in the data, which can then be used to obtain more accurate prediction results by a decision support system. Neither the data collection, data preparation, nor result interpretation and reporting is part of the data mining step, but do belong to the overall KDD process as additional steps.\nThe related terms data dredging, data fishing, and data snooping refer to the use of data mining methods to sample parts of a larger population data set that are (or may be) too small for reliable statistical inferences to be made about the validity of any patterns discovered. These methods can, however, be used in creating new hypotheses to test against the larger data populations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0c/Spurious_correlations_-_spelling_bee_spiders.svg", "https://upload.wikimedia.org/wikipedia/commons/8/89/Symbol_book_class2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/6/6c/Wiki_letter_w.svg"], "links": ["AAAI", "ACM Computing Classification System", "ADVISE", "Academic Press", "Academic journal", "Agent mining", "Aggregate (Data Warehouse)", "Aggregate function", "Algorithm", "Algorithm design", "Algorithmic efficiency", "Analysis of algorithms", "Analytics", "Anchor Modeling", "Angoss", "Anomaly detection", "Application security", "Applied statistics", "Artificial intelligence", "Artificial neural network", "Artificial neural networks", "Association for Computing Machinery", "Association rule learning", "Association rule mining", "Autoencoder", "Automata theory", "Automated machine learning", "Automated planning and scheduling", "Automatic number plate recognition in the United Kingdom", "Automatic summarization", "BIRCH", "Bayes' theorem", "Bayesian network", "Behavior informatics", "Bias-variance dilemma", "Big Data", "Bill Inmon", "Bioinformatics", "Boosting (machine learning)", "Bootstrap aggregating", "Business intelligence", "Business intelligence software", "Buzzword", "C++", "CIKM Conference", "CURE data clustering algorithm", "Cambridge University Press", "Canonical correlation analysis", "Carrot2", "Chemicalize.org", "Clarabridge", "Cluster analysis", "Column-oriented DBMS", "Comparison of OLAP Servers", "Compiler construction", "Computational biology", "Computational chemistry", "Computational complexity theory", "Computational engineering", "Computational geometry", "Computational learning theory", "Computational mathematics", "Computational physics", "Computational social science", "Computer accessibility", "Computer animation", "Computer architecture", "Computer data storage", "Computer graphics", "Computer hardware", "Computer network", "Computer science", "Computer security", "Computer security compromised by hardware failure", "Computer vision", "Computing platform", "Concurrency (computer science)", "Concurrent computing", "Conditional random field", "Conference on Information and Knowledge Management", "Conference on Knowledge Discovery and Data Mining", "Conference on Neural Information Processing Systems", "Control theory", "Convolutional neural network", "Copyright Directive", "Counterpunch.org", "Cross-validation (statistics)", "Cross Industry Standard Process for Data Mining", "Cryptography", "Curlie", "Customer analytics", "Cyberwarfare", "DATADVANCE", "DBSCAN", "Dashboard (business)", "Data", "Data (computing)", "Data Mining Extensions", "Data Mining and Knowledge Discovery", "Data analysis", "Data archaeology", "Data cleansing", "Data collection", "Data compression", "Data corruption", "Data curation", "Data degradation", "Data dictionary", "Data dredging", "Data editing", "Data extraction", "Data farming", "Data format management", "Data fusion", "Data integration", "Data integrity", "Data library", "Data loading", "Data loss", "Data management", "Data mart", "Data migration", "Data pre-processing", "Data preservation", "Data quality", "Data recovery", "Data reduction", "Data retention", "Data science", "Data scraping", "Data scrubbing", "Data security", "Data set", "Data stewardship", "Data storage", "Data transformation", "Data validation", "Data vault modeling", "Data visualization", "Data warehouse", "Data warehouse automation", "Data wrangling", "Database", "Database Directive", "Database management", "Database management system", "Database system", "Decision rules", "Decision support system", "Decision tree", "Decision tree learning", "DeepDream", "Deep learning", "Degenerate dimension", "Dependability", "Digital art", "Digital library", "Digital marketing", "Digital object identifier", "Dimension (data warehouse)", "Dimension table", "Dimensional modeling", "Dimensionality reduction", "Discrete mathematics", "Distributed artificial intelligence", "Distributed computing", "Document management system", "Domain-specific language", "Domain driven data mining", "Drug discovery", "E-commerce", "ELKI", "Early-arriving fact", "Educational data mining", "Educational technology", "Edward Snowden", "Electronic design automation", "Electronic discovery", "Electronic publishing", "Electronic voting", "Embedded system", "Empirical risk minimization", "Ensemble learning", "Enterprise information system", "Enterprise software", "European Commission", "European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases", "Examples of data mining", "Expectation\u2013maximization algorithm", "Exploratory data analysis", "Extract, transform, load", "Fact (data warehouse)", "Fact table", "Factor analysis", "Fair use", "Family Educational Rights and Privacy Act", "Feature engineering", "Feature learning", "Formal language", "Formal methods", "Forrester Research", "GNU Project", "Gartner", "Gated recurrent unit", "General Architecture for Text Engineering", "Genetic algorithms", "Geographic information system", "Global surveillance disclosure", "Glossary of artificial intelligence", "Google Book Search Settlement Agreement", "Google Scholar", "Grammar induction", "Graphical model", "Graphics processing unit", "Green computing", "Gregory I. Piatetsky-Shapiro", "Gregory Piatetsky-Shapiro", "HOLAP", "Hardware acceleration", "Hargreaves review", "Health Insurance Portability and Accountability Act", "Health informatics", "Hewlett-Packard", "Hidden Markov model", "Hierarchical clustering", "Human\u2013computer interaction", "IBM", "Ian H. Witten", "Image compression", "Independent component analysis", "InformationWeek", "Information extraction", "Information integration", "Information privacy", "Information processing", "Information retrieval", "Information security", "Information system", "Information theory", "Integrated Authority File", "Integrated circuit", "Integrated development environment", "Intention mining", "Interaction design", "Interdisciplinary", "International Conference on Machine Learning", "International Conference on Very Large Data Bases", "International Journal of Data Warehousing and Mining", "International Safe Harbor Privacy Principles", "International Standard Book Number", "Interpreter (computing)", "Intrusion detection system", "JSTOR", "Java (programming language)", "Java Data Mining", "Jerome H. Friedman", "Jiawei Han", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "KDD-95", "KDD Conference", "KNIME", "KXEN Inc.", "Kluwer Academic Publishers", "Knowledge representation and reasoning", "LIONsolver", "Learning classifier system", "Learning to rank", "Library (computing)", "Limitations and exceptions to copyright", "Linear discriminant analysis", "Linear regression", "List of computer science conferences", "List of datasets for machine-learning research", "List of reporting software", "Local outlier factor", "Logic in computer science", "Logistic regression", "Long short-term memory", "Lua (programming language)", "MOA (Massive Online Analysis)", "MOLAP", "Machine Learning (journal)", "Machine learning", "Mass surveillance", "Mathematical analysis", "Mathematical optimization", "Mathematical software", "Mean-shift", "Measure (data warehouse)", "Megaputer Intelligence", "Metadata", "Michael Lovell", "Microsoft", "Microsoft Academic Search", "Microsoft Analysis Services", "Middleware", "Misnomer", "Missing data", "Mixed reality", "Mlpack", "Model of computation", "Modeling language", "Morgan Kaufmann", "Multi-task learning", "MultiDimensional eXpressions", "Multi expression programming", "Multilayer perceptron", "Multilinear subspace learning", "Multimedia database", "Multiprocessing", "Multithreading (computer architecture)", "Multivariate statistics", "NLTK", "Naive Bayes classifier", "Named-entity recognition", "National Diet Library", "National Security Agency", "Natural Language Toolkit", "Natural language processing", "NetOwl", "Network architecture", "Network performance", "Network protocol", "Network scheduler", "Network security", "Network service", "Networking hardware", "Neural networks", "Non-negative matrix factorization", "Numerical analysis", "OCLC", "OLAP cube", "OPTICS algorithm", "Occam learning", "Online algorithm", "Online analytical processing", "Online machine learning", "Open-source software", "OpenNN", "Open Text Corporation", "Open access", "Open source model", "Operating system", "Operational data store", "Operations research", "Oracle Corporation", "Oracle Data Mining", "Orange (software)", "Outline of machine learning", "Overfitting", "PSeven", "Parallel computing", "Perceptron", "Peripheral", "Personally identifiable information", "Philip S. Yu", "Philosophy of artificial intelligence", "Photo manipulation", "Predictive Model Markup Language", "Predictive analytics", "Prentice Hall", "Principal component analysis", "Printed circuit board", "Probability", "Probably approximately correct learning", "Process control", "Profiling (information science)", "Programming language", "Programming language theory", "Programming paradigm", "Programming team", "Programming tool", "Psychometrics", "PubMed Identifier", "Python (programming language)", "Q-learning", "Qlucore", "Quantitative structure\u2013activity relationship", "ROLAP", "R (programming language)", "Ralph Kimball", "Random forest", "Randomized algorithm", "RapidMiner", "Real-time computing", "Receiver operating characteristic", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Rendering (computer graphics)", "Reproducibility", "Requirements analysis", "Restricted Boltzmann machine", "Reverse star schema", "Review of Economic Studies", "Rexer's Annual Data Miner Survey", "Robert Tibshirani", "SAS (software)", "SAS Institute", "SEMMA", "SIGKDD", "SIGMOD", "SPSS Modeler", "STATISTICA", "Scientific computing", "Scikit-learn", "Security service (telecommunication)", "Self-organizing map", "Semantics (computer science)", "Semi-supervised learning", "Sequence mining", "Sequential pattern mining", "Sixth normal form", "Slowly changing dimension", "Snowflake schema", "Social Science Research Network", "Social computing", "Social media mining", "Social software", "Software configuration management", "Software construction", "Software deployment", "Software design", "Software development", "Software development process", "Software framework", "Software maintenance", "Software quality", "Software repository", "Solid modeling", "Spatial index", "Spreadsheets", "Springer Verlag", "Star schema", "StatSoft", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical hypothesis testing", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical noise", "Statistics", "Stellar Wind (code name)", "Structured data analysis (statistics)", "Structured prediction", "Subspace clustering", "Supervised learning", "Support vector machine", "Support vector machines", "Surrogate key", "Surveillance", "Surveillance capitalism", "System on a chip", "T-distributed stochastic neighbor embedding", "Tanagra (machine learning)", "Temporal difference learning", "Test set", "Text mining", "The American Statistician", "Theory of computation", "Time series", "Torch (machine learning)", "Total Information Awareness", "Training set", "Trevor Hastie", "U-Net", "UIMA", "US Congress", "Ubiquitous computing", "Unsupervised learning", "Usama Fayyad", "Vapnik\u2013Chervonenkis theory", "Vertica", "Very Large Scale Integration", "Video games", "Virtual machine", "Virtual reality", "Visualization (computer graphics)", "Wayback Machine", "Web mining", "Web scraping", "Weka (machine learning)", "Word processor", "World Wide Web", "XML", "XML for Analysis"], "references": ["http://proquest.safaribooksonline.com.proxy.library.carleton.ca/book/databases/data-warehouses/9780123814791", "http://cs.nju.edu.cn/zhouzh/zhouzh.files/course/dm/reading/reading01/chen_tkde96.pdf", "http://www.britannica.com/EBchecked/topic/1056150/data-mining", "http://www.forrester.com/rb/Research/wave™_predictive_analytics_and_data_mining_solutions,/q/id/56077/t/2", "http://mediaproducts.gartner.com/reprints/sas/vol5/article3/article3.html", "http://hurwitz.com/recent-research/item/advanced-analytics-the-hurwitz-victory-index", "http://www.information-management.com/specialreports/20060124/1046025-1.html", "http://cdn.intechopen.com/pdfs/5937/InTech-A_data_mining_amp_knowledge_discovery_process_model.pdf", "http://www.kdnuggets.com/data_mining_course/x1-intro-to-data-mining-notes.html", "http://www.kdnuggets.com/gpspubs/aimag-kdd-overview-1996-Fayyad.pdf", "http://www.kdnuggets.com/meetings/kdd89/", "http://www.kdnuggets.com/polls/2002/methodology.htm", "http://www.kdnuggets.com/polls/2004/data_mining_methodology.htm", "http://www.kdnuggets.com/polls/2007/data_mining_methodology.htm", "http://www.kdnuggets.com/polls/2014/analytics-data-mining-data-science-methodology.html", "http://www.lexology.com/library/detail.aspx?g=a18c5b92-5a20-4d1d-a098-a3095046a88e", "http://academic.research.microsoft.com/?SearchDomain=2&SubDomain=7&entitytype=2", "http://www.out-law.com/en/articles/2014/june/researchers-given-data-mining-right-under-new-uk-copyright-laws/", "http://www.securityfocus.com/brief/277", "http://ssrn.com/abstract=546782", "http://www.washingtonspectator.com/articles/20070315surveillance_1.cfm", "http://www-stat.stanford.edu/~tibs/ElemStatLearn/", "http://libres.uncg.edu/ir/uncg/f/N_Kshetri_Big_2014.pdf", "http://ec.europa.eu/licences-for-europe-dialogue/en/content/about-site", "http://libereurope.eu/news/text-and-data-mining-its-importance-and-the-need-for-change-in-europe/", "http://www.ncbi.nlm.nih.gov/pubmed/14741005", "http://www.iadis.net/dl/final_uploads/200812P033.pdf", "http://www.analytics-magazine.org/may-june-2011/320-understanding-data-miners", "http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=451120", "http://www.counterpunch.org/2013/09/11/inside-the-tech-industrys-startup-conference/", "http://www.counterpunch.org/2013/12/03/iron-cagebook/", "http://doi.org/10.1002%2Fwidm.24", "http://doi.org/10.1016%2Fj.telpol.2014.10.002", "http://doi.org/10.1021%2Fci0342472", "http://doi.org/10.1145%2F2023598.2023605", "http://doi.org/10.1145%2F2207243.2207269", "http://doi.org/10.2307%2F1924403", "http://blogs.hbr.org/cs/2012/08/dont_build_a_database_of_ruin.html", "http://www.jstor.org/stable/1924403", "http://www.kdd.org/conferences.php", "http://www.kdd.org/curriculum/index.html", "http://www.kdd.org/exploration_files/survey.pdf", "http://www.kdd.org/explorations/about.php", "http://www.kdd.org/explorations/view/june-1999-volume-1-issue-1", "http://www.nascio.org/publications/documents/NASCIO-dataMining.pdf", "http://www.okairp.org/documents/2005%20Fall/F05_ROMEDataQualityETC.pdf", "http://www.stlr.org/cite.cgi?volume=5&article=2", "http://www.worldcat.org/oclc/45263753", "http://www.worldcat.org/oclc/50055336", "https://johnresig.com/files/research/SIAMPaper.pdf", "https://scholar.google.de/citations?view_op=top_venues&hl=en&vq=eng_datamininganalysis", "https://d-nb.info/gnd/4428654-5", "https://id.ndl.go.jp/auth/ndlna/00948240", "https://ww2.amstat.org/committees/ethics/linksdir/Jsm2005Seltzer.pdf", "https://web.archive.org/web/20081217063043/http://www.nascio.org/publications/documents/NASCIO-dataMining.pdf", "https://web.archive.org/web/20091110212529/http://www-stat.stanford.edu/~tibs/ElemStatLearn/", "https://web.archive.org/web/20100430120252/http://www.kdd.org/conferences.php", "https://web.archive.org/web/20130109114939/http://www.iadis.net/dl/final_uploads/200812P033.pdf", "https://web.archive.org/web/20140201170452/http://www.okairp.org/documents/2005%20Fall/F05_ROMEDataQualityETC.pdf", "https://web.archive.org/web/20140609020315/http://www.out-law.com/en/articles/2014/june/researchers-given-data-mining-right-under-new-uk-copyright-laws/", "https://arxiv.org/list/cs.LG/recent", "https://curlie.org/Computers/Software/Databases/Data_Mining/Tool_Vendors", "https://curlie.org/Reference/Knowledge_Management/Knowledge_Discovery/Software", "https://doi.org/10.1017%2FS0269888906000737", "https://www.jstor.org/pss/30037299", "https://www.webcitation.org/5SwZyJc43?url=http://www.washingtonspectator.com/articles/20070315surveillance_1.cfm", "https://www.wikidata.org/wiki/Q172491"]}, "Dynamic Bayesian network": {"categories": ["All stub articles", "Bayesian networks", "Statistics stubs"], "title": "Dynamic Bayesian network", "method": "Dynamic Bayesian network", "url": "https://en.wikipedia.org/wiki/Dynamic_Bayesian_network", "summary": "A Dynamic Bayesian Network (DBN) is a Bayesian network which relates variables to each other over adjacent time steps. This is often called a Two-Timeslice BN (2TBN) because it says that at any point in time T, the value of a variable can be calculated from the internal regressors and the immediate prior value (time T-1). DBNs were developed by Paul Dagum in the early 1990s at Stanford University's Section on Medical Informatics. Dagum developed DBNs to unify and extend traditional linear state-space models such as Kalman filters, linear and normal forecasting models such as ARMA and simple dependency models such as hidden Markov models into a general probabilistic representation and inference mechanism for arbitrary nonlinear and non-normal time-dependent domains.Today, DBNs are common in robotics, and have shown potential for a wide range of data mining applications. For example, they have been used in speech recognition, digital forensics, protein sequencing, and bioinformatics. DBN is a generalization of hidden Markov models and Kalman filters.DBNs are conceptually related to Probabilistic Boolean Networks and can, similarly, be used to model dynamical systems at steady-state.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f0/R%C3%A9seau_bay%C3%A9sien_3t.svg", "https://upload.wikimedia.org/wikipedia/commons/5/56/R%C3%A9seau_bay%C3%A9sien_dynamique.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d0/R%C3%A9seau_bay%C3%A9sien_simplifi%C3%A9.svg"], "links": ["ARMA model", "Adam Galper", "Adam Seiver", "Bayesian network", "Bioinformatics", "CiteSeerX", "Data mining", "Digital forensics", "Digital object identifier", "Eric Horvitz", "FreeBSD license", "GNU General Public License", "Generalized filtering", "GitHub", "Google Code", "Harri L\u00e4hdesm\u00e4ki", "Hidden Markov model", "Hidden Markov models", "Ilya Shmulevich", "International Standard Book Number", "Kalman filter", "Lecture Notes in Computer Science", "Olli Yli-Harjaa", "Paul Dagum", "Peter Norvig", "Prentice Hall", "Probabilistic logic network", "Protein", "PubMed Central", "Recursive Bayesian estimation", "Robotics", "Sampsa Hautaniemi", "Sequencing", "Speech recognition", "Stanford University", "State Space Model", "Statistics", "Stuart J. Russell"], "references": ["http://www.cs.ubc.ca/~murphyk/Thesis/thesis.html", "http://51lica.com/wp-content/uploads/2012/05/Artificial-Intelligence-A-Modern-Approach-3rd-Edition.pdf", "http://code.google.com/p/globalmit", "http://research.microsoft.com/en-us/um/people/horvitz/FORECAST.HTM", "http://research.microsoft.com/en-us/um/people/horvitz/dynamic_network_models_UAI_1992.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.7874", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.2969", "http://www-ksl.stanford.edu/KSL_Abstracts/KSL-91-64.html", "http://melodi.ee.washington.edu/gmtk/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1847796", "http://agrum.gitlab.io", "http://staff.science.uva.nl/~jmooij1/libDAI/", "http://doi.org/10.1016%2F0169-2070(94)02009-e", "http://www.bioss.ac.uk/~dirk/software/DBmcmc/", "https://github.com/bayesnet/bnt", "https://github.com/sysbiolux/FALCON/", "https://web.archive.org/web/20141020191456/http://51lica.com/wp-content/uploads/2012/05/Artificial-Intelligence-A-Modern-Approach-3rd-Edition.pdf", "https://dslpitt.org/uai/papers/93/p64-dagum.pdf"]}, "Cancer cluster": {"categories": ["Cancer clusters", "Epidemiology", "Medical statistics", "Use British English from December 2017", "Use dmy dates from December 2017", "Webarchive template wayback links"], "title": "Cancer cluster", "method": "Cancer cluster", "url": "https://en.wikipedia.org/wiki/Cancer_cluster", "summary": "A cancer cluster is a disease cluster in which a high number of cancer cases occurs in a group of people in a particular geographic area over a limited period of time.Historical examples of work-related cancer clusters are well documented in the medical literature. Notable examples include: scrotal cancer among chimney sweeps in 18th century London; osteosarcoma among female watch dial painters in the 20th century; skin cancer in farmers; bladder cancer in dye workers exposed to aniline compounds; and leukemia and lymphoma in chemical workers exposed to benzene.Cancer cluster suspicions usually arise when members of the general public report that their family members, friends, neighbors, or coworkers have been diagnosed with the same or related cancers. State or local health departments will investigate the possibility of a cancer cluster when a claim is filed. In order to justify investigating such claims, health departments conduct a preliminary review. Data will be collected and verified regarding: the types of cancer reported, numbers of cases, geographic area of the cases, and the patients clinical history. At this point, a committee of medical professionals will examine the data and determine whether or not an investigation (often lengthy and expensive) is justified.In the U.S., state and local health departments respond to more than 1,000 inquiries about suspected cancer clusters each year. It is possible that a suspected cancer cluster may be due to chance alone; however, only clusters that have a disease rate that is statistically significantly greater than the disease rate of the general population are investigated. Given the number of inquiries it is likely that many of these are due to chance alone. It is a well-known problem in interpreting data that random cases of cancer can appear to form clumps that are misinterpreted as a cluster.A cluster is less likely to be coincidental if the case consists of one type of cancer, a rare type of cancer, or a type of cancer that is not usually found in a certain age group. Between 5% to 15% of suspected cancer clusters are statistically significant.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/aa/Texas_Sharpshooter_Fallacy_illustration.png", "https://upload.wikimedia.org/wikipedia/commons/d/d6/WHO_Rod.svg"], "links": ["Aniline", "Benzene", "Biostatistics", "Bladder cancer", "Camp Lejeune water contamination", "Cancer", "Cancer Alley", "Cancer epidemiology", "Chimney sweep", "Clear cell carcinoma", "Cuzick\u2013Edwards test", "Diethylstilbestrol", "Digital object identifier", "Disease cluster", "Dye", "Environmental racism", "Fooled by Randomness", "Incidence (epidemiology)", "Leukemia", "List of cancer clusters", "London", "Lymphoma", "Osteosarcoma", "PubMed Identifier", "Radium Girls", "Risk assessment", "Skin cancer", "Statistical significance", "Texas sharpshooter fallacy", "Toms River (book)", "Toxicology", "Wayback Machine"], "references": ["http://www.abc.net.au/austory/content/2007/s1870108.htm", "http://www.epa.gov/region02/health/cancer_clusters.htm", "http://cis.nci.nih.gov/fact/3_58.htm", "http://www.niehs.nih.gov/", "http://www.ncbi.nlm.nih.gov/pubmed/15371285", "http://www.ncbi.nlm.nih.gov/pubmed/2356832", "http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1797849", "http://doi.org/10.3322%2Fcanjclin.54.5.273", "http://aje.oxfordjournals.org/cgi/content/abstract/132/supp1/23", "https://www.bbc.com/news/magazine-13374325", "https://www.cdc.gov/DES/consumers/research/understanding_cohort.html", "https://www.cdc.gov/nceh/clusters/default.htm", "https://www.cdc.gov/nceh/clusters/faq.htm", "https://web.archive.org/web/20041010003350/http://cis.nci.nih.gov/fact/3_58.htm", "https://web.archive.org/web/20041015033041/http://www3.cancer.gov/atlasplus/new.html"]}, "Parabolic fractal distribution": {"categories": ["Discrete distributions"], "title": "Parabolic fractal distribution", "method": "Parabolic fractal distribution", "url": "https://en.wikipedia.org/wiki/Parabolic_fractal_distribution", "summary": "In probability and statistics, the parabolic fractal distribution is a type of discrete probability distribution in which the logarithm of the frequency or size of entities in a population is a quadratic polynomial of the logarithm of the rank (with the largest example having rank 1). This can markedly improve the fit over a simple power-law relationship (see references below).\nIn the Laherr\u00e8re/Deheuvels paper below, examples include galaxy sizes (ordered by luminosity), towns (in the USA, France, and world), spoken languages (by number of speakers) in the world, and oil fields in the world (by size). They also mention utility for this distribution in fitting seismic events (no example). The authors assert the advantage of this distribution is that it can be fitted using the largest known examples of the population being modeled, which are often readily available and complete, then the fitted parameters found can be used to compute the size of the entire population. So, for example, the populations of the hundred largest cities on the planet can be sorted and fitted, and the parameters found used to extrapolate to the smallest villages, to estimate the population of the planet. Another example is estimating total world oil reserves using the largest fields.\nIn a number of applications, there is a so-called King effect where the top-ranked item(s) have a significantly greater frequency or size than the model predicts on the basis of the other items. The Laherr\u00e8re/Deheuvels paper shows the example of Paris, when sorting the sizes of towns in France. When the paper was written Paris was the largest city with about ten million inhabitants, but the next largest town had only about 1.5 million. Towns in France excluding Paris closely follow a parabolic distribution, well enough that the 56 largest gave a very good estimate of the population of the country. But that distribution would predict the largest city to have about two million inhabitants, not 10 million. The King Effect is named after the notion that a King must defeat all rivals for the throne and takes their wealth, estates and power, thereby creating a buffer between himself and the next-richest of his subjects. That specific effect (intentionally created) may apply to corporate sizes, where the largest businesses use their wealth to buy up smaller rivals. Absent intent, the King Effect may occur as a result of some persistent growth advantage due to scale, or to some unique advantage. Larger cities are more efficient connectors of people, talent and other resources. Unique advantages might include being a port city, or a Capital city where law is made, or a center of activity where physical proximity increases opportunity and creates a feedback loop. An example is the motion picture industry; where actors, writers and other workers move to where the most studios are, and new studios are founded in the same place because that is where the most talent resides.\nTo test for the King Effect, the distribution must be fitted excluding the 'k' top-ranked items, but without assigning new rank numbers to the remaining members of the \npopulation. For example, in France the ranks are (as of 2010):\n1. Paris, 12.09M \n2. Lyon, 2.12M \n3. Marseille, 1.72M \n4. Toulouse, 1.20M \n5. Lille, 1.15M\nA fitting algorithm would process pairs {(1,12.09), (2,2.12), (3,1.72), (4,1.20), (5,1.15)} and find the parameters for the best parabolic fit through those points. To test for the King Effect we just exclude the first pair (or first 'k' pairs), and find parabolic parameters that fit the remainder of the points. So for France we would\nfit the four points {(2,2.12), (3,1.72), (4,1.20), (5,1.15)}. Then we can use those parameters to estimate the size of cities ranked [1,k] and determine if they are King Effect members or normal members.\nBy comparison, Zipf's law fits a line through the points (also using the log of the rank and log of the value). A parabola (with one more parameter) will fit better, but far from the vertex the parabola is also nearly linear. Thus, although it is a judgment call for the statistician, if the fitted parameters put the vertex far from the points fitted, or if the parabolic curve is not a significantly better fit than a line, those may be symptomatic of overfitting (aka over-parameterization). The line (with two parameters instead of three) is probably the better generalization. More parameters always fit better, but at the cost of adding unexplained parameters or unwarranted assumptions (such as the assumption that a slight parabolic curve is a more appropriate model than a line).\nAlternatively, it is possible to force the fitted parabola to have its vertex at the rank 1 position. In that case, it is not certain the parabola will fit better (have less error) than a straight line; and the choice might be made between the two based on which has the least error.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Comptes rendus de l'Acad\u00e9mie des sciences", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "King effect", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Overfitting", "Parabola", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability distribution", "Probability mass function", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quadratic polynomial", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.hubbertpeak.com/laherrere/fractal.htm", "http://doi.org/10.1016%2FS1674-5264(09)60017-X"]}, "Lindeberg's condition": {"categories": ["Central limit theorem", "Statistical theorems"], "title": "Lindeberg's condition", "method": "Lindeberg's condition", "url": "https://en.wikipedia.org/wiki/Lindeberg%27s_condition", "summary": "In probability theory, Lindeberg's condition is a sufficient condition (and under certain conditions also a necessary condition) for the central limit theorem (CLT) to hold for a sequence of independent random variables. Unlike the classical CLT, which requires that the random variables in question have finite variance and be both independent and identically distributed, Lindeberg's CLT only requires that they have finite variance, satisfy Lindeberg's condition, and be independent. It is named after the Finnish mathematician Jarl Waldemar Lindeberg.", "images": [], "links": ["Central limit theorem", "Convergence in distribution", "Digital object identifier", "Independent and identically-distributed random variables", "Indicator function", "Jarl Waldemar Lindeberg", "Lyapunov condition", "Mathematische Zeitschrift", "Necessary and sufficient condition", "Normal distribution", "Probability space", "Probability theory", "Random variables", "Statistical independence", "Variance"], "references": ["http://gdz.sub.uni-goettingen.de/en/dms/load/img/?PPN=PPN266833020_0015&DMDID=dmdlog21", "http://doi.org/10.1007%2FBF01494395", "https://books.google.com/books?id=Q2IPAQAAMAAJ&pg=PA369"]}, "Congruence coefficient": {"categories": ["Factor analysis", "Psychometrics"], "title": "Congruence coefficient", "method": "Congruence coefficient", "url": "https://en.wikipedia.org/wiki/Congruence_coefficient", "summary": "In multivariate statistics, the congruence coefficient is an index of the similarity between factors that have been derived in a factor analysis. It was introduced in 1948 by Cyril Burt who referred to it as unadjusted correlation. It is also called Tucker's congruence coefficient after Ledyard Tucker who popularized the technique. Its values range between -1 and +1. It can be used to study the similarity of extracted factors across different samples of, for example, test takers who have taken the same test.", "images": [], "links": ["Column vector", "Cosine", "Cosine similarity", "Cyril Burt", "Factor analysis", "Ledyard Tucker", "Multivariate statistics", "Pearson product-moment correlation coefficient", "RV coefficient"], "references": ["http://wwwpub.utdallas.edu/~herve/Abdi-RV2007-pretty.pdf"]}, "Actuarial science": {"categories": ["Actuarial science", "All articles with unsourced statements", "Applied statistics", "Articles with Curlie links", "Articles with unsourced statements from December 2010", "Demography", "Formal sciences", "Insurance", "Use Harvard referencing from August 2014"], "title": "Actuarial science", "method": "Actuarial science", "url": "https://en.wikipedia.org/wiki/Actuarial_science", "summary": "Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, finance and other industries and professions. Actuaries are professionals who are qualified in this field through intense education and experience. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations.\nActuarial science includes a number of interrelated subjects, including mathematics, probability theory, statistics, finance, economics, and computer science. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes during the last 30 years due to the proliferation of high speed computers and the union of stochastic actuarial models with modern financial theory (Frees 1990).\nMany universities have undergraduate and graduate degree programs in actuarial science. In 2010, a study published by job search website CareerCast ranked actuary as the #1 job in the United States (Needleman 2010). The study used five key criteria to rank jobs: environment, income, employment outlook, physical demands, and stress. A similar study by U.S. News & World Report in 2006 included actuaries among the 25 Best Professions that it expects will be in great demand in the future (Nemko 2006).", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/47/Excerpt_from_CDC_2003_Table_1.pdf", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial control cycle", "Actuarial exam", "Actuary", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arbitrage-free", "Arithmetic mean", "Arlington, Virginia", "Armstrong investigation of 1905", "Asset allocation", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Black swan theory", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burial society", "California State Library", "Canonical correlation", "Cartography", "Casualty Actuarial Society", "Casualty insurance", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Chicago Sun-Times", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort (statistics)", "Cointegration", "Collective bargaining", "Columbarium", "Completeness (statistics)", "Compound interest", "Computer science", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curlie", "Data collection", "Data mining", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Deterministic", "Dickey\u2013Fuller test", "Digital object identifier", "Directors and officers liability insurance", "Discounted cash flow", "Divergence (statistics)", "Draper", "Durbin\u2013Watson statistic", "Econometrics", "Economics", "Edmond Halley", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "FASB", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finance", "Financial Accounting Standards Board", "Financial economics", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Friendly society", "G-test", "General insurance", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glass\u2013Steagall Act of 1932", "Goodness of fit", "Granger causality", "Graphical model", "Greece", "Grouped data", "Halley's comet", "Harmonic mean", "Harold Whetstone Johnston", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Institute and Faculty of Actuaries", "Insurance", "Interaction (statistics)", "Interest", "International Standard Book Number", 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(United States)", "Social Security Administration", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Supplemental Security Income", "Surety", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The Equitable Life Assurance Society", "Thucydides", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "U.S. News & World Report", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wall Street Journal", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.casualtyactuarialsociety.com/pubs/proceed/proceed80/80049.pdf", "http://www.economist.com/finance/displayStory.cfm?story_id=5436947", "http://cjb.sagepub.com/cgi/reprint/29/5/538.pdf", "http://www.suntimes.com/output/news/cst-nws-phil19.html", "http://mason.gmu.edu/~ihs/w91essay.html", "http://www.hsph.harvard.edu/faculty/WilliamHsiao.html", "http://www.hsph.harvard.edu/phcf/Papers/Ideology%20and%20theory%20-%20Hsiao.pdf", "http://classics.mit.edu/Thucydides/pelopwar.2.second.html", "http://classics.mit.edu/Thucydides/pelopwar.html", "http://www.math.umd.edu/~evs/s470/BookChaps/01Book.pdf", "http://www.math.umd.edu/~evs/s470/BookChaps/Chp6.pdf", "http://www.library.ca.gov/crb/06/08/06-008.pdf", "http://lccn.loc.gov/2001088378", "http://lccn.loc.gov/32007692", "http://lccn.loc.gov/94042650", "http://www.ncbi.nlm.nih.gov/pubmed/11523960", "http://www.actuarialfoundation.org/research_edu/fundamental.pdf", "http://www.casact.org/library/astin/vol27no2/165.pdf", "http://www.casact.org/pubs/proceed/proceed19/19201.pdf", "http://www.casact.org/pubs/proceed/proceed89/89045.pdf", "http://www.chbrp.org/documents/hearingaids174final.pdf", "http://www.contingencies.org/julaug06/actuarys_new_clothes_0706.asp", "http://doi.org/10.1098%2Frstl.1693.0007", "http://doi.org/10.1177%2F009385402236732", "http://doi.org/10.1215%2F03616878-26-4-733", "http://doi.org/10.2143%2Fast.27.2.542046", "http://doi.org/10.2307%2F1600548", "http://www.forumromanum.org/life/johnston.html", "http://www.forumromanum.org/life/johnston_14.html", "http://www.jstor.org/stable/1600548", "http://library.soa.org/library/tsa/1990-95/TSA90V427.pdf", "http://www.worldcat.org/issn/0041-9494", "http://www.worldcat.org/issn/0093-8548", "http://www.worldcat.org/issn/0260-7085", "http://www.worldcat.org/issn/0515-0361", "http://www.york.ac.uk/depts/maths/histstat/halley.pdf", "http://www.wiley.co.uk/eoas/pdfs/TAH012-.pdf", "http://www.actuaries.org.uk/knowledge/actuarial_history/history_of_profession", "http://www.actuaries.org.uk/research-and-resources/documents/overview-actuarial-history-slides-notes", "http://www.actuaries.org.uk/sites/all/files/documents/pdf/0233-0246.pdf", "http://www.the-actuary.org.uk/pdfs/02_12_08.pdf", "https://www.usnews.com/usnews/biztech/best_careers_2007/", "https://www.wsj.com/articles/SB10001424052748703580904574638321841284190", "https://chicagounbound.uchicago.edu/uclrev/vol70/iss1/8/", "https://web.archive.org/web/20060103161211/http://library.soa.org/library/tsa/1990-95/TSA90V427.pdf", "https://web.archive.org/web/20060629155610/http://www.actuarialfoundation.org/research_edu/fundamental.pdf", "https://web.archive.org/web/20060724173339/http://www.wiley.co.uk/eoas/pdfs/TAH012-.pdf", "https://web.archive.org/web/20060724173342/http://www.the-actuary.org.uk/pdfs/02_12_08.pdf", "https://web.archive.org/web/20070327231215/http://www.hsph.harvard.edu/faculty/WilliamHsiao.html", "https://web.archive.org/web/20071118105300/http://www.usnews.com/usnews/biztech/best_careers_2007/careertable-njs.htm", "https://web.archive.org/web/20080404072019/http://www.actuaries.org.uk/knowledge/actuarial_history/history_of_profession", "https://web.archive.org/web/20120320062211/http://www.actuaries.org.uk/sites/all/files/documents/pdf/0233-0246.pdf", "https://curlie.org/Business/Financial_Services/Insurance/Actuarial_Science"]}, "Orthogonal array testing": {"categories": ["Design of experiments", "Pages containing links to subscription-only content", "Survival analysis"], "title": "Orthogonal array testing", "method": "Orthogonal array testing", "url": "https://en.wikipedia.org/wiki/Orthogonal_array_testing", "summary": "Orthogonal array testing is a black box testing technique that is a systematic, statistical way of software testing. It is used when the number of inputs to the system is relatively small, but too large to allow for exhaustive testing of every possible input to the systems. It is particularly effective in finding errors associated with faulty logic within computer software systems. Orthogonal arrays can be applied in user interface testing, system testing, regression testing, configuration testing and performance testing.\nThe permutations of factor levels comprising a single treatment are so chosen that their responses are uncorrelated and therefore each treatment gives a unique piece of information. The net effects of organizing the experiment in such treatments is that the same piece of information is gathered in the minimum number of experiments.", "images": [], "links": ["All-pairs testing", "Black box testing", "Computer", "Configuration testing", "Digital object identifier", "Experiment", "Independence (probability theory)", "Information", "International Standard Book Number", "Latin square", "Logic", "Orthogonality", "Permutations", "Regression testing", "Software performance testing", "Software system", "Software systems", "Software testing", "Statistical", "System testing", "User interface"], "references": ["http://www.51testing.com/ddimg/uploadsoft/20090113/OATSEN.pdf", "http://www.phadkeassociates.com/index_rdexperttestplanning.htm", "http://support.sas.com/techsup/technote/ts723.html", "http://www.stickyminds.com/stickyfile.asp?i=3638556&j=94197&ext=.pdf", "http://doi.org/10.4249%2Fscholarpedia.9076", "http://www.scholarpedia.org/article/Orthogonal_arrays", "http://www.york.ac.uk/depts/maths/tables/orthogonal.htm", "https://paportal.phadkeassociates.net/learning.aspx"]}, "Spatial variability": {"categories": ["Global Positioning System", "Spatial data analysis"], "title": "Spatial variability", "method": "Spatial variability", "url": "https://en.wikipedia.org/wiki/Spatial_variability", "summary": "Spatial variability occurs when a quantity that is measured at different spatial locations exhibits values that differ across the locations. Spatial variability can be assessed using spatial descriptive statistics such as the range.\nLet us suppose, that the Rev' z(x) is perfectly known at any point x within the field under study. Then the uncertainty about z(x) is reduced to zero, whereas its spatial variability still exists. Uncertainty is closely related to the amount of spatial variability, but it is also strongly dependent upon sampling.4Geostatistical analyses have been strictly performed to study the spatial variability of pesticide sorption5-7 and degradation8 in the field. Webster and Oliver9 provided a description of geostatistical techniques. Describing uncertainty using geostatistics is not an activity exempt from uncertainty itself as variogram uncertainty may be large10 and spatial interpolation may be undertaken using different techniques.11\n\n", "images": [], "links": ["Descriptive statistics", "Geostatistics", "Range (statistics)", "Spatial descriptive statistics", "Variogram"], "references": ["http://gis.esri.com/library/userconf/proc05/papers/pap1184.pdf", "https://web.archive.org/web/20061001123614/http://amethyst.epa.gov/revatoolkit/Definitions.jsp", "https://web.archive.org/web/20100110102738/http://willingtoncropservices.co.uk/case_study_GPS-soil-sampling-nutrient-mapping.htm"]}, "Jarque\u2013Bera test": {"categories": ["Normality tests"], "title": "Jarque\u2013Bera test", "method": "Jarque\u2013Bera test", "url": "https://en.wikipedia.org/wiki/Jarque%E2%80%93Bera_test", "summary": "In statistics, the Jarque\u2013Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. The test is named after Carlos Jarque and Anil K. Bera. The test statistic JB is defined as\n\n \n \n \n \n \n J\n B\n \n \n =\n \n \n \n n\n \u2212\n k\n +\n 1\n \n 6\n \n \n \n (\n \n \n S\n \n 2\n \n \n +\n \n \n 1\n 4\n \n \n (\n C\n \u2212\n 3\n \n )\n \n 2\n \n \n \n )\n \n \n \n {\\displaystyle {\\mathit {JB}}={\\frac {n-k+1}{6}}\\left(S^{2}+{\\frac {1}{4}}(C-3)^{2}\\right)}\n where n is the number of observations (or degrees of freedom in general); S is the sample skewness, C is the sample kurtosis, and k is the number of regressors:\n\n \n \n \n S\n =\n \n \n \n \n \n \n \u03bc\n ^\n \n \n \n \n 3\n \n \n \n \n \n \n \u03c3\n ^\n \n \n \n \n 3\n \n \n \n \n =\n \n \n \n \n \n 1\n n\n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n (\n \n x\n \n i\n \n \n \u2212\n \n \n \n x\n \u00af\n \n \n \n \n )\n \n 3\n \n \n \n \n \n (\n \n \n \n 1\n n\n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n (\n \n x\n \n i\n \n \n \u2212\n \n \n \n x\n \u00af\n \n \n \n \n )\n \n 2\n \n \n \n )\n \n \n 3\n \n /\n \n 2\n \n \n \n \n ,\n \n \n {\\displaystyle S={\\frac {{\\hat {\\mu }}_{3}}{{\\hat {\\sigma }}^{3}}}={\\frac {{\\frac {1}{n}}\\sum _{i=1}^{n}(x_{i}-{\\bar {x}})^{3}}{\\left({\\frac {1}{n}}\\sum _{i=1}^{n}(x_{i}-{\\bar {x}})^{2}\\right)^{3/2}}},}\n \n\n \n \n \n C\n =\n \n \n \n \n \n \n \u03bc\n ^\n \n \n \n \n 4\n \n \n \n \n \n \n \u03c3\n ^\n \n \n \n \n 4\n \n \n \n \n =\n \n \n \n \n \n 1\n n\n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n (\n \n x\n \n i\n \n \n \u2212\n \n \n \n x\n \u00af\n \n \n \n \n )\n \n 4\n \n \n \n \n \n (\n \n \n \n 1\n n\n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n (\n \n x\n \n i\n \n \n \u2212\n \n \n \n x\n \u00af\n \n \n \n \n )\n \n 2\n \n \n \n )\n \n \n 2\n \n \n \n \n ,\n \n \n {\\displaystyle C={\\frac {{\\hat {\\mu }}_{4}}{{\\hat {\\sigma }}^{4}}}={\\frac {{\\frac {1}{n}}\\sum _{i=1}^{n}(x_{i}-{\\bar {x}})^{4}}{\\left({\\frac {1}{n}}\\sum _{i=1}^{n}(x_{i}-{\\bar {x}})^{2}\\right)^{2}}},}\n where \n \n \n \n \n \n \n \n \u03bc\n ^\n \n \n \n \n 3\n \n \n \n \n {\\displaystyle {\\hat {\\mu }}_{3}}\n and \n \n \n \n \n \n \n \n \u03bc\n ^\n \n \n \n \n 4\n \n \n \n \n {\\displaystyle {\\hat {\\mu }}_{4}}\n are the estimates of third and fourth central moments, respectively, \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n is the sample mean, and\n\n \n \n \n \n \n \n \n \u03c3\n ^\n \n \n \n \n 2\n \n \n \n \n {\\displaystyle {\\hat {\\sigma }}^{2}}\n is the estimate of the second central moment, the variance.\nIf the data comes from a normal distribution, the JB statistic asymptotically has a chi-squared distribution with two degrees of freedom, so the statistic can be used to test the hypothesis that the data are from a normal distribution. The null hypothesis is a joint hypothesis of the skewness being zero and the excess kurtosis being zero. Samples from a normal distribution have an expected skewness of 0 and an expected excess kurtosis of 0 (which is the same as a kurtosis of 3). As the definition of JB shows, any deviation from this increases the JB statistic.\nFor small samples the chi-squared approximation is overly sensitive, often rejecting the null hypothesis when it is true. Furthermore, the distribution of p-values departs from a uniform distribution and becomes a right-skewed uni-modal distribution, especially for small p-values. This leads to a large Type I error rate. The table below shows some p-values approximated by a chi-squared distribution that differ from their true alpha levels for small samples.\n\n(These values have been approximated using Monte Carlo simulation in Matlab)\nIn MATLAB's implementation, the chi-squared approximation for the JB statistic's distribution is only used for large sample sizes (> 2000). For smaller samples, it uses a table derived from Monte Carlo simulations in order to interpolate p-values.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anil K. 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control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Statsmodels", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Type I error", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Wolfram Mathematica", "Z-test"], "references": ["http://www.mathworks.com/access/helpdesk/help/toolbox/stats/jbtest.html", "http://reference.wolfram.com/language/ref/JarqueBeraALMTest.html", "http://www.alglib.net/statistics/hypothesistesting/jarqueberatest.php", "http://doi.org/10.1016%2F0165-1765(80)90024-5", "http://doi.org/10.1016%2F0165-1765(81)90035-5", "http://doi.org/10.1093%2Fbiomet%2F62.2.243", "http://www.jstor.org/stable/1403192", "http://www.jstor.org/stable/2335355", "https://cran.r-project.org/web/packages/moments/index.html", "https://cran.r-project.org/web/packages/tseries/index.html"]}, "Subgroup analysis": {"categories": ["All stub articles", "Design of experiments", "Medical statistics", "Statistical analysis", "Statistics stubs"], "title": "Subgroup analysis", "method": "Subgroup analysis", "url": "https://en.wikipedia.org/wiki/Subgroup_analysis", "summary": "Subgroup analysis, in the context of design and analysis of experiments, refers to looking for pattern in a subset of the subjects.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Design of experiments", "Digital object identifier", "NEJM", "Post-hoc analysis", "PubMed Identifier", "Statistics"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/16625007", "http://doi.org/10.1056%2FNEJMp068070", "http://www.nejm.org/doi/full/10.1056/NEJMp068070"]}, "Decision boundary": {"categories": ["All articles needing additional references", "All stub articles", "Articles needing additional references from September 2014", "Artificial intelligence stubs", "Classification algorithms", "Pattern recognition", "Statistical classification"], "title": "Decision boundary", "method": "Decision boundary", "url": "https://en.wikipedia.org/wiki/Decision_boundary", "summary": "In a statistical-classification problem with two classes, a decision boundary or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each class. The classifier will classify all the points on one side of the decision boundary as belonging to one class and all those on the other side as belonging to the other class.\nA decision boundary is the region of a problem space in which the output label of a classifier is ambiguous.If the decision surface is a hyperplane, then the classification problem is linear, and the classes are linearly separable.\nDecision boundaries are not always clear cut. That is, the transition from one class in the feature space to another is not discontinuous, but gradual. This effect is common in fuzzy logic based classification algorithms, where membership in one class or another is ambiguous.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/91/LampFlowchart.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Artificial intelligence", "Artificial neural network", "Backpropagation", "Compact space", "Continuous function", "Euclidean space", "Hyperplane", "Hypersurface", "Kernel trick", "Linearly separable", "Maximum-margin hyperplane", "Pattern recognition", "Perceptron", "Statistical classification", "Support vector machine", "Universal approximation theorem", "Vector space"], "references": ["http://www.cse.buffalo.edu/~jcorso/t/CSE555/files/quiz01_solutions.pdf"]}, "Forecast skill": {"categories": ["Climate and weather statistics", "Statistical forecasting", "Weather forecasting"], "title": "Forecast skill", "method": "Forecast skill", "url": "https://en.wikipedia.org/wiki/Forecast_skill", "summary": "Forecast skill (or skill score, forecast skill, prediction skill), in the fields of forecasting and prediction, is any measure of the accuracy and/or degree of association of prediction to an observation or estimate of the actual value of what is being predicted (formally, the predictand). \nIn meteorology, forecast skill in weather forecasting, a motivating application, measures the superiority of a forecast over a simple historical baseline of past observations. The same forecast methodology can result in different skill measurements at different places, or even in the same place for different seasons (e.g. spring weather might be driven by erratic local conditions, whereas winter cold snaps might correlate with observable polar winds). Forecast skill is often presented in the form of seasonal geographical maps. \nForecast skill for single-value forecasts is commonly represented in terms of metrics such as correlation, root mean squared error, mean absolute error, relative mean absolute error, bias, and the Brier score, among others. A number of scores associated with the concept of entropy in information theory are also being used.The term 'forecast skill' can be used both quantitatively and qualitatively. In the former case, skill could be equal to a statistic describing forecast performance, such as the correlation of the forecast with observations. In the latter case, it could either refer to forecast performance according to a single metric or to the overall forecast performance based on multiple metrics.", "images": [], "links": ["Bias (statistics)", "Bibcode", "Brier score", "Calibration (statistics)", "Correlation", "Data visualization", "Detection theory", "Digital object identifier", "Entropy (information theory)", "Forecasting", "International Standard Book Number", "International Standard Serial Number", "Mean absolute error", "Mean squared error", "Meteorology", "Prediction", "Relative mean absolute error", "Root mean squared error", "Weather forecasting"], "references": ["http://www.cawcr.gov.au/projects/verification/", "http://ams.allenpress.com/perlserv/?request=get-abstract&doi=10.1175/1520-0493(1988)116%3C2417:SSBOTM%3E2.0.CO%3B2", "http://ams.allenpress.com/perlserv/?request=get-document&doi=10.1175/1520-0434(1998)013%3C0783:TRDODD%3E2.0.CO%3B2", "http://amsglossary.allenpress.com/glossary/search?id=skill1", "http://store.elsevier.com/Statistical-Methods-in-the-Atmospheric-Sciences/Daniel-Wilks/isbn-9780123850225/", "http://amstat.tandfonline.com/doi/abs/10.1198/016214506000001437", "http://adsabs.harvard.edu/abs/1988MWRv..116.2417M", "http://adsabs.harvard.edu/abs/1998WtFor..13..783R", "http://adsabs.harvard.edu/abs/2010MWRv..138..203B", "http://doi.org/10.1175%2F1520-0434(1998)013%3C0783:TRDODD%3E2.0.CO;2", "http://doi.org/10.1175%2F1520-0493(1988)116%3C2417:SSBOTM%3E2.0.CO;2", "http://doi.org/10.1175%2F2009MWR2945.1", "http://doi.org/10.1198%2F016214506000001437", "http://www.worldcat.org/issn/0162-1459", "https://journals.ametsoc.org/doi/abs/10.1175/2009MWR2945.1"]}, "Graph cuts in computer vision": {"categories": ["Bayesian statistics", "Computational problems in graph theory", "Computer vision", "Image segmentation"], "title": "Graph cuts in computer vision", "method": "Graph cuts in computer vision", "url": "https://en.wikipedia.org/wiki/Graph_cuts_in_computer_vision", "summary": "As applied in the field of computer vision, graph cuts can be employed to efficiently solve a wide variety of low-level computer vision problems (early vision), such as image smoothing, the stereo correspondence problem, image segmentation, and many other computer vision problems that can be formulated in terms of energy minimization. Many of these energy minimization problems can be approximated by solving a maximum flow problem in a graph (and thus, by the max-flow min-cut theorem, define a minimal cut of the graph). Under most formulations of such problems in computer vision, the minimum energy solution corresponds to the maximum a posteriori estimate of a solution. Although many computer vision algorithms involve cutting a graph (e.g., normalized cuts), the term \"graph cuts\" is applied specifically to those models which employ a max-flow/min-cut optimization (other graph cutting algorithms may be considered as graph partitioning algorithms).\n\"Binary\" problems (such as denoising a binary image) can be solved exactly using this approach; problems where pixels can be labeled with more than two different labels (such as stereo correspondence, or denoising of a grayscale image) cannot be solved exactly, but solutions produced are usually near the global optimum.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20090117131236%21Wikibooks-logo-en-noslogan.svg"], "links": ["Bayesian statistics", "Binary image", "Computer vision", "Conditional random field", "Correspondence problem", "Cut (graph theory)", "Donald Geman", "Durham University", "Energy function", "Energy minimization", "Flow network", "Global optimum", "Graph (discrete mathematics)", "Graph coloring", "Graph partitioning", "Grayscale", "Greedy algorithm", "Image segmentation", "Iterated conditional modes", "Journal of the Royal Statistical Society", "Julian Besag", "MAP estimate", "Markov random field", "Max-flow min-cut theorem", "Maximum flow problem", "Polynomial time", "Random walker algorithm", "Simulated annealing", "Smoothing", "Watershed (image processing)"], "references": ["http://pub.ist.ac.at/~vnk/software.html", "http://step.polymtl.ca/~rv101/bandedgraphcuts.pdf", "http://vision.csd.uwo.ca/code/", "http://gridcut.com/", "http://research.microsoft.com/pubs/69040/lazysnapping_siggraph04.pdf", "http://virtualscalpel.com/", "http://www.cs.berkeley.edu/~malik/papers/MalikBLS.pdf", "http://www.cs.cornell.edu/~rdz/Papers/BVZ-cvpr98.pdf", "http://www.cs.cornell.edu/~rdz/Papers/BVZ-pami01-final.pdf", "http://persci.mit.edu/pub_pdfs/elements91.pdf", "http://www.research.rutgers.edu/~xiaolei/EMMCVPR_paper.pdf", "http://lipn.fr/~lerme/docs/reducing_graphs_in_graph_cut_segmentation.pdf", "http://leogrady.net/wp-content/uploads/2017/01/couprie2011power.pdf", "http://leogrady.net/wp-content/uploads/2017/01/grady2009combinatorial.pdf"]}, "Augmented Dickey\u2013Fuller test": {"categories": ["CS1 maint: Archived copy as title", "Time series statistical tests", "Wikipedia articles needing page number citations from June 2012"], "title": "Augmented Dickey\u2013Fuller test", "method": "Augmented Dickey\u2013Fuller test", "url": "https://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test", "summary": "In statistics and econometrics, an augmented Dickey\u2013Fuller test (ADF) tests the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity. It is an augmented version of the Dickey\u2013Fuller test for a larger and more complicated set of time series models.\nThe augmented Dickey\u2013Fuller (ADF) statistic, used in the test, is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence.\n\n", "images": [], "links": ["ADF-GLS test", "Akaike information criterion", "Alternative hypothesis", "Bayesian information criterion", "Biometrika", "David Dickey", "Dickey\u2013Fuller test", "Digital object identifier", "EViews", "Econometrica", "Econometrics", "Gretl", "Hannan\u2013Quinn information criterion", "International Standard Book Number", "JSTOR", "Java (programming language)", "KPSS test", "Matlab", "Null hypothesis", "Phillips\u2013Perron test", "Python (programming language)", "R (programming language)", "Random walk", "SAS (software)", "Sample (statistics)", "Stata", "Stationarity (statistics)", "Statistics", "Statsmodels", "T-value", "Time series", "Trend stationary", "Unit root", "Unit root test", "William Greene (economist)", "YouTube"], "references": ["http://econterms.com/glossary.cgi?action%3D++Search++%26query%3Daugmented+dickey-fuller", "http://forums.eviews.com/viewtopic.php?f=18&t=939#p3291", "http://www.mathworks.com/access/helpdesk/help/toolbox/econ/adftest.html", "http://www.mathworks.com/products/econometrics", "http://www.numericalmethod.com/trac/numericalmethod/wiki/SuanShu", "http://www2.sas.com/proceedings/sugi30/192-30.pdf", "http://www.spatial-econometrics.com/", "http://spot.colorado.edu/~mcnownr/gretl_lab/Introduction-to-gretl-presentation.pdf", "http://faculty.smu.edu/tfomby/eco6375/BJ%20Notes/ADF%20Notes.pdf", "http://finzi.psych.upenn.edu/R/library/tseries/html/adf.test.html", "http://www.hkbu.edu.hk/~billhung/econ3600/application/app01/app01.html", "http://statsmodels.sourceforge.net/devel/generated/statsmodels.tsa.stattools.adfuller.html", "http://doi.org/10.1093%2Fbiomet%2F71.3.599", "http://www.inside-r.org/packages/cran/forecast/docs/ndiffs", "http://www.jstor.org/stable/2171846", "https://www.stata.com/manuals13/tsdfuller.pdf", "https://www.youtube.com/watch?v=lTpUcY3d3qQ", "https://fabian-kostadinov.github.io/2015/01/27/comparing-adf-test-functions-in-r/", "https://web.archive.org/web/20090302082540/http://econterms.com/glossary.cgi?action=++Search++&query=augmented+dickey-fuller", "https://cran.r-project.org/web/packages/urca/urca.pdf"]}, "Wilcoxon signed-rank test": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from February 2017", "Nonparametric statistics", "Statistical tests", "U-statistics"], "title": "Wilcoxon signed-rank test", "method": "Wilcoxon signed-rank test", "url": "https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test", "summary": "The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test, t-test for matched pairs, or the t-test for dependent samples when the population cannot be assumed to be normally distributed. A Wilcoxon signed-rank test is a nonparametric test that can be used to determine whether two dependent samples were selected from populations having the same distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute value", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frank Wilcoxon", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "GNU Octave", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Interval scale", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann-Whitney-Wilcoxon test", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normally distributed", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal scale", "Ordinary least squares", "Outline of statistics", "P-value", "Paired difference test", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Ranking", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sidney Siegel", "Sign function", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Z-test", "Z score"], "references": ["http://www.r-tutor.com/elementary-statistics/non-parametric-methods/wilcoxon-signed-rank-test", "http://journals.sagepub.com/doi/full/10.2466/11.IT.3.1", "http://core.ecu.edu/psyc/wuenschk/docs30/Nonparametric-EffectSize.pdf", "http://sci2s.ugr.es/keel/pdf/algorithm/articulo/wilcoxon1945.pdf", "http://accord-framework.net/docs/html/T_Accord_Statistics_Testing_WilcoxonSignedRankTest.htm", "http://www.alglib.net/statistics/hypothesistesting/wilcoxonsignedrank.php", "http://vassarstats.net/textbook/ch12a.html", "http://vassarstats.net/wilcoxon.html", "http://doi.org/10.1080%2F01621459.1959.10501526", "http://doi.org/10.2307%2F3001968", "http://doi.org/10.2466%2F11.IT.3.1", "http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wilcoxon.html", "http://www.sussex.ac.uk/Users/grahamh/RM1web/WilcoxonTable2005.pdf", "https://books.google.com/books?id=YI0kT8cuiVUC&pg=PA99", "https://books.google.com/books?id=ebfRAAAAMAAJ&dq=Wilcoxon+statistics+for+the+behavioral+sciences+Non-parametric&q=Wilcoxon#search_anchor"]}, "Principal stratification": {"categories": ["All stub articles", "Causal inference", "Statistical methods", "Statistics stubs"], "title": "Principal stratification", "method": "Principal stratification", "url": "https://en.wikipedia.org/wiki/Principal_stratification", "summary": "Principal stratification is a statistical technique used in causal inference when adjusting results for post-treatment covariates. The idea is to identify underlying strata and then compute causal effects only within strata. It is a generalization of the Local Average Treatment Effect (LATE).", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Causal inference", "Digital object identifier", "Instrumental variable", "Journal of the American Statistical Association", "PubMed Identifier", "Rubin causal model", "Statistical", "Statistics"], "references": ["http://www.biostat.jhsph.edu/~cfrangak/papers/preffects.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/11890317", "http://doi.org/10.1111/j.0006-341X.2002.00021.x", "https://doi.org/10.1093%2Fbiostatistics%2Fkxm027", "https://doi.org/10.1177%2F1098214013481666", "https://doi.org/10.1177%2F1740774510367811", "https://doi.org/10.1198%2F016214503000071", "https://doi.org/10.3102%2F10769986028004353"]}, "Item response theory": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from December 2015", "Articles needing additional references from July 2014", "Articles with unsourced statements from March 2016", "Comparison of assessments", "Educational assessment and evaluation", "Latent variable models", "Psychometrics", "Webarchive template wayback links"], "title": "Item response theory", "method": "Item response theory", "url": "https://en.wikipedia.org/wiki/Item_response_theory", "summary": "In psychometrics, item response theory (IRT) (also known as latent trait theory, strong true score theory, or modern mental test theory) is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. It is a theory of testing based on the relationship between individuals' performances on a test item and the test takers' levels of performance on an overall measure of the ability that item was designed to measure. Several different statistical models are used to represent both item and test taker characteristics. Unlike simpler alternatives for creating scales and evaluating questionnaire responses, it does not assume that each item is equally difficult. This distinguishes IRT from, for instance, Likert scaling, in which \"All items are assumed to be replications of each other or in other words items are considered to be parallel instruments\" (p. 197). By contrast, item response theory treats the difficulty of each item (the item characteristic curves, or ICCs) as information to be incorporated in scaling items. \nIt is based on the application of related mathematical models to testing data. Because it is often regarded as superior to classical test theory, it is the preferred method for developing scales in the United States, especially when optimal decisions are demanded, as in so-called high-stakes tests, e.g., the Graduate Record Examination (GRE) and Graduate Management Admission Test (GMAT).\nThe name item response theory is due to the focus of the theory on the item, as opposed to the test-level focus of classical test theory. Thus IRT models the response of each examinee of a given ability to each item in the test. The term item is generic, covering all kinds of informative items. They might be multiple choice questions that have incorrect and correct responses, but are also commonly statements on questionnaires that allow respondents to indicate level of agreement (a rating or Likert scale), or patient symptoms scored as present/absent, or diagnostic information in complex systems.\nIRT is based on the idea that the probability of a correct/keyed response to an item is a mathematical function of person and item parameters. The person parameter is construed as (usually) a single latent trait or dimension. Examples include general intelligence or the strength of an attitude. Parameters on which items are characterized include their difficulty (known as \"location\" for their location on the difficulty range); discrimination (slope or correlation), representing how steeply the rate of success of individuals varies with their ability; and a pseudoguessing parameter, characterising the (lower) asymptote at which even the least able persons will score due to guessing (for instance, 25% for pure chance on a multiple choice item with four possible responses).\nIn the same manner, IRT can be used to measure human behaviour in online social networks. The views expressed by different people can be aggregated to be studied using IRT. Its use in classifying information as misinformation or true information has also been evaluated.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/7b/3PL_IRF.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accuracy", "Additive map", "Asymptote", "Benjamin Drake Wright", "Certification", "Chi-square statistic", "Classical test theory", "Computer-adaptive test", "Concept inventory", "Confirmation bias", "Correlation", "Cronbach's alpha", "Cumulative distribution function", "Cumulative normal", "Data", "David Andrich", "Differential item functioning", "Digital object identifier", "Educational Testing Service", "Equating", "Factor analysis", "Fisher information", "Frederic M. Lord", "Georg Rasch", "Google Books", "Graduate Management Admission Test", "Graduate Record Examination", "High-stakes testing", "Intelligence", "International Standard Book Number", "Karl Gustav J\u00f6reskog", "Likert scale", "Likert scaling", "Local independence", "Logistic function", "Logit", "Marginal maximum likelihood", "Mathematical function", "Mathematical model", "Mean", "Measurement", "Measurement error", "Monotonic function", "Multiple choice", "Newton-Raphson", "Odds", "Ogive", "Ogive (statistics)", "Orthogonal", "Parameters", "Paul Lazarsfeld", "Person-fit analysis", "Personal computer", "Point-biserial correlation coefficient", "Probability", "Psychometrics", "PubMed Identifier", "Questionnaire", "Rasch model", "Rating scale", "Reliability (psychometric)", "Reliability (statistics)", "Scale (social sciences)", "Specific objectivity", "Standard deviation", "Standard error of estimation", "Standard error of measurement", "Standardized test", "Stata", "Test (student assessment)", "University of Illinois at Chicago", "Wayback Machine"], "references": ["http://www.assess.com/docs/Thompson_(2009)_-_Ability_estimation_with_IRT.pdf", "http://www.creative-wisdom.com/computer/sas/IRT.pdf", "http://sites.google.com/site/benroydo/irt-tutorial", "http://www.john-uebersax.com/stat/lta.htm", "http://www.john-uebersax.com/stat/papers.htm", "http://larrynelsonstuff.com/Documentation/IRTinLertap5.pdf", "http://journals.lww.com/lww-medicalcare/Abstract/2004/01001/Controversy_and_the_Rasch_Model__A_Characteristic.2.aspx", "http://www.rasch-analysis.com/", "http://apm.sagepub.com/content/23/4/283.short", "http://www.springerlink.com/content/c676744078511265/", "http://www.ssicentral.com/irt/index.html", "http://www.vpgcentral.com/irt-software/", "http://onlinelibrary.wiley.com/doi/10.1111/j.1745-3984.1995.tb00471.x/abstract", "http://onlinelibrary.wiley.com/doi/10.1111/j.1745-3984.1996.tb00485.x/abstract", "http://www.winsteps.com", "http://www.uic.edu/classes/ot/ot540/history.html", "http://www.umass.edu/remp/main_software.html", "http://eric.ed.gov/ERICWebPortal/custom/portlets/recordDetails/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=ED441789&ERICExtSearch_SearchType_0=no&accno=ED441789", "http://www.ncbi.nlm.nih.gov/pubmed/14707751", "http://www.apa.org/science/standards.html", "http://doi.org/10.1007%2FBF02293801", "http://doi.org/10.1097%2F01.mlr.0000103528.48582.7c", "http://doi.org/10.1111%2Fj.1745-3984.1995.tb00471.x", "http://doi.org/10.1111%2Fj.1745-3984.1996.tb00485.x", "http://doi.org/10.1177%2F01466219922031400", "http://edres.org/irt/", "http://edres.org/irt/baker/", "http://www.ets.org/portal/site/ets/menuitem.c988ba0e5dd572bada20bc47c3921509/?vgnextoid=26fdaf5e44df4010VgnVCM10000022f95190RCRD&vgnextchannel=ceb2be3a864f4010VgnVCM10000022f95190RCRD", "http://www.ncme.org/ncme/NCME/Resource_Center/Glossary/NCME/Resource_Center/Glossary1.aspx?hkey=4bb87415-44dc-4088-9ed9-e8515326a061#anchorI", "http://rasch.org/rmt/rmt34b.htm", "https://books.google.com/books?id=BZcPc4ffSTEC", "https://books.google.com/books?id=M2NYAAAAYAAJ", "https://books.google.com/books?id=aytUuwl4ku0C", "https://books.google.com/books?id=pDeLy5L14mAC", "https://books.google.com/books?id=rYU7rsi53gQC", "https://books.google.com/books?id=wS8VEMtJ3UYC", "https://books.google.com/books?id=y-Q_Q7pasJ0C", "https://web.archive.org/web/20041210140342/http://work.psych.uiuc.edu/irt/tutorial.asp", "https://web.archive.org/web/20060613221419/http://www.b-a-h.com/software/irt/icl/", "https://web.archive.org/web/20170722194028/http://www.ncme.org/ncme/NCME/Resource_Center/Glossary/NCME/Resource_Center/Glossary1.aspx?hkey=4bb87415-44dc-4088-9ed9-e8515326a061#anchorI", "https://cran.r-project.org/web/views/Psychometrics.html"]}, "Probit model": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2009", "Categorical regression models", "Classification algorithms"], "title": "Probit model", "method": "Probit model", "url": "https://en.wikipedia.org/wiki/Probit_model", "summary": "In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from probability + unit. The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model.\nA probit model is a popular specification for an ordinal or a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. The probit model, which employs a probit link function, is most often estimated using the standard maximum likelihood procedure, such an estimation being called a probit regression.\nProbit models were introduced by Chester Bliss in 1934; a fast method for computing maximum likelihood estimates for them was proposed by Ronald Fisher as an appendix to Bliss' work in 1935.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Binary classification", "Binomial regression", "Chester Ittner Bliss", "Christian Gouri\u00e9roux", "Concave function", "Consistent estimator", "Cumulative distribution function", "Dependent variable", "Digital object identifier", "Discrete choice", "Efficiency (statistics)", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Gibbs sampling", "Goodness of fit", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Iverson bracket", "JSTOR", "John Nelder", "Latent variable model", "Least-angle regression", "Least absolute deviations", "Least squares", "Limited dependent variable", "Linear least squares", "Linear regression", "Link function", "Local regression", "Logistic regression", "Logit model", "Loss of generality", "Mark Thoma", "Maximum likelihood", "Maximum likelihood estimation", "Mean and predicted response", "Minimum chi-square estimation", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Normal distribution", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Peter McCullagh", "Poisson regression", "Polynomial regression", "Portmanteau", "Principal component regression", "Prior distribution", "Probability", "Probability density function", "Probit", "Probit function", "PubMed Identifier", "Quantile regression", "R (programming language)", "Random effects model", "Regression analysis", "Regression model validation", "Regressor", "Regularized least squares", "Rejection sampling", "Robust regression", "Ronald Fisher", "Science (journal)", "Segmented regression", "Semiparametric regression", "Separation (statistics)", "Simple linear regression", "Statistical unit", "Statistics", "Studentized residual", "Tikhonov regularization", "Tobit model", "Total least squares", "Truncated distribution", "Truncated normal distribution", "Weighted least squares", "YouTube"], "references": ["http://ebooks.adelaide.edu.au/dspace/handle/2440/15223", "http://www.ats.ucla.edu/stat/stata/dae/ologit.htm", "http://www.ncbi.nlm.nih.gov/pubmed/17813446", "http://doi.org/10.1080%2F01621459.1993.10476321", "http://doi.org/10.1111%2Fj.1744-7348.1935.tb07713.x", "http://doi.org/10.1126%2Fscience.79.2037.38", "http://www.jstor.org/stable/2290350", "https://books.google.com/books?id=0bzGQE14CwEC&pg=PA267", "https://books.google.com/books?id=dE2prs_U0QMC&pg=PA6", "https://www.youtube.com/watch?v=JvioZoK1f4o&list=PLD15D38DC7AA3B737&index=17&t=44m11s", "https://archive.is/20140430203018/http://ebooks.adelaide.edu.au/dspace/handle/2440/15223"]}, "Kernel principal component analysis": {"categories": ["Dimension reduction", "Kernel methods for machine learning", "Machine learning algorithms", "Signal processing"], "title": "Kernel principal component analysis", "method": "Kernel principal component analysis", "url": "https://en.wikipedia.org/wiki/Kernel_principal_component_analysis", "summary": "In the field of multivariate statistics, kernel principal component analysis (kernel PCA) \n\nis an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_pca_input.png", "https://upload.wikimedia.org/wikipedia/commons/d/d0/Kernel_pca_output.png", "https://upload.wikimedia.org/wikipedia/commons/d/da/Kernel_pca_output_gaussian.png"], "links": ["Almost always", "Cluster analysis", "Covariance matrix", "Digital object identifier", "Eigendecomposition of a matrix", "Gaussian", "Gramian matrix", "Hyperplane", "Kernel methods", "Kernel trick", "Linear separability", "Multilinear principal component analysis", "Multilinear subspace learning", "Multivariate statistics", "Nonlinear dimensionality reduction", "Principal component analysis", "Reproducing kernel Hilbert space", "Spectral clustering"], "references": ["http://www.heikohoffmann.de/kpca.html", "http://citeseer.ist.psu.edu/old/mika99kernel.html", "http://doi.org/10.1016%2Fj.patcog.2006.07.009", "http://doi.org/10.1162%2F089976698300017467", "http://www.face-rec.org/algorithms/Kernel/kernelPCA_scholkopf.pdf"]}, "Neyman construction": {"categories": ["All stub articles", "Estimation methods", "Statistics stubs"], "title": "Neyman construction", "method": "Neyman construction", "url": "https://en.wikipedia.org/wiki/Neyman_construction", "summary": "Neyman construction is a frequentist method to construct an interval at a confidence level \n \n \n \n C\n ,\n \n \n \n {\\displaystyle C,\\,}\n such that if we repeat the experiment many times the interval will contain the true value of some parameter a fraction \n \n \n \n C\n \n \n \n {\\displaystyle C\\,}\n of the time. It is named after Jerzy Neyman.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Confidence level", "Coverage probability", "Frequentist", "Jerzy Neyman", "Probability interpretations", "Pseudo-experiment", "Statistics"], "references": ["https://www.jstor.org/stable/91337"]}, "Shrinkage (statistics)": {"categories": ["All stub articles", "Estimation theory", "Statistics stubs"], "title": "Shrinkage (statistics)", "method": "Shrinkage (statistics)", "url": "https://en.wikipedia.org/wiki/Shrinkage_(statistics)", "summary": "In statistics, shrinkage has two meanings:\n\nIn relation to the general observation that, in regression analysis, a fitted relationship appears to perform less well on a new data set than on the data set used for fitting. In particular the value of the coefficient of determination 'shrinks'. This idea is complementary to overfitting and, separately, to the standard adjustment made in the coefficient of determination to compensate for the subjunctive effects of further sampling, like controlling for the potential of new explanatory terms improving the model by chance: that is, the adjustment formula itself provides \"shrinkage.\" But the adjustment formula yields an artificial shrinkage, in contrast to the first definition.\nTo describe general types of estimators, or the effects of some types of estimation, whereby a naive or raw estimate is improved by combining it with other information (see shrinkage estimator). The term relates to the notion that the improved estimate is at a reduced distance from the value supplied by the 'other information' than is the raw estimate. In this sense, shrinkage is used to regularize ill-posed inference problems.A common idea underlying both of these meanings is the reduction in the effects of sampling variation.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Coefficient of determination", "Estimator", "Ill-posed problem", "International Standard Book Number", "Overfitting", "Regression analysis", "Regularization (mathematics)", "Shrinkage estimator", "Statistical inference", "Statistics"], "references": []}, "Seasonal adjustment": {"categories": ["All articles needing additional references", "All pages needing cleanup", "Articles needing additional references from July 2011", "Articles needing cleanup from March 2017", "Cleanup tagged articles with a reason field from March 2017", "Seasonality", "Time series", "Wikipedia pages needing cleanup from March 2017"], "title": "Seasonal adjustment", "method": "Seasonal adjustment", "url": "https://en.wikipedia.org/wiki/Seasonal_adjustment", "summary": "Seasonal adjustment is a statistical method for removing the seasonal component of a time series that exhibits a seasonal pattern. It is usually done when wanting to analyse the trend, and cyclical deviations from trend, of a time series independently of the seasonal components. It is normal to report seasonally adjusted data for unemployment rates to reveal the underlying trends and cycles in labor markets. Many economic phenomena have seasonal cycles, such as agricultural production and consumer consumption, e.g. greater consumption leading up to Christmas. It is necessary to adjust for this component in order to understand what underlying trends are in the economy and so official statistics are often adjusted to remove seasonal components.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bank of Spain", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias (statistics)", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Bureau of Labor Statistics", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Christmas", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demetra+", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Dummy variable (statistics)", "Durbin\u2013Watson statistic", "EViews", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric Ghysels", "Errors and residuals in statistics", "Estimating equations", "European Central Bank", "European Union", "Eurostat", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Frisch\u2013Waugh\u2013Lovell theorem", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Bank of Belgium", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Periodic sequence", "Permutation test", "Phillips\u2013Perron test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Pork cycle", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "SAS programming language", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonality", "Seasonally adjusted annual rate", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "TRAMO", "The Guardian", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Unemployment", "Uniformly most powerful test", "Unit root", "United States Census Bureau", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "X-12-ARIMA", "Z-test"], "references": ["http://www.stamp-software.com/stamp.html", "http://ec.europa.eu/eurostat/documents/3859598/5910549/KS-RA-09-006-EN.PDF", "http://www.bls.gov/cps/seasfaq.htm", "https://www.theguardian.com/business/2012/feb/17/retail-spending-rise-uk-recession", "https://www.bls.gov/osmr/pdf/ec140040.pdf", "https://www.census.gov/const/www/faq2.html", "https://web.archive.org/web/20101117151240/http://epp.eurostat.ec.europa.eu/cache/ITY_OFFPUB/KS-RA-09-006/EN/KS-RA-09-006-EN.PDF", "https://web.archive.org/web/20110720161129/http://circa.europa.eu/irc/dsis/eurosam/info/data/demetra.htm", "https://web.archive.org/web/20111018232034/http://www.cros-portal.eu/page/seasonal-adjustment", "https://web.archive.org/web/20111220031628/http://www.bls.gov/cps/seasfaq.htm", "https://web.archive.org/web/20140426234157/https://stats.oecd.org/glossary/detail.asp?ID=2398", "https://web.archive.org/web/20150509170945/http://www.stamp-software.com/stamp.html", "https://web.archive.org/web/20161206010053/https://cran.r-project.org/web/packages/x12/x12.pdf", "https://web.archive.org/web/20170113192428/http://www.census.gov/const/www/faq2.html", "https://web.archive.org/web/20170308150132/https://www.theguardian.com/business/2012/feb/17/retail-spending-rise-uk-recession", "https://web.archive.org/web/20180117032938/https://www.otexts.org/fpp/2/1", "https://web.archive.org/web/20180117033723/https://www.otexts.org/fpp/6/4", "https://web.archive.org/web/20180512020106/https://www.otexts.org/fpp/6/5", "https://web.archive.org/web/20180512020106/https://www.otexts.org/fpp/6/1", "https://stats.oecd.org/glossary/detail.asp?ID=2398", "https://www.otexts.org/fpp/2/1", "https://www.otexts.org/fpp/6/1", "https://www.otexts.org/fpp/6/4", "https://www.otexts.org/fpp/6/5", "https://cran.r-project.org/web/packages/x12/x12.pdf"]}, "Cram\u00e9r's theorem (large deviations)": {"categories": ["Large deviations theory", "Probability theorems"], "title": "Cram\u00e9r's theorem (large deviations)", "method": "Cram\u00e9r's theorem (large deviations)", "url": "https://en.wikipedia.org/wiki/Cram%C3%A9r%27s_theorem_(large_deviations)", "summary": "Cram\u00e9r's theorem is a fundamental result in the theory of large deviations, a subdiscipline of probability theory. It determines the rate function of a series of iid random variables.\nA weak version of this result was first shown by Harald Cram\u00e9r in 1938.", "images": [], "links": ["Cumulant", "Digital object identifier", "Encyclopedia of Mathematics", "Harald Cram\u00e9r", "Iid", "International Standard Book Number", "Large deviation principle", "Large deviations theory", "Legendre transform", "Michiel Hazewinkel", "Probability theory", "Random variable", "Random variables", "Rate function"], "references": ["http://doi.org/10.1007%2F978-1-84800-048-3", "https://www.encyclopediaofmath.org/index.php?title=p/c027000"]}, "CURE data clustering algorithm": {"categories": ["All articles with unsourced statements", "Articles with example pseudocode", "Articles with unsourced statements from May 2015", "Articles with unsourced statements from May 2018", "Cluster analysis algorithms"], "title": "CURE algorithm", "method": "CURE data clustering algorithm", "url": "https://en.wikipedia.org/wiki/CURE_algorithm", "summary": "CURE (Clustering Using REpresentatives) is an efficient data clustering algorithm for large databases. Compared with K-means clustering it is more robust to outliers and able to identify clusters having non-spherical shapes and size variances.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Analysis of algorithms", "Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BFR algorithm", "BIRCH", "BIRCH (data clustering)", "Bayesian network", "Bias-variance dilemma", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Cluster analysis", "Computational complexity theory", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "DBSCAN", "Data clustering", "Data mining", "Data point", "Database", "Decision tree learning", "DeepDream", "Deep learning", "Digital object identifier", "Dimensionality reduction", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature engineering", "Feature learning", "Gated recurrent unit", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "Independent component analysis", "International Conference on Machine Learning", "International Standard Book Number", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kd-tree", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Mean-shift", "Middle ground", "Multilayer perceptron", "Naive Bayes classifier", "Non-negative matrix factorization", "OPTICS algorithm", "Occam learning", "Online machine learning", "Outlier", "Outline of machine learning", "Perceptron", "Primary storage", "Principal component analysis", "Probably approximately correct learning", "Q-learning", "Random forest", "Random sample", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Robust statistics", "Sample space", "Sampling (statistics)", "Self-organizing map", "Semi-supervised learning", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Structured prediction", "Sum of squared error", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Trade-off", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory"], "references": ["http://www.cs.sfu.ca/CC/459/han/papers/guha98.pdf", "http://doi.org/10.1016%2FS0306-4379(01)00008-4", "https://github.com/annoviko/pyclustering", "https://books.google.com/books?id=gAGRCmp8Sp8C&pg=PA572", "https://arxiv.org/list/cs.LG/recent"]}, "Proportional hazards model": {"categories": ["Poisson point processes", "Semi-parametric models", "Survival analysis"], "title": "Proportional hazards model", "method": "Proportional hazards model", "url": "https://en.wikipedia.org/wiki/Proportional_hazards_model", "summary": "Proportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed may double its hazard rate for failure. Other types of survival models such as accelerated failure time models do not exhibit proportional hazards. The accelerated failure time model describes a situation where the biological or mechanical life history of an event is accelerated (or decelerated).", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Additive hazards model", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Statistics", "ArXiv", "Arithmetic mean", "Association (statistics)", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Censoring (statistics)", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Christian Gouri\u00e9roux", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "David Cox (statistician)", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Electronic Journal of Statistics", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hazard function", "Hazard rate", "Hazard ratio", "Hessian matrix", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "L1-norm", "Lasso (statistics)", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Morbidity", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Newton's method", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Norman Breslow", "Observational study", "Official statistics", "One- and two-tailed tests", "One in ten rule", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score (statistics)", "Score test", "Seasonal adjustment", "Semiparametric model", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistica Sinica", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Statistics in Medicine (journal)", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time-varying covariate", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0341758", "http://arxiv.org/abs/1010.5233", "http://arxiv.org/abs/1204.1992", "http://arxiv.org/abs/1306.4847", "http://doi.org/10.1002%2F(SICI)1097-0258(19970228)16:4%3C385::AID-SIM380%3E3.0.CO;2-3", "http://doi.org/10.1002%2Fsim.2369", "http://doi.org/10.1007%2F0-387-33960-4", "http://doi.org/10.1007%2Fs10958-010-9929-6", "http://doi.org/10.1016%2Fj.ejor.2016.07.052", "http://doi.org/10.1080%2F01621459.1977.10480613", "http://doi.org/10.1214%2F11-AOS911", "http://doi.org/10.1214%2F13-AOS1098", "http://doi.org/10.1214%2F15-EJS1004", "http://doi.org/10.1214%2Faos%2F1176345976", "http://doi.org/10.1214%2Fss%2F1177010394", "http://doi.org/10.2307%2F1402659", "http://doi.org/10.2307%2F2287816", "http://doi.org/10.5705%2Fss.2012.240", "http://www.jstor.org/stable/1402659", "http://www.jstor.org/stable/2240714", "http://www.jstor.org/stable/2286217", "http://www.jstor.org/stable/2287816", "http://www.jstor.org/stable/2985181", "https://books.google.com/books?id=dE2prs_U0QMC&pg=PA284", "https://books.google.com/books?id=eDWG3728OxcC&pg=PA503", "https://cran.r-project.org/web/packages/timereg/index.html"]}, "Multidimensional analysis": {"categories": ["All stub articles", "Dimension reduction", "Statistics stubs"], "title": "Multidimensional analysis", "method": "Multidimensional analysis", "url": "https://en.wikipedia.org/wiki/Multidimensional_analysis", "summary": "In statistics, econometrics, and related fields, multidimensional analysis (MDA) is a data analysis process that groups data into two categories: data dimensions and measurements. For example, a data set consisting of the number of wins for a single football team at each of several years is a single-dimensional (in this case, longitudinal) data set. A data set consisting of the number of wins for several football teams in a single year is also a single-dimensional (in this case, cross-sectional) data set. A data set consisting of the number of wins for several football teams over several years is a two-dimensional data set.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Data analysis", "Data dimension", "Data set", "Dimension (data warehouse)", "Dimension table", "Econometrics", "MultiDimensional eXpressions", "Multidimensional panel data", "Online analytical processing", "Panel data", "Pivot table", "Relational database", "Spreadsheet", "Statistics"], "references": []}, "Probability interpretations": {"categories": ["All articles needing additional references", "Articles needing additional references from April 2011", "CS1 errors: dates", "Epistemology", "Interpretation (philosophy)", "Probability interpretations", "Probability theory", "Use dmy dates from September 2010", "Wikipedia articles needing clarification from April 2010"], "title": "Probability interpretations", "method": "Probability interpretations", "url": "https://en.wikipedia.org/wiki/Probability_interpretations", "summary": "The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical tendency of something to occur or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory.\nThere are two broad categories of probability interpretations which can be called \"physical\" and \"evidential\" probabilities. Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. In such systems, a given type of event (such as a die yielding a six) tends to occur at a persistent rate, or \"relative frequency\", in a long run of trials. Physical probabilities either explain, or are invoked to explain, these stable frequencies. The two main kinds of theory of physical probability are frequentist accounts (such as those of Venn, Reichenbach and von Mises) and propensity accounts (such as those of Popper, Miller, Giere and Fetzer).Evidential probability, also called Bayesian probability, can be assigned to any statement whatsoever, even when no random process is involved, as a way to represent its subjective plausibility, or the degree to which the statement is supported by the available evidence. On most accounts, evidential probabilities are considered to be degrees of belief, defined in terms of dispositions to gamble at certain odds. The four main evidential interpretations are the classical (e.g. Laplace's) interpretation, the subjective interpretation (de Finetti and Savage), the epistemic or inductive interpretation (Ramsey, Cox) and the logical interpretation (Keynes and Carnap). There are also evidential interpretations of probability covering groups, which are often labelled as 'intersubjective' (proposed by Gillies and Rowbottom).\nSome interpretations of probability are associated with approaches to statistical inference, including theories of estimation and hypothesis testing. The physical interpretation, for example, is taken by followers of \"frequentist\" statistical methods, such as Ronald Fisher, Jerzy Neyman and Egon Pearson. Statisticians of the opposing Bayesian school typically accept the existence and importance of physical probabilities, but also consider the calculation of evidential probabilities to be both valid and necessary in statistics. This article, however, focuses on the interpretations of probability rather than theories of statistical inference.\nThe terminology of this topic is rather confusing, in part because probabilities are studied within a variety of academic fields. The word \"frequentist\" is especially tricky. To philosophers it refers to a particular theory of physical probability, one that has more or less been abandoned. To scientists, on the other hand, \"frequentist probability\" is just another name for physical (or objective) probability. Those who promote Bayesian inference view \"frequentist statistics\" as an approach to statistical inference that recognises only physical probabilities. Also the word \"objective\", as applied to probability, sometimes means exactly what \"physical\" means here, but is also used of evidential probabilities that are fixed by rational constraints, such as logical and epistemic probabilities.\n\nIt is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6a/Dice.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/26/Roulette_wheel.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/07/Tokyo_Racecourse_3.jpg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["A Treatise on Probability", "Aleatory", "Andrey Kolmogorov", "Arthur W. Burks", "Atom", "Axiom", "Bayesian probability", "Belief", "Blaise Pascal", "Brian Skyrms", "British Journal for the Philosophy of Science", "Bruno de Finetti", "CRC Press", "Celestial mechanics", "Charles Sanders Peirce", "Charles Sanders Peirce bibliography", "Classical definition of probability", "Coherence (physics)", "Coin", "Credence (statistics)", "David Kellogg Lewis", "David Miller (philosopher)", "Determinism", "Dice", "Digital object identifier", "Donald A. Gillies", "Edward N. Zalta", "Egon Pearson", "Electrical charge", "Elsevier", "Empirical evidence", "Entailment", "Epistemic", "Epistemology", "Estimation theory", "Evidence-based medicine", "Exchangeability", "Frank P. Ramsey", "Frequency (statistics)", "Frequency probability", "Frequentist probability", "Gambling", "Games of chance", "Hans Reichenbach", "Ian Hacking", "Indiana Philosophy Ontology Project", "Infinity", "International Standard Book Number", "JSTOR", "Jerzy Neyman", "John Maynard Keynes", "John Venn", "Karl Popper", "Laurence Jonathan Cohen", "Law of large numbers", "Laws of probability", "Leonard Jimmie Savage", "Logic", "Logical consequence", "Ludlow, Massachusetts", "Mathematics", "Negative probability", "Patrick Suppes", "Paul Humphreys (philosopher)", "PhilPapers", "Philosophy of mathematics", "Philosophy of statistics", "Pierre-Simon Laplace", "Pierre de Fermat", "Pignistic probability", "Playing card", "Predictive inference", "Principle of indifference", "Prior probability", "Probabilistic logic", "Probabilistically checkable proof", "Probability", "Probability amplitude", "Probability axioms", "Probability theory", "Propensity probability", "Quantum physics", "Radioactive decay", "Randomness", "Reference class problem", "Richard Threlkeld Cox", "Richard von Mises", "Roger Ludlow", "Ronald Fisher", "Ronald N. Giere", "Roulette", "Rudolf Carnap", "Seymour Geisser", "Six sigma", "Stanford Encyclopedia of Philosophy", "Statistical hypothesis testing", "Statistical inference", "String theory landscape", "Sunrise problem", "Susan Haack", "Theory of justification", "Thomas Bayes", "Thought experiment", "Urn model"], "references": ["http://www.nlx.com/collections/95", "http://www.sciencedirect.com/science/article/pii/S0049237X09703805", "http://www.sciencedirect.com/science/bookseries/0049237X", "http://plato.stanford.edu/archives/win2012/entries/probability-interpret/", "http://www.socsci.uci.edu/~bskyrms/bio/readings/pascal_fermat.pdf", "http://www.tc.umn.edu/~pemeehl/167GroveMeehlClinstix.pdf", "http://philosophy.elte.hu/colloquium/2001/October/Szabo/angol011008/angol011008.html", "http://philosophy.elte.hu/leszabo/Preprints/lesz_no_probability_preprint.pdf", "http://doi.org/10.1037%2F1076-8971.2.2.293", "http://doi.org/10.1093%2Fbjps%2F26.2.123", "http://doi.org/10.1175%2Fmwr2913.1", "http://fitelson.org/probability/ramsey.pdf", "http://www.jstor.org/stable/4106816", "http://bjps.oxfordjournals.org", "https://books.google.com/books?id=es0AAAAAcAAJ", "https://books.google.com/books?id=wfdlBZ_iwZoC", "https://www.stat.berkeley.edu/~stark/Preprints/611.pdf", "https://inpho.cogs.indiana.edu/idea/1155", "https://plato.stanford.edu/entries/probability-interpret/", "https://web.archive.org/web/20111030214359/http://www.tc.umn.edu/~pemeehl/167GroveMeehlClinstix.pdf", "https://www.gutenberg.org/ebooks/32625", "https://philpapers.org/browse/interpretation-of-probability/"]}, "Exponential family": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from November 2010", "Articles with unsourced statements from June 2011", "CS1 French-language sources (fr)", "Continuous distributions", "Discrete distributions", "Exponentials", "Types of probability distributions"], "title": "Exponential family", "method": "Exponential family", "url": "https://en.wikipedia.org/wiki/Exponential_family", "summary": "\"Natural parameter\" links here. For the usage of this term in differential geometry, see differential geometry of curves.In probability and statistics, an exponential family is a set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The concept of exponential families is credited to E. J. G. Pitman, G. Darmois, and B. O. Koopman in 1935\u201336. The term exponential class is sometimes used in place of \"exponential family\".The exponential family of distributions provides a general framework for selecting a possible alternative parameterisation of the distribution, in terms of natural parameters, and for defining useful sample statistics, called the natural sufficient statistics of the family.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARGUS distribution", "Absolutely continuous", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Mathematical Statistics", "ArXiv", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayes network", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernard Koopman", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bibcode", "Bijection", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Calculus of variations", "Canonical correlation", "Canonical form", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson distribution", "Compound probability distribution", "Confidence interval", "Confounding", "Conjugate prior", "Contingency table", "Continuous probability distribution", "Continuous uniform distribution", "Control chart", "Convex set", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation and dependence", "Correlogram", "Count data", "Counting measure", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulant generating function", "Cumulative distribution function", "Dagum distribution", "Data collection", "Davis distribution", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Derivative", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Differential geometry of curves", "Digamma function", "Digital object identifier", "Dimension", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Divergence (statistics)", "Dot product", "Durbin\u2013Watson statistic", "E. J. G. Pitman", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Ewens's sampling formula", "Experiment", "Exponential-logarithmic distribution", "Exponential dispersion model", "Exponential distribution", "Exponential smoothing", "Exponentiation", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Factorize", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized linear models", "Generalized normal distribution", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "Georges Darmois", "Geostatistics", "Gibbs measure", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harmonic mean", "Heavy-tailed distribution", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hyperparameter", "Hyperprior", "Hypoexponential distribution", "Hypothesis testing", "Independent identically distributed", "Index of dispersion", "Information entropy", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse Wishart distribution", "Inverse gamma distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "Iverson bracket", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kernel (statistics)", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Lagrange multipliers", "Landau distribution", "Laplace distribution", "Lebesgue\u2013Stieltjes integral", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logistic function", "Logistic regression", "Logit", "Logit-normal distribution", "Logit function", "Lognormal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Mathematical Proceedings of the Cambridge Philosophical Society", "Mathematical Reviews", "Matrix-exponential distribution", "Matrix calculus", "Matrix gamma distribution", "Matrix normal distribution", "Matrix product", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Measure (mathematics)", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture density", "Mixture distribution", "Mixture model", "Mode (statistics)", "Model selection", "Moment-generating function", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate gamma function", "Multivariate normal distribution", "Multivariate random variable", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonidentifiable", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normalization (statistics)", "Normalization constant", "Normalization factor", "Normalizing constant", "Normalizing factor", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabolic fractal distribution", "Parameterization", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition function (mathematics)", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Population (statistics)", "Population statistics", "Posterior distribution", "Posterior predictive distribution", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principle of maximum entropy", "Prior distribution", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability mass function", "Proportional hazards model", "Psychometrics", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Rademacher distribution", "Radon\u2013Nikodym derivative", "Raised cosine distribution", "Random assignment", "Random matrix", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rice distribution", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sample statistic", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Skellam distribution", "Skew-logistic distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Social statistics", "Softmax function", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable distribution", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical physics", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Step function", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Student's t distribution", "Sufficiency (statistics)", "Sufficient statistic", "Support (mathematics)", "Support of a distribution", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Theory of probability", "Time domain", "Time series", "Tolerance interval", "Trace (linear algebra)", "Tracy\u2013Widom distribution", "Transactions of the American Mathematical Society", "Trend estimation", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-gamma distribution", "Variational Bayes", "Vector autoregression", "Vectorization (mathematics)", "Voigt profile", "Von Mises-Fisher distribution", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://jeff560.tripod.com/e.html", "http://jeff560.tripod.com/mathword.html", "http://adsabs.harvard.edu/abs/1936PCPS...32..567P", "http://adsabs.harvard.edu/abs/2009arXiv0911.4863N", "http://www.ams.org/mathscinet-getitem?mr=0268992", "http://www.ams.org/mathscinet-getitem?mr=1501854", "http://arxiv.org/abs/0911.4863", "http://www.casact.org/pubs/dpp/dpp04/04dpp117.pdf", "http://doi.org/10.1017%2FS0305004100019307", "http://doi.org/10.2307%2F1989758", "http://doi.org/10.2307%2F2284291", "http://www.jstor.org/stable/1989758", "http://www.jstor.org/stable/2284291", "https://vincentfpgarcia.github.com/jMEF/", "https://www.cs.princeton.edu/courses/archive/fall11/cos597C/lectures/variational-inference-i.pdf", "https://www.jstor.org/stable/2237349"]}, "Linear classifier": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2017", "Classification algorithms", "Statistical classification"], "title": "Linear classifier", "method": "Linear classifier", "url": "https://en.wikipedia.org/wiki/Linear_classifier", "summary": "In the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class (or group) it belongs to. A linear classifier achieves this by making a classification decision based on the value of a linear combination of the characteristics. An object's characteristics are also known as feature values and are typically presented to the machine in a vector called a feature vector. Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables (features), reaching accuracy levels comparable to non-linear classifiers while taking less time to train and use.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/20/Svm_separating_hyperplanes.png"], "links": ["Backpropagation", "Conditional probability distribution", "Convex function", "Convex optimization", "Coordinate descent", "Dimensionality reduction", "Discriminative model", "Document-term matrix", "Document classification", "Dot product", "Feature vector", "Features (pattern recognition)", "Generative model", "Gradient descent", "High-dimensional space", "Hinge loss", "Hyperplane", "International Standard Book Number", "Kernel trick", "L-BFGS", "Linear combination", "Linear discriminant analysis", "Linear functional", "Linear regression", "Log loss", "Logistic regression", "Loss function", "Machine learning", "Margin (machine learning)", "Naive Bayes classifier", "Newton method", "Normal distribution", "One-form", "Optimization algorithm", "Overfitting", "Perceptron", "Principal components analysis", "Quadratic classifier", "Real number", "Regularization (machine learning)", "Regularization (mathematics)", "Statistical classification", "Stochastic gradient descent", "Supervised learning", "Support vector machine", "Support vector machines", "Training set", "Unsupervised learning", "Winnow (algorithm)"], "references": ["http://www.cs.berkeley.edu/~jordan/papers/ng-jordan-nips01.ps", "http://www.cs.cmu.edu/~tom/mlbook/NBayesLogReg.pdf", "http://citeseer.ist.psu.edu/yang99reexamination.html"]}, "Np-chart": {"categories": ["Quality control tools", "Statistical charts and diagrams"], "title": "Np-chart", "method": "Np-chart", "url": "https://en.wikipedia.org/wiki/Np-chart", "summary": "In statistical quality control, the np-chart is a type of control chart used to monitor the number of nonconforming units in a sample. It is an adaptation of the p-chart and used in situations where personnel find it easier to interpret process performance in terms of concrete numbers of units rather than the somewhat more abstract proportion.The np-chart differs from the p-chart in only the three following aspects:\n\nThe control limits are \n \n \n \n n\n \n \n \n p\n \u00af\n \n \n \n \u00b1\n 3\n \n \n n\n \n \n \n p\n \u00af\n \n \n \n (\n 1\n \u2212\n \n \n \n p\n \u00af\n \n \n \n )\n \n \n \n \n {\\displaystyle n{\\bar {p}}\\pm 3{\\sqrt {n{\\bar {p}}(1-{\\bar {p}})}}}\n , where n is the sample size and \n \n \n \n \n \n \n p\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {p}}}\n is the estimate of the long-term process mean established during control-chart setup.\nThe number nonconforming (np), rather than the fraction nonconforming (p), is plotted against the control limits.\nThe sample size, \n \n \n \n n\n \n \n {\\displaystyle n}\n , is constant.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c3/Np_control_chart.svg"], "links": ["Binomial distribution", "Control chart", "Hoboken, New Jersey", "International Standard Book Number", "John Wiley & Sons", "Nonconformity (quality)", "OCLC", "P-chart", "Sample (statistics)", "Statistical process control", "Variable and attribute (research)", "Walter A. Shewhart"], "references": ["http://www.eas.asu.edu/~masmlab/montgomery/", "http://www.worldcat.org/oclc/56729567", "https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/"]}, "Prior probability distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2008", "Articles with unsourced statements from May 2011", "Articles with unsourced statements from October 2010", "Bayesian statistics", "CS1 maint: Multiple names: authors list", "Probability assessment", "Wikipedia articles needing clarification from August 2015", "Wikipedia articles needing clarification from May 2011", "Wikipedia articles needing clarification from September 2015"], "title": "Prior probability", "method": "Prior probability distribution", "url": "https://en.wikipedia.org/wiki/Prior_probability", "summary": "In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable.\nBayes' theorem calculates the renormalized pointwise product of the prior and the likelihood function, to produce the posterior probability distribution, which is the conditional distribution of the uncertain quantity given the data.\nSimilarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is assigned before any relevant evidence is taken into account.\nPriors can be created using a number of methods. A prior can be determined from past information, such as previous experiments. A prior can be elicited from the purely subjective assessment of an experienced expert. An uninformative prior can be created to reflect a balance among outcomes when no information is available. Priors can also be chosen according to some principle, such as symmetry or maximizing entropy given constraints; examples are the Jeffreys prior or Bernardo's reference prior. When a family of conjugate priors exists, choosing a prior from that family simplifies calculation of the posterior distribution.\nParameters of prior distributions are a kind of hyperparameter. For example, if one uses a beta distribution to model the distribution of the parameter p of a Bernoulli distribution, then:\n\np is a parameter of the underlying system (Bernoulli distribution), and\n\u03b1 and \u03b2 are parameters of the prior distribution (beta distribution); hence hyperparameters.Hyperparameters themselves may have hyperprior distributions expressing beliefs about their values. A Bayesian model with more than one level of prior like this is called a hierarchical Bayes model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg"], "links": ["A priori probability", "Admissible decision rule", "Affine group", "Algorithmic probability", "Andrew Gelman", "Annals of Statistics", "Approximate Bayesian computation", "ArXiv", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernoulli distribution", "Bernstein-von Mises theorem", "Bernstein\u2013von Mises theorem", "Beta distribution", "Coding theory", "Conjugate prior", "Continuous random variable", "Credible interval", "Cromwell's rule", "Decision theory", "Digital object identifier", "Edwin T. Jaynes", "Empirical Bayes method", "Expected value", "Frequentist", "Frequentist matching", "Frequentist statistics", "Haar measure", "Haldane prior", "Harold Jeffreys", "Hierarchical Bayes model", "Hyperparameter", "Hyperprior", "Improper prior", "Inductive inference", "Information theory", "International Standard Book Number", "International Standard Serial Number", "J.B.S. Haldane", "JSTOR", "James Berger (statistician)", "Jeffreys prior", "Jos\u00e9-Miguel Bernardo", "Journal of the Royal Statistical Society", "Kullback\u2013Leibler divergence", "Latent variable", "Lie group", "Likelihood function", "Marginal probability", "Markov chain Monte Carlo", "Mathematical Reviews", "Maximum a posteriori estimation", "Minimum description length", "Minxent", "Normal distribution", "Observable variable", "Parameter", "Positive reals", "Posterior predictive distribution", "Posterior probability", "Posterior probability distribution", "Principle of indifference", "Principle of maximum entropy", "Principle of transformation groups", "Probability distribution", "Probability interpretations", "PubMed Central", "PubMed Identifier", "Radical probabilism", "Random event", "Reference prior", "Regularization (mathematics)", "Schwarz criterion", "Shannon entropy", "Solomonoff's theory of inductive inference", "Statistical inference", "Statistics", "Transformation group", "Translation group", "Uniform distribution (continuous)", "Uninformative prior", "Variance", "Zentralblatt MATH"], "references": ["http://bayes.wustl.edu/etj/articles/prior.pdf", "http://www-biba.inrialpes.fr/Jaynes/prob.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5751802", "http://www.ncbi.nlm.nih.gov/pubmed/29297278", "http://www.ams.org/mathscinet-getitem?mr=0547240", "http://www.ams.org/mathscinet-getitem?mr=0804611", "http://www.ams.org/mathscinet-getitem?mr=1401831", "http://www.ams.org/mathscinet-getitem?mr=2027492", "http://arxiv.org/abs/0904.0156", "http://doi.org/10.1093%2Fphilmat%2Fnkp019", "http://doi.org/10.1109%2FTSSC.1968.300117", "http://doi.org/10.1186%2Fs12859-017-1893-4", "http://doi.org/10.1214%2F07-AOS587", "http://doi.org/10.1214%2Faos%2F1032526950", "http://www.jstor.org/stable/2985028", "http://www.worldcat.org/issn/1471-2105", "http://zbmath.org/?format=complete&q=an:0865.62004", "http://www.kent.ac.uk/secl/philosophy/jw/2009/deFinetti.pdf", "https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-017-1893-4", "https://web.archive.org/web/20110609175653/http://www.kent.ac.uk/secl/philosophy/jw/2009/deFinetti.pdf", "https://doi.org/10.1017%2FS0305004100010495", "https://doi.org/10.2307%2F2332350", "https://ieeexplore.ieee.org/document/6654120/", "https://www.jstor.org/stable/2332350"]}, "Hypergeometric distribution": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from August 2011", "Discrete distributions", "Factorial and binomial topics", "Pages using deprecated image syntax"], "title": "Hypergeometric distribution", "method": "Hypergeometric distribution", "url": "https://en.wikipedia.org/wiki/Hypergeometric_distribution", "summary": "In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of \n \n \n \n k\n \n \n {\\displaystyle k}\n successes (random draws for which the object drawn has a specified feature) in \n \n \n \n n\n \n \n {\\displaystyle n}\n draws, without replacement, from a finite population of size \n \n \n \n N\n \n \n {\\displaystyle N}\n that contains exactly \n \n \n \n K\n \n \n {\\displaystyle K}\n objects with that feature, wherein each draw is either a success or a failure. In contrast, the binomial distribution describes the probability of \n \n \n \n k\n \n \n {\\displaystyle k}\n successes in \n \n \n \n n\n \n \n {\\displaystyle n}\n draws with replacement.\nIn statistics, the hypergeometric test uses the hypergeometric distribution to calculate the statistical significance of having drawn a specific \n \n \n \n k\n \n \n {\\displaystyle k}\n successes (out of \n \n \n \n n\n \n \n {\\displaystyle n}\n total draws) from the aforementioned population. The test is often used to identify which sub-populations are over- or under-represented in a sample. This test has a wide range of applications. For example, a marketing group could use the test to understand their customer base by testing a set of known customers for over-representation of various demographic subgroups (e.g., women, people under 30).", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/95/Election_Samples.png", "https://upload.wikimedia.org/wikipedia/commons/b/b4/HypergeometricCDF.png", "https://upload.wikimedia.org/wikipedia/commons/c/c1/HypergeometricPDF.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/a/aa/Youngronaldfisher2.JPG"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Binary variable", "Bingham distribution", "Binomial coefficient", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Combinatorics", "Compound Poisson distribution", "Conjugate prior", "Contingency table", "Conway\u2013Maxwell\u2013Poisson distribution", "Coupon collector's problem", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Election audits", "Elliptical distribution", "Eric W. Weisstein", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Exchangeable random variables", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's exact test", "Fisher's noncentral hypergeometric distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Flush (poker)", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized hypergeometric function", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hold'em", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the American Statistical Association", "Keno", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kullback-Leibler divergence", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marbles", "Marchenko\u2013Pastur distribution", "MathWorld", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative hypergeometric distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral hypergeometric distribution", "Noncentral hypergeometric distributions", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Population", "Probability distribution", "Probability mass function", "Probability theory", "PubMed Identifier", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Ronald Fisher", "Sampling (statistics)", "Sampling without replacement", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard normal distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "The Annals of Statistics", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Urn problem", "Vandermonde's identity", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wolfram Demonstrations Project", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://ansuz.sooke.bc.ca/professional/hypergeometric.pdf", "http://demonstrations.wolfram.com/BinomialApproximationToAHypergeometricRandomVariable/", "http://demonstrations.wolfram.com/TheHypergeometricDistribution/", "http://mathworld.wolfram.com/HypergeometricDistribution.html", "http://www.stat.yale.edu/~pollard/Courses/600.spring2010/Handouts/Symmetry%5BPolyaUrn%5D.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/17182697", "http://doi.org/10.1016%2Fj.jda.2006.01.001", "http://doi.org/10.1093%2Fbioinformatics%2Fbtl633", "http://doi.org/10.2307%2F2282952", "http://www.ncsl.org/research/elections-and-campaigns/post-election-audits635926066.aspx#state", "http://quantpsy.org/fisher/fisher.htm", "https://ahlenotes.wordpress.com/2015/12/08/hypergeometric_tail/", "https://hal-espci.archives-ouvertes.fr/hal-00801557/document", "https://www.verifiedvoting.org/state-audit-laws/"]}, "Tracy\u2013Widom distribution": {"categories": ["Continuous distributions", "Random matrices", "Special functions"], "title": "Tracy\u2013Widom distribution", "method": "Tracy\u2013Widom distribution", "url": "https://en.wikipedia.org/wiki/Tracy%E2%80%93Widom_distribution", "summary": "The Tracy\u2013Widom distribution, introduced by Craig Tracy and Harold Widom (1993, 1994), is the probability distribution of the normalized largest eigenvalue of a random Hermitian matrix.\nIn practical terms, Tracy\u2013Widom is the crossover function between the two phases of weakly versus strongly coupled components in a system.\nIt also appears in the distribution of the length of the longest increasing subsequence of random permutations, in current fluctuations of the asymmetric simple exclusion process (ASEP) with step initial condition, and in simplified mathematical models of the behavior of the longest common subsequence problem on random inputs. See Takeuchi & Sano (2010) and Takeuchi et al. (2011) for experimental testing (and verifying) that the interface fluctuations of a growing droplet (or substrate) are described by the TW distribution \n \n \n \n \n F\n \n 2\n \n \n \n \n {\\displaystyle F_{2}}\n (or \n \n \n \n \n F\n \n 1\n \n \n \n \n {\\displaystyle F_{1}}\n ) as predicted by Pr\u00e4hofer & Spohn (2000).\nThe distribution F1 is of particular interest in multivariate statistics. For a discussion of the universality of F\u03b2, \u03b2 = 1, 2, and 4, see Deift (2007). For an application of F1 to inferring population structure from genetic data see Patterson, Price & Reich (2006).\nIn 2017 it was proved that the distribution F is not infinitely divisible.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c2/Tracy-Widom_distr.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/c/c2/20141229071604%21Tracy-Widom_distr.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/c/c2/20141229051953%21Tracy-Widom_distr.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/c/c2/20141229042255%21Tracy-Widom_distr.svg"], "links": ["ARGUS distribution", "Airy function", "Annals of Applied Statistics", "Annals of Statistics", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Asymmetric simple exclusion process", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Communications in Mathematical Physics", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Craig Tracy", "Cumulative distribution function", "Dagum distribution", "David Reich (geneticist)", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Eigenvalue", "Elliptical distribution", "Erlang distribution", "European Mathematical Society", "Ewens's sampling formula", "Excess kurtosis", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fredholm determinant", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gaussian unitary ensemble", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harold Widom", "Hermitian matrix", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Integral transform", "International Congress of Mathematicians", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Journal of Multivariate Analysis", "Journal of the American Mathematical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Longest common subsequence", "Longest increasing subsequence", "L\u00e9vy distribution", "MATLAB", "Marchenko\u2013Pastur distribution", "Mathematical Reviews", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "PLoS Genetics", "Painlev\u00e9 equation", "Painlev\u00e9 transcendent", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Permutation", "Phase-type distribution", "Physical Review Letters", "Physics Letters B", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "PubMed Central", "PubMed Identifier", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quanta Magazine", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "S-PLUS", "Scaled inverse chi-squared distribution", "Scientific Reports", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://adsabs.harvard.edu/abs/1993PhLB..305..115T", "http://adsabs.harvard.edu/abs/1994CMaPh.159..151T", "http://adsabs.harvard.edu/abs/1996CMaPh.177..727T", "http://adsabs.harvard.edu/abs/2000CMaPh.209..437J", "http://adsabs.harvard.edu/abs/2000PhRvL..84.4882P", "http://adsabs.harvard.edu/abs/2005PhRvE..72b0901M", "http://adsabs.harvard.edu/abs/2005math.ph...1068E", "http://adsabs.harvard.edu/abs/2006math......7331R", "http://adsabs.harvard.edu/abs/2009CMaPh.290..129T", "http://adsabs.harvard.edu/abs/2009arXiv0904.1581B", "http://adsabs.harvard.edu/abs/2010PhRvL.104w0601T", "http://adsabs.harvard.edu/abs/2011NatSR...1E..34T", "http://web.mit.edu/sea06/agenda/talks/Kuijlaars.pdf", "http://www.math.ucdavis.edu/~tracy/talks/SITE7.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1713260", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2821031", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2880335", "http://www.ncbi.nlm.nih.gov/pubmed/10990822", "http://www.ncbi.nlm.nih.gov/pubmed/17194218", "http://www.ncbi.nlm.nih.gov/pubmed/20157626", "http://www.ncbi.nlm.nih.gov/pubmed/20526465", "http://www.ncbi.nlm.nih.gov/pubmed/20867221", "http://www.ams.org/mathscinet-getitem?mr=1257246", "http://www.ams.org/mathscinet-getitem?mr=1385083", "http://www.ams.org/mathscinet-getitem?mr=1682248", "http://www.ams.org/mathscinet-getitem?mr=1957518", "http://www.ams.org/mathscinet-getitem?mr=1989209", "http://www.ams.org/mathscinet-getitem?mr=2177365", "http://www.ams.org/mathscinet-getitem?mr=2334189", "http://www.ams.org/mathscinet-getitem?mr=2334195", "http://arxiv.org/abs/0803.3408", "http://arxiv.org/abs/0807.1713", "http://arxiv.org/abs/0904.1581", "http://arxiv.org/abs/1001.5121", "http://arxiv.org/abs/1009.5854", "http://arxiv.org/abs/1108.2118", "http://arxiv.org/abs/1209.3394", "http://arxiv.org/abs/cond-mat/9912264", "http://arxiv.org/abs/hep-th/9210074", "http://arxiv.org/abs/hep-th/9211141", "http://arxiv.org/abs/math-ph/0501068", "http://arxiv.org/abs/math-ph/0603038", "http://arxiv.org/abs/math/0607331", "http://arxiv.org/abs/math/0611589", "http://arxiv.org/abs/math/9903134", "http://arxiv.org/abs/q-bio/0410012", "http://arxiv.org/abs/solv-int/9509007", "http://doi.org/10.1007%2FBF02099545", "http://doi.org/10.1007%2FBF02100489", "http://doi.org/10.1007%2Fs00220-009-0761-0", "http://doi.org/10.1007%2Fs002200050027", "http://doi.org/10.1016%2F0370-2693(93)91114-3", "http://doi.org/10.1016%2Fj.jmva.2014.04.002", "http://doi.org/10.1038%2Fsrep00034", "http://doi.org/10.1090%2FS0894-0347-2011-00703-0", "http://doi.org/10.1090%2FS0894-0347-99-00307-0", "http://doi.org/10.1103%2FPhysRevE.72.020901", "http://doi.org/10.1103%2FPhysRevLett.104.230601", "http://doi.org/10.1103%2FPhysRevLett.84.4882", "http://doi.org/10.1214%2F08-AOAS220", "http://doi.org/10.1214%2F08-AOS605", "http://doi.org/10.1371%2Fjournal.pgen.0020190", "http://doi.org/10.4171%2F022-1%2F13", "http://doi.org/10.4171%2F022-1%2F7", "http://www.icm2006.org/proceedings/Vol_I/17.pdf", "http://www.jstor.org/stable/2646100", "http://icm2006.mathunion.org/proceedings/Vol_I/11.pdf", "http://www.mathunion.org/ICM/ICM2002.1/Main/icm2002.1.0587.0596.ocr.pdf", "http://www.mathunion.org/ICM/ICM2002.3/Main/icm2002.3.0053.0062.ocr.pdf", "http://www.simonsfoundation.org/quanta/20141015-at-the-far-ends-of-a-new-universal-law/", "http://www.cl.cam.ac.uk/~aib29/TWinSplus.pdf", "https://www.wired.com/2014/10/tracy-widom-mysterious-statistical-law/", "https://cran.r-project.org/web/packages/RMTstat/RMTstat.pdf"]}, "Autocorrelation": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2018", "Autocorrelation", "Signal processing", "Time domain analysis", "Wikipedia articles needing page number citations from March 2013"], "title": "Autocorrelation", "method": "Autocorrelation", "url": "https://en.wikipedia.org/wiki/Autocorrelation", "summary": "Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals.\nUnit root processes, trend stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Acf_new.svg", "https://upload.wikimedia.org/wikipedia/commons/2/21/Comparison_convolution_correlation.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algorithmic efficiency", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anti-correlation", "ArXiv", "Arithmetic mean", "Astrophysics", "Asymptotic theory (statistics)", "Autocorrelation (words)", "Autocorrelation matrix", "Autocorrelation technique", "Autocorrelator", "Autocovariance", "Autoregressive-moving-average model", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average model", "Autoregressive model", "Autoregressive process", "Autoregressive\u2013moving-average model", "BLUE", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Beat (music)", "Bias of an estimator", "Biased estimator", "Bibcode", "Big O notation", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "CUSUM", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Circular convolution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochrane\u2013Orcutt estimation", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Complex conjugate", "Complex function", "Computer Physics Communications", "Confidence interval", "Confounding", "Contingency table", "Continuous-time", "Continuous probability distribution", "Control chart", "Convolution", "Correlation", "Correlation and dependence", "Correlation function", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degree of coherence", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension", "Dirac delta function", "Discrete-time", "Discrete signal", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dynamic light scattering", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Ergodic process", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimating equations", "Even function", "Execution (computing)", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fast Fourier transform", "First-hitting-time model", "Fluorescence correlation spectroscopy", "Forest plot", "Fourier analysis", "Fourier transform", "Frequency", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Galaxy", "Galton's problem", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic", "Harmonic mean", "Hermitian function", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Integer", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Intertemporal portfolio choice", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jan Kmenta", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laser", "Lehmann\u2013Scheff\u00e9 theorem", "Light", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logarithm", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mark Thoma", "Markov chain Monte Carlo", "Mass spectrum", "MathWorld", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Medical ultrasound", "Method of moments (statistics)", "Methods engineering", "Micelle", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Missing fundamental frequency", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving average model", "Moving average process", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Music", "Music Recording", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Newey West", "Noise (signal processing)", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optical autocorrelation", "Optical spectrum", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Panel data", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Particle size distribution", "Partition of sums of squares", "Patterson function", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Peptide", "Percentile", "Periodic function", "Periodic signal", "Periodogram", "Permutation test", "Pie chart", "Pitch detection algorithm", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prais\u2013Winsten transformation", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Pulsar", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random process", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rate of return", "Real function", "Real number", "Realization (probability)", "Rearrangement inequality", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "SEQUEST", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled Correlation", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Short-time Fourier transform", "Sign test", "Signal (electronics)", "Signal (information theory)", "Signal processing", "Simple linear regression", "Simultaneous equations model", "Sine", "Skewness", "Small-angle X-ray scattering", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Speckle pattern", "Spectral density", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dependence", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-statistics", "Tempo", "Three-dimensional space", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "Trend stationary", "Triple correlation", "U-statistic", "Ultrashort pulse", "Unbiased estimation of standard deviation", "Uniformly most powerful test", "Unit root", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "White noise", "Whittle likelihood", "Wide-sense stationary process", "Wiener\u2013Khinchin theorem", "Wilcoxon signed-rank test", "X-ray binary", "YouTube", "Z-test", "Z-transform"], "references": ["http://statisticalideas.blogspot.com/2014/05/serial-correlation-techniques.html", "http://www.dsprelated.com/comp.dsp/keyword/Autocorrelation.php", "http://itfeature.com/time-series-analysis-and-forecasting/autocorrelation-time-series-data", "http://www.time.com/time/magazine/article/0,9171,1877372,00.html", "http://mathworld.wolfram.com/Autocorrelation.html", "http://adsabs.harvard.edu/abs/2011CoPhC.182.1120C", "http://arxiv.org/abs/0912.3824", "http://www.cambridge.org/us/academic/subjects/computer-science/cryptography-cryptology-and-coding/signal-design-good-correlation-wireless-communication-cryptography-and-radar", "http://doi.org/10.1016%2Fj.cpc.2011.01.009", "http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6142119", "http://www.iop.org/EJ/abstract/1367-2630/11/9/093024/", "https://www.youtube.com/watch?v=3bipJW_vuBU&list=PLD15D38DC7AA3B737&index=7"]}, "Marcinkiewicz\u2013Zygmund inequality": {"categories": ["Probabilistic inequalities", "Probability theorems", "Statistical inequalities", "Theorems in functional analysis"], "title": "Marcinkiewicz\u2013Zygmund inequality", "method": "Marcinkiewicz\u2013Zygmund inequality", "url": "https://en.wikipedia.org/wiki/Marcinkiewicz%E2%80%93Zygmund_inequality", "summary": "In mathematics, the Marcinkiewicz\u2013Zygmund inequality, named after J\u00f3zef Marcinkiewicz and Antoni Zygmund, gives relations between moments of a collection of independent random variables. It is a generalization of the rule for the sum of variances of independent random variables to moments of arbitrary order.\n\n", "images": [], "links": ["Antoni Zygmund", "Independent random variables", "J\u00f3zef Marcinkiewicz", "Khintchine inequality", "Mathematics", "Moment (mathematics)", "Rosenthal inequalities", "Statistic", "Variance"], "references": []}, "Ratio estimator": {"categories": ["All articles with unsourced statements", "Articles containing proofs", "Articles with unsourced statements from May 2018", "Statistical deviation and dispersion", "Statistical ratios"], "title": "Ratio estimator", "method": "Ratio estimator", "url": "https://en.wikipedia.org/wiki/Ratio_estimator", "summary": "The ratio estimator is a statistical parameter and is defined to be the ratio of means of two random variables. Ratio estimates are biased and corrections must be made when they are used in experimental or survey work. The ratio estimates are asymmetrical and symmetrical tests such as the t test should not be used to generate confidence intervals.\nThe bias is of the order O(1/n) (see big O notation) so as the sample size (n) increases, the bias will asymptotically approach 0. Therefore, the estimator is approximately unbiased for large sample sizes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias (statistics)", "Bias of an estimator", "Big O notation", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlate", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "England", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "France", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen's inequality", "Johansen test", "John Graunt", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laplace", "Lehmann\u2013Scheff\u00e9 theorem", "Leptokurtic", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mark and recapture", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Origin (mathematics)", "Outline of statistics", "Parametric statistics", "Parish", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population census", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Ratio", "Ratio distribution", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T test", "Taylor expansion", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniform distribution (discrete)", "Uniformly most powerful test", "Unimodal", "V-statistic", "Variance", "Vector autoregression", "Vysochanski\u00ef\u2013Petunin inequality", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Markov random field": {"categories": ["Graphical models", "Markov networks", "Wikipedia articles needing clarification from July 2018"], "title": "Markov random field", "method": "Markov random field", "url": "https://en.wikipedia.org/wiki/Markov_random_field", "summary": "In the domain of physics and probability, a Markov random field (often abbreviated as MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it satisfies Markov properties.\nA Markov network or MRF is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies); on the other hand, it can't represent certain dependencies that a Bayesian network can (such as induced dependencies). The underlying graph of a Markov random field may be finite or infinite.\nWhen the joint probability density of the random variables is strictly positive, it is also referred to as a Gibbs random field, because, according to the Hammersley\u2013Clifford theorem, it can then be represented by a Gibbs measure for an appropriate (locally defined) energy function. The prototypical Markov random field is the Ising model; indeed, the Markov random field was introduced as the general setting for the Ising model.\nIn the domain of artificial intelligence, a Markov random field is used to model various low- to mid-level tasks in image processing and computer vision.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f7/Markov_random_field_example.png"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Andrew McCallum", "Andrey Markov, Jr.", "Artificial intelligence", "Association for Computing Machinery", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bayesian network", "Belief propagation", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Carla Brodley", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Chordal graph", "Chow\u2013Liu tree", "Classical Wiener space", "Clique (graph theory)", "Compound Poisson process", "Computer graphics (computer science)", "Computer stereo vision", "Computer vision", "Conditional distribution", "Conditional independence", "Conditional random field", "Conference on Neural Information Processing Systems", "Configuration space (physics)", "Constant elasticity of variance model", "Constraint Composite Graph", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Correlation function", "Covariance matrix", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Daphne Koller", "Determinant", "Diffusion process", "Digital object identifier", "Directed acyclic graph", "Dirichlet process", "Discrete-time stochastic process", "Discriminative model", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dot product", "Dynkin's formula", "Econometrics", "Empirical process", "Entropy", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exact inference", "Exchangeable random variables", "Expectation value", "Extreme value theory", "Factor graph", "Feller-continuous process", "Feller process", "Fernando C.N. Pereira", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Graphical model", "Hammersley\u2013Clifford theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Hopfield network", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Image processing", "Image registration", "Incidence matrix", "Independent and identically distributed random variables", "Indicator function", "Infinitesimal generator (stochastic processes)", "Information retrieval", "Interacting particle system", "International Conference on Machine Learning", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "John D. Lafferty", "Joint probability distribution", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Log-linear analysis", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "MIT Press", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov chain Monte Carlo", "Markov logic network", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical Reviews", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "Maximum a posteriori", "Maximum entropy method", "Maximum likelihood estimate", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Multivariate normal distribution", "Neighborhood (graph theory)", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Partition function (mathematics)", "Percolation theory", "Perturbation theory", "Physics", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potential energy", "Potts model", "Precision matrix", "Predictable process", "Probability", "Probability density function", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sharp-P-complete", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistical mechanics", "Statistics", "Stochastic analysis", "Stochastic cellular automata", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Super-resolution", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Texture synthesis", "Time reversibility", "Time series", "Time series analysis", "Trace (linear algebra)", "Undirected graph", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Variational method", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://icml.cc/2013/?page_id=21", "http://papers.nips.cc/paper/3117-using-combinatorial-optimization-within-max-product-belief-propagation", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.649.303&rep=rep1&type=pdf", "http://www.tiny-clues.eu/Research/Petitjean2013-ICDM.pdf", "http://www.cmap.polytechnique.fr/~rama/ehess/mrfbook.pdf", "http://www.ams.org/mathscinet-getitem?mr=0432132", "http://www.ams.org/mathscinet-getitem?mr=0620955", "http://doi.org/10.1007%2FBF01011714", "http://doi.org/10.1145%2F1015330.1015444", "http://doi.org/10.2140%2Fmemocs.2017..101", "https://books.google.com/books?id=rDsObhDkCIAC&printsec=frontcover#v=onepage&q&f=false", "https://bitbucket.org/rukletsov/b"]}, "Kent distribution": {"categories": ["All articles with dead external links", "Articles with dead external links from December 2017", "Articles with permanently dead external links", "Continuous distributions", "Directional statistics"], "title": "Kent distribution", "method": "Kent distribution", "url": "https://en.wikipedia.org/wiki/Kent_distribution", "summary": "In directional statistics, the 5-parameter Fisher\u2013Bingham distribution or Kent distribution, named after Ronald Fisher, Christopher Bingham, and John T. Kent, is a probability distribution on the two-dimensional unit sphere \n \n \n \n \n S\n \n 2\n \n \n \n \n \n {\\displaystyle S^{2}\\,}\n in \n \n \n \n \n \n \n R\n \n \n \n 3\n \n \n \n \n {\\displaystyle {\\mathbb {R} }^{3}}\n . It is the analogue on the two-dimensional unit sphere of the bivariate normal distribution with an unconstrained covariance matrix. The Kent distribution was proposed by John T. Kent in 1982, and is used in geology as well as bioinformatics.\nThe probability density function \n \n \n \n f\n (\n \n x\n \n )\n \n \n \n {\\displaystyle f(\\mathbf {x} )\\,}\n of the Kent distribution is given by:\n\n \n \n \n f\n (\n \n x\n \n )\n =\n \n \n 1\n \n \n \n c\n \n \n (\n \u03ba\n ,\n \u03b2\n )\n \n \n \n exp\n \u2061\n {\n \u03ba\n \n \n \u03b3\n \n \n 1\n \n \n \u22c5\n \n x\n \n +\n \u03b2\n [\n (\n \n \n \u03b3\n \n \n 2\n \n \n \u22c5\n \n x\n \n \n )\n \n 2\n \n \n \u2212\n (\n \n \n \u03b3\n \n \n 3\n \n \n \u22c5\n \n x\n \n \n )\n \n 2\n \n \n ]\n }\n \n \n {\\displaystyle f(\\mathbf {x} )={\\frac {1}{{\\textrm {c}}(\\kappa ,\\beta )}}\\exp\\{\\kappa {\\boldsymbol {\\gamma }}_{1}\\cdot \\mathbf {x} +\\beta [({\\boldsymbol {\\gamma }}_{2}\\cdot \\mathbf {x} )^{2}-({\\boldsymbol {\\gamma }}_{3}\\cdot \\mathbf {x} )^{2}]\\}}\n where \n \n \n \n \n x\n \n \n \n \n {\\displaystyle \\mathbf {x} \\,}\n is a three-dimensional unit vector and the normalizing constant \n \n \n \n \n \n c\n \n \n (\n \u03ba\n ,\n \u03b2\n )\n \n \n \n {\\displaystyle {\\textrm {c}}(\\kappa ,\\beta )\\,}\n is:\n\n \n \n \n c\n (\n \u03ba\n ,\n \u03b2\n )\n =\n 2\n \u03c0\n \n \u2211\n \n j\n =\n 0\n \n \n \u221e\n \n \n \n \n \n \u0393\n (\n j\n +\n \n \n 1\n 2\n \n \n )\n \n \n \u0393\n (\n j\n +\n 1\n )\n \n \n \n \n \u03b2\n \n 2\n j\n \n \n \n \n (\n \n \n \n 1\n 2\n \n \n \u03ba\n \n )\n \n \n \u2212\n 2\n j\n \u2212\n \n \n 1\n 2\n \n \n \n \n \n I\n \n 2\n j\n +\n \n \n 1\n 2\n \n \n \n \n (\n \u03ba\n )\n \n \n {\\displaystyle c(\\kappa ,\\beta )=2\\pi \\sum _{j=0}^{\\infty }{\\frac {\\Gamma (j+{\\frac {1}{2}})}{\\Gamma (j+1)}}\\beta ^{2j}\\left({\\frac {1}{2}}\\kappa \\right)^{-2j-{\\frac {1}{2}}}I_{2j+{\\frac {1}{2}}}(\\kappa )}\n \nWhere \n \n \n \n \n I\n \n v\n \n \n (\n \u03ba\n )\n \n \n {\\displaystyle I_{v}(\\kappa )}\n is the modified Bessel function. Note that \n \n \n \n c\n (\n 0\n ,\n 0\n )\n =\n 4\n \u03c0\n \n \n {\\displaystyle c(0,0)=4\\pi }\n and \n \n \n \n c\n (\n \u03ba\n ,\n 0\n )\n =\n 4\n \u03c0\n (\n \n \u03ba\n \n \u2212\n 1\n \n \n )\n sinh\n \u2061\n (\n \u03ba\n )\n \n \n {\\displaystyle c(\\kappa ,0)=4\\pi (\\kappa ^{-1})\\sinh(\\kappa )}\n , the normalizing constant of the Von Mises\u2013Fisher distribution.\nThe parameter \n \n \n \n \u03ba\n \n \n \n {\\displaystyle \\kappa \\,}\n (with \n \n \n \n \u03ba\n >\n 0\n \n \n \n {\\displaystyle \\kappa >0\\,}\n ) determines the concentration or spread of the distribution, while \n \n \n \n \u03b2\n \n \n \n {\\displaystyle \\beta \\,}\n (with \n \n \n \n 0\n \u2264\n 2\n \u03b2\n <\n \u03ba\n \n \n {\\displaystyle 0\\leq 2\\beta <\\kappa }\n ) determines the ellipticity of the contours of equal probability. The higher the \n \n \n \n \u03ba\n \n \n \n {\\displaystyle \\kappa \\,}\n and \n \n \n \n \u03b2\n \n \n \n {\\displaystyle \\beta \\,}\n parameters, the more concentrated and elliptical the distribution will be, respectively. Vector \n \n \n \n \n \u03b3\n \n 1\n \n \n \n \n \n {\\displaystyle \\gamma _{1}\\,}\n is the mean direction, and vectors \n \n \n \n \n \u03b3\n \n 2\n \n \n ,\n \n \u03b3\n \n 3\n \n \n \n \n \n {\\displaystyle \\gamma _{2},\\gamma _{3}\\,}\n are the major and minor axes. The latter two vectors determine the orientation of the equal probability contours on the sphere, while the first vector determines the common center of the contours. The 3\u00d73 matrix \n \n \n \n (\n \n \u03b3\n \n 1\n \n \n ,\n \n \u03b3\n \n 2\n \n \n ,\n \n \u03b3\n \n 3\n \n \n )\n \n \n \n {\\displaystyle (\\gamma _{1},\\gamma _{2},\\gamma _{3})\\,}\n must be orthogonal.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ca/Point_sets_from_Kent_distributions_mapped_onto_a_sphere_-_journal.pcbi.0020131.g004.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bioinformatics", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Christopher Bingham", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Covariance matrix", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geology", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Modified Bessel function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Ronald Fisher", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Sphere", "Stable distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://citeseer.ist.psu.edu/235663.html", "http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0020131", "http://www.maths.leeds.ac.uk/statistics/workshop/lasr2005/Proceedings/kent.pdf", "http://www.maths.leeds.ac.uk/statistics/workshop/lasr2006/proceedings/hamelryck.pdf", "https://www.jstor.org/stable/2984712"]}, "Psephology": {"categories": ["All articles that may contain original research", "All articles with unsourced statements", "Articles that may contain original research from November 2010", "Articles with unsourced statements from April 2018", "Psephology"], "title": "Psephology", "method": "Psephology", "url": "https://en.wikipedia.org/wiki/Psephology", "summary": "Psephology (from Greek psephos \u03c8\u1fc6\u03c6\u03bf\u03c2, 'pebble', as the Greeks used pebbles as ballots) is a branch of political science which deals with the study and scientific analysis of elections.Psephology uses historical precinct voting data, public opinion polls, campaign finance information and similar statistical data. The term was coined in 1948 in the United Kingdom by W. F. R. Hardie (1902\u20131990) after he was asked by his friend R. B. McCallum for a word to describe the study of elections; first written use in 1952.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg"], "links": ["Abnormal psychology", "Anonymous elector", "Anthropology", "Anthrozoology", "Antony Green", "Apportionment (politics)", "Archaeology", "Area studies", "Behavioral neuroscience", "Biological anthropology", "Board of directors", "Boundary delimitation", "British Polling Council", "Business studies", "By-election", "Campaign finance", "Cash For Vote", "Charlie Cook", "Cognitive psychology", "Cognitive science", "Communication studies", "Community studies", "Criminology", "Criticisms of electoral politics", "Crossover voting", "Cultural anthropology", "Cultural history", "Cultural studies", "Curtis Gans", "David Butler (academic)", "Demography", "Development studies", "Developmental psychology", "Direct election", "Economic history", "Economics", "Education", "Election", "Election audits", "Election security", "Election silence", "Elections by country", "Electoral Calculus", "Electoral fraud", "Electoral geography", "Electoral system", "Environmental social science", "Environmental studies", "FiveThirtyEight", "Fixed-term election", "Food studies", "Gallagher Index", "Geisteswissenschaft", "Gender studies", "General election", "Geography", "Gerrymandering", "Global studies", "History", "History of science", "History of technology", "Human ecology", "Human geography", "Human science", "Humanities", "Index of sociology articles", "Indirect election", "Information science", "Initiative", "Integrated geography", "International Standard Book Number", "International relations", "International studies", "Investment theory of party competition", "Jurisprudence", "Land-use planning", "Law", "Legal history", "Linguistics", "List of close election results", "List of national legal systems", "List of next general elections", "List of psephologists", "List of social science journals", "List of the most recent elections by country", "Local election", "Local electoral calendar 2018", "Mackerras pendulum", "Macroeconomics", "Malcolm Mackerras", "Media studies", "Michael Barone (pundit)", "Microeconomics", "Midterm election", "Military history", "Nate Silver", "National electoral calendar 2018", "Opinion poll", "Outline of social science", "Personality psychology", "Philosophy and economics", "Philosophy of history", "Philosophy of psychology", "Philosophy of science", "Philosophy of social science", "Plurality voting", "Political ecology", "Political economy", "Political history", "Political party", "Political science", "Primary election", "Proportional representation", "Psepholograph", "Psychology", "Public administration", "Public health", "Public opinion polls", "Public policy", "R. B. McCallum", "Recall election", "Referendum", "Referendums by country", "Regional planning", "Regional science", "Robert McKenzie (psephologist)", "Rural sociology", "Science, technology and society", "Science studies", "Scientific analysis", "Secret ballot", "Show election", "Snap election", "Social anthropology", "Social history", "Social psychology", "Social science", "Social work", "Sociology", "Sociology of the Internet", "Sortition", "Suffrage", "Swing (politics)", "Swingometer", "The Almanac of American Politics", "The Cook Political Report", "Thomas Ferguson (academic)", "Two-round system", "Types of democracy", "United Kingdom", "Urban planning", "Urban sociology", "Voting", "W. F. R. Hardie", "William Safire", "Yogendra Yadav"], "references": ["http://blogs.abc.net.au/antonygreen/psephology/", "http://www.idea.int", "http://psephos.adam-carr.net/", "http://www.aceproject.org", "https://books.google.bg/books?id=hhCfzoqaLK0C&pg=PA250&lpg=PA250&dq=%22Psephology%22+Hardie&source=bl&ots=LfI6O8GmPX&sig=8NkWsaTJ4qTQYV_z01vej1QKm_w&hl=en&sa=X&ved=0ahUKEwiOge_Bu5_VAhXBL8AKHckbCssQ6AEILDAB#v=onepage&q=%22Psephology%22%20Hardie&f=false"]}, "Hoeffding's independence test": {"categories": ["All stub articles", "Covariance and correlation", "Nonparametric statistics", "Statistical tests", "Statistics stubs"], "title": "Hoeffding's independence test", "method": "Hoeffding's independence test", "url": "https://en.wikipedia.org/wiki/Hoeffding%27s_independence_test", "summary": "In statistics, Hoeffding's test of independence, named after Wassily Hoeffding, is a test based on the population measure of deviation from independence\n\n \n \n \n H\n =\n \u222b\n (\n \n F\n \n 12\n \n \n \u2212\n \n F\n \n 1\n \n \n \n F\n \n 2\n \n \n \n )\n \n 2\n \n \n \n d\n \n F\n \n 12\n \n \n \n \n {\\displaystyle H=\\int (F_{12}-F_{1}F_{2})^{2}\\,dF_{12}}\n where \n \n \n \n \n F\n \n 12\n \n \n \n \n {\\displaystyle F_{12}}\n is the joint distribution function of two random variables, and \n \n \n \n \n F\n \n 1\n \n \n \n \n {\\displaystyle F_{1}}\n and \n \n \n \n \n F\n \n 2\n \n \n \n \n {\\displaystyle F_{2}}\n are their marginal distribution functions.\nHoeffding derived an unbiased estimator of \n \n \n \n H\n \n \n {\\displaystyle H}\n that can be used to test for independence, and is consistent for any continuous alternative. The test should only be applied to data drawn from a continuous distribution, since \n \n \n \n H\n \n \n {\\displaystyle H}\n has a defect for discontinuous \n \n \n \n \n F\n \n 12\n \n \n \n \n {\\displaystyle F_{12}}\n , namely that it is not necessarily zero when \n \n \n \n \n F\n \n 12\n \n \n =\n \n F\n \n 1\n \n \n \n F\n \n 2\n \n \n \n \n {\\displaystyle F_{12}=F_{1}F_{2}}\n .\nA recent paper describes both the calculation of a sample based version of this measure for use as a test statistic, and calculation of the null distribution of this test statistic.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg"], "links": ["Alternative hypothesis", "Consistent estimator", "Continuous probability distribution", "Correlation", "Distance correlation", "Independence (probability theory)", "Joint distribution function", "Kendall's tau", "Marginal distribution", "Spearman's rank correlation coefficient", "Statistics", "Unbiased estimator", "Wassily Hoeffding"], "references": ["http://www.sciencedirect.com/science/article/B7CRS-4PJ04Y7-1/2/e10c0f978e665a0d5ffd41a594f9a9ba", "https://www.jstor.org/stable/2236021"]}, "Behrens\u2013Fisher problem": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from February 2010", "Articles with unsourced statements from July 2014", "Articles with unsourced statements from September 2010", "Mathematical problems", "Pages with listed invalid ISBNs", "Statistical hypothesis testing"], "title": "Behrens\u2013Fisher problem", "method": "Behrens\u2013Fisher problem", "url": "https://en.wikipedia.org/wiki/Behrens%E2%80%93Fisher_problem", "summary": "In statistics, the Behrens\u2013Fisher problem, named after Walter Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/dd/Question_dropshade.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Annals of Mathematical Statistics", "Annals of Statistics", "ArXiv", "B. L. Welch", "Bayesian inference", "Behrens\u2013Fisher distribution", "Biometrika", "Chi-squared distribution", "Confidence interval", "Digital object identifier", "Fiducial inference", "Frequentist inference", "Harold Ruben", "Hypothesis testing", "I.i.d.", "International Standard Book Number", "Interval estimation", "Judith Rousseau", "List of unsolved problems in statistics", "Location-scale family", "Mathematical Reviews", "Moment (mathematics)", "Multivariate Behrens\u2013Fisher problem", "Multivariate normal distribution", "Nonparametric statistics", "Normal distribution", "Pearson distribution", "Probability distribution", "Ronald Fisher", "Sample mean", "Sankhya (journal)", "Significance level", "Standard deviation", "Statistical independence", "Statistics", "Student's t-test", "Student's t distribution", "T-test", "University College London", "Variance", "Wald test", "Walter Behrens (statistician)", "Walter Ulrich Behrens", "Welch's t test", "Welch\u2013Satterthwaite equation"], "references": ["http://web.uvic.ca/econ/research/papers/pdfs/ewp0404.pdf", "http://www.hss.cmu.edu/philosophy/seidenfeld/relating%20to%20Fisher/Fisher's%20Fiducial%20Argument%20and%20Bayes%20Theorem.pdf", "http://education.wayne.edu/jmasm/sawilowsky_behrens_fisher.pdf", "http://sankhya.isical.ac.in/search/servlet/SSearch?s_order=2&choice1=author&text1=Ruben&opt1=And&choice2=title&text2=&opt2=And&choice3=title&text3=&opt3=And&choice4=keyword&text4=&rel_yr=equalto&yearsrch=2002&rel_vol=equalto&volumesrch=64&series=on&part=on&amssrch=&num=20&cntr=0", "http://www.ams.org/mathscinet-getitem?mr=0019277", "http://arxiv.org/abs/0811.0672", "http://doi.org/10.1002%2F(SICI)1521-4036(200001)42:1%3C17::AID-BIMJ17%3E3.0.CO;2-U", "http://doi.org/10.1016%2Fj.jspi.2006.09.007", "http://doi.org/10.1016%2Fj.jspi.2009.11.010", "http://doi.org/10.1080%2F01966324.1998.10737471", "http://doi.org/10.1080%2F01966324.1999.10737478", "http://doi.org/10.1080%2F03610910802049599", "http://doi.org/10.1093%2Fbiomet%2F34.1-2.28", "http://doi.org/10.1093%2Fbiomet%2Fasm093", "http://doi.org/10.1108%2F03684920710749866", "http://doi.org/10.1111%2Fj.1469-1809.1941.tb02281.x", "http://doi.org/10.1214%2F07-AOS528", "http://doi.org/10.1214%2Faoms%2F1177729755", "http://doi.org/10.18637%2Fjss.v064.i09", "http://doi.org/10.2307%2F2332010", "http://catalog.hathitrust.org/Record/007924569", "https://www.researchgate.net/publication/313652727_Comparison_of_confidence_intervals_for_the_behrens_fisher_problem", "https://web.archive.org/web/20120425091706/http://education.wayne.edu/jmasm/sawilowsky_behrens_fisher.pdf", "https://www.jstatsoft.org/article/view/v064i09"]}, "Moderator variable": {"categories": ["CS1 maint: Multiple names: authors list", "Psychometrics", "Regression analysis"], "title": "Moderation (statistics)", "method": "Moderator variable", "url": "https://en.wikipedia.org/wiki/Moderation_(statistics)", "summary": "In statistics and regression analysis, moderation occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator variable or simply the moderator. The effect of a moderating variable is characterized statistically as an interaction; that is, a categorical (e.g., sex, ethnicity, class) or quantitative (e.g., level of reward) variable that affects the direction and/or strength of the relation between dependent and independent variables. Specifically within a correlational analysis framework, a moderator is a third variable that affects the zero-order correlation between two other variables, or the value of the slope of the dependent variable on the independent variable. In analysis of variance (ANOVA) terms, a basic moderator effect can be represented as an interaction between a focal independent variable and a factor that specifies the appropriate conditions for its operation.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c1/Two-way_interaction_effect_example.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavioral sciences", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Personality and Social Psychology", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Life satisfaction", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multicollinearity", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "Omitted-variable bias", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variable (mathematics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.psy.mq.edu.au/psystat/documents/interaction.pdf", "http://www.jeremydawson.co.uk/slopes.htm"]}, "Least squares": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles needing expert attention", "All articles that are too technical", "Articles lacking in-text citations from June 2014", "Articles needing additional references from February 2012", "Articles needing expert attention from February 2016", "CS1 French-language sources (fr)", "Least squares", "Optimization algorithms and methods", "Single-equation methods (econometrics)", "Wikipedia articles that are too technical from February 2016", "Wikipedia articles with NDL identifiers"], "title": "Least squares", "method": "Least squares", "url": "https://en.wikipedia.org/wiki/Least_squares", "summary": "The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns. \"Least squares\" means that the overall solution minimizes the sum of the squares of the residuals made in the results of every single equation.\nThe most important application is in data fitting. The best fit in the least-squares sense minimizes the sum of squared residuals (a residual being: the difference between an observed value, and the fitted value provided by a model). When the problem has substantial uncertainties in the independent variable (the x variable), then simple regression and least-squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares.\nLeast-squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. The nonlinear problem is usually solved by iterative refinement; at each iteration the system is approximated by a linear one, and thus the core calculation is similar in both cases.\nPolynomial least squares describes the variance in a prediction of the dependent variable as a function of the independent variable and the deviations from the fitted curve.\nWhen the observations come from an exponential family and mild conditions are satisfied, least-squares estimates and maximum-likelihood estimates are identical. The method of least squares can also be derived as a method of moments estimator.\nThe following discussion is mostly presented in terms of linear functions but the use of least squares is valid and practical for more general families of functions. Also, by iteratively applying local quadratic approximation to the likelihood (through the Fisher information), the least-squares method may be used to fit a generalized linear model.\nThe least-squares method is usually credited to Carl Friedrich Gauss (1795), but it was first published by Adrien-Marie Legendre (1805).", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/33/Bendixen_-_Carl_Friedrich_Gau%C3%9F%2C_1828.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/9/94/Linear_least_squares2.png", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1f/X33-ellips-1.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Adjustment of observations", "Adrien-Marie Legendre", "Age of Exploration", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Approximation theory", "Arithmetic mean", "Astronomy", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bayesian statistics", "Best linear unbiased prediction", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "C. R. Rao", "Calibration curve", "Canonical correlation", "Carl Friedrich Gauss", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Ceres (dwarf planet)", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Closed-form solution", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compressed sensing", "Computational statistics", "Confidence interval", "Confidence limits", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convex optimization", "Correlated", "Correlation and dependence", "Correlation does not imply causation", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curve fitting", "Data collection", "David Luenberger", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete choice", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elastic net regularization", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher information", "Fixed effects model", "Force constant", "Forest plot", "Fourier analysis", "Franz Xaver von Zach", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gauss' method", "Gaussian quadrature", "Gauss\u2013Markov theorem", "Gauss\u2013Newton algorithm", "Gauss\u2013Seidel", "General linear model", "Generalized least squares", "Generalized linear model", "Geodesy", "Geographic information system", "Geometric mean", "George Casella", "Geostatistics", "Giuseppe Piazzi", "Goodness of fit", "Gradient", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "Harmonic mean", "Helge Toutenburg", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hooke's law", "Hypothesis testing", "Independent variable", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jackknife resampling", "Jacobian matrix and determinant", "Jarque\u2013Bera test", "Jerome H. Friedman", "Johansen test", "Jonckheere's trend test", "Journal of the Royal Statistical Society", "Jupiter", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kepler's laws of planetary motion", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "L1-norm", "L2-norm", "L2 norm", "Lagrange multipliers", "Laplace distribution", "Least-angle regression", "Least-squares function approximation", "Least absolute deviation", "Least absolute deviations", "Least angle regression", "Least squares approximation", "Lehmann\u2013Scheff\u00e9 theorem", "Libration", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear", "Linear combination", "Linear discriminant analysis", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Maxima and minima", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimator", "McNemar's test", "Mean", "Mean and predicted response", "Measurement uncertainty", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Minimum mean square error", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-linear least squares", "Non-negative least squares", "Nonlinear least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Orthogonal projection", "Outline of statistics", "Overdetermined system", "Parameter estimation", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pierre-Simon Laplace", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial least squares", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal component regression", "Prior distribution", "Prior probability", "Probabilistic design", "Probability", "Probability density", "Probability distribution", "Probit model", "Proportional hazards model", "Proximal gradient methods for learning", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quadratic loss function", "Quadratic programming", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effects model", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regularization (machine learning)", "Regularized least squares", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Ridge regression", "Rob Tibshirani", "Robert Adrain", "Robust regression", "Robust statistics", "Roger Cotes", "Roger Joseph Boscovich", "Root mean square", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sara van de Geer", "Saturn", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Squared deviations", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taylor series", "Tikhonov regularization", "Time domain", "Time series", "Tobias Mayer", "Tolerance interval", "Total least squares", "Trend estimation", "Trevor Hastie", "U-statistic", "Unbiased", "Uncorrelated", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wayne Fuller", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.biomedcentral.com/1471-2164/14/S1/S14", "http://www-stat.stanford.edu/~tibs/ElemStatLearn/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549810", "http://www.ncbi.nlm.nih.gov/pubmed/23369194", "http://dl.acm.org/citation.cfm?id=1390161", "http://doi.org/10.1080%2F01621459.1976.10481508", "http://doi.org/10.1111%2Fj.1751-5823.1998.tb00406.x", "http://doi.org/10.1145%2F1390156.1390161", "http://doi.org/10.1186%2F1471-2164-14-S1-S14", "http://doi.org/10.1198%2F016214508000000337", "http://doi.org/10.1214%2Faos%2F1176345451", "http://www.jstor.org/stable/2346178", "http://projecteuclid.org/euclid.aos/1176345451", "https://books.google.com/books/about/Nouvelles_m%C3%A9thodes_pour_la_d%C3%A9terminati.html?id=FRcOAAAAQAAJ", "https://books.google.com/books?id=3LK9JoGEyN4C", "https://books.google.com/books?id=lZU0CAH4RccC&pg=PA78", "https://id.ndl.go.jp/auth/ndlna/00570033", "https://web.archive.org/web/20091110212529/http://www-stat.stanford.edu/~tibs/ElemStatLearn/", "https://www.wikidata.org/wiki/Q74304"]}, "Statistical dispersion": {"categories": ["Accuracy and precision", "All articles needing additional references", "Articles needing additional references from December 2010", "Statistical deviation and dispersion", "Summary statistics"], "title": "Statistical dispersion", "method": "Statistical dispersion", "url": "https://en.wikipedia.org/wiki/Statistical_dispersion", "summary": "In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.\nDispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f9/Comparison_standard_deviations.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Absolute value", "Accelerated failure time model", "Accuracy and precision", "Actuarial science", "Akaike information criterion", "Allan variance", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Average absolute deviation", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biological sciences", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of dispersion", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimensionless", "Distance standard deviation", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Entropy (information theory)", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finance", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Gini coefficient", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Hadamard variance", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Information entropy", "Inter-rater variability", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Economic Theory", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Linear transformation", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean-preserving spread", "Mean absolute difference", "Measurement uncertainty", "Median", "Median-unbiased estimator", "Median absolute deviation", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational error", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outliers", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial ordering", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Physical sciences", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Qualitative variation", "Quality control", "Quantity", "Quartile coefficient of dispersion", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real number", "Regression analysis", "Regression model validation", "Relative mean difference", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust measures of scale", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale factor", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Summary statistics", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Units of measurement", "V-statistic", "Variance", "Variance-to-mean ratio", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.itl.nist.gov/div898/handbook/eda/section3/eda364.htm", "http://doi.org/10.1016%2F0022-0531(70)90038-4"]}, "Exploratory factor analysis": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from June 2017", "Articles with specifically marked weasel-worded phrases from February 2014", "Articles with unsourced statements from June 2018", "Factor analysis"], "title": "Exploratory factor analysis", "method": "Exploratory factor analysis", "url": "https://en.wikipedia.org/wiki/Exploratory_factor_analysis", "summary": "In multivariate statistics, exploratory factor analysis (EFA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. EFA is a technique within factor analysis whose overarching goal is to identify the underlying relationships between measured variables. It is commonly used by researchers when developing a scale (a scale is a collection of questions used to measure a particular research topic) and serves to identify a set of latent constructs underlying a battery of measured variables. It should be used when the researcher has no a priori hypothesis about factors or patterns of measured variables. Measured variables are any one of several attributes of people that may be observed and measured. Examples of a measured variables could be the physical height, weight, and pulse rate of a human being. Usually, researchers would have large number of measured variables, which are assumed to be related to a smaller number of \"unobserved\" factors. Researchers must carefully consider the number of measured variables to include in the analysis. EFA procedures are more accurate when each factor is represented by multiple measured variables in the analysis.\nEFA is based on the common factor model. In this model, manifest variables are expressed as a function of common factors, unique factors, and errors of measurement. Each unique factor influences only one manifest variable, and does not explain correlations between manifest variables. Common factors influence more than one manifest variable and \"Factor loadings\" are measures of the influence of a common factor on a manifest variable. For the EFA procedure, we are more interested in identifying the common factors and the related manifest variables. \nEFA assumes that any indicator/measured variable may be associated with any factor. When developing a scale, researchers should use EFA first before moving on to confirmatory factor analysis (CFA). EFA is essential to determine underlying factors/constructs for a set of measured variables; while CFA allows the researcher to test the hypothesis that a relationship between the observed variables and their underlying latent factor(s)/construct(s) exists. \nEFA requires the researcher to make a number of important decisions about how to conduct the analysis because there is no one set method.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Angle", "Confidence interval", "Confirmatory factor analysis", "Digital object identifier", "Factor analysis", "Goodness of fit", "International Standard Book Number", "Latent variable", "Maximum likelihood", "Multivariate statistics", "Occam's razor", "Orthogonality", "Statistical significance", "Variable (research)"], "references": ["http://www.unc.edu/~rcm/book/factornew.htm", "http://pareonline.net/getvn.asp?v=18&n=8", "http://pareonline.net/pdf/v10n7.pdf", "http://doi.org/10.1006%2Fjrpe.1997.2194", "http://doi.org/10.1007%2FBF02289447", "http://doi.org/10.1007%2Fbf02293557", "http://doi.org/10.1007%2Fs10803-009-0816-2", "http://doi.org/10.1037%2F0033-2909.115.3.475.1994-32085-00110.1037%2F0033-2909.115.3.475", "http://doi.org/10.1037%2F1082-989X.4.3.272", "http://doi.org/10.1037%2Fa0025697", "http://doi.org/10.1177%2F001316446002000116", "http://doi.org/10.1177%2F001316446902900303", "http://doi.org/10.1177%2F001316447103100301", "http://doi.org/10.1207%2Fs15327906mbr2502_2", "http://doi.org/10.3758%2FBRM.42.3.871", "http://en.wikiversity.org/wiki/Exploratory_factor_analysis", "https://ppw.kuleuven.be/okp/_pdf/Raiche2013NGSFC.pdf", "https://web.archive.org/web/20131021052759/https://ppw.kuleuven.be/okp/_pdf/Raiche2013NGSFC.pdf", "https://web.archive.org/web/20150317145450/http://pareonline.net/getvn.asp?v=18&n=8"]}, "Additive smoothing": {"categories": ["All articles to be merged", "All articles with unsourced statements", "Articles to be merged from July 2018", "Articles with unsourced statements from December 2013", "Categorical data", "Probability theory", "Statistical natural language processing", "Wikipedia articles needing clarification from October 2018"], "title": "Additive smoothing", "method": "Additive smoothing", "url": "https://en.wikipedia.org/wiki/Additive_smoothing", "summary": "In statistics, additive smoothing, also called Laplace smoothing (not to be confused with Laplacian smoothing as used in image processing), or Lidstone smoothing, is a technique used to smooth categorical data. Given an observation \n \n \n \n \n \n \n x\n \n \n =\n \n \n \u27e8\n \n \n x\n \n 1\n \n \n ,\n \n \n x\n \n 2\n \n \n ,\n \n \u2026\n ,\n \n \n x\n \n d\n \n \n \n \u27e9\n \n \n \n \n \n {\\textstyle \\scriptstyle {\\mathbf {x} \\ =\\ \\left\\langle x_{1},\\,x_{2},\\,\\ldots ,\\,x_{d}\\right\\rangle }}\n from a multinomial distribution with \n \n \n \n \n \n N\n \n \n \n \n {\\textstyle \\scriptstyle {N}}\n trials, a \"smoothed\" version of the data gives the estimator:\n\n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n i\n \n \n =\n \n \n \n \n x\n \n i\n \n \n +\n \u03b1\n \n \n N\n +\n \u03b1\n d\n \n \n \n \n (\n i\n =\n 1\n ,\n \u2026\n ,\n d\n )\n ,\n \n \n {\\displaystyle {\\hat {\\theta }}_{i}={\\frac {x_{i}+\\alpha }{N+\\alpha d}}\\qquad (i=1,\\ldots ,d),}\n where the \"pseudocount\" \u03b1 > 0 is a smoothing parameter. \u03b1 = 0 corresponds to no smoothing. (This parameter is explained in \u00a7 Pseudocount below.) Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) \n \n \n \n \n \n \n \n x\n \n i\n \n \n N\n \n \n \n \n \n {\\textstyle \\scriptstyle {\\frac {x_{i}}{N}}}\n , and the uniform probability \n \n \n \n \n \n \n 1\n d\n \n \n \n \n \n {\\textstyle \\scriptstyle {\\frac {1}{d}}}\n . Invoking Laplace's rule of succession, some authors have argued that \u03b1 should be 1 (in which case the term add-one smoothing is also used), though in practice a smaller value is typically chosen.\nFrom a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter \u03b1 as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a Beta distribution as the conjugate prior for the parameters of Binomial distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20161219000653%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20071115071721%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20070702231905%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20070702215640%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20070404041444%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20070316075541%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20060817065722%21Mergefrom.svg"], "links": ["0 (number)", "Artificial neural network", "Bag of words model", "Bayesian average", "Bayesian inference", "Beta distribution", "Binomial distribution", "Categorical data", "Categorical distribution", "Cromwell's rule", "Density estimation", "Dirichlet distribution", "Discrete uniform distribution", "Empirical probability", "Estimator", "Event (probability theory)", "Expected value", "George James Lidstone", "Halting problem", "Hidden Markov model", "Image processing", "International Standard Book Number", "Jeffreys prior", "Laplacian smoothing", "Machine learning", "Model (abstract)", "Multinomial distribution", "Naive Bayes classifier", "PPM compression algorithm", "Parameter", "Pierre-Simon Laplace", "Posterior distribution", "Prediction by partial matching", "Principle of indifference", "Prior distribution", "Prior probability", "Probability", "Recommender system", "Relative frequency", "Relevance feedback", "Rule of Succession", "Rule of succession", "Sample (statistics)", "Shrinkage estimator", "Smoothing", "Statistics", "Sunrise problem"], "references": ["http://www.aclweb.org/anthology/P/P96/P96-1041.pdf", "http://dl.acm.org/citation.cfm?id=2809471", "http://dl.acm.org/citation.cfm?id=2934737", "https://www.youtube.com/watch?v=qRJ3GKMOFrE#t=4124", "https://archive.is/20130419033054/http://www.soe.ucsc.edu/research/compbio/html_format_papers/tr-95-11/node30.html", "https://web.archive.org/web/20040909153902/http://www.soe.ucsc.edu/research/compbio/html_format_papers/tr-95-11/node8.html"]}, "Multivariate adaptive regression splines": {"categories": ["All articles that may contain original research", "Articles that may contain original research from October 2016", "Machine learning", "Nonparametric regression", "Wikipedia external links cleanup from October 2016", "Wikipedia spam cleanup from October 2016"], "title": "Multivariate adaptive regression splines", "method": "Multivariate adaptive regression splines", "url": "https://en.wikipedia.org/wiki/Multivariate_adaptive_regression_splines", "summary": "In statistics, multivariate adaptive regression splines (MARS) is a form of regression analysis introduced by Jerome H. Friedman in 1991. It is a non-parametric regression technique\nand can be seen as an extension of linear models that automatically models nonlinearities and interactions between variables.\nThe term \"MARS\" is trademarked and licensed to Salford Systems. In order to avoid trademark infringements, many open source implementations of MARS are called \"Earth\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/74/Friedmans_mars_hinge_functions.png", "https://upload.wikimedia.org/wikipedia/commons/6/6f/Friedmans_mars_linear_model.png", "https://upload.wikimedia.org/wikipedia/commons/9/9e/Friedmans_mars_ozone_model.png", "https://upload.wikimedia.org/wikipedia/commons/a/a7/Friedmans_mars_simple_model.png", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Artificial neural network", "Basis function", "Boosting (meta-algorithm)", "Brute-force search", "Cross-validation (statistics)", "Decision tree learning", "Dependent and independent variables", "Digital object identifier", "Errors and residuals in statistics", "Friedman, J. H.", "Generalized additive model", "Generalized linear model", "Grace Wahba", "Greedy algorithm", "Heuristics", "Ice hockey stick", "International Standard Book Number", "Inverse problem", "JSTOR", "Jerome H. Friedman", "Linear model", "Linear regression", "Local regression", "Logistic regression", "Mathematical Reviews", "Model selection", "Multicollinearity", "Non-parametric regression", "Nonlinear regression", "Overfit", "Piecewise", "Predictive analytics", "R (programming language)", "Ramp function", "Random forest", "Rational function modeling", "Rectifier (neural networks)", "Recursive partitioning", "Regression analysis", "Regularization (machine learning)", "Residual sum of squares", "Segmented regression", "Spline (mathematics)", "Spline interpolation", "Spline regression", "Statistics", "Stepwise regression", "Support Vector Machine", "TSMARS", "Well-posed problem", "Zentralblatt MATH"], "references": ["http://www.salford-systems.com/mars.php", "http://support.sas.com/documentation/cdl/en/statug/65328/HTML/default/viewer.htm#statug_adaptivereg_overview.htm", "http://statsoft.com/products/data-mining-solutions/", "http://www-stat.stanford.edu/~tibs/ElemStatLearn", "http://www.stat.tamu.edu/~bmallick/wileybook/book_code.html", "http://www.cs.rtu.lv/jekabsons/regression.html", "http://www.ams.org/mathscinet-getitem?mr=1091842", "http://doi.org/10.1214%2Faos%2F1176347963", "http://www.jstor.org/stable/2241837", "http://zbmath.org/?format=complete&q=an:0765.62064", "http://orange.biolab.si/blog/2011/12/20/earth-multivariate-adaptive-regression-splines/", "http://www.maths.bath.ac.uk/~jjf23", "https://www.amazon.com/Recursive-Partitioning-Applications-Springer-Statistics/dp/1441968237", "https://github.com/jcrudy/py-earth/", "https://cran.r-project.org/web/packages/earth/index.html", "https://cran.r-project.org/web/packages/mda/index.html", "https://cran.r-project.org/web/packages/polspline/index.html"]}, "Placebo-controlled study": {"categories": ["All articles with dead external links", "All articles with unsourced statements", "Articles with dead external links from March 2018", "Articles with permanently dead external links", "Articles with unsourced statements from February 2009", "Clinical research", "Clinical trials", "Design of experiments"], "title": "Placebo-controlled study", "method": "Placebo-controlled study", "url": "https://en.wikipedia.org/wiki/Placebo-controlled_study", "summary": "Placebo-controlled studies are a way of testing a medical therapy in which, in addition to a group of subjects that receives the treatment to be evaluated, a separate control group receives a sham \"placebo\" treatment which is specifically designed to have no real effect. Placebos are most commonly used in blinded trials, where subjects do not know whether they are receiving real or placebo treatment. Often, there is also a further \"natural history\" group that does not receive any treatment at all.\nThe purpose of the placebo group is to account for the placebo effect, that is, effects from treatment that do not depend on the treatment itself. Such factors include knowing one is receiving a treatment, attention from health care professionals, and the expectations of a treatment's effectiveness by those running the research study. Without a placebo group to compare against, it is not possible to know whether the treatment itself had any effect.\nPatients frequently show improvement even when given a sham or \"fake\" treatment. Such intentionally inert placebo treatments can take many forms, such as a pill containing only sugar, a surgery where nothing efficacious is actually done (just an incision and sometimes some minor touching or handling of the underlying structures), or a medical device (such as an ultrasound machine) that is not actually turned on. Also, due to the body's natural healing ability and statistical effects such as regression to the mean, many patients will get better even when given no treatment at all. Thus, the relevant question when assessing a treatment is not \"does the treatment work?\" but \"does the treatment work better than a placebo treatment, or no treatment at all?\" As one early clinical trial researcher wrote, \"the first object of a therapeutic trial is to discover whether the patients who receive the treatment under investigation are cured more rapidly, more completely or more frequently, than they would have been without it.\"p.195 More broadly, the aim of a clinical trial is to determine what treatments, delivered in what circumstances, to which patients, in what conditions, are the most effective.Therefore, the use of placebos is a standard control component of most clinical trials, which attempt to make some sort of quantitative assessment of the efficacy of medicinal drugs or treatments. Such a test or clinical trial is called a placebo-controlled study, and its control is of the negative type. A study whose control is a previously tested treatment, rather than no treatment, is called a positive-control study, because its control is of the positive type. Government regulatory agencies approve new drugs only after tests establish not only that patients respond to them, but also that their effect is greater than that of a placebo (by way of affecting more patients, by affecting responders more strongly, or both).", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1c/Cebocap.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/77/James_lind.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg"], "links": ["Academic clinical trials", "Acute (medical)", "Adaptive clinical trial", "Amphetamine", "Analysis of clinical trials", "Animal magnetism", "Animal testing", "Animal testing on non-human primates", "Antidepressant", "Attributable fraction among the exposed", "Attributable fraction for the population", "Austin Flint murmur", "Balsam of Peru", "Bed-rest", "Beneficence (ethics)", "Bias of an estimator", "Bioethics", "Blind experiment", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Ceteris paribus", "Cider", "Citrus fruit", "Clinical data acquisition", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Clinical trial management", "Coercion", "Cohort study", "Complication (medicine)", "Confounding factor", "Correlation does not imply causation", "Cross-sectional study", "Cumulative incidence", "Declaration of Helsinki", "Design of experiments", "Digital object identifier", "Doctors' Trial", "Double-blind", "Ecological study", "Electuary", "Endocarditis", "Epidemiological methods", "Evidence-based medicine", "Experiment", "Experimental design", "First-in-man study", "Fluorescent light", "Franz Mesmer", "Garlic", "Glossary of clinical research", "HMS Salisbury", "Hazard ratio", "Headache", "Hippocratic Oath", "Hypnotherapy", "Hypochondria", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Informed consent", "Intention-to-treat analysis", "International Standard Book Number", "James Lind (physician)", "John Haygarth", "Lactic acid", "Lemon", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Marsh Chapel Experiment", "Medical Research Council (UK)", "Medical ethics", "Medical ultrasonography", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "Mustard (condiment)", "Myrrh", "Natural history group", "Nazi human experimentation", "Nazism", "Nested case\u2013control study", "Niacin", "Null result", "Number needed to harm", "Number needed to treat", "Nuremberg Code", "Observational study", "Odds ratio", "Open-label trial", "Orange (fruit)", "Pericarditis", "Period prevalence", "Perkins tractors", "Permutation", "Philosophy of medicine", "Pint", "Placebo", "Placebo effect", "Placebo in history", "Pneumonia", "Point prevalence", "Population Impact Measures", "Prayer", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "Psilocybin", "Psychedelic drug", "Psychiatry", "Psychoactive", "Psychosomatic illness", "Psychotherapy", "PubMed Central", "PubMed Identifier", "Pulmonary tuberculosis", "Quantitative property", "Quassia", "Randomized clinical trial", "Randomized controlled trial", "Regression to the mean", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Rheumatic fever", "Rheumatism", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Royal Commission", "Scientific control", "Scientific method", "Screening (medicine)", "Scurvy", "Seeding trial", "Selection bias", "Ship's doctor", "Specificity and sensitivity", "Streptomycin", "Sulfuric acid", "Survivorship bias", "Systematic review", "Vaccine trial", "Verification and validation", "Vinegar", "Virulence", "Vitriol", "World Medical Association", "World War II"], "references": ["http://bmj.com/cgi/pmidlookup?view=long&pmid=9794865", "http://qhc.bmj.com/cgi/pmidlookup?view=long&pmid=12792017", "http://student.bmj.com/issues/02/02/education/12.php", "http://jmb.rsmjournals.com/cgi/pmidlookup?view=long&pmid=16059528", "http://onlinelibrary.wiley.com/doi/10.1002/jclp.v61:7/issuetoc", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1114162", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1299353", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1720613", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1743715", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1918604", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2091872", "http://www.ncbi.nlm.nih.gov/pubmed/10768687", "http://www.ncbi.nlm.nih.gov/pubmed/12461388", "http://www.ncbi.nlm.nih.gov/pubmed/12792017", "http://www.ncbi.nlm.nih.gov/pubmed/13155508", "http://www.ncbi.nlm.nih.gov/pubmed/13158365", "http://www.ncbi.nlm.nih.gov/pubmed/15082620", "http://www.ncbi.nlm.nih.gov/pubmed/15082623", "http://www.ncbi.nlm.nih.gov/pubmed/15827994", "http://www.ncbi.nlm.nih.gov/pubmed/16059528", "http://www.ncbi.nlm.nih.gov/pubmed/16319443", "http://www.ncbi.nlm.nih.gov/pubmed/18890300", "http://www.ncbi.nlm.nih.gov/pubmed/5942087", "http://www.ncbi.nlm.nih.gov/pubmed/6999345", "http://www.ncbi.nlm.nih.gov/pubmed/8336377", "http://www.ncbi.nlm.nih.gov/pubmed/9059193", "http://www.ncbi.nlm.nih.gov/pubmed/9489259", "http://www.ncbi.nlm.nih.gov/pubmed/9794865", "http://archpsyc.ama-assn.org/cgi/pmidlookup?view=long&pmid=10768687", "http://content.apa.org/journals/ccp/66/1/7", "http://doi.org/10.1001%2Farchpsyc.57.4.311", "http://doi.org/10.1001%2Fjama.270.6.742", "http://doi.org/10.1002%2Fjclp.20128", "http://doi.org/10.1002%2Fjclp.20133", "http://doi.org/10.1016%2F0002-9343(54)90441-6", "http://doi.org/10.1037%2F0022-006X.66.1.7", "http://doi.org/10.1056%2FNEJM198010303031804", "http://doi.org/10.1093%2Fije%2Fdyh028", "http://doi.org/10.1093%2Fije%2Fdyh162", "http://doi.org/10.1136%2Fbmj.2.4582.769", "http://doi.org/10.1136%2Fbmj.317.7167.1220", "http://doi.org/10.1136%2Ffn.76.1.F64", "http://doi.org/10.1136%2Fqhc.12.3.232", "http://doi.org/10.1258%2Fj.jmb.2005.04-01", "http://doi.org/10.1258%2Fjrsm.98.12.572", "http://doi.org/10.2466%2Fpr0.1966.19.1.211", "http://www.jameslindlibrary.org/index.html", "http://www.jameslindlibrary.org/trial_records/19th_Century/haygarth/pamphlet/haygarth_pamphlet.pdf", "http://www.jameslindlibrary.org/trial_records/19th_Century/flint/flint_tp.html", "http://www.jameslindlibrary.org/trial_records/20th_Century/1940s/MRC_bmj/MRC_bmj_kp.html", "http://www.jameslindlibrary.org/trial_records/20th_Century/1940s/elvainio_et_al/elvainio_commentary.html", "http://www.jrsm.org/cgi/pmidlookup?view=long&pmid=16319443", "http://ije.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15082623", "http://ije.oxfordjournals.org/cgi/reprint/33/2/243", "https://web.archive.org/web/20080828040111/http://www.jameslindlibrary.org/trial_records/20th_Century/1940s/elvainio_et_al/elvainio_commentary.html", "https://web.archive.org/web/20090220183350/http://www.wma.net/e/policy/b3.htm", "https://www.jstor.org/pss/3001983"]}, "Astrostatistics": {"categories": ["All stub articles", "Applied statistics", "Astrophysics", "Data mining and machine learning software", "Statistics stubs"], "title": "Astrostatistics", "method": "Astrostatistics", "url": "https://en.wikipedia.org/wiki/Astrostatistics", "summary": "Astrostatistics is a discipline which spans astrophysics, statistical analysis and data mining. It is used to process the vast amount of data produced by automated scanning of the cosmos, to characterize complex datasets, and to link astronomical data to astrophysical theory. Many branches of statistics are involved in astronomical analysis including nonparametrics, multivariate regression and multivariate classification, time series analysis, and especially Bayesian inference.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["American Astronomical Society", "American Statistical Association", "Astronomical data", "Astrophysical theory", "Astrophysics", "Automated scanning", "Bayesian inference", "Data mining", "International Astronomical Union", "International Astrostatistics Association", "International Statistical Institute", "Multivariate classification", "Multivariate regression", "Nonparametrics", "Statistical analysis", "Statistics", "Time series analysis"], "references": ["http://asaip.psu.edu", "https://asaip.psu.edu"]}, "Population variance": {"categories": ["All articles lacking in-text citations", "All articles with incomplete citations", "All articles with unsourced statements", "Articles containing proofs", "Articles lacking in-text citations from November 2018", "Articles with excessive see also sections from May 2017", "Articles with incomplete citations from March 2013", "Articles with inconsistent citation formats", "Articles with unsourced statements from February 2012", "Articles with unsourced statements from June 2015", "Articles with unsourced statements from September 2016", "CS1 maint: Uses authors parameter", "Moment (mathematics)", "Statistical deviation and dispersion", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Variance", "method": "Population variance", "url": "https://en.wikipedia.org/wiki/Variance", "summary": "In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of (random) numbers are spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n {\\displaystyle \\sigma ^{2}}\n , \n \n \n \n \n s\n \n 2\n \n \n \n \n {\\displaystyle s^{2}}\n , or \n \n \n \n Var\n \u2061\n (\n X\n )\n \n \n {\\displaystyle \\operatorname {Var} (X)}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Comparison_standard_deviations.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/6/60/Scaled_chi_squared.svg", "https://upload.wikimedia.org/wikipedia/commons/9/97/Scaled_chi_squared_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/6/64/Variance_visualisation.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algebraic formula for the variance", "Algorithms for calculating variance", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average absolute deviation", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bessel's correction", "Bhatia\u2013Davis inequality", "Bias of an estimator", "Biased estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biometry", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box test", "Box\u2013Anderson test", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cantor distribution", "Capon test", "Cartography", "Catastrophic cancellation", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central moment", "Central tendency", "Characteristic function (probability theory)", "Chebyshev's inequality", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi square test", "CiteSeerX", "Classical mechanics", "Classical test theory", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinant", "Common-method variance", "Completeness (statistics)", "Complex conjugate", "Complex number", "Concave function", "Conditional expectation", "Conditional variance", "Confidence interval", "Confounding", "Conjugate transpose", "Consistent estimator", "Contingency table", "Continuous distribution", "Continuous probability distribution", "Continuous random variable", "Control chart", "Correlated", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Covariance matrix", "Credible interval", "Crime statistics", "Cronbach's alpha", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulative distribution function", "Data collection", "Data set", "Decomposition of time series", "Definite integral", "Degrees of freedom (statistics)", "Delta method", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Deviation (statistics)", "Dice", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete probability distribution", "Discrete random variable", "Distance variance", "Divergence (statistics)", "Downside risk", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation of covariance matrices", "Estimation theory", "Estimator", "Euclidean distance", "Excess kurtosis", "Expected value", "Experiment", "Explained variance", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "F test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Floating point arithmetic", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heavy-tailed distribution", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis testing", "Independence (probability theory)", "Index of dispersion", "Integrated Authority File", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Invariant (mathematics)", "Investment", "Ir\u00e9n\u00e9e-Jules Bienaym\u00e9", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen's inequality", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Klotz test", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Law of total variance", "Lehmann test", "Lehmann\u2013Scheff\u00e9 theorem", "Leo Goodman", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean absolute difference", "Mean absolute error", "Mean preserving spread", "Mean square error", "Mean squared error", "Measurement error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michel Lo\u00e8ve", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment-generating function", "Moment (mathematics)", "Moment (physics)", "Moment of inertia", "Moment of inertia tensor", "Monotone likelihood ratio", "Monte Carlo method", "Mood test", "Moses test", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Observations", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Pareto distribution", "Pareto index", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Pooled variance", "Popoviciu's inequality on variances", "Population (statistics)", "Population statistics", "Positive definite matrix", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability-generating function", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Proportional hazards model", "Psychometrics", "Qualitative variation", "Quality control", "Quantile function", "Quasi-experiment", "Quasi-variance", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raw moment", "Reduced chi-squared", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Root mean square deviation", "Run chart", "Sample (statistics)", "Sample covariance", "Sample mean", "Sample mean and covariance", "Sample median", "Sample size determination", "Sample standard deviation", "Sampling (statistics)", "Sampling distribution", "Samuelson's inequality", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Semivariance", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shrinkage estimator", "Sigma", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spearman\u2013Brown prediction formula", "Spectral density estimation", "Square root", "Squared deviations", "Standard deviation", "Standard error", "Standard error (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sukhatme test", "Sum of normally distributed random variables", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taylor's law", "Taylor expansion", "Taylor expansions for the moments of functions of random variables", "The Correlation Between Relatives on the Supposition of Mendelian Inheritance", "Time domain", "Time series", "Tolerance interval", "Trace (linear algebra)", "Transpose", "Trend estimation", "U-statistic", "Unbiased estimation of standard deviation", "Uncorrelated", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-covariance matrix", "Variance (disambiguation)", "Vector autoregression", "Vector space", "Wald test", "Wavelet", "Weighted mean", "Weighted variance", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15097/1/9.pdf", "http://www.mathstatica.com/book/Mathematical_Statistics_with_Mathematica.pdf", "http://mathworld.wolfram.com/SampleVarianceDistribution.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.551.9397", "http://www.ijpam.eu/contents/2005-21-3/10/10.pdf", "http://www.ijpam.eu/contents/2009-52-1/5/5.pdf", "http://gallica.bnf.fr/ark:/12148/bpt6k16411c/f166.image.n19", "http://visualiseur.bnf.fr/CadresFenetre?O=NUMM-2994&I=313", "http://sites.mathdoc.fr/JMPA/PDF/JMPA_1867_2_12_A10_0.pdf", "http://krishikosh.egranth.ac.in/bitstream/1/2025521/1/G2257.pdf", "http://doi.org/10.1006%2Fjmaa.1999.6688", "http://doi.org/10.1016%2FS0167-7152(98)00041-8", "http://doi.org/10.1080%2F01621459.1968.10480944", "http://doi.org/10.2307%2F2281592", "http://doi.org/10.7153%2Fjmi-02-11", "http://www.jstor.org/stable/2281592", "http://www.jstor.org/stable/2285901", "https://d-nb.info/gnd/4078739-4", "https://id.ndl.go.jp/auth/ndlna/00561029", "https://www.wikidata.org/wiki/Q175199"]}, "SPRT": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2015", "Mathematical psychology", "Psychometrics", "Sequential methods", "Statistical tests"], "title": "Sequential probability ratio test", "method": "SPRT", "url": "https://en.wikipedia.org/wiki/Sequential_probability_ratio_test", "summary": "The sequential probability ratio test (SPRT) is a specific sequential hypothesis test, developed by Abraham Wald and later proven to be optimal by Wald and Jacob Wolfowitz. Neyman and Pearson's 1933 result inspired Wald to reformulate it as a sequential analysis problem. The Neyman-Pearson lemma, by contrast, offers a rule of thumb for when all the data is collected (and its likelihood ratio known).\nWhile originally developed for use in quality control studies in the realm of manufacturing, SPRT has been formulated for use in the computerized testing of human examinees as a termination criterion.\n\n", "images": [], "links": ["Abraham Wald", "Addison-Wesley", "Alternative hypothesis", "Bhaskar Kumar Ghosh", "CUSUM", "Classical test theory", "Computerized classification test", "David Spiegelhalter", "Digital object identifier", "Exponential distribution", "Harold Shipman", "High-stakes testing", "Hypothesis testing", "International Standard Book Number", "Item response theory", "JSTOR", "Jacob Wolfowitz", "Likelihood-ratio test", "Neyman\u2013Pearson lemma", "Null hypothesis", "Parallel lines", "Parameter estimation", "Probability distribution function", "Quality control", "Resistance thermometer", "Rule of thumb", "SPRT", "Sampling frequency", "Sequential analysis", "Slope", "Standard-setting study", "Stopping rule", "Type I and type II errors", "Wald test"], "references": ["http://www.tandfonline.com/doi/full/10.1080/07474946.2011.539924", "http://eric.ed.gov/ERICWebPortal/custom/portlets/recordDetails/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=ED034406&ERICExtSearch_SearchType_0=no&accno=ED034406", "http://doi.org/10.1080%2F07474946.2011.539924", "http://doi.org/10.1177%2F01466219922031365", "http://doi.org/10.1214%2Faoms%2F1177731118", "http://www.jstor.org/stable/2235638", "http://www.jstor.org/stable/2235829", "http://intqhc.oxfordjournals.org/content/15/1/7.full.pdf", "https://cran.r-project.org/web/packages/SPRT/SPRT.pdf"]}, "Conditional dependence": {"categories": ["All articles to be merged", "Articles created via the Article Wizard", "Articles to be merged from July 2018", "Independence (probability theory)", "Webarchive template wayback links"], "title": "Conditional dependence", "method": "Conditional dependence", "url": "https://en.wikipedia.org/wiki/Conditional_dependence", "summary": "In probability theory, conditional dependence is a relationship between two or more events that are dependent when a third event occurs. For example, if A and B are two events that individually increase the probability of a third event C, and do not directly affect each other, then initially (when it has not been observed whether or not the event C occurs)\n\n \n \n \n \n P\n \n (\n A\n \u2223\n B\n )\n =\n \n P\n \n (\n A\n )\n \n and \n \n \n P\n \n (\n B\n \u2223\n A\n )\n =\n \n P\n \n (\n B\n )\n \n \n {\\displaystyle {\\text{P}}(A\\mid B)={\\text{P}}(A){\\text{ and }}{\\text{P}}(B\\mid A)={\\text{P}}(B)}\n (A and B are independent).But suppose that now C is observed to occur. If event B occurs the probability of occurrence of the event A will decrease because its positive relation to C is less needed as an explanation of the occurrence of C. (Similarly, event A occurring will decrease the probability of occurrence of B). Hence, now the two events A and B are conditionally negatively dependent on each other because the probability of occurrence of each is negatively dependent on whether the other occurs. We have\n\n \n \n \n \n P\n \n (\n A\n \u2223\n C\n ,\n B\n )\n <\n \n P\n \n (\n A\n \u2223\n C\n )\n .\n \n \n {\\displaystyle {\\text{P}}(A\\mid C,B)<{\\text{P}}(A\\mid C).}\n Conditional dependence is different from conditional independence. In conditional independence two events (which may be dependent or not) become independent given the occurrence of a third event.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/97/Conditional_Dependence.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/aa/Merge-arrow.svg"], "links": ["Bayesian network", "Conditional expectation", "Conditional independence", "De Finetti's theorem", "If and only if", "Probability", "Probability theory", "Wayback Machine"], "references": ["http://www.britannica.com/EBchecked/topic/477530/probability-theory/32768/Applications-of-conditional-probability#toc32769", "http://edlab-www.cs.umass.edu/cs589/2010-lectures/conditional%20independence%20in%20statistical%20theory.pdf", "http://www.bioss.sari.ac.uk/staff/dirk/papers/sbb_bnets.pdf", "https://www.ai-class.com/course/video/quizquestion/60", "https://www.ai-class.com/course/video/videolecture/33", "https://web.archive.org/web/20131227164541/http://edlab-www.cs.umass.edu/cs589/2010-lectures/conditional%20independence%20in%20statistical%20theory.pdf"]}, "Generalized canonical correlation": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from June 2012", "Articles needing additional references from June 2012", "Covariance and correlation", "Dimension reduction"], "title": "Generalized canonical correlation", "method": "Generalized canonical correlation", "url": "https://en.wikipedia.org/wiki/Generalized_canonical_correlation", "summary": "In statistics, the generalized canonical correlation analysis (gCCA), is a way of making sense of cross-correlation matrices between the sets of random variables when there are more than two sets. While a conventional CCA generalizes principal component analysis (PCA) to two sets of random variables, a gCCA generalizes PCA to more than two sets of random variables. The canonical variables represent those common factors that can be found by a large PCA of all of the transformed random variables after each set underwent its own PCA.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Canonical correlation", "Cross-correlation", "Digital object identifier", "Helmert-Wolf blocking", "Linear regression", "Principal component analysis", "R programming language", "Statistics"], "references": ["http://www.sciencedirect.com/science/article/pii/S1053811912001644", "http://factominer.free.fr/", "https://doi.org/10.1016%2Fj.neuroimage.2012.01.137"]}, "Inverse probability weighting": {"categories": ["Epidemiology", "Survey methodology"], "title": "Inverse probability weighting", "method": "Inverse probability weighting", "url": "https://en.wikipedia.org/wiki/Inverse_probability_weighting", "summary": "Inverse probability weighting is a statistical technique for calculating statistics standardized to a population different from that in which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application. There may be prohibitive factors barring researchers from directly sampling from the target population such as cost, time, or ethical concerns. A solution to this problem is to use an alternate design strategy, e.g. stratified sampling. Weighting, when correctly applied, can potentially improve the efficiency and reduce the bias of unweighted estimators.\nOne very early weighted estimator is the Horvitz\u2013Thompson estimator of the mean. When the sampling probability is known, from which the sampling population is drawn from the target population, then the inverse of this probability is used to weight the observations. This approach has been generalized to many aspects of statistics under various frameworks. In particular, there are weighted likelihoods, weighted estimating equations, and weighted probability densities from which a majority of statistics are derived. These applications codified the theory of other statistics and estimators such as marginal structural models, the standardized mortality ratio, and the EM algorithm for coarsened or aggregate data.\nInverse probability weighting is also used to account for missing data when subjects with missing data cannot be included in the primary analysis.\nWith an estimate of the sampling probability, or the probability that the factor would be measured in another measurement, inverse probability weighting can be used to inflate the weight for subjects who are under-represented due to a large degree of missing data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["CiteSeerX", "Digital object identifier", "EM algorithm", "Generalized estimating equations", "Horvitz\u2013Thompson estimator", "International Standard Serial Number", "Journal of the American Statistical Association", "Likelihood function", "Marginal structural models", "Marie Davidian", "Missing data", "Probability density function", "PubMed Central", "PubMed Identifier", "Sampling probability", "Standardized mortality ratio"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.157.9366", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2652882", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2768499", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2798744", "http://www.ncbi.nlm.nih.gov/pubmed/19357328", "http://www.ncbi.nlm.nih.gov/pubmed/20161511", "http://doi.org/10.1080/01621459.1952.10483446", "http://doi.org/10.1080/01621459.1994.10476818", "http://doi.org/10.1093/aje/kwp055", "http://doi.org/10.1093/biomet/asp033", "http://doi.org/10.1136/jech.2004.029496", "http://www.worldcat.org/issn/0006-3444"]}, "Bessel process": {"categories": ["Stochastic processes"], "title": "Bessel process", "method": "Bessel process", "url": "https://en.wikipedia.org/wiki/Bessel_process", "summary": "In mathematics, a Bessel process, named after Friedrich Bessel, is a type of stochastic process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3f/BesselProcess1D.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/3f/20161113090602%21BesselProcess1D.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost surely", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "Friedrich Bessel", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Mathematics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Norm (mathematics)", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Real number", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": []}, "It\u014d's lemma": {"categories": ["Equations", "Lemmas", "Probability theorems", "Statistical theorems", "Stochastic calculus"], "title": "It\u00f4's lemma", "method": "It\u014d's lemma", "url": "https://en.wikipedia.org/wiki/It%C3%B4%27s_lemma", "summary": "In mathematics, It\u00f4's lemma is an identity used in It\u00f4 calculus to find the differential of a time-dependent function of a stochastic process. It serves as the stochastic calculus counterpart of the chain rule. It can be heuristically derived by forming the Taylor series expansion of the function up to its second derivatives and retaining terms up to first order in the time increment and second order in the Wiener process increment. The lemma is widely employed in mathematical finance, and its best known application is in the derivation of the Black\u2013Scholes equation for option values.\nIt\u00f4's lemma, which is named after Kiyosi It\u00f4, is occasionally referred to as the It\u00f4\u2013Doeblin theorem in recognition of posthumously discovered work of Wolfgang Doeblin.", "images": [], "links": ["AM\u2013GM inequality", "Annualized return", "Bernt \u00d8ksendal", "Black\u2013Scholes", "Black\u2013Scholes equation", "Black\u2013Scholes formula", "Chain rule", "Compensated process", "Convexity correction", "C\u00e0dl\u00e0g", "Differentiable function", "Differential (calculus)", "Digital object identifier", "Dol\u00e9ans-Dade exponential", "Feynman\u2013Kac formula", "Geometric Brownian motion", "Gradient", "Group theory", "Hessian matrix", "International Standard Book Number", "It\u00f4's theorem", "It\u00f4 calculus", "Kiyosi It\u00f4", "Log-normal distribution", "Marc Yor", "Martingale (probability theory)", "Mathematical Reviews", "Mathematical finance", "Mathematics", "Option (finance)", "Poisson process", "Probability distribution", "Product rule", "Semimartingale", "Stochastic differential equation", "Stochastic process", "Taylor series", "Wiener process", "Wolfgang Doeblin"], "references": ["http://www.ftsmodules.com/public/texts/optiontutor/chap6.8.htm", "http://www2.sjsu.edu/faculty/watkins/ito.htm", "http://www.ams.org/mathscinet-getitem?mr=1885582", "http://doi.org/10.1007%2Fs780-002-8399-0", "http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.pja/1195572786", "https://books.google.com/books?id=UCG3AAAAIAAJ&pg=PA220", "https://archive.org/details/onstochasticdiff029540mbp"]}, "Anderson\u2013Darling test": {"categories": ["Nonparametric statistics", "Normality tests", "Statistical tests"], "title": "Anderson\u2013Darling test", "method": "Anderson\u2013Darling test", "url": "https://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test", "summary": "The Anderson\u2013Darling test is a statistical test of whether a given sample of data is drawn from a given probability distribution. In its basic form, the test assumes that there are no parameters to be estimated in the distribution being tested, in which case the test and its set of critical values is distribution-free. However, the test is most often used in contexts where a family of distributions is being tested, in which case the parameters of that family need to be estimated and account must be taken of this in adjusting either the test-statistic or its critical values. When applied to testing whether a normal distribution adequately describes a set of data, it is one of the most powerful statistical tools for detecting most departures from normality.K-sample Anderson\u2013Darling tests are available for testing whether several collections of observations can be modelled as coming from a single population, where the distribution function does not have to be specified.\nIn addition to its use as a test of fit for distributions, it can be used in parameter estimation as the basis for a form of minimum distance estimation procedure.\nThe test is named after Theodore Wilbur Anderson (1918\u20132016) and Donald A. Darling (1915\u20132014), who invented it in 1952.", "images": [], "links": ["Cram\u00e9r\u2013von Mises criterion", "Critical values", "Cumulative distribution function", "Digital object identifier", "Donald Allan Darling", "Empirical distribution function", "Exponential distribution", "Goodness of fit", "Gumbel distribution", "Hypothesis testing", "International Standard Book Number", "Jarque\u2013Bera test", "Journal of the American Statistical Association", "Kolmogorov\u2013Smirnov test", "Kuiper's test", "Log-normal distribution", "Logistic distribution", "Minimum distance estimation", "Normal distribution", "P-value", "Probability distribution", "R (programming language)", "Sample (statistics)", "Shapiro-Wilk", "Shapiro\u2013Wilk test", "Test statistic", "Theodore W. Anderson", "Theodore Wilbur Anderson", "Uniform distribution (continuous)", "Weibull distribution"], "references": ["http://www.itl.nist.gov/div898/handbook/eda/section3/eda35e.htm", "http://instatmy.org.my/downloads/e-jurnal%202/3.pdf", "http://doi.org/10.1080%2F01621459.1987.10478517", "http://doi.org/10.1214%2Faoms%2F1177729437", "http://doi.org/10.2307%2F2281537", "http://doi.org/10.2307%2F2286009", "https://web.archive.org/web/20150630110326/http://instatmy.org.my/downloads/e-jurnal%202/3.pdf", "https://cran.r-project.org/web/packages/kSamples/index.html"]}, "Gompertz function": {"categories": ["Curves", "Demography", "Time series models"], "title": "Gompertz function", "method": "Gompertz function", "url": "https://en.wikipedia.org/wiki/Gompertz_function", "summary": "The Gompertz curve or Gompertz function, is a type of mathematical model for a time series and is named after Benjamin Gompertz (1779-1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-hand or future value asymptote of the function is approached much more gradually by the curve than the left-hand or lower valued asymptote. This is in contrast to the simple logistic function in which both asymptotes are approached by the curve symmetrically. It is a special case of the generalised logistic function. The function was originally designed to describe human mortality, but since has been modified to be applied in biology, with regards to detailing populations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0a/Gompertz-a.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Gompertz-b.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5b/Gompertz-c.svg", "https://upload.wikimedia.org/wikipedia/commons/3/33/Sigmoid_function_01.png"], "links": ["ArXiv", "Asymptote", "Benjamin Gompertz", "Bibcode", "Carrying capacity", "Digital object identifier", "E (mathematical constant)", "Energy conservation", "Eric W. Weisstein", "Exponential function", "Generalised logistic curve", "Generalised logistic function", "Gompertz-Makeham law of mortality", "Gompertz distribution", "Growth curve (statistics)", "Inflection point", "International Standard Book Number", "Lag phase", "Life insurance", "Limiting factor", "Log phase", "Logistic function", "MathWorld", "Mathematical constant", "Mathematical model", "Metabolism", "Metastasis", "Mobile phone", "Murine", "Natural log", "Population dynamics", "Robert Malthus", "Royal Society", "Sigmoid function", "Taxon", "Time series", "Tissue (biology)"], "references": ["http://chemoth.com/tumorgrowth", "http://mathworld.wolfram.com/GompertzCurve.html", "http://adsabs.harvard.edu/abs/2005PhyD..208..220D", "http://adsabs.harvard.edu/abs/2016PhRvE..94b2315C", "http://cancerres.aacrjournals.org/content/70/1/46", "http://arxiv.org/abs/1309.3337", "http://arxiv.org/abs/1510.05123", "http://aem.asm.org/content/56/6/1875", "http://doi.org/10.1016%2FS0169-2070(02)00073-0", "http://doi.org/10.1016%2Fj.physd.2005.06.032", "http://doi.org/10.1038%2Fbjc.1964.55", "http://doi.org/10.1103%2FPhysRevE.94.022315", "https://archive.org/details/philtrans04942340"]}, "Hausman specification test": {"categories": ["Econometric modeling", "Statistical tests"], "title": "Durbin\u2013Wu\u2013Hausman test", "method": "Hausman specification test", "url": "https://en.wikipedia.org/wiki/Durbin%E2%80%93Wu%E2%80%93Hausman_test", "summary": "The Durbin\u2013Wu\u2013Hausman test (also called Hausman specification test) is a statistical hypothesis test in econometrics named after James Durbin, De-Min Wu, and Jerry A. Hausman. The test evaluates the consistency of an estimator when compared to an alternative, less efficient estimator which is already known to be consistent. It helps one evaluate if a statistical model corresponds to the data.", "images": [], "links": ["Alternative hypothesis", "Chi-squared distribution", "Consistent estimator", "De-Min Wu", "Delta method", "Digital object identifier", "Econometrica", "Econometrics", "Efficiency (statistics)", "Efficient estimator", "Endogeneity (economics)", "Error term", "Fixed effects model", "Instrumental variable", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "James Durbin", "Jerry A. Hausman", "Moore\u2013Penrose pseudoinverse", "Null hypothesis", "Ordinary least squares", "Random effects model", "Regression model validation", "Regressor", "Review of the International Statistical Institute", "Statistic", "Statistical consistency", "Statistical hypothesis test"], "references": ["http://doi.org/10.2307%2F1401917", "http://www.jstor.org/stable/1911420", "http://www.jstor.org/stable/1913827", "http://www.jstor.org/stable/1914093", "http://www.worldcat.org/issn/0012-9682", "https://books.google.com/books?id=MrkUeviIvYkC&pg=PA78", "https://books.google.com/books?id=Ot6DByCF6osC&pg=PA237"]}, "Renewal theory": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2010", "Point processes"], "title": "Renewal theory", "method": "Renewal theory", "url": "https://en.wikipedia.org/wiki/Renewal_theory", "summary": "Renewal theory is the branch of probability theory that generalizes Poisson processes for arbitrary holding times. Applications include calculating the best strategy for replacing worn-out machinery in a factory (example below) and comparing the long-term benefits of different insurance policies.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6e/Renewal-reward_process.reetep.png", "https://upload.wikimedia.org/wikipedia/commons/5/55/Renewal_process.reetep.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/0/0c/Inspection_paradox.reetep.png"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost surely", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Campbell's theorem (probability)", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time Markov process", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Cumulative distribution function", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Don Towsley", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Erhan Cinlar", "Exchangeable random variables", "Expected value", "Exponential distribution", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "IID", "Independent and identically distributed random variables", "Independent identically distributed", "Indicator function", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "JSTOR", "Journal of the Royal Statistical Society, Series B", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Little's lemma", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Markov renewal process", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Palm\u2013Khintchine theorem", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Poisson processes", "Potts model", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Residual time", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semi-Markov process", "Semimartingale", "Sigma-martingale", "Sir David Cox (statistician)", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stochastically larger", "Stopping time", "Stratonovich integral", "Strong law of large numbers", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://hal.inria.fr/hal-00676735", "http://www.ams.org/journals/tran/1948-063-03/S0002-9947-1948-0025098-8/S0002-9947-1948-0025098-8.pdf", "http://doi.org/10.2307%2F1990567", "http://www.jstor.org/stable/1426216", "http://www.jstor.org/stable/1990567", "http://www.jstor.org/stable/2983891", "http://www.jstor.org/stable/2984914"]}, "Semantic similarity": {"categories": ["All articles covered by WikiProject Wikify", "All articles needing additional references", "All articles needing references cleanup", "All articles with unsourced statements", "Articles covered by WikiProject Wikify from December 2010", "Articles needing additional references from December 2010", "Articles with multiple maintenance issues", "Articles with unsourced statements from February 2016", "CS1 maint: Multiple names: authors list", "Computational linguistics", "Semantics", "Statistical distance", "Wikipedia references cleanup from December 2010"], "title": "Semantic similarity", "method": "Semantic similarity", "url": "https://en.wikipedia.org/wiki/Semantic_similarity", "summary": "Semantic similarity is a metric defined over a set of documents or terms, where the idea of distance between them is based on the likeness of their meaning or semantic content as opposed to similarity which can be estimated regarding their syntactical representation (e.g. their string format). These are mathematical tools used to estimate the strength of the semantic relationship between units of language, concepts or instances, through a numerical description obtained according to the comparison of information supporting their meaning or describing their nature. The term semantic similarity is often confused with semantic relatedness. Semantic relatedness includes any relation between two terms, while semantic similarity only includes \"is a\" relations.\nFor example, \"car\" is similar to \"bus\", but is also related to \"road\" and \"driving\".\nComputationally, semantic similarity can be estimated by defining a topological similarity, by using ontologies to define the distance between terms/concepts. For example, a naive metric for the comparison of concepts ordered in a partially ordered set and represented as nodes of a directed acyclic graph (e.g., a taxonomy), would be the shortest-path linking the two concept nodes. Based on text analyses, semantic relatedness between units of language (e.g., words, sentences) can also be estimated using statistical means such as a vector space model to correlate words and textual contexts from a suitable text corpus.\nSeveral tools are used to measure the semantic similarity between concepts such as WNetSS API, which is a Java API manipulating a wide variety of semantic similarity measurements based on the WordNet semantic resource.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/d/de/Globe_of_letters.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Alessandro Vespignani", "Analogy", "Antonymy", "ArXiv", "Bibcode", "ChEBI", "CiteSeerX", "Coherence (linguistics)", "Concept maps", "Correlation", "DiShIn", "Digital object identifier", "Dijkstra's algorithm", "Directed acyclic graph", "Filippo Menczer", "Gene Ontology", "Gene ontology", "Genes", "GraSM", "Human Phenotype Ontology", "Information content", "International Standard Book Number", "International Standard Serial Number", "Jaccard index", "Latent semantic analysis", "Levenshtein distance", "Lowest common ancestor", "Medical Subject Headings", "Meronymy", "Mind maps", "Natural language processing", "Normalized Compression Distance", "Normalized Google distance", "Ontology (computer science)", "OpenStreetMap", "Open Biomedical Ontologies", "Open Directory Project", "Partially ordered set", "Pixel", "Pointwise mutual information", "Proteins", "PubMed Central", "PubMed Identifier", "RDF Schema", "SNOMED CT", "Second-order co-occurrence pointwise mutual information", "Semantic Web", "Semantic differential", "Semantic folding", "Semantic similarity network", "Sequence similarity", "SimRank", "Similarity learning", "Syntax", "Taxonomy (general)", "Terminology extraction", "Text corpus", "Topological", "UniProt", "Vector space model", "WNetSS API", "Web Ontology Language", "Wikipedia", "Word2vec", "WordNet"], "references": ["http:ftp://www-vhost.cs.toronto.edu/public_html/public_html/pub/gh/Budanitsky+Hirst-2001.pdf", "http://www.oegai.at/konvens2012/proceedings/23_panchenko12p/23_panchenko12p.pdf", "http://serelex.cental.be/", "http://iknowate.blogspot.com/2011/10/google-similarity-distance.html", "http://chronicle.com/wiredcampus/article/3041/six-degrees-of-wikipedia", "http://downloads.hindawi.com/journals/cin/2015/712835.pdf", "http://www.morganclaypool.com/doi/10.2200/S00639ED1V01Y201504HLT027", "http://www.samerhassan.com/images/4/48/Hassan.pdf", "http://semantic-link.com/", "http://www.f%C3%A4hndrich.de", "http://www.linguatools.de/disco/disco-builder.html", "http://www.linguatools.de/disco/disco_en.html", "http://www.similarity-blog.de/?page_id=3", "http://www.stat.cmu.edu/~cshalizi/350/2008/readings/Landauer-Dumais.pdf", "http://lsa.colorado.edu/papers/dp1.LSAintro.pdf", "http://adsabs.harvard.edu/abs/2009LNCS.5872..848D", "http://adsabs.harvard.edu/abs/2009PLSCB...5E0443P", "http://adsabs.harvard.edu/abs/2010PLSCB...6E0937F", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.55.1832&rep=rep1&type=pdf", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.893.7406&rep=rep1&type=pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.5544", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.6956", "http://www.personal.psu.edu/kuj13/janowicz_etal_simdl_geos2007.pdf", "http://csjarchive.cogsci.rpi.edu/Proceedings/2006/docs/p2624.pdf", "http://www.cogsci.rpi.edu/vekslv/pubs/pp718-veksler.pdf", "http://swoogle.umbc.edu/SimService/", "http://sitemaker.umich.edu/iccm2007.org/files/lindsey__veksler__grintsvayg____gray.pdf", "http://atlas.ahc.umn.edu/", "http://www.d.umn.edu/~tpederse/Pubs/prath-thesis.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1130488", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2375122", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2712090", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2756558", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2944781", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3098105", "http://www.ncbi.nlm.nih.gov/pubmed/15468759", "http://www.ncbi.nlm.nih.gov/pubmed/15901854", "http://www.ncbi.nlm.nih.gov/pubmed/18221506", "http://www.ncbi.nlm.nih.gov/pubmed/19649320", "http://www.ncbi.nlm.nih.gov/pubmed/19800049", "http://www.ncbi.nlm.nih.gov/pubmed/20885779", "http://www.ncbi.nlm.nih.gov/pubmed/21122125", "http://www.ncbi.nlm.nih.gov/pubmed/21702778", "http://www.ncbi.nlm.nih.gov/pubmed/22138322", "http://takelab.fer.hr/sts/", "http://irserver.ucd.ie/bitstream/handle/10197/3973/2012_-_Geographic_Knowledge_Extraction_and_Semantic_Similarity_in_OpenStreetMap_-_Ballatore_et_al.pdf?sequence=1", "http://www.cs.technion.ac.il/~gabr/papers/ijcai-2007-sim.pdf", "http://www.di.uniba.it/~cdamato/PhDThesis_dAmato.pdf", "http://wwwusers.di.uniroma1.it/~navigli/pubs/ACL_2013_Pilehvar_Jurgens_Navigli.pdf", "http://www.dsi.uniroma1.it/~navigli/pubs/PAMI_2010_Navigli_Lapata.pdf", "http://lcl.uniroma1.it/adw/", "http://lcl.uniroma1.it/nasari/", "http://disi.unitn.it/~p2p/RelatedWork/Matching/Gracia_wise08.pdf", "http://hdl.handle.net/10455/2935", "http://umls-similarity.sourceforge.net/", "http://wn-similarity.sourceforge.net/", "http://ilk.uvt.nl/~swubben/publications/wubben2008-techrep.pdf", "http://www.aaai.org/Papers/IJCAI/2007/IJCAI07-272.pdf", "http://aclweb.org/anthology/N/N15/N15-1059.pdf", "http://aclweb.org/anthology/P/P15/P15-1072.pdf", "http://doi.acm.org/10.1145/1232425.1232448", "http://arxiv.org/abs/1704.05295", "http://arxiv.org/abs/cs/0412098", "http://www.babelnet.org/", "http://www.bioconductor.org/", "http://cogprints.org/3779/01/cogsci04_2.pdf", "http://doi.org/10.1007%2F3-540-44963-9_8", "http://doi.org/10.1007%2F978-3-642-05290-3_103", "http://doi.org/10.1007%2Fs00500-016-2438-x", "http://doi.org/10.1016%2FB978-0-12-809633-8.20401-9", "http://doi.org/10.1016%2Fj.ajhg.2009.09.003", "http://doi.org/10.1016%2Fj.datak.2006.05.003", "http://doi.org/10.1017%2FS0269888917000029", "http://doi.org/10.1037%2F0033-295x.104.2.211", "http://doi.org/10.1080%2F01638539809545028", "http://doi.org/10.1081%2FBIP-200025659", "http://doi.org/10.1093%2Fbib%2Fbbr066", "http://doi.org/10.1093%2Fnar%2Fgki573", "http://doi.org/10.1109%2FTKDE.2007.48", "http://doi.org/10.1145%2F1054972.1054980", "http://doi.org/10.1145%2F1099554.1099658", "http://doi.org/10.1186%2F1471-2105-11-588", "http://doi.org/10.1186%2F1471-2105-9-50", "http://doi.org/10.1186%2F2041-1480-2-5", "http://doi.org/10.1207%2Fs15516709cog0000_20", "http://doi.org/10.1207%2Fs15516709cog2703_7", "http://doi.org/10.1371%2Fjournal.pcbi.1000443", "http://doi.org/10.1371%2Fjournal.pcbi.1000937", "http://doi.org/10.2200%2FS00639ED1V01Y201504HLT027", "http://doi.org/10.3115%2F1072228.1072318", "http://doi.org/10.5311%2Fjosis.2011.2.3", "http://www.josis.org/index.php/josis/article/view/26/23", "http://wiki.openstreetmap.org/wiki/OSM_Semantic_Network", "http://www.semantic-measures-library.org/", "http://semanticsimilarity.org/", "http://www.worldcat.org/issn/1432-7643", "http://wwwconference.org/proceedings/www2005/docs/p107.pdf", "http://xldb.di.fc.ul.pt/biotools/cmpsim/", "http://labs.fc.ul.pt/dishin/", "http://webpages.fc.ul.pt/~fjcouto/files/journal%20fcouto-jbcb2013%20preprint.pdf", "http://xldb.fc.ul.pt/biotools/cessm/", "http://xldb.fc.ul.pt/biotools/proteinon/", "http://xldb.fc.ul.pt/wiki/Geo-Net-PT_02_in_English", "http://xldb.fc.ul.pt/wiki/Geographic_Similarity_calculator_GeoSSM", "http://xldb.fc.ul.pt/xldb/publications/Ferreira.etal:GenericSemanticRelatedness:2011_document.pdf", "https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-9-S5-S4", "https://github.com/lasigeBioTM/DiShIn", "https://www.hindawi.com/journals/cin/2015/712835/", "https://link.springer.com/article/10.1007/s00500-016-2438-x", "https://link.springer.com/chapter/10.1007/978-3-642-36973-5_97?no-access=true", "https://www.researchgate.net/publication/220105255_A_context-aware_semantic_similarity_model_for_ontology", "https://www.researchgate.net/publication/44241193_A_Hybrid_Concept_Similarity_Measure_Model_for_Ontology_Environment", "https://www.aclweb.org/aclwiki/index.php?title=Similarity_(State_of_the_art)", "https://dl.acm.org/citation.cfm?id=1434078", "https://arxiv.org/pdf/1402.3371", "https://arxiv.org/pdf/cmp-lg/9709008.pdf", "https://arxiv.org/pdf/cs/0212033", "https://www.cambridge.org/core/journals/natural-language-engineering/article/recent-advances-in-methods-of-lexical-semantic-relatedness-a-survey/35BA94697B86B4B797FCF3ACCDE24FBD", "https://doi.org/10.1007%2F978-3-540-87696-0_7", "https://dx.doi.org/10.1371/journal.pcbi.1000937", "https://cloudfront.escholarship.org/dist/prd/content/qt0p7528tp/qt0p7528tp.pdf", "https://www.cs.york.ac.uk/semeval-2012/task6/"]}, "Jackknife (statistics)": {"categories": ["Computational statistics", "Resampling (statistics)"], "title": "Jackknife resampling", "method": "Jackknife (statistics)", "url": "https://en.wikipedia.org/wiki/Jackknife_resampling", "summary": "In statistics, the jackknife is a resampling technique especially useful for variance and bias estimation. The jackknife predates other common resampling methods such as the bootstrap. The jackknife estimator of a parameter is found by systematically leaving out each observation from a dataset and calculating the estimate and then finding the average of these calculations. Given a sample of size \n \n \n \n n\n \n \n {\\displaystyle n}\n , the jackknife estimate is found by aggregating the estimates of each \n \n \n \n (\n n\n \u2212\n 1\n )\n \n \n {\\displaystyle (n-1)}\n -sized sub-sample.\nThe jackknife technique was developed by Maurice Quenouille (1924-1973) from 1949, and refined in 1956. John Tukey expanded on the technique in 1958 and proposed the name \"jackknife\" since, like a physical jack-knife (a compact folding knife), it is a rough-and-ready tool that can improvise a solution for a variety of problems even though specific problems may be more efficiently solved with a purpose-designed tool.The jackknife is a linear approximation of the bootstrap.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrap (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Bradley Efron", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Charles Stein (statistician)", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jarque\u2013Bera test", "Johansen test", "John Tukey", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maurice Quenouille", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://people.bu.edu/aimcinto/jackknife.pdf", "http://doi.org/10.1093%2Fbiomet%2F43.3-4.353", "http://doi.org/10.1214%2Faoms%2F1177706647", "http://doi.org/10.1214%2Faoms%2F1177729989", "http://doi.org/10.1214%2Faos%2F1176345462", "http://www.jstor.org/stable/2236533", "http://www.jstor.org/stable/2240822", "http://www.jstor.org/stable/2332914"]}, "Noncentrality parameter": {"categories": ["Statistical parameters"], "title": "Noncentrality parameter", "method": "Noncentrality parameter", "url": "https://en.wikipedia.org/wiki/Noncentrality_parameter", "summary": "Noncentrality parameters are parameters of families of probability distributions that are related to other \"central\" families of distributions. Whereas the central distribution describes how a test statistic is distributed when the difference tested is null, noncentral distributions describe the distribution of a test statistic when the null is false (so the alternative hypothesisis true). This leads to their use in calculating statistical power.\nIf the noncentrality parameter of a distribution is zero, the distribution is identical to a distribution in the central family. For example, the Student's t-distribution is the central family of distributions for the noncentral t-distribution family.\nNoncentrality parameters are used in the following distributions:\n\nNoncentral t-distribution\nNoncentral chi-squared distribution\nNoncentral chi-distribution\nNoncentral F-distribution\nNoncentral beta distributionIn general, noncentrality parameters occur in distributions that are transformations of a normal distribution. The \"central\" versions are derived from normal distributions that have a mean of zero; the noncentral versions generalize to arbitrary means. For example, the standard (central) chi-squared distribution is the distribution of a sum of squared independent standard normal distributions, i.e., normal distributions with mean 0, variance 1. The noncentral chi-squared distribution generalizes this to normal distributions with arbitrary mean and variance.\nEach of these distributions has a single noncentrality parameter. However, there are extended versions of these distributions which have two noncentrality parameters: the doubly noncentral beta distribution, the doubly noncentral F distribution and the doubly noncentral t distribution. These types of distributions occur for distributions that are defined as the quotient of two independent distributions. When both source distributions are central (either with a zero mean or a zero noncentrality parameter, depending on the type of distribution), the result is a central distribution. When one is noncentral, a (singly) noncentral distribution results, while if both are noncentral, the result is a doubly noncentral distribution. As an example, a t-distribution is defined (ignoring constant values) as the quotient of a normal distribution and the square root of an independent chi-squared distribution. Extending this definition to encompass a normal distribution with arbitrary mean produces a noncentral t-distribution, while further extending it to allow a noncentral chi-squared distribution in the denominator while produces a doubly noncentral t-distribution.\nNote also that there are some \"noncentral distributions\" that are not usually formulated in terms of a \"noncentrality parameter\": see noncentral hypergeometric distributions, for example.\nThe noncentrality parameter of the t-distribution may be negative or positive while the noncentral parameters of the other three distributions must be greater than zero.", "images": [], "links": ["Alternative hypothesis", "Chi-squared distribution", "Doubly noncentral t-distribution", "International Standard Book Number", "Mean", "Noncentral F-distribution", "Noncentral beta distribution", "Noncentral chi-distribution", "Noncentral chi-squared distribution", "Noncentral hypergeometric distributions", "Noncentral t-distribution", "Normal distribution", "Null hypothesis", "Probability distribution", "Standard normal", "Statistical power", "Student's t-distribution", "Variance"], "references": ["https://web.archive.org/web/20081103102838/http://mars.wiwi.hu-berlin.de/mediawiki/slides/index.php/Comparison_of_noncentral_and_central_distributions"]}, "Acceptable quality limit": {"categories": ["Sampling (statistics)", "Statistical process control"], "title": "Acceptable quality limit", "method": "Acceptable quality limit", "url": "https://en.wikipedia.org/wiki/Acceptable_quality_limit", "summary": "The acceptable quality limit (AQL) is the worst tolerable process average (mean) in percentage or ratio that is still considered acceptable; that is, it is at an acceptable quality level. Closely related terms are the rejectable quality limit and rejectable quality level (RQL). \nIn a quality control procedure, a process is said to be at an acceptable quality level if the appropriate statistic used to construct a control chart does not fall outside the bounds of the acceptable quality limits. Otherwise, the process is said to be at a rejectable control level.\nIn 2008 the usage of the abbreviation AQL for the term \"acceptable quality limit\" was changed in the standards issued by at least one national standards organization (ANSI/ASQ) to relate to the term \"acceptance quality level\". It is unclear whether this interpretation will be brought into general usage, but the underlying meaning remains the same.\nAn acceptable quality level is a test and/or inspection standard that prescribes the range of the number of defective components that is considered acceptable when random sampling those components during an inspection. The defects found during an electronic or electrical test, or during a physical (mechanical) inspection, are sometimes classified into three levels: critical, major and minor. Critical defects are those that render the product unsafe or hazardous for the end user or that contravene mandatory regulations. Major defects can result in the product's failure, reducing its marketability, usability or saleability. Lastly, minor defects do not affect the product's marketability or usability, but represent workmanship defects that make the product fall short of defined quality standards. Different companies maintain different interpretations of each defect type. In order to avoid argument, buyers and sellers agree on an AQL standard, chosen according to the level of risk each party assumes, which they use as a reference during pre-shipment inspection.", "images": [], "links": ["Acceptance sampling", "American National Standards Institute", "American Society for Quality", "Control chart", "Control limits", "International Standard Book Number", "Quality control", "RQL", "Random sampling", "Risk", "Saleability", "Standards organization", "Statistical process control", "Superconducting logic", "Usability", "Workmanship"], "references": ["http://www.aqlinspectorsrule.com/Z1-4-2008.html", "https://books.google.com/books?id=NKpitRCwolgC&pg=PA161&dq=RQL+quality&cd=5#v=onepage&q=RQL%20quality&f=false", "https://books.google.com/books?id=O4Ap0idKEccC&pg=PA73&dq=RQL+quality&cd=1#v=onepage&q=RQL%20quality&f=false"]}, "Transition rate matrix": {"categories": ["All stub articles", "Markov processes", "Probability stubs"], "title": "Transition rate matrix", "method": "Transition rate matrix", "url": "https://en.wikipedia.org/wiki/Transition_rate_matrix", "summary": "In probability theory, a transition rate matrix (also known as an intensity matrix or infinitesimal generator matrix) is an array of numbers describing the rate a continuous time Markov chain moves between states.\nIn a transition rate matrix Q (sometimes written A) element qij (for i \u2260 j) denotes the rate departing from i and arriving in state j. Diagonal elements qii are defined such that \n\n \n \n \n \n q\n \n i\n i\n \n \n =\n \u2212\n \n \u2211\n \n j\n \u2260\n i\n \n \n \n q\n \n i\n j\n \n \n .\n \n \n {\\displaystyle q_{ii}=-\\sum _{j\\neq i}q_{ij}.}\n and therefore the rows of the matrix sum to zero.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["Continuous time Markov chain", "Digital object identifier", "Infinitesimal generator (stochastic processes)", "International Standard Book Number", "JSTOR", "James R. Norris", "Laplacian matrix", "M/M/1 queue", "Probability", "Probability theory"], "references": ["http://doi.org/10.1007/0-387-21525-5_2", "http://doi.org/10.1007/3-540-56863-8_38", "http://doi.org/10.1017/CBO9780511810633", "http://doi.org/10.3233/978-1-60750-950-9-i", "http://www.jstor.org/stable/3214379"]}, "Detrended fluctuation analysis": {"categories": ["All articles with dead external links", "Articles with dead external links from January 2018", "Articles with permanently dead external links", "Autocorrelation", "CS1 maint: Explicit use of et al.", "Fractals"], "title": "Detrended fluctuation analysis", "method": "Detrended fluctuation analysis", "url": "https://en.wikipedia.org/wiki/Detrended_fluctuation_analysis", "summary": "In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation function) or 1/f noise.\nThe obtained exponent is similar to the Hurst exponent, except that DFA may also be applied to signals whose underlying statistics (such as mean and variance) or dynamics are non-stationary (changing with time). It is related to measures based upon spectral techniques such as autocorrelation and Fourier transform.\nPeng et al. introduced DFA in 1994 in a paper that has been cited over 2,000 times as of 2013 and represents an extension of the (ordinary) fluctuation analysis (FA), which is affected by non-stationarities.", "images": [], "links": ["1/f noise", "ArXiv", "Autocorrelation", "Autocorrelation function", "Bibcode", "Box-counting dimension", "Brownian noise", "Chaos theory", "Chung-Kang Peng", "Color of noise", "Correlation function", "Correlation time", "Digital object identifier", "Fluctuation analysis", "Fourier transform", "Fractal dimension", "Fractional Brownian motion", "Fractional Gaussian noise", "Hausdorff dimension", "Hurst exponent", "I.i.d.", "Integral", "Least squares", "Log-log graph", "Long-memory", "MATLAB", "MF-DFA", "Multifractal", "Neurophysiological Biomarker Toolbox", "Pink noise", "Power spectrum", "PubMed Central", "PubMed Identifier", "Random walk", "Rescaled range", "Self-affinity", "Self-organized criticality", "Self-similarity", "Stationary process", "Stochastic processes", "Time series", "Time series analysis", "White noise", "Wiener\u2013Khinchin theorem"], "references": ["http://adsabs.harvard.edu/abs/1994PhRvE..49.1685P", "http://adsabs.harvard.edu/abs/1995Chaos...5...82P", "http://adsabs.harvard.edu/abs/1995PhRvE..51.5084B", "http://adsabs.harvard.edu/abs/2000PhRvE..62.6103H", "http://adsabs.harvard.edu/abs/2000PhRvL..85.3736B", "http://adsabs.harvard.edu/abs/2001PhRvE..64a1114H", "http://adsabs.harvard.edu/abs/2001PhyA..295..441K", "http://adsabs.harvard.edu/abs/2002PhyA..316...87K", "http://adsabs.harvard.edu/abs/2012NatSR...2E.315B", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3303145", "http://www.ncbi.nlm.nih.gov/pubmed/11030994", "http://www.ncbi.nlm.nih.gov/pubmed/11538314", "http://www.ncbi.nlm.nih.gov/pubmed/22419991", "http://havlin.biu.ac.il/Publications.php?keyword=Multifractal+detrended+fluctuation+analysis+of+nonstationary+time+series++&year=*&match=all", "http://www.maxlittle.net/software/", "http://prola.aps.org/abstract/PRE/v51/i5/p5084_1", "http://prola.aps.org/abstract/PRE/v62/i5/p6103_1", "http://prola.aps.org/pdf/PRE/v49/i2/p1685_1", "http://arxiv.org/abs/0706.1062", "http://arxiv.org/abs/cond-mat/0102214", "http://arxiv.org/abs/physics/0103018", "http://arxiv.org/abs/physics/0202070", "http://doi.org/10.1016%2Fs0378-4371(01)00144-3", "http://doi.org/10.1016%2Fs0378-4371(02)01383-3", "http://doi.org/10.1038%2Fsrep00315", "http://doi.org/10.1063%2F1.166141", "http://doi.org/10.1103%2Fphysreve.49.1685", "http://doi.org/10.1103%2Fphysreve.51.5084", "http://doi.org/10.1103%2Fphysreve.62.6103", "http://doi.org/10.1103%2Fphysreve.64.011114", "http://doi.org/10.1103%2Fphysrevlett.85.3736", "http://doi.org/10.1137%2F070710111", "http://doi.org/10.3389%2Ffphys.2012.00450", "http://www.physionet.org/physiotools/dfa", "http://www.physics.ox.ac.uk/users/littlem/publications/dfafullpath.pdf", "https://www.nbtwiki.net/doku.php?id=tutorial:detrended_fluctuation_analysis_dfa", "https://epubs.siam.org/doi/abs/10.1137/070710111"]}, "Estimator": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from October 2009", "Estimator"], "title": "Estimator", "method": "Estimator", "url": "https://en.wikipedia.org/wiki/Estimator", "summary": "In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished.There are point and interval estimators. The point estimators yield single-valued results, although this includes the possibility of single vector-valued results and results that can be expressed as a single function. This is in contrast to an interval estimator, where the result would be a range of plausible values (or vectors or functions).\nEstimation theory is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same data. Such properties can be used to determine the best rules to use under given circumstances. However, in robust statistics, statistical theory goes on to consider the balance between having good properties, if tightly defined assumptions hold, and having less good properties that hold under wider conditions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Accuracy and precision", "Algebra of random variables", "Almost sure convergence", "Asymptotic distribution", "Asymptotic normality", "Best linear unbiased estimator", "Bias of an estimator", "Cambridge University Press", "Central limit theorem", "Central tendency", "Circumflex", "Consistent estimator", "Convergence in probability", "Convergence of random variables", "Cram\u00e9r\u2013Rao bound", "Decision rule", "Decision theory", "Density estimation", "Digital object identifier", "Dirac delta function", "Edwin Thompson Jaynes", "Efficiency (statistics)", "Encyclopedia of Mathematics", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimand", "Estimation theory", "Estimator bias", "Expected value", "Gauss\u2013Markov theorem", "Generalized method of moments", "Google Books", "If and only if", "International Standard Book Number", "Interval estimator", "Invariant estimator", "Kalman filter", "Lehmann\u2013Scheff\u00e9 theorem", "Loss function", "MVUE", "Markov chain Monte Carlo", "Maximum a posteriori", "Maximum likelihood", "Mean square error", "Mean squared error", "Median", "Method of moments (statistics)", "Michiel Hazewinkel", "Minimum mean squared error", "Non-parametric model", "Normal distribution", "Parameter", "Parametric model", "Particle filter", "Pitman closeness criterion", "Point estimate", "Point estimator", "Probability density function", "Random variable", "Rao\u2013Blackwell theorem", "Robust estimator", "Robust regression", "Robust statistics", "Sample mean", "Sample size", "Sample space", "Scale factor", "Scale parameter", "Semi-parametric model", "Sensitivity and specificity", "Shrinkage estimator", "Signal Processing", "Spectral density", "Square root", "Standard deviation", "Standard error (statistics)", "Statistic", "Statistical dispersion", "Statistical model", "Statistics", "Testimator", "Time series", "Unbiasedness", "Variance", "Well-behaved statistic", "Wiener filter"], "references": ["http://doi.org/10.1007%2F978-0-387-74978-5", "https://books.google.com/books?id=C1guHWTlVVoC&pg=PA633", "https://www.springer.com/mathematics/probability/book/978-0-387-74977-8", "https://web.archive.org/web/20060628221855/http://lmi.bwh.harvard.edu/papers/pdfs/2004/martin-fernandezCOURSE04b.pdf", "https://www.encyclopediaofmath.org/index.php?title=s/s087360"]}, "Holtsmark distribution": {"categories": ["Continuous distributions", "Location-scale family probability distributions", "Pages using deprecated image syntax", "Power laws", "Probability distributions with non-finite variance", "Stable distributions"], "title": "Holtsmark distribution", "method": "Holtsmark distribution", "url": "https://en.wikipedia.org/wiki/Holtsmark_distribution", "summary": "The (one-dimensional) Holtsmark distribution is a continuous probability distribution. The Holtsmark distribution is a special case of a stable distribution with the index of stability or shape parameter \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n equal to 3/2 and skewness parameter \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n of zero. Since \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n equals zero, the distribution is symmetric, and thus an example of a symmetric alpha-stable distribution. The Holtsmark distribution is one of the few examples of a stable distribution for which a closed form expression of the probability density function is known. However, its probability density function is not expressible in terms of elementary functions; rather, the probability density function is expressed in terms of hypergeometric functions.\nThe Holtsmark distribution has applications in plasma physics and astrophysics. In 1919, Norwegian physicist J. Holtsmark proposed the distribution as a model for the fluctuating fields in plasma due to chaotic motion of charged particles. It is also applicable to other types of Coulomb forces, in particular to modeling of gravitating bodies, and thus is important in astrophysics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/32/Levy_distributionCDF.png", "https://upload.wikimedia.org/wikipedia/commons/0/01/Levy_distributionPDF.png"], "links": ["ARGUS distribution", "American Mathematical Society", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chaotic", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elementary functions", "Elliptical distribution", "Elsevier", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized hypergeometric function", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypergeometric function", "Hypergeometric functions", "Hypoexponential distribution", "International Standard Book Number", "International Standard Serial Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johan Peter Holtsmark", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "University of Nottingham", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://lpmt-theory.wdfiles.com/local--files/michael-blog/stablePDF.pdf", "http://onlinelibrary.wiley.com/doi/10.1002/andp.19193630702/abstract", "http://adsabs.harvard.edu/abs/1919AnP...363..577H", "http://adsabs.harvard.edu/abs/1942ApJ....95..489C", "http://adsabs.harvard.edu/abs/1943RvMP...15....1C", "http://adsabs.harvard.edu/doi/10.1086/144420", "http://link.aps.org/doi/10.1103/RevModPhys.15.1", "http://doi.org/10.1002%2Fandp.19193630702", "http://doi.org/10.1016%2F0022-4073(86)90011-7", "http://doi.org/10.1086%2F144420", "http://doi.org/10.1103%2FRevModPhys.15.1", "http://www.worldcat.org/issn/0004-637X", "http://etheses.nottingham.ac.uk/11194/1/Thesis_Wai_Ha_Lee.pdf", "https://books.google.com/books?id=ydwt9SotnN0C&pg=PR7&dq=Vladimir+Zolotarev+One-dimensional+stable+laws#v=onepage&q=holtsmark&f=false", "https://zenodo.org/record/1253952/files/article.pdf"]}, "Raw score": {"categories": ["All articles lacking sources", "All stub articles", "Articles lacking sources from May 2017", "Statistical data types", "Statistics stubs"], "title": "Raw score", "method": "Raw score", "url": "https://en.wikipedia.org/wiki/Raw_score", "summary": "In statistics and data analysis, a raw score is an original datum that has not been transformed. This may include, for example, the original result obtained by a student on a test (i.e., the number of correctly answered items) as opposed to that score after transformation to a standard score or percentile (%) rank or the like.\nOften the conversion must be made to a standard score before the data can be used. For example, an open ended survey question will yield raw data that cannot be used for statistical purposes as it is; however a multiple choice question will yield raw data that is either easy to convert to a standard score, or even can be used as it is.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Standard score", "Statistics", "Test (student assessment)"], "references": []}, "Log-log plot": {"categories": ["All articles needing additional references", "Articles needing additional references from December 2009", "Logarithmic scales of measurement", "Statistical charts and diagrams"], "title": "Log\u2013log plot", "method": "Log-log plot", "url": "https://en.wikipedia.org/wiki/Log%E2%80%93log_plot", "summary": "In science and engineering, a log\u2013log graph or log\u2013log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Monomials \u2013 relationships of the form \n \n \n \n y\n =\n a\n \n x\n \n k\n \n \n \n \n {\\displaystyle y=ax^{k}}\n \u2013 appear as straight lines in a log\u2013log graph, with the power term corresponding to the slope, and the constant term corresponding to the intercept of the line. Thus these graphs are very useful for recognizing these relationships and estimating parameters. Any base can be used for the logarithm, though most common are 10, e, and 2.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/92/LogLog_exponentials.svg", "https://upload.wikimedia.org/wikipedia/commons/5/56/Slope_of_log-log_plot.PNG", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ArXiv", "Bibcode", "Bode plot", "Cobb\u2013Douglas production function", "Coefficient of determination", "Digital object identifier", "E (mathematical constant)", "Economics", "Elasticity (economics)", "Engineering", "Estimating parameters", "Fractal", "Fractal dimension", "Frequency response", "Goodness of fit", "Grade (slope)", "Linear regression", "Lin\u2013log graph", "Logarithmic scale", "Lognormal distribution", "Money", "Money demand", "Monomial", "Normal distribution", "Ordinary least squares", "Plot (graphics)", "Rate of return", "Real income", "Science", "Semi-log plot", "Statistical power", "Vilfredo Pareto"], "references": ["http://www.intmath.com/Exponential-logarithmic-functions/7_Graphs-log-semilog.php", "http://adsabs.harvard.edu/abs/2009SIAMR..51..661C", "http://arxiv.org/abs/0706.1062", "http://doi.org/10.1137%2F070710111"]}, "Pocock boundary": {"categories": ["Clinical research", "Design of experiments", "Sequential experiments"], "title": "Pocock boundary", "method": "Pocock boundary", "url": "https://en.wikipedia.org/wiki/Pocock_boundary", "summary": "The Pocock boundary is a method for determining whether to stop a clinical trial prematurely. The typical clinical trial compares two groups of patients. One group are given a placebo or conventional treatment, while the other group of patients are given the treatment that is being tested. The investigators running the clinical trial will wish to stop the trial early for ethical reasons if the treatment group clearly shows evidence of benefit. In other words, \"when early results proved so promising it was no longer fair to keep patients on the older drugs for comparison, without giving them the opportunity to change.\"The concept was introduced by the medical statistician Stuart Pocock in 1977. The many reasons underlying when to stop a clinical trial for benefit were discussed in his editorial from 2005.", "images": [], "links": ["Clinical trial", "Digital object identifier", "Haybittle\u2013Peto boundary", "JSTOR", "P-value", "Placebo", "PubMed Identifier", "Stuart Pocock"], "references": ["http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(05)66516-6/abstract", "http://www.ncbi.nlm.nih.gov/pubmed/15885299", "http://www.ncbi.nlm.nih.gov/pubmed/16264167", "http://jama.ama-assn.org/cgi/content/full/294/17/2228", "http://doi.org/10.1001%2Fjama.294.17.2228", "http://doi.org/10.1016%2FS0140-6736(05)66516-6", "http://doi.org/10.1093%2Fbiomet%2F64.2.191", "http://www.jstor.org/stable/2335684", "https://www.telegraph.co.uk/news/uknews/1497648/Heart-attacks-may-be-cut-by-half.html"]}, "Null distribution": {"categories": ["Statistical hypothesis testing", "Theory of probability distributions"], "title": "Null distribution", "method": "Null distribution", "url": "https://en.wikipedia.org/wiki/Null_distribution", "summary": "In statistical hypothesis testing, the null distribution is the probability distribution of the test statistic when the null hypothesis is true.\nFor example, in an F-test, the null distribution is an F-distribution.\nNull distribution is a tool scientists often use when conducting experiments. The null distribution is the distribution of two sets of data under a null hypothesis. If the results of the two sets of data are not outside the parameters of the expected results, then the null hypothesis is said to be true.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ca/Null_and_alternative_distribution.jpg"], "links": ["Bootstrapping (statistics)", "Hypothesis testing", "International Standard Book Number", "Null hypothesis", "Probability distribution", "Statistical hypothesis testing", "Statistical power", "Type I error", "Type I errors"], "references": ["http://docs.statwing.com/examples-and-definitions/t-test/statistical-significance/"]}, "Exchangeable random variables": {"categories": ["Statistical randomness", "Types of probability distributions"], "title": "Exchangeable random variables", "method": "Exchangeable random variables", "url": "https://en.wikipedia.org/wiki/Exchangeable_random_variables", "summary": "In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence such that future observations behave like earlier observations. More formally, this means that given a finite sequence of observations (i.e. of realizations of the random variables), any re-ordering of this sequence is equally likely to occur. This formalizes the notion of \"the future being predictable on the basis of past experience.\" It is closely related to the use of independent and identically distributed random variables in statistical models. Exchangeable sequences of random variables arise in cases of simple random sampling.", "images": [], "links": ["Banach limit", "Bayesian statistics", "Bernoulli trials", "Birkhoff-Khinchin theorem", "Bivariate normal distribution", "Bruno de Finetti", "Cesaro summation", "Convex combination", "De Finetti's theorem", "Density function", "Digital object identifier", "Empirical distribution function", "Frequentist statistics", "Iid", "Independent and identically-distributed random variables", "Independent and identically distributed random variables", "Indicator function", "International Standard Book Number", "JSTOR", "Joint probability distribution", "Law of large numbers", "Leonard Jimmie Savage", "Mathematical Reviews", "Mixture distribution", "Olav Kallenberg", "Paul Halmos", "Pearson product-moment correlation coefficient", "Permutation", "Persi Diaconis", "Predictive inference", "Random variable", "Randomness extractor", "Resampling (statistics)", "Simple random sampling", "Statistical control", "Statistics", "Strictly stationary", "U-statistic", "U statistic", "Urn model", "Von Neumann extractor", "Walter Shewhart", "William Ernest Johnson"], "references": ["http://www.ams.org/journals/bull/2009-46-04/S0273-0979-09-01262-2/home.html", "http://www.ams.org/mathscinet-getitem?mr=1419498", "http://www.ams.org/mathscinet-getitem?mr=2525743", "http://doi.org/10.1007%2Fbf00485351", "http://doi.org/10.1090%2FS0273-0979-09-01262-2", "https://books.google.com/books?id=6RaoAAAAIAAJ", "https://mathscinet.ams.org/mathscinet-getitem?mr=494344", "https://doi.org/10.1007%2FBFb0099421", "https://doi.org/10.1111%2Fj.1751-5823.2008.00059.x", "https://www.jstor.org/stable/2243211"]}, "Beta (finance)": {"categories": ["All articles covered by WikiProject Wikify", "All articles with unsourced statements", "All pages needing cleanup", "Articles covered by WikiProject Wikify from May 2016", "Articles with unsourced statements from November 2008", "Financial ratios", "Fundamental analysis", "Mathematical finance", "Pages using div col with small parameter", "Statistical ratios", "Wikipedia introduction cleanup from May 2016"], "title": "Beta (finance)", "method": "Beta (finance)", "url": "https://en.wikipedia.org/wiki/Beta_(finance)", "summary": "In finance, the beta (\u03b2 or beta coefficient) of an investment indicates whether the investment is more or less volatile than the market as a whole. \nBeta is a measure of the risk arising from exposure to general market movements as opposed to idiosyncratic factors. The market portfolio of all investable assets has a beta of exactly 1. A beta below 1 can indicate either an investment with lower volatility than the market, or a volatile investment whose price movements are not highly correlated with the market. An example of the first is a treasury bill: the price does not go up or down a lot, so it has a low beta. An example of the second is gold. The price of gold does go up and down a lot, but not in the same direction or at the same time as the market.A beta greater than 1 generally means that the asset both is volatile and tends to move up and down with the market. An example is a stock in a big technology company. Negative betas are possible for investments that tend to go down when the market goes up, and vice versa. There are few fundamental investments with consistent and significant negative betas, but some derivatives like put options can have large negative betas.Beta is important because it measures the risk of an investment that cannot be reduced by diversification. It does not measure the risk of an investment held on a stand-alone basis, but the amount of risk the investment adds to an already-diversified portfolio. In the Capital Asset Pricing Model (CAPM), beta risk is the only kind of risk for which investors should receive an expected return higher than the risk-free rate of interest.The definition above covers only theoretical beta. The term is used in many related ways in finance. For example, the betas commonly quoted in mutual fund analyses generally measure the risk of the fund arising from exposure to a benchmark for the fund, rather than from exposure to the entire market portfolio. Thus they measure the amount of risk the fund adds to a diversified portfolio of funds of the same type, rather than to a portfolio diversified among all fund types.Beta decay refers to the tendency for a company with a high beta coefficient (\u03b2 > 1) to have its beta coefficient decline to the market beta. It is an example of regression toward the mean.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9f/Chicklet-currency.jpg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["AT&T Inc.", "Absolute value", "Activist shareholder", "Algorithmic trading", "Alpha (finance)", "Alpha (investment)", "Altria Group", "ArXiv", "Arbitrage", "Arbitrage pricing theory", "Asset", "Assets under management", "Authorised capital", "Benchmark (surveying)", "Beta (disambiguation)", "Beta coefficient", "Bid\u2013ask spread", "Black\u2013Scholes model", "Block trade", "Bond market", "Book value", "Broker-dealer", "Buy and hold", "Capital Asset Pricing Model", "Capital asset pricing model", "Capital market", "Capital market line", "Capital structure", "Capital structure substitution theory", "Commodity market", "Commodity trading advisor", "Common stock", "Contrarian investing", "Convergence trade", "Convertible arbitrage", "Correlation", "Correlation and dependence", "Cost of capital", "Cost of equity", "Covariance", "Cross listing", "Dark pool", "Day trader", "Day trading", "Delta neutral", "Derivative (finance)", "Digital object identifier", "Distressed securities", "Diversification (finance)", "Dividend", "Dividend discount model", "Dividend yield", "Dollar cost averaging", "Dot-com bubble", "Downside beta", "Downside risk", "DuPont analysis", "Dual-beta", "Dual-listed company", "Earnings per share", "Earnings yield", "Efficient-market hypothesis", "Efficient frontier", "Elasticity (economics)", "Electronic communication network", "Event-driven investing", "Expected return", "Family office", "Finance", "Financial endowment", "Financial law", "Financial market", "Financial regulation", "Financial risk", "Fixed-income relative-value investing", "Fixed income arbitrage", "Flight-to-quality", "Floor broker", "Floor trader", "Foreign exchange market", "Fourth market", "Fund governance", "Fund of funds", "Fundamental analysis", "Global macro", "Gold", "Golden share", "Greeks (finance)", "Growth stock", "Haircut (finance)", "Hamada's equation", "Hedge (finance)", "Hedge Fund Standards Board", "Hedge fund", "High-frequency trading", "High-net-worth individual", "Initial public offering", "Institutional investor", "Insurance", "International Standard Book Number", "Inverse exchange-traded fund", "Investment", "Investment banking", "Investor", "Issued shares", "Johnson & Johnson", "Joseph Williams (economist)", "Leverage (finance)", "Linear least squares (mathematics)", "Linear regression", "Liquidity", "List of stock exchange trading hours", "List of stock exchanges", "Long/short equity", "Long (finance)", "MSCI EAFE", "Macro risk", "Managed futures account", "Margin (finance)", "Margin of Safety", "Market (economics)", "Market anomaly", "Market capitalization", "Market depth", "Market maker", "Market manipulation", "Market neutral", "Market portfolio", "Market timing", "Market trend", "Mean reversion (finance)", "Merchant bank", "Modern portfolio theory", "Momentum (finance)", "Momentum investing", "Money market", "Money market fund", "Mosaic theory (investments)", "Multi-manager investment", "Multilateral trading facility", "Mutual fund", "Myron Scholes", "Net asset value", "Open outcry", "Options pricing", "Over-the-counter (finance)", "Pairs trade", "Pension fund", "Position (finance)", "Post-modern portfolio theory", "Preferred stock", "Primary market", "Prime brokerage", "Procter & Gamble", "Program trading", "Proprietary trading", "Proxy contests", "Public float", "Public offering", "Put option", "Quantitative analyst", "R square", "Rally (stock market)", "Random walk hypothesis", "Rate of return", "Regression analysis", "Regression toward the mean", "Relative value (economics)", "Restricted stock", "Returns-based style analysis", "Reverse stock split", "Risk", "Risk-free interest rate", "Risk-free rate", "Risk arbitrage", "Risk factor (finance)", "Roll's critique", "Roulette", "S&P 100", "S&P 500", "S&P Global 100", "Secondary market", "Sector rotation", "Securitization", "Security characteristic line", "Security market line", "Seth Klarman", "Share capital", "Share repurchase", "Shares outstanding", "Short (finance)", "Slippage (finance)", "Sovereign wealth fund", "Special situation", "Speculation", "Standardized coefficient", "Statistical arbitrage", "Stock", "Stock dilution", "Stock exchange", "Stock market", "Stock market index", "Stock split", "Stock trader", "Stock valuation", "Structured finance", "Style investing", "Swing trading", "Systematic risk", "T-model", "Taxation of private equity and hedge funds", "Technical analysis", "Third market", "Time series", "Tracking stock", "Trade (financial instrument)", "Trading strategy", "Treasury stock", "Trend following", "Treynor ratio", "United States Treasury security", "Upside beta", "Upside risk", "Uptick rule", "Value averaging", "Value investing", "Variance", "Volatility (finance)", "Volatility arbitrage", "Voting interest", "Vulture fund", "Weighted average cost of capital", "Wikinvest", "Yield (finance)"], "references": ["http://rdcohen.50megs.com/IDRHEqabstract.htm", "http://www.etf.com/sections/research/5911-etfs-a-diversification.html?iu=1", "http://business.financialpost.com/2010/06/22/low-risk-tsx-stocks-have-outearned-riskiest-peers-over-30-year-period-analyst/", "http://www.macrorisk.com/wp-content/uploads/2013/04/MRA-WP-2013-e.pdf", "http://investexcel.net/367/calculate-stock-beta-with-excel", "http://arxiv.org/abs/1109.4422", "http://doi.org/10.1016%2F0304-405X(77)90041-1", "http://doi.org/10.1016%2Fj.ejor.2006.09.018", "http://www.lse.co.uk/financeglossary.asp?searchTerm=equity&iArticleID=1688&definition=equity_beta", "https://marketxls.com/beta-formula-in-excel/", "https://marketxls.com/calculate-sharpe-ratio-of-portfolio-in-excel/", "https://unicornbay.com/tools/beta-calculator"]}, "Piecewise-deterministic Markov process": {"categories": ["All stub articles", "Markov processes", "Probability stubs"], "title": "Piecewise-deterministic Markov process", "method": "Piecewise-deterministic Markov process", "url": "https://en.wikipedia.org/wiki/Piecewise-deterministic_Markov_process", "summary": "In probability theory, a piecewise-deterministic Markov process (PDMP) is a process whose behaviour is governed by random jumps at points in time, but whose evolution is deterministically governed by an ordinary differential equation between those times. The class of models is \"wide enough to include as special cases virtually all the non-diffusion models of applied probability.\" The process is defined by three quantities: the \ufb02ow, the jump rate, and the transition measure.The model was first introduced in a paper by Mark H. A. Davis in 1984.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg"], "links": ["Applied probability", "ArXiv", "B. subtilis", "Biochemistry", "Continuous-time Markov chain", "Digital object identifier", "Earthquake", "Eukaryotes", "Fluid queue", "GI/G/1 queue", "International Standard Book Number", "JSTOR", "M/G/1 queue", "Mark H. A. Davis", "Markov chain", "Onno Boxma", "Ordinary differential equation", "Probability", "Probability theory", "Queueing theory", "Reversed process", "Ruin theory"], "references": ["http://www.nt.ntnu.no/users/skoge/prost/proceedings/hygea-workshop-july07-systems_biology/publications/JL2/Chapter9.pdf", "http://arxiv.org/abs/0809.0477", "http://arxiv.org/abs/1001.2474", "http://arxiv.org/abs/1110.3813", "http://doi.org/10.1016/0304-4149(84)90009-7", "http://doi.org/10.1017/S0269964805050011", "http://doi.org/10.1137/060670109", "http://doi.org/10.1137/080718541", "http://doi.org/10.1214/EJP.v18-1958", "http://doi.org/10.1239/aap/1282924062", "http://doi.org/10.2307/1427443", "http://www.jstor.org/stable/1427443", "http://www.jstor.org/stable/2345677", "http://www.jstor.org/stable/3214906", "https://sites.google.com/site/gwainrib/papers"]}, "Control chart": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from December 2013", "Articles with unsourced statements from April 2010", "Articles with unsourced statements from December 2010", "Articles with unsourced statements from March 2010", "Articles with unsourced statements from September 2010", "Change detection", "Commons category link is on Wikidata", "Product management", "Quality", "Quality control tools", "Statistical charts and diagrams"], "title": "Control chart", "method": "Control chart", "url": "https://en.wikipedia.org/wiki/Control_chart", "summary": "Control charts, also known as Shewhart charts (after Walter A. Shewhart) or process-behavior charts, are a statistical process control tool used to determine if a manufacturing or business process is in a state of control.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/9/93/Xbar_chart_for_a_paired_xbar_and_R_chart.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "American Society for Quality", "Amplifier", "Analysis of covariance", "Analysis of variance", "Analytic and enumerative statistical studies", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bell Labs", "Bias of an estimator", "Binomial regression", "BioMed Central", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "British Standard", "Brownian motion", "Business process", "C-chart", "CUSUM", "Canonical correlation", "Cartography", "Categorical variable", "Cause system", "Census", "Central limit theorem", "Central tendency", "Chebyshev's inequality", "Check sheet", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Common- and special-causes", "Common cause and special cause", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control limits", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Donald J. Wheeler", "Durbin\u2013Watson statistic", "EWMA chart", "Econometrics", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Engineering tolerance", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "Exponentially weighted moving average", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric distribution", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hawthorne facility", "Heteroscedasticity", "Heuristic", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis test", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Ishikawa diagram", "Isotonic regression", "Jackknife resampling", "Japan", "Jarque\u2013Bera test", "Johansen test", "John Oakland", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Knoxville, Tennessee", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Leonard Henry Caleb Tippett", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood principle", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "London, UK", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Manufacturing process management", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Milwaukee, Wisconsin", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson rules", "Nelson\u2013Aalen estimator", "Neyman\u2013Pearson lemma", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Np-chart", "OCLC", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-chart", "Parametric statistics", "Pareto chart", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Process capability", "Proportional hazards model", "Psychometrics", "Quality (business)", "Quality Digest", "Quality control", "Quality costs", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression control chart", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling frame", "Scale parameter", "Scatter diagram", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Seven Basic Tools of Quality", "Seven basic tools of quality", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shewhart individuals control chart", "Sign test", "Simple linear regression", "Simultaneous equations model", "Six Sigma", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Specification", "Specification (technical standard)", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical control", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Supreme Commander for the Allied Powers", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Telephony", "Testing hypotheses suggested by the data", "Three-way chart", "Time domain", "Time series", "Tolerance interval", "Total quality management", "Trend estimation", "Type I and type II errors", "Type I error", "U-chart", "U-statistic", "Uniformly most powerful test", "Unimodal probability distribution", "United States Census Bureau", "United States Department of Agriculture", "V-statistic", "Variance", "Vector autoregression", "Vysochanskii\u2013Petunin inequality", "W. Edwards Deming", "Wald test", "Walter A. Shewhart", "Wavelet", "Western Electric rules", "Whittle likelihood", "Wilcoxon signed-rank test", "World War II", "Xbar and R chart", "Xbar and s chart", "Z-test"], "references": ["http://www.biomedcentral.com/1472-6947/12/86", "http://www.qualitydigest.com/inside/quality-insider-article/some-problems-attribute-charts.html", "http://www.qualitydigest.com/inside/quality-insider-column/are-you-sure-we-don-t-need-normally-distributed-data.html", "http://www.qualitydigest.com/jul/spctool.html", "http://www.spcforexcel.com/overcontrolling-process-funnel-experiment", "http://www.itl.nist.gov/div898/handbook/index.htm", "http://www.itl.nist.gov/div898/handbook/pmc/pmc.htm", "http://www.asq.org/learn-about-quality/seven-basic-quality-tools/overview/overview.html", "http://doi.org/10.1007%2Fs00170-016-9412-8", "http://doi.org/10.2307%2F2683482", "http://www.porticus.org/bell/doc/western_electric.doc", "http://www.porticus.org/bell/westernelectric_history.html#Western+Electric+-+A+Brief+History", "http://www.worldcat.org/issn/0268-3768", "http://www.worldcat.org/oclc/27187772", "https://link.springer.com/article/10.1007/s00170-016-9412-8", "https://web.archive.org/web/20080511183038/http://www.porticus.org/bell/doc/western_electric.doc", "https://www.webcitation.org/5wDkkOkcj?url=http://www.porticus.org/bell/westernelectric_history.html#Western+Electric+-+A+Brief+History"]}, "Kuiper's test": {"categories": ["1960 introductions", "Directional statistics", "Nonparametric statistics", "Statistical tests"], "title": "Kuiper's test", "method": "Kuiper's test", "url": "https://en.wikipedia.org/wiki/Kuiper%27s_test", "summary": "Kuiper's test is used in statistics to test that whether a given distribution, or family of distributions, is contradicted by evidence from a sample of data. It is named after Dutch mathematician Nicolaas Kuiper.Kuiper's test is closely related to the better-known Kolmogorov\u2013Smirnov test (or K-S test as it is often called). As with the K-S test, the discrepancy statistics D+ and D\u2212 represent the absolute sizes of the most positive and most negative differences between the two cumulative distribution functions that are being compared. The trick with Kuiper's test is to use the quantity D+ + D\u2212 as the test statistic. This small change makes Kuiper's test as sensitive in the tails as at the median and also makes it invariant under cyclic transformations of the independent variable. The Anderson\u2013Darling test is another test that provides equal sensitivity at the tails as the median, but it does not provide the cyclic invariance.\nThis invariance under cyclic transformations makes Kuiper's test invaluable when testing for cyclic variations by time of year or day of the week or time of day, and more generally for testing the fit of, and differences between, circular probability distributions.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d7/KuiperTestVisualization_2Sample.png"], "links": ["Anderson\u2013Darling test", "Biometrika", "Circular distribution", "Comb", "Cram\u00e9r\u2013von Mises criterion", "Cumulative distribution function", "Egon Pearson", "Empirical distribution function", "Estimation theory", "International Standard Book Number", "JSTOR", "Kolmogorov\u2013Smirnov test", "Median", "Nicolaas Kuiper", "Null hypothesis", "Random variable", "Seasonality", "Statistical hypothesis test", "Statistics", "Uniform distribution (continuous)"], "references": ["https://www.jstor.org/stable/2333135"]}, "Asymptotic relative efficiency": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "Articles with unsourced statements from January 2012", "Estimation theory"], "title": "Efficiency (statistics)", "method": "Asymptotic relative efficiency", "url": "https://en.wikipedia.org/wiki/Efficiency_(statistics)", "summary": "In the comparison of various statistical procedures, efficiency is a measure of quality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator, experiment, or test needs fewer observations than a less efficient one to achieve a given performance. This article primarily deals with efficiency of estimators.\nThe relative efficiency of two procedures is the ratio of their efficiencies, although often this concept is used where the comparison is made between a given procedure and a notional \"best possible\" procedure. The efficiencies and the relative efficiency of two procedures theoretically depend on the sample size available for the given procedure, but it is often possible to use the asymptotic relative efficiency (defined as the limit of the relative efficiencies as the sample size grows) as the principal comparison measure.\nEfficiencies are often defined using the variance or mean square error as the measure of desirability.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptote", "Asymptotic analysis", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Cram\u00e9r\u2013Rao bound", "Cram\u00e9r\u2013Rao inequality", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Dominating decision rule", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficient estimator", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Estimator bias", "Experiment", "Experimental design", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher information", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann efficiency", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis testing", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-estimator", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean square error", "Mean squared error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum variance unbiased estimator", "Missing data", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "OCLC", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pitman closeness criterion", "Pitman efficiency", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.math.binghamton.edu/arcones/prep/pv.pdf", "http://faculty.wcas.northwestern.edu/~iac879/wp/HL.pdf", "http://www.encyclopediaofmath.org/index.php/Bahadur_efficiency", "http://www.encyclopediaofmath.org/index.php/Efficiency,_asymptotic", "http://www.jstor.org/stable/91208", "http://www.worldcat.org/oclc/183886598", "https://www.encyclopediaofmath.org/index.php?title=E/e035070", "https://www.encyclopediaofmath.org/index.php?title=E/e035080"]}, "Population genetics": {"categories": ["Articles with short description", "CS1 maint: Extra text: authors list", "CS1 maint: Multiple names: authors list", "Commons category link from Wikidata", "Evolutionary biology", "Genetics", "Population genetics", "Statistical genetics", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Population genetics", "method": "Population genetics", "url": "https://en.wikipedia.org/wiki/Population_genetics", "summary": "Population genetics is a subfield of genetics that deals with genetic differences within and between populations, and is a part of evolutionary biology. Studies in this branch of biology examine such phenomena as adaptation, speciation, and population structure.Population genetics was a vital ingredient in the emergence of the modern evolutionary synthesis. Its primary founders were Sewall Wright, J. B. S. Haldane and Ronald Fisher, who also laid the foundations for the related discipline of quantitative genetics. Traditionally a highly mathematical discipline, modern population genetics encompasses theoretical, lab, and field work. Population genetic models are used both for statistical inference from DNA sequence data and for proof/disproof of concept.What sets population genetics apart today from newer, more phenotypic approaches to modelling evolution, such as evolutionary game theory and adaptive dynamics, is its emphasis on genetic phenomena as dominance, epistasis, and the degree to which genetic recombination breaks up linkage disequilibrium. This makes it appropriate for comparison to population genomics data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6c/Biston.betularia.7200.jpg", "https://upload.wikimedia.org/wikipedia/commons/d/db/Biston.betularia.f.carbonaria.7209.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Drosophila_melanogaster_-_side_%28aka%29.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/47/Gene_flow_final.png", "https://upload.wikimedia.org/wikipedia/commons/9/92/Open_book_nae_02.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/86/Synergistic_versus_antagonistic_epistasis.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1b/Tree_Of_Life_%28with_horizontal_gene_transfer%29.svg", "https://upload.wikimedia.org/wikipedia/commons/0/09/Tree_of_life.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/commons/d/db/Greatwall_large.jpg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abiogenesis", "Adaptation", "Adaptation (biology)", "Adaptive radiation", "African Pygmies", "Allele", "Allele frequency", "Allele frequency spectrum", "Allopatric speciation", "Alternatives to evolution by natural selection", "Anagenesis", "Ancient Beringian", "Ancient North Eurasian", "Animal breeding", "Anisogamy", "Antibiotic resistance", "Applications of evolution", "ArXiv", "Archaeogenetics", "Archaeogenetics of the Near East", "Asexual reproduction", "Australo-Melanesian", "Autocorrelation", "Bacillus subtilis", "Background selection", "Bacteria", "Balding\u2013Nichols model", "Baldwin effect", "Bdelloidea", "Behavioural genetics", "Bibcode", "Biodiversity", "Biogeography", "Biological life cycle", "Biological process", "Biosocial criminology", "Biostatistics", "Blending inheritance", "Blood type", "Blood type distribution by country", "Branching process", "Callosobruchus chinensis", "Canalisation (genetics)", "Cat gap", "Catagenesis (biology)", "Catastrophism", "Caucasian Hunter-Gatherer", "Cell nucleus", "Charles Darwin", "Chimpanzee\u2013human last common ancestor", "Chloroplast", "Chromosome", "Cladistics", "Cladogenesis", "Classical genetics", "Climate change", "Clonal interference", "Co-operation (evolution)", "Coalescent theory", "Coefficient of relatedness", "Coefficient of relationship", "Coevolution", "Coextinction", "Common descent", "Computational phylogenetics", "Conservation genetics", "Convergent evolution", "Copy-number variation", "Cospeciation", "Creation\u2013evolution controversy", "DNA", "DNA history of Egypt", "Darwinism", "Death", "Diffusion equation", "Digital object identifier", "Divergent evolution", "Domain (biology)", "Dominance (genetics)", "Drosophila melanogaster", "E.B. Ford", "Earliest known life forms", "Early Anatolian Farmers", "Ecological genetics", "Ecological selection", "Ecological speciation", "Effective population size", "Emergence", "Empathy", "Endomembrane system", "Endospore", "Epigenetics", "Epistasis", "Ernst Mayr", "Eukaryote", "Evidence of common descent", "Evidence of evolution", "Evolution", "Evolution as fact and theory", "Evolution of ageing", "Evolution of biological complexity", "Evolution of birds", "Evolution of brachiopods", "Evolution of butterflies", "Evolution of canids", "Evolution of cells", "Evolution of cephalopods", "Evolution of cetaceans", "Evolution of color vision", "Evolution of color vision in primates", "Evolution of dinosaurs", "Evolution of dominance", "Evolution of emotion", "Evolution of eusociality", "Evolution of fish", "Evolution of flagella", "Evolution of fungi", "Evolution of hair", "Evolution of hyenas", "Evolution of influenza", "Evolution of insects", "Evolution of lemurs", "Evolution of mammalian auditory ossicles", "Evolution of mammals", "Evolution of molluscs", "Evolution of morality", "Evolution of multicellularity", "Evolution of nervous systems", "Evolution of primates", "Evolution of reptiles", "Evolution of sexual reproduction", "Evolution of sirenians", "Evolution of snake venom", "Evolution of spiders", "Evolution of tetrapods", "Evolution of the brain", "Evolution of the eye", "Evolution of the horse", "Evolution of the wolf", "Evolutionary aesthetics", "Evolutionary anthropology", "Evolutionary biology", "Evolutionary capacitance", "Evolutionary computation", "Evolutionary developmental biology", "Evolutionary ecology", "Evolutionary economics", "Evolutionary epistemology", "Evolutionary ethics", "Evolutionary game theory", "Evolutionary history of life", "Evolutionary history of plants", "Evolutionary ideas of the Renaissance and Enlightenment", "Evolutionary invasion analysis", "Evolutionary linguistics", "Evolutionary medicine", "Evolutionary neuroscience", "Evolutionary physiology", "Evolutionary psychology", "Evolutionary rescue", "Evolutionary taxonomy", "Experimental evolution", "Extended evolutionary synthesis", "Extinction", "Extinction event", "F-statistics", "Fisher's fundamental theorem of natural selection", "Fitness (biology)", "Fitness landscape", "Fixation (population genetics)", "Fixation index", "Founder effect", "Gene-centered view of evolution", "Gene duplication", "Gene flow", "Gene pool", "Gene product", "Genealogical DNA test", "Genetic and anthropometric studies on Japanese people", "Genetic assimilation", "Genetic code", "Genetic diversity", "Genetic drift", "Genetic engineering", "Genetic genealogy", "Genetic history of Central Asia", "Genetic history of East Asians", "Genetic history of Europe", "Genetic history of Italy", "Genetic history of North Africa", "Genetic history of Sub-Saharan Africa", "Genetic history of indigenous peoples of the Americas", "Genetic history of the British Isles", "Genetic history of the Caucasus", "Genetic history of the Iberian Peninsula", "Genetic hitchhiking", "Genetic linkage", "Genetic load", "Genetic monitoring", "Genetic recombination", "Genetic studies on Albanians", "Genetic studies on Arabs", "Genetic studies on Bosniaks", "Genetic studies on Bulgarians", "Genetic studies on Croats", "Genetic studies on Gujarati people", "Genetic studies on Han Chinese", "Genetic studies on Hutu and Tutsi", "Genetic studies on Jews", "Genetic studies on Moroccans", "Genetic studies on Romanians", "Genetic studies on Russians", "Genetic studies on Sami", "Genetic studies on Serbs", "Genetic studies on Sinhalese", "Genetic studies on Sri Lankan Tamils", "Genetic studies on Turkish people", "Genetic variance", "Genetic variation", "Geneticist", "Genetics", "Genetics (journal)", "Genetics and archaeogenetics of South Asia", "Genetics and the Origin of Species", "Genographic Project", "Genome", "Genomics", "Genotype-phenotype distinction", "George R. 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Rousseeuw"], "references": ["http://arxiv.org/abs/1602.06989", "http://doi.org/10.1016%2F0377-0427(87)90125-7", "http://doi.org/10.1016%2Fj.ins.2015.06.039"]}, "Degenerate distribution": {"categories": ["All articles lacking sources", "Articles lacking sources from December 2009", "Discrete distributions", "Infinitely divisible probability distributions", "Pages using deprecated image syntax", "Types of probability distributions"], "title": "Degenerate distribution", "method": "Degenerate distribution", "url": "https://en.wikipedia.org/wiki/Degenerate_distribution", "summary": "In mathematics, a degenerate distribution is a probability distribution in a space (discrete or continuous) with support only on a space of lower dimension. If the degenerate distribution is univariate (involving only a single random variable) it is a deterministic distribution and takes only a single value. Examples include a two-headed coin and rolling a die whose sides all show the same number. This distribution satisfies the definition of \"random variable\" even though it does not appear random in the everyday sense of the word; hence it is considered degenerate.\nIn the case of a real-valued random variable, the degenerate distribution is localized at a point k0 on the real line. The probability mass function equals 1 at this point and 0 elsewhere.\nThe degenerate univariate distribution can be viewed as the limiting case of a continuous distribution whose variance goes to 0 causing the probability density function to be a delta function at k0, with infinite height there but area equal to 1.\nThe cumulative distribution function of the univariate degenerate distribution is:\n\n \n \n \n \n F\n \n \n k\n \n 0\n \n \n \n \n (\n x\n )\n =\n \n {\n \n \n \n \n 1\n ,\n \n \n \n \n if \n \n \n x\n \u2265\n \n k\n \n 0\n \n \n \n \n \n \n 0\n ,\n \n \n \n \n if \n \n \n x\n <\n \n k\n \n 0\n \n \n \n \n \n \n \n \n \n \n {\\displaystyle F_{k_{0}}(x)=\\left\\{{\\begin{matrix}1,&{\\mbox{if }}x\\geq k_{0}\\\\0,&{\\mbox{if }}x<k_{0}\\end{matrix}}\\right.}", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2a/Degenerate.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["0/0", "ARGUS distribution", "Almost surely", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Constant function", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Covariance matrix", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degeneracy (mathematics)", "Delaporte distribution", "Delta function", "Determinant", "Dice", "Dimension (mathematics)", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete random variable", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Event (probability theory)", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heaviside step function", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mathematics", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Positive semi-definite", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Randomness", "Rayleigh distribution", "Real line", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Step function", "Student's t-distribution", "Support (mathematics)", "Symmetric distribution", "Tracy\u2013Widom distribution", "Translation (geometry)", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Univariate distribution", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": []}, "Structural break": {"categories": ["Change detection", "Econometric modeling", "Panel data", "Regression analysis", "Time series", "Use dmy dates from October 2017"], "title": "Structural break", "method": "Structural break", "url": "https://en.wikipedia.org/wiki/Structural_break", "summary": "In econometrics, a structural break, or structural change, is an unexpected shift in a time series that can lead to huge forecasting errors and unreliability of the model in general. This issue was popularised by David Hendry, who argued that lack of stability of coefficients frequently caused forecast failure, and therefore we must routinely test for structural stability. Structural stability \u2212 i.e., the time-invariance of regression coefficients \u2212 is a central issue in all applications of linear regression models.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6d/Chow_test_example.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Applied Economics (journal)", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "CUSUM", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Change detection", "Chemometrics", "Chi-squared test", "Chow test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "David Hendry", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Donald Andrews", "Durbin\u2013Watson statistic", "Econometrics", "Economic model", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Exact test", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forecasting", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "GAUSS", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Great Moderation", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Homoskedasticity", "Independent and identically distributed random variables", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Applied Econometrics", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lagrange multiplier statistics", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratio statistics", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical packages", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural change", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Supremum", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald statistics", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.15.4.117", "http://doi.org/10.1002%2Fjae.616", "http://doi.org/10.1002%2Fjae.659", "http://doi.org/10.1016%2Fj.econmod.2010.07.009", "http://doi.org/10.1080%2F00036840500405763", "http://doi.org/10.1080%2F03610926.2016.1235200", "http://doi.org/10.1111%2F1468-0262.00405", "http://doi.org/10.1111%2Fj.1468-0084.1996.mp58003008.x", "http://doi.org/10.1257%2Fjep.15.4.117", "http://doi.org/10.2307%2F2951764", "https://books.google.com/books?id=86rWI7WzFScC&pg=PA169", "https://www.ssc.wisc.edu/~bhansen/718/Andrews1993.pdf", "https://web.archive.org/web/20171106014215/https://pdfs.semanticscholar.org/780a/6188c4ef4c388e902c0872338fc24ef12b0b.pdf", "https://web.archive.org/web/20171106014407/https://www.ssc.wisc.edu/~bhansen/718/Andrews1993.pdf", "https://pdfs.semanticscholar.org/780a/6188c4ef4c388e902c0872338fc24ef12b0b.pdf"]}, "C-chart": {"categories": ["Quality control tools", "Statistical charts and diagrams"], "title": "C-chart", "method": "C-chart", "url": "https://en.wikipedia.org/wiki/C-chart", "summary": "In statistical quality control, the c-chart is a type of control chart used to monitor \"count\"-type data, typically total number of nonconformities per unit. It is also occasionally used to monitor the total number of events occurring in a given unit of time.\nThe c-chart differs from the p-chart in that it accounts for the possibility of more than one nonconformity per inspection unit, and that (unlike the p-chart and u-chart) it requires a fixed sample size. The p-chart models \"pass\"/\"fail\"-type inspection only, while the c-chart (and u-chart) give the ability to distinguish between (for example) 2 items which fail inspection because of one fault each and the same two items failing inspection with 5 faults each; in the former case, the p-chart will show two non-conformant items, while the c-chart will show 10 faults. \nNonconformities may also be tracked by type or location which can prove helpful in tracking down assignable causes. \nExamples of processes suitable for monitoring with a c-chart include:\n\nMonitoring the number of voids per inspection unit in injection molding or casting processes\nMonitoring the number of discrete components that must be re-soldered per printed circuit board\nMonitoring the number of product returns per dayThe Poisson distribution is the basis for the chart and requires the following assumptions:\nThe number of opportunities or potential locations for nonconformities is very large\nThe probability of nonconformity at any location is small and constant\nThe inspection procedure is same for each sample and is carried out consistently from sample to sampleThe control limits for this chart type are \n \n \n \n \n \n \n c\n \u00af\n \n \n \n \u00b1\n 3\n \n \n \n \n c\n \u00af\n \n \n \n \n \n \n {\\displaystyle {\\bar {c}}\\pm 3{\\sqrt {\\bar {c}}}}\n where \n \n \n \n \n \n \n c\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {c}}}\n is the estimate of the long-term process mean established during control-chart setup.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/90/C_control_chart.svg"], "links": ["Assignable cause", "Casting", "Control chart", "Hoboken, New Jersey", "Injection molding", "International Standard Book Number", "John Wiley & Sons", "National Institute of Standards and Technology", "OCLC", "P-chart", "Poisson distribution", "Printed circuit board", "Soldered", "Statistical process control", "U-chart", "Variable and attribute (research)", "Walter A. Shewhart"], "references": ["http://www.eas.asu.edu/~masmlab/montgomery/", "http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc331.htm", "http://www.worldcat.org/oclc/56729567", "https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/#"]}, "Expected value of sample information": {"categories": ["All articles needing additional references", "All articles to be expanded", "Articles needing additional references from June 2012", "Articles to be expanded from July 2016", "Articles using small message boxes", "Bayesian inference", "Expected utility", "Game theory"], "title": "Expected value of sample information", "method": "Expected value of sample information", "url": "https://en.wikipedia.org/wiki/Expected_value_of_sample_information", "summary": "In decision theory, the expected value of sample information (EVSI) is the expected increase in utility that a decision-maker could obtain from gaining access to a sample of additional observations before making a decision. The additional information obtained from the sample may allow them to make a more informed, and thus better, decision, thus resulting in an increase in expected utility. EVSI attempts to estimate what this improvement would be before seeing actual sample data; hence, EVSI is a form of what is known as preposterior analysis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b8/EVSI_diagram.png", "https://upload.wikimedia.org/wikipedia/commons/8/88/EVSI_prior_marginals.png", "https://upload.wikimedia.org/wikipedia/commons/8/8f/EVSI_result.png", "https://upload.wikimedia.org/wikipedia/commons/c/c9/EVSI_trial_data.png", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayes' Theorem", "Bayes' theorem", "Decision theory", "Dirichlet distribution", "Expected value of including uncertainty", "Expected value of perfect information", "Influence diagram", "Marginal distribution", "Monte Carlo integration", "Monte Carlo method", "Monte Carlo methods", "Multinomial distribution", "Probability density function", "Sample (statistics)"], "references": ["https://www.gwern.net/docs/statistics/1961-raiffa-appliedstatisticaldecisiontheory.pdf"]}, "L\u00e9vy flight": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2011", "Articles with unsourced statements from December 2010", "CS1 maint: Multiple names: authors list", "Fractals", "Markov processes", "Paul L\u00e9vy (mathematician)"], "title": "L\u00e9vy flight", "method": "L\u00e9vy flight", "url": "https://en.wikipedia.org/wiki/L%C3%A9vy_flight", "summary": "A L\u00e9vy flight, named for French mathematician Paul L\u00e9vy, is a random walk in which the step-lengths have a probability distribution that is heavy-tailed. When defined as a walk in a space of dimension greater than one, the steps made are in isotropic random directions.\nThe term \"L\u00e9vy flight\" was coined by Beno\u00eet Mandelbrot, who used this for one specific definition of the distribution of step sizes. He used the term Cauchy flight for the case where the distribution of step sizes is a Cauchy distribution, and Rayleigh flight for when the distribution is a normal distribution (which is not an example of a heavy-tailed probability distribution).\nLater researchers have extended the use of the term \"L\u00e9vy flight\" to include cases where the random walk takes place on a discrete grid rather than on a continuous space.The particular case for which Mandelbrot used the term \"L\u00e9vy flight\" is defined by the survivor function (commonly known as the survival function) of the distribution of step-sizes, U, being\n\n \n \n \n Pr\n (\n U\n >\n u\n )\n =\n \n \n {\n \n \n \n 1\n \n \n :\n \n u\n <\n 1\n ,\n \n \n \n \n \n u\n \n \u2212\n D\n \n \n \n \n :\n \n u\n \u2265\n 1.\n \n \n \n \n \n \n \n \n {\\displaystyle \\Pr(U>u)={\\begin{cases}1&:\\ u<1,\\\\u^{-D}&:\\ u\\geq 1.\\end{cases}}}\n Here D is a parameter related to the fractal dimension and the distribution is a particular case of the Pareto distribution. Later researchers allow the distribution of step sizes to be any distribution for which the survival function has a power-like tail\n\n \n \n \n Pr\n (\n U\n >\n u\n )\n =\n O\n (\n \n u\n \n \u2212\n k\n \n \n )\n ,\n \n \n {\\displaystyle \\Pr(U>u)=O(u^{-k}),}\n for some k satisfying 1 < k < 3. (Here the notation O is the Big O notation.) Such distributions have an infinite variance. Typical examples are the symmetric stable distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/66/BrownianMotion.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4b/Fractal_fern_explained.png", "https://upload.wikimedia.org/wikipedia/commons/d/d0/LevyFlight.svg"], "links": ["Affine transformation", "Aleksandr Lyapunov", "ArXiv", "Assouad dimension", "Astronomy", "Barnsley fern", "Benoit Mandelbrot", "Beno\u00eet Mandelbrot", "Bibcode", "Big O notation", "Biology", "Brownian motion", "Brownian tree", "Buddhabrot", "Burning Ship fractal", "Cantor set", "Cauchy distribution", "Central limit theorem", "Chaos: Making a New Science", "Chaos theory", "Coastline paradox", "Correlation dimension", "Cryptography", "David Sims (biologist)", "Diffusion-limited aggregation", "Digital object identifier", "Dragon curve", "Earthquake", "Fat-tailed distribution", "Felix Hausdorff", "Filled Julia set", "Financial mathematics", "Fractal", "Fractal art", "Fractal canopy", "Fractal dimension", "Fractal landscape", "Gaston Julia", "Georg Cantor", "H. Eugene Stanley", "H tree", "Hausdorff dimension", "Heavy-tailed distribution", "Helge von Koch", "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", "International Standard Book Number", "Isotropy", "Iterated function system", "Julia set", "Koch snowflake", "L-system", "Lebesgue covering dimension", "Lewis Fry Richardson", "List of fractals by Hausdorff dimension", "Lyapunov fractal", "L\u00e9vy alpha-stable distribution", "L\u00e9vy flight foraging hypothesis", "L\u00e9vy process", "Mandelbox", "Mandelbrot set", "Mandelbulb", "Markov property", "Menger sponge", "Minkowski\u2013Bouligand dimension", "Multifractal system", "N-flake", "Nature (journal)", "Newton fractal", "Normal distribution", "OCLC", "Orbit trap", "Packing dimension", "Pareto distribution", "Paul L\u00e9vy (mathematician)", "Percolation theory", "Physics", "Pickover stalk", "Power-law tail", "Probability distribution", "PubMed Central", "PubMed Identifier", "Random walk", "Recursion", "Scale invariance", "Self-avoiding walk", "Self-similarity", "Shlomo Havlin", "Sierpinski carpet", "Sierpinski triangle", "Silky shark", "Space-filling curve", "Stable distribution", "Strange attractor", "Survival function", "Survivor function", "T-square (fractal)", "The Beauty of Fractals", "The Fractal Geometry of Nature", "The New York Times", "Tricorn (mathematics)", "Variance", "Wac\u0142aw Sierpi\u0144ski", "Yellowfin tuna"], "references": ["http://news.discovery.com/animals/sharks/sharks-math-hunt.htm", "http://www.nature.com/nature/journal/v451/n7182/full/nature06518.html", "http://www.nature.com/nature/journal/v465/n7301/full/nature09116.html", "http://well.blogs.nytimes.com/2014/01/01/navigating-our-world-like-birds-and-bees/", "http://physicsworld.com/cws/article/news/2010/jun/11/sharks-hunt-via-levy-flights", "http://www.sciencedirect.com/science/article/pii/S0022519314003051", "http://adsabs.harvard.edu/abs/1987JMP....28..592C", "http://adsabs.harvard.edu/abs/1999AmJPh..67.1253S", "http://adsabs.harvard.edu/abs/1999Natur.401..911V", "http://adsabs.harvard.edu/abs/2000Natur.406..845K", "http://adsabs.harvard.edu/abs/2000PhyA..282....1V", "http://adsabs.harvard.edu/abs/2002PhyA..314..208V", "http://adsabs.harvard.edu/abs/2008Natur.451.1098S", "http://adsabs.harvard.edu/abs/2010Natur.465.1066H", "http://adsabs.harvard.edu/abs/2010PhRvL.104a8701L", "http://adsabs.harvard.edu/abs/2014PNAS..11111073S", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4121825", "http://www.ncbi.nlm.nih.gov/pubmed/10972276", "http://www.ncbi.nlm.nih.gov/pubmed/25024221", "http://havlin.biu.ac.il/Publications.php?keyword=Towards+Design+Principles+for+Optimal+Transport+Networks&year=*&match=all", "http://arxiv.org/abs/0908.3869", "http://doi.org/10.1016%2FS0378-4371(00)00071-6", "http://doi.org/10.1016%2FS0378-4371(02)01157-3", "http://doi.org/10.1016%2Fj.jtbi.2014.05.032", "http://doi.org/10.1038%2F35022643", "http://doi.org/10.1038%2F44831", "http://doi.org/10.1038%2Fnature06518", "http://doi.org/10.1038%2Fnature09116", "http://doi.org/10.1063%2F1.527644", "http://doi.org/10.1073%2Fpnas.1405966111", "http://doi.org/10.1103%2FPhysRevLett.104.018701", "http://doi.org/10.1119%2F1.19112", "http://plus.maths.org/issue11/features/physics_world/", "http://www.pnas.org/content/111/30/11073.abstract", "http://www.pnas.org/content/early/2014/07/11/1405966111", "http://www.worldcat.org/oclc/7876824", "http://caos.fs.usb.ve/~srojas/Teaching/USB/MC_Intro/MC_readings_a/MC_a4_brownian_1.pdf", "https://deepblue.lib.umich.edu/bitstream/2027.42/70735/2/JMAPAQ-28-3-592-1.pdf", "https://web.archive.org/web/20120328105732/http://caos.fs.usb.ve/~srojas/Teaching/USB/MC_Intro/MC_readings_a/MC_a4_brownian_1.pdf"]}, "Lists of country-related topics": {"categories": ["Lists by country", "Lists of lists"], "title": "Lists of country-related topics", "method": "Lists of country-related topics", "url": "https://en.wikipedia.org/wiki/Lists_of_country-related_topics", "summary": "Each entry below presents a list of topics about a specific nation or state (country), followed by a link to the main article for that country. 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"Algeria", "American Samoa", "Andorra", "Angola", "Anguilla", "Antigua and Barbuda", "Argentina", "Armenia", "Aruba", "Ascension Island", "Australia", "Austria", "Azerbaijan", "Bahrain", "Bangladesh", "Barbados", "Belarus", "Belgium", "Belize", "Benin", "Bermuda", "Bhutan", "Bolivia", "Bosnia and Herzegovina", "Botswana", "Brazil", "British Virgin Islands", "Brunei", "Bulgaria", "Burkina Faso", "Burundi", "Cambodia", "Cameroon", "Canada", "Cape Verde", "Cayman Islands", "Central African Republic", "Chad", "Chile", "China", "Christmas Island", "Cocos (Keeling) Islands", "Colombia", "Comoros", "Cook Islands", "Costa Rica", "Croatia", "Cuba", "Cura\u00e7ao", "Cyprus", "Czech Republic", "Democratic Republic of the Congo", "Denmark", "Djibouti", "Dominica", "Dominican Republic", "East Timor", "Ecuador", "Egypt", "El Salvador", "England", "Equatorial Guinea", "Eritrea", "Estonia", "Eswatini", "Ethiopia", "Falkland Islands", "Faroe Islands", "Federated States of Micronesia", "Fiji", "Finland", "France", "French Guiana", "French Polynesia", "Gabon", "Georgia (country)", "Germany", "Ghana", "Gibraltar", "Greece", "Greenland", "Grenada", "Guadeloupe", "Guam", "Guatemala", "Guernsey", "Guinea", "Guinea-Bissau", "Guyana", "Haiti", "Honduras", "Hong Kong", "Hungary", "Iceland", "Index of Abkhazia-related articles", "Index of Afghanistan-related articles", "Index of Akrotiri and Dhekelia-related articles", "Index of Albania-related articles", "Index of Algeria-related articles", "Index of American Samoa-related articles", "Index of Angola-related articles", "Index of Anguilla-related articles", "Index of Antigua and Barbuda-related articles", "Index of Argentina-related articles", "Index of Armenia-related articles", "Index of Artsakh-related articles", "Index of Aruba-related articles", "Index of Ascension Island-related articles", "Index of Australia-related articles", "Index of Austria-related articles", "Index of Azerbaijan-related articles", "Index of 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Dominican Republic-related articles", "Index of Ecuador-related articles", "Index of Egypt-related articles", "Index of El Salvador-related articles", "Index of Equatorial Guinea-related articles", "Index of Eritrea-related articles", "Index of Estonia-related articles", "Index of Eswatini-related articles", "Index of Ethiopia-related articles", "Index of Falkland Islands-related articles", "Index of Federated States of Micronesia-related articles", "Index of Fiji-related articles", "Index of French Guiana-related articles", "Index of French Polynesia-related articles", "Index of Gabon-related articles", "Index of Gambia-related articles", "Index of Georgia (country)-related articles", "Index of Germany-related articles", "Index of Ghana-related articles", "Index of Greece-related articles", "Index of Greenland-related articles", "Index of Grenada-related articles", "Index of Guadeloupe-related articles", "Index of Guam-related articles", "Index of Guatemala-related articles", "Index of Guernsey-related articles", "Index of Guinea-Bissau-related articles", "Index of Guinea-related articles", "Index of Guyana-related articles", "Index of Haiti-related articles", "Index of Hong Kong-related articles", "Index of Hungary-related articles", "Index of Iceland-related articles", "Index of India-related articles", "Index of Iraq-related articles", "Index of Israel-related articles", "Index of Italy-related articles", "Index of Ivory Coast-related articles", "Index of Jamaica-related articles", "Index of Japan-related articles", "Index of Jordan-related articles", "Index of Kazakhstan-related articles", "Index of Kenya-related articles", "Index of Kuwait-related articles", "Index of Kyrgyzstan-related articles", "Index of Lebanon-related articles", "Index of Lesotho-related articles", "Index of Liberia-related articles", "Index of Libya-related articles", "Index of Macau-related articles", "Index of Madagascar-related articles", "Index of Malawi-related articles", "Index of Mali-related articles", "Index of Malta-related articles", "Index of Marshall Islands-related articles", "Index of Martinique-related articles", "Index of Mauritania-related articles", "Index of Mexico-related articles", "Index of Mongolia-related articles", "Index of Montserrat-related articles", "Index of Mozambique-related articles", "Index of Myanmar-related articles", "Index of Namibia-related articles", "Index of Nauru-related articles", "Index of Netherlands Antilles-related articles", "Index of Nicaragua-related articles", "Index of Nigeria-related articles", "Index of North Korea-related articles", "Index of Northern Mariana Islands-related articles", "Index of Oman-related articles", "Index of Pakistan-related articles", "Index of Palau-related articles", "Index of Panama-related articles", "Index of Paraguay-related articles", "Index of Peru-related articles", "Index of Portugal-related articles", "Index of Puerto Rico-related articles", "Index of Republic of the Congo-related articles", "Index of Saint Barth\u00e9lemy-related articles", "Index of Saint Kitts and Nevis-related articles", "Index of Saint Lucia-related articles", "Index of Saint Pierre and Miquelon-related articles", "Index of Saint Vincent and the Grenadines-related articles", "Index of San Marino-related articles", "Index of Saudi Arabia-related articles", "Index of Senegal-related articles", "Index of Sierra Leone-related articles", "Index of Somalia-related articles", "Index of South Georgia and the South Sandwich Islands-related articles", "Index of South Korea-related articles", "Index of Soviet Union-related articles", "Index of Suriname-related articles", "Index of Switzerland-related articles", "Index of Syria-related articles", "Index of Taiwan-related articles", "Index of Tajikistan-related articles", "Index of Tanzania-related articles", "Index of Thailand-related articles", "Index of Togo-related articles", "Index of Turkey-related articles", "Index of Turkmenistan-related articles", "Index of Turks and Caicos Islands-related articles", "Index of Uganda-related articles", "Index of United States-related articles", "Index of United States Virgin Islands-related articles", "Index of Uruguay-related articles", "Index of Uzbekistan-related articles", "Index of Vanuatu-related articles", "Index of Vatican City-related articles", "Index of Venezuela-related articles", "Index of Vietnam-related articles", "Index of Zimbabwe-related articles", "Index of the Collectivity of Saint Martin-related articles", "Index of \u00c5land-related articles", "India", "Indonesia", "Iran", "Iraq", "Ireland", "Isle of Man", "Israel", "Italy", "Ivory Coast", "Jamaica", "Japan", "Jersey", "Jordan", "Kazakhstan", "Kenya", "Kiribati", "Kosovo", "Kuwait", "Kyrgyzstan", "Laos", "Latvia", "Lebanon", "Lesotho", "Liberia", "Libya", "Liechtenstein", "List of Bangladesh-related topics", "List of Belarus-related topics", "List of Belize-related topics", "List of Bermuda-related topics", "List of Bolivia-related topics", "List of Botswana-related topics", "List of British Virgin Islands-related topics", "List of Brunei-related topics", "List of Central African Republic-related topics", "List of Chile-related topics", "List of Czech Republic-related topics", "List of East Timor-related topics", "List of Falkland Islands-related topics", "List of Finland-related topics", "List of Honduras-related topics", "List of Indonesia-related topics", "List of Iran-related topics", "List of Ireland-related topics", "List of Laos-related topics", "List of Malaysia-related topics", "List of Maldives-related topics", "List of Mauritius-related topics", "List of Mayotte-related topics", "List of Northern Ireland-related topics", "List of Philippines-related topics", "List of Qatar-related topics", "List of Singapore-related topics", "List of South Africa-related topics", "List of Sweden-related topics", "List of S\u00e3o Tom\u00e9 and Pr\u00edncipe-related topics", "List of Trinidad and Tobago-related topics", "List of United Arab Emirates-related topics", "List of Yemen-related topics", "List of sovereign states", "List of timelines", "Lists of countries and territories", "Lists of people", "Lithuania", "Luxembourg", "Macau", "Madagascar", "Malawi", "Malaysia", "Maldives", "Mali", "Malta", "Marshall Islands", "Martinique", "Mauritania", "Mauritius", "Mayotte", "Mexico", "Moldova", "Monaco", "Mongolia", "Montenegro", "Montserrat", "Morocco", "Mozambique", "Myanmar", "Namibia", "Nauru", "Nepal", "Netherlands", "Netherlands Antilles", "New Caledonia", "New Zealand", "Nicaragua", "Niger", "Nigeria", "Niue", "Norfolk Island", "North Korea", "Northern Cyprus", "Northern Ireland", "Northern Mariana Islands", "Norway", "Oman", "Outline of Andorra", "Outline of Bahrain", "Outline of Benin", "Outline of Bosnia and Herzegovina", "Outline of Bulgaria", "Outline of Burundi", "Outline of Chad", "Outline of England", "Outline of France", "Outline of Gibraltar", "Outline of Jersey", "Outline of Kiribati", "Outline of Kosovo", "Outline of Latvia", "Outline of Liechtenstein", "Outline of Lithuania", "Outline of Luxembourg", "Outline of Macedonia", "Outline of Moldova", "Outline of Monaco", "Outline of Montenegro", "Outline of Morocco", "Outline of Nepal", "Outline of New Caledonia", "Outline of New Zealand", "Outline of Niger", "Outline of Niue", "Outline of Norfolk Island", "Outline of Northern Cyprus", "Outline of Norway", "Outline of Papua New Guinea", "Outline of Poland", "Outline of Romania", "Outline of Russia", "Outline of Rwanda", "Outline of Saint Helena", "Outline of Samoa", "Outline of Scotland", "Outline of Serbia", "Outline of Seychelles", "Outline of Slovakia", "Outline of Slovenia", "Outline of Somaliland", "Outline of Spain", "Outline of Sri Lanka", "Outline of Sudan", "Outline of Svalbard", "Outline of Tokelau", "Outline of Tonga", "Outline of Transnistria", "Outline of Tristan da Cunha", "Outline of Tunisia", "Outline of Tuvalu", "Outline of Ukraine", "Outline of Wales", "Outline of Wallis and Futuna", "Outline of Zambia", "Outline of the Bahamas", "Outline of the Faroe Islands", "Outline of the Isle of Man", "Outline of the Netherlands", "Outline of the Pitcairn Islands", "Outline of the Sahrawi Arab Democratic Republic", "Outline of the Solomon Islands", "Outline of the United Kingdom", "Pakistan", "Palau", "Panama", "Papua New Guinea", "Paraguay", "People's Republic of China", "Peru", "Philippines", "Pitcairn Islands", "Poland", "Portugal", "Puerto Rico", "Qatar", "Republic of Artsakh", "Republic of China", "Republic of Ireland", "Republic of Macedonia", "Republic of the Congo", "Romania", "Russia", "Rwanda", "Saint Barth\u00e9lemy", "Saint Helena", "Saint Kitts and Nevis", "Saint Lucia", "Saint Martin (France)", "Saint Pierre and Miquelon", "Saint Vincent and the Grenadines", "Samoa", "San Marino", "Saudi Arabia", "Scotland", "Senegal", "Serbia", "Seychelles", "Sierra Leone", "Singapore", "Slovakia", "Slovenia", "Solomon Islands", "Somalia", "Somaliland", "South Africa", "South Georgia and the South Sandwich Islands", "South Korea", "Soviet Union", "Spain", "Sri Lanka", "Sudan", "Suriname", "Svalbard", "Sweden", "Switzerland", "Syria", "S\u00e3o Tom\u00e9 and Pr\u00edncipe", "Taiwan", "Tajikistan", "Tanzania", "Thailand", "The Bahamas", "The Gambia", "Togo", "Tokelau", "Tonga", "Transnistria", "Trinidad and Tobago", "Tristan da Cunha", "Tunisia", "Turkey", "Turkmenistan", "Turks and Caicos Islands", "Tuvalu", "Uganda", "Ukraine", "United Arab Emirates", "United Kingdom", "United States", "United States Virgin Islands", "Uruguay", "Uzbekistan", "Vanuatu", "Vatican City", "Venezuela", "Vietnam", "Wales", "Wallis and Futuna", "Western Sahara", "Yemen", "Zambia", "Zimbabwe", "\u00c5land Islands"], "references": []}, "Multiple correspondence analysis": {"categories": ["CS1 maint: Extra text: authors list", "CS1 maint: Multiple names: authors list", "Dimension reduction"], "title": "Multiple correspondence analysis", "method": "Multiple correspondence analysis", "url": "https://en.wikipedia.org/wiki/Multiple_correspondence_analysis", "summary": "In statistics, multiple correspondence analysis (MCA) is a data analysis technique for nominal categorical data, used to detect and represent underlying structures in a data set. It does this by representing data as points in a low-dimensional Euclidean space. The procedure thus appears to be the counterpart of principal component analysis for categorical data. MCA can be viewed as an extension of simple correspondence analysis (CA) in that it is applicable to a large set of categorical variables.", "images": [], "links": ["Blasius, J\u00f6rg", "Cluster analysis", "Correspondence analysis", "Covariance matrix", "Data analysis", "Eigenvalues", "Euclidean space", "Factor analysis", "Factor analysis of mixed data", "Field (Bourdieu)", "Geometric data analysis", "International Standard Book Number", "Jean-Paul Benz\u00e9cri", "La Distinction", "Pierre Bourdieu", "Principal component analysis", "Statistics", "The State Nobility"], "references": ["http://factominer.free.fr/", "https://books.google.com/books?id=a6bDBUF58XwC&lpg=PP1&dq=geometric%20data%20analysis&hl=no&pg=PP1#v=onepage&q=&f=false", "https://web.archive.org/web/20100325141907/http://www.fbbva.es/TLFU/tlfu/esp/publicaciones/libros/fichalibro/index.jsp?codigo=300"]}, "Centering matrix": {"categories": ["Data processing", "Matrices"], "title": "Centering matrix", "method": "Centering matrix", "url": "https://en.wikipedia.org/wiki/Centering_matrix", "summary": "In mathematics and multivariate statistics, the centering matrix is a symmetric and idempotent matrix, which when multiplied with a vector has the same effect as subtracting the mean of the components of the vector from every component.", "images": [], "links": ["Covariance matrix", "Eigenvalue", "Idempotent", "Idempotent matrix", "Identity matrix", "International Standard Book Number", "Kernel (matrix)", "Linear subspace", "Mathematics", "Matrix of ones", "Matrix transpose", "Mean", "Multinomial distribution", "Multivariate statistics", "Positive semi-definite", "Projection matrix", "Sample mean", "Scatter matrix", "Singular matrix", "Symmetric matrix"], "references": []}, "Foundations of statistics": {"categories": ["All pages needing cleanup", "Articles needing cleanup from April 2017", "Articles with sections that need to be turned into prose from April 2017", "Philosophy of statistics"], "title": "Foundations of statistics", "method": "Foundations of statistics", "url": "https://en.wikipedia.org/wiki/Foundations_of_statistics", "summary": "The foundations of statistics concern the epistemological debate in statistics over how one should conduct inductive inference from data. Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist inference, the distinction between Fisher's \"significance testing\" and Neyman\u2013Pearson \"hypothesis testing\", and whether the likelihood principle should be followed. Some of these issues have been debated for up to 200 years without resolution.Bandyopadhyay & Forster describe four statistical paradigms: \"(1) classical statistics or error statistics, (ii) Bayesian statistics, (iii) likelihood-based statistics, and (iv) the Akaikean-Information Criterion-based statistics\".\nSavage's text Foundations of Statistics has been cited over 15000 times on Google Scholar. It tells the following.\n\nIt is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["A. W. F. Edwards", "Ad infinitum", "Akaike information criterion", "All models are wrong", "Allan Birnbaum", "Andrew Gelman", "ArXiv", "Bayes' theorem", "Bayesian inference", "Bibcode", "Bradley Efron", "Bruno de Finetti", "Chapman & Hall", "Confidence intervals", "Correlation does not imply causation", "David Cox (statistician)", "Deborah Mayo", "Dennis Lindley", "Digital object identifier", "E. L. Lehmann", "Egon Pearson", "Epistemology", "Evidence", "Fiducial inference", "Founders of statistics", "Frequentist inference", "George E. P. Box", "Gerd Gigerenzer", "Google Scholar", "Harold Jeffreys", "History of statistics", "I. J. Good", "Inductive inference", "Inductive reasoning", "International Standard Book Number", "JSTOR", "Jerzy Neyman", "Jim Berger (statistician)", "Joseph Born Kadane", "Jos\u00e9-Miguel Bernardo", "Journal of the Royal Statistical Society, Series B", "Journal of the Royal Statistical Society, Series D", "Leo Breiman", "Leonard Jimmie Savage", "Likelihood function", "Likelihood principle", "M. J. Bayarri", "Model selection", "Modus tollens", "Neyman\u2013Pearson lemma", "Philosophy of mathematics", "Philosophy of probability", "Philosophy of science", "Philosophy of statistics", "Principle of indifference", "Probability interpretations", "PubMed Identifier", "Robert P. Abelson", "Ronald A Fisher", "Ronald Fisher", "Sample size determination", "Statistical Science", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistics", "Stein's paradox", "Structural equation modeling", "Student's t-test", "Synthese", "The American Statistician"], "references": ["http://www.stat.cmu.edu/~kass/papers/about-bayes-rule.pdf", "http://www.stat.columbia.edu/~gelman/presentations/redbluetalkubc.pdf", "http://ftp.isds.duke.edu/WorkingPapers/03-26.pdf", "http://adsabs.harvard.edu/abs/1933RSPTA.231..289N", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.173.4608", "http://plato.stanford.edu/entries/probability-interpret/", "http://plato.stanford.edu/entries/statistics/", "http://disc-nt.cba.uh.edu/chin/ais/", "http://www.phil.vt.edu/dmayo/PhilStatistics/Triad/Fisher%201955.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/17286092", "http://www.cimat.mx/reportes/enlinea/D-99-10.html", "http://imyy.net/research/BSTT566__Slides.pdf", "http://arxiv.org/abs/1006.3868", "http://doi.org/10.1007%2FBF00485352", "http://doi.org/10.1016%2Fj.edurev.2007.04.001", "http://doi.org/10.1080%2F00031305.2012.752410", "http://doi.org/10.1080%2F01621459.1993.10476404", "http://doi.org/10.1086%2F392737", "http://doi.org/10.1090%2Fs0273-0979-2012-01374-5", "http://doi.org/10.1093%2Fbjps%2Faxi152", "http://doi.org/10.1098%2Frsta.1933.0009", "http://doi.org/10.1111%2F1467-9884.00238", "http://doi.org/10.1111%2Fj.1751-5823.2002.tb00350.x", "http://doi.org/10.1111%2Fj.2044-8317.2011.02037.x", "http://doi.org/10.1214%2F06-ba101", "http://doi.org/10.1214%2F08-BA318REJ", "http://doi.org/10.1214%2Fss%2F1009213726", "http://doi.org/10.1214%2Fss%2F1056397485", "http://doi.org/10.1214%2Fss%2F1177012754", "http://doi.org/10.2307%2F20445367", "http://doi.org/10.2307%2F2321163", "http://doi.org/10.2307%2F2683105", "http://www.jstor.org/stable/20445367", "http://www.jstor.org/stable/2245388", "http://www.jstor.org/stable/2683105", "http://mathdl.maa.org/images/upload_library/22/Ford/BradleyEfron.pdf", "http://www.repository.utl.pt/bitstream/10400.5/2327/1/wp022008.pdf", "https://scholar.google.co.uk/scholar?cites=9531312933296806388"]}, "Siegel\u2013Tukey test": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2009", "Nonparametric statistics", "Statistical tests"], "title": "Siegel\u2013Tukey test", "method": "Siegel\u2013Tukey test", "url": "https://en.wikipedia.org/wiki/Siegel%E2%80%93Tukey_test", "summary": "In statistics, the Siegel\u2013Tukey test, named after Sidney Siegel and John Tukey, is a non-parametric test which may be applied to data measured at least on an ordinal scale. It tests for differences in scale between two groups.\nThe test is used to determine if one of two groups of data tends to have more widely dispersed values than the other. In other words, the test determines whether one of the two groups tends to move, sometimes to the right, sometimes to the left, but away from the center (of the ordinal scale).\nThe test was published in 1960 by Sidney Siegel and John Wilder Tukey in the Journal of the American Statistical Association, in the article \"A Nonparametric Sum of Ranks Procedure for Relative Spread in Unpaired Samples.\"\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Alternative hypothesis", "John Tukey", "John Wilder Tukey", "Journal of the American Statistical Association", "Level of measurement", "Non-parametric statistics", "Non-parametric test", "Null hypothesis", "Sidney Siegel", "Statistical hypothesis testing", "Statistical power", "Statistics", "Wilcoxon rank sum test"], "references": ["http://www.r-statistics.com/2010/02/siegel-tukey-a-non-parametric-test-for-equality-in-variability-r-code/"]}, "Multiple baseline design": {"categories": ["Design of experiments", "Experimental psychology", "Quantitative analysis of behavior", "Quantitative research"], "title": "Multiple baseline design", "method": "Multiple baseline design", "url": "https://en.wikipedia.org/wiki/Multiple_baseline_design", "summary": "A multiple baseline design is a style of research that cannot be used in sealant testing. This design is used in medical, psychological and biological research to name a few areas. It has several advantages over AB designs which only measure a single case. It is important to note that the start of treatment conditions is staggered (started at different times) across individuals. Because treatment is started at different times we can conclude that changes are due to the treatment rather than to a chance factor. By gathering data from many subjects (instances), inferences can be made about the likeliness that the measured trait generalizes to a greater population. \nIn multiple baseline designs, the experimenter starts by measuring a trait of interest, then applying a treatment before measuring that trait again. Treatment should not begin until a stable baseline has been recorded, and should not finish until measures regain stability. If a significant change occurs across all participants the experimenter may infer that the treatment is effective.\nMultiple base-line experiments are most commonly used in cases where the dependent variable is not expected to return to normal after the treatment has been applied, or when medical reasons forbid the withdrawal of a treatment. They often employ particular methods or recruiting participants. Multiple base-line designs are associated with potential confounds introduced by an experimenter bias which must be addressed in order to preserve objectivity. Particularly, researchers are advised to develop all test schedules and data collection limits beforehand.", "images": [], "links": ["A priori and a posteriori", "Confounds and Artifacts", "Declaration of Helsinki", "Design of experiments", "Digital object identifier", "Experimenter's bias", "Generalization", "Hypothesis", "Inference", "Quasi-experimental design", "Sampling bias", "Single-subject design", "Single-subject research", "Validity (statistics)"], "references": ["http://allpsych.com/researchmethods/multiplebaselines.html", "http://findarticles.com/p/articles/mi_hb6516/is_4_41/ai_n29146430/", "https://www.msu.edu/user/sw/ssd/issd10d.htm", "https://doi.org/10.1002%2Fbin.191", "https://doi.org/10.1002%2Fpits.20237", "https://doi.org/10.1007%2FBF00961078", "https://doi.org/10.1016%2F0005-7916(81)90055-0", "https://doi.org/10.1023%2FB:JOBE.0000044735.51022.5d"]}, "Infinite monkey theorem": {"categories": ["All articles lacking reliable references", "Articles containing French-language text", "Articles containing proofs", "Articles lacking reliable references from August 2012", "Articles with short description", "CS1 maint: Archived copy as title", "CS1 maint: Extra text: authors list", "CS1 maint: Multiple names: authors list", "Fictional monkeys", "Infinity", "Literary theory", "Metaphors referring to animals", "Probability theorems", "Random text generation", "Statistical randomness", "Thought experiments", "Webarchive template wayback links"], "title": "Infinite monkey theorem", "method": "Infinite monkey theorem", "url": "https://en.wikipedia.org/wiki/Infinite_monkey_theorem", "summary": "The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible finite text an infinite number of times. However, the probability that monkeys filling the observable universe would type a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero).\nIn this context, \"almost surely\" is a mathematical term with a precise meaning, and the \"monkey\" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the \"monkey metaphor\" is that of French mathematician \u00c9mile Borel in 1913, but the first instance may have been even earlier.\nVariants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. Jorge Luis Borges traced the history of this idea from Aristotle's On Generation and Corruption and Cicero's De natura deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, up to modern statements with their iconic simians and typewriters. In the early 20th century, Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3c/Chimpanzee_seated_at_typewriter.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d7/Thomas_Henry_Huxley_-_Project_Gutenberg_eText_16935.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["1860 Oxford evolution debate", "ASCII", "Abstract algebra", "Aeschylus", "Age of the universe", "Algebra", "Algebraic geometry", "Almost surely", "Analytic geometry", "Applied mathematics", "April Fools' Day Request for Comments", "Areas of mathematics", "Arif Zaman", "Aristotle", "Arithmetic", "Arthur Eddington", "Arthur Koestler", "Arts Council", "Arts Council England", "Begging the question", "Bibcode", "Big Bang", "Binary numeral system", "Blaise Pascal", "Boltzmann brain", "Borel\u2013Cantelli lemma", "British Association for the Advancement of Science", "Calculus", "Category theory", "Celebes crested macaque", "Charles Darwin", "Charles Kittel", "Chimpanzee", "Christian apologist", "Cicero", "Complexity", "Computational mathematics", "Computer science", "Context-free grammar", "Control theory", "DNA", "De natura deorum", "Devon", "Diehard tests", "Differential equation", "Differential geometry", "Digital object identifier", "Digits of pi", "Discrete geometry", "Discrete mathematics", "Douglas Adams", "Dynamical systems theory", "Earthquake", "Edwin Drood", "Elementary algebra", "Eliot Weinberger", "End of the universe", "England", "Event (probability theory)", "Evolutionary biology", "Expected value", "Exponential growth", "Fermat's last theorem", "Finite geometry", "Fitness function", "Ford Prefect (character)", "Foundations of mathematics", "French language", "Functional analysis", "Future of an expanding universe", "Gambler's fallacy", "Game theory", "Garamantes", "Geometry", "George Marsaglia", "Gifford Lectures", "Gospel of Basilides", "Graph theory", "G\u00e9rard Genette", "Hamlet", "Hamlet (play)", "Henry IV, Part 2", "Herbert Kroemer", "Hilbert's paradox of the Grand Hotel", "History of mathematics", "Homer Simpson", "Infinite monkey theorem in popular culture", "Infinite set", "Infinity", "Information theory", "International Standard Book Number", "International Standard Serial Number", "Irrational numbers", "It was the best of times, it was the worst of times", "James Hopwood Jeans", "James W. Valentine", "Java applet", "John F. MacArthur", "Jonathan Swift", "Jorge J. E. Gracia", "Jorge Luis Borges", "Last Exit to Springfield", "Law of truly large numbers", "Leucippus", "Limit of a function", "Linear algebra", "Lists of mathematics topics", "Mathematical analysis", "Mathematical logic", "Mathematical optimization", "Mathematical physics", "Mathematical statistics", "Mathematics", "Mathematics and art", "Mathematics education", "Metaphor", "Metazoa", "Moscow", "Mr. Burns", "Multilinear algebra", "Murphy's Law", "Mutation", "Natural language generation", "Natural selection", "Nelson Goodman", "Non-random", "Normal number", "Number theory", "Numerical analysis", "Observable universe", "On Generation and Corruption", "On the Origin of Species", "Order theory", "Outline of mathematics", "Paignton Zoo", "Philosophy of mathematics", "Pierre Fermat", "Pierre Menard, Author of the Quixote", "Postmodernism Generator", "Probability", "Probability theory", "Proton decay", "Pure mathematics", "R. G. Collingwood", "Random", "Random number generator", "Random sequence", "Randomness", "Randomness tests", "Rational number", "Real number", "Recreational mathematics", "Richard Dawkins", "SCIgen", "Samuel Wilberforce", "San Francisco", "Set theory", "SnarXiv", "Statistical mechanics", "Statistically independent", "Statistics", "Stephen Dedalus", "String (computer science)", "Substring", "The Blind Watchmaker", "The Engine", "The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos", "The Hitchhiker's Guide to the Galaxy", "The Infinite Monkey Cage", "The Library of Babel", "The New Yorker", "The Simpsons", "The Washington Post", "Theory of computation", "Thermodynamics", "Thomas Henry Huxley", "Thomas Huxley", "Thought experiment", "Topology", "Trigonometry", "Tuple", "Uncountably", "Uniform distribution (discrete)", "University of Plymouth", "Wayback Machine", "Weasel program", "William Shakespeare", "Wired (magazine)", "Words per minute", "\u00c9mile Borel"], "references": ["http://www.angelfire.com/in/hypnosonic/Parable_of_the_Monkeys.html", "http://azureworld.blogspot.com/2007/04/planck-monkeys.html", "http://io9.gizmodo.com/5809583/the-story-of-the-monkey-shakespeare-simulator-project", "http://www.newyorker.com/arts/critics/books/2007/04/09/070409crbo_books_acocella?currentPage=all", "http://www.quotationspage.com/quote/27695.html", "http://skylla.wz-berlin.de/pdf/2002/ii02-101.pdf", "http://stat.fsu.edu/pub/diehard/cdrom/pscript/monkey.ps", "http://adsabs.harvard.edu/abs/2005Natur.435...20P", "http://www.vivaria.net/experiments/notes/documentation/press/", "http://www.vivaria.net/experiments/notes/publication/NOTES_EN.pdf", "http://doi.org/10.1016%2F0898-1221(93)90001-C", "http://doi.org/10.1038%2F435020a", "http://doi.org/10.1093%2Fbjaesthetics%2F15.1.14", "http://www.giffordlectures.org/Browse.asp?PubID=TPNOPW&Volume=0&Issue=0&ArticleID=6", "http://www.gutenberg.org/dirs/etext99/1ws2611.txt", "http://www.gutenberg.org/etext/14988", "http://i-dat.org", "http://i-dat.org/mike-phillips/", "http://tools.ietf.org/html/rfc2795", "http://mathforum.org/library/drmath/view/55871.html", "http://www.nutters.org/docs/more-monkeys", "http://www.pixelmonkeys.org/", "http://www.worldcat.org/issn/0898-1221", "http://arquivo.pt/wayback/20091016011846/http://www.nutters.org/docs/more-monkeys", "http://news.bbc.co.uk/2/hi/3013959.stm", "https://books.google.com/books?id=FctEAAAAYAAJ&printsec=frontcover&dq=The+Prose+Works+of+Jonathan+Swift&hl=en&ei=JdyDTb-yM8u3tweNmcy8BA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC4Q6AEwAA#v=onepage&q&f=false", "https://www.washingtonpost.com/ac2/wp-dyn/A28521-2002Oct27?language=printer", "https://www.wired.com/news/culture/0,1284,58790,00.html", "https://www.wired.com/science/discoveries/magazine/15-06/st_best", "https://web.archive.org/web/20040201230858/http://www.wired.com/news/culture/0,1284,58790,00.html", "https://web.archive.org/web/20080513012236/http://skylla.wz-berlin.de/pdf/2002/ii02-101.pdf", "https://web.archive.org/web/20090308150708/http://www.giffordlectures.org/Browse.asp?PubID=TPNOPW&Volume=0&Issue=0&ArticleID=6", "https://web.archive.org/web/20130120215600/http://www.vivaria.net/experiments/notes/publication/NOTES_EN.pdf"]}, "Doomsday argument": {"categories": ["1983 introductions", "All accuracy disputes", "All articles lacking reliable references", "All articles needing additional references", "All articles with style issues", "All articles with unsourced statements", "Articles lacking reliable references from August 2016", "Articles needing additional references from August 2016", "Articles that may contain original research from August 2016", "Articles with disputed statements from March 2009", "Articles with multiple maintenance issues", "Articles with unsourced statements from April 2018", "Articles with unsourced statements from June 2014", "Articles with unsourced statements from March 2013", "Articles with unsourced statements from May 2009", "CS1 errors: external links", "Doomsday scenarios", "Probabilistic arguments", "Wikipedia articles with style issues from November 2010"], "title": "Doomsday argument", "method": "Doomsday argument", "url": "https://en.wikipedia.org/wiki/Doomsday_argument", "summary": "The Doomsday argument (DA) is a probabilistic argument that claims to predict the number of future members of the human species given an estimate of the total number of humans born so far. Simply put, it says that supposing that all humans are born in a random order, chances are that any one human is born roughly in the middle.\nIt was first proposed in an explicit way by the astrophysicist Brandon Carter in 1983, from which it is sometimes called the Carter catastrophe; the argument was subsequently championed by the philosopher John A. Leslie and has since been independently discovered by J. Richard Gott and Holger Bech Nielsen. Similar principles of eschatology were proposed earlier by Heinz von Foerster, among others. A more general form was given earlier in the Lindy effect, in which for certain phenomena the future life expectancy is proportional to (though not necessarily equal to) the current age, and is based on decreasing mortality rate over time: old things endure.\nDenoting by N the total number of humans who were ever or will ever be born, the Copernican principle suggests that any one human is equally likely (along with the other N \u2212 1 humans) to find themselves at any position n of the total population N, so humans assume that our fractional position f = n/N is uniformly distributed on the interval [0, 1] prior to learning our absolute position.\nf is uniformly distributed on (0, 1) even after learning of the absolute position n. That is, for example, there is a 95% chance that f is in the interval (0.05, 1), that is f > 0.05. In other words, we could assume that we could be 95% certain that we would be within the last 95% of all the humans ever to be born. If we know our absolute position n, this implies an upper bound for N obtained by rearranging n/N > 0.05 to give N < 20n.\nIf Leslie's figure is used, then 60 billion humans have been born so far, so it can be estimated that there is a 95% chance that the total number of humans N will be less than 20 \u00d7 60 billion = 1.2 trillion. Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, it can be estimated that the remaining 1140 billion humans will be born in 9120 years. Depending on the projection of world population in the forthcoming centuries, estimates may vary, but the main point of the argument is that it is unlikely that more than 1.2 trillion humans will ever live on Earth. This problem is similar to the famous German tank problem.\nThe title \"Doomsday Argument\" is arguably a misnomer. Its popularity as a way of referring to this concept is perhaps based on the widespread belief that there are more people now alive than have ever lived, which would make the current generation of humans statistically likely to be the last one. According to the Population Reference Bureau, however, the number of biologically modern humans who have ever lived and died is closer to 107 billion, which is considerably more than the 7 billion alive today. That being the case, the argument actually implies it is unlikely that this is the last generation. Instead, it paints a relatively optimistic portrait of how long humanity is likely to last, even given current population growth. It is further worth noting that even if the argument is accepted at face value, it does not entail extinction\u2013humanity could conversely evolve into something distinctly enough different that people born after that point would no longer compose part of the same reference group. For both these reasons, the invocation of \"doomsday\" is misleading.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1b/Ambox_question.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b7/Population_curve.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["A posteriori", "A priori and a posteriori", "Accident", "Acta Physica Polonica", "Actuary", "Aleatory probability", "Amnesia chamber", "Andrey Korotayev", "Anthropic bias", "Anthropic principle", "Anthropology", "Atomic bombings of Hiroshima and Nagasaki", "Batsman", "Batting (cricket)", "Bayes' theorem", "Bayes's theorem", "Bayes factor", "Bayesian inference", "Bayesian probability", "Bertrand's paradox (probability)", "Bibcode", "Brandon Carter", "Bulletin of the Atomic Scientists", "Carlton M. Caves", "Conditional probability", "Conditioning (probability)", "Consciousness", "Continuous random variable", "Copernican principle", "Copernicus principle", "Correlation", "Cricket", "Cyborg", "Dan Brown", "Demographics", "Dennis Dieks", "Digital object identifier", "Doomsday Argument", "Doomsday argument", "Doomsday clock", "Doomsday event", "Early adopter", "Earth", "Empirical", "Epistemic probability", "Epistemology", "Eschatology", "Expected value", "Exponential distribution", "Extinct", "Extinction", "Extinction level event", "Extraterrestrial intelligence", "Fermi paradox", "Geological time", "German tank problem", "Global warming", "Heinz von Foerster", "Holger Bech Nielsen", "Human", "Human evolution", "Human extinction", "Human species", "Hypothesis", "Immortality", "Improper integral", "Improper prior", "Inferno (Dan Brown novel)", "Infinity", "Integral", "International Standard Book Number", "Interval (mathematics)", "J. Richard Gott", "Jean-Paul Delahaye", "Jeff Dewynne", "Jesus", "John A. Leslie", "Journal of Philosophy", "Life expectancy", "Lindy effect", "List of disasters", "Longevity", "Manifold: Time", "Mean", "Mediocrity principle", "Monotonic function", "Mortality rate", "Nature (journal)", "Nick Bostrom", "Normalizing constant", "Nuclear weapon", "Odds", "Paradox", "Parameter", "Peter Landsberg", "Philosopher", "Philosophical Transactions of the Royal Society of London", "Philosophy", "Philosophy of Science (journal)", "Population", "Posterior probability", "Predict", "Predictive power", "Principle of indifference", "Prior probability", "Probability density function", "Probability distribution", "Probability theory", "Quantum immortality", "Reference class problem", "Regression toward the mean", "Robin Hanson", "Royal Society", "Self-Indication Assumption", "Self-Indication Assumption Doomsday argument rebuttal", "Self-Sampling Assumption", "Self-referencing doomsday argument rebuttal", "Sic transit gloria mundi", "Simulated reality", "Species", "St. Petersburg paradox", "Statistical significance", "Stephen Baxter (author)", "Survival analysis", "Survivalism", "Sustainable development", "Technological singularity", "Test cricket", "Uniform", "Uniform distribution (continuous)", "Uninformative prior", "Variance", "World Population", "World population"], "references": ["http://anthropic-principle.com/preprints/self-location.html", "http://www.anthropic-principle.com/preprints.html#doomsday", "http://www.anthropic-principle.com/preprints/ali/alive.html", "http://adsabs.harvard.edu/abs/1983RSPTA.310..347C", "http://adsabs.harvard.edu/abs/1993Natur.363..315G", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.49.5899&rep=rep1&type=pdf", "http://images.math.cnrs.fr/L-Argument-de-l-Apocalypse-selon.html", "http://www.lifl.fr/~delahaye/pls/107.pdf", "http://xxx.lanl.gov/abs/gr-qc/0009081", "http://flatrock.org.nz/topics/environment/doom_soon.htm", "http://www.amstat.org/meetings/jsm/2014/onlineprogram/AbstractDetails.cfm?abstractid=313738", "http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=82931", "http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2400044", "http://cogprints.org/7044/", "http://doi.org/10.1038%2F363315a0", "http://doi.org/10.1086%2F599273", "http://doi.org/10.1098%2Frsta.1983.0096", "http://philpapers.org/browse/doomsday-argument", "http://pthbb.org/manual/services/grim/laster.html", "http://thebulletin.org/timeline", "http://urss.ru/cgi-bin/db.pl?cp=&page=Book&id=34250&lang=en&blang=en&list=38", "http://www.lrb.co.uk/v21/n13/gree04_.html", "https://www.bbc.com/news/magazine-16870579", "https://web.archive.org/web/20040217141525/http://hanson.gmu.edu/nodoom.html", "https://web.archive.org/web/20041205094143/http://info.phys.unm.edu/papers/2000/Caves2000a.pdf", "https://arxiv.org/abs/0806.3538v1", "https://arxiv.org/abs/gr-qc/9407002", "https://dx.doi.org/10.1093/mind/107.426.403"]}, "Simultaneous equations model": {"categories": ["Mathematical and quantitative methods (economics)", "Regression models", "Simultaneous equation methods (econometrics)"], "title": "Simultaneous equations model", "method": "Simultaneous equations model", "url": "https://en.wikipedia.org/wiki/Simultaneous_equations_model", "summary": "Simultaneous equation models are a type of statistical model in the form of a set of linear simultaneous equations. They are often used in econometrics. One can estimate these models equation by equation; however, estimation methods that exploit the system of equations, such as generalized method of moments (GMM) and instrumental variables estimation (IV) tend to be more efficient.", "images": [], "links": ["2SLS", "Annals of Mathematical Statistics", "Arnold Zellner", "Coefficient", "Demography", "Digital object identifier", "Econometrica", "Econometrics", "Economics", "Efficiency (statistics)", "Endogenous", "G. S. Maddala", "General linear model", "Generalized eigenvalue problem", "Generalized method of moments", "Gregory R. Hancock", "Henri Theil", "Identification condition", "Independent and identically distributed", "Instrumental variable", "Instrumental variables estimation", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Linear simultaneous equations", "Mark Thoma", "Ordinary least squares", "Parameter identification problem", "Political science", "Reduced form", "Robert Basmann", "Seemingly unrelated regressions", "Sociology", "Statistical model", "Two-stage least squares", "Wayne Fuller", "YouTube"], "references": ["http://economics.about.com/library/glossary/bldef-ils.htm", "http://orm.sagepub.com/content/2/1/69", "http://onlinelibrary.wiley.com/doi/10.1111/psj.12171/abstract", "http://doi.org/10.1016%2F0005-1098(87)90027-6", "http://doi.org/10.1093%2Fjeg%2Flbp031", "http://doi.org/10.1111%2Fpsj.12171", "http://doi.org/10.1177%2F109442819921005", "http://doi.org/10.1214%2Faoms%2F1177730090", "http://doi.org/10.2307%2F1907743", "http://doi.org/10.2307%2F1911287", "http://doi.org/10.2307%2F1912683", "http://doi.org/10.2307%2F1953990", "http://doi.org/10.2307%2F2095464", "http://doi.org/10.2307%2F2111666", "http://www.jstor.org/stable/1907743", "http://www.jstor.org/stable/1911287", "http://www.jstor.org/stable/2095464", "http://www.jstor.org/stable/2111666", "http://www.jstor.org/stable/2236803", "http://www.worldcat.org/issn/0003-0554", "http://www.worldcat.org/issn/1094-4281", "http://www.worldcat.org/issn/1468-2702", "http://www.worldcat.org/issn/1541-0072", "https://books.google.com/books?id=Bxq7AAAAIAAJ&pg=PA695", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA276", "https://academic.oup.com/joeg/article-lookup/doi/10.1093/jeg/lbp031", "https://www.youtube.com/watch?v=D5lt9bhOshc&list=PLD15D38DC7AA3B737&index=15", "https://www.cambridge.org/core/journals/american-political-science-review/article/reciprocal-effects-of-policy-preferences-party-loyalties-and-the-vote/D837D22D662FBFEB7779001CF52DB361", "https://www.jstor.org/stable/3314964"]}, "List of scientific journals in statistics": {"categories": ["Lists of academic journals", "Statistics-related lists", "Statistics journals"], "title": "List of statistics journals", "method": "List of scientific journals in statistics", "url": "https://en.wikipedia.org/wiki/List_of_statistics_journals", "summary": "This is a list of scientific journals published in the field of statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407084002%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407083328%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407082944%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20110430032449%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20090922000234%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041048%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041018%21Fisher_iris_versicolor_sepalwidth.svg"], "links": ["AStA Wirtschafts- und Sozialstatistisches Archiv", "American Review of Mathematics and Statistics", "Annals of Statistics", "Applied Econometrics and International Development", "Atmospheric Environment", "Australian & New Zealand Journal of Statistics", "Bayesian Analysis (journal)", "Behaviormetrika", "Biometrical Journal", "Biometrics (journal)", "Biometrika", "Biostatistics", "Biostatistics (journal)", "Brazilian Journal of Probability and Statistics", "British journal of mathematical and statistical psychology", "Chemometrics and Intelligent Laboratory Systems", "Chilean Journal of Statistics", "Communications in Biometry and Crop Science", "Communications in Statistics", "Comparison of statistics journals", "Computational Statistics", "Computational Statistics & Data Analysis", "Current Index to Statistics", "Delayed open access journal", "Econometric Reviews", "Econometric Theory", "Econometrica", "Environmental and Ecological Statistics", "Environmetrics", "Glossary of probability and statistics", "International Journal of Forecasting", "International Statistical Review", "Journal of Agricultural, Biological, and Environmental Statistics", "Journal of Applied Econometrics", "Journal of Applied Statistics", "Journal of Business & Economic Statistics", "Journal of Chemometrics", "Journal of Computational and Graphical Statistics", "Journal of Econometrics", "Journal of Economic and Social Measurement", "Journal of Educational and Behavioral Statistics", "Journal of Environmental Statistics", "Journal of Japanese Society of Computational Statistics", "Journal of Machine Learning Research", "Journal of Modern Applied Statistical Methods", "Journal of Multivariate Analysis", "Journal of Official Statistics", "Journal of Probability and Statistical Sciences", "Journal of Statistical Computation and Simulation", "Journal of Statistical Physics", "Journal of Statistical Planning and Inference", "Journal of Statistical Software", "Journal of Statistics Education", "Journal of Time Series Analysis", "Journal of the American Statistical Association", "Journal of the Japanese Statistical Association", "Journal of the Royal Statistical Society", "List of mathematics journals", "List of probability journals", "List of scientific journals", "List of statisticians", "List of statistics articles", "Lists of statistics topics", "Multivariate Behavioral Research", "Notation in probability and statistics", "Open access (publishing)", "Open access journal", "Outline of statistics", "Pharmaceutical Statistics", "Physica A", "Psychological Methods", "Psychometrika", "REVSTAT", "Revista Colombiana de Estadistica", "SORT (journal)", "Sankhya (journal)", "Scandinavian Journal of Statistics", "Scientific journal", "Significance (magazine)", "South African Statistical Journal", "Stat (Wiley)", "Stata", "Statistica Neerlandica", "Statistica Sinica", "Statistical Applications in Genetics and Molecular Biology", "Statistical Methods in Medical Research", "Statistical Modelling", "Statistical Science", "Statistics", "Statistics & Probability Letters", "Statistics Education Research Journal", "Statistics Surveys", "Statistics and Applications", "Statistics and Computing", "Statistics and Risk Modeling", "Statistics and its Interface", "Statistics in Biopharmaceutical Research", "Statistics in Medicine", "Statistics in Medicine (journal)", "Stochastic Environmental Research and Risk Assessment", "Stochastic Processes and their Applications", "Structural Equation Modeling (journal)", "Subscription business model", "Survey Methodology", "Teaching Statistics", "Technology Innovations in Statistics Education", "Technometrics", "The American Statistician", "The Annals of Applied Statistics", "The Canadian Journal of Statistics", "The International Journal of Biostatistics", "The R Journal", "The Review of Economics and Statistics", "Time-series analysis", "Turkiye Klinikleri Journal of Biostatistics"], "references": ["http://www.iospress.nl/html/07479662.php"]}, "Normal-inverse Gaussian distribution": {"categories": ["Continuous distributions"], "title": "Normal-inverse Gaussian distribution", "method": "Normal-inverse Gaussian distribution", "url": "https://en.wikipedia.org/wiki/Normal-inverse_Gaussian_distribution", "summary": "The normal-inverse Gaussian distribution (NIG) is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the inverse Gaussian distribution. The NIG distribution was noted by Blaesild in 1977 as a subclass of the generalised hyperbolic distribution discovered by Ole Barndorff-Nielsen. In the next year Barndorff-Nielsen published the NIG in another paper. It was introduced in the mathematical finance literature in 1997.The parameters of the normal-inverse Gaussian distribution are often used to construct a heaviness and skewness plot called the NIG-triangle.", "images": [], "links": ["ARGUS distribution", "Affine transformation", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bessel function", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Convolution of probability distributions", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized hyperbolic distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Infinitely divisible", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "L\u00e9vy processes", "Marchenko\u2013Pastur distribution", "Mathematical finance", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal distribution", "Normal variance-mean mixture", "Ole Barndorff-Nielsen", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wiener process", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://doi.org/10.1098%2Frspa.1977.0041", "http://www.jstor.org/stable/79167"]}, "General matrix notation of a VAR(p)": {"categories": ["All pages needing cleanup", "Articles containing how-to sections", "Articles needing cleanup from August 2013", "Multivariate time series"], "title": "General matrix notation of a VAR(p)", "method": "General matrix notation of a VAR(p)", "url": "https://en.wikipedia.org/wiki/General_matrix_notation_of_a_VAR(p)", "summary": "This page shows the details for different matrix notations of a vector autoregression process with k variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["Helmut L\u00fctkepohl", "International Standard Book Number", "Ordinary least squares", "Vector autoregression"], "references": []}, "Extended Kalman filter": {"categories": ["Articles with short description", "Nonlinear filters", "Robot control", "Signal estimation"], "title": "Extended Kalman filter", "method": "Extended Kalman filter", "url": "https://en.wikipedia.org/wiki/Extended_Kalman_filter", "summary": "In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about an estimate of the current mean and covariance. In the case of well defined transition models, the EKF has been considered the de facto standard in the theory of nonlinear state estimation, navigation systems and GPS.", "images": [], "links": ["Academic Press", "Consistency (statistics)", "Covariance", "Covariance matrix", "De facto", "Differentiable function", "Digital object identifier", "Ensemble Kalman filter", "Estimation theory", "Fast Kalman filter", "GPS", "Gaussian", "Implicit function", "International Standard Book Number", "International Standard Serial Number", "Invariant extended Kalman filter", "Jacobian matrix and determinant", "Kalman Filter", "Kalman filter", "Moment (mathematics)", "Monte Carlo methods", "Moving horizon estimation", "Multivariate normal distribution", "NASA Ames", "Navigation system", "Nonlinear", "Particle filter", "Particle filters", "Riccati equation", "State-space", "Symmetry-preserving filter", "Taylor Series", "Unscented transform"], "references": ["http://www.intechopen.com/books/smoothing-filtering-and-prediction-estimating-the-past-present-and-future", "http://correll.cs.colorado.edu/?p=1464", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.26.4070&rep=rep1&type=pdf", "http://www.eecs.tufts.edu/~khan/Courses/Spring2014/EE130/Lecs/KalmanBucy1961.pdf", "http://doi.org/10.1016%2Fs0262-8856(96)01112-2", "http://doi.org/10.1109%2F78.782219", "http://doi.org/10.1109%2FNSSPW.2006.4378854", "http://doi.org/10.1109%2Fjproc.2003.823141", "http://doi.org/10.1109%2Ftsp.2003.815376", "http://ieeexplore.ieee.org/document/4543252/?arnumber=4543252", "http://ieeexplore.ieee.org/iel5/78/16975/00782219.pdf?arnumber=782219", "http://ieeexplore.ieee.org/iel5/78/27482/01223541.pdf?arnumber=1223541", "http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1271397", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4378854", "http://www.worldcat.org/issn/0262-8856", "https://www.cs.unc.edu/~welch/kalman/media/pdf/Kalman1960.pdf", "https://archive.org/details/nasa_techdoc_19620006857"]}, "False discovery rate": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2012", "CS1 maint: Multiple names: authors list", "Multiple comparisons", "Statistical hypothesis testing", "Summary statistics for contingency tables"], "title": "False discovery rate", "method": "False discovery rate", "url": "https://en.wikipedia.org/wiki/False_discovery_rate", "summary": "The false discovery rate (FDR) is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. FDR-controlling procedures are designed to control the expected proportion of \"discoveries\" (rejected null hypotheses) that are false (incorrect rejections). FDR-controlling procedures provide less stringent control of Type I errors compared to familywise error rate (FWER) controlling procedures (such as the Bonferroni correction), which control the probability of at least one Type I error. Thus, FDR-controlling procedures have greater power, at the cost of increased numbers of Type I errors.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Adaptive", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Statistics", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", 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"Single-nucleotide polymorphism", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Type I and type II errors", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Yoav Benjamini", "Yosef Hochberg", "YouTube", "Z-test"], "references": ["http://adsabs.harvard.edu/abs/2003PNAS..100.9440S", "http://adsabs.harvard.edu/abs/2004math.....10072D", "http://adsabs.harvard.edu/abs/2005math......5374A", "http://adsabs.harvard.edu/abs/2006math......2311D", "http://adsabs.harvard.edu/abs/2009arXiv0905.2819B", "http://adsabs.harvard.edu/abs/2014RSOS....140216C", "http://genomics.princeton.edu/storeylab/papers/Storey_Annals_2003.pdf", "http://genomics.princeton.edu/storeylab/papers/directfdr.pdf", "http://www-stat.wharton.upenn.edu/~steele/Courses/956/Resource/MultipleComparision/Hochberg88.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC170937", "http://www.ncbi.nlm.nih.gov/pubmed/12883005", "http://www.ncbi.nlm.nih.gov/pubmed/21154895", "http://www.ncbi.nlm.nih.gov/pubmed/2218183", "http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_hochberg1995.pdf", "http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_yekutieli_ANNSTAT2001.pdf", "http://www.ams.org/mathscinet-getitem?mr=0538597", "http://www.ams.org/mathscinet-getitem?mr=1325392", "http://www.ams.org/mathscinet-getitem?mr=1869245", "http://arxiv.org/abs/0808.0603", "http://arxiv.org/abs/0903.5373", "http://arxiv.org/abs/0905.2819", "http://arxiv.org/abs/1407.5296", "http://arxiv.org/abs/math/0410072", "http://arxiv.org/abs/math/0505374", "http://arxiv.org/abs/math/0602311", "http://doi.org/10.1002%2Fbimj.200900299", "http://doi.org/10.1002%2Fsim.4780090710", "http://doi.org/10.1016%2FS0378-3758(99)00041-5", "http://doi.org/10.1073%2Fpnas.1530509100", "http://doi.org/10.1080%2F01621459.1989.10478811", "http://doi.org/10.1080%2F02664760500079373", "http://doi.org/10.1093%2Fbiomet%2F69.3.493", "http://doi.org/10.1093%2Fbiomet%2F73.3.751", "http://doi.org/10.1093%2Fbiomet%2F75.2.383", "http://doi.org/10.1093%2Fbiomet%2F75.4.800", "http://doi.org/10.1093%2Fbiomet%2F93.3.491", "http://doi.org/10.1098%2Frsos.140216", "http://doi.org/10.1098%2Frsos.171085", "http://doi.org/10.1111%2F1467-9868.00346", "http://doi.org/10.1111%2Fj.1467-9868.2004.00439.x", "http://doi.org/10.1111%2Fj.1467-9868.2010.00746.x", "http://doi.org/10.1111%2Fj.1467-9868.2012.01033.x", "http://doi.org/10.1198%2F016214504000001907", "http://doi.org/10.1214%2F009053604000000265", "http://doi.org/10.1214%2F009053606000000074", "http://doi.org/10.1214%2F009053606000000920", "http://doi.org/10.1214%2F07-AOS586", "http://doi.org/10.1214%2F07-STS236", "http://doi.org/10.1214%2F08-AOAS194", "http://doi.org/10.1214%2F08-EJS180", "http://doi.org/10.1214%2Faos%2F1013699998", "http://doi.org/10.1214%2Faos%2F1074290335", "http://www.jstor.org/stable/2289950", "http://www.jstor.org/stable/4615733", "http://www.pnas.org/content/100/16/9440.full.pdf", "http://rsos.royalsocietypublishing.org/content/4/12/171085#abstract-1", "http://strimmerlab.org/notes/fdr.html", "https://aeon.co/essays/it-s-time-for-science-to-abandon-the-term-statistically-significant", "https://eranraviv.com/understanding-false-discovery-rate/", "https://github.com/puolival/multipy", "https://www.youtube.com/watch?v=K8LQSvtjcEo", "https://archive.is/20120712123608/http://dx.doi.org/10.1146/annurev.ps.46.020195.003021"]}, "Theory of conjoint measurement": {"categories": ["All articles lacking in-text citations", "All articles with dead external links", "All articles with incomplete citations", "Articles lacking in-text citations from August 2011", "Articles with dead external links from June 2018", "Articles with incomplete citations from November 2012", "Articles with permanently dead external links", "Economic theories", "Latent variable models", "Mathematical psychology", "Psychometrics", "Statistical theory", "Wikipedia articles needing page number citations from July 2012"], "title": "Theory of conjoint measurement", "method": "Theory of conjoint measurement", "url": "https://en.wikipedia.org/wiki/Theory_of_conjoint_measurement", "summary": "The theory of conjoint measurement (also known as conjoint measurement or additive conjoint measurement) is a general, formal theory of continuous quantity. It was independently discovered by the French economist G\u00e9rard Debreu (1960) and by the American mathematical psychologist R. Duncan Luce and statistician John Tukey (Luce & Tukey 1964).\nThe theory concerns the situation where at least two natural attributes, A and X, non-interactively relate to a third attribute, P. It is not required that A, X or P are known to be quantities. Via specific relations between the levels of P, it can be established that P, A and X are continuous quantities. Hence the theory of conjoint measurement can be used to quantify attributes in empirical circumstances where it is not possible to combine the levels of the attributes using a side-by-side operation or concatenation. The quantification of psychological attributes such as attitudes, cognitive abilities and utility is therefore logically plausible. This means that the scientific measurement of psychological attributes is possible. That is, like physical quantities, a magnitude of a psychological quantity may possibly be expressed as the product of a real number and a unit magnitude.\nApplication of the theory of conjoint measurement in psychology, however, has been limited. It has been argued that this is due to the high level of formal mathematics involved (e.g., Cliff 1992) and that the theory cannot account for the \"noisy\" data typically discovered in psychological research (e.g., Perline, Wright & Wainer 1979). It has been argued that the Rasch model is a stochastic variant of the theory of conjoint measurement (e.g., Brogden 1977; Embretson & Reise 2000; Fischer 1995; Keats 1967; Kline 1998; Scheiblechner 1999), however, this has been disputed (e.g., Karabatsos, 2001; Kyngdon, 2008). Order restricted methods for conducting probabilistic tests of the cancellation axioms of conjoint measurement have been developed in the past decade (e.g., Karabatsos, 2001; Davis-Stober, 2009).\nThe theory of conjoint measurement is (different but) related to conjoint analysis, which is a statistical-experiments methodology employed in marketing to estimate the parameters of additive utility functions. Different multi-attribute stimuli are presented to respondents, and different methods are used to measure their preferences about the presented stimuli. The coefficients of the utility function are estimated using alternative regression-based tools.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Wikipage_double_cancellation.JPG", "https://upload.wikimedia.org/wikipedia/commons/5/55/Wikipage_single_cancellation.JPG", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Wikipage_triple_cancellation.JPG"], "links": ["Allais Paradox", "Amos Tversky", "Anders Celsius", "Archimedean axiom", "Archimedes", "Axioms", "Bayesian inference", "Bibcode", "British Association for the Advancement of Science", "Concatenation (mathematics)", "Conjoint Commutativity", "Conjoint analysis (marketing)", "Dana Scott", "Daniel Kahneman", "Digital object identifier", "Euclid", "Euclid's Elements", "G\u00e9rard Debreu", "Integers", "Interval scale", "Item response theory", "Jean-Claude Falmagne", "John Tukey", "L.L. Thurstone", "Lexile", "Marketing", "Markov chain Monte Carlo", "Mathematical psychology", "Metrology", "Nobel Memorial Prize in Economics", "Norman Robert Campbell", "Otto H\u00f6lder", "Patrick Suppes", "Physics", "Polynomial conjoint measurement", "Prospect theory", "Psychometric", "Psychophysics", "PubMed Identifier", "Quantity", "R. Duncan Luce", "Rasch model", "Real number", "Stanley Smith Stevens", "Thomsen Condition", "Topological"], "references": ["http://www.sciencedirect.com/science/article/pii/0022249664900033", "http://www.sciencedirect.com/science/article/pii/002224966490015X", "http://www.sciencedirect.com/science/article/pii/0022249664900021", "http://www.sciencedirect.com/science/article/pii/0022249677900359", "http://www.sciencedirect.com/science/article/pii/0022249688900247", "http://www.sciencedirect.com/science/article/pii/S0022249608000758", "http://www.sciencedirect.com/science/article/pii/S0022249684710169", "http://www.sciencedirect.com/science/article/pii/S0022249696900231", "http://onlinelibrary.wiley.com/doi/10.1080/00049539408259468/abstract", "http://onlinelibrary.wiley.com/doi/10.1111/j.2044-8317.1972.tb00477.x/abstract", "http://onlinelibrary.wiley.com/doi/10.1348/000711007X243582/abstract", "http://psych.fullerton.edu/mbirnbaum/programs.htm", "http://adsabs.harvard.edu/abs/1946Sci...103..677S", "http://adsabs.harvard.edu/abs/2008Metro..45..134E", "http://www.imbs.uci.edu/files/personnel/luce/2005/SteingrimssonLuce_JMP_2005a.pdf", "http://www.imbs.uci.edu/files/personnel/luce/2011/Luce-Steingrimsson_JMP-2011.pdf", "http://tigger.uic.edu/~georgek/HomePage/KarabatsosJMP.pdf", "http://tigger.uic.edu/~georgek/HomePage/publications.htm", "http://deepblue.lib.umich.edu/bitstream/2027.42/33362/1/0000760.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/12011506", "http://www.ncbi.nlm.nih.gov/pubmed/16807496", "http://www.ncbi.nlm.nih.gov/pubmed/17068378", "http://www.ncbi.nlm.nih.gov/pubmed/17215563", "http://www.ncbi.nlm.nih.gov/pubmed/17750512", "http://www.ncbi.nlm.nih.gov/pubmed/18426300", "http://www.ncbi.nlm.nih.gov/pubmed/18753694", "http://www.ncbi.nlm.nih.gov/pubmed/21973097", "http://www.ncbi.nlm.nih.gov/pubmed/5031649", "http://www.ncbi.nlm.nih.gov/pubmed/5333423", "http://www.ncbi.nlm.nih.gov/pubmed/8979975", "http://doi.org/10.1006%2Fjmps.1993.1037", "http://doi.org/10.1006%2Fjmps.1994.1016", "http://doi.org/10.1006%2Fjmps.1996.0023", "http://doi.org/10.1007%2FBF02294219", "http://doi.org/10.1007%2FBF02294273", "http://doi.org/10.1007%2FBF02294297", "http://doi.org/10.1007%2FBF02295985", "http://doi.org/10.1016%2F0022-2496(64)90002-1", "http://doi.org/10.1016%2F0022-2496(64)90003-3", "http://doi.org/10.1016%2F0022-2496(64)90015-X", "http://doi.org/10.1016%2F0022-2496(67)90039-9", "http://doi.org/10.1016%2F0022-2496(76)90036-5", "http://doi.org/10.1016%2F0022-2496(77)90035-9", "http://doi.org/10.1016%2F0022-2496(88)90024-7", "http://doi.org/10.1016%2F0165-4896(85)90031-9", "http://doi.org/10.1016%2F1041-6080(93)90009-H", "http://doi.org/10.1016%2FS0165-4896(02)00024-0", "http://doi.org/10.1016%2Fj.jmp.2004.11.001", "http://doi.org/10.1016%2Fj.jmp.2005.03.003", "http://doi.org/10.1016%2Fj.jmp.2008.08.003", "http://doi.org/10.1016%2Fj.jmp.2011.05.004", "http://doi.org/10.1037%2F0033-295X.115.2.463", "http://doi.org/10.1037%2F0096-1523.9.1.126", "http://doi.org/10.1037%2Fh0030637", "http://doi.org/10.1037%2Fh0070288", "http://doi.org/10.1080%2F00049530108255118", "http://doi.org/10.1080%2F00049539408259468", "http://doi.org/10.1088%2F0026-1394%2F45%2F2%2F002", "http://doi.org/10.1111%2Fj.1467-9280.1992.tb00024.x", "http://doi.org/10.1111%2Fj.2044-8317.1972.tb00477.x", "http://doi.org/10.1126%2Fscience.103.2684.677", "http://doi.org/10.1146%2Fannurev.ps.18.020167.001245", "http://doi.org/10.1177%2F0146621603260678", "http://doi.org/10.1177%2F014662167900300213", "http://doi.org/10.1177%2F0959354307086924", "http://doi.org/10.1348%2F000711007X243582", "http://doi.org/10.1348%2F2044-8317.002004", "http://doi.org/10.2307%2F1914185", "http://www.r-project.org/", "https://link.springer.com/article/10.1007/BF02294219", "https://link.springer.com/article/10.1007/BF02294273", "https://link.springer.com/article/10.1007/BF02294297", "https://link.springer.com/article/10.1007/BF02295985", "https://web.archive.org/web/20130708083656/https://sites.google.com/site/drandrewkyngdon/home"]}, "Mann\u2013Whitney U test": {"categories": ["All articles with incomplete citations", "All articles with unsourced statements", "Articles with incomplete citations from November 2012", "Articles with unsourced statements from February 2012", "Articles with unsourced statements from November 2009", "Articles with unsourced statements from September 2009", "CS1 maint: Uses authors parameter", "Nonparametric statistics", "Statistical tests", "U-statistics", "Wikipedia articles needing clarification from September 2009"], "title": "Mann\u2013Whitney U test", "method": "Mann\u2013Whitney U test", "url": "https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test", "summary": "In statistics, the Mann\u2013Whitney U test (also called the Mann\u2013Whitney\u2013Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon\u2013Mann\u2013Whitney test) is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample.\nUnlike the t-test it does not require the assumption of normal distributions. It is nearly as efficient as the t-test on normal distributions.\nThis test can be used to determine whether two independent samples were selected from populations having the same distribution; a similar nonparametric test used on dependent samples is the Wilcoxon signed-rank test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Aesop", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Mathematical Statistics", "Apache Commons", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", 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dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrimination learning", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frank 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"http://commons.apache.org/proper/commons-math/javadocs/api-3.3/org/apache/commons/math3/stat/inference/MannWhitneyUTest.html", "http://doi.org/10.1002%2Fejsp.2420020412", "http://doi.org/10.1006%2Fanbe.2001.1691", "http://doi.org/10.1007%2F978-1-4419-0468-3", "http://doi.org/10.1007%2FBF02289138", "http://doi.org/10.1023%2FA:1010920819831", "http://doi.org/10.1037%2F0003-066X.54.8.594", "http://doi.org/10.1037%2F0022-006X.62.2.281", "http://doi.org/10.1037%2F0033-2909.111.2.361", "http://doi.org/10.1037%2F0097-7403.2.4.285", "http://doi.org/10.1080%2F00031305.2000.10474513", "http://doi.org/10.1111%2Fj.1469-185X.2007.00027.x", "http://doi.org/10.1148%2Fradiology.143.1.7063747", "http://doi.org/10.1214%2F09-SS051", "http://doi.org/10.1214%2Faoms%2F1177704172", "http://doi.org/10.1214%2Faoms%2F1177730491", "http://doi.org/10.1256%2F003590002320603584", "http://doi.org/10.2307%2F2280906", "http://doi.org/10.2307%2F2527532", "http://doi.org/10.2307%2F2683975", "http://doi.org/10.2307%2F3001968", "http://www.jstor.org/stable/2238406", "http://www.jstor.org/stable/2280906", "http://www.jstor.org/stable/2527532", "http://www.jstor.org/stable/2683975", "http://www.jstor.org/stable/2685616", "http://www.jstor.org/stable/3001968", "http://projecteuclid.org/euclid.aoms/1177704172", "http://projecteuclid.org/euclid.jdg/euclid.aoms/1177704172", "http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html", "http://zbmath.org/?format=complete&q=an:0041.26103", "http://zbmath.org/?format=complete&q=an:0119.15604", "http://zbmath.org/?format=complete&q=an:0203.21105", "http://www.mathworks.co.uk/help/stats/ranksum.html", "https://www.stata.com/help.cgi?ranksum", "https://doi.org/10.2466%2F11.IT.3.1", "https://www.gnu.org/software/pspp/manual/html_node/WILCOXON.html", "https://www.jstor.org/stable/2283092", "https://onlinepubs.trb.org/onlinepubs/nchrp/cd-22/manual/v2chapter6.pdf"]}, "Van der Waerden test": {"categories": ["Nonparametric statistics", "Statistical tests", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Van der Waerden test", "method": "Van der Waerden test", "url": "https://en.wikipedia.org/wiki/Van_der_Waerden_test", "summary": "Named after the Dutch mathematician Bartel Leendert van der Waerden, the Van der Waerden test is a statistical test that k population distribution functions are equal. The Van der Waerden test converts the ranks from a standard Kruskal-Wallis one-way analysis of variance to quantiles of the standard normal distribution (details given below). These are called normal scores and the test is computed from these normal scores.\nThe k population version of the test is an extension of the test for two populations published by Van der Waerden (1952,1953).", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["Analysis of Variance", "Bartel Leendert van der Waerden", "Chi-squared distribution", "Copyright status of work by the U.S. government", "Data analysis", "Independent variables", "Kruskal-Wallis one-way analysis of variance", "Multiple comparisons", "National Institute of Standards and Technology", "Non-parametric test", "Normal distribution", "Quantile", "Quantile function", "Significance level", "Statistical test", "Student's t-distribution", "Two sample t-test"], "references": ["http://www.nist.gov"]}, "Pharmaceutical statistics": {"categories": ["All pages needing cleanup", "Applied statistics", "Articles needing cleanup from September 2014", "Articles with sections that need to be turned into prose from September 2014", "Biostatistics", "Medical specialties", "Medical statistics", "Pharmaceutical statistics"], "title": "Medical statistics", "method": "Pharmaceutical statistics", "url": "https://en.wikipedia.org/wiki/Medical_statistics", "summary": "Medical statistics deals with applications of statistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research. Medical statistics has been a recognized branch of statistics in the United Kingdom for more than 40 years but the term has not come into general use in North America, where the wider term 'biostatistics' is more commonly used. However, \"biostatistics\" more commonly connotes all applications of statistics to biology. Medical statistics is a subdiscipline of statistics. \"It is the science of summarizing, collecting, presenting and interpreting data in medical practice, and using them to estimate the magnitude of associations and test hypotheses. It has a central role in medical investigations. It not only provides a way of organizing information on a wider and more formal basis than relying on the exchange of anecdotes and personal experience, but also takes into account the intrinsic variation inherent in most biological processes.\"", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute risk reduction", "Accelerated failure time model", "Actuarial science", "Age-standardized mortality rate", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biology", "Biostatistics", "Biplot", "Birth weight", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Cancer cluster", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical research", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Control event rate", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative incidence", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Doug Altman", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Endemic (epidemiology)", "Engineering statistics", "Environmental statistics", "Epidemic", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental event rate", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "False negative", "False positive", "False positives and false negatives", "Fan chart (statistics)", "First-hitting-time model", "Force of infection", "Forensic medicine", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Health science", "Herd immunity", "Heteroscedasticity", "Hilda Mary Woods", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Incidence (epidemiology)", "Incubation period", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maternal mortality rate", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medicine", "Method of moments (statistics)", "Methods engineering", "Minimal clinically important difference", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Mortality rate", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Pandemic", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perinatal mortality rate", "Permutation test", "Peter Armitage", "Pharmaceutical Statistics", "Pharmaceutical industry", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Prevalence", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Proportional hazards models", "Psychometrics", "Public health", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rare disease", "Regression analysis", "Regression model validation", "Relative risk", "Relative risk reduction", "Relative survival", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Serial interval", "Sexual network", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standardized mortality ratio", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statisticians In The Pharmaceutical Industry", "Statistics", "Statistics in Medicine", "Statistics in Medicine (journal)", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Syndemic", "System identification", "Time domain", "Time series", "Tolerance interval", "Transmission risks and rates", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Years of potential life lost", "Z-test"], "references": ["http://www.Learn-Medical-Statistics.com", "http://ec.europa.eu/health-eu/health_in_the_eu/statistics/index_en.htm", "http://doi.org/10.1001%2Fjama.1963.03060120024016", "https://books.google.com/books?hl=en"]}, "Squared deviations": {"categories": ["All articles needing expert attention", "Analysis of variance", "Articles needing expert attention", "Articles needing expert attention with no reason or talk parameter", "Articles needing unspecified expert attention", "Statistical deviation and dispersion"], "title": "Squared deviations from the mean", "method": "Squared deviations", "url": "https://en.wikipedia.org/wiki/Squared_deviations_from_the_mean", "summary": "Squared deviations from the mean (SDM) are involved in various calculations. In probability theory and statistics, the definition of variance is either the expected value of the SDM (when considering a theoretical distribution) or its average value (for actual experimental data). Computations for analysis of variance involve the partitioning of a sum of SDM.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["Absolute deviation", "Algorithms for calculating variance", "Analysis of variance", "Degrees of freedom (statistics)", "Errors and residuals", "Expected value", "Explained sum of squares", "Least squares", "Mean squared error", "Partition of sums of squares", "Probability distribution", "Probability theory", "Random variable", "Residual sum of squares", "Sample variance", "Statistics", "Total sum of squares", "Two-way analysis of variance", "Variance", "Variance decomposition"], "references": []}, "Outline of probability": {"categories": ["Mathematics-related lists", "Probability", "Statistics-related lists", "Wikipedia outlines"], "title": "Outline of probability", "method": "Outline of probability", "url": "https://en.wikipedia.org/wiki/Outline_of_probability", "summary": "Probability is a measure of the likeliness that an event will occur. Probability is used to quantify an attitude of mind towards some proposition of whose truth we are not certain. The proposition of interest is usually of the form \"A specific event will occur.\" The attitude of mind is of the form \"How certain are we that the event will occur?\" The certainty we adopt can be described in terms of a numerical measure and this number, between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty), we call probability. Probability theory is used extensively in statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.", "images": [], "links": ["Almost sure convergence", "Almost surely", "Autocorrelation", "Autoregressive process", "Axioms of probability", "Azuma's inequality", "Bayes' theorem", "Bayesian probability", "Benford's law", "Bernoulli distribution", "Berry\u2013Esseen theorem", "Beta distribution", "Binomial distribution", "Boole's inequality", "Borel's paradox", "Borel\u2013Cantelli lemma", "Branching process", "Brownian bridge", "Brownian motion", "Cantor distribution", "Catalog of articles in probability theory", "Cauchy distribution", "Central limit theorem", "Characteristic function (probability theory)", "Chebyshev's inequality", "Chi-squared distribution", "Complementary event", "Compound Poisson process", "Concrete illustration of the central limit theorem", "Conditional distribution", "Conditional event algebra", "Conditional expectation", "Conditional independence", "Conditional probability", "Conditional probability distribution", "Conditioning (probability)", "Constant random variable", "Continuous random variable", "Convergence in distribution", "Convergence in probability", "Convergence of random variables", "Correlation", "Correlation function", "Covariance", "Cumulative distribution function", "Degenerate distribution", "Diffusion", "Discrete random variable", "Disintegration theorem", "Dominated convergence theorem", "Dynkin system", "Elementary event", "Erlang distribution", "Event (probability theory)", "Examples of Markov chains", "Expected value", "Exponential distribution", "F-distribution", "Fatou's lemma", "Fisher\u2013Tippett distribution", "Fractional Brownian motion", "Frequency probability", "Functions of random variables", "Galton\u2013Watson process", "Gamma distribution", "Gamma process", "Geometric Brownian motion", "Geometric distribution", "Glossary of probability and statistics", "Goodman\u2013Nguyen\u2013van Fraassen algebra", "Hypergeometric distribution", "Illustration of the central limit theorem", "Independence (probability theory)", "Integral transform", "Jensen's inequality", "Joint distribution", "Kolmogorov's zero\u2013one law", "Laplace transform", "Laplace\u2013Stieltjes transform", "Law of large numbers", "Law of the iterated logarithm", "Law of total expectation", "Law of total probability", "Law of total variance", "List of mathematical probabilists", "List of probability distributions", "List of probability topics", "List of scientific journals in probability", "Marginal distribution", "Markov's inequality", "Markov chain", "Markov property", "Martingale (probability theory)", "Martingale central limit theorem", "Mathematics", "Mean", "Measure theory", "Modes of convergence (annotated index)", "Moment-generating function", "Moment about the mean", "Monotone convergence theorem", "Moving average model", "Multivariate normal distribution", "Mutually exclusive", "Negative binomial distribution", "Normal distribution", "Normalizing constant", "Notation in probability and statistics", "Ornstein\u2013Uhlenbeck process", "Pareto distribution", "Philosophy", "Poisson distribution", "Poisson process", "Population process", "Probability", "Probability-generating function", "Probability axioms", "Probability density function", "Probability interpretations", "Probability mass function", "Probability measure", "Probability space", "Probability theory", "Queueing theory", "Random compact set", "Random element", "Random sums of random variables", "Random variable", "Random walk", "Randomness", "Regular conditional probability", "Rule of succession", "Sample space", "Science", "Set theory", "Sigma-algebra", "Simple theorems in the algebra of sets", "Skorokhod's representation theorem", "Standard probability space", "Statistical independence", "Statistics", "Stochastic calculus", "Stochastic process", "Student's t-distribution", "Sums of random variables", "Time series", "Timeline of probability and statistics", "Topic outline of statistics", "Uncorrelated", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Variance", "Venn diagram", "Wiener equation", "Wiener process"], "references": []}, "Random variable": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from February 2012", "Articles with unsourced statements from October 2018", "Statistical randomness"], "title": "Random variable", "method": "Random variable", "url": "https://en.wikipedia.org/wiki/Random_variable", "summary": "In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon. More specifically, a random variable is defined as a function that maps the outcomes of unpredictable processes to numerical quantities (labels), typically real numbers. In this sense, it is a procedure for assigning a numerical quantity to each physical outcome. Contrary to its name, this procedure itself is neither random nor variable. Rather, the underlying process providing the input to this procedure yields random (possibly non-numerical) output that the procedure maps to a real-numbered value.\nA random variable's possible values might represent the possible outcomes of a yet-to-be-performed experiment, or the possible outcomes of a past experiment whose already-existing value is uncertain (for example, due to imprecise measurements or quantum uncertainty). They may also conceptually represent either the results of an \"objectively\" random process (such as rolling a die) or the \"subjective\" randomness that results from incomplete knowledge of a quantity. The meaning of the probabilities assigned to the potential values of a random variable is not part of probability theory itself but is instead related to philosophical arguments over the interpretation of probability. The mathematics works the same regardless of the particular interpretation in use.\nAs a function, a random variable is required to be measurable, which rules out certain pathological cases where the quantity which the random variable returns is infinitely sensitive to small changes in the outcome. In this respect, it is common that the outcomes depend on some physical variables that are not well understood. For example, when tossing a fair coin, the final outcome of heads or tails depends on the uncertain physics. Which outcome will be observed is not certain. The coin could get caught in a crack in the floor, but such a possibility is excluded from consideration. \nThe domain of a random variable is the set of possible outcomes. In the case of the coin, there are only two possible outcomes, namely heads or tails. Since one of these outcomes must occur, either the event that the coin lands heads or the event that the coin lands tails must have non-zero probability.\nA random variable has a probability distribution, which specifies the probability of its values. Random variables can be discrete, that is, taking any of a specified finite or countable list of values, endowed with a probability mass function characteristic of the random variable's probability distribution; or continuous, taking any numerical value in an interval or collection of intervals, via a probability density function that is characteristic of the random variable's probability distribution; or a mixture of both types. \nTwo random variables with the same probability distribution can still differ in terms of their associations with, or independence from, other random variables. The realizations of a random variable, that is, the results of randomly choosing values according to the variable's probability distribution function, are called random variates.\nThe formal mathematical treatment of random variables is a topic in probability theory. In that context, a random variable is understood as a function defined on a sample space whose outcomes are numerical values.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/12/Dice_Distribution_%28bar%29.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolutely continuous", "Absolutely continuous measure", "Absolutely continuous random variable", "Accelerated failure time model", "Actuarial science", "Adjacency matrix", "Akademie Verlag", "Akaike information criterion", "Aleatoricism", "Algebra of random variables", "Almost never", "Almost surely", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arbitrarily small", "Arithmetic mean", "Asymptotic theory (statistics)", "Athanasios Papoulis", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Axiomatic", "Banach\u2013Tarski paradox", "Bar chart", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Boole's inequality", "Boolean-valued function", "Bootstrapping (statistics)", "Borel \u03c3-algebra", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Clopen set", "Closed interval", "Closure (mathematics)", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Complementary event", "Completeness (statistics)", "Computer science", "Conditional independence", "Conditional probability", "Confidence interval", "Confounding", "Contingency table", "Continuous function", "Continuous probability distribution", "Continuous random variable", "Continuous uniform distribution", "Control chart", "Convergence of random variables", "Correlation and dependence", "Correlogram", "Count data", "Countably infinite", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Data structure", "Data type", "Decomposition of time series", "Degree of freedom (statistics)", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Differentiability", "Discontinuity (mathematics)", "Discrete mathematics", "Discrete random variable", "Divergence (statistics)", "Domain of a function", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Element (mathematics)", "Elementary event", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Equality (mathematics)", "Errors and residuals in statistics", "Essential supremum", "Estimating equations", "Event (probability theory)", "Expected value", "Experiment", "Experiment (probability theory)", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fair coin", "Fair die", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Function (mathematics)", "Function composition", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graph theory", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Image (mathematics)", "Independence (probability theory)", "Independent and identically distributed random variables", "Index of dispersion", "Indicator function", "Interaction (statistics)", "International Standard Book Number", "Interpretation of probability", "Interquartile range", "Intersection (set theory)", "Interval (mathematics)", "Interval estimation", "Inverse function", "Inverse function theorem", "Isotonic regression", "Iverson bracket", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Joint distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laplace transform", "Law of large numbers", "Law of total probability", "Lebesgue's decomposition theorem", "Lebesgue measurable", "Lebesgue measure", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Machine learning", "Manifold", "Mann\u2013Whitney U test", "Marginal distribution", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McGraw\u2013Hill", "McNemar's test", "Mean", "Measurable function", "Measurable space", "Measure space", "Measure theory", "Measure zero", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Moment generating function", "Monotone likelihood ratio", "Monotonic", "Monotonic function", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate random variable", "Multivariate statistics", "Mutual information", "National accounts", "Natural experiment", "Natural language processing", "Nelson\u2013Aalen estimator", "Nominal data", "Noncentral chi-squared distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null set", "OCLC", "Observable variable", "Observational study", "Official statistics", "Olav Kallenberg", "One- and two-tailed tests", "Open interval", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outcome (probability)", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pathological (mathematics)", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Piecewise constant", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Preimage", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability and statistics", "Probability axioms", "Probability density function", "Probability distribution", "Probability mass function", "Probability measure", "Probability space", "Probability theory", "Problem of moments", "Proportional hazards model", "Proportionality (mathematics)", "Psychometrics", "Quality control", "Quantile function", "Quantum uncertainty", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random compact set", "Random element", "Random field", "Random function", "Random graph", "Random matrix", "Random measure", "Random number generation", "Random number generator", "Random sequence", "Random variate", "Random vector", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Randomness", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real-valued", "Real number", "Real numbers", "Regression analysis", "Regression model validation", "Relationships among probability distributions", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sample space", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequence", "Set (mathematics)", "Shape", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sigma-algebra", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Springer Verlag", "Standard deviation", "Standard error", "Standard normal distribution", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic process", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Subsets", "Sufficient statistic", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Topological space", "Tree (graph theory)", "Tree diagram (probability theory)", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Union (set theory)", "Unit interval", "V-statistic", "Variance", "Vector autoregression", "Venn diagram", "W. H. Freeman and Company", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "\u03a3-algebra"], "references": ["http://www.mhhe.com/engcs/electrical/papoulis/", "http://bcs.whfreeman.com/yates2e/", "http://econ.ucsb.edu/~doug/245a/Lectures/Measure%20Theory.pdf", "http://www.ee.cityu.edu.hk/~zukerman/classnotes.pdf", "http://www.ee.cityu.edu.hk/~zukerman/probability.pdf", "http://www.ams.org/mathscinet-getitem?mr=0854102", "http://www.worldcat.org/oclc/51441829", "https://books.google.com/books/about/A_Modern_Approach_to_Probability_Theory.html?id=5D5O8xyM-kMC", "https://books.google.com/books/about/Foundations_of_Modern_Probability.html?hl=de&id=L6fhXh13OyMC", "https://books.google.com/books/about/Random_measures.html?id=bBnvAAAAMAAJ", "https://books.google.com/books?id=zxXRn-Qmtk8C&pg=PA67", "https://web.archive.org/web/20050209001108/http://bcs.whfreeman.com/yates2e/", "https://www.encyclopediaofmath.org/index.php?title=p/r077360", "https://www.worldcat.org/oclc/51441829"]}, "Cluster sampling": {"categories": ["Market research", "Sampling techniques"], "title": "Cluster sampling", "method": "Cluster sampling", "url": "https://en.wikipedia.org/wiki/Cluster_sampling", "summary": "Cluster sampling is a sampling plan used when mutually homogeneous yet internally heterogeneous groupings are evident in a statistical population. It is often used in marketing research. In this sampling plan, the total population is divided into these groups (known as clusters) and a simple random sample of the groups is selected. The elements in each cluster are then sampled. If all elements in each sampled cluster are sampled, then this is referred to as a \"one-stage\" cluster sampling plan. If a simple random subsample of elements is selected within each of these groups, this is referred to as a \"two-stage\" cluster sampling plan. A common motivation for cluster sampling is to reduce the total number of interviews and costs given the desired accuracy. For a fixed sample size, the expected random error is smaller when most of the variation in the population is present internally within the groups, and not between the groups.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9a/ClusterSampling.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Area sampling", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Famine", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geographical cluster sampling", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marketing research", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multistage sampling", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural disaster", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational error", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling error", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simple random sample", "Simple random sampling", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "War", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.bmj.com/cgi/content/full/316/7142/1455", "http://www.ij-healthgeographics.com/content/11/1/12", "http://ocw.jhsph.edu/courses/statmethodsforsamplesurveys/PDFs/Lecture5.pdf", "https://books.google.com/?id=waHxMgEACAAJ", "https://www.washingtonpost.com/wp-dyn/content/article/2006/10/10/AR2006101001442.html"]}, "Econometric software": {"categories": ["CS1 maint: Archived copy as title", "CS1 maint: BOT: original-url status unknown", "Comparisons of mathematical software", "Mathematical and quantitative methods (economics)", "Statistical software", "Statistics-related lists"], "title": "Comparison of statistical packages", "method": "Econometric software", "url": "https://en.wikipedia.org/wiki/Comparison_of_statistical_packages", "summary": "The following tables compare general and technical information for a number of statistical analysis packages.\n\n", "images": [], "links": ["ADMB", "ADaMSoft", "ANOVA", "ARIMA", "ASReml", "Affero General Public License", "Analyse-it", "BMDP", "BSD license", "BV4.1 (software)", "Bar chart", "Berkeley Software Distribution", "Box plot", "C++", "CSPro", "C (programming language)", "C Sharp (programming language)", "Charts", "Cointegration test", "Command-line interface", "Command line interface", "Commercial software", "Comparison of computer algebra systems", "Comparison of deep learning software", "Comparison of numerical analysis software", "Comparison of survey software", "Correlogram", "Cox regression", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "Diagrams", "Digital object identifier", "ELKI", "EViews", "Enthought", "Epi Info", "Fortran", "Freeware", "GARCH", "GAUSS (software)", "GNU GPL", "GNU General Public License", "GNU Octave", "GNU Project", "GenStat", "General linear model", "Generalized linear models", "GraphPad InStat", "GraphPad Prism", "Graphical user interface", "Gretl", "H2O (software)", "Histogram", "IBM", "International Standard Book Number", "JASP", "JMP (statistical software)", "JMulTi", "JSTOR", "Java (programming language)", "Java SDK", "Journal of Applied Econometrics", "Journal of Economic Literature", "Julia (programming language)", "Just another Gibbs sampler", "LGPL", "LIMDEP", "LISREL", "Latin squares", "Least absolute deviation", "Line chart", "Linux", "List of scientific journals in statistics", "List of statistical packages", "Logistic regression", "Ludwig Maximilian University of Munich", "MANOVA", "MATLAB", "MLwiN", "Mac OS", "Maple (software)", "Mathcad", "Mathematica", "MaxStat", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Mixed model", "Multiple linear regression", "Multivariate GARCH", "NCSS (statistical software)", "NCSS Statistical Software", "NLOGIT", "NMath Stats", "Nonlinear least squares", "NumPy", "NumXL", "Open-source software", "OpenBUGS", "OpenEpi", "Open source", "Orange (software)", "Ordinary least squares", "Origin (data analysis software)", "OxMetrics", "Ox programming language", "PSPP", "PSPP-Perl", "Pearson Education", "Perl", "Poisson regression", "Post-hoc analysis", "Primer-E Primer", "Probit model", "Proprietary software", "Public-domain software", "Public domain", "Python (programming language)", "Python SDK", "Quantile regression", "RATS (software)", "RATS (statistical package)", "RExcel", "RKWard", "ROOT", "RPy", "RStudio", "R (programming language)", "R Commander", "R programming language", "Regression analysis", "Revolution Analytics", "S-PLUS", "SAS (software)", "SAS Institute", "SAS System", "SAS language", "SHAZAM (software)", "SOCR", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SPlus", "SQL", "SUDAAN", "SYSTAT (software)", "SYSTAT (statistics)", "SageMath", "Salstat", "Scatterplot", "SciPy", "SegReg", "Shell (computing)", "SigmaStat", "SigmaXL", "Sigmaxl", "SimFiT", "Skytree, Inc", "SmartPLS", "Software", "Software as a service", "Software developer", "Software license", "Stan (software)", "StatCrunch", "StatPlus", "StatView", "StatXact", "Stata", "StataCorp LLC", "Statgraphics", "Statistica", "Statistical", "Statistical analysis", "StatsDirect", "Statsmodels", "Stepwise regression", "TSP (econometrics software)", "The Unscrambler", "Time series analysis", "Two-stage least squares", "UCLA", "UNISTAT", "Unit root test", "University of Ljubljana", "University of Michigan", "Unix", "User interface", "Vector autoregression", "WINKS", "WINdows KwikStat", "Weighted least squares", "WinBUGS", "Winpepi", "World Programming", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://librestats.com/2011/08/27/how-much-of-r-is-written-in-r/", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/BarChart&term=BarChart", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/BoxPlot&term=BoxPlot", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/LineChart&term=LineChart", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/ScatterPlot&term=Scatterplot", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=ProcessControl&term=processcontrol", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/OneWayANOVA", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/NonlinearFit", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/Histogram", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/ShapiroWilkWTest", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/GridPlot", "http://www.mathworks.com/help/curvefit/least-squares-fitting.html", "http://reference.wolfram.com/mathematica/BarCharts/ref/BarChart.html", "http://reference.wolfram.com/mathematica/Histograms/ref/Histogram.html", "http://reference.wolfram.com/mathematica/guide/SurvivalAnalysis.html", "http://reference.wolfram.com/mathematica/ref/ARIMAProcess.html", "http://reference.wolfram.com/mathematica/ref/ARProcess.html", "http://reference.wolfram.com/mathematica/ref/BoxWhiskerChart.html", "http://reference.wolfram.com/mathematica/ref/CoxModelFit.html", "http://reference.wolfram.com/mathematica/ref/GARCHProcess.html", "http://reference.wolfram.com/mathematica/ref/GeneralizedLinearModelFit.html", "http://reference.wolfram.com/mathematica/ref/LinearModelFit.html", "http://reference.wolfram.com/mathematica/ref/ListLinePlot.html", "http://reference.wolfram.com/mathematica/ref/ListPlot.html", "http://reference.wolfram.com/mathematica/ref/ListPointPlot3D.html", "http://reference.wolfram.com/mathematica/ref/LogitModelFit.html", "http://reference.wolfram.com/mathematica/ref/NormFunction.html", "http://reference.wolfram.com/mathematica/ref/ProbitModelFit.html", "http://reference.wolfram.com/mathematica/ref/UnitRootTest.html", "http://www.wolfram.com/mathematica/quick-revision-history.html", "http://search.cpan.org/~pdonelan/PSPP-Perl/", "http://doi.org/10.1002%2F(SICI)1099-1255(199903%2F04)14:2%3C191::AID-JAE524%3E3.0.CO;2-K", "http://www.jstor.org/stable/2565215", "http://www.nait.org/jit/Articles/zhu031105.pdf", "http://www.sagemath.org/", "https://books.google.com/books?id=CZg42jo02CEC", "https://www.maplesoft.com/support/help/Maple/view.aspx?path=MOLS", "https://web.archive.org/web/20051025165844/http://nait.org/jit/Articles/zhu031105.pdf", "https://savannah.gnu.org/forum/forum.php?forum_id=8936", "https://www.webcitation.org/5ElLwqoZN?url=http://www.partek.com/", "https://www.webcitation.org/5gbmX1GNH?url=http://rkward.sourceforge.net/"]}, "Prior probability": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2008", "Articles with unsourced statements from May 2011", "Articles with unsourced statements from October 2010", "Bayesian statistics", "CS1 maint: Multiple names: authors list", "Probability assessment", "Wikipedia articles needing clarification from August 2015", "Wikipedia articles needing clarification from May 2011", "Wikipedia articles needing clarification from September 2015"], "title": "Prior probability", "method": "Prior probability", "url": "https://en.wikipedia.org/wiki/Prior_probability", "summary": "In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable.\nBayes' theorem calculates the renormalized pointwise product of the prior and the likelihood function, to produce the posterior probability distribution, which is the conditional distribution of the uncertain quantity given the data.\nSimilarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is assigned before any relevant evidence is taken into account.\nPriors can be created using a number of methods. A prior can be determined from past information, such as previous experiments. A prior can be elicited from the purely subjective assessment of an experienced expert. An uninformative prior can be created to reflect a balance among outcomes when no information is available. Priors can also be chosen according to some principle, such as symmetry or maximizing entropy given constraints; examples are the Jeffreys prior or Bernardo's reference prior. When a family of conjugate priors exists, choosing a prior from that family simplifies calculation of the posterior distribution.\nParameters of prior distributions are a kind of hyperparameter. For example, if one uses a beta distribution to model the distribution of the parameter p of a Bernoulli distribution, then:\n\np is a parameter of the underlying system (Bernoulli distribution), and\n\u03b1 and \u03b2 are parameters of the prior distribution (beta distribution); hence hyperparameters.Hyperparameters themselves may have hyperprior distributions expressing beliefs about their values. A Bayesian model with more than one level of prior like this is called a hierarchical Bayes model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg"], "links": ["A priori probability", "Admissible decision rule", "Affine group", "Algorithmic probability", "Andrew Gelman", "Annals of Statistics", "Approximate Bayesian computation", "ArXiv", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernoulli distribution", "Bernstein-von Mises theorem", "Bernstein\u2013von Mises theorem", "Beta distribution", "Coding theory", "Conjugate prior", "Continuous random variable", "Credible interval", "Cromwell's rule", "Decision theory", "Digital object identifier", "Edwin T. Jaynes", "Empirical Bayes method", "Expected value", "Frequentist", "Frequentist matching", "Frequentist statistics", "Haar measure", "Haldane prior", "Harold Jeffreys", "Hierarchical Bayes model", "Hyperparameter", "Hyperprior", "Improper prior", "Inductive inference", "Information theory", "International Standard Book Number", "International Standard Serial Number", "J.B.S. Haldane", "JSTOR", "James Berger (statistician)", "Jeffreys prior", "Jos\u00e9-Miguel Bernardo", "Journal of the Royal Statistical Society", "Kullback\u2013Leibler divergence", "Latent variable", "Lie group", "Likelihood function", "Marginal probability", "Markov chain Monte Carlo", "Mathematical Reviews", "Maximum a posteriori estimation", "Minimum description length", "Minxent", "Normal distribution", "Observable variable", "Parameter", "Positive reals", "Posterior predictive distribution", "Posterior probability", "Posterior probability distribution", "Principle of indifference", "Principle of maximum entropy", "Principle of transformation groups", "Probability distribution", "Probability interpretations", "PubMed Central", "PubMed Identifier", "Radical probabilism", "Random event", "Reference prior", "Regularization (mathematics)", "Schwarz criterion", "Shannon entropy", "Solomonoff's theory of inductive inference", "Statistical inference", "Statistics", "Transformation group", "Translation group", "Uniform distribution (continuous)", "Uninformative prior", "Variance", "Zentralblatt MATH"], "references": ["http://bayes.wustl.edu/etj/articles/prior.pdf", "http://www-biba.inrialpes.fr/Jaynes/prob.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5751802", "http://www.ncbi.nlm.nih.gov/pubmed/29297278", "http://www.ams.org/mathscinet-getitem?mr=0547240", "http://www.ams.org/mathscinet-getitem?mr=0804611", "http://www.ams.org/mathscinet-getitem?mr=1401831", "http://www.ams.org/mathscinet-getitem?mr=2027492", "http://arxiv.org/abs/0904.0156", "http://doi.org/10.1093%2Fphilmat%2Fnkp019", "http://doi.org/10.1109%2FTSSC.1968.300117", "http://doi.org/10.1186%2Fs12859-017-1893-4", "http://doi.org/10.1214%2F07-AOS587", "http://doi.org/10.1214%2Faos%2F1032526950", "http://www.jstor.org/stable/2985028", "http://www.worldcat.org/issn/1471-2105", "http://zbmath.org/?format=complete&q=an:0865.62004", "http://www.kent.ac.uk/secl/philosophy/jw/2009/deFinetti.pdf", "https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-017-1893-4", "https://web.archive.org/web/20110609175653/http://www.kent.ac.uk/secl/philosophy/jw/2009/deFinetti.pdf", "https://doi.org/10.1017%2FS0305004100010495", "https://doi.org/10.2307%2F2332350", "https://ieeexplore.ieee.org/document/6654120/", "https://www.jstor.org/stable/2332350"]}, "Levene's test": {"categories": ["Analysis of variance", "Statistical tests"], "title": "Levene's test", "method": "Levene's test", "url": "https://en.wikipedia.org/wiki/Levene%27s_test", "summary": "In statistics, Levene's test is an inferential statistic used to assess the equality of variances for a variable calculated for two or more groups. Some common statistical procedures assume that variances of the populations from which different samples are drawn are equal. Levene's test assesses this assumption. It tests the null hypothesis that the population variances are equal (called homogeneity of variance or homoscedasticity). If the resulting p-value of Levene's test is less than some significance level (typically 0.05), the obtained differences in sample variances are unlikely to have occurred based on random sampling from a population with equal variances. Thus, the null hypothesis of equal variances is rejected and it is concluded that there is a difference between the variances in the population.\nSome of the procedures typically assuming homoscedasticity, for which one can use Levene's tests, include analysis of variance and t-tests.\nLevene's test is often used before a comparison of means. When Levene's test shows significance, one should switch to more generalized tests that is free from homoscedasticity assumptions (sometimes even non-parametric tests).\nLevene's test may also be used as a main test for answering a stand-alone question of whether two sub-samples in a given population have equal or different variances.", "images": [], "links": ["Analysis of variance", "Bartlett's test", "Brown\u2013Forsythe test", "Cauchy distribution", "Chi-squared distribution", "F-distribution", "F-test of equality of variances", "Harold Hotelling", "Heavy-tailed", "Homoscedasticity", "Ingram Olkin", "Monte Carlo method", "Null hypothesis", "P-value", "Robust statistics", "Skewness", "Statistical power", "Statistics", "Student's t-test", "Trimmed mean", "Variance"], "references": ["http://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm", "https://www.youtube.com/watch?v=O6taUlWejB0"]}, "Teletraffic queuing theory": {"categories": ["All articles with dead external links", "All articles with unsourced statements", "Articles with dead external links from April 2018", "Articles with permanently dead external links", "Articles with unsourced statements from August 2017", "Customer experience", "Formal sciences", "Markov models", "Markov processes", "Network performance", "Operations research", "Production planning", "Queueing theory", "Rationing", "Stochastic processes", "Wikipedia articles with BNF identifiers", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers", "Wikipedia external links cleanup from May 2017", "Wikipedia spam cleanup from May 2017"], "title": "Queueing theory", "method": "Teletraffic queuing theory", "url": "https://en.wikipedia.org/wiki/Queueing_theory", "summary": "Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.\nQueueing theory has its origins in research by Agner Krarup Erlang when he created models to describe the Copenhagen telephone exchange. The ideas have since seen applications including telecommunication, traffic engineering, computing\nand, particularly in industrial engineering, in the design of factories, shops, offices and hospitals, as well as in project management.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d3/Fifo_queue.png", "https://upload.wikimedia.org/wikipedia/commons/6/60/Poiuy.png", "https://upload.wikimedia.org/wikipedia/commons/2/2b/ServidorParalelo.jpg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Agner Krarup Erlang", "Aleksandr Khinchin", "Andrey Markov", "Arrival theorem", "BCMP network", "Backpressure routing", "Balance equation", "Bene\u0161 method", "Biblioth\u00e8que nationale de France", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Cass Business School", "Computing", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "David George Kendall", "Decomposition method (queueing theory)", "Diffusion process", "Digital object identifier", "Ehrenfest model", "Empirical measure", "Equilibrium distribution", "Erlang (unit)", "Erlang distribution", "Erlang unit", "Erol Gelenbe", "Exponentially distributed", "FIFO (computing and electronics)", "Felix Pollaczek", "Flow-equivalent server method", "Flow control (data)", "Flow network", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "Frank Kelly (mathematician)", "G-network", "G-networks", "G/G/1 queue", "G/M/1 queue", "Gordon F. Newell", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Industrial engineering", "Information system", "Integral equation", "Integrated Authority File", "International Standard Book Number", "JSTOR", "Jackson network", "James R. Jackson", "Jeffrey P. Buzen", "John Kingman", "Journal of the ACM", "K. Mani Chandy", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Library of Congress Control Number", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/D/k queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Management Science: A Journal of the Institute for Operations Research and the Management Sciences", "Markov chain", "Markovian arrival process", "Mathematical Proceedings of the Cambridge Philosophical Society", "Matrix analytic method", "Matrix geometric method", "Mean field model", "Mean field theory", "Mean sojourn time", "Mean value analysis", "Message queue", "Mor Harchol-Balter", "National Diet Library", "Network congestion", "Network scheduler", "Network simulation", "Normalizing constant", "Onno Boxma", "Operations Research (journal)", "Operations research", "Ornstein\u2013Uhlenbeck process", "Orthant", "Peter Whittle (mathematician)", "Phase-type distribution", "Pipeline (software)", "Poisson distribution", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability distribution", "Processor sharing", "Product-form solution", "Product-form stationary distribution", "Project Production Management", "Quality of service", "Quasireversibility", "Queue area", "Queue management system", "Queueing Systems", "Queueing delay", "Queueing theory", "Queuing Rule of Thumb", "Queuing algorithm", "Random early detection", "Rational arrival process", "Reflected Brownian motion", "Renewal theory", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining processing time", "Shortest remaining time", "Stack (data structure)", "Stochastic scheduling", "Telecommunication", "Teletraffic engineering", "Throughput", "Traffic engineering (transportation)", "Traffic equations", "Traffic generation model", "Traffic jam", "Transient state", "YouTube"], "references": ["http://web2.uwindsor.ca/math/hlynka/queue.html", "http://www.eventhelix.com/RealtimeMantra/CongestionControl/queueing_theory.htm", "http://www.pennlive.com/midstate/index.ssf/2009/03/hershey_med_to_open_redesigned.html", "http://people.revoledu.com/kardi/tutorial/Queuing/index.html", "http://www.slate.com/articles/business/operations/2012/06/queueing_theory_what_people_hate_most_about_waiting_in_line_.html", "http://www.supositorio.com/rcalc/rcalclite.htm", "http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf", "http://www.cs.gmu.edu/~menasce/perfbyd/", "http://www-unix.ecs.umass.edu/~krishna/ece673/buzen.pdf", "http://www.cs.washington.edu/homes/lazowska/qsp/", "http://www.netlab.tkk.fi/opetus/s383143/kalvot/english.shtml", "http://data.bnf.fr/ark:/12148/cb12647707b", "http://queueing-systems.ens-lyon.fr/", "http://www.ee.cityu.edu.hk/~zukerman/classnotes.pdf", "http://jmt.sf.net/", "http://portal.acm.org/citation.cfm?id=79046&dl=GUIDE&coll=GUIDE", "http://doi.org/10.1007%2FBF01149260", "http://doi.org/10.1007%2Fs11134-009-9147-4", "http://doi.org/10.1007%2Fs11134-009-9151-8", "http://doi.org/10.1016%2F0169-7552(93)90073-D", "http://doi.org/10.1017%2FCBO9781139226424.039", "http://doi.org/10.1017%2FCBO9781139226424.040", "http://doi.org/10.1017%2FCBO9781139226424.041", "http://doi.org/10.1017%2FS0305004100036094", "http://doi.org/10.1080%2F15326348808807077", "http://doi.org/10.1109%2FQEST.2008.47", "http://doi.org/10.1145%2F321879.321887", "http://doi.org/10.1145%2F322186.322195", "http://doi.org/10.1145%2F362342.362345", "http://doi.org/10.1214%2Faoap%2F1029962815", "http://doi.org/10.1214%2Faoap%2F1177004602", "http://doi.org/10.1214%2Faoms%2F1177728975", "http://doi.org/10.1287%2Fmnsc.1040.0268", "http://doi.org/10.1287%2Fopre.15.2.254", "http://doi.org/10.1287%2Fopre.5.4.518", "http://doi.org/10.1287%2Fopre.50.1.227.17792", "http://doi.org/10.2307%2F3212869", "http://doi.org/10.2307%2F3214781", "http://www.jstor.org/stable/167249", "http://www.jstor.org/stable/168557", "http://www.jstor.org/stable/2236285", "http://www.jstor.org/stable/2245101", "http://www.jstor.org/stable/2627213", "http://www.jstor.org/stable/2667284", "http://www.jstor.org/stable/2984229", "http://www.jstor.org/stable/3088474", "http://www.jstor.org/stable/3212869", "http://www.jstor.org/stable/3214781", "http://projecteuclid.org/euclid.aoms/1177728975", "http://www.cass.city.ac.uk/media/stories/story_96_105659_69284.html", "http://www.stats.ox.ac.uk/~winkel/bs3a07l13-14.pdf#page=4", "http://pass.maths.org.uk/issue2/erlang/index.html", "https://books.google.com/books?id=K3lQGeCtAJgC", "https://books.google.com/books?id=d-V8c8YRJikC&pg=PA178&dq=%22First-come,+first-served%22+business&hl=en&sa=X&ved=0ahUKEwiB18-Tg9vWAhUqxlQKHcXsDIwQ6AEIKDAA#v=onepage&q=%22First-come,%20first-served%22%20business&f=false", "https://www.youtube.com/watch?v=st8HRgHOErw", "https://catalogue.bnf.fr/ark:/12148/cb12647707b", "https://id.loc.gov/authorities/subjects/sh85109832", "https://d-nb.info/gnd/4255044-0", "https://id.ndl.go.jp/auth/ndlna/00567524", "https://web.archive.org/web/20111001212934/http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf", "https://www.wikidata.org/wiki/Q847526"]}, "Standardized coefficient": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles needing expert attention", "Articles lacking in-text citations from December 2010", "Articles needing additional references from December 2010", "Articles needing expert attention from March 2017", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Regression analysis", "Statistics articles needing expert attention"], "title": "Standardized coefficient", "method": "Standardized coefficient", "url": "https://en.wikipedia.org/wiki/Standardized_coefficient", "summary": "In statistics, standardized [regression] coefficients, also called beta coefficients or beta weights, are the estimates resulting from a regression analysis that have been standardized so that the variances of dependent and independent variables are 1. Therefore, standardized coefficients refer to how many standard deviations a dependent variable will change, per standard deviation increase in the predictor variable. For simple linear regression, the absolute value of the unstandardized regression coefficient equals the correlation between the independent and dependent variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Beta (finance)", "DAP (software)", "Dependent and independent variables", "Dependent variable", "Dollar", "Family size", "Income", "Individual", "International Standard Book Number", "List of statistical packages", "Mean", "Multiple regression", "Nonparametric regression", "Normal distribution", "Number", "PSPP", "Parametric statistics", "Regression analysis", "SAS System", "SPSS", "SYSTAT (statistics)", "Sampling error", "Scale of units", "Skewness", "Standard deviation", "Statistics", "Unit-weighted regression", "Units of measurement", "Variance"], "references": ["http://www.jerrydallal.com/LHSP/importnt.htm", "http://www.theanalysisfactor.com/how-to-get-standardized-regression-coefficients/", "http://www.socialresearchmethods.net/selstat/glossary.htm"]}, "L\u00e9vy process": {"categories": ["All articles with links needing disambiguation", "Articles with links needing disambiguation from November 2018", "L\u00e9vy processes", "Paul L\u00e9vy (mathematician)", "Wikipedia articles needing clarification from October 2018", "Wikipedia articles with GND identifiers"], "title": "L\u00e9vy process", "method": "L\u00e9vy process", "url": "https://en.wikipedia.org/wiki/L%C3%A9vy_process", "summary": "In probability theory, a L\u00e9vy process, named after the French mathematician Paul L\u00e9vy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random and independent, and statistically identical over different time intervals of the same length.\nA L\u00e9vy process may thus be viewed as the continuous-time analog of a random walk.\nThe most well known examples of L\u00e9vy processes are the Wiener process, often called the Brownian motion process, and the Poisson process. Aside from Brownian motion with drift, all other proper L\u00e9vy processes have discontinuous paths.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20161201223606%21Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20120912121406%21Blue_pencil.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost surely", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Binomial type", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Characteristic exponent", "Characteristic function (probability theory)", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compensated generalized Poisson process", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discontinuous", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Expected value", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Greg Lawler", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independence (probability theory)", "Independent and identically distributed random variables", "Independent increments", "Indicator function", "Infinite divisibility (probability)", "Infinitely divisible distribution", "Infinitesimal generator (stochastic processes)", "Integrated Authority File", "Interacting particle system", "International Standard Book Number", "International Standard Serial Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law (stochastic processes)", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy flight", "L\u00e9vy jump process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moment (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Normal distribution", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Pairwise independence", "Paul L\u00e9vy (mathematician)", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson distribution", "Poisson point process", "Poisson process", "Polynomial function", "Potts model", "Predictable process", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Pure jump model", "Quadratic variation", "Queueing model", "Queueing theory", "Random", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://www.math.uchicago.edu/~lawler/finbook2.pdf", "http://www.ams.org/notices/200411/fea-applebaum.pdf", "http://doi.org/10.1007%2F978-3-642-37632-0_2", "http://www.worldcat.org/issn/1088-9477", "http://dispenser.info.tm/~dispenser/cgi-bin/dab_solver.py?page=L%C3%A9vy_process&editintro=Template:Disambiguation_needed/editintro&client=Template:Dn", "https://link.springer.com/chapter/10.1007/978-3-642-37632-0_2", "https://d-nb.info/gnd/4463623-4", "https://web.archive.org/web/20180329130220/http://www.math.uchicago.edu/~lawler/finbook2.pdf", "https://www.wikidata.org/wiki/Q1557613"]}, "Statistical model": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2010", "Mathematical and quantitative methods (economics)", "Mathematical modeling", "Scientific modeling", "Statistical models", "Statistical theory"], "title": "Statistical model", "method": "Statistical model", "url": "https://en.wikipedia.org/wiki/Statistical_model", "summary": "A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of some sample data and similar data from a larger population. A statistical model represents, often in considerably idealized form, the data-generating process.\nThe assumptions embodied by a statistical model describe a set of probability distributions, some of which are assumed to adequately approximate the distribution from which a particular data set is sampled. The probability distributions inherent in statistical models are what distinguishes statistical models from other, non-statistical, mathematical models.\nA statistical model is usually specified by mathematical equations that relate one or more random variables and possibly other non-random variables. As such, a statistical model is \"a formal representation of a theory\" (Herman Ad\u00e8r quoting Kenneth Bollen).All statistical hypothesis tests and all statistical estimators are derived from statistical models. More generally, statistical models are part of the foundation of statistical inference.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "All models are wrong", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Statistics", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli process", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Cambridge University Press", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Coin tossing", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confirmatory data analysis", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "David Cox (statistician)", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Deterministic system", "Dice", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension", "Discrete uniform distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometric model", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Event (probability theory)", "Experiment", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Herman J. Ad\u00e8r", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "I.i.d.", "Identifiability", "Index of dispersion", "Injective function", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kenneth A. Bollen", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical model", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multilevel models", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric model", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter McCullagh", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability distributions", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Random variables", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real numbers", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sample space", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific modelling", "Score test", "Seasonal adjustment", "Semiparametric model", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Springer Science+Business Media", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical assumption", "Statistical assumptions", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic", "Stochastic process", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Wiley-Interscience", "World Scientific", "Z-test"], "references": ["http://www.stat.uchicago.edu/~pmcc/pubs/AOS023.pdf", "http://doi.org/10.1214%2Faos%2F1035844977", "https://books.google.com/books?id=LCnOj4ZFyjkC&pg=PA280"]}, "Statistical learning theory": {"categories": ["Estimation theory", "Machine learning"], "title": "Statistical learning theory", "method": "Statistical learning theory", "url": "https://en.wikipedia.org/wiki/Statistical_learning_theory", "summary": "Statistical learning theory is a framework for machine learning\ndrawing from the fields of statistics and functional analysis. Statistical learning theory deals with the problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields such as computer vision, speech recognition, bioinformatics and baseball.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f4/Overfitting_on_Training_Set_Data.pdf", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Baseball", "Bayesian network", "Bias-variance dilemma", "Bioinformatics", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Cluster analysis", "Computational learning theory", "Computer vision", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Dimensionality reduction", "Empirical risk", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Expected risk", "Facial recognition system", "Factor analysis", "Feature engineering", "Feature learning", "Functional analysis", "Gated recurrent unit", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Heaviside step function", "Hidden Markov model", "Hierarchical clustering", "Independent component analysis", "Indicator function", "International Conference on Machine Learning", "International Standard Book Number", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "L1-norm", "L2-norm", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Loss function", "Lp space", "Machine Learning (journal)", "Machine learning", "Mean-shift", "Mehryar Mohri", "Multilayer perceptron", "Naive Bayes classifier", "Non-negative matrix factorization", "OPTICS algorithm", "Occam learning", "Ohm's Law", "Online machine learning", "Ordinary least squares regression", "Outline of machine learning", "Overfitting", "Perceptron", "Principal component analysis", "Probably approximately correct learning", "Proximal gradient methods for learning", "Q-learning", "Random forest", "Recurrent neural network", "Regression analysis", "Regularization (mathematics)", "Reinforcement learning", "Relevance vector machine", "Reproducing kernel Hilbert spaces", "Restricted Boltzmann machine", "Self-organizing map", "Semi-supervised learning", "Speech recognition", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning in language acquisition", "Statistics", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Tikhonov regularization", "Training set", "Trevor Hastie", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory"], "references": ["http://ai2-s2-pdfs.s3.amazonaws.com/a36b/028d024bf358c4af1a5e1dc3ca0aed23b553.pdf", "http://www.mit.edu/~9.520/spring12/slides/class01/class01.pdf", "http://www.mit.edu/~9.520/spring12/slides/class02/class02.pdf", "https://arxiv.org/list/cs.LG/recent"]}, "Error bar": {"categories": ["All stub articles", "Statistical charts and diagrams", "Statistics stubs"], "title": "Error bar", "method": "Error bar", "url": "https://en.wikipedia.org/wiki/Error_bar", "summary": "Error bars are graphical representations of the variability of data and used on graphs to indicate the error or uncertainty in a reported measurement. They give a general idea of how precise a measurement is, or conversely, how far from the reported value the true (error free) value might be. Error bars often represent one standard deviation of uncertainty, one standard error, or a particular confidence interval (e.g., a 95% interval). These quantities are not the same and so the measure selected should be stated explicitly in the graph or supporting text.\nError bars can be used to compare visually two quantities if various other conditions hold. This can determine whether differences are statistically significant. Error bars can also suggest goodness of fit of a given function, i.e., how well the function describes the data. Scientific papers in the experimental sciences are expected to include error bars on all graphs, though the practice differs somewhat between sciences, and each journal will have its own house style. It has also been shown that error bars can be used as a direct manipulation interface for controlling probabilistic algorithms for approximate computation. Error bars can also be expressed in a plus-minus sign (\u00b1), plus the upper limit of the error and minus the lower limit of the error.A notorious misconception in elementary statistics is that error bars show whether or not a statistically significant difference exists, by checking simply for whether or not the error bars overlap; this is not the case.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Confidenceinterval.png"], "links": ["Bar chart", "Box plot", "Confidence interval", "Digital object identifier", "Direct manipulation interface", "Errors and residuals in statistics", "Goodness of fit", "Information graphics", "Model selection", "Plus-minus sign", "PubMed Central", "Significant figures", "Standard deviation", "Standard error", "Statistically significant", "Statistics", "Style guide"], "references": ["http://scienceblogs.com/cognitivedaily/2008/07/31/most-researchers-dont-understa-1/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2064100", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3088813", "http://doi.org/10.1001%2Farchpedi.1982.03970460067015", "http://doi.org/10.1007%2Fs10654-011-9563-8", "http://doi.org/10.1037%2F1082-989X.10.4.389", "http://doi.org/10.1083%2Fjcb.200611141", "http://doi.org/10.2312%2Feurovisshort.20151138", "https://www.cl.cam.ac.uk/~as2006/files/sarkar_2015_uncertainty_vis.pdf"]}, "Latin rectangle": {"categories": ["Design of experiments", "Latin squares"], "title": "Latin rectangle", "method": "Latin rectangle", "url": "https://en.wikipedia.org/wiki/Latin_rectangle", "summary": "In combinatorial mathematics, a Latin rectangle is an r \u00d7 n matrix that has the numbers 1, 2, 3, ..., n as its entries with no number occurring more than once in any row or column where r \u2264 n. An n \u00d7 n Latin rectangle is called a Latin square. If r < n, then it is possible to append n \u2212 r rows to an r \u00d7 n Latin rectangle to form a Latin square, using Hall's marriage theorem.\nIn statistics, Latin rectangles have applications in the design of experiments.", "images": [], "links": ["Analysis of covariance", "Analysis of variance", "Bayesian experimental design", "Bayesian linear regression", "Blind experiment", "Blocking (statistics)", "Box\u2013Behnken design", "Central composite design", "Cochran's theorem", "Combinatorial design", "Combinatorics", "Comparing means", "Completely randomized design", "Confounding", "Contrast (statistics)", "Covariate", "Crossover study", "Design of experiments", "Effect size", "Experiment", "Experimental unit", "External validity", "Factorial experiment", "Fractional factorial design", "Generalized randomized block design", "Glossary of experimental design", "Graeco-Latin square", "Hall's marriage theorem", "Hierarchical Bayes model", "Hierarchical linear modeling", "Interaction (statistics)", "Internal validity", "Latin hypercube sampling", "Latin square", "Leon Mirsky", "Linear regression", "List of statistics articles", "Matrix (mathematics)", "Mixed model", "Multiple comparison", "Multivariate analysis of variance", "Nuisance variable", "Optimal design", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Plackett-Burman design", "Polynomial and rational function modeling", "Random assignment", "Random effect", "Randomization", "Randomized block design", "Randomized controlled trial", "Repeated measures design", "Replication (statistics)", "Response surface methodology", "Restricted randomization", "Sample size", "Scientific control", "Scientific method", "Sequential analysis", "Sequential probability ratio test", "Statistical inference", "Statistical model", "Statistics", "Taguchi methods", "Validity (statistics)"], "references": []}, "Average": {"categories": ["All articles with dead external links", "All articles with failed verification", "Arithmetic functions", "Articles with dead external links from October 2018", "Articles with failed verification from May 2015", "Articles with permanently dead external links", "Means", "Summary statistics"], "title": "Average", "method": "Average", "url": "https://en.wikipedia.org/wiki/Average", "summary": "In colloquial language, an average is a single number taken as representative of a list of numbers. Different concepts of average are used in different contexts. Often \"average\" refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage any of these might be called an average value.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/de/Comparison_mean_median_mode.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg"], "links": ["Antilog", "Arithmetic mean", "Average absolute deviation", "Central limit theorem", "Central tendency", "Colloquial", "Compound annual growth rate", "Continuous function", "Cubic mean", "Descriptive statistics", "Digital filter", "Digital object identifier", "Digital signal processing", "Domesday Book", "Draught animal", "Estimation", "Expected value", "General average", "Generalized f-mean", "Generalized mean", "Geometric mean", "Geometric median", "Glasgow Mathematical Journal", "Harmonic mean", "Inequality of arithmetic and geometric means", "International Standard Book Number", "International Standard Serial Number", "Interquartile mean", "Interquartile range", "Invariant (mathematics)", "John Ray", "Law of averages", "Log-normal distribution", "Logarithm", "Mean", "Measurement", "Median", "Mid-range", "Midrange", "Mode (statistics)", "Monotonicity", "Moving average", "Multiplicative calculus", "Multiplicative inverse", "Normalized mean", "Oxford English Dictionary", "Permutation", "Pythagorean means", "Quadratic mean", "Rotation (mathematics)", "Skewness", "Summation", "Table of mathematical symbols", "Time series", "Trimean", "Trimedian", "Truncated mean", "Weighted arithmetic mean", "Weighted average", "Winsorized mean"], "references": ["http://oed.com/search?searchType=dictionary&q=average", "http://www.oxforddnb.com/help/subscribe#public", "http://www.sengpielaudio.com/calculator-geommean.htm", "http://www.upo.es/RevMetCuant/art.php?id=38", "http://www.amstat.org/publications/jse/v11n1/bakker.html", "http://doi.org/10.1017%2Fs0017089500002135", "http://doi.org/10.2307%2F2333051", "http://babel.hathitrust.org/cgi/pt?id=njp.32101037601729;view=1up;seq=19", "http://www.worldcat.org/issn/1886-516X", "http://www.york.ac.uk/depts/maths/histstat/eisenhart.pdf", "https://arcaneknowledgeofthedeep.files.wordpress.com/2014/02/theologyarithmetic.pdf", "https://web.archive.org/web/20070810034709/http://economicsbulletin.vanderbilt.edu/2004/volume3/EB-04C10011A.pdf"]}, "Dot plot (bioinformatics)": {"categories": ["Bioinformatics", "Statistical charts and diagrams"], "title": "Dot plot (bioinformatics)", "method": "Dot plot (bioinformatics)", "url": "https://en.wikipedia.org/wiki/Dot_plot_(bioinformatics)", "summary": "In bioinformatics a dot plot is a graphical method for comparing two biological sequences and identifying regions of close similarity. It is a type of recurrence plot.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/33/Zinc-finger-dot-plot.png"], "links": ["Bioinformatics", "DNA", "Digital object identifier", "Direct relationship", "Dot plot (statistics)", "Human", "International Standard Serial Number", "Low-complexity regions", "Protein contact map", "PubMed Central", "PubMed Identifier", "Recurrence plot", "Self-similarity", "Self-similarity matrix", "Sequence (biology)", "Sequence alignment", "Transcription factor", "Tuple", "Zinc finger"], "references": ["http://cube.univie.ac.at/gepard", "http://virology.uvic.ca/virology-ca-tools/jdotter/", "http://myhits.isb-sib.ch/cgi-bin/dotlet", "http://globin.bx.psu.edu/dist/laj/", "http://www.csb.yale.edu/userguides/graphics/whatif/html/chap13.html", "http://www.ac-nice.fr/svt/productions/html5/dotplot/index.htm?arn=true", "http://dgenies.toulouse.inra.fr/", "http://bioinfo.cristal.univ-lille.fr/yass/index.php", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1160238", "http://www.ncbi.nlm.nih.gov/pubmed/10827456", "http://www.ncbi.nlm.nih.gov/pubmed/15980530", "http://www.ncbi.nlm.nih.gov/pubmed/8566757", "http://www.code10.info/index.php?option=com_content&view=category&id=52&Itemid=76", "http://www.code10.info/index.php?view=article&catid=50:cat_coding_software_serolis&id=63:serolis-software-package-for-dot-plot-creation&option=com_content&Itemid=61", "http://sourceforge.net/projects/genomdiff", "http://www.bioinformatics.nl/cgi-bin/emboss/dotmatcher", "http://doi.org/10.1093%2Fbioinformatics%2Fbtg406", "http://doi.org/10.1093%2Fbioinformatics%2Fbtm039", "http://doi.org/10.1093%2Fbioinformatics%2Fbty395", "http://doi.org/10.1093%2Fnar%2Fgki478", "http://doi.org/10.1111%2Fj.1432-1033.1970.tb01046.x", "http://doi.org/10.7287%2Fpeerj.preprints.26567v1", "http://www.worldcat.org/issn/0168-9525", "http://www.worldcat.org/issn/0378-1119", "http://www.worldcat.org/issn/1367-4803", "http://sonnhammer.sbc.su.se/Dotter.html", "https://github.com/evolvedmicrobe/dotplot", "https://github.com/molbio-dresden/flexidot", "https://academic.oup.com/bioinformatics/advance-article/doi/10.1093/bioinformatics/bty395/4995848", "https://academic.oup.com/bioinformatics/article/20/2/279/204948", "https://academic.oup.com/bioinformatics/article/23/8/1026/198110", "https://www.bx.psu.edu/~rsharris/lastz/", "https://web.archive.org/web/20160416103836/https://ugene.unipro.ru/wiki/display/UUOUM15/Dotplot", "https://doi.org/10.7287/peerj.preprints.26567v1", "https://genomevolution.org/coge/SynMap.pl", "https://cran.r-project.org/web/packages/seqinr/index.html"]}, "M/M/1 queue": {"categories": ["Single queueing nodes"], "title": "M/M/1 queue", "method": "M/M/1 queue", "url": "https://en.wikipedia.org/wiki/M/M/1_queue", "summary": "In queueing theory, a discipline within the mathematical theory of probability, an M/M/1 queue represents the queue length in a system having a single server, where arrivals are determined by a Poisson process and job service times have an exponential distribution. The model name is written in Kendall's notation. The model is the most elementary of queueing models and an attractive object of study as closed-form expressions can be obtained for many metrics of interest in this model. An extension of this model with more than one server is the M/M/c queue.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e6/MM1_queue_state_space.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Mm1_queue.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Adversarial queueing network", "Arrival theorem", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "BCMP network", "Balance equation", "Bene\u0161 method", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burke's theorem", "Burkholder\u2013Davis\u2013Gundy inequalities", "Buzen's algorithm", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Closed-form expression", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time Markov chain", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Continuous time Markov chain", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Edward G. 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The theorem is named after Ukrainian mathematicians Vladimir Marchenko and Leonid Pastur who proved this result in 1967.\nIf \n \n \n \n X\n \n \n {\\displaystyle X}\n denotes a \n \n \n \n m\n \u00d7\n n\n \n \n {\\displaystyle m\\times n}\n random matrix whose entries are independent identically distributed random variables with mean 0 and variance \n \n \n \n \n \u03c3\n \n 2\n \n \n <\n \u221e\n \n \n {\\displaystyle \\sigma ^{2}<\\infty }\n , let\n\n \n \n \n \n Y\n \n n\n \n \n =\n \n \n 1\n n\n \n \n X\n \n X\n \n T\n \n \n \n \n {\\displaystyle Y_{n}={\\frac {1}{n}}XX^{T}}\n and let \n \n \n \n \n \u03bb\n \n 1\n \n \n ,\n \n \n \u03bb\n \n 2\n \n \n ,\n \n \u2026\n ,\n \n \n \u03bb\n \n m\n \n \n \n \n {\\displaystyle \\lambda _{1},\\,\\lambda _{2},\\,\\dots ,\\,\\lambda _{m}}\n be the eigenvalues of \n \n \n \n \n Y\n \n n\n \n \n \n \n {\\displaystyle Y_{n}}\n (viewed as random variables). Finally, consider the random measure\n\n \n \n \n \n \u03bc\n \n m\n \n \n (\n A\n )\n =\n \n \n 1\n m\n \n \n #\n \n {\n \n \n \u03bb\n \n j\n \n \n \u2208\n A\n \n }\n \n ,\n \n A\n \u2282\n \n R\n \n .\n \n \n {\\displaystyle \\mu _{m}(A)={\\frac {1}{m}}\\#\\left\\{\\lambda _{j}\\in A\\right\\},\\quad A\\subset \\mathbb {R} .}\n Theorem. Assume that \n \n \n \n m\n ,\n \n n\n \n \u2192\n \n \u221e\n \n \n {\\displaystyle m,\\,n\\,\\to \\,\\infty }\n so that the ratio \n \n \n \n m\n \n /\n \n n\n \n \u2192\n \n \u03bb\n \u2208\n (\n 0\n ,\n +\n \u221e\n )\n \n \n {\\displaystyle m/n\\,\\to \\,\\lambda \\in (0,+\\infty )}\n . Then \n \n \n \n \n \u03bc\n \n m\n \n \n \n \u2192\n \n \u03bc\n \n \n {\\displaystyle \\mu _{m}\\,\\to \\,\\mu }\n (in weak* topology in distribution), where\n\n \n \n \n \u03bc\n (\n A\n )\n =\n \n \n {\n \n \n \n (\n 1\n \u2212\n \n \n 1\n \u03bb\n \n \n )\n \n \n 1\n \n \n 0\n \u2208\n A\n \n \n +\n \u03bd\n (\n A\n )\n ,\n \n \n \n if \n \n \u03bb\n >\n 1\n \n \n \n \n \u03bd\n (\n A\n )\n ,\n \n \n \n if \n \n 0\n \u2264\n \u03bb\n \u2264\n 1\n ,\n \n \n \n \n \n \n \n \n {\\displaystyle \\mu (A)={\\begin{cases}(1-{\\frac {1}{\\lambda }})\\mathbf {1} _{0\\in A}+\\nu (A),&{\\text{if }}\\lambda >1\\\\\\nu (A),&{\\text{if }}0\\leq \\lambda \\leq 1,\\end{cases}}}\n and\n\n \n \n \n d\n \u03bd\n (\n x\n )\n =\n \n \n 1\n \n 2\n \u03c0\n \n \u03c3\n \n 2\n \n \n \n \n \n \n \n \n (\n \n \u03bb\n \n +\n \n \n \u2212\n x\n )\n (\n x\n \u2212\n \n \u03bb\n \n \u2212\n \n \n )\n \n \n \u03bb\n x\n \n \n \n \n \n \n 1\n \n \n [\n \n \u03bb\n \n \u2212\n \n \n ,\n \n \u03bb\n \n +\n \n \n ]\n \n \n \n d\n x\n \n \n {\\displaystyle d\\nu (x)={\\frac {1}{2\\pi \\sigma ^{2}}}{\\frac {\\sqrt {(\\lambda _{+}-x)(x-\\lambda _{-})}}{\\lambda x}}\\,\\mathbf {1} _{[\\lambda _{-},\\lambda _{+}]}\\,dx}\n with\n\n \n \n \n \n \u03bb\n \n \u00b1\n \n \n =\n \n \u03c3\n \n 2\n \n \n (\n 1\n \u00b1\n \n \n \u03bb\n \n \n \n )\n \n 2\n \n \n .\n \n \n {\\displaystyle \\lambda _{\\pm }=\\sigma ^{2}(1\\pm {\\sqrt {\\lambda }})^{2}.}\n The Marchenko\u2013Pastur law also arises as the free Poisson law in free probability theory, having rate \n \n \n \n 1\n \n /\n \n \u03bb\n \n \n {\\displaystyle 1/\\lambda }\n and jump size \n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n {\\displaystyle \\sigma ^{2}}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/ba/Marchenko-Pastur_distribution.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Asymptotic", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Convergence in distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Eigenvalue", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Free Poisson law", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Leonid Pastur", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Matematicheskii Sbornik", "Mathematicians", "Matrix-exponential distribution", "Matrix gamma 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distribution", "Poly-Weibull distribution", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Roland Speicher", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Singular value", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Ukraine", "Uniform distribution (continuous)", "Variance-gamma distribution", "Vladimir Marchenko", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weak topology", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.ebooksdownloadfree.com/Science-Technology/Lectures-on-the-Combinatorics-of-Free-Probability-BI9525.html", "http://doi.org/10.1070%2FSM1967v001n04ABEH001994", "http://doi.org/10.3150%2Fbj%2F1089206408", "http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=4101&option_lang=eng", "https://www.google.com/search?tbs=bks:1&q=isbn:0521858526"]}, "Nuremberg Code": {"categories": ["1940s in Bavaria", "1947 documents", "1947 in West Germany", "1947 in law", "1947 in science", "Articles containing German-language text", "Design of experiments", "Ethics and statistics", "History of Nuremberg", "Human subject research", "International criminal law", "Research ethics", "The Holocaust", "United States Nuremberg Military Tribunals"], "title": "Nuremberg Code", "method": "Nuremberg Code", "url": "https://en.wikipedia.org/wiki/Nuremberg_Code", "summary": "The Nuremberg Code (German: N\u00fcrnberger Kodex) is a set of research ethics principles for human experimentation created as a result of the Nuremberg trials at the end of the Second World War.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/4c/20140410103855%21Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/4c/20060627134716%21Wikisource-logo.svg"], "links": ["Adolf Hitler", "American Medical 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Brandt (physician)", "Leo Alexander", "List of medical ethics cases", "Maurice Henry Pappworth", "Medical ethics", "Medical torture", "Monitoring in clinical trials", "Nazi eugenics", "Nazism", "Non-maleficence", "Nuremberg", "Nuremberg Laws", "Nuremberg Principles", "Nuremberg trials", "Political prisoner", "Privacy for research participants", "PubMed Identifier", "Racial hygiene", "Research ethics", "Research participant", "Respect for persons", "Return of results", "Right to withdraw", "Scientific", "Social research", "Sterilization (medicine)", "Subsequent Nuremberg trials", "Unethical human experimentation", "United Kingdom", "United States Department of Health and Human Services", "Universal Declaration of Human Rights", "War crime", "Weimar", "Wikisource", "World Health Organization", "World Medical Association", "World War II"], "references": ["http://www.credoreference.com/entry.do?ta=abcgeamrle&uh=eugenics_euthanasia", "http://www.geocities.com/travbailey/Michael_R_Marrus_The_Nuremberg_Doctors_Trial.htm", "http://www.geocities.com/travbailey/Paul_Weindling_The_Origins_of_Informed_Consent_Nuremburg_Code.htm", "http://motherjones.com/environment/2010/09/dan-markingson-drug-trial-astrazeneca", "http://www.stanford.edu/group/psylawseminar/The%20Nuremburg%20Code.htm", "http://www.access.gpo.gov/nara/cfr/waisidx_00/45cfr46_00.html", "http://www.ncbi.nlm.nih.gov/pubmed/10189729", "http://www.ncbi.nlm.nih.gov/pubmed/11420451", "http://doi.org/10.1353%2Fbhm.1999.0037", "http://doi.org/10.1353%2Fbhm.2001.0049", "http://www.historyandpolicy.org/papers/policy-paper-03.html", "https://archive.hhs.gov/ohrp/references/nurcode.htm", "https://web.archive.org/web/20071201020045/http://www.geocities.com/travbailey/Michael_R_Marrus_The_Nuremberg_Doctors_Trial.htm", "https://www.webcitation.org/query?url=http://www.geocities.com/travbailey/Paul_Weindling_The_Origins_of_Informed_Consent_Nuremburg_Code.htm&date=2009-10-25+23:15:42"]}, "Latent Dirichlet allocation": {"categories": ["All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from August 2017", "Latent variable models", "Probabilistic models", "Statistical natural language processing", "Wikipedia articles that are too technical from August 2017", "Wikipedia external links cleanup from June 2016", "Wikipedia spam cleanup from June 2016"], "title": "Latent Dirichlet allocation", "method": "Latent Dirichlet allocation", "url": "https://en.wikipedia.org/wiki/Latent_Dirichlet_allocation", "summary": "In natural language processing, latent Dirichlet allocation (LDA) is a generative statistical model that allows sets of observations to be explained by unobserved groups that explain why some parts of the data are similar. For example, if observations are words collected into documents, it posits that each document is a mixture of a small number of topics and that each word's presence is attributable to one of the document's topics. LDA is an example of a topic model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d3/Latent_Dirichlet_allocation.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4d/Smoothed_LDA.png", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["AI-complete", "Andrew Ng", "Apache Spark", "Automated essay scoring", "Automated online assistant", "Automatic identification and data capture", "Automatic summarization", "Bag-of-words model", "Bag of words model", "Bayesian inference", "Bayesian network", "Bigram", "Categorical distribution", "Chatbot", "Chinese restaurant process", "Collapsed Gibbs sampling", "Collocation extraction", "Compound term processing", "Computer-assisted reviewing", "Computer-assisted translation", "Concept mining", "Concordancer", "Coreference", "David Blei", "De Finetti's theorem", "Digital object identifier", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Epistemology", "Example-based machine translation", "Expectation propagation", "Function word", "Gamma-Poisson distribution", "Gamma function", "Generative model", "Gensim", "Gibbs sampling", "Grammar checker", "Graphical models", "Hadoop", "Hierarchical Dirichlet process", "Independent component analysis", "Information retrieval", "Interactive fiction", "International Standard Book Number", "International Standard Serial Number", "Jonathan K. Pritchard", "Journal of Machine Learning Research", "LDA-dual model", "Latent semantic analysis", "Latent semantic indexing", "Latent variable", "Lemmatisation", "Linear discriminant analysis", "Logistic normal distribution", "Machine translation", "MapReduce", "Matthew Stephens (statistician)", "Michael I. Jordan", "Mixture model", "Multi-document summarization", "Multinomial distribution", "N-gram", "Named-entity recognition", "Natural language generation", "Natural language processing", "Natural language understanding", "Natural language user interface", "Non-negative matrix factorization", "NumPy", "Observable variable", "Ontology learning", "Optical character recognition", "PLSA", "Pachinko allocation", "Parsing", "Part-of-speech tagging", "Peter Donnelly", "Plate notation", "Population genetics", "Posterior distribution", "Predictive text", "Prior probability", "Probabilistic graphical model", "Probabilistic latent semantic indexing", "PubMed Central", "PubMed Identifier", "Question answering", "R (programming language)", "Rule-based machine translation", "STTM", "Semantics", "Sentence extraction", "Sentiment analysis", "Shallow parsing", "Spatial Latent Dirichlet Allocation", "Speech corpus", "Speech recognition", "Speech synthesis", "Spell checker", "Stemming", "Stop words", "Syntax guessing", "Terminology extraction", "Text corpus", "Text mining", "Text segmentation", "Text simplification", "Tf-idf", "Topic model", "Trigram", "Truecasing", "Variational Bayes", "Variational Bayesian methods", "Voice user interface", "Word-sense disambiguation"], "references": ["http://research.microsoft.com/en-us/um/cambridge/projects/infernet/docs/Latent%20Dirichlet%20Allocation.aspx", "http://www.r-bloggers.com/RUG/2010/10/285/", "http://cocosci.berkeley.edu/tom/papers/ncrp.pdf", "http://www.cs.binghamton.edu/~meng/pub.d/icde09-LatentTopic.pdf", "http://www.cs.cmu.edu/~lafferty/pub/ctm.pdf", "http://mimno.infosci.cornell.edu/topics.html", "http://jmlr.csail.mit.edu/papers/v3/blei03a.html", "http://mallet.cs.umass.edu/index.php", "http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2007_102.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC387300", "http://www.ncbi.nlm.nih.gov/pubmed/14872004", "http://videolectures.net/mlss09uk_blei_tm/", "http://doi.org/10.1073%2Fpnas.0307752101", "http://doi.org/10.1162%2Fjmlr.2003.3.4-5.993", "http://genetics.org/content/155/2/945", "http://www.worldcat.org/issn/0016-6731", "http://www.cs.bham.ac.uk/~axk/sigir2003_mgak.pdf", "https://scholar.google.ca/scholar?cites=17756175773309118945&as_sdt=2005&sciodt=0,5&hl=en", "https://scholar.google.ca/scholar?safe=active&biw=1680&bih=956&bav=on.2,or.&bvm=bv.113943665,d.cWw&um=1&ie=UTF-8&lr&cites=281659566077639093", "https://github.com/AmazaspShumik/BayesianML-MCMC/blob/master/Gibbs%20LDA/coll_gibbs_lda.m", "https://github.com/AmazaspShumik/BayesianML-MCMC/blob/master/Gibbs%20LDA/nips_example.m", "https://github.com/datquocnguyen/jLDADMM", "https://github.com/qiang2100/STTM", "https://code.google.com/p/topic-modeling-tool/", "https://research.microsoft.com/~minka/papers/aspect/minka-aspect.pdf", "https://www.youtube.com/watch?v=DDq3OVp9dNA/", "https://mahout.apache.org/users/clustering/latent-dirichlet-allocation.html", "https://spark.apache.org/docs/latest/mllib-clustering.html#latent-dirichlet-allocation-lda", "https://cran.r-project.org/web/packages/lda/index.html", "https://cran.r-project.org/web/packages/topicmodels/index.html"]}, "Statisticians' and engineers' cross-reference of statistical terms": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from April 2016", "Articles that may contain original research from April 2016", "Detection theory", "Statistical hypothesis testing"], "title": "Statisticians' and engineers' cross-reference of statistical terms", "method": "Statisticians' and engineers' cross-reference of statistical terms", "url": "https://en.wikipedia.org/wiki/Statisticians%27_and_engineers%27_cross-reference_of_statistical_terms", "summary": "The following terms are used by electrical engineers in statistical signal processing studies instead of typical statistician's terms.\n\nIn other engineering fields, particularly mechanical engineering, uncertainty analysis examines systematic and random components of variations in measurements associated with physical experiments.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1b/Ambox_question.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Alternative hypothesis", "Critical region", "Electrical engineer", "International Standard Book Number", "Mechanical engineering", "Null hypothesis", "Statistical signal processing", "Type II error", "Type I error"], "references": []}, "Normal score": {"categories": ["Nonparametric statistics"], "title": "Normal score", "method": "Normal score", "url": "https://en.wikipedia.org/wiki/Normal_score", "summary": "The term normal score is used with two different meanings in statistics. One of them relates to creating a single value which can be treated as if it had arisen from a standard (zero mean, unit variance) normal distribution. The second relates to assigning alternative values to data points within a dataset, with the broad intention of creating data values than can be interpreted as being approximations for values that might have been observed had the data arisen from a standard normal distribution.\nThe first meaning is as an alternative name for the standard score or z score, where values are standardised by subtracting the sample or estimated mean and dividing by the sample or other estimate of the standard deviation. Particularly in applications where the name \"normal score\" is used, there is usually a presumption that the value can be referred to a table of standard normal probabilities as a means of providing a significance test of some hypothesis, such as a difference in means.\nThe second meaning of normal score is associated with data values derived from the ranks of the observations within the dataset. A given data point is assigned a value which is either exactly, or an approximation, to the expectation of the order statistic of the same rank in a sample of standard normal random variables of the same size as the observed data set. Thus the meaning of a normal score of this type is essentially the same as a rankit, although the term \"rankit\" is becoming obsolete. In this case the transformation creates a set of values which is matched in a certain way to what would be expected had the original set of data values arisen from a normal distribution.\n\n", "images": [], "links": ["International Standard Book Number", "Normal distribution", "Normal probability plot", "Normalization (statistics)", "Order statistic", "Q-Q plot", "Ranking", "Rankit", "Significance test", "Standard normal random variable", "Standard score", "Statistics", "Z score"], "references": []}, "Akaike information criterion": {"categories": ["All articles containing potentially dated statements", "Articles containing potentially dated statements from October 2014", "CS1 Japanese-language sources (ja)", "Entropy and information", "Model selection", "Regression variable selection", "Scientific modeling"], "title": "Akaike information criterion", "method": "Akaike information criterion", "url": "https://en.wikipedia.org/wiki/Akaike_information_criterion", "summary": "The Akaike information criterion (AIC) is an estimator of the relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to each of the other models. Thus, AIC provides a means for model selection.\nAIC is founded on information theory. When a statistical model is used to represent the process that generated the data, the representation will almost never be exact; so some information will be lost by using the model to represent the process. AIC estimates the relative information lost by a given model: the less information a model loses, the higher the quality of that model. (In making an estimate of the information lost, AIC deals with the trade-off between the goodness of fit of the model and the simplicity of the model.)\nThe Akaike information criterion is named after the statistician Hirotugu Akaike, who formulated it. It now forms the basis of a paradigm for the foundations of statistics; as well, it is widely used for statistical inference.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/bc/Akaike.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akad\u00e9miai Kiad\u00f3", "All models are wrong", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Statistics", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavioral Ecology and Sociobiology", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrics (journal)", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "CRC Press", "Cambridge University Press", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Communications in Statistics", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Current Contents", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Deviance information criterion", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Ecology (journal)", "Econometrics", "Effect size", "Efficiency (statistics)", "Electronic Journal of Statistics", "Elliptical distribution", "Emanuel Parzen", "Empirical distribution function", "Engineering statistics", "Entropy", "Entropy (information theory)", "Environmental statistics", "Epidemiology", "Errors and residuals", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "First order approximation", "Focused information criterion", "Forest plot", "Foundations of statistics", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Gerda Claeskens", "Goodness of fit", "Google Scholar", "Granger causality", "Graphical model", "Grouped data", "Hannan\u2013Quinn information criterion", "Harmonic mean", "Heteroscedasticity", "Hirotugu Akaike", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "I.i.d.", "Independence (probability theory)", "Index of dispersion", "Information theory", "Integration by substitution", "Interaction (statistics)", "International Standard Book Number", "International Statistical Review", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jan de Leeuw", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the Royal Statistical Society, Series B", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kullback\u2013Leibler divergence", "Kurtosis", "L-moment", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-normal distribution", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "Ludwig Boltzmann", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McNemar's test", "Mean", "Mean squared error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural logarithm", "Nature (journal)", "Nelson\u2013Aalen estimator", "Nils Lid Hjort", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Norman Lloyd Johnson", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Overfitting", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principle of maximum entropy", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychological Methods", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Residual sum of squares", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Kotz", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Second Law of Thermodynamics", "Second order approximation", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Sociological Methods & Research", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Springer-Verlag", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen Fienberg", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Univariate", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Web of Science", "Whittle likelihood", "Wilcoxon signed-rank test", "World Scientific", "Z-test"], "references": ["http://www.jds-online.com/file_download/278/JDS-652a.pdf", "http://www.nature.com/top100", "http://gifi.stat.ucla.edu/janspubs/1990/chapters/deleeuw_C_90c.pdf", "http://www.garfield.library.upenn.edu/classics1981/A1981MS54100001.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3366160", "http://www.ncbi.nlm.nih.gov/pubmed/22309957", "http://www.ams.org/mathscinet-getitem?mr=0423716", "http://arxiv.org/abs/math/0602326", "http://doi.org/10.1007%2F978-1-4612-1694-0", "http://doi.org/10.1007%2Fs00265-010-1029-6", "http://doi.org/10.1016%2Fs0167-7152(96)00128-9", "http://doi.org/10.1037%2Fa0027127", "http://doi.org/10.1080%2F03610927808827599", "http://doi.org/10.1093%2Fbiomet%2F76.2.297", "http://doi.org/10.1093%2Fbiomet%2F92.4.937", "http://doi.org/10.1109%2FTAC.1974.1100705", "http://doi.org/10.1111%2Finsr.12052", "http://doi.org/10.1111%2Fj.0006-341X.2001.00120.x", "http://doi.org/10.1177%2F0049124104268644", "http://doi.org/10.1214%2F009053605000000525", "http://doi.org/10.1214%2F14-EJS881", "http://doi.org/10.1890%2F13-0590.1", "http://doi.org/10.1890%2F13-1452.1", "http://www.jstor.org/stable/2984877", "http://www.sortie-nd.org/lme/Statistical%20Papers/Burnham_and_Anderson_2004_Multimodel_Inference.pdf", "https://scholar.google.com/scholar?as_vis=0&q=Akaike+AIC&as_sdt=1,5", "https://wolfweb.unr.edu/~ldyer/classes/396/burnham2011.pdf", "https://projecteuclid.org/euclid.aos/1132936568", "https://pdfs.semanticscholar.org/d1e7/7111d45d4299e91c5b3beb9318a381d4d27c.pdf"]}, "Paired comparison analysis": {"categories": ["Psychometrics"], "title": "Pairwise comparison", "method": "Paired comparison analysis", "url": "https://en.wikipedia.org/wiki/Pairwise_comparison", "summary": "Pairwise comparison generally is any process of comparing entities in pairs to judge which of each entity is preferred, or has a greater amount of some quantitative property, or whether or not the two entities are identical. The method of pairwise comparison is used in the scientific study of preferences, attitudes, voting systems, social choice, public choice, requirements engineering and multiagent AI systems. In psychology literature, it is often referred to as paired comparison.\nProminent psychometrician L. L. Thurstone first introduced a scientific approach to using pairwise comparisons for measurement in 1927, which he referred to as the law of comparative judgment. Thurstone linked this approach to psychophysical theory developed by Ernst Heinrich Weber and Gustav Fechner. Thurstone demonstrated that the method can be used to order items along a dimension such as preference or importance using an interval-type scale.", "images": [], "links": ["Analytic Hierarchy Process", "Bradley\u2013Terry model", "Digital object identifier", "Equivalence relation", "Ernst Heinrich Weber", "Gustav Fechner", "International Standard Book Number", "Just noticeable difference", "L. L. Thurstone", "Law of comparative judgment", "Logistic function", "Logit", "Multiagent AI system", "Neil Sloane", "Ogive (statistics)", "On-Line Encyclopedia of Integer Sequences", "PROMETHEE", "Paired difference test", "Potentially all pairwise rankings of all possible alternatives", "Preference", "Preference (economics)", "Psychology", "Psychometrician", "Public choice", "Quantitative property", "Rasch model", "Requirements engineering", "Social choice", "Spanish Royal Academy of Sciences", "Stirling number of the second kind", "Strict weak order", "Strict weak ordering", "Thomas L. Saaty", "Thurstone scale", "Total preorder", "Voting systems", "XOR"], "references": ["http://www.danko-nikolic.com/wp-content/uploads/2011/09/Nikolic-Transitivity-2007.pdf", "http://resolver.sub.uni-goettingen.de/purl?GDZPPN002370808", "http://www.rac.es/ficheros/doc/00576.PDF", "http://doi.org/10.1007%2Fbf03191825", "https://oeis.org/A000142", "https://oeis.org/A000670"]}, "Generalized multivariate log-gamma distribution": {"categories": ["Continuous distributions", "Multivariate continuous distributions"], "title": "Generalized multivariate log-gamma distribution", "method": "Generalized multivariate log-gamma distribution", "url": "https://en.wikipedia.org/wiki/Generalized_multivariate_log-gamma_distribution", "summary": "In probability theory and statistics, the generalized multivariate log-gamma (G-MVLG) distribution is a multivariate distribution introduced by Demirhan and Hamurkaroglu in 2011. The G-MVLG is a flexible distribution. Skewness and kurtosis are well controlled by the parameters of the distribution. This enables one to control dispersion of the distribution. Because of this property, the distribution is effectively used as a joint prior distribution in Bayesian analysis, especially when the likelihood is not from the location-scale family of distributions such as normal distribution.", "images": [], "links": ["ARGUS distribution", "Absolute value", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian analysis", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Determinant", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "Likelihood", "List of probability distributions", "Location-scale family", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Moment generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Prior distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Risk analysis", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical dispersion", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Trigamma function", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "Type I extreme value distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://doi.org/10.1016%2Fj.jspi.2010.09.015"]}, "Economic statistics": {"categories": ["All articles needing additional references", "All articles with dead external links", "Applied statistics", "Articles needing additional references from July 2007", "Articles with dead external links from September 2017", "Articles with permanently dead external links", "Commons category link from Wikidata", "Mathematical and quantitative methods (economics)", "Social statistics"], "title": "Economic statistics", "method": "Economic statistics", "url": "https://en.wikipedia.org/wiki/Economic_statistics", "summary": "Economic statistics is a topic in applied statistics that concerns the collection, processing, compilation, dissemination, and analysis of economic data. It is also common to call the data themselves 'economic statistics', but for this usage see economic data. The data of concern to economic statistics may include those of an economy of region, country, or group of countries. Economic statistics may also refer to a subtopic of official statistics for data produced by official organizations (e.g. national statistical services, intergovernmental organizations such as United Nations, European Union or OECD, central banks, ministries, etc.). Analyses within economic statistics both make use of and provide the empirical data needed in economic research, whether descriptive or econometric. They are a key input for decision making as to economic policy.\nThe subject includes statistical analysis of topics and problems in microeconomics, macroeconomics, business, finance, forecasting, data quality, and policy evaluation. It also includes such considerations as what data to collect in order to quantify some particular aspect of an economy and of how best to collect in any given instance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f3/Emblem-money.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accounting", "Adam Smith", "Advisory board", "Agricultural economics", "Alfred Marshall", "Annual general meeting", "Applied economics", "Applied statistics", "Arnold Zellner", "Arthur Cecil Pigou", "Asset management", "Audit committee", "Behavioral economics", "Board of directors", "Brand management", "Business", "Business administration", "Business analysis", "Business development", "Business economics", "Business ethics", "Business intelligence", "Business judgment rule", "Business model", "Business operations", "Business plan", "Business process", "Business statistics", "Capacity management", "Capital budgeting", "Cash conversion cycle", "Central bank", "Change management", "Commercial bank", "Commercial law", "Commercial management", "Commodity", "Communications management", "Computational economics", "Configuration management", "Conflict management", "Constitutional documents", "Consumer behaviour", "Content management", "Contract", "Cooperative", "Corporate crime", "Corporate finance", "Corporate governance", "Corporate law", "Corporate liability", "Corporation", "Crisis management", "Cultural economics", "Customer relationship management", "Data analysis", "Data collection", "Data quality", "David Ricardo", "Demographic economics", "Derivative (finance)", "Development economics", "Distributed management", "Earned value management", "Ecological economics", "Econometric", "Econometrics", "Economic data", "Economic development", "Economic forecasting", "Economic geography", "Economic growth", "Economic history", "Economic methodology", "Economic planning", "Economic policy", "Economic sociology", "Economic system", "Economic theory", "Economics", "Economics of digitization", "Economist", "Economy", "Education economics", "Electronic business", "Engineering economics", "Enterprise resource planning", "Environmental economics", "Eric Ghysels", "European Union", "Evolutionary economics", "Expeditionary economics", "Experimental economics", "Factoring (finance)", "Finance", "Financial accounting", "Financial audit", "Financial economics", "Financial institution", "Financial management", "Financial market", "Financial risk", "Financial statement", "Financial statement analysis", "Fran\u00e7ois Quesnay", "Game theory", "Glossary of economics", "Health economics", "Heterodox economics", "Hierarchical organization", "History of economic thought", "Human resource management", "Human resources", "Incident management", "Index of economics articles", "Industrial organization", "Information economics", "Innovation management", "Insider dealing", "Insolvency law", "Institutional economics", "Insurance", "Integrated management", "International Standard Book Number", "International business", "International economics", "International finance", "International trade", "International trade law", "JEL classification codes", "John Maynard Keynes", "John Stuart Mill", "Journal of Business and Economic Statistics", "Karl Marx", "Knowledge economy", "Knowledge management", "Labour economics", "Law and economics", "Legal personality", "Limited liability company", "Liquidation", "List of economics journals", "List of economists", "List of important publications in economics", "List of national and international statistical services", "L\u00e9on Walras", "Macroeconomics", "Mainstream economics", "Management", "Management accounting", "Management information system", "Managerial economics", "Managerial finance", "Market (economics)", "Market economy", "Marketing", "Marketing management", "Marketing research", "Materials management", "Mathematical economics", "Mergers and acquisitions", "Microeconomics", "Mixed economy", "Monetary economics", "National accounts", "Natural resource economics", "Network administrator", "Network management", "OECD", "Office management", "Official statistics", "Open economy", "Operations management", "Operations management for services", "Operations research", "Organization", "Organization development", "Organizational architecture", "Organizational behavior", "Organizational communication", "Organizational conflict", "Organizational culture", "Organizational economics", "Organizational engineering", "Organizational patterns", "Organizational space", "Organizational structure", "Oskar Morgenstern", "Outline of economics", "Partnership", "Paul Samuelson", "Performance management", "Personnel economics", "Planned economy", "Policy analysis", "Political economy", "Power management", "Problem management", "Process management", "Product life-cycle management", "Product management", "Project management", "Public choice", "Public economics", "Public finance", "Public relations", "Quality management", "R. G. D. Allen", "Records management", "Regional economics", "Resource management", "Review of Economics and Statistics", "Risk management", "Ronald J. Wonnacott", "Rural economics", "Sales", "Sales management", "Schools of economic thought", "Security management", "Service economy", "Service management", "Social choice theory", "Socioeconomics", "Sole proprietorship", "State-owned enterprise", "Stock market", "Strategic management", "Supervisory board", "Supply chain management", "Survey of production", "System administrator", "Systems management", "Talent management", "Tax", "Technology management", "Thomas Robert Malthus", "Trade", "United Nations", "Urban economics", "Venture capital", "Welfare", "Welfare economics", "Working capital"], "references": ["http://fxtradeinfocenter.oanda.com/fxeconostats/", "http://orton.catie.ac.cr/cgi-bin/wxis.exe/?IsisScript=MIAGRO.xis&method=post&formato=2&cantidad=1&expresion=mfn=004689", "http://ucblibraries.colorado.edu/govpubs/us/stats.htm", "http://epp.eurostat.ec.europa.eu/portal/page/portal/eurostat/home", "http://pubs.amstat.org/page/jbes/aims-and-scope", "http://www.amstat.org/publications/jbes.cfm", "http://www.centerforfinancialstability.org/hfs.php", "http://www.oecd.org/statistics", "http://www.oecd.org/statistics/understandingeconomicstatistics", "http://unstats.un.org/unsd/goodprac/bpabout.asp", "http://live.unece.org/stats/archive/act.02.e.html", "http://www.unece.org/stats/archive/act.02.e.htm", "https://books.google.com/books?hl=en&lr=&id=JxMj3UcSc_EC&oi=fnd&pg=PR3&dq=onepage&q&f=false#v=onepage&q&f=false", "https://books.google.com/books?hl=en&lr=&id=JxMj3UcSc_EC&oi=fnd&pg=PA628&dq=onepage&q&f=false#v=onepage&q&f=false", "https://books.google.com/books?id=JxMj3UcSc_EC&dq=onepage&lr=&source=gbs_navlinks_s", "https://books.google.com/books?id=Wsu2AAAAIAAJ&source=gbs_ViewAPI", "https://georgewbush-whitehouse.archives.gov/fsbr/esbr.html", "https://archive.is/20120721213836/http://pubs.amstat.org/doi/abs/10.1198/073500102753410345?journalCode=jbes", "https://web.archive.org/web/20120402185757/http://dido.econ.yale.edu/P/cm/m13/m13-16.pdf", "https://www.jstor.org/pss/2551462", "https://www.jstor.org/stable/1928753", "https://www.jstor.org/stable/2964825"]}, "Jackson's theorem (queueing theory)": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from June 2012", "Queueing theory", "Wikipedia articles needing clarification from January 2013"], "title": "Jackson network", "method": "Jackson's theorem (queueing theory)", "url": "https://en.wikipedia.org/wiki/Jackson_network", "summary": "In queueing theory, a discipline within the mathematical theory of probability, a Jackson network (sometimes Jacksonian network) is a class of queueing network where the equilibrium distribution is particularly simple to compute as the network has a product-form solution. It was the first significant development in the theory of networks of queues, and generalising and applying the ideas of the theorem to search for similar product-form solutions in other networks has been the subject of much research, including ideas used in the development of the Internet. The networks were first identified by James R. Jackson and his paper was re-printed in the journal Management Science\u2019s \u2018Ten Most Influential Titles of Management Sciences First Fifty Years.\u2019Jackson was inspired by the work of Burke and Reich, though Jean Walrand notes \"product-form results \u2026 [are] a much less immediate result of the output theorem than Jackson himself appeared to believe in his fundamental paper\".An earlier product-form solution was found by R. R. P. Jackson for tandem queues (a finite chain of queues where each customer must visit each queue in order) and cyclic networks (a loop of queues where each customer must visit each queue in order).A Jackson network consists of a number of nodes, where each node represents a queue in which the service rate can be both node-dependent (different nodes have different service rates) and state-dependent (service rates change depending on queue lengths). Jobs travel among the nodes following a fixed routing matrix. All jobs at each node belong to a single \"class\" and jobs follow the same service-time distribution and the same routing mechanism. Consequently, there is no notion of priority in serving the jobs: all jobs at each node are served on a first-come, first-served basis.\nJackson networks where a finite population of jobs travel around a closed network also have a product-form solution described by the Gordon\u2013Newell theorem.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/Open_jackson_network_%28final%29.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Annals of Mathematical Statistics", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Equilibrium distribution", "Erlang (unit)", "Erlang distribution", "F. P. Kelly", "FIFO (computing and electronics)", "First-come, first-served", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid network", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Geometric distribution", "Gordon F. Newell", "Gordon\u2013Newell network", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "IEEE Transactions on Information Theory", "Information system", "International Standard Book Number", "JSTOR", "James R. Jackson", "Jean Walrand", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 model", "M/M/1 queue", "M/M/c model", "M/M/c queue", "M/M/\u221e queue", "Management Science: A Journal of the Institute for Operations Research and the Management Sciences", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Operations Research (journal)", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability mass function", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Renewal process", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations", "Unit vector", "Utilization"], "references": ["http://www.dtic.mil/dtic/tr/fulltext/u2/296776.pdf", "http://doi.org/10.1093%2Fimaman%2F6.4.382", "http://doi.org/10.1109%2FTIT.1983.1056762", "http://doi.org/10.1214%2Faoms%2F1177706889", "http://doi.org/10.1287%2Fmnsc.1040.0268", "http://doi.org/10.1287%2Fopre.15.2.254", "http://doi.org/10.1287%2Fopre.5.4.518", "http://doi.org/10.2307%2F1425912", "http://doi.org/10.2307%2F1426753", "http://doi.org/10.2307%2F3213702", "http://www.jstor.org/stable/1425912", "http://www.jstor.org/stable/1426753", "http://www.jstor.org/stable/167249", "http://www.jstor.org/stable/168557", "http://www.jstor.org/stable/2237237", "http://www.jstor.org/stable/2627213", "http://www.jstor.org/stable/30046149", "http://www.jstor.org/stable/30046150"]}, "Policy capturing": {"categories": ["All articles lacking sources", "Articles lacking sources from April 2014", "Comparison of assessments", "Recruitment", "Regression analysis"], "title": "Policy capturing", "method": "Policy capturing", "url": "https://en.wikipedia.org/wiki/Policy_capturing", "summary": "Policy capturing or \"the PC technique\" is a statistical method used in social psychology to quantify the relationship between a person's judgement and the information that was used to make that judgement. Policy capturing assessments rely upon regression analysis models. Policy capturing is frequently used by businesses to assess employee performance.\nPolicy capturing is a technique that is used to examine how individuals reach decisions. Policy capturing is regarded as a form of judgment analysis and has been applied to a variety of settings and contexts (see Cooksey, 1996).\nA typical example was reported by Sherer, Schwab and Heneman (1987), in their study of how supervisors, in the setting of a private hospital, reach decisions about salary raises. Participants of this study, called judges, received information about a set of employees. The employees differed on five key factors: performance level was average or superior, performance was consistent or inconsistent, current salary was low, medium, or high, and the individuals either had or had not been offered another job from a different organization. After reading information about each employee, participants then decided whether the percentage and absolute increase in salary they would recommend. Which of these five factors shaped the decisions varied appreciably across the participants.\nHitt and Barr reported another excellent example of policy capturing. This study assessed which factors determine evaluations of job applicants and corresponding salaries. The participants or judges-66 managers who often need to reach similar decisions in their work lives-read the applications of these applicants and watched a video presentation that each candidate had prepared. Several variables differed across applicants: the applicants, for example, had accumulated either 10 or 15 years of experience, were 35 or 35 years of age, were male or female, were African or Caucasian, had completed a BS or MBA, and were applying to be a regional sales manager or vice president of sales. Subsequent analysis showed that factors unrelated to experience, such as age and sex, affected decisions. Furthermore, the relevance of each factor interacted with one another.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Analysis", "Linear programming", "Mathematical modelling", "Regression analysis", "Statistics"], "references": []}, "Free statistical software": {"categories": ["All pages needing cleanup", "Articles needing cleanup from February 2013", "CS1 maint: Multiple names: authors list", "Cleanup tagged articles with a reason field from February 2013", "Free statistical software", "Wikipedia articles incorporating text from Citizendium", "Wikipedia pages needing cleanup from February 2013"], "title": "Free statistical software", "method": "Free statistical software", "url": "https://en.wikipedia.org/wiki/Free_statistical_software", "summary": "Free statistical software is a practical alternative to commercial packages. In general, free statistical software gives results that are the same as the results from commercial programs, and many of the packages are fairly easy to learn, using menu systems, although a few are command-driven. These packages come from a variety of sources, including governments, nongovernmental organizations (NGOs) like UNESCO, and universities, and are also developed by individuals.\nSome packages are developed for specific purposes (e.g., time series analysis, factor analysis, calculators for probability distributions, etc.), while others are general packages, with a variety of statistical procedures. Others are meta-packages or statistical computing environments, which allow the user to code completely new statistical procedures. This article is a review of the general statistical packages.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["ADMB", "Advanced Simulation Library", "Analyse-it", "BMDP", "BV4.1 (software)", "CSPro", "Centers for Disease Control and Prevention", "Chapel (programming language)", "Citizendium", "Comma-separated values", "Commercial software", "Comparison of numerical analysis software", "Comparison of statistical packages", "Correlation", "Cross-platform", "CumFreq", "DADiSP", "DAP (software)", "DataMelt", "Data Desk", "Dataplot", "Digital object identifier", "EViews", "Epi Info", "Euler (software)", "FEATool Multiphysics", "Fortress (programming language)", "FreeFem++", "FreeMat", "Free software", "Freeware", "GAUSS (software)", "GNU Octave", "GNU Project", "GenStat", "Genius (mathematics software)", "Gmsh", "Government", "GraphPad InStat", "GraphPad Prism", "Gretl", "Groovy (programming language)", "H2O (software)", "IDAMS", "International Standard Book Number", "JASP", "JMP (statistical software)", "JMulTi", "JRuby", "Java (programming language)", "Journal of Statistical Software", "Julia (programming language)", "Just another Gibbs sampler", "Jython", "LIMDEP", "LISREL", "LabVIEW", "List of numerical analysis software", "List of statistical packages", "List of statistical software", "MATLAB", "MFEM", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "Maxima (software)", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Missing data", "NCSS (statistical software)", "NGO", "Nongovernmental organization", "Open-source software", "OpenBUGS", "OpenFOAM", "Orange (software)", "OxMetrics", "PSPP", "Proprietary software", "PubMed Central", "PubMed Identifier", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Regression analysis", "Revolution Analytics", "S-PLUS", "SAS (software)", "SCaVis", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "Salome (software)", "ScicosLab", "Scilab", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Speakeasy (computational environment)", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistics", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNESCO", "UNISTAT", "University", "VisSim", "Weka (machine learning)", "WinBUGS", "WinIDAMS", "Wolfram Mathematica", "World Programming System", "X-12-ARIMA", "X10 (programming language)", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.biochempress.com/cv07_i03.html", "http://www.biomedcentral.com/1471-2105/9/106", "http://sirpabs.ilahas.com/ebooks/Computer%20&%20Technology/Irristat%20Tutorial.pdf", "http://www.ingentaconnect.com/content/beech/rev/2007/00000016/00000001/art00004", "http://www.microsiris.com/", "http://www.microsiris.com/MicrOsiris.htm", "http://www.sas.com/", "http://www.scientific-computing.com/scwsepoct04free_statistics.html", "http://www.scientificcomputing.com/comparative-statistical-software.aspx", "http://www.sofastatistics.com/home.php", "http://www.spss.com/", "http://www.statistics.com/resources/software/commercial/fulllist.php3", "http://statistiksoftware.com/free_software.html", "http://www.brown.edu/Departments/Economics/Papers/Papers/2003/2003-16_paper.pdf", "http://www.cccco.edu/SystemOffice/Divisions/TechResearchInfo/ResearchandPlanning/AbstractsofResearch/ResearchMethods/tabid/302/Default.aspx", "http://lib.stat.cmu.edu/R/CRAN/doc/FAQ/R-FAQ.html", "http://www.sph.emory.edu/~cdckms/", "http://www.galaxy.gmu.edu/", "http://GKing.Harvard.Edu/zelig", "http://www.math.ilstu.edu/dhkim/Rstuff/Rtutor.html", "http://econ.la.psu.edu/~hbierens/EASYREG.HTM", "http://econ.la.psu.edu/~hbierens/ERITOURS.HTM", "http://dsdr-kb.psc.isr.umich.edu/answer.html?i=1076", "http://forrest.psych.unc.edu/research/", "http://nccphp.sph.unc.edu/training/index.html", "http://gpvec.unl.edu/videos/epi-stats.asp", "http://economicsbulletin.vanderbilt.edu/2008/volume3/EB-08C30021A.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1839133", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2323673", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2350113", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2447931", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2519268", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2587528", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC538959", "http://www.ncbi.nlm.nih.gov/pubmed/15618195", "http://www.ncbi.nlm.nih.gov/pubmed/17266762", "http://www.ncbi.nlm.nih.gov/pubmed/18284666", "http://www.ncbi.nlm.nih.gov/pubmed/18464900", "http://www.ncbi.nlm.nih.gov/pubmed/18586972", "http://www.ncbi.nlm.nih.gov/pubmed/18618019", "http://www.ncbi.nlm.nih.gov/pubmed/18780840", "http://www.ncbi.nlm.nih.gov/pubmed/18834901", "http://www.evaluation.lars-balzer.name/links/tools-free-no-cost/statistical-software/english-language/", "http://statistics.altervista.org/?p=comp", "http://jama.ama-assn.org/cgi/reprint/300/10/1131", "http://aem.asm.org/cgi/content/abstract/74/16/5241", "http://iai.asm.org/cgi/content/full/73/1/552", "http://repositories.cdlib.org/postprints/1865.", "http://doi.org/10.1001%2Fjama.300.10.1131", "http://doi.org/10.1016%2Fj.ijforecast.2005.02.003", "http://doi.org/10.1016%2Fj.neuro.2008.08.008", "http://doi.org/10.1016%2Fj.respol.2006.04.004", "http://doi.org/10.1111%2Fj.1741-3737.2005.00196.x", "http://doi.org/10.1128%2Faem.02580-07", "http://doi.org/10.1128%2Fiai.73.1.552-562.2005", "http://doi.org/10.1186%2F1471-2105-9-106", "http://doi.org/10.1186%2Fgb-2007-8-1-r14", "http://doi.org/10.3152%2F095820207x196768", "http://www.fao.org/DOCREP/005/Y4391E/y4391e00.htm", "http://lists.gnu.org/mailman/listinfo/pspp-users", "http://gsociology.icaap.org/methods/soft.html", "http://www.jstatsoft.org/", "http://jwork.org/dmelt/wikidoc/", "http://www.nait.org/jit/current.html", "http://personality-project.org/r/", "http://statpages.org/javasta2.html", "http://www.statpages.org/miller/openstat/", "http://www.statsci.org/free.html", "http://portal.unesco.org/ci/en/ev.php-URL_ID=17447&URL_DO=DO_TOPIC&URL_SECTION=201.html", "http://portal.unesco.org/ci/en/ev.php-URL_ID=2070&URL_DO=DO_TOPIC&URL_SECTION=201.html", "http://portal.unesco.org/ci/en/ev.php-URL_ID=25081&URL_DO=DO_TOPIC&URL_SECTION=-465.html", "http://www.unesco.org/webworld/idams/advguide/TOC.htm", "http://www.unesco.org/webworld/idams/selfteaching/eng/emissing-data.htm", "http://www.unesco.org/webworld/portal/idams/html/english/TOC.htm", "http://www2.napier.ac.uk/depts/fhls/peas/rpackage.asp", "http://www.ssc.rdg.ac.uk/software/instat/instat.html", "https://stat.ethz.ch/mailman/listinfo/r-help", "https://www.springer.com/computer/book/978-1-84996-286-5", "https://www.cdc.gov/EID/content/13/11/1791.htm", "https://www.cdc.gov/EID/content/13/9/1361.htm", "https://www.cdc.gov/cogh/dgphcd/training/softwaretraining.htm", "https://www.cdc.gov/epiinfo/communityhealth.htm", "https://www.cdc.gov/epiinfo/index.htm", "https://www.gnu.org/software/pspp/", "https://www.gnu.org/software/pspp/documentation.html", "https://cran.r-project.org/", "https://cran.r-project.org/doc/manuals/R-intro.html", "https://cran.r-project.org/other-docs.html"]}, "False nearest neighbor algorithm": {"categories": ["Algorithms and data structures stubs", "All Wikipedia articles needing context", "All pages needing cleanup", "All stub articles", "Computer science stubs", "Dynamical systems", "Nonlinear time series analysis", "Statistical algorithms", "Wikipedia articles needing context from October 2009", "Wikipedia introduction cleanup from October 2009"], "title": "False nearest neighbor algorithm", "method": "False nearest neighbor algorithm", "url": "https://en.wikipedia.org/wiki/False_nearest_neighbor_algorithm", "summary": "The false nearest neighbor algorithm is an algorithm for estimating the embedding dimension. The concept was proposed by Kennel et al. The main idea is to examine how the number of neighbors of a point along a signal trajectory change with increasing embedding dimension. In too low an embedding dimension, many of the neighbors will be false, but in an appropriate embedding dimension or higher, the neighbors are real. With increasing dimension, the false neighbors will no longer be neighbors. Therefore, by examining how the number of neighbors change as a function of dimension, an appropriate embedding can be determined.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f7/Binary_tree.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Algorithm", "Bibcode", "Data structure", "Digital object identifier", "Embedding dimension", "Nearest neighbor (disambiguation)", "PubMed Identifier", "Time series"], "references": ["http://adsabs.harvard.edu/abs/1992PhRvA..45.3403K", "http://adsabs.harvard.edu/abs/1999PhRvE..60.4970H", "http://www.ncbi.nlm.nih.gov/pubmed/9907388", "http://doi.org/10.1016%2FS0098-1354(97)87657-0", "http://doi.org/10.1103%2FPhysRevA.45.3403", "http://doi.org/10.1103%2FPhysRevE.60.4970"]}, "Skorokhod's representation theorem": {"categories": ["Probability theorems", "Statistical theorems"], "title": "Skorokhod's representation theorem", "method": "Skorokhod's representation theorem", "url": "https://en.wikipedia.org/wiki/Skorokhod%27s_representation_theorem", "summary": "In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well-behaved can be represented as the distribution/law of a pointwise convergent sequence of random variables defined on a common probability space. It is named for the soviet mathematician A. V. Skorokhod.", "images": [], "links": ["Anatoliy Skorokhod", "Convergence of random variables", "International Standard Book Number", "Mathematician", "Mathematics", "Metric space", "Pointwise convergence", "Probability measure", "Probability space", "Random variable", "Separable space", "Sequence", "Soviet Union", "Statistics", "Support (measure theory)", "Weak convergence of measures"], "references": []}, "Selective recruitment": {"categories": ["All articles lacking in-text citations", "All articles lacking sources", "All articles with style issues", "Articles lacking in-text citations from February 2011", "Articles lacking sources from December 2009", "Car safety", "Sampling (statistics)", "Wikipedia articles with style issues from January 2011"], "title": "Selective recruitment", "method": "Selective recruitment", "url": "https://en.wikipedia.org/wiki/Selective_recruitment", "summary": "Selective recruitment is an observed effect in traffic safety. When safety belt laws are passed, belt wearing rates increase, but casualties decline by smaller percentages than estimated in a simple calculation. This is because those converted from non-use to use are not \u201crecruited\u201d random members of the driving population. Instead, users differ from non-users in many ways that influence safety. Two effects are:\n\n1.\tWhen non-wearers crash, they have more severe crashes.\n2.\tNon-wearers are more likely to crash", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Risk compensation", "Traffic Safety (book)", "Traffic safety"], "references": []}, "Reliability block diagram": {"categories": ["All articles with dead external links", "Articles with dead external links from April 2018", "Articles with permanently dead external links", "Engineering statistics", "Reliability engineering"], "title": "Reliability block diagram", "method": "Reliability block diagram", "url": "https://en.wikipedia.org/wiki/Reliability_block_diagram", "summary": "A reliability block diagram (RBD) is a diagrammatic method for showing how component reliability contributes to the success or failure of a complex system. RBD is also known as a dependence diagram (DD).\n\nAn RBD or DD is drawn as a series of blocks connected in parallel or series configuration. Each block represents a component of the system with a failure rate. Parallel paths are redundant, meaning that all of the parallel paths must fail for the parallel network to fail. By contrast, any failure along a series path causes the entire series path to fail.An RBD may be drawn using switches in place of blocks, where a closed switch represents a working component and an open switch represents a failed component. If a path may be found through the network of switches from beginning to end, the system still works.\nAn RBD may be converted to a success tree by replacing series paths with AND gates and parallel paths with OR gates. A success tree may then be converted to a fault tree by applying de Morgan's theorem.\nIn order to evaluate RBD, closed form solution are available in the case of statistical independence among blocks or components.\nIn the case the statistical independence assumption is not satisfied, specific formalisms and solution tools, such as dynamic RBD, have to be considered.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/03/Reliability_block_diagram.png"], "links": ["ARP4761", "And gate", "Block diagram", "Complex system", "De Morgan's laws", "Diagrammatic", "Failure rate", "Fault Tree Analysis", "International Standard Book Number", "Or gate", "Redundancy (engineering)", "Reliability engineering", "Series and parallel circuits", "System safety", "United States Department of Defense"], "references": ["http://www.reliabilityeducation.com/rbd.pdf", "http://www.imdr.fr/submitted/document_site/Method_sheets_EN_343.pdf", "http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4385723", "https://books.google.com/books?id=IZ5VKc-Y4_4C&pg=PA198", "https://assist.daps.dla.mil/quicksearch/basic_profile.cfm?ident_number=54022", "https://web.archive.org/web/20110722222601/https://assist.daps.dla.mil/quicksearch/basic_profile.cfm?ident_number=54022"]}, "Language model": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2017", "CS1 maint: Uses authors parameter", "Language modeling", "Markov models", "Statistical natural language processing", "Wikipedia articles needing clarification from November 2018"], "title": "Language model", "method": "Language model", "url": "https://en.wikipedia.org/wiki/Language_model", "summary": "A statistical language model is a probability distribution over sequences of words. Given such a sequence, say of length m, it assigns a probability \n \n \n \n P\n (\n \n w\n \n 1\n \n \n ,\n \u2026\n ,\n \n w\n \n m\n \n \n )\n \n \n {\\displaystyle P(w_{1},\\ldots ,w_{m})}\n to the whole sequence. Having a way to estimate the relative likelihood of different phrases is useful in many natural language processing applications, especially ones that generate text as an output. Language modeling is used in speech recognition, machine translation, part-of-speech tagging, parsing, Optical Character Recognition, handwriting recognition, information retrieval and other applications.\nIn speech recognition, the computer tries to match sounds with word sequences. The language model provides context to distinguish between words and phrases that sound similar. For example, in American English, the phrases \"recognize speech\" and \"wreck a nice beach\" are pronounced almost the same but mean very different things. These ambiguities are easier to resolve when evidence from the language model is incorporated with the pronunciation model and the acoustic model.\nLanguage models are used in information retrieval in the query likelihood model. Here a separate language model is associated with each document in a collection. Documents are ranked based on the probability of the query Q in the document's language model \n \n \n \n P\n (\n Q\n \u2223\n \n M\n \n d\n \n \n )\n \n \n {\\displaystyle P(Q\\mid M_{d})}\n . Commonly, the unigram language model is used for this purpose\u2014otherwise known as the bag of words model.\nData sparsity is a major problem in building language models. Most possible word sequences will not be observed in training. One solution is to make the assumption that the probability of a word only depends on the previous n words. This is known as an n-gram model or unigram model when n = 1.", "images": [], "links": ["Acoustic model", "Advances in Neural Information Processing Systems", "American English", "ArXiv", "Artificial neural network", "Backpropagation", "Bag of words model", "Cache language model", "CiteSeerX", "Compositionality", "Curse of dimensionality", "Distributed representation", "Document", "Exponential growth", "Factored language model", "Feature vector", "Feedforward neural network", "Finite-state machine", "Good-Turing discounting", "Handwriting recognition", "Heaps' law", "Information retrieval", "International Standard Book Number", "Katz's back-off model", "Kneser\u2013Ney smoothing", "Linear combination", "Linear interpolation", "Machine translation", "Markov property", "N-gram", "Natural language processing", "Nearest neighbor search", "OpenFst", "Optical Character Recognition", "Parsing", "Part-of-speech tagging", "Partition function (mathematics)", "Positional language model", "Principle of maximum entropy", "Probabilistic classifier", "Probability distribution", "Query likelihood model", "Randomised language modeling", "Recurrent neural network", "Relative likelihood", "Scholarpedia", "Skip-gram", "Speech recognition", "Statistical model", "Stochastic gradient descent", "Unigram", "Uninformative prior", "Word2vec", "Word embedding"], "references": ["http://papers.nips.cc/paper/5021-distributed-representations-of-words-and-phrases-and-their-compositionality.pdf", "http://trimc-nlp.blogspot.com/2013/04/language-modeling.html", "http://www.keithv.com/software/csr/", "http://kheafield.com/code/kenlm", "http://www.phontron.com/kylm", "http://www.cs.columbia.edu/~mcollins/", "http://nlg.isi.edu/software/nplm", "http://openfst.cs.nyu.edu/twiki/bin/view/GRM/NGramLibrary", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.4237", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.131.5458", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.6467", "http://sifaka.cs.uiuc.edu/~ylv2/pub/plm/plm.htm", "http://times.cs.uiuc.edu/czhai/pub/sigir09-PLM.pdf", "http://www-lium.univ-lemans.fr/cslm", "http://www.ngram.info/", "http://karpathy.github.io/2015/05/21/rnn-effectiveness/", "http://sourceforge.net/projects/irstlm", "http://sourceforge.net/projects/randlm", "http://arxiv.org/abs/1301.3781", "http://rnnlm.org", "http://www.scholarpedia.org/article/Neural_net_language_models", "https://lmsharp.codeplex.com/", "https://gigaom.com/2013/08/16/were-on-the-cusp-of-deep-learning-for-the-masses-you-can-thank-google-later/", "https://github.com/jnory/DALM", "https://github.com/pauldb89/OxLM", "https://code.google.com/p/mitlm", "https://vsiivola.github.io/variKN", "https://web.archive.org/web/20120302151523/http://www-speech.sri.com/projects/srilm/"]}, "Thurstone scale": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from August 2010", "Psychometrics", "Questionnaire construction", "Social research"], "title": "Thurstone scale", "method": "Thurstone scale", "url": "https://en.wikipedia.org/wiki/Thurstone_scale", "summary": "In psychology and sociology, the Thurstone scale was the first formal technique to measure an attitude. It was developed by Louis Leon Thurstone in 1928, as a means of measuring attitudes towards religion. It is made up of statements about a particular issue, and each statement has a numerical value indicating how favorable or unfavorable it is judged to be. People check each of the statements to which they agree, and a mean score is computed, indicating their attitude.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Attitude (psychology)", "Bogardus scale", "Diamond of opposites", "Earl Babbie", "Guttman scale", "International Standard Book Number", "Law of comparative judgment", "Likert scale", "Louis Leon Thurstone", "Mean", "Normal distribution", "Psychology", "Rasch model", "Religion", "Semantic differential", "Sociology", "Thurstonian model"], "references": ["http://www.visualstatistics.net/Readings/Thurstone%20Crimes%20Scale/Thurstone%20Crimes%20Scale.htm", "https://web.archive.org/web/20090215012052/http://www.visualstatistics.net/Scaling/Domain%20Referenced%20Scaling/Domain-Referenced%20Scaling.htm"]}, "Panel data": {"categories": ["Mathematical and quantitative methods (economics)", "Multivariate time series", "Panel data", "Statistical data types"], "title": "Panel data", "method": "Panel data", "url": "https://en.wikipedia.org/wiki/Panel_data", "summary": "In statistics and econometrics, panel data or longitudinal data are multi-dimensional data involving measurements over time. Panel data contain observations of multiple phenomena obtained over multiple time periods for the same firms or individuals.\nTime series and cross-sectional data can be thought of as special cases of panel data that are in one dimension only (one panel member or individual for the former, one time point for the latter).\nA study that uses panel data is called a longitudinal study or panel study.", "images": [], "links": ["Arellano\u2013Bond estimator", "British Household Panel Survey", "China Family Panel Studies", "Cross-sectional data", "Data set", "Digital object identifier", "Econometrics", "Endogeneity (econometrics)", "Exogeneity (econometrics)", "First-difference estimator", "Fixed effects model", "Generalized least squares", "German Family Panel", "Household, Income and Labour Dynamics in Australia Survey", "International Standard Book Number", "Journal of Econometrics", "Korean Labor and Income Panel Study", "Korean Longitudinal Study of Aging", "Korean Youth Panel", "LLMDB", "Labour Force Survey", "Lag operator", "Longitudinal study", "Multidimensional panel data", "National Longitudinal Surveys", "Panel Study of Income Dynamics", "Panel analysis", "Panel study", "Random effects model", "Russia Longitudinal Monitoring Survey", "Socio-Economic Panel", "Statistics", "Survey of Family Income and Employment", "Survey of Income and Program Participation", "Time series"], "references": ["http://psidonline.isr.umich.edu/", "http://www.kli.re.kr/klips/", "http://doi.org/10.1016%2F0304-4076(94)01649-K", "https://15writers.com/free-products/", "https://www.lissdata.nl/Home", "https://web.archive.org/web/20110719101922/http://www.pairfam.uni-bremen.de/en/study.html", "https://web.archive.org/web/20140416182301/http://survey.keis.or.kr/ENCOMAM0000N.do"]}, "Circular distribution": {"categories": ["Directional statistics", "Statistical charts and diagrams", "Types of probability distributions"], "title": "Circular distribution", "method": "Circular distribution", "url": "https://en.wikipedia.org/wiki/Circular_distribution", "summary": "In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range [0, 2\u03c0). A circular distribution is often a continuous probability distribution, and hence has a probability density, but such distributions can also be discrete, in which case they are called circular lattice distributions. Circular distributions can be used even when the variables concerned are not explicitly angles: the main consideration is that there is not usually any real distinction between events occurring at the lower or upper end of the range, and the division of the range could notionally be made at any point.\n\n", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular mean", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Curve", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Graphonomics", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slant (handwriting)", "Slash distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.codeproject.com/Articles/190833/Circular-Values-Math-and-Statistics-with-Cplusplus"]}, "Efficiency (statistics)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "Articles with unsourced statements from January 2012", "Estimation theory"], "title": "Efficiency (statistics)", "method": "Efficiency (statistics)", "url": "https://en.wikipedia.org/wiki/Efficiency_(statistics)", "summary": "In the comparison of various statistical procedures, efficiency is a measure of quality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator, experiment, or test needs fewer observations than a less efficient one to achieve a given performance. This article primarily deals with efficiency of estimators.\nThe relative efficiency of two procedures is the ratio of their efficiencies, although often this concept is used where the comparison is made between a given procedure and a notional \"best possible\" procedure. The efficiencies and the relative efficiency of two procedures theoretically depend on the sample size available for the given procedure, but it is often possible to use the asymptotic relative efficiency (defined as the limit of the relative efficiencies as the sample size grows) as the principal comparison measure.\nEfficiencies are often defined using the variance or mean square error as the measure of desirability.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptote", "Asymptotic analysis", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Cram\u00e9r\u2013Rao bound", "Cram\u00e9r\u2013Rao inequality", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Dominating decision rule", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficient estimator", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Estimator bias", "Experiment", "Experimental design", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher information", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann efficiency", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis testing", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-estimator", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean square error", "Mean squared error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum variance unbiased estimator", "Missing data", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "OCLC", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pitman closeness criterion", "Pitman efficiency", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.math.binghamton.edu/arcones/prep/pv.pdf", "http://faculty.wcas.northwestern.edu/~iac879/wp/HL.pdf", "http://www.encyclopediaofmath.org/index.php/Bahadur_efficiency", "http://www.encyclopediaofmath.org/index.php/Efficiency,_asymptotic", "http://www.jstor.org/stable/91208", "http://www.worldcat.org/oclc/183886598", "https://www.encyclopediaofmath.org/index.php?title=E/e035070", "https://www.encyclopediaofmath.org/index.php?title=E/e035080"]}, "Modifiable areal unit problem": {"categories": ["All articles lacking reliable references", "All articles with unsourced statements", "Articles lacking reliable references from August 2018", "Articles with unsourced statements from January 2018", "Bias", "Geographic information systems", "Spatial data analysis"], "title": "Modifiable areal unit problem", "method": "Modifiable areal unit problem", "url": "https://en.wikipedia.org/wiki/Modifiable_areal_unit_problem", "summary": "The modifiable areal unit problem (MAUP) is a source of statistical bias that can significantly impact the results of statistical hypothesis tests. MAUP affects results when point-based measures of spatial phenomena are aggregated into districts, for example, population density or illness rates. The resulting summary values (e.g., totals, rates, proportions, densities) are influenced by both the shape and scale of the aggregation unit.For example, census data may be aggregated into county districts, census tracts, postcode areas, police precincts, or any other arbitrary spatial partition. Thus the results of data aggregation are dependent on the mapmaker's choice of which \"modifiable areal unit\" to use in their analysis. A census choropleth map calculating population density using state boundaries will yield radically different results than a map that calculates density based on county boundaries. Furthermore, census district boundaries are also subject to change over time, meaning the MAUP must be considered when comparing past data to current data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/16/CC-BY_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/ab/Maup_rate_numbers.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Aggregate data", "Annals of the Association of American Geographers", "Boundary problem (in spatial analysis)", "Choropleth map", "Correlation", "Digital object identifier", "Ecological fallacy", "Gerrymandering", "Human geography", "Illness rate", "Institute of British Geographers", "International Standard Book Number", "OCLC", "Papers in Regional Science", "Population density", "Progress in Human Geography", "Regression analysis", "Representation theory", "Spatial analysis", "Spatial autocorrelation", "Spatial econometrics", "Spatial epidemiology", "Spatial statistics", "Stan Openshaw", "Statistical bias", "Statistical hypothesis test", "Transportation Research Board"], "references": ["http://support.esri.com/other-resources/gis-dictionary/term/MAUP", "http://wiki.gis.com/wiki/index.php/Modifiable_areal_unit_problem", "http://sustainability.water.ca.gov/documents/3380372/3384417/Excess+Commuting+and+the+Modifiable+Areal+Unit+Problem.pdf", "http://www.badpets.net/Thesis", "http://doi.org/10.1068%2Fb34033", "http://doi.org/10.1080%2F00045608.2012.687349", "http://doi.org/10.1080%2F00420980220099113", "http://doi.org/10.1111%2Fj.1435-5957.2011.00350.x", "http://doi.org/10.1111%2Fj.1538-4632.1996.tb00933.x", "http://doi.org/10.1177%2F030913259602000408", "http://doi.org/10.2307%2F2277827", "http://doi.org/10.3141%2F1902-09", "http://meipokwan.org/Paper/Kwan_UGCoP_2012.pdf", "http://www.worldcat.org/oclc/12052482", "http://www.worldcat.org/oclc/30895028", "http://www.worldcat.org/oclc/85898184", "http://core.ac.uk/download/pdf/6234148.pdf", "https://app.box.com/s/a84w16x7hffljjvkhtlr72eisj4qiene", "https://books.google.com/books?hl=en&lr=&id=phEgXfbCU_YC&pg=PA105", "https://www.census.gov/geo/reference/boundary-changes.html", "https://www.researchgate.net/profile/David_Unwin/publication/237238258_GIS_spatial_analysis_and_spatial_statistics/links/02e7e52d3f953cfbad000000.pdf", "https://www.researchgate.net/profile/Neil_Wrigley/publication/229876830_Aggregation_and_Ecological_Effects_in_Geographically_Based_Data/links/543fbd930cf2fd72f99d7709.pdf", "https://creativecommons.org/licenses/by/3.0/"]}, "Dudley's theorem": {"categories": ["Entropy", "Theorems regarding stochastic processes"], "title": "Dudley's theorem", "method": "Dudley's theorem", "url": "https://en.wikipedia.org/wiki/Dudley%27s_theorem", "summary": "In probability theory, Dudley\u2019s theorem is a result relating the expected upper bound and regularity properties of a Gaussian process to its entropy and covariance structure.", "images": [], "links": ["Continuous stochastic process", "Covariance", "Digital object identifier", "Entropy", "Entropy number", "Expected value", "Gaussian process", "International Standard Book Number", "Mathematical Reviews", "Michel Talagrand", "Probability theory", "Pseudometric space", "Richard M. Dudley", "Upper bound", "Volker Strassen"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0220340", "http://www.ams.org/mathscinet-getitem?mr=1102015", "http://doi.org/10.1016%2F0022-1236(67)90017-1"]}, "Fleiss' kappa": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2015", "Articles with unsourced statements from June 2017", "Categorical variable interactions", "Good articles", "Inter-rater reliability"], "title": "Fleiss' kappa", "method": "Fleiss' kappa", "url": "https://en.wikipedia.org/wiki/Fleiss%27_kappa", "summary": "Fleiss' kappa (named after Joseph L. Fleiss) is a statistical measure for assessing the reliability of agreement between a fixed number of raters when assigning categorical ratings to a number of items or classifying items. This contrasts with other kappas such as Cohen's kappa, which only work when assessing the agreement between not more than two raters or the interrater reliability for one appraiser versus themself. The measure calculates the degree of agreement in classification over that which would be expected by chance. There is no generally agreed-upon measure of significance, although guidelines have been given.\nFleiss' kappa can be used only with binary or nominal-scale ratings. No version is available for ordered-categorical ratings.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg", "https://upload.wikimedia.org/wikipedia/en/9/94/Symbol_support_vote.svg"], "links": ["Categorical rating", "Cohen's kappa", "Inter-rater reliability", "International Standard Book Number", "Joseph L. Fleiss", "Matrix (mathematics)", "Matthews correlation coefficient", "Nominal data", "Pearson product-moment correlation coefficient", "Scott's pi", "Statistical", "Statistical measure", "Youden's J statistic"], "references": ["http://www.agreestat.com/book_excerpts.html", "http://www.agreestat.com/research_papers/bjmsp2008_interrater.pdf", "http://www.john-uebersax.com/stat/kappa.htm", "http://justus.randolph.name/kappa"]}, "Generalized Procrustes analysis": {"categories": ["All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from August 2018", "Biometrics", "Euclidean symmetries", "Multivariate statistics", "Wikipedia articles that are too technical from August 2018"], "title": "Generalized Procrustes analysis", "method": "Generalized Procrustes analysis", "url": "https://en.wikipedia.org/wiki/Generalized_Procrustes_analysis", "summary": "Generalized Procrustes analysis (GPA) is a method of statistical analysis that can be used to compare the shapes of objects, or the results of surveys, interviews, or panels. It was developed for analysing the results of free-choice profiling, a survey technique which allows respondents (such as sensory panelists) to describe a range of products in their own words or language. GPA is one way to make sense of free-choice profiling data; other ways can be multiple factor analysis (MFA), or the STATIS method. The method was first published by J. C. Gower in 1975.Generalized Procrustes analysis estimates the scaling factor applied to respondent scale usage, generating a weighting factor that is used to compensate for individual scale usage differences. Unlike measures such as a principal component analysis, GPA uses individual level data and a measure of variance is utilized in the analysis.\nThe Procrustes distance provides a metric to minimize in order to superimpose a pair of shape instances annotated by landmark points. GPA applies the Procrustes analysis method to superimpose a population of shapes instead of only two shape instances. \nThe algorithm outline is the following:\n\narbitrarily choose a reference shape (typically by selecting it among the available instances)\nsuperimpose all instances to current reference shape\ncompute the mean shape of the current set of superimposed shapes\nif the Procrustes distance between the mean shape and the reference is above a certain threshold, set the reference to mean shape and continue to step 2.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Digital object identifier", "Free-choice profiling", "International Standard Book Number", "Landmark point", "Multiple factor analysis", "Orthogonal Procrustes problem", "Principal component analysis", "Procrustes analysis", "Procrustes distance", "Procrustes superimposition", "Sensory analysis", "Statistical analysis"], "references": ["http://doi.org/10.1002%2F9780470277539", "http://doi.org/10.1007%2FBF02291478", "http://doi.org/10.1016%2F0167-9473(94)90134-1", "http://doi.org/10.1016%2F0167-9473(94)90135-X"]}, "Stratonovich integral": {"categories": ["All articles with unsourced statements", "Articles with inconsistent citation formats", "Articles with unsourced statements from September 2016", "Definitions of mathematical integration", "Stochastic calculus"], "title": "Stratonovich integral", "method": "Stratonovich integral", "url": "https://en.wikipedia.org/wiki/Stratonovich_integral", "summary": "In stochastic processes, the Stratonovich integral (developed simultaneously by Ruslan Stratonovich and Donald Fisk) is a stochastic integral, the most common alternative to the It\u00f4 integral. Although the It\u00f4 integral is the usual choice in applied mathematics, the Stratonovich integral is frequently used in physics.\nIn some circumstances, integrals in the Stratonovich definition are easier to manipulate. Unlike the It\u00f4 calculus, Stratonovich integrals are defined such that the chain rule of ordinary calculus holds.\nPerhaps the most common situation in which these are encountered is as the solution to Stratonovich stochastic differential equations (SDEs). These are equivalent to It\u00f4 SDEs and it is possible to convert between the two whenever one definition is more convenient.", "images": [], "links": ["Adapted process", "Bernt \u00d8ksendal", "Chain rule", "Convergence in mean", "Differentiable manifold", "Digital object identifier", "Donald Fisk", "Euler\u2013Maruyama method", "Filtration (abstract algebra)", "International Standard Book Number", "It\u00f4's lemma", "It\u00f4 calculus", "Langevin equation", "Limit (mathematics)", "Numerical integration", "Partition of an interval", "Quadratic variation", "Riemann integral", "Riemann sum", "Riemann\u2013Stieltjes integral", "Ruslan Stratonovich", "Semimartingale", "Springer-Verlag", "Stochastic calculus", "Stochastic differential equation", "Stochastic integral", "Stochastic process", "Supersymmetric theory of stochastic dynamics", "Wiener process", "Wong\u2013Zakai theorem"], "references": ["http://www.mdpi.com/1099-4300/18/4/108", "http://doi.org/10.1103%2FPhysRevE.81.032104", "http://doi.org/10.3390%2Fe18040108", "https://journals.aps.org/pre/abstract/10.1103/PhysRevE.81.032104"]}, "ASReml": {"categories": ["All stub articles", "Science software stubs", "Statistical software"], "title": "ASReml", "method": "ASReml", "url": "https://en.wikipedia.org/wiki/ASReml", "summary": "ASReml is a statistical software package for fitting linear mixed models using restricted maximum likelihood, a technique commonly used in plant and animal breeding and quantitative genetics as well as other fields. It is notable for its ability to fit very large and complex data sets efficiently, due to its use of the average information algorithm \nand sparse matrix methods.\nIt was originally developed by Arthur Gilmour.ASREML can be used in Windows, Linux, and as an add-on to S-PLUS and R.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/75/Science-symbol-2.svg"], "links": ["Animal breeding", "Data set", "Mixed model", "Plant breeding", "Quantitative genetics", "R (programming language)", "Restricted maximum likelihood", "S-PLUS", "Scientific software", "Sparse matrix"], "references": ["http://www.cargovale.com.au/ASReml/faq.htm", "http://www.scientific-computing.com/products/review_details.php?review_id=2", "http://uncronopio.org/ASReml/HomePage", "http://www.vsni.co.uk/software/asreml/"]}, "Box\u2013Pierce test": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from June 2011", "Articles with unsourced statements from June 2011", "Time domain analysis", "Time series statistical tests", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Ljung\u2013Box test", "method": "Box\u2013Pierce test", "url": "https://en.wikipedia.org/wiki/Ljung%E2%80%93Box_test", "summary": "The Ljung\u2013Box test (named for Greta M. Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the \"overall\" randomness based on a number of lags, and is therefore a portmanteau test.\nThis test is sometimes known as the Ljung\u2013Box Q test, and it is closely connected to the Box\u2013Pierce test (which is named after George E. P. Box and David A. Pierce). In fact, the Ljung\u2013Box test statistic was described explicitly in the paper that led to the use of the Box-Pierce statistic, and from which that statistic takes its name. The Box-Pierce test statistic is a simplified version of the Ljung\u2013Box statistic for which subsequent simulation studies have shown poor performance.\nThe Ljung\u2013Box test is widely applied in econometrics and other applications of time series analysis. A similar assessment can be also carried out with the Breusch\u2013Godfrey test and the Durbin\u2013Watson test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Answers.com", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Critical region", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fumio Hayashi", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George E. P. Box", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Greta M. Ljung", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Portmanteau test", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Python (programming language)", "Q-statistic", "Quality control", "Quantile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Randomness", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical test", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wald\u2013Wolfowitz runs test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.answers.com/topic/box-pierce-statistic", "http://www.nist.gov", "http://doi.org/10.1080%2F01621459.1970.10481180", "http://doi.org/10.1093%2Fbiomet%2F65.2.297", "http://www.jstor.org/stable/2284333", "https://stat.ethz.ch/R-manual/R-devel/library/stats/html/box.test.html", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA142", "https://books.google.com/books?id=Tc4RPwAACAAJ&pg=PA69", "https://books.google.com/books?id=VHB4OSAmwcUC&pg=PA35", "https://books.google.com/books?id=shWtvsFbxlkC&pg=PA162", "https://www.statsmodels.org/dev/generated/statsmodels.stats.diagnostic.acorr_ljungbox.html"]}, "Multiple comparisons": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2012", "Articles with unsourced statements from January 2012", "Articles with unsourced statements from June 2016", "CS1 maint: Multiple names: authors list", "Multiple comparisons", "Statistical hypothesis testing"], "title": "Multiple comparisons problem", "method": "Multiple comparisons", "url": "https://en.wikipedia.org/wiki/Multiple_comparisons_problem", "summary": "In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or infers a subset of parameters selected based on the observed values. In certain fields it is known as the look-elsewhere effect.\nThe more inferences are made, the more likely erroneous inferences are to occur. Several statistical techniques have been developed to prevent this from happening, allowing significance levels for single and multiple comparisons to be directly compared. These techniques generally require a stricter significance threshold for individual comparisons, so as to compensate for the number of inferences being made.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/6/66/Quantile_meta_test.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a7/Split-arrows.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0c/Spurious_correlations_-_spelling_bee_spiders.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bonferroni bound", "Bonferroni correction", "Boole's inequality", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Closed testing procedure", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Coverage probability", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "DNA microarray", "Data collection", "Data dredging", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Eli Upfal", "Elliptical distribution", "Empirical distribution function", "Empirical research", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected number", "Experiment", "Experimental unit", "Experimentwise error rate", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "False coverage rate", "False discovery rate", "False positive", "False positive rate", "Family-wise error rate", "Familywise error rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Genetic association", "Genomics", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Holm\u2013Bonferroni method", "Homoscedasticity", "Index of dispersion", "Information technology", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Israel", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Neter", "Jonckheere's trend test", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society, Series B", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Look-elsewhere effect", "Loss function", "Lp space", "M-estimator", "MANOVA", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michael Mitzenmacher", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo simulation", "Multiple comparison", "Multiple comparisons", "Multiple testing correction", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Null hypothesis", "Observational study", "Official statistics", "Omnibus test", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pharmacology", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Post-hoc analysis", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Q-Q plot", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Random variable", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling error", "Scale parameter", "Scatter plot", "Scheff\u00e9", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard score", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Test statistic", "Testing hypotheses suggested by the data", "Texas sharpshooter fallacy", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tukey", "Tukey's range test", "Type I and type II errors", "Type I error", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Voxel", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "\u0160id\u00e1k correction"], "references": ["http://www.nature.com/nbt/journal/v27/n12/full/nbt1209-1135.html", "http://www.tylervigen.com/spurious-correlations", "http://adsabs.harvard.edu/abs/2003PNAS..100.9440S", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1124898", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1380484", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC170937", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2907892", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3270946", "http://www.ncbi.nlm.nih.gov/pubmed/12493654", "http://www.ncbi.nlm.nih.gov/pubmed/12883005", "http://www.ncbi.nlm.nih.gov/pubmed/15110000", "http://www.ncbi.nlm.nih.gov/pubmed/18064589", "http://www.ncbi.nlm.nih.gov/pubmed/20010596", "http://www.ncbi.nlm.nih.gov/pubmed/2081237", "http://www.ncbi.nlm.nih.gov/pubmed/20926032", "http://www.ncbi.nlm.nih.gov/pubmed/21154895", "http://www.ncbi.nlm.nih.gov/pubmed/8629727", "http://arxiv.org/abs/1002.1104", "http://doi.org/10.1002%2Fbimj.200900299", "http://doi.org/10.1002%2Fhbm.20471", "http://doi.org/10.1016%2Fj.neuroimage.2003.12.047", "http://doi.org/10.1038%2Fnbt1209-1135", "http://doi.org/10.1073%2Fpnas.1530509100", "http://doi.org/10.1097%2F00001648-199001000-00010", "http://doi.org/10.1136%2Fbmj.325.7378.1437", "http://doi.org/10.1145%2F2220357.2220359", "http://doi.org/10.1198%2F016214501753382129", "http://doi.org/10.2105%2Fajph.86.5.726", "http://www.jstor.org/stable/20065622", "http://www.jstor.org/stable/2346101", "http://www.jstor.org/stable/3085878", "http://www.jstor.org/stable/3144228", "http://www.mcp-conference.org", "http://www.niss.org/sites/default/files/Young%20Karr%20Obs%20Study%20Problem.pdf", "http://www.worldcat.org/issn/0147-958X", "http://www.worldcat.org/issn/1087-0156", "https://doi.org/10.2202%2F1544-6155.1585"]}, "Signal-to-noise statistic": {"categories": ["All articles needing additional references", "All stub articles", "Articles needing additional references from August 2010", "Statistical distance", "Statistical ratios", "Statistics stubs"], "title": "Signal-to-noise statistic", "method": "Signal-to-noise statistic", "url": "https://en.wikipedia.org/wiki/Signal-to-noise_statistic", "summary": "In mathematics the signal-to-noise statistic distance between two vectors a and b with mean values \n \n \n \n \n \u03bc\n \n a\n \n \n \n \n {\\displaystyle \\mu _{a}}\n and \n \n \n \n \n \u03bc\n \n b\n \n \n \n \n {\\displaystyle \\mu _{b}}\n and standard deviation \n \n \n \n \n \u03c3\n \n a\n \n \n \n \n {\\displaystyle \\sigma _{a}}\n and \n \n \n \n \n \u03c3\n \n b\n \n \n \n \n {\\displaystyle \\sigma _{b}}\n respectively is:\n\n \n \n \n \n D\n \n s\n n\n \n \n =\n \n \n \n (\n \n \u03bc\n \n a\n \n \n \u2212\n \n \u03bc\n \n b\n \n \n )\n \n \n (\n \n \u03c3\n \n a\n \n \n +\n \n \u03c3\n \n b\n \n \n )\n \n \n \n \n \n {\\displaystyle D_{sn}={(\\mu _{a}-\\mu _{b}) \\over (\\sigma _{a}+\\sigma _{b})}}\n In the case of Gaussian-distributed data and unbiased class distributions, this statistic can be related to classification accuracy given an ideal linear discrimination, and a decision boundary can be derived.This distance is frequently used to identify vectors that have significant difference. One usage is in bioinformatics to locate genes that are differential expressed on microarray experiments.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Arithmetic Mean", "Bioinformatics", "Distance", "Gene expression", "Genes", "Manhattan distance", "Mathematics", "Microarray", "Signal-to-noise ratio", "Signal to noise ratio (imaging)", "Standard deviation", "Statistics", "Uniform norm", "Vector (geometric)"], "references": ["http://www.broad.mit.edu/mpr/CNS/", "http://archive.broadinstitute.org/mpr/publications/projects/Leukemia/Golub_et_al_1999.pdf", "https://www.researchgate.net/publication/225143114_Comparison_of_Redundancy_and_Relevance_Measures_for_Feature_Selection_in_Tissue_Classification_of_CT_Images", "https://www.researchgate.net/publication/2804500_Class_Prediction_and_Discovery_Using_Gene_Expression_Data"]}, "Conditional expectation": {"categories": ["All articles lacking in-text citations", "All pages needing cleanup", "Articles lacking in-text citations from November 2010", "Articles needing cleanup from June 2017", "CS1 German-language sources (de)", "Cleanup tagged articles with a reason field from June 2017", "Conditional probability", "Statistical theory", "Wikipedia articles needing clarification from January 2017", "Wikipedia articles needing page number citations from December 2010", "Wikipedia pages needing cleanup from June 2017"], "title": "Conditional expectation", "method": "Conditional expectation", "url": "https://en.wikipedia.org/wiki/Conditional_expectation", "summary": "In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value \u2013 the value it would take \u201con average\u201d over an arbitrarily large number of occurrences \u2013 given that a certain set of \"conditions\" is known to occur. If the random variable can take on only a finite number of values, the \u201cconditions\u201d are that the variable can only take on a subset of those values. More formally, in the case when the random variable is defined over a discrete probability space, the \"conditions\" are a partition of this probability space. \nWith multiple random variables, for one random variable to be mean independent of all others both individually and collectively means that each conditional expectation equals the random variable's (unconditional) expected value. This always holds if the variables are independent, but mean independence is a weaker condition.\nDepending on the nature of the conditioning, the conditional expectation can be either a random variable itself or a fixed value. With two random variables, if the expectation of a random variable \n \n \n \n X\n \n \n {\\displaystyle X}\n is expressed conditional on another random variable \n \n \n \n Y\n \n \n {\\displaystyle Y}\n without a particular value of \n \n \n \n Y\n \n \n {\\displaystyle Y}\n being specified, then the expectation of \n \n \n \n X\n \n \n {\\displaystyle X}\n conditional on \n \n \n \n Y\n \n \n {\\displaystyle Y}\n , denoted \n \n \n \n E\n (\n X\n \n |\n \n Y\n )\n \n \n {\\displaystyle E(X|Y)}\n , is a function of the random variable \n \n \n \n Y\n \n \n {\\displaystyle Y}\n and hence is itself a random variable. Alternatively, if the expectation of \n \n \n \n X\n \n \n {\\displaystyle X}\n is expressed conditional on the occurrence of a particular value of \n \n \n \n Y\n \n \n {\\displaystyle Y}\n , denoted \n \n \n \n y\n \n \n {\\displaystyle y}\n , then the conditional expectation \n \n \n \n E\n (\n X\n \n |\n \n Y\n =\n y\n )\n \n \n {\\displaystyle E(X|Y=y)}\n is a fixed value.\nThis concept generalizes to any probability space using measure theory.\nIn modern probability theory the concept of conditional probability is defined in terms of conditional expectation.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ce/Conditional_expectation_commutative_diagram.png", "https://upload.wikimedia.org/wikipedia/commons/7/74/LokaleMittelwertbildung.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Absolute continuity", "Algebraic formula for the variance", "Almost surely", "Andrey Kolmogorov", "Andrey Nikolaevich Kolmogorov", "Borel\u2013Kolmogorov paradox", "Cardinality", "Change of variables", "Classical definition of probability", "Commutative diagram", "Conditional density", "Conditional probability", "Conditional variance", "Conditionally independent", "Conditioning (probability)", "Continuous random variable", "Contraction (operator theory)", "Convex function", "Dice", "Digital object identifier", "Discrete random variable", "Disintegration theorem", "Dominated convergence theorem", "Doob martingale", "Encyclopedia of Mathematics", "Expected value", "Fatou's lemma", "Geoffrey Grimmett", "Hilbert projection theorem", "Hilbert space", "Independence (probability)", "Independence (probability theory)", "International Standard Book Number", "Jensen's inequality", "John Wiley & Sons", "Joint distribution", "Joint probability distribution", "Joseph L. Doob", "Law of total cumulance", "Law of total expectation", "Law of total probability", "Law of total variance", "Lebesgue measure", "Linear subspace", "Lp space", "Martingale convergence theorem", "Mean independent", "Measurable function", "Measurable space", "Measure theory", "Michiel Hazewinkel", "Monotone convergence theorem", "Natural injection", "Non-commutative conditional expectation", "Null set", "Orthogonal projection", "Partition of a set", "Patrick Billingsley", "Paul Halmos", "Pierre-Simon Laplace", "Pre-image", "Probability space", "Probability theory", "Pushforward measure", "Radon\u2013Nikodym derivative", "Radon\u2013Nikodym theorem", "Random variable", "Range (mathematics)", "Self-adjoint operator", "Sigma-algebra", "Square-integrable", "Variance", "William Feller"], "references": ["http://www.mathematik.com/Kolmogorov/index.html", "http://www.ams.org/journals/bull/1953-59-01/S0002-9904-1953-09662-8/S0002-9904-1953-09662-8.pdf", "http://doi.org/10.1090%2Fs0002-9904-1953-09662-8", "https://www.encyclopediaofmath.org/index.php?title=c/c024500"]}, "Absolute deviation": {"categories": ["All articles lacking sources", "Articles lacking sources from February 2007", "Statistical deviation and dispersion", "Statistical distance"], "title": "Deviation (statistics)", "method": "Absolute deviation", "url": "https://en.wikipedia.org/wiki/Deviation_(statistics)", "summary": "In mathematics and statistics, deviation is a measure of difference between the observed value of a variable and some other value, often that variable's mean. The sign of the deviation (positive or negative), reports the direction of that difference (the deviation is positive when the observed value exceeds the reference value). The magnitude of the value indicates the size of the difference.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Absolute difference", "Accuracy and precision", "Anomaly (natural sciences)", "Average", "Average absolute deviation", "Bias of an estimator", "Central tendency", "Data set", "Deviance (statistics)", "Errors and residuals", "Formula", "Least absolute deviation", "Level of measurement", "Mathematics", "Maximum absolute deviation", "Mean", "Mean signed deviation", "Median", "Median absolute deviation", "Nondimensionalization", "Normalization (statistics)", "Robust statistics", "Square (algebra)", "Squared deviations", "Standard deviation", "Standardizing", "Statistical dispersion", "Statistics", "Studentized residual", "Studentizing", "Variance"], "references": []}, "Distribution fitting": {"categories": ["Probability distribution fitting", "Use dmy dates from August 2012"], "title": "Probability distribution fitting", "method": "Distribution fitting", "url": "https://en.wikipedia.org/wiki/Probability_distribution_fitting", "summary": "Probability distribution fitting or simply distribution fitting is the fitting of a probability distribution to a series of data concerning the repeated measurement of a variable phenomenon.\nThe aim of distribution fitting is to predict the probability or to forecast the frequency of occurrence of the magnitude of the phenomenon in a certain interval.\nThere are many probability distributions (see list of probability distributions) of which some can be fitted more closely to the observed frequency of the data than others, depending on the characteristics of the phenomenon and of the distribution. The distribution giving a close fit is supposed to lead to good predictions.\nIn distribution fitting, therefore, one needs to select a distribution that suits the data well.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0f/BinomialConfBelts.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f6/CumList.png", "https://upload.wikimedia.org/wikipedia/commons/9/9e/FitGumbelDistr.tif", "https://upload.wikimedia.org/wikipedia/commons/1/17/GEVdistrHistogr%2BDensity.png", "https://upload.wikimedia.org/wikipedia/commons/a/a9/Gumbel_distribution_and_Gumbel_mirrored.png", "https://upload.wikimedia.org/wikipedia/commons/f/f8/Negative_and_positive_skew_diagrams_%28English%29.svg", "https://upload.wikimedia.org/wikipedia/commons/7/74/Normal_Distribution_PDF.svg", "https://upload.wikimedia.org/wikipedia/commons/5/51/SampleFreqCurves.tif", "https://upload.wikimedia.org/wikipedia/commons/3/3a/SanLor.jpg"], "links": ["Arithmetic mean", "Binomial distribution", "Burr distribution", "Cauchy distribution", "Chi square", "Confidence band", "Confidence interval", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Cumulative probability", "Dagum distribution", "Density estimation", "Digital object identifier", "Distribution fitting", "Expected value", "Exponential distribution", "Forecasting", "Frequency (statistics)", "Fr\u00e9chet distribution", "GEV distribution", "Gompertz distribution", "Goodness of fit", "Gumbel distribution", "Histogram", "Hydrology", "International Standard Book Number", "JSTOR", "Kurtosis", "L-moment", "Laplace distribution", "Linear relation", "List of probability distributions", "Logistic distribution", "Loglogistic distribution", "Lognormal distribution", "MathWorks", "Mathematical Reviews", "Maximum likelihood", "Maximum spacing estimation", "Mean", "Method of moments (statistics)", "Mixture distribution", "Mode (statistics)", "Normal distribution", "Normal probability plot", "Numerical method", "Parameter", "Pareto distribution", "Plotting position", "Prediction", "Probability", "Probability density function", "Probability distribution", "Probability plot", "Product distribution", "P\u2013P plot", "Q\u2013Q plot", "R (programming language)", "Random error", "Return period", "Skewness", "Software", "Standard deviation", "StatSoft", "Student's t-distribution", "Surinam", "Survival function", "Uncertainty", "Variance", "Weibull distribution"], "references": ["http://www.waterlog.info/articles.htm", "http://www.waterlog.info/pdf/binomial.pdf", "http://www.waterlog.info/pdf/freqtxt.pdf", "http://www.ams.org/mathscinet-getitem?mr=1617519", "http://doi.org/10.1214%2Fss%2F1030037906", "http://www.jstor.org/stable/2345653", "https://www.waterlog.info/composite.htm", "https://www.waterlog.info/cumfreq.htm"]}, "Leverage (statistics)": {"categories": ["Regression diagnostics"], "title": "Leverage (statistics)", "method": "Leverage (statistics)", "url": "https://en.wikipedia.org/wiki/Leverage_(statistics)", "summary": "In statistics and in particular in regression analysis, leverage is a measure of how far away the independent variable values of an observation are from those of the other observations.\nHigh-leverage points are those observations, if any, made at extreme or outlying values of the independent variables such that the lack of neighboring observations means that the fitted regression model will pass close to that particular observation.Modern computer packages for statistical analysis include, as part of their facilities for regression analysis, various quantitative measures for identifying influential observations: among these measures is partial leverage, a measure of how a variable contributes to the leverage of a datum.", "images": [], "links": ["Cook's distance", "DFFITS", "Design matrix", "Errors and residuals", "Homoscedastic", "Idempotent matrix", "Independent variable", "Influential observation", "International Standard Book Number", "Linear regression", "Mahalanobis distance", "Observation (statistics)", "Ordinary least squares", "Outliers", "Partial leverage", "Projection matrix", "Regression analysis", "Statistics", "Studentized residual"], "references": ["https://www.ecmwf.int/sites/default/files/elibrary/2013/16938-observation-influence-diagnostic-data-assimilation-system.pdf"]}, "Hoeffding's lemma": {"categories": ["All stub articles", "Probabilistic inequalities", "Probability stubs"], "title": "Hoeffding's lemma", "method": "Hoeffding's lemma", "url": "https://en.wikipedia.org/wiki/Hoeffding%27s_lemma", "summary": "In probability theory, Hoeffding's lemma is an inequality that bounds the moment-generating function of any bounded random variable. It is named after the Finnish\u2013American mathematical statistician Wassily Hoeffding.\nThe proof of Hoeffding's lemma uses Taylor's theorem and Jensen's inequality. Hoeffding's lemma is itself used in the proof of McDiarmid's inequality.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["Almost surely", "Bennett's inequality", "Bounded function", "Convex function", "Expected value", "Finnish people", "Hoeffding's inequality", "Inequality (mathematics)", "International Standard Book Number", "Jensen's inequality", "Mathematical statistics", "McDiarmid's inequality", "Moment-generating function", "Probability", "Probability theory", "Random variable", "Taylor's theorem", "United States", "Wassily Hoeffding"], "references": ["https://books.google.com/books?id=ZI67BQAAQBAJ&pg=PA21"]}, "Accelerated failure time model": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2018", "Survival analysis"], "title": "Accelerated failure time model", "method": "Accelerated failure time model", "url": "https://en.wikipedia.org/wiki/Accelerated_failure_time_model", "summary": "In the statistical area of survival analysis, an accelerated failure time model (AFT model) is a parametric model that provides an alternative to the commonly used proportional hazards models. Whereas a proportional hazards model assumes that the effect of a covariate is to multiply the hazard by some constant, an AFT model assumes that the effect of a covariate is to accelerate or decelerate the life course of a disease by some constant. This is especially appealing in a technical context where the 'disease' is a result of some mechanical process with a known sequence of intermediary stages.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Censoring (statistics)", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Closed-form expression", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "David Cox (statistician)", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gamma distribution", "General linear model", "Generalized gamma distribution", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hazard rate", "Hazard ratio", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse Gaussian distribution", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Life expectancy", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear model", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monotonic", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Proportional hazards models", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2394368", "http://www.ncbi.nlm.nih.gov/pubmed/11318147", "http://www.ncbi.nlm.nih.gov/pubmed/12888808", "http://www.ncbi.nlm.nih.gov/pubmed/1480879", "http://www.ncbi.nlm.nih.gov/pubmed/15449337", "http://www.ncbi.nlm.nih.gov/pubmed/9004393", "http://doi.org/10.1002%2F(SICI)1097-0258(19970130)16:2%3C215::AID-SIM481%3E3.0.CO;2-J", "http://doi.org/10.1002%2Fsim.1876", "http://doi.org/10.1002%2Fsim.4780111409", "http://doi.org/10.1038%2Fsj.bjc.6601119", "http://doi.org/10.1093%2Fbiomet%2F66.3.429", "http://doi.org/10.1111%2Fj.0006-341X.1999.00013.x", "http://doi.org/10.1177%2F009286150203600312", "http://www.jstor.org/stable/2335161", "https://www.researchgate.net/profile/Richard_Kay2/publication/254087561_On_the_Use_of_the_Accelerated_Failure_Time_Model_as_an_Alternative_to_the_Proportional_Hazards_Model_in_the_Treatment_of_Time_to_Event_Data_A_Case_Study_in_Influenza/links/548ed67e0cf225bf66a710ce.pdf"]}, "Gauss\u2013Kuzmin distribution": {"categories": ["Continued fractions", "Discrete distributions"], "title": "Gauss\u2013Kuzmin distribution", "method": "Gauss\u2013Kuzmin distribution", "url": "https://en.wikipedia.org/wiki/Gauss%E2%80%93Kuzmin_distribution", "summary": "In mathematics, the Gauss\u2013Kuzmin distribution is a discrete probability distribution that arises as the limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1). The distribution is named after Carl Friedrich Gauss, who derived it around 1800, and Rodion Kuzmin, who gave a bound on the rate of convergence in 1929. It is given by the probability mass function\n\n \n \n \n p\n (\n k\n )\n =\n \u2212\n \n log\n \n 2\n \n \n \u2061\n \n (\n \n 1\n \u2212\n \n \n 1\n \n (\n 1\n +\n k\n \n )\n \n 2\n \n \n \n \n \n \n )\n \n \n .\n \n \n {\\displaystyle p(k)=-\\log _{2}\\left(1-{\\frac {1}{(1+k)^{2}}}\\right)~.}", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Bulletin de la Soci\u00e9t\u00e9 Math\u00e9matique de France", "Burr distribution", "Cantor distribution", "Carl Friedrich Gauss", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continued fraction", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Eduard Wirsing", "Elliptical distribution", "Eric W. Weisstein", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gauss-Kuzmin-Wirsing constant", "Gaussian q-distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Jahrbuch \u00fcber die Fortschritte der Mathematik", "Johann Carl Friedrich Gauss", "Johnson's SU-distribution", "Joint probability distribution", "K.I.Babenko", "Kent distribution", "Khinchin's constant", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Levy's constant", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "MathWorld", "Mathematics", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Paul L\u00e9vy (mathematician)", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Probability mass function", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Rodion Kuzmin", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://mathworld.wolfram.com/Gauss-KuzminDistribution.html", "http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN236018647", "http://doi.org/10.1007%2F978-3-642-80350-5_41", "http://doi.org/10.1109%2FTIT.1984.1056924", "http://linas.org/math/entropy.pdf", "http://www.numdam.org/item?id=BSMF_1929__57__178_0", "http://zbmath.org/?format=complete&q=an:55.0916.02"]}, "Latent variable": {"categories": ["Bayesian networks", "Econometric modeling", "Latent variable models", "Psychometrics", "Social research", "Wikipedia articles needing page number citations from November 2010"], "title": "Latent variable", "method": "Latent variable", "url": "https://en.wikipedia.org/wiki/Latent_variable", "summary": "In statistics, latent variables (from Latin: present participle of lateo (\u201clie hidden\u201d), as opposed to observable variables), are variables that are not directly observed but are rather inferred (through a mathematical model) from other variables that are observed (directly measured). Mathematical models that aim to explain observed variables in terms of latent variables are called latent variable models. Latent variable models are used in many disciplines, including psychology, demography, economics, engineering, medicine, physics, machine learning/artificial intelligence, bioinformatics, natural language processing, econometrics, management and the social sciences.\nSometimes latent variables correspond to aspects of physical reality, which could in principle be measured, but may not be for practical reasons. In this situation, the term hidden variables is commonly used (reflecting the fact that the variables are \"really there\", but hidden). Other times, latent variables correspond to abstract concepts, like categories, behavioral or mental states, or data structures. The terms hypothetical variables or hypothetical constructs may be used in these situations.\nOne advantage of using latent variables is that they can serve to reduce the dimensionality of data. A large number of observable variables can be aggregated in a model to represent an underlying concept, making it easier to understand the data. In this sense, they serve a function similar to that of scientific theories. At the same time, latent variables link observable (\"sub-symbolic\") data in the real world to symbolic data in the modeled world.", "images": [], "links": ["Artificial intelligence", "Bayesian statistics", "Big Five personality traits", "Bioinformatics", "Charles Spearman", "Chinese Restaurant Process", "Confounding", "Demography", "Digital object identifier", "Dimensionality reduction", "EM algorithm", "Econometrics", "Economics", "Engineering", "Evidence lower bound", "Factor analysis", "G factor (psychometrics)", "Gideon J. Mellenbergh", "Hidden Markov model", "Indian buffet process", "International Standard Book Number", "Intervening variable", "Item response theory", "JSTOR", "Jan Kmenta", "Latent Dirichlet Allocation", "Latent semantic analysis", "Latent variable model", "Latin", "Machine learning", "Management", "Mathematical model", "Medicine", "Natural language processing", "Observable variable", "Partial least squares path modeling", "Partial least squares regression", "Physics", "Present participle", "Principal component analysis", "Probabilistic latent semantic analysis", "Proxy (statistics)", "Psychology", "Psychometrics", "PubMed Identifier", "Quality of life", "Rasch model", "Social sciences", "Spearman's g", "Statistical inference", "Statistics", "Structural equation modeling", "Sub-symbolic", "Variable (mathematics)"], "references": ["http://rhowell.ba.ttu.edu/BorsboomLatentvars2003.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/19711618", "http://doi.org/10.1037%2F0033-295X.110.2.203", "http://doi.org/10.2307%2F1412107", "http://www.jstor.org/stable/1412107", "https://books.google.com/books?id=Bxq7AAAAIAAJ&pg=PA581"]}, "Censoring (clinical trials)": {"categories": ["Reliability engineering", "Statistical data types", "Survival analysis"], "title": "Censoring (statistics)", "method": "Censoring (clinical trials)", "url": "https://en.wikipedia.org/wiki/Censoring_(statistics)", "summary": "In statistics, engineering, economics, and medical research, censoring is a condition in which the value of a measurement or observation is only partially known.\nFor example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known that an individual's age at death is at least 75 years (but may be more). Such a situation could occur if the individual withdrew from the study at age 75, or if the individual is currently alive at the age of 75.\nCensoring also occurs when a value occurs outside the range of a measuring instrument. For example, a bathroom scale might only measure up to 300 pounds (140 kg). If a 350 lb (160 kg) individual is weighed using the scale, the observer would only know that the individual's weight is at least 300 pounds (140 kg).\nThe problem of censored data, in which the observed value of some variable is partially known, is related to the problem of missing data, where the observed value of some variable is unknown.\nCensoring should not be confused with the related idea truncation. With censoring, observations result either in knowing the exact value that applies, or in knowing that the value lies within an interval. With truncation, observations never result in values outside a given range: values in the population outside the range are never seen or never recorded if they are seen. Note that in statistics, truncation is not the same as rounding.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b1/Censored_Data_Example.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Censored regression model", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Daniel Bernoulli", "Data analysis", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Imputation (statistics)", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval (mathematics)", "Interval estimation", "Inverse probability weighting", "Isotonic regression", "JSTOR", "Jackknife resampling", "James Tobin", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan-Meier estimator", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kibibyte", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement", "Measuring instrument", "Median", "Median-unbiased estimator", "Medical research", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Mortality rate", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observation", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Rounding", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling bias", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smallpox", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistically independent", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tobit model", "Tolerance interval", "Trend estimation", "Truncation (statistics)", "U-statistic", "Uniformly most powerful test", "V-statistic", "Vaccination", "Value (mathematics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Winsorising", "Z-test"], "references": ["http://www.semel.ucla.edu/sites/all/files/biomedicalmodeling/pdf/Bernoulli&Blower.pdf", "http://www.itl.nist.gov/div898/handbook/", "http://doi.org/10.2307%2F1907382", "http://www.jstor.org/stable/1907382"]}, "Dirichlet distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2011", "Articles with unsourced statements from November 2011", "CS1 errors: dates", "Conjugate prior distributions", "Continuous distributions", "Exponential family distributions", "Multivariate continuous distributions", "Pages using deprecated image syntax"], "title": "Dirichlet distribution", "method": "Dirichlet distribution", "url": "https://en.wikipedia.org/wiki/Dirichlet_distribution", "summary": "In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted \n \n \n \n Dir\n \u2061\n (\n \n \u03b1\n \n )\n \n \n {\\displaystyle \\operatorname {Dir} ({\\boldsymbol {\\alpha }})}\n , is a family of continuous multivariate probability distributions parameterized by a vector \n \n \n \n \n \u03b1\n \n \n \n {\\displaystyle {\\boldsymbol {\\alpha }}}\n of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative name of Multivariate Beta distribution (MBD). Dirichlet distributions are commonly used as prior distributions in Bayesian statistics, and in fact the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution.\nThe infinite-dimensional generalization of the Dirichlet distribution is the Dirichlet process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2b/Dirichlet-3d-panel.png", "https://upload.wikimedia.org/wikipedia/commons/8/86/Dirichlet_example.png", "https://upload.wikimedia.org/wikipedia/commons/5/54/LogDirichletDensity-alpha_0.3_to_alpha_2.0.gif"], "links": ["ARGUS distribution", "Almost sure convergence", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Base measure", "Bates distribution", "Bayesian inference", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Concentration parameter", "Confluent hypergeometric function", "Conjugate prior", "Continuous probability distribution", "Convergence in mean", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet process", "Discrete Weibull distribution", "Discrete distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Encyclopedia of Mathematics", "Equilateral triangle", "Erlang distribution", "Euclidean space", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gibbs sampling", "Gompertz distribution", "Grouped Dirichlet distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hierarchical Bayesian model", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hyperprior", "Hypoexponential distribution", "Independence (probability theory)", "Information entropy", "Integer", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverted Dirichlet distribution", "Invertible matrix", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kronecker delta", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Latent Dirichlet allocation", "Lauricella hypergeometric series", "Lebesgue measure", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Marginal distribution", "Marginalization", "Marginalized out", "Martingale (probability theory)", "Martingale convergence theorem", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Matrix variate Dirichlet distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Methods of contour integration", "Michiel Hazewinkel", "Mittag-Leffler distribution", "Mixture distribution", "Mixture model", "Mode (statistics)", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate random variable", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Natural language processing", "Negative binomial distribution", "Negative multinomial distribution", "Neutral vector", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normalizing constant", "Open set", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Peter Gustav Lejeune Dirichlet", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Posterior distribution", "Prior distribution", "Probability", "Probability density function", "Probability distribution", "Pseudocount", "P\u00f3lya urn model", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Random variate", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "R\u00e9nyi entropy", "Scalar (mathematics)", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Simplex", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard simplex", "Statistical inference", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangle", "Triangular distribution", "Trigamma function", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Variational Bayes", "Vector (mathematics and physics)", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471183873.html", "http://www.cs.princeton.edu/courses/archive/fall07/cos597C/scribe/20071130.pdf", "http://www.cis.hut.fi/ahonkela/dippa/node95.html", "http://cvsp.cs.ntua.gr/publications/jpubl+bchap/LefkimmiatisMaragosPapandreou_BayesianMultiscalePoissonIntensityEstimation_ieee-j-ip09.pdf", "http://arxiv.org/abs/1811.05266", "http://luc.devroye.org/rnbookindex.html", "http://doi.org/10.1016%2FS0378-3758(00)00169-5", "http://doi.org/10.1016%2Fj.aam.2016.08.001", "http://doi.org/10.1214%2Faos%2F1176342372", "http://doi.org/10.2307%2F2283728", "http://www.jstor.org/stable/2283728", "http://mayagupta.org/publications/EMbookGuptaChen2010.pdf", "http://www.mas.ncl.ac.uk/~nmf16/teaching/mas3301/week6.pdf", "https://mast.queensu.ca/~communications/Papers/msc-jiayu-lin.pdf", "https://books.google.com/books?id=kTNoQgAACAAJ", "https://www.ee.washington.edu/techsite/papers/documents/UWEETR-2010-0006.pdf", "https://tillahoffmann.github.io/Moments-of-the-Dirichlet-distribution/", "https://www.encyclopediaofmath.org/index.php?title=p/d032840", "https://www.jstor.org/stable/2238036", "https://cran.r-project.org/web/packages/SciencesPo/index.html"]}, "Simple moving average crossover": {"categories": ["All articles needing additional references", "Articles needing additional references from September 2014", "Mathematical finance", "Technical indicators", "Time series"], "title": "Moving average crossover", "method": "Simple moving average crossover", "url": "https://en.wikipedia.org/wiki/Moving_average_crossover", "summary": "In the statistics of time series, and in particular the analysis of financial time series for stock trading purposes, a moving-average crossover occurs when, on plotting two moving averages each based on different degrees of smoothing, the traces of these moving averages cross. It does not predict future direction but shows trends. This indicator uses two (or more) moving averages, a slower moving average and a faster moving average. The faster moving average is a short term moving average. For end-of-day stock markets, for example, it may be 5-, 10- or 25-day period while the slower moving average is medium or long term moving average (e.g. 50-, 100- or 200-day period). A short term moving average is faster because it only considers prices over short period of time and is thus more reactive to daily price changes. On the other hand, a long term moving average is deemed slower as it encapsulates prices over a longer period and is more lethargic. However, it tends to smooth out price noises which are often reflected in short term moving averages.\nA moving average, as a line by itself, is often overlaid in price charts to indicate price trends. A crossover occurs when a faster moving average (i.e., a shorter period moving average) crosses a slower moving average (i.e. a longer period moving average). In other words, this is when the shorter period moving average line crosses a longer period moving average line. In stock investing, this meeting point is used either to enter (buy or sell) or exit (sell or buy) the market.\nThe particular case where simple equally weighted moving-averages are used is sometimes called a simple moving-average (SMA) crossover. Such a crossover can be used to signal a change in trend and can be used to trigger a trade in a Black Box trading system.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Moving_average_crossover.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Black box", "Moving average", "Statistical finance", "Statistics", "Stock trading", "Time series"], "references": ["http://www.nasdaq.com/investing/glossary/g/death-cross", "http://www.nasdaq.com/investing/glossary/g/golden-cross"]}, "Gini coefficient": {"categories": ["All articles with unsourced statements", "Articles containing Italian-language text", "Articles with unsourced statements from March 2016", "Articles with unsourced statements from May 2014", "Articles with unsourced statements from November 2018", "Articles with unsourced statements from October 2012", "Commons category link from Wikidata", "Demographic economics", "Income inequality metrics", "Pages containing citation needed template with deprecated parameters", "Pages with DOIs inactive since 2018", "Use dmy dates from August 2017", "Welfare economics", "Wikipedia articles needing page number citations from December 2012", "Wikipedia articles with NDL identifiers"], "title": "Gini coefficient", "method": "Gini coefficient", "url": "https://en.wikipedia.org/wiki/Gini_coefficient", "summary": "In economics, the Gini coefficient ( JEE-nee), sometimes called Gini index, or Gini ratio, is a measure of statistical dispersion intended to represent the income or wealth distribution of a nation's residents, and is the most commonly used measurement of inequality. It was developed by the Italian statistician and sociologist Corrado Gini and published in his 1912 paper Variability and Mutability (Italian: Variabilit\u00e0 e mutabilit\u00e0).The Gini coefficient measures the inequality among values of a frequency distribution (for example, levels of income). A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income). A Gini coefficient of 1 (or 100%) expresses maximal inequality among values (e.g., for a large number of people, where only one person has all the income or consumption, and all others have none, the Gini coefficient will be very nearly one). However, a value greater than one may occur if some persons represent negative contribution to the total (for example, having negative income or wealth). For larger groups, values close to or above 1 are very unlikely in practice. Given the normalization of both the cumulative population and the cumulative share of income used to calculate the Gini coefficient, the measure is not overly sensitive to the specifics of the income distribution, but rather only on how incomes vary relative to the other members of a population. The exception to this is in the redistribution of income resulting in a minimum income for all people. When the population is sorted, if their income distribution were to approximate a well-known function, then some representative values could be calculated.\nThe Gini coefficient was proposed by Gini as a measure of inequality of income or wealth. For OECD countries, in the late 20th century, considering the effect of taxes and transfer payments, the income Gini coefficient ranged between 0.24 and 0.49, with Slovenia being the lowest and Chile the highest. African countries had the highest pre-tax Gini coefficients in 2008\u20132009, with South Africa the world's highest, variously estimated to be 0.63 to 0.7, although this figure drops to 0.52 after social assistance is taken into account, and drops again to 0.47 after taxation. The global income Gini coefficient in 2005 has been estimated to be between 0.61 and 0.68 by various sources.There are some issues in interpreting a Gini coefficient. The same value may result from many different distribution curves. The demographic structure should be taken into account. Countries with an aging population, or with a baby boom, experience an increasing pre-tax Gini coefficient even if real income distribution for working adults remains constant. Scholars have devised over a dozen variants of the Gini coefficient.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0c/2014_Gini_Index_World_Map%2C_income_inequality_distribution_by_country_per_World_Bank.svg", "https://upload.wikimedia.org/wikipedia/commons/4/41/Berg_Ostry_2011_Chart_4.gif", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ee/Gini_coefficient_for_distribution_with_only_two_income_or_wealth_levels.svg", "https://upload.wikimedia.org/wikipedia/commons/0/01/Gini_since_WWII.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/5/59/Economics_Gini_coefficient2.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute difference", "African trypanosomiasis", "Alfred W. Crosby", "Alter-globalization", "Amartya Sen", "American imperialism", "Andre Gunder Frank", "Angus Deaton", "Anthony Giddens", "Anthony Shorrocks", "Anti-globalization movement", "Antonio Negri", "ArXiv", "Archaic globalization", "Area", "Arjun Appadurai", "Asset poverty", "Atkinson index", "BRIC", "Barter", "Below Poverty Line (India)", "Beta distribution", "Bibcode", "Biodiversity", "British Empire", "Capital accumulation", "Carstairs index", "Causes of mental disorders", "Chagas disease", "Chi-squared distribution", "Chile", "Cholera", "Christopher Chase-Dunn", "CiteSeerX", "Climate change", "Climate justice", "Consistent estimator", "Corrado Gini", "Counter-hegemonic globalization", "Credit rating", "Credit risk", "Cultural globalization", "Cumulative distribution function", "Dani Rodrik", "Daniele Archibugi", "David Harvey", "David Held", "Debt bondage", "Decision tree learning", "Deglobalization", "Democratic globalization", "Department of Environment Index", "Dependency theory", "Deprivation index", "Development aid", "Development theory", "Diarrhea", "Digital object identifier", "Dirac delta function", "Disability-adjusted life year", "Disability and poverty", "Disadvantaged", "Discrete probability distribution", "Diseases of poverty", "Diversity index", "Dracunculiasis", "Earth system science", "Ecological modernization", "Economic globalization", "Economic inequality", "Economics", "Egalitarianism", "Endangered language", "Energy poverty", "Environmental globalization", "Error function", "Estimator", "Exponential distribution", "Extended family", "Fair trade", "Feminization of poverty", "Fiscal localism", "Food security", "Forced displacement", "Frequency distribution", "Fush\u016bgaku", "Gamma distribution", "Gender-related Development Index", "Gender Parity Index", "Generalized entropy index", "Genuine progress indicator", "George Ritzer", "Gini coefficient", "Giovanni Arrighi", "Global Hunger Index", "Global Peace Index", "Global citizenship", "Global citizenship education", "Global digital divide", "Global financial system", "Global governance", "Global health", "Global labor arbitrage", "Global studies", "Global warming", "Global workforce", "Globalization", "Globalization and disease", "Granularity", "Great Gatsby curve", "Gross domestic product", "HIV/AIDS", "Handle System", "Herfindahl index", "Hikikomori", "History of globalization", "History of modernisation theory", "Homeless Vulnerability Index", "Hoover index", "Housing stress", "Human Development Index", "Human Poverty Index", "Human capital flight", "Human rights", "IEEE Computer Society", "Ibn Khaldun", "Illicit financial flows", "Immanuel Wallerstein", "Income", "Income deficit", "Income inequality metrics", "Index of Multiple Deprivation 2000", "India State Hunger Index", "Indices of deprivation 2004", "Indices of deprivation 2007", "Indices of deprivation 2010", "Informal sector", "Information entropy", "Integral", "Integration by parts", "International Standard Book Number", "Interpolation", "Invasive species", "Investor-state dispute settlement", "Italian language", "Italians", "JSTOR", "Jagdish Bhagwati", "Jean Baudrillard", "Jeffrey Sachs", "John Ralston Saul", "John Urry (sociologist)", "Joseph Stiglitz", "Kuznets curve", "Kwame Anthony Appiah", "Laeken indicators", "Legatum Prosperity Index", "List of U.S. states by Gini coefficient", "List of countries by Social Progress Index", "List of countries by distribution of wealth", "List of countries by income equality", "List of globalization-related journals", "Living Planet Index", "Living wage", "Log-normal distribution", "Lognormal distribution", "Lorenz curve", "Malaria", "Malnutrition", "Mann\u2013Whitney U", "Manuel Castells", "Mathematics", "McDonaldization", "Mean log deviation", "Measles", "Michael Hardt", "Michael Hudson (economist)", "Military globalization", "Misery index (economics)", "Modernization theory", "Money-rich, time-poor", "Multidimensional Poverty Index", "Naomi Klein", "National Diet Library", "Nature (journal)", "Neglected tropical diseases", "New international division of labour", "Noam Chomsky", "Normal distribution", "North\u2013South divide", "Nuclear family", "Numerical integration", "Offshoring", "Onchocerciasis", "Organisation for Economic Co-operation and Development", "Outline of globalization", "Pareto distribution", "Pareto principle", "Paul Hirst", "Paul James (academic)", "Pen's parade", "Per capita income", "Peter Gowan", "Physical Quality of Life Index", "Pierre Janet", "Pneumonia", "Political globalization", "Pollution haven hypothesis", "Post-materialism", "Poverty", "Poverty gap index", "Poverty threshold", "Primitive accumulation of capital", "Priority review voucher", "Probability density function", "Probability distribution function", "Progress out of Poverty Index", "Progressive tax", "Protein kinase inhibitors", "Proto-globalization", "Providing Urban Amenities to Rural Areas", "PubMed Central", "PubMed Identifier", "Quality of Life", "Quality of life", "Quantile function", "ROC analysis", "Race to the bottom", "Random distribution", "Ratio", "Ratio analysis", "Ravi Batra", "Receiver operating characteristic", "Relative deprivation", "Relative mean absolute difference", "Resampling (statistics)", "Reverse brain drain", "Robert Brenner", "Rural poverty", "Samir Amin", "Saskia Sassen", "Schistosomiasis", "Scottish index of multiple deprivation", "Secondary poverty", "Self-perceived quality-of-life scale", "Shlomo Yitzhaki (economics)", "Shorrocks index", "Simpson's rule", "Slovenia", "Social Science Research Network", "Social and psychological value of money", "Social change", "Social determinants of health in poverty", "Social exclusion", "Social inequality", "Social vulnerability", "Social welfare", "Social welfare provision", "Sociology", "Statistical dispersion", "Statistics", "Stress (psychological)", "Structural violence", "Subjective well-being", "Suboptimal health", "Subsistence farming", "Suits index", "Survival sex", "Theil Index", "Theories of poverty", "Thomas Friedman", "Townsend deprivation index", "Trachoma", "Trade globalization", "Transfer payments", "Transnational organized crime", "Trapezoidal rule", "Tuberculosis", "Ulrich Beck", "Underprivileged area score", "Uniform distribution (continuous)", "Utopia", "Vandana Shiva", "Visceral leishmaniasis", "Walden Bello", "Water security", "Wealth concentration", "Weibull distribution", "Welfare", "Welfare economics", "Welfare states", "Well-being", "Wellness (medicine)", "Westernization", "World-systems theory", "World Bank", "World history", "World population", "World war", "Zygmunt Bauman"], "references": ["http:ftp://ftp.fao.org/docrep/fao/012/ak968e/ak968e00.pdf", "http://economics.dal.ca/RePEc/dal/wparch/howgini.pdf", "http://web.uvic.ca/econ/ewp0202.pdf", "http://www.ebrd.com/downloads/research/economics/workingpapers/wp0114.pdf", "http://www.kpmg.com/Africa/en/KPMG-in-Africa/Documents/2013%20Q4%20snapshots/KPMG_South%20Africa%202013Q4.pdf", "http://ssrn.com/abstract=636661", "http://ssrn.com/abstract=931479", "http://www.theresearchkitchen.com/archives/219", "http://mathworld.wolfram.com/GiniCoefficient.html", "http://fmwww.bc.edu/repec/es2000/0883.pdf", "http://emlab.berkeley.edu/~saez/kopczuk-saez-songQJE09SSA.pdf", "http://ias7.berkeley.edu/academics/courses/center/fall2007/sehnbruch/atkinson%201998%20contributions%20of%20sen%20to%20welf%20economics.pdf", "http://adsabs.harvard.edu/abs/2009Natur.458..623W", "http://adsabs.harvard.edu/abs/2010PhyA..389..117E", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.365.4156", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.403.4725", "http://www.wider.unu.edu/research/Database/en_GB/database/", "http://utip.gov.utexas.edu/tutorials/theo_basic_ineq_measures.doc", "http://cowles.econ.yale.edu/P/cp/p11a/p1139.pdf", "http://www.ucm.es/info/econeuro/documentos/documentos/dt192002.pdf", "http://ec.europa.eu/regional_policy/sources/docgener/work/200801_convergence.pdf", "http://www.eurofound.europa.eu/areas/qualityoflife/eurlife/index.php?template=3&radioindic=158&idDomain=3", "http://www.cbo.gov/doc.cfm?index=12485", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1192818", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2652960", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2850525", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5082574", "http://www.ncbi.nlm.nih.gov/pubmed/10070686", "http://www.ncbi.nlm.nih.gov/pubmed/16014174", "http://www.ncbi.nlm.nih.gov/pubmed/17873219", "http://www.ncbi.nlm.nih.gov/pubmed/17948979", "http://www.ncbi.nlm.nih.gov/pubmed/19270679", "http://www.ncbi.nlm.nih.gov/pubmed/20401157", "http://www.ncbi.nlm.nih.gov/pubmed/27840788", "http://www.ncbi.nlm.nih.gov/pubmed/8016689", "http://pdf.usaid.gov/pdf_docs/PNABK503.pdf", "http://www.eabfu.gov.hk/en/pdf/income.pdf", 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"http://image.guardian.co.uk/sys-files/Guardian/documents/2009/03/13/inequality.pdf", "http://www.moneyweb.co.za/moneyweb-economic-trends/the-gini-is-still-in-the-bottle", "https://www.forbes.com/forbes/2003/0317/098.html", "https://link.springer.com/content/pdf/10.1023%2FA:1010920819831.pdf", "https://www.theguardian.com/money/2015/oct/13/half-world-wealth-in-hands-population-inequality-report", "https://www.census.gov/population/www/cps/cpsdef.html", "https://www.census.gov/prod/2011pubs/p60-239.pdf", "https://www.cia.gov/library/publications/the-world-factbook/rankorder/2172rank.html", "https://id.ndl.go.jp/auth/ndlna/01126754", "https://wayback.archive-it.org/all/20171020065423/ftp://ftp.fao.org/docrep/fao/012/ak968e/ak968e00.pdf", "https://web.archive.org/web/20030519155531/https://www.econometricsociety.org/meetings/wc00/pdf/0883.pdf", "https://web.archive.org/web/20081201193249/http://www.eurofound.europa.eu/areas/qualityoflife/eurlife/index.php?template=3&radioindic=158&idDomain=3", "https://web.archive.org/web/20081218111312/http://www.bundesbank.de/download/bankenaufsicht/dkp/200503dkp_b.pdf", "https://web.archive.org/web/20120803160551/http://ias7.berkeley.edu/academics/courses/center/fall2007/sehnbruch/atkinson%201998%20contributions%20of%20sen%20to%20welf%20economics.pdf", "https://web.archive.org/web/20130605143955/http://www-wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2001/02/17/000094946_01020605310354/Rendered/PDF/multi_page.pdf", "https://web.archive.org/web/20140524045505/http://www.kpmg.com/Africa/en/KPMG-in-Africa/Documents/2013%20Q4%20snapshots/KPMG_South%20Africa%202013Q4.pdf", "https://web.archive.org/web/20140712032137/https://data.undp.org/dataset/Income-Gini-coefficient/36ku-rvrj", "https://web.archive.org/web/20141109193609/http://stats.oecd.org/Index.aspx?QueryId=26068", "https://www.npr.org/sections/goatsandsoda/2017/01/25/511594991/what-the-stat-about-the-8-richest-men-doesnt-tell-us-about-inequality", "https://www.un.org/esa/desa/papers/2006/wp27_2006.pdf", "https://data.undp.org/dataset/Income-Gini-coefficient/36ku-rvrj", "https://www.wikidata.org/wiki/Q162455", "https://openknowledge.worldbank.org/bitstream/handle/10986/25078/9781464809583.pdf"]}, "Stochastic gradient descent": {"categories": ["All articles with dead external links", "All articles with unsourced statements", "Articles with dead external links from June 2018", "Articles with inconsistent citation formats", "Articles with permanently dead external links", "Articles with unsourced statements from July 2015", "Articles with unsourced statements from October 2017", "Computational statistics", "Convex optimization", "Gradient methods", "M-estimators", "Machine learning algorithms", "Statistical approximations", "Stochastic optimization", "Wikipedia articles needing clarification from October 2017"], "title": "Stochastic gradient descent", "method": "Stochastic gradient descent", "url": "https://en.wikipedia.org/wiki/Stochastic_gradient_descent", "summary": "Stochastic gradient descent (often shortened to SGD), also known as incremental gradient descent, is an iterative method for optimizing a differentiable objective function, a stochastic approximation of gradient descent optimization. A recent article implicitly credits Herbert Robbins and Sutton Monro for developing SGD in their 1951 article titled \"A Stochastic Approximation Method\"; see Stochastic approximation for more information. It is called stochastic because samples are selected randomly (or shuffled) instead of as a single group (as in standard gradient descent) or in the order they appear in the training set.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f3/Stogra.png"], "links": ["ADALINE", "Adaptive learning rate", "Advances in Neural Information Processing Systems", "ArXiv", "Artificial neural network", "Artificial neural networks", "Backpropagation", "Bibcode", "Bisection method", "C Sharp (programming language)", "Conditional random field", "Convex function", "Convex optimization", "Coordinate descent", "Data set", "David O. Siegmund", "David Rumelhart", "Differentiable function", "Digital object identifier", "Dimitri P. 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Williams", "Rprop", "Sampling (statistics)", "Score (statistics)", "Springer International Publishing", "Stationary point", "Statistics", "Stochastic approximation", "Support vector machine", "Vectorization (mathematics)", "Vowpal Wabbit", "William C. Davidon"], "references": ["http://www.cs.utoronto.ca/~ilya/pubs/2013/1051_2.pdf", "http://www.cs.utoronto.ca/~ilya/pubs/ilya_sutskever_phd_thesis.pdf", "http://yann.lecun.com/exdb/publis/pdf/lecun-98b.pdf", "http://extras.springer.com/2018/978-3-319-77585-2", "http://studyofai.com/machine-learning-algorithms/", "http://adsabs.harvard.edu/abs/1986Natur.323..533R", "http://www.seas.harvard.edu/courses/cs181/files/lecture05-notes.pdf", "http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf", "http://seed.ucsd.edu/mediawiki/images/6/6a/Adagrad.pdf", "http://www.meyn.ece.ufl.edu/archive/spm_files/Courses/ECE555-2011/555media/poljud92.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/12662478", "http://codingplayground.blogspot.it/2013/05/stocastic-gradient-descent.html", "http://www.aclweb.org/anthology/P08-1109", "http://www.ams.org/mathscinet-getitem?mr=0418461", "http://www.ams.org/mathscinet-getitem?mr=1819784", "http://www.ams.org/mathscinet-getitem?mr=2085944", "http://arxiv.org/abs/1212.5701", "http://arxiv.org/abs/1412.6980", "http://arxiv.org/abs/1512.01139", "http://arxiv.org/abs/1703.00209", "http://leon.bottou.org/papers/bottou-98x", "http://leon.bottou.org/papers/bottou-bousquet-2008", "http://leon.bottou.org/papers/bottou-mlss-2004", "http://leon.bottou.org/projects/sgd", "http://doi.org/10.1007%2FBF00935703", "http://doi.org/10.1007%2FPL00011414", "http://doi.org/10.1038%2F323533a0", "http://doi.org/10.1073%2Fpnas.1806579115", "http://doi.org/10.1080%2F01621459.1982.10477894", "http://doi.org/10.1137%2F15M1048239", "http://doi.org/10.1137%2FS1052623400376366", "http://doi.org/10.1137%2FS1052623494268522", "http://ieeexplore.ieee.org/abstract/document/5726679/", "http://jmlr.org/papers/volume12/duchi11a/duchi11a.pdf", "http://jmlr.org/papers/volume15/gupta14a/gupta14a.pdf", "http://www.jstor.org/stable/2287314", "http://library.seg.org/doi/abs/10.1190/1.3627777", "http://epubs.siam.org/doi/10.1137/15M1048239", "http://epubs.siam.org/doi/10.1137/S1052623494268522", "http://www.worldcat.org/issn/0025-5610", "http://www.worldcat.org/issn/1052-6234", "https://github.com/JohnLangford/vowpal_wabbit", "https://www.springer.com/gp/book/9783319775852", "https://web.archive.org/web/20131224113826/http://klcl.pku.edu.cn/member/sunxu/code.htm", "https://web.archive.org/web/20150330033637/http://seed.ucsd.edu/mediawiki/images/6/6a/Adagrad.pdf"]}, "Weight function": {"categories": ["Combinatorial optimization", "Functional analysis", "Mathematical analysis", "Measure theory", "Types of functions"], "title": "Weight function", "method": "Weight function", "url": "https://en.wikipedia.org/wiki/Weight_function", "summary": "A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more \"weight\" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis, and are closely related to the concept of a measure. Weight functions can be employed in both discrete and continuous settings. 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In the lowest order product the adjustment corresponds to subtracting off the mean value, to leave a result whose mean is zero. For the higher order products the adjustment involves subtracting off lower order (ordinary) products of the random variables, in a symmetric way, again leaving a result whose mean is zero. The Wick product is a polynomial function of the random variables, their expected values, and expected values of their products.\nThe definition of the Wick product immediately leads to the Wick power of a single random variable and this allows analogues of other functions of random variables to be defined on the basis of replacing the ordinary powers in a power-series expansions by the Wick powers. The Wick powers of commonly-seen random variables can be expressed in terms of special functions such as Bernoulli polynomials or Hermite polynomials.\nThe Wick product is named after physicist Gian-Carlo Wick, cf. 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For the presence of I(2) variables see Ch. 9 of his 1995 textbook. This test permits more than one cointegrating relationship so is more generally applicable than the Engle\u2013Granger test which is based on the Dickey\u2013Fuller (or the augmented) test for unit roots in the residuals from a single (estimated) cointegrating relationship.There are two types of Johansen test, either with trace or with eigenvalue, and the inferences might be a little bit different. The null hypothesis for the trace test is that the number of cointegration vectors is r=r*<k, vs. the alternative that r=k. Testing proceeds sequentially for r*=1,2,etc. and the first non-rejection of the null is taken as an estimate of r. The null hypothesis for the \"maximum eigenvalue\" test is as for the trace test but the alternative is r=r*+1 and, again, testing proceeds sequentially for r*=1,2,etc., with the first non-rejection used as an estimator for r.\nJust like a unit root test, there can be a constant term, a trend term, both, or neither in the model. For a general VAR(p) model:\n\n \n \n \n \n X\n \n t\n \n \n =\n \u03bc\n +\n \u03a6\n \n D\n \n t\n \n \n +\n \n \u03a0\n \n p\n \n \n \n X\n \n t\n \u2212\n p\n \n \n +\n \u22ef\n +\n \n \u03a0\n \n 1\n \n \n \n X\n \n t\n \u2212\n 1\n \n \n +\n \n e\n \n t\n \n \n ,\n \n t\n =\n 1\n ,\n \u2026\n ,\n T\n \n \n {\\displaystyle X_{t}=\\mu +\\Phi D_{t}+\\Pi _{p}X_{t-p}+\\cdots +\\Pi _{1}X_{t-1}+e_{t},\\quad t=1,\\dots ,T}\n There are two possible specifications for error correction: that is, two VECM (vector error correction models):\n1. The longrun VECM:\n\n \n \n \n \u0394\n \n X\n \n t\n \n \n =\n \u03bc\n +\n \u03a6\n \n D\n \n t\n \n \n +\n \u03a0\n \n X\n \n t\n \u2212\n p\n \n \n +\n \n \u0393\n \n p\n \u2212\n 1\n \n \n \u0394\n \n X\n \n t\n \u2212\n p\n +\n 1\n \n \n +\n \u22ef\n +\n \n \u0393\n \n 1\n \n \n \u0394\n \n X\n \n t\n \u2212\n 1\n \n \n +\n \n \u03b5\n \n t\n \n \n ,\n \n t\n =\n 1\n ,\n \u2026\n ,\n T\n \n \n {\\displaystyle \\Delta X_{t}=\\mu +\\Phi D_{t}+\\Pi X_{t-p}+\\Gamma _{p-1}\\Delta X_{t-p+1}+\\cdots +\\Gamma _{1}\\Delta X_{t-1}+\\varepsilon _{t},\\quad t=1,\\dots ,T}\n \nwhere\n\n \n \n \n \n \u0393\n \n i\n \n \n =\n \n \u03a0\n \n 1\n \n \n +\n \u22ef\n +\n \n \u03a0\n \n i\n \n \n \u2212\n I\n ,\n \n i\n =\n 1\n ,\n \u2026\n ,\n p\n \u2212\n 1.\n \n \n \n {\\displaystyle \\Gamma _{i}=\\Pi _{1}+\\cdots +\\Pi _{i}-I,\\quad i=1,\\dots ,p-1.\\,}\n 2. The transitory VECM:\n\n \n \n \n \u0394\n \n X\n \n t\n \n \n =\n \u03bc\n +\n \u03a6\n \n D\n \n t\n \n \n \u2212\n \n \u0393\n \n p\n \u2212\n 1\n \n \n \u0394\n \n X\n \n t\n \u2212\n p\n +\n 1\n \n \n \u2212\n \u22ef\n \u2212\n \n \u0393\n \n 1\n \n \n \u0394\n \n X\n \n t\n \u2212\n 1\n \n \n +\n \u03a0\n \n X\n \n t\n \u2212\n 1\n \n \n +\n \n \u03b5\n \n t\n \n \n ,\n \n t\n =\n 1\n ,\n \u22ef\n ,\n T\n \n \n {\\displaystyle \\Delta X_{t}=\\mu +\\Phi D_{t}-\\Gamma _{p-1}\\Delta X_{t-p+1}-\\cdots -\\Gamma _{1}\\Delta X_{t-1}+\\Pi X_{t-1}+\\varepsilon _{t},\\quad t=1,\\cdots ,T}\n \nwhere\n\n \n \n \n \n \u0393\n \n i\n \n \n =\n \n (\n \n \n \u03a0\n \n i\n +\n 1\n \n \n +\n \u22ef\n +\n \n \u03a0\n \n p\n \n \n \n )\n \n ,\n \n i\n =\n 1\n ,\n \u2026\n ,\n p\n \u2212\n 1.\n \n \n \n {\\displaystyle \\Gamma _{i}=\\left(\\Pi _{i+1}+\\cdots +\\Pi _{p}\\right),\\quad i=1,\\dots ,p-1.\\,}\n Be aware that the two are the same. In both VECM (Vector Error Correction Model),\n\n \n \n \n \u03a0\n =\n \n \u03a0\n \n 1\n \n \n +\n \u22ef\n +\n \n \u03a0\n \n p\n \n \n \u2212\n I\n .\n \n \n \n {\\displaystyle \\Pi =\\Pi _{1}+\\cdots +\\Pi _{p}-I.\\,}\n Inferences are drawn on \u03a0, and they will be the same, so is the explanatory power.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Augmented Dickey\u2013Fuller test", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrica", "Econometrics", "Effect size", "Efficiency (statistics)", "Eigenvalue", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Engle\u2013Granger test", "Environmental statistics", "Epidemiology", "Error correction model", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "G. S. Maddala", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order of integration", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "S\u00f8ren Johansen", "Time domain", "Time series", "Tolerance interval", "Trace (linear algebra)", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Unit root", "Unit root test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.jstor.org/stable/2938278", "https://books.google.com/books?id=BH7nCwAAQBAJ&dq=Johansen+1995&source=gbs_navlinks_s", "https://books.google.com/books?id=ZQsaRNl5J60C&pg=PA219", "https://books.google.com/books?id=llXBvougICMC&pg=PA198", "https://books.google.com/books?id=shWtvsFbxlkC"]}, "Spearman\u2013Brown prediction formula": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from January 2012", "Comparison of assessments", "Psychometrics"], "title": "Spearman\u2013Brown prediction formula", "method": "Spearman\u2013Brown prediction formula", "url": "https://en.wikipedia.org/wiki/Spearman%E2%80%93Brown_prediction_formula", "summary": "The Spearman\u2013Brown prediction formula, also known as the Spearman\u2013Brown prophecy formula, is a formula relating psychometric reliability to test length and used by psychometricians to predict the reliability of a test after changing the test length. The method was published independently by Spearman (1910) and Brown (1910).\n\n", "images": [], "links": ["Charles Spearman", "Cronbach's alpha", "Digital object identifier", "Howard Wainer", "International Standard Book Number", "Item response theory", "Psychometric", "Reliability (psychometric)", "William Brown (psychologist)"], "references": ["http://doi.org/10.1007%2Fs00038-012-0416-3"]}, "D'Agostino's K-squared test": {"categories": ["All articles lacking reliable references", "All articles with unsourced statements", "Articles lacking reliable references from November 2010", "Articles with unsourced statements from January 2012", "Normality tests", "Parametric statistics"], "title": "D'Agostino's K-squared test", "method": "D'Agostino's K-squared test", "url": "https://en.wikipedia.org/wiki/D%27Agostino%27s_K-squared_test", "summary": "In statistics, D\u2019Agostino\u2019s K2 test, named for Ralph D'Agostino, is a goodness-of-fit measure of departure from normality, that is the test aims to establish whether or not the given sample comes from a normally distributed population. The test is based on transformations of the sample kurtosis and skewness, and has power only against the alternatives that the distribution is skewed and/or kurtic.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central moment", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness-of-fit", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "K. O. Bowman", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normality tests", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The American Statistician", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.cee.mtu.edu/~vgriffis/CE%205620%20materials/CE5620%20Reading/DAgostino%20et%20al%20-%20normaility%20tests.pdf", "http://doi.org/10.1080%2F01621459.1977.10479940", "http://doi.org/10.1093%2Fbiomet%2F22.3-4.423", "http://doi.org/10.1093%2Fbiomet%2F57.3.679", "http://doi.org/10.1093%2Fbiomet%2F70.1.227", "http://doi.org/10.2307%2F2684359", "http://www.jstor.org/stable/2286939", "http://www.jstor.org/stable/2332104", "http://www.jstor.org/stable/2334794", "http://www.jstor.org/stable/2335960", "http://www.jstor.org/stable/2684359", "https://web.archive.org/web/20120325140006/http://www.cee.mtu.edu/~vgriffis/CE%205620%20materials/CE5620%20Reading/DAgostino%20et%20al%20-%20normaility%20tests.pdf"]}, "Sampling error": {"categories": ["Auditing terms", "Errors and residuals", "Sampling (statistics)"], "title": "Sampling error", "method": "Sampling error", "url": "https://en.wikipedia.org/wiki/Sampling_error", "summary": "In statistics, sampling error is incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics on the sample, such as means and quantiles, generally differ from the characteristics of the entire population, which are known as parameters. For example, if one measures the height of a thousand individuals from a country of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country. Since sampling is typically done to determine the characteristics of a whole population, the difference between the sample and population values is considered an error. Exact measurement of sampling error is generally not feasible since the true population values are unknown.", "images": [], "links": ["Errors and residuals", "Errors and residuals in statistics", "Estimator", "International Standard Book Number", "Margin of error", "Non-sampling error", "Observation", "Population bottleneck", "Probability", "Propagation of uncertainty", "Random sample", "Random sampling", "Ratio estimator", "Sample (statistics)", "Sample size determination", "Sampling (statistics)", "Sampling bias", "Standard error", "Statistic", "Statistical power", "Statistical theory", "Statistics", "Systematic error", "Systematic errors"], "references": ["http://itfeature.com/statistics/sampling-error-definition-example-formula", "http://www.itl.nist.gov/div898/handbook/ppc/section3/ppc333.htm", "http://www.amstat.org/sections/srms/pamphlet.pdf"]}, "Factorial experiment": {"categories": ["CS1 maint: Uses authors parameter", "Design of experiments", "Statistical process control"], "title": "Factorial experiment", "method": "Factorial experiment", "url": "https://en.wikipedia.org/wiki/Factorial_experiment", "summary": "In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or \"levels\", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.\nFor the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a 2\u00d72 factorial design.\nIf the number of combinations in a full factorial design is too high to be logistically feasible, a fractional factorial design may be done, in which some of the possible combinations (usually at least half) are omitted.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/58/Cube_plot_for_bearing_life.svg", "https://upload.wikimedia.org/wikipedia/commons/9/94/Factorial_Design.svg", "https://upload.wikimedia.org/wikipedia/commons/0/00/Interaction_plots_filtration_rate.png", "https://upload.wikimedia.org/wikipedia/commons/d/dd/Montgomery_filtration_cube_plot.png", "https://upload.wikimedia.org/wikipedia/commons/e/e5/Montgomery_filtration_rates.svg", "https://upload.wikimedia.org/wikipedia/commons/7/75/Pareto_plot_filtration_rate.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cc/Response_surface_metodology.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Biased sample", "Binomial regression", "Biographical Memoirs of Fellows of the Royal Society", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinatorial design", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental error", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Fractional factorial designs", "Frank Yates", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "George E. P. Box", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Bennet Lawes", "Jonckheere's trend test", "Joseph Henry Gilbert", "Journal of the Ministry of Agriculture of Great Britain", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kenneth Mather", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Main effect", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal probability plot", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Parametric statistics", "Pareto chart", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plackett\u2013Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quadratic function", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Reproducibility", "Resampling (statistics)", "Response surface methodology", "Response variable", "Restricted randomization", "Robust regression", "Robust statistics", "Ronald Fisher", "Rothamsted Experimental Station", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Sparsity-of-effects principle", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "The Design of Experiments", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Welch's t-test", "Whittle likelihood", "Wilcoxon signed-rank test", "Yates analysis", "Z-test"], "references": ["http://digital.library.adelaide.edu.au/coll/special//fisher/fisherbiog.pdf", "http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15191/1/48.pdf", "http://jeff560.tripod.com/f.html", "http://psych.csufresno.edu/psy144/Content/Design/Experimental/factorial.html", "http://methodology.psu.edu/ra/most/factorial", "http://users.stat.umn.edu/~gary/Book.html", "http://doi.org/10.1037%2Fh0026714", "http://doi.org/10.1098%2Frsbm.1963.0006", "http://doi.org/10.1098%2Frsta.1989.0008", "https://web.archive.org/web/20090218135035/http://digital.library.adelaide.edu.au/coll/special/"]}, "Generalized Tobit": {"categories": ["All Wikipedia articles needing context", "All pages needing cleanup", "All stub articles", "Econometrics stubs", "Single-equation methods (econometrics)", "Wikipedia articles needing context from October 2009", "Wikipedia introduction cleanup from October 2009"], "title": "Generalized Tobit", "method": "Generalized Tobit", "url": "https://en.wikipedia.org/wiki/Generalized_Tobit", "summary": "In econometrics, the generalized Tobit model is a generalization of the Tobit model named after James Tobin. It is also called the Heckit model after James Heckman. Another \nname is \"type 2 Tobit model\".Tobit models assume that a random variable is censored.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Arthur Goldberger", "Censoring (statistics)", "Econometrics", "Herman Wouk", "International Standard Book Number", "James Heckman", "James Tobin", "Probit", "The Caine Mutiny", "Tobit model"], "references": ["http://korora.econ.yale.edu/et/interview/tobin.pdf", "http://pan.oxfordjournals.org/content/8/2/167.short"]}, "Copula (statistics)": {"categories": ["Actuarial science", "All articles with unsourced statements", "Articles with unsourced statements from March 2015", "CS1 maint: Multiple names: authors list", "Independence (probability theory)", "Multivariate statistics", "Systems of probability distributions", "Wikipedia articles needing clarification from September 2011"], "title": "Copula (probability theory)", "method": "Copula (statistics)", "url": "https://en.wikipedia.org/wiki/Copula_(probability_theory)", "summary": "In probability theory and statistics, a copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform. Copulas are used to describe the dependence between random variables. Their name comes from the Latin for \"link\" or \"tie\", similar but unrelated to grammatical copulas in linguistics. Copulas have been used widely in quantitative finance to model and minimize tail risk and portfolio optimization applications.Sklar's theorem states that any multivariate joint distribution can be written in terms of univariate marginal-distribution functions and a copula which describes the dependence structure between the variables.\nCopulas are popular in high-dimensional statistical applications as they allow one to easily model and estimate the distribution of random vectors by estimating marginals and copulae separately. There are many parametric copula families available, which usually have parameters that control the strength of dependence. Some popular parametric copula models are outlined below.\nTwo-dimensional copulas are known in some other areas of mathematics under the name permutons and doubly-stochastic measures.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/67/Biv_gumbel_dist.png", "https://upload.wikimedia.org/wikipedia/commons/6/64/Copula_gaussian.svg", "https://upload.wikimedia.org/wikipedia/commons/b/bc/Copule_ord.svg", "https://upload.wikimedia.org/wikipedia/commons/6/60/Four_Correlations.png", "https://upload.wikimedia.org/wikipedia/commons/6/6b/Gaussian_copula_gaussian_marginals.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abe Sklar", "Absolutely continuous", "Accelerated failure time model", "Actuarial analysis", "Actuarial science", "Agent-based computational economics", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Statistics", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Basket option", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartesian product", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Collateralized debt obligation", "Comonotonicity", "Completely monotone function", "Completeness (statistics)", "Confidence interval", "Confounding", "Constant maturity swap", "Contingency table", "Continuous probability distribution", "Control chart", "Convex function", "Copula (linguistics)", "Correlation and dependence", "Correlation matrix", "Correlogram", "Count data", "Credible interval", "Credit derivative", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "D-monotone function", "Data collection", "David Clayton", "David X. Li", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Derivatives pricing", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Emergent phenomenon", "Emil Julius Gumbel", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Equity derivative", "Errors and residuals in statistics", "Estimating equations", "Exotic derivative", "Experiment", "Exponential family", "Exponential smoothing", "Extreme value theory", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Financial Times", "Financial panic", "Financial risk modeling", "First-hitting-time model", "Flight-to-quality", "Foreign exchange derivatives", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Global financial crisis of 2008\u20132009", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Herd behavior", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hyperrectangle", "Implied volatility", "Index of dispersion", "Interaction (statistics)", "Interest rate derivative", "International Standard Book Number", "Interquartile range", "Interval estimation", "Investment management", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Futures Markets", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Linguistics", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marginal distribution", "Marginal probability", "Maurice Ren\u00e9 Fr\u00e9chet", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Mir Maswood Ali", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo methods in finance", "Multiple comparisons", "Multivariable calculus", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate probability distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Pairs trading", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Portfolio optimization", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability integral transform", "Probability theory", "Proportional hazards model", "Pseudo-random", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quantitative finance", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (mathematics)", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability (statistics)", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Risk management", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Securitization", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simulation", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spread option", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical arbitrage", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Stress test (financial)", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Systemic risk", "Tail risk", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Two-moment decision model", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "Unit cube", "University of Edinburgh School of Social and Political Sciences", "V-statistic", "Value-at-Risk", "Variance", "Vector autoregression", "Vine copula", "Volatility smile", "Wald test", "Warranty", "Wassily Hoeffding", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.mathfinance.cn/tags/copula", "http://www.crystalballservices.com/Resources/ConsultantsCornerBlog/tagid/21/Correlation.aspx", "http://www.ft.com/cms/s/2/912d85e8-2d75-11de-9eba-00144feabdc0.html", "http://sites.google.com/site/copulawiki/", "http://trb.metapress.com/content/m3146tg612k80771/?p=d6b0d7200af148b8a4e18e592ca1e269&pi=3", "http://ssrn.com/abstract=1752702", "http://www.worldscientific.com/doi/suppl/10.1142/p842/suppl_file/p842_chap01.pdf", "http://adsabs.harvard.edu/abs/2009IJCli..29..937L", "http://adsabs.harvard.edu/abs/2009PLSCB...5E0577O", "http://adsabs.harvard.edu/abs/2011HESS...15.2401L", "http://adsabs.harvard.edu/abs/2017SoEn..143...10M", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2776173", "http://www.ncbi.nlm.nih.gov/pubmed/19956759", "http://rogermcooke.net/rogermcooke_files/Vines%20Arise%20Handbook%20VCM.pdf", "http://arxiv.org/abs/0908.3750", "http://arxiv.org/abs/1603.04166", "http://doi.org/10.1002%2Ffut.10110", "http://doi.org/10.1002%2Fjoc.1852", "http://doi.org/10.1007%2Fs11009-011-9224-0", "http://doi.org/10.1016%2Fj.compstruc.2015.02.029", "http://doi.org/10.1016%2Fj.ejor.2014.03.016", "http://doi.org/10.1016%2Fj.insmatheco.2007.02.001", "http://doi.org/10.1016%2Fj.jbankfin.2013.02.036", "http://doi.org/10.1016%2Fj.jeconbus.2016.01.003", "http://doi.org/10.1016%2Fj.solener.2016.12.022", "http://doi.org/10.1016%2Fj.solener.2017.09.028", "http://doi.org/10.1016%2Fs0304-405x(02)00068-5", "http://doi.org/10.1080%2F00102202.2012.696566", "http://doi.org/10.1080%2F13647830.2014.898409", "http://doi.org/10.1080%2F14697688.2016.1164337", "http://doi.org/10.1093%2Fbiomet%2F65.1.141", "http://doi.org/10.1111%2F0022-1082.00340", "http://doi.org/10.1111%2Facfi.12274", "http://doi.org/10.1111%2Frssb.12162", "http://doi.org/10.1145%2F1537614.1537654", "http://doi.org/10.1214%2F07-AOS556", "http://doi.org/10.1371%2Fjournal.pcbi.1000577", "http://doi.org/10.3141%2F2262-20", "http://doi.org/10.5194%2Fhess-15-2401-2011", "http://doi.org/10.5194%2Fnpg-15-761-2008", "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6134288", "http://jmlr.org/proceedings/papers/v31/eban13a.pdf", "http://www.jstor.org/stable/2335289", "http://www.ploscompbiol.org/article/info:doi%2F10.1371%2Fjournal.pcbi.1000577", "http://www.sps.ed.ac.uk/__data/assets/pdf_file/0003/84243/Gaussian14.pdf", "http://www-history.mcs.st-andrews.ac.uk/Biographies/Hoeffding.html", "http://www.lrb.co.uk/v30/n09/mack01_.html", "https://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=all", "https://web.archive.org/web/20100705040514/http://www.tu-chemnitz.de/mathematik/fima/publikationen/TSchmidt_Copulas.pdf", "https://www.encyclopediaofmath.org/index.php?title=p/c110410", "https://cran.r-project.org/package=TruncatedNormal"]}, "Tucker decomposition": {"categories": ["All stub articles", "Dimension reduction", "Statistics stubs"], "title": "Tucker decomposition", "method": "Tucker decomposition", "url": "https://en.wikipedia.org/wiki/Tucker_decomposition", "summary": "In mathematics, Tucker decomposition decomposes a tensor into a set of matrices and one small core tensor. It is named after Ledyard R. Tucker\nalthough it goes back to Hitchcock in 1927.\nInitially described as a three-mode extension of factor analysis and principal component analysis it may actually be generalized to higher mode analysis.\nIt may be regarded as a more flexible PARAFAC (parallel factor analysis) model. In PARAFAC the core tensor is restricted to be \"diagonal\".\nIn practice, Tucker decomposition is used as a modelling tool. For instance, it is used to model three-way (or higher way) data by means of relatively small numbers of components for each of the three or more modes, and the components are linked to each other by a three- (or higher-) way core array. The model parameters are estimated in such a way that, given fixed numbers of components, the modelled data optimally resemble the actual data in the least squares sense. The model gives a summary of the information in the data, in the same way as principal components analysis does for two-way data.\nFor a third-order tensor T (n1 x n2 x n3) , a core tensor R (r1 x r2 x r3) , and matrices A (n1 x r1) ;B (n2 x r2) ;C (n3 x r3)\nT \u2248 R x1 A x2 B x3 C.\nWhere x1 is mode-1 product and similarly x2 and x3.\nThere are two special cases of Tucker decomposition (order three tensors):\nTucker1: B an C are identity, thus T \u2248 R x1 A\nTucker2: C is identity, thus T \u2248 R x1 A x2 B.\nRESCAL decomposition can be seen as a special case of Tucker where C is identity and A is equal to B.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Digital object identifier", "F. L. Hitchcock", "Factor analysis", "Frank Lauren Hitchcock", "Higher-order singular value decomposition", "Journal of Mathematics and Physics", "Ledyard R. Tucker", "Multilinear principal component analysis", "PARAFAC", "Principal component analysis", "Psychometrika", "Statistics", "Tensor"], "references": ["http://doi.org/10.1007%2FBF02289464"]}, "Neighbourhood components analysis": {"categories": ["Statistical classification"], "title": "Neighbourhood components analysis", "method": "Neighbourhood components analysis", "url": "https://en.wikipedia.org/wiki/Neighbourhood_components_analysis", "summary": "Neighbourhood components analysis is a supervised learning method for classifying multivariate data into distinct classes according to a given distance metric over the data. Functionally, it serves the same purposes as the K-nearest neighbors algorithm, and makes direct use of a related concept termed stochastic nearest neighbours.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Affine combination", "Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Boosting (machine learning)", "Bootstrap aggregating", "C++", "CURE data clustering algorithm", "Canonical correlation analysis", "Cluster analysis", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Conjugate gradient method", "Convolutional neural network", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Dimensionality reduction", "Empirical risk minimization", "Ensemble learning", "Euclidean distance", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature engineering", "Feature learning", "Gated recurrent unit", "Glossary of artificial intelligence", "Gradient", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "Independent component analysis", "International Conference on Machine Learning", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Large margin nearest neighbor", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Mean-shift", "Metric (mathematics)", "Mlpack", "Model selection", "Multilayer perceptron", "Multivariate statistics", "Naive Bayes classifier", "Non-negative matrix factorization", "OPTICS algorithm", "Occam learning", "Online machine learning", "Outline of machine learning", "Perceptron", "Principal component analysis", "Probably approximately correct learning", "Q-learning", "Random forest", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Self-organizing map", "Semi-supervised learning", "Softmax activation function", "Spectral clustering", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Stochastic gradient descent", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory"], "references": ["http://www.csri.utoronto.ca/~roweis/papers/ncanips.pdf", "https://github.com/vomjom/nca", "https://arxiv.org/list/cs.LG/recent"]}, "SPC XL": {"categories": ["Microsoft Office-related statistical software", "Pages using Infobox software with unknown parameters", "Windows-only software"], "title": "SPC XL", "method": "SPC XL", "url": "https://en.wikipedia.org/wiki/SPC_XL", "summary": "SPC XL is a statistical add-in for Microsoft Excel. SPC XL is a replacement for SPC KISS which was released in 1993 making it one of the oldest statistical addons to Excel. SPC XL provides statistical analysis including Control chart, Process capability, Histogram, Pareto chart, and ANOVA Gage R&R. \nSPC XL is compatible with Microsoft Excel 2000, 2002 & 2003, and Excel 2007.", "images": [], "links": ["ADMB", "ANOVA Gage R&R", "Analyse-it", "BMDP", "BV4.1 (software)", "CSPro", "Commercial software", "Comparison of statistical packages", "Control chart", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "EViews", "Epi Info", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "Histogram", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Pareto chart", "Process capability", "Proprietary software", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistics", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.qualitymag.com/", "http://www.sigmazone.com/spcxl.htm", "http://www.ject.org/"]}, "Group size measures": {"categories": ["Behavioral ecology", "Behavioural sciences", "Ethology", "Group processes", "Herding", "Psychometrics", "Sociobiology"], "title": "Group size measures", "method": "Group size measures", "url": "https://en.wikipedia.org/wiki/Group_size_measures", "summary": "Many animals, including humans, tend to live in groups, herds, flocks, bands, packs, shoals, or colonies (hereafter: groups) of conspecific individuals. The size of these groups, as expressed by the number of people/etc in a group such as 8 groups of 9 people in each one, is an important aspect of their social environment. Group size tend to be highly variable even within the same species, thus we often need statistical measures to quantify group size and statistical tests to compare these measures between two or more samples. Group size measures are notoriously hard to handle statistically since groups sizes typically follow an aggregated (right-skewed) distribution: most groups are small, few are large, and a very few are very large. \nStatistical measures of group size roughly fall into two categories.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/35/ARS_sheep_herding.jpg", "https://upload.wikimedia.org/wikipedia/commons/5/5e/Auklet_flock_Shumagins_1986.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/45/Canis_lupus_pack_surrounding_Bison.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/2e/Common_Coots_I_IMG_9270.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/7d/Common_Cranes_%28Grus_grus%29_at_Sultanpur_I_Picture_076.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/b0/Dolphins_gesture_language.jpg", "https://upload.wikimedia.org/wikipedia/commons/5/51/Flamingos_flying.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/03/Great_Woodswallow_group.jpg", "https://upload.wikimedia.org/wikipedia/commons/6/6b/Lutjanus_kasmira_school.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a9/Rook_colonies_smoothed_2.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f0/Sa_aphid_colony_highres.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/0e/T%C3%B6lpelperce.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/30/Vicugna_vicugna.JPG", "https://upload.wikimedia.org/wikipedia/commons/8/87/Wild_Dog_Kruger_National_Park_South_Africa.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/84/Yellow_Paper_Wasp.jpg", "https://upload.wikimedia.org/wikipedia/en/2/29/CapeBuffalo-Mara.JPG", "https://upload.wikimedia.org/wikipedia/commons/b/bd/Elephant_seal_colony_edit.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/95/Red-billed_quelea_flocking_at_waterhole.jpg"], "links": ["Active matter", "African buffalo", "African wild dog", "Agent-based model", "Agent-based model in biology", "Allee effect", "Altitudinal migration", "Animal migration", "Animal migration tracking", "Animal navigation", "Ant colony optimization algorithms", "Ant robotics", "Aphid", "Arithmetic mean", "Artificial ants", "Bait ball", "Bird colony", "Bird migration", "Bluestripe snapper", "Boids", "Bottlenose dolphin", "Cell migration", "Clustering of self-propelled particles", "Coded wire tag", "Collective animal behavior", "Collective intelligence", "Collective motion", "Common coot", "Common crane", "Confidence interval", "Crowd simulation", "Decentralised system", "Diel vertical migration", "Elephant seal", "European Journal of Ecology", "Eusociality", "Feeding frenzy", "Fish migration", "Flamingo", "Flock (birds)", "Flocking (behavior)", "Gannet", "Great woodswallow", "Herd", "Herd behavior", "Homing (biology)", "Insect migration", "Intelligent Small World Autonomous Robots for Micro-manipulation", "Lepidoptera migration", "Lessepsian migration", "Median", "Microbial intelligence", "Microbotics", "Mixed-species foraging flock", "Mobbing (animal behavior)", "Monarch butterfly migration", "Mutualism (biology)", "Nanorobotics", "Natal homing", "Pack (canine)", "Pack hunter", "Parametric statistics", "Particle swarm optimization", "Patterns of self-organization in ants", "Philopatry", "Polistes dominula", "Predator satiation", "Quorum sensing", "Red-billed quelea", "Reverse migration (birds)", "Rook (bird)", "Salmon run", "Sardine run", "Sea turtle migration", "Self-propelled particles", "Sheep", "Shoaling and schooling", "Size of groups, organizations, and communities", "Skewness", "Sort sol", "Spatial organization", "Stigmergy", "Swarm (simulation)", "Swarm behaviour", "Swarm intelligence", "Swarm robotics", "Swarming (honey bee)", "Swarming (military)", "Swarming motility", "Symbrion", "Symmetry breaking of escaping ants", "Task allocation and partitioning of social insects", "Vicsek model", "Vicu\u00f1a", "Wolf"], "references": ["http://www.degruyter.com/abstract/j/eje.2015.1.issue-2/eje-2015-0011/eje-2015-0011.pdf", "http://digital.csic.es/bitstream/10261/49882/1/animal%20behav.doc", "http://www.zoologia.hu/flocker/flocker.html", "http://www.zoologia.hu/list/AnimBehav.pdf", "http://www.zoologia.hu/list/LWfG.pdf"]}, "Noncentral t-distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2014", "Continuous distributions", "Pages using deprecated image syntax"], "title": "Noncentral t-distribution", "method": "Noncentral t-distribution", "url": "https://en.wikipedia.org/wiki/Noncentral_t-distribution", "summary": "As with other probability distributions with noncentrality parameters, the noncentral t-distribution generalizes a probability distribution \u2013 Student's t-distribution \u2013 using a noncentrality parameter. Whereas the central distribution describes how a test statistic t is distributed when the difference tested is null, the noncentral distribution describes how t is distributed when the null is false. This leads to its use in statistics, especially calculating statistical power. The noncentral t-distribution is also known as the singly noncentral t-distribution, and in addition to its primary use in statistical inference, is also used in robust modeling for data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/88/Nc_student_t_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARGUS distribution", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confluent hypergeometric function", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Dagum distribution", "Data", "Data collection", "Davis distribution", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Divergence (statistics)", "Doubly noncentral t-distribution", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Experiment", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "Geostatistics", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Index of dispersion", "Interaction (statistics)", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Noncentral F-distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentrality parameter", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabolic fractal distribution", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrix", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Recursion", "Regression analysis", "Regression model validation", "Regularized incomplete beta function", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rice distribution", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable distribution", "Standard deviation", "Standard error", "Standard normal distribution", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Time domain", "Time series", "Tolerance interval", "Tolerance intervals", "Tracy\u2013Widom distribution", "Trend estimation", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://keisan.casio.com/menu/system/000000000610", "http://www.sciencedirect.com/science/article/B6TY8-47G44WX-V/2/7705d2642b1a384b13e0578898a22d48", "http://mathworld.wolfram.com/NoncentralStudentst-Distribution.html", "http://doi.org/10.1016%2FS0096-3003(02)00316-8", "http://doi.org/10.1080%2F00401706.1979.10489781", "http://doi.org/10.1093%2Fbiomet%2F48.3-4.465", "http://www.jstatsoft.org/v36/i05", "http://www.jstor.org/stable/1267759", "http://www.jstor.org/stable/2332772", "http://www.jstor.org/stable/2347693", "http://www.worldcat.org/issn/1548-7660"]}, "Recurrence period density entropy": {"categories": ["Dynamical systems", "Entropy", "Signal processing", "Stochastic processes"], "title": "Recurrence period density entropy", "method": "Recurrence period density entropy", "url": "https://en.wikipedia.org/wiki/Recurrence_period_density_entropy", "summary": "Recurrence period density entropy (RPDE) is a method, in the fields of dynamical systems, stochastic processes, and time series analysis, for determining the periodicity, or repetitiveness of a signal.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/8/86/RPDE_detail.gif", "https://upload.wikimedia.org/wikipedia/en/8/8a/RPDE_ranking.gif", "https://upload.wikimedia.org/wikipedia/en/d/d3/RPDE_real.gif"], "links": ["Autocorrelation", "Bibcode", "Digital object identifier", "Dynamical systems", "Embedding", "Embedding dimension", "Entropy", "Fourier transform", "Histogram", "I.i.d.", "Linear prediction", "Linear systems", "Mutual information", "Normal distribution", "Phase space", "Recurrence plot", "Recurrence quantification analysis", "Speech communication", "Stochastic processes", "Time series analysis", "White noise"], "references": ["http://adsabs.harvard.edu/abs/2007PhR...438..237M", "http://www.maxlittle.net/publications/bmeo.pdf", "http://www.maxlittle.net/publications/dfafullpath.pdf", "http://www.maxlittle.net/software/", "http://doi.org/10.1016%2Fj.physrep.2006.11.001", "http://www.recurrence-plot.tk/"]}, "Design effect": {"categories": ["Design of experiments", "Medical statistics"], "title": "Design effect", "method": "Design effect", "url": "https://en.wikipedia.org/wiki/Design_effect", "summary": "In statistics, the design effect (or estimates of unit variance) is an adjustment used in some kinds of studies, such as cluster randomised trials, to allow for the design structure. The adjustment inflates the variance of parameter estimates, and therefore their standard errors, which is necessary to allow for correlations among clusters of observations. It is similar to the variance inflation factor and is used in sample size calculations. The term was introduced by Leslie Kish in 1965.", "images": [], "links": ["Cluster analysis", "Cluster randomised trial", "Correlation", "Digital object identifier", "Estimator", "International Standard Book Number", "Intra-cluster correlation", "Leslie Kish", "Sample size", "Standard error (statistics)", "Statistics", "Variance", "Variance inflation factor"], "references": ["http://www3.interscience.wiley.com/journal/123212319/abstract", "http://nces.ed.gov/statprog/2002/glossary.asp", "http://doi.org/10.1002%2Fsim.3806", "http://doi.org/10.1093%2Fintqhc%2F14.6.521", "http://intqhc.oxfordjournals.org/cgi/content/full/14/6/521", "http://www-users.york.ac.uk/~mb55/talks/clusml.htm"]}, "Diffusion-limited aggregation": {"categories": ["Computer art", "Wiener process"], "title": "Diffusion-limited aggregation", "method": "Diffusion-limited aggregation", "url": "https://en.wikipedia.org/wiki/Diffusion-limited_aggregation", "summary": "Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T.A. Witten Jr. and L.M. Sander in 1981, is applicable to aggregation in any system where diffusion is the primary means of transport in the system. DLA can be observed in many systems such as electrodeposition, Hele-Shaw flow, mineral deposits, and dielectric breakdown.\n\nThe clusters formed in DLA processes are referred to as Brownian trees. These clusters are an example of a fractal. In 2D these fractals exhibit a dimension of approximately 1.71 for free particles that are unrestricted by a lattice, however computer simulation of DLA on a lattice will change the fractal dimension slightly for a DLA in the same embedding dimension. Some variations are also observed depending on the geometry of the growth, whether it be from a single point radially outward or from a plane or line for example. Two examples of aggregates generated using a microcomputer by allowing random walkers to adhere to an aggregate (originally (i) a straight line consisting 1300 particles and (ii) one particle at center) are shown on the right. \nComputer simulation of DLA is one of the primary means of studying this model. Several methods are available to accomplish this. Simulations can be done on a lattice of any desired geometry of embedding dimension (this has been done in up to 8 dimensions) or the simulation can be done more along the lines of a standard molecular dynamics simulation where a particle is allowed to freely random walk until it gets within a certain critical range whereupon it is pulled onto the cluster. Of critical importance is that the number of particles undergoing Brownian motion in the system is kept very low so that only the diffusive nature of the system is present.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2d/Brownian_tree_vertical_large.png", "https://upload.wikimedia.org/wikipedia/commons/b/b8/DLA_Cluster.JPG", "https://upload.wikimedia.org/wikipedia/commons/5/5b/DLA_spiral.png", "https://upload.wikimedia.org/wikipedia/commons/4/4b/Fractal_fern_explained.png", "https://upload.wikimedia.org/wikipedia/commons/5/55/Lichtenberg_figure_in_block_of_Plexiglas.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/3d/Of7_p0001_15h.jpg", "https://upload.wikimedia.org/wikipedia/commons/c/c4/Rec8_3kc2p.jpg", "https://upload.wikimedia.org/wikipedia/commons/5/55/Lichtenberg_figure_in_block_of_Plexiglas.jpg"], "links": ["Affine transformation", "Aleksandr Lyapunov", "Assouad dimension", "Barnsley fern", "Benoit Mandelbrot", "Bibcode", "Brownian motion", "Brownian tree", "Buddhabrot", "Burning Ship fractal", "Cantor set", "Chaos: Making a New Science", "Coastline paradox", "Correlation dimension", "Dielectric breakdown", "Diffusion", "Digital object identifier", "Dragon curve", "Eden growth model", "Embedding dimension", "Felix Hausdorff", "Filled Julia set", "Fractal", "Fractal art", "Fractal canopy", "Fractal dimension", "Fractal landscape", "Gaston Julia", "Georg Cantor", "H tree", "Hausdorff dimension", "Hele-Shaw flow", "Helge von Koch", "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", "Iterated function system", "Java programming language", "Julia set", "Koch snowflake", "L-system", "Lebesgue covering dimension", "Lewis Fry Richardson", "Lichtenberg figure", "List of fractals by Hausdorff dimension", "Lyapunov fractal", "L\u00e9vy flight", "Mandelbox", "Mandelbrot set", "Mandelbulb", "Menger sponge", "Minkowski\u2013Bouligand dimension", "Molecular dynamics", "Multifractal system", "N-flake", "Newton fractal", "Open source", "Orbit trap", "Packing dimension", "Paul L\u00e9vy (mathematician)", "Percolation theory", "Pickover stalk", "Point cloud", "Random walk", "Recursion", "Self-avoiding walk", "Self-similarity", "Sierpinski carpet", "Sierpinski triangle", "Space-filling curve", "Strange attractor", "Sunflow", "T-square (fractal)", "The Beauty of Fractals", "The Fractal Geometry of Nature", "Thomas Witten", "Toxiclibs", "Transport phenomena", "Tricorn (mathematics)", "Wac\u0142aw Sierpi\u0144ski"], "references": ["http://lichdesc.teslamania.com", "http://adsabs.harvard.edu/abs/1981PhRvL..47.1400W", "http://adsabs.harvard.edu/abs/1984PhRvA..29.2017B", "http://rsb.info.nih.gov/ij/plugins/DLA.html", "http://apricot.polyu.edu.hk/~lam/dla/", "http://codepen.io/DonKarlssonSan/full/BopXpq/", "http://doi.org/10.1103%2FPhysRevA.29.2017", "http://doi.org/10.1103%2FPhysRevLett.47.1400", "http://toxiclibs.org/2010/02/new-package-simutils/", "https://itunes.apple.com/jp/app/thedla/id506499656?mt=8", "https://github.com/markstock/dla-nd", "https://web.archive.org/web/20070405094836/http://aip.org/pt/vol-53/iss-11/p36.html"]}, "Allan variance": {"categories": ["All articles needing additional references", "Articles needing additional references from January 2018", "CS1 maint: Archived copy as title", "Clocks", "Measurement", "Signal processing metrics", "Use dmy dates from June 2013", "Webarchive template wayback links"], "title": "Allan variance", "method": "Allan variance", "url": "https://en.wikipedia.org/wiki/Allan_variance", "summary": "The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers, named after David W. Allan and expressed mathematically as \n \n \n \n \n \u03c3\n \n y\n \n \n 2\n \n \n (\n \u03c4\n )\n \n \n {\\displaystyle \\sigma _{y}^{2}(\\tau )}\n .\nThe Allan deviation (ADEV), also known as sigma-tau, is the square root of Allan variance, \n \n \n \n \n \u03c3\n \n y\n \n \n (\n \u03c4\n )\n \n \n {\\displaystyle \\sigma _{y}(\\tau )}\n .\nThe M-sample variance is a measure of frequency stability using M samples, time T between measures and observation time \n \n \n \n \u03c4\n \n \n {\\displaystyle \\tau }\n . M-sample variance is expressed as\n\n \n \n \n \n \u03c3\n \n y\n \n \n 2\n \n \n (\n M\n ,\n T\n ,\n \u03c4\n )\n .\n \n \n {\\displaystyle \\sigma _{y}^{2}(M,T,\\tau ).}\n The Allan variance is intended to estimate stability due to noise processes and not that of systematic errors or imperfections such as frequency drift or temperature effects. The Allan variance and Allan deviation describe frequency stability. See also the section Interpretation of value below.\nThere are also different adaptations or alterations of Allan variance, notably the modified Allan variance MAVAR or MVAR, the total variance, and the Hadamard variance. There also exist time-stability variants such as time deviation TDEV or time variance TVAR. Allan variance and its variants have proven useful outside the scope of timekeeping and are a set of improved statistical tools to use whenever the noise processes are not unconditionally stable, thus a derivative exists.\nThe general M-sample variance remains important, since it allows dead time in measurements, and bias functions allows conversion into Allan variance values. Nevertheless, for most applications the special case of 2-sample, or \"Allan variance\" with \n \n \n \n T\n =\n \u03c4\n \n \n {\\displaystyle T=\\tau }\n is of greatest interest.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/dd/AllanDeviation.svg", "https://upload.wikimedia.org/wikipedia/commons/a/aa/AllanDeviationExample.gif", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Allan deviation", "Amplifier", "Angular frequency", "ArXiv", "Atomic clock", "Bandwidth (signal processing)", "Bibcode", "Chi-squared distribution", "Clock", "Confidence interval", "Crystal oscillator", "David W. Allan", "Dead time", "Degrees of freedom (statistics)", "Digital object identifier", "Estimator", "Expected value", "Fiber optic gyroscope", "Flicker noise", "Frequency", "Frequency deviation", "Gyroscopes", "Hadamard variance", "Hemispherical resonator gyroscope", "Hertz", "I. I. Rabi Award", "International Standard Book Number", "Laser", "Leeson's equation", "Leeson effect", "Log\u2013log plot", "Metrology", "Microelectromechanical systems", "Modified Allan variance", "Modified Hadamard variance", "Modified total variance", "National Institute of Standards and Technology", "Network time protocol", "Noise identification", "Nyquist rate", "Oscillator", "Phase noise", "Power-law noise", "Precision Time Protocol", "Pulse per second", "Root mean square", "Scaled chi-squared distribution", "Semivariance", "Shannon\u2013Hartley theorem", "Standard deviation", "Standard variance", "Synchronization", "Systematic bias", "Theo variance", "Time deviation", "Timekeeping", "Total variance", "Variance", "Variogram", "Wayback Machine", "White noise"], "references": ["http://www.alamath.com/", "http://www.allanstime.com/", "http://www.allanstime.com/AllanVariance/", "http://www.allanstime.com/Publications/DWA/Conversion_from_Allan_variance_to_Spectral_Densities.pdf", "http://fr.mathworks.com/matlabcentral/fileexchange/55765-avar", "http://www.wriley.com/", "http://adsabs.harvard.edu/abs/2005RScI...76e4703R", "http://ccnet.stanford.edu/cgi-bin/course.cgi?cc=ee246&action=handout_download&handout_id=ID113350669026291", "http://www.femto-st.fr/~rubiola/pdf-articles/conference/2005-ifcs-counters.pdf", "http://www.femto-st.fr/~rubiola/pdf-articles/journal/2005rsi-hi-res-freq-counters.pdf", "http://www.femto-st.fr/~rubiola/pdf-slides/2008T-femto-counters.pdf", "http://tf.boulder.nist.gov/general/pdf/11.pdf", "http://tf.boulder.nist.gov/general/pdf/118.pdf", "http://tf.boulder.nist.gov/general/pdf/264.pdf", "http://tf.boulder.nist.gov/general/pdf/554.pdf", "http://tf.boulder.nist.gov/general/pdf/59.pdf", "http://tf.boulder.nist.gov/general/pdf/6.pdf", "http://tf.boulder.nist.gov/general/pdf/7.pdf", "http://tf.boulder.nist.gov/general/pdf/878.pdf", "http://tf.nist.gov/timefreq/general/pdf/2220.pdf", "http://www.itu.int/rec/T-REC-G.813/recommendation.asp?lang=en&parent=T-REC-G.813-200303-I", "http://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-G.810-199608-I!!PDF-E&type=items", "http://wwwusers.ts.infn.it/~milotti/Didattica/Segnali/Cutler&Searle_1966.pdf", "http://home.dei.polimi.it/bregni/public.htm", "http://arxiv.org/abs/physics/0411227", "http://doi.org/10.1063%2F1.1898203", "http://doi.org/10.1109%2FIEEESTD.1999.90575", "http://doi.org/10.1109%2FIPIN.2017.8115944", "http://doi.org/10.1109%2Fproc.1966.4627", "http://doi.org/10.1109%2Fproc.1966.4682", "http://www.etsi.org/deliver/etsi_en/300400_300499/3004620701/01.01.01_20/en_3004620701v010101c.pdf", "http://www.ieee-uffc.org/publications/tr/special-issue-variance-50th.asp", "http://ieeexplore.ieee.org/document/8115944/", "http://rubiola.org/", "http://www.afahc.ro/ro/afases/2014/mecanica/marinov_petrov_allan.pdf", "https://books.google.com/books?id=APEBaL4WHNoC&printsec=frontcover", "https://tf.nist.gov/general/publications.htm", "https://wayback.archive-it.org/all/20100206151245/http://hdl.handle.net/2060/19660001092", "https://web.archive.org/web/20080916102549/http://horology.jpl.nasa.gov/noiseinfo.html", "https://web.archive.org/web/20100226011555/http://www.ieee-uffc.org/frequency_control/teaching.asp", "https://web.archive.org/web/20110612003610/http://tf.nist.gov/timefreq/general/pdf/2220.pdf", "https://web.archive.org/web/20110720220221/http://www.femto-st.fr/~rubiola/pdf-articles/journal/2005rsi-hi-res-freq-counters.pdf", "https://web.archive.org/web/20110720220233/http://www.femto-st.fr/~rubiola/pdf-articles/conference/2005-ifcs-counters.pdf", "https://web.archive.org/web/20110720220251/http://www.femto-st.fr/~rubiola/pdf-slides/2008T-femto-counters.pdf", "https://web.archive.org/web/20140201231407/http://ccnet.stanford.edu/cgi-bin/course.cgi?cc=ee246&action=handout_download&handout_id=ID113350669026291", "https://web.archive.org/web/20140903100218/http://www.ieee-uffc.org/publications/tr/special-issue-variance-50th.asp", "https://ieee-uffc.org/download/stable32-software-frequency-stability-analysis-william-riley/", "https://pypi.python.org/pypi/AllanTools", "https://cran.r-project.org/web/packages/allanvar/index.html"]}, "Variable (mathematics)": {"categories": ["Algebra", "Calculus", "Elementary mathematics", "Syntax (logic)", "Variables (mathematics)"], "title": "Variable (mathematics)", "method": "Variable (mathematics)", "url": "https://en.wikipedia.org/wiki/Variable_(mathematics)", "summary": "In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown. Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation. A typical example is the quadratic formula, which allows one to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation to the variables that represent them.\nThe concept of a variable is also fundamental in calculus.\nTypically, a function y = f(x) involves two variables, y and x, representing respectively the value and the argument of the function. The term \"variable\" comes from the fact that, when the argument (also called the \"variable of the function\") varies, then the value varies accordingly.In more advanced mathematics, a variable is a symbol that denotes a mathematical object, which could be a number, a vector, a matrix, or even a function. In this case, the original property of \"variability\" of a variable is not kept (except, sometimes, for informal explanations).\nSimilarly, in computer science, a variable is a name (commonly an alphabetic character or a word) representing some value stored in computer memory. In mathematical logic, a variable is either a symbol representing an unspecified term of the theory, or a basic object of the theory, which is manipulated without referring to its possible intuitive interpretation.", "images": [], "links": ["Addison-Wesley", "Algebra", "Angle", "Antiderivative", "Argument of a function", "Axis (mathematics)", "Brahmagupta", "Br\u0101hmasphu\u1e6dasiddh\u0101nta", "Calculus", "Cartesian coordinates", "Coefficient", "Complex number", "Computer science", "Constant (mathematics)", "Constant function", "Constant of integration", "Constant term", "Continuous function", "Coordinate space", "Correlation coefficient", "Cubic equation", "Dependent and independent variables", "Dictionary.com", "Differentiable function", "Eigenvalues", "Elementary mathematics", "Equation", "Euclidean geometry", "Expression (mathematics)", "Formal power series", "Fran\u00e7ois Vi\u00e8te", "Free variables and bound variables", "Function (mathematics)", "Function of a real variable", "Gottfried Wilhelm Leibniz", "Group (mathematics)", "Identity element", "Indeterminate (variable)", "Indexed family", "Infinitesimal", "Infinitesimal calculus", "Integer", "International Standard Book Number", "Isaac Newton", "Italic type", "JSTOR", "Karl Weierstrass", "Lambda calculus", "Leonhard Euler", "Limit (mathematics)", "Mathematical constant", "Mathematical expression", "Mathematical logic", "Mathematical object", "Mathematics", "Matrix (mathematics)", "Mechanics", "Naming convention", "Normal distribution", "Number", "Observable variable", "Parameter", "Physical constant", "Physical quantity", "Physics", "Pi", "Polynomial", "Polynomial function", "Polynomial ring", "Polynomials", "Prentice Hall", "Pressure", "Prime number", "Prime power", "Probability", "Probability theory", "Quadratic equation", "Quadratic formula", "Quotient", "Radius", "Random variable", "Real number", "Remainder", "Ren\u00e9 Descartes", "Semantics", "Sequence", "Series (mathematics)", "Set (mathematics)", "Standard deviation", "Statistics", "Subscript", "Symbol", "Syntax (logic)", "Syracuse University", "Temperature", "Term (logic)", "Time", "Unit vector", "Value (mathematics)", "Variable (computer science)", "Variable (disambiguation)", "Vector (mathematics)"], "references": ["http://dictionary.reference.com/browse/variable", "http://cstl.syr.edu/fipse/algebra/unit1/..%5Cpart4%5Cappend1.htm", "https://books.google.com/books?id=ad0P0elU1_0C&pg=PA71", "https://books.google.com/books?id=h-zRieb7VbwC&pg=PA40", "https://books.google.com/books?id=unltAAAAMAAJ&pg=PA1", "https://web.archive.org/web/20140116020503/http://cstl.syr.edu/fipse/algebra/part4/append1.htm", "https://www.jstor.org/stable/685170"]}, "FastICA": {"categories": ["All articles needing additional references", "Articles needing additional references from April 2013", "Computational statistics", "Factor analysis", "Machine learning algorithms"], "title": "FastICA", "method": "FastICA", "url": "https://en.wikipedia.org/wiki/FastICA", "summary": "FastICA is an efficient and popular algorithm for independent component analysis invented by Aapo Hyv\u00e4rinen at Helsinki University of Technology. Like most ICA algorithms, FastICA seeks an orthogonal rotation of prewhitened data, through a fixed-point iteration scheme, that maximizes a measure of non-Gaussianity of the rotated components. Non-gaussianity serves as a proxy for statistical independence, which is a very strong condition and requires infinite data to verify. FastICA can also be alternatively derived as an approximative Newton iteration.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["C++", "Covariance matrix", "Digital object identifier", "Eigenvalue decomposition", "Expected value", "FastICA", "Function (mathematics)", "Helsinki University of Technology", "IT++", "Independence (probability theory)", "Independent component analysis", "Infomax", "Iterative method", "Linear transformation", "Machine learning", "Non-Gaussianity", "Nonlinear", "PubMed Identifier", "R programming language", "RapidMiner", "SourceForge", "Statistical independence", "Unsupervised learning"], "references": ["http://rapid-i.com/wiki/index.php?title=Independent_Component_Analysis", "http://www.cs.helsinki.fi/u/ahyvarin/papers/NN00new.pdf", "http://www.cs.helsinki.fi/u/ahyvarin/papers/TNN99new.pdf", "http://www.cis.hut.fi/projects/ica/fastica/", "http://www.ncbi.nlm.nih.gov/pubmed/10946390", "http://www.ncbi.nlm.nih.gov/pubmed/18252563", "http://sourceforge.net/projects/fastica", "http://doi.org/10.1016%2FS0893-6080(00)00026-5", "http://doi.org/10.1109%2F72.761722", "https://cran.r-project.org/web/packages/fastICA/index.html"]}, "Pollyanna Creep": {"categories": ["All articles with minor POV problems", "All articles with unsourced statements", "Articles with minor POV problems from March 2013", "Articles with unsourced statements from June 2016", "Misuse of statistics"], "title": "Pollyanna Creep", "method": "Pollyanna Creep", "url": "https://en.wikipedia.org/wiki/Pollyanna_Creep", "summary": "Pollyanna Creep is a phrase that originated in 2004 with John Williams, a California-based economic analyst and statistician. It describes the way the U.S. government has modified the way important economic measures are calculated with the purpose of giving a better impression of economic development. This is a clear reference, in a sarcastic way, to Pollyanna's proverbial optimism. Williams and other economic analysts, such as Kevin P. Phillips, argue that such manipulations distort the perception of electors and economic factors and have ill effects on political and investment decisions.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Unbalanced_scales.svg"], "links": ["California", "Consumer Price Index (United Kingdom)", "Eleanor H. Porter", "Federal government of the United States", "Inflation", "List of The Story of Pollyanna, Girl of Love episodes", "Polly (1989 film)", "Pollyanna", "Pollyanna (1920 film)", "Pollyanna (1960 film)", "Pollyanna Grows Up", "Pollyanna principle", "Statistics", "The Story of Pollyanna, Girl of Love", "United Kingdom"], "references": ["http://www.shadowstats.com/article/57", "http://harpers.org/archive/2008/05/0082023"]}, "C\u00e0dl\u00e0g": {"categories": ["Real analysis", "Stochastic processes"], "title": "C\u00e0dl\u00e0g", "method": "C\u00e0dl\u00e0g", "url": "https://en.wikipedia.org/wiki/C%C3%A0dl%C3%A0g", "summary": "In mathematics, a c\u00e0dl\u00e0g (French: \"continue \u00e0 droite, limite \u00e0 gauche\"), RCLL (\"right continuous with left limits\"), or corlol (\"continuous on (the) right, limit on (the) left\") function is a function defined on the real numbers (or a subset of them) that is everywhere right-continuous and has left limits everywhere. C\u00e0dl\u00e0g functions are important in the study of stochastic processes that admit (or even require) jumps, unlike Brownian motion, which has continuous sample paths. The collection of c\u00e0dl\u00e0g functions on a given domain is known as Skorokhod space.\nTwo related terms are c\u00e0gl\u00e0d, standing for \"continue \u00e0 gauche, limite \u00e0 droite\", the left-right reversal of c\u00e0dl\u00e0g, and c\u00e0ll\u00e0l for \"continue \u00e0 l'un, limite \u00e0 l\u2019autre\" (continuous on one side, limit on the other side), for a function which is interchangeably either c\u00e0dl\u00e0g or c\u00e0gl\u00e0d at each point of the domain.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/82/Discrete_probability_distribution_illustration.png"], "links": ["Anatoliy Skorokhod", "Arzel\u00e0\u2013Ascoli theorem", "Bijection", "Brownian motion", "Complete space", "Convex function", "Cumulative distribution function", "Cumulative distribution functions", "Domain of a function", "If and only if", "Infimum", "International Standard Book Number", "Interval (mathematics)", "Left limit", "Limit of a function", "Mathematician", "Mathematics", "Metric (mathematics)", "Metric space", "Modulus of continuity", "Polish space", "Probability measure", "Real number", "Right-continuous", "Right limit", "Separable space", "Soviet", "Stochastic processes", "Strictly increasing", "Subset", "Subspace topology", "Tightness of measures", "Topology", "Uniform convergence"], "references": []}, "Observational equivalence": {"categories": ["All stub articles", "Computer science stubs", "Econometric modeling", "Econometrics stubs", "Programming language semantics", "Statistical theory"], "title": "Observational equivalence", "method": "Observational equivalence", "url": "https://en.wikipedia.org/wiki/Observational_equivalence", "summary": "Observational equivalence is the property of two or more underlying entities being indistinguishable on the basis of their observable implications. Thus, for example, two scientific theories are observationally equivalent if all of their empirically testable predictions are identical, in which case empirical evidence cannot be used to distinguish which is closer to being correct; indeed, it may be that they are actually two different perspectives on one underlying theory.\nIn econometrics, two parameter values (or two structures, from among a class of statistical models) are considered observationally equivalent if they both result in the same probability distribution of observable data. This term often arises in relation to the identification problem.\nIn the formal semantics of programming languages, two terms M and N are observationally equivalent if and only if, in all contexts C[...] where C[M] is a valid term, it is the case that C[N] is also a valid term with the same value. Thus it is not possible, within the system, to distinguish between the two terms. This definition can be made precise only with respect to a particular calculus, one that comes with its own specific definitions of term, context, and the value of a term.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/LampFlowchart.svg"], "links": ["Computer science", "Digital object identifier", "Econometrics", "Formal semantics of programming languages", "Free On-line Dictionary of Computing", "GNU Free Documentation License", "Parameter identification problem", "Scientific theory", "Term (mathematics)", "Underdetermination"], "references": ["http://www.dictionaryofeconomics.com/article?id=pde2008_I000004", "http://doi.org/10.2307%2F1905689", "http://www.nber.org/WNE/slides7-14-08/Lecture3.pdf"]}, "Panel analysis": {"categories": ["Multivariate time series", "Panel data"], "title": "Panel analysis", "method": "Panel analysis", "url": "https://en.wikipedia.org/wiki/Panel_analysis", "summary": "Panel (data) analysis is a statistical method, widely used in social science, epidemiology, and econometrics to analyze two-dimensional (typically cross sectional and longitudinal) panel data. The data are usually collected over time and over the same individuals and then a regression is run over these two dimensions. Multidimensional analysis is an econometric method in which data are collected over more than two dimensions (typically, time, individuals, and some third dimension).A common panel data regression model looks like \n \n \n \n \n y\n \n i\n t\n \n \n =\n a\n +\n b\n \n x\n \n i\n t\n \n \n +\n \n \u03b5\n \n i\n t\n \n \n \n \n {\\displaystyle y_{it}=a+bx_{it}+\\varepsilon _{it}}\n , where y is the dependent variable, x is the independent variable, a and b are coefficients, i and t are indices for individuals and time. The error \n \n \n \n \n \u03b5\n \n i\n t\n \n \n \n \n {\\displaystyle \\varepsilon _{it}}\n is very important in this analysis. Assumptions about the error term determine whether we speak of fixed effects or random effects. In a fixed effects model, \n \n \n \n \n \u03b5\n \n i\n t\n \n \n \n \n {\\displaystyle \\varepsilon _{it}}\n is assumed to vary non-stochastically over \n \n \n \n i\n \n \n {\\displaystyle i}\n or \n \n \n \n t\n \n \n {\\displaystyle t}\n making the fixed effects model analogous to a dummy variable model in one dimension. In a random effects model, \n \n \n \n \n \u03b5\n \n i\n t\n \n \n \n \n {\\displaystyle \\varepsilon _{it}}\n is assumed to vary stochastically over \n \n \n \n i\n \n \n {\\displaystyle i}\n or \n \n \n \n t\n \n \n {\\displaystyle t}\n requiring special treatment of the error variance matrix.Panel data analysis has three more-or-less independent approaches:\n\nindependently pooled panels;\nrandom effects models;\nfixed effects models or first differenced models.The selection between these methods depends upon the objective of the analysis, and the problems concerning the exogeneity of the explanatory variables.", "images": [], "links": ["Dependent variable", "Digital object identifier", "Econometrics", "Epidemiology", "Factor analysis", "Fixed effects estimator", "Hausman test", "Independent variable", "Indexed family", "International Standard Book Number", "Journal of Econometrics", "Linear regression", "Multidimensional analysis", "Panel data", "Panel study", "Random effects model", "Social science"], "references": ["http://doi.org/10.1016%2F0304-4076(94)01649-K"]}, "Big O in probability notation": {"categories": ["Convergence (mathematics)", "Mathematical notation", "Probability theory", "Statistical theory"], "title": "Big O in probability notation", "method": "Big O in probability notation", "url": "https://en.wikipedia.org/wiki/Big_O_in_probability_notation", "summary": "The order in probability notation is used in probability theory and statistical theory in direct parallel to the big-O notation that is standard in mathematics. Where the big-O notation deals with the convergence of sequences or sets of ordinary numbers, the order in probability notation deals with convergence of sets of random variables, where convergence is in the sense of convergence in probability.", "images": [], "links": ["Big-O notation", "Chebyshev's inequality", "Convergence in probability", "Convergence of random variables", "International Standard Book Number", "Mathematics", "Probability theory", "Statistical theory", "Yvonne Bishop"], "references": []}, "Exposure variable": {"categories": ["Design of experiments", "Independence (probability theory)", "Mathematical terminology", "Regression analysis", "Webarchive template wayback links"], "title": "Dependent and independent variables", "method": "Exposure variable", "url": "https://en.wikipedia.org/wiki/Dependent_and_independent_variables", "summary": "In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables. The dependent variables represent the output or outcome whose variation is being studied. The independent variables, also known in a statistical context as regressors, represent inputs or causes, that is, potential reasons for variation. In an experiment, any variable that the experimenter manipulates can be called an independent variable. Models and experiments test the effects that the independent variables have on the dependent variables. Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential confounding effect.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f8/Polynomialdeg2.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg"], "links": ["Abscissa", "Bias (statistics)", "Blocking (statistics)", "Calculus", "Cartesian product", "Confounding", "Control variable", "Covariance", "Data mining", "Dependent variable", "Design of experiments", "Digital object identifier", "Econometrics", "Errors and residuals", "Experimental science", "Feature (machine learning)", "Function (mathematics)", "Goodness of fit", "Graph of a function", "Horizontal axis", "Hypothesis", "Independence (probability theory)", "International Standard Book Number", "Linear model", "Machine learning", "Manifold (mathematics)", "Mathematical modeling", "Medical statistics", "Multivariable calculus", "Multivariate statistics", "Omitted variable bias", "Ordinate", "Pattern recognition", "Prediction", "RapidMiner", "Reliability theory", "Risk factor", "Set (mathematics)", "Set theory", "Simulation", "Statistical model", "Stochastic", "Subset", "Supervised learning", "Test data", "Variable and attribute (research)", "Vector-valued functions", "Vertical axis", "Wayback Machine"], "references": ["http://1xltkxylmzx3z8gd647akcdvov.wpengine.netdna-cdn.com/wp-content/uploads/2013/10/rapidminer-5.0-manual-english_v1.0.pdf", "http://onlinestatbook.com/2/introduction/variables.html", "http://doi.org/10.1080%2F15210608709379549", "https://web.archive.org/web/20140210002634/http://1xltkxylmzx3z8gd647akcdvov.wpengine.netdna-cdn.com/wp-content/uploads/2013/10/rapidminer-5.0-manual-english_v1.0.pdf"]}, "Data reduction": {"categories": ["Exploratory data analysis"], "title": "Data reduction", "method": "Data reduction", "url": "https://en.wikipedia.org/wiki/Data_reduction", "summary": "Data reduction is the transformation of numerical or alphabetical digital information derived empirically or experimentally into a corrected, ordered, and simplified form. The basic concept is the reduction of multitudinous amounts of data down to the meaningful parts.\nWhen information is derived from instrument readings there may also be a transformation from analog to digital form. When the data are already in digital form the 'reduction' of the data typically involves some editing, scaling, encoding, sorting, collating, and producing tabular summaries. When the observations are discrete but the underlying phenomenon is continuous then smoothing and interpolation are often needed. Often the data reduction is undertaken in the presence of reading or measurement errors. Some idea of the nature of these errors is needed before the most likely value may be determined.\nAn example in astronomy is the data reduction in the Kepler satellite. This satellite records 95-megapixel images once every six seconds, generating tens of megabytes of data per second, which is orders of magnitudes more than the downlink bandwidth of 550 KBps. The on-board data reduction encompasses co-adding the raw frames for thirty minutes, reducing the bandwidth by a factor of 300. Furthermore, interesting targets are pre-selected and only the relevant pixels are processed, which is 6% of the total. This reduced data is then sent to Earth where it is processed further.\nResearch has also been carried out on the use of data reduction in wearable (wireless) devices for health monitoring and diagnosis applications. For example, in the context of epilepsy diagnosis, data reduction has been used to increase the battery lifetime of a wearable EEG device by selecting, and only transmitting, EEG data that is relevant for diagnosis and discarding background activity.\n\n", "images": [], "links": ["Andrew S. C. Ehrenberg", "Chartjunk", "Data (computing)", "Data analysis", "Data archaeology", "Data cleansing", "Data collection", "Data compression", "Data corruption", "Data curation", "Data degradation", "Data editing", "Data farming", "Data format management", "Data fusion", "Data integration", "Data integrity", "Data library", "Data loss", "Data management", "Data migration", "Data mining", "Data pre-processing", "Data preservation", "Data quality", "Data recovery", "Data retention", "Data science", "Data scraping", "Data scrubbing", "Data security", "Data stewardship", "Data storage", "Data validation", "Data warehouse", "Data wrangling", "Digital information", "Digital object identifier", "Digitization", "Encoding", "Experimental data", "Handle System", "Information privacy", "Interpolation", "Kepler (spacecraft)", "Measurement error", "Scaling (geometry)", "Smoothing", "Sorting", "Table diagonalization"], "references": ["http://business.nmsu.edu/~mhyman/M610_Articles/Ehrenberg_Marketing_Research_2001.pdf", "http://hdl.handle.net/10044%2F1%2F48764", "http://doi.org/10.1109%2FJSSC.2017.2720636"]}, "McDonald\u2013Kreitman test": {"categories": ["Molecular evolution", "Phylogenetics", "Statistical genetics"], "title": "McDonald\u2013Kreitman test", "method": "McDonald\u2013Kreitman test", "url": "https://en.wikipedia.org/wiki/McDonald%E2%80%93Kreitman_test", "summary": "The McDonald\u2013Kreitman test is a statistical test often used by evolution and population biologists to detect and measure the amount of adaptive evolution within a species by determining whether adaptive evolution has occurred, and the proportion of substitutions that resulted from positive selection (also known as directional selection). To do this, the McDonald\u2013Kreitman test compares the amount of variation within a species (polymorphism) to the divergence between species (substitutions) at two types of sites, neutral and nonneutral. A substitution refers to a nucleotide that is fixed within one species, but a different nucleotide is fixed within a second species at the same base pair of homologous DNA sequences. A site is nonneutral if it is either advantageous or deleterious. The two types of sites can be either synonymous or nonsynonymous within a protein-coding region. In a protein-coding sequence of DNA, a site is synonymous if a point mutation at that site would not change the amino acid, also known as a silent mutation. Because the mutation did not result in a change in the amino acid that was originally coded for by the protein-coding sequence, the phenotype, or the observable trait, of the organism is generally unchanged by the silent mutation. A site in a protein-coding sequence of DNA is nonsynonymous if a point mutation at that site results in a change in the amino acid, resulting in a change in the organism's phenotype. Typically, silent mutations in protein-coding regions are used as the \"control\" in the McDonald\u2013Kreitman test.\nIn 1991, John H. McDonald and Martin Kreitman derived the McDonald\u2013Kreitman test while performing an experiment with Drosophila (fruit flies) and their differences in amino acid sequence of the alcohol dehydrogenase gene. McDonald and Kreitman proposed this method to estimate the proportion of substitutions that are fixed by positive selection rather than by genetic drift.In order to set up the McDonald\u2013Kreitman test, we must first set up a two-way contingency table of our data on the species being investigated as shown below:\n\nDs: the number of synonymous substitutions per gene\nDn: the number of non-synonymous substitutions per gene\nPs: the number of synonymous polymorphisms per gene\nPn: the number of non-synonymous polymorphisms per geneTo quantify the values for Ds, Dn, Ps, and Pn, you count the number of differences in the protein-coding region for each type of variable in the contingency table.\nThe null hypothesis of the McDonald\u2013Kreitman test is that the ratio of nonsynonymous to synonymous variation within a species is going to equal the ratio of nonsynonymous to synonymous variation between species (i.e. Dn/Ds = Pn/Ps). When positive or negative selection (natural selection) influences nonsynonymous variation, the ratios will no longer equal. The ratio of nonsynonymous to synonymous variation between species is going to be lower than the ratio of nonsynonymous to synonymous variation within species (i.e. Dn/Ds < Pn/Ps) when negative selection is at work, and deleterious mutations strongly affect polymorphism. The ratio of nonsynonymous to synonymous variation within species is lower than the ratio of nonsynonymous to synonymous variation between species (i.e. Dn/Ds > Pn/Ps) when we observe positive selection. Since mutations under positive selection spread through a population rapidly, they don't contribute to polymorphism but do have an effect on divergence.Using an equation derived by Smith and Eyre-Walker, we can estimate the proportion of base substitutions fixed by natural selection, \u03b1, using the following formula:\n\n \n \n \n \u03b1\n =\n 1\n \u2212\n \n \n \n \n D\n \n s\n \n \n \n P\n \n n\n \n \n \n \n \n D\n \n n\n \n \n \n P\n \n s\n \n \n \n \n \n \n \n {\\displaystyle \\alpha =1-{\\frac {D_{s}P_{n}}{D_{n}P_{s}}}}\n Alpha represents the proportion of substitutions driven by positive selection. Alpha can be equal to any number between -\u221e and 1. Negative values of alpha are produced by sampling error or violations of the model, such as the segregation of slightly deleterious amino acid mutations. Similar to above, our null hypothesis here is that \u03b1=0, and we expect Dn/Ds to equal Pn/Ps.", "images": [], "links": ["Adaptive Evolution", "Adaptive evolution", "Contingency table", "Digital object identifier", "Directional selection", "Drosophila", "Ka/Ks ratio", "Martin Kreitman", "Nearly neutral theory of molecular evolution", "Negative selection (natural selection)", "Null hypothesis", "Point mutation", "Polymorphism (biology)", "PubMed Central", "PubMed Identifier", "Silent mutation", "Synonymous substitution", "Type II error", "Type I error"], "references": ["http://www.sciencedirect.com/science/article/pii/S0168952507001102#", "http://udel.edu/~mcdonald/pdfs/mcdonaldkreitman.pdf", "http://www.zoology.wisc.edu/courses/611/Part2/Readings/3eyre-walker_tree2006.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2447769", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2581974", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3666677", "http://www.ncbi.nlm.nih.gov/pubmed/11875568", "http://www.ncbi.nlm.nih.gov/pubmed/16820244", "http://www.ncbi.nlm.nih.gov/pubmed/17185560", "http://www.ncbi.nlm.nih.gov/pubmed/17418445", "http://www.ncbi.nlm.nih.gov/pubmed/18195052", "http://www.ncbi.nlm.nih.gov/pubmed/18515345", "http://www.ncbi.nlm.nih.gov/pubmed/18791238", "http://www.ncbi.nlm.nih.gov/pubmed/1904993", "http://www.ncbi.nlm.nih.gov/pubmed/19126864", "http://www.ncbi.nlm.nih.gov/pubmed/19215289", "http://www.ncbi.nlm.nih.gov/pubmed/20837603", "http://www.ncbi.nlm.nih.gov/pubmed/23650353", "http://doi.org/10.1016%2Fj.tig.2007.03.008", "http://doi.org/10.1016%2Fj.tree.2006.06.015", "http://doi.org/10.1038%2F351652a0", "http://doi.org/10.1038%2F4151022a", "http://doi.org/10.1073%2Fpnas.1220835110", "http://doi.org/10.1093%2Fmolbev%2Fmsn005", "http://doi.org/10.1093%2Fmolbev%2Fmsn297", "http://doi.org/10.1093%2Fmolbev%2Fmsq249", "http://doi.org/10.1093%2Fnar%2Fgkn337", "http://doi.org/10.1111%2Fj.1558-5646.2008.00560.x", "http://doi.org/10.1126%2Fscience.1135308", "http://doi.org/10.1534%2Fgenetics.108.091850", "http://www.genetics.org/content/162/4/2017.full.pdf", "http://www.genetics.org/content/180/3/1767", "http://mbe.oxfordjournals.org/content/25/6/1007.short", "http://mbe.oxfordjournals.org/content/26/3/691", "http://mbe.oxfordjournals.org/content/26/3/691.full.pdf+html", "http://mbe.oxfordjournals.org/content/28/1/63", "http://www.pnas.org/content/110/21/8615", "http://www.sciencemag.org/content/315/5811/525"]}, "Neural network": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles with unsourced statements", "Articles lacking in-text citations from October 2010", "Articles needing additional references from June 2010", "Articles with hAudio microformats", "Articles with unsourced statements from August 2012", "CS1 errors: dates", "Computational neuroscience", "Econometrics", "Information, knowledge, and uncertainty", "Network architecture", "Networks", "Neural networks", "Spoken articles"], "title": "Neural network", "method": "Neural network", "url": "https://en.wikipedia.org/wiki/Neural_network", "summary": "A neural network is a network or circuit of neurons, or in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus a neural network is either a biological neural network, made up of real biological neurons, or an artificial neural network, for solving artificial intelligence (AI) problems. The connections of the biological neuron are modeled as weights. A positive weight reflects an excitatory connection, while negative values mean inhibitory connections. All inputs are modified by a weight and summed. This activity is referred as a linear combination. Finally, an activation function controls the amplitude of the output. For example, an acceptable range of output is usually between 0 and 1, or it could be \u22121 and 1.\nUnlike von Neumann model computations, artificial neural networks do not separate memory and processing and operate via the flow of signals through the net connections, somewhat akin to biological networks.\nThese artificial networks may be used for predictive modeling, adaptive control and applications where they can be trained via a dataset. Self-learning resulting from experience can occur within networks, which can derive conclusions from a complex and seemingly unrelated set of information.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a3/En-Neural_network.ogg", "https://upload.wikimedia.org/wikipedia/commons/b/be/Forest_of_synthetic_pyramidal_dendrites_grown_using_Cajal%27s_laws_of_neuronal_branching.png", "https://upload.wikimedia.org/wikipedia/commons/9/99/Neural_network_example.svg", "https://upload.wikimedia.org/wikipedia/commons/4/47/Sound-icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["3Blue1Brown", "A. K. Dewdney", "ADALINE", "Acetylcholine", "Adaptive control", "Adaptive resonance theory", "Adaptive system", "Alan Turing", "Alexander Bain", "Amplitude", "Analog signal", "Artificial intelligence", "Artificial neural network", "Artificial neuron", "Autonomous robot", "Axons", "BCM theory", "Back-propagation", "Backpropagation", "Biological cybernetics", "Biological neural network", "Biological neuron models", "Biologically inspired computing", "Biophysics", "Blind signal separation", "Boltzmann machine", "CPU", "Cerebellar Model Articulation Controller", "Charles Scott Sherrington", "CiteSeerX", "Cognitive architecture", "Cognitive modeling", "Cognitive science", "Computation", "Computational neuroscience", "Computer simulation", "Connectionism", "Connectomics", "Convolution", "Cultured neuronal networks", "Data mining", "Data modeling", "Data processing", "Database", "David H. Hubel", "Decision making", "Deep learning", "Dendrite", "Dendrites", "Dendrodendritic synapse", "Digital data", "Digital morphogenesis", "Digital object identifier", "Donald Hebb", "Dopamine", "E-mail spam", "Exclusive-or", "Exclusive or", "Feedforward neural network", "Frank Rosenblatt", "Function approximation", "GPU", "Gene expression programming", "Geoff Hinton", "Geoffrey Hinton", "Group method of data handling", "Habituation", "Hard drive", "Hebbian learning", "Hopfield network", "IDSIA", "Image analysis", "In Situ Adaptive Tabulation", "Information processing", "Information theory", "International Standard Book Number", "J\u00fcrgen Schmidhuber", "Kunihiko Fukushima", "Learning", "Long short term memory", "Long term potentiation", "Machine learning", "Marvin Minsky", "Mathematical model", "Memristor", "Multilinear subspace learning", "NYU", "Nanodevice", "Nature Nanotechnology", "Nature Neuroscience", "Neocognitron", "Neural Computation", "Neural backpropagation", "Neural computing", "Neural network (disambiguation)", "Neural network software", "Neural processing", "Neuromodulators", "Neuromorphic computing", "Neurons", "Neurotransmitter", "Non-linear", "Nonlinear system identification", "Parallel Constraint Satisfaction Processes", "Parallel distributed processing", "Pattern recognition", "Perceptron", "Predictive analytics", "Predictive modeling", "Principal component", "Programming language", "PubMed Identifier", "Pyramidal neuron", "Radial basis function network", "Radial basis networks", "Random-access memory", "Recurrent neural network", "Regression analysis", "Roger Bridgman", "Scientific American", "Self-organizing map", "Serotonin", "Simulated reality", "Software agents", "Speech recognition", "Statistical", "Statistical classification", "Support vector machine", "Synapses", "Synaptic plasticity", "Tensor product network", "Threshold logic", "Time delay neural network", "Time series prediction", "Tomaso Poggio", "Torsten Wiesel", "University of Chicago", "University of Toronto", "Unorganized machine", "Unsupervised learning", "Video game", "Visual cortex", "Von Neumann", "Von Neumann model", "Walter Pitts", "Warren McCulloch", "Warren Sturgis McCulloch", "William James", "Yann LeCun", "YouTube"], "references": ["http://www.iro.umontreal.ca/~lisa/publications2/index.php/publications/show/4", "http://papers.nips.cc/paper/3449-offline-handwriting-recognition-with-multidimensional-recurrent-neural-networks", "http://www.dkriesel.com/en/science/neural_networks", "http://members.fortunecity.com/templarseries/popper.html", "http://uhaweb.hartford.edu/compsci/neural-networks-definition.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.4502", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.588.3775", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.76.1541", "http://www.cs.toronto.edu/~hinton/absps/fastnc.pdf", "http://www.gc.ssr.upm.es/inves/neural/ann1/anntutorial.html", "http://www.nasa.gov/centers/dryden/news/NewsReleases/2003/03-49.html", "http://www.ncbi.nlm.nih.gov/pubmed/10526343", "http://www.ncbi.nlm.nih.gov/pubmed/13602029", "http://www.ncbi.nlm.nih.gov/pubmed/16764513", "http://www.ncbi.nlm.nih.gov/pubmed/18451858", "http://www.ncbi.nlm.nih.gov/pubmed/18654568", "http://www.ncbi.nlm.nih.gov/pubmed/19299860", "http://www.ncbi.nlm.nih.gov/pubmed/7370364", "http://www.kurzweilai.net/how-bio-inspired-deep-learning-keeps-winning-competitions", "http://doi.org/10.1007%2FBF00344251", "http://doi.org/10.1007%2FBF02478259", "http://doi.org/10.1037%2Fh0042519", "http://doi.org/10.1038%2F14819", "http://doi.org/10.1038%2Fnature06932", "http://doi.org/10.1038%2Fnnano.2008.160", "http://doi.org/10.1073%2Fpnas.79.8.2554", "http://doi.org/10.1109%2FTIT.1954.1057468", "http://doi.org/10.1109%2FTIT.1956.1056810", "http://doi.org/10.1109%2FTPAMI.2008.137", "http://doi.org/10.1162%2Fneco.2006.18.7.1527", "http://doi.org/10.1371%2Fimage.pcbi.v06.i08", "http://www.msm.cam.ac.uk/phase-trans/2009/performance.html", "http://www.msm.cam.ac.uk/phase-trans/2009/review_Bhadeshia_SADM.pdf", "http://www.msm.cam.ac.uk/phase-trans/abstracts/neural.review.html", "http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html", "https://www.gartner.com/it-glossary/neural-net-or-neural-network", "https://www.youtube.com/watch?v=AyzOUbkUf3M", "https://www.youtube.com/watch?v=aircAruvnKk&list=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi"]}, "Reciprocal distribution": {"categories": ["Continuous distributions"], "title": "Reciprocal distribution", "method": "Reciprocal distribution", "url": "https://en.wikipedia.org/wiki/Reciprocal_distribution", "summary": "In probability and statistics, the reciprocal distribution is a continuous probability distribution. It is characterised by its probability density function, within the support of the distribution, being proportional to the reciprocal of the variable.\nThe reciprocal distribution is an example of an inverse distribution, and the reciprocal (inverse) of a random variable with a reciprocal distribution itself has a reciprocal distribution.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Computer", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "E (mathematical constant)", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multiplicative inverse", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Natural log", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Numerical analysis", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability and statistics", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Richard Hamming", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Significand", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Support of a distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["https://archive.org/details/bstj49-8-1609"]}, "Truncated regression model": {"categories": ["Actuarial science", "All stub articles", "Econometrics stubs", "Mathematical and quantitative methods (economics)", "Regression models", "Single-equation methods (econometrics)"], "title": "Truncated regression model", "method": "Truncated regression model", "url": "https://en.wikipedia.org/wiki/Truncated_regression_model", "summary": "Truncated regression models arise in many applications of statistics, for example in econometrics, in cases where observations with values in the outcome variable below or above certain thresholds are systematically excluded from the sample. Therefore, whole observations are missing, so that neither the dependent nor the independent variable is known.\nTruncated regression models are often confused with censored regression models where only the value of the dependent variable is clustered at a lower threshold, an upper threshold, or both, while the value for independent variables is available.\nEstimation of truncated regression models is usually done via parametric, semi-parametric and non-parametric maximum likelihood methods.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170527191524%21Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170519203409%21Emoji_u1f4c8.svg"], "links": ["Censored regression model", "Dependent variable", "Digital object identifier", "Econometrics", "Economics and Human Biology", "Independent variables", "JSTOR", "Journal of the Royal Statistical Society", "Sampling bias", "Statistics", "Truncated dependent variable", "Truncation (statistics)"], "references": ["http://doi.org/10.1016%2Fj.ehb.2003.12.003", "http://doi.org/10.2307%2F2346748", "http://www.jstor.org/stable/2346749", "https://ideas.repec.org/a/eee/econom/v146y2008i1p185-198.html"]}, "Completeness (statistics)": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles with unsourced statements", "Articles lacking in-text citations from February 2012", "Articles needing additional references from August 2009", "Articles with unsourced statements from May 2011", "Articles with unsourced statements from September 2010", "CS1 maint: Uses authors parameter", "Statistical theory"], "title": "Completeness (statistics)", "method": "Completeness (statistics)", "url": "https://en.wikipedia.org/wiki/Completeness_(statistics)", "summary": "In statistics, completeness is a property of a statistic in relation to a model for a set of observed data. In essence, it ensures that the distributions corresponding to different values of the parameters are distinct.\nIt is closely related to the idea of identifiability, but in statistical theory it is often found as a condition imposed on a sufficient statistic from which certain optimality results are derived.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Ancillary statistic", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bahadur's theorem", "Bar chart", "Basu's theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli distribution", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convex function", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Deb. Basu", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Henry Scheff\u00e9", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Identifiability", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laplace transform", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurable function", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimal sufficient", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric model", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter J. Bickel", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial", "Population (statistics)", "Population statistics", "Positive reals", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R. R. Bahadur", "Radar chart", "Random assignment", "Random sample", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sankhya (journal)", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficiency (statistics)", "Sufficient", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.springerlink.com/content/978-0-387-98864-1#section=545952&page=1", "http://www.tandfonline.com/doi/abs/10.1080/00031305.2015.1100683?journalCode=utas20", "http://web.mit.edu/jorloff/www/18.03-esg/notes/extra/laplaceuniqueness.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4960505", "http://www.ncbi.nlm.nih.gov/pubmed/27499547", "http://www.ams.org/mathscinet-getitem?mr=0039201", "http://www.ams.org/mathscinet-getitem?mr=0072410", "http://www.ams.org/mathscinet-getitem?mr=0443141", "http://www.ams.org/mathscinet-getitem?mr=0953081", "http://www.ams.org/mathscinet-getitem?mr=2135927", "http://doi.org/10.1007%2F978-1-4614-1412-4_23", "http://doi.org/10.1007%2F978-1-4614-1412-4_24", "http://doi.org/10.1080%2F00031305.2015.1100683", "http://www.jstor.org/stable/25048038", "http://www.jstor.org/stable/25048243"]}, "Compound probability distribution": {"categories": ["Compound probability distributions", "Types of probability distributions"], "title": "Compound probability distribution", "method": "Compound probability distribution", "url": "https://en.wikipedia.org/wiki/Compound_probability_distribution", "summary": "In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables.\nThe compound distribution (\"unconditional distribution\") is the result of marginalizing (integrating) over the latent random variable(s) representing the parameter(s) of the parametrized distribution (\"conditional distribution\").", "images": [], "links": ["ArXiv", "Bayesian inference", "Beta-binomial distribution", "Beta distribution", "Beta prime distribution", "Bibcode", "Binomial distribution", "Chi-squared distribution", "Collapsed Gibbs sampling", "Conditional probability distribution", "Convolution", "Digital object identifier", "Dirichlet-multinomial distribution", "Dirichlet distribution", "EM-algorithm", "Estimation theory", "Exponential distribution", "Exponential family", "Exponentially modified Gaussian distribution", "F-test", "Gamma distribution", "Gaussian distribution", "Heavy tail", "International Standard Book Number", "Inverse gamma distribution", "JSTOR", "Joint probability distribution", "Location parameter", "Lomax distribution", "Marginal distribution", "Maximum-likelihood estimation", "Maximum a posteriori estimation", "Mean", "Mixture distribution", "Moment (mathematics)", "Monte Carlo method", "Multinomial distribution", "Negative binomial distribution", "Normal-exponential-gamma distribution", "Normal distribution", "Overdispersion", "Poisson distribution", "Posterior distribution", "Posterior predictive distribution", "Precision (statistics)", "Prior distribution", "Prior predictive distribution", "Probability and statistics", "Probability density function", "Probability distribution", "Random variable", "Rate parameter", "Shape parameter", "Student's t-distribution", "Student's t-test", "Support (mathematics)", "Test statistic", "Variance"], "references": ["http://adsabs.harvard.edu/abs/1989JOSAA...6...80T", "http://arxiv.org/abs/1602.04060", "http://doi.org/10.1007%2F978-3-642-04898-2", "http://doi.org/10.1007%2FBF02613934", "http://doi.org/10.1080%2F10618600.2016.1276840", "http://doi.org/10.1364%2FJOSAA.6.000080", "http://doi.org/10.2307%2F3314912", "http://www.jstor.org/stable/4153184"]}, "Jump-diffusion model": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2012", "Options (finance)", "Stochastic processes"], "title": "Jump diffusion", "method": "Jump-diffusion model", "url": "https://en.wikipedia.org/wiki/Jump_diffusion", "summary": "Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics, in Pattern theory and computational vision and in option pricing.", "images": [], "links": ["Abstract Wiener space", "Actuarial mathematics", "American option", "Amortising swap", "Asian option", "Asset swap", "Atomic diffusion", "Autocorrelation function", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Backspread", "Barrier option", "Basic affine jump diffusion", "Basis swap", "Basket option", "Bear spread", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Binary option", "Binomial options pricing model", "Birth\u2013death process", "Black model", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Bond option", "Boolean network", "Box spread (options)", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Bull spread", "Burkholder\u2013Davis\u2013Gundy inequalities", "Butterfly (options)", "B\u00fchlmann model", "Calendar spread", "Call option", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Chooser option", "Classical Wiener space", "Cliquet", "Collar (finance)", "Collateralized debt obligation", "Commodore option", "Compound Poisson process", "Compound option", "Computational vision", "Condensed matter physics", "Conditional variance swap", "Constant elasticity of variance model", "Constant maturity swap", "Constant proportion portfolio insurance", "Consumer debt", "Contact process (mathematics)", "Contango", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Contract for difference", "Convergence of random variables", "Coronal mass ejection", "Corporate bond", "Correlation swap", "Covered call", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Credit-linked note", "Credit default option", "Credit default swap", "Credit derivative", "Credit risk", "Credit spread (options)", "Currency future", "Currency swap", "C\u00e0dl\u00e0g", "Debit spread", "Derivative (finance)", "Derivatives market", "Diagonal spread", "Diffusion", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dividend future", "Dividend swap", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Employee stock option", "Energy derivative", "Equity-linked note", "Equity derivative", "Equity swap", "Ergodic", "Ergodic theorem", "Ergodic theory", "Ergodicity", "European option", "Exchangeable random variables", "Exercise (options)", "Exotic derivative", "Exotic option", "Expiration (options)", "Extreme value theory", "Feller-continuous process", "Feller process", "Fence (finance)", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Finite difference methods for option pricing", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fixed income", "Fleming\u2013Viot process", "Fluid queue", "Foreign-exchange option", "Foreign exchange derivative", "Foreign exchange swap", "Forward contract", "Forward market", "Forward price", "Forward rate", "Forward rate agreement", "Forward start option", "Fractional Brownian motion", "Freight derivative", "Fund derivative", "Futures contract", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Government debt", "Great Recession", "Greeks (finance)", "Handle System", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Hybrid system", "IVX", "Implied volatility", "Independent and identically distributed random variables", "Inelastic neutron scattering", "Infinitesimal generator (stochastic processes)", "Inflation derivative", "Inflation swap", "Interacting particle system", "Interest rate derivative", "Interest rate future", "Interest rate option", "Interest rate swap", "Intermarket Spread", "Iron butterfly (options strategy)", "Iron condor", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "JSTOR", "Journal of Financial Economics", "Jump-diffusion models", "Jump discontinuity", "Jump model", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Local volatility", "Lookback option", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Magnetic reconnection", "Malliavin calculus", "Margin (finance)", "Margrabe's formula", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Medical imaging", "Mixing (mathematics)", "Mixture model", "Moneyness", "Monte Carlo methods for option pricing", "Moran process", "Mortgage-backed security", "Mountain range (options)", "Moving-average model", "Municipal debt", "M\u00f6\u00dfbauer spectroscopy", "Non-homogeneous Poisson process", "Normal backwardation", "Open interest", "Option (finance)", "Option pricing", "Option style", "Optional stopping theorem", "Options spread", "Options strategy", "Ornstein\u2013Uhlenbeck process", "Overnight indexed swap", "Pattern theory", "Percolation theory", "Piecewise deterministic Markov process", "Pin risk (options)", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Power reverse dual-currency note", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Property derivative", "Protective put", "Put option", "Put\u2013call parity", "Quadratic variation", "Queueing model", "Queueing theory", "Rainbow option", "Random dynamical system", "Random field", "Random graph", "Random sampling", "Random walk", "Ratio spread", "Real options valuation", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk-free interest rate", "Risk process", "Risk reversal", "Robert C. Merton", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Short-rate model", "Sigma-martingale", "Single-stock futures", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Slippage (finance)", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stochastic volatility", "Stock market index future", "Stopping time", "Straddle", "Strangle (options)", "Stratonovich integral", "Strike price", "Submartingale", "Supermartingale", "Superprocess", "Swap (finance)", "Swaption", "System on a chip", "Tanaka equation", "Tax policy", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Total return swap", "Trinomial tree", "Uniform integrability", "Usual hypotheses", "VIX", "Valuation of options", "Vanilla option", "Vanna\u2013Volga pricing", "Variance gamma process", "Variance swap", "Vasicek model", "Vertical spread", "Volatility (finance)", "Volatility arbitrage", "Volatility clustering", "Volatility smile", "Volatility swap", "Warrant (finance)", "Weather derivative", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "Year-on-Year Inflation-Indexed Swap", "Zero-Coupon Inflation-Indexed Swap", "Zero coupon swap"], "references": ["http://hdl.handle.net/1721.1%2F1899", "http://doi.org/10.1016%2F0304-405X(76)90022-2", "http://doi.org/10.1080%2F00268978100100521", "http://doi.org/10.1088%2F0370-1328%2F77%2F2%2F319", "http://doi.org/10.1103%2FPhysRev.120.1093", "http://doi.org/10.1139%2Fp66-108", "http://doi.org/10.1139%2Fp67-025", "http://www.jstor.org/stable/2346184"]}, "VC dimension": {"categories": ["Commons category link is on Wikidata", "Computational learning theory", "Dimension", "Measures of complexity", "Pages with DOIs inactive since 2018", "Statistical classification"], "title": "VC dimension", "method": "VC dimension", "url": "https://en.wikipedia.org/wiki/VC_dimension", "summary": "In Vapnik\u2013Chervonenkis theory, the VC dimension (for Vapnik\u2013Chervonenkis dimension) is a measure of the capacity (complexity, expressive power, richness, or flexibility) of a space of functions that can be learned by a statistical classification algorithm. It is defined as the cardinality of the largest set of points that the algorithm can shatter. It was originally defined by Vladimir Vapnik and Alexey Chervonenkis.Formally, the capacity of a classification model is related to how complicated it can be. For example, consider the thresholding of a high-degree polynomial: if the polynomial evaluates above zero, that point is classified as positive, otherwise as negative. A high-degree polynomial can be wiggly, so it can fit a given set of training points well. But one can expect that the classifier will make errors on other points, because it is too wiggly. Such a polynomial has a high capacity. A much simpler alternative is to threshold a linear function. This function may not fit the training set well, because it has a low capacity. This notion of capacity is made rigorous below.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d9/VC1.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b8/VC2.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b5/VC3.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/VC4.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Alexey Chervonenkis", "Algorithm", "ArXiv", "Bernard Chazelle", "Bibcode", "Boosting (machine learning)", "Cardinality", "Computational geometry", "Convex hull", "Degree of a polynomial", "Digital object identifier", "Directed acyclic graph", "E-net (computational geometry)", "Finite projective plane", "Growth function", "Heaviside step function", "Independent identically-distributed random variables", "International Standard Book Number", "Karpinski-Macintyre theorem", "Kernel methods", "Linear classifier", "Manfred K. Warmuth", "Mehryar Mohri", "Natarajan dimension", "Neural network", "Overfitting", "Perceptron", "Polynomial", "Probabilistic", "Rademacher complexity", "Radon's theorem", "Sample-complexity bounds", "Sauer\u2013Shelah lemma", "Set family", "Shattered set", "Shattering (machine learning)", "Sigmoid function", "Sign function", "Sine", "Statistical classification", "Symmetric set difference", "Upper bound", "Vapnik\u2013Chervonenkis theory", "Vladimir Vapnik"], "references": ["http://papers.nips.cc/paper/5766-on-the-pseudo-dimension-of-nearly-optimal-auctions", "http://www.sciencedirect.com/science/article/pii/S002200009791477X", "http://www-2.cs.cmu.edu/~awm/tutorials/vcdim.html", "http://adsabs.harvard.edu/abs/2015arXiv150603684M", "http://www.cs.princeton.edu/~chazelle/book.html", "http://l2r.cs.uiuc.edu/~danr/Teaching/CS446-16/Papers/p929-blumer.pdf", "http://arxiv.org/abs/1506.03684", "http://doi.org/10.1006%2Fjcss.1997.1477", "http://doi.org/10.1007%2F978-3-319-21852-6_3", "http://doi.org/10.1007%2FBF00114804%23page-1", "http://doi.org/10.1137%2F1116025", "http://doi.org/10.1145%2F130385.130423", "http://doi.org/10.1145%2F41958.41994", "http://doi.org/10.1145%2F76359.76371", "https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/svmtutorial.pdf", "https://link.springer.com/article/10.1007%2FBF00114804#page-1"]}, "Fisher's method": {"categories": ["All articles lacking reliable references", "Articles lacking reliable references from March 2017", "Meta-analysis", "Statistical tests"], "title": "Fisher's method", "method": "Fisher's method", "url": "https://en.wikipedia.org/wiki/Fisher%27s_method", "summary": "In statistics, Fisher's method, also known as Fisher's combined probability test, is a technique for data fusion or \"meta-analysis\" (analysis of analyses). It was developed by and named for Ronald Fisher. In its basic form, it is used to combine the results from several independent tests bearing upon the same overall hypothesis (H0).", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/46/R._A._Fischer.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Zlogp.pdf", "https://upload.wikimedia.org/wikipedia/en/e/e5/Kequals2.jpg"], "links": ["Chi-squared distribution", "Cumulative distribution function", "Data fusion", "Degrees of freedom (statistics)", "Diabetes", "Digital object identifier", "Effect size", "Exponential distribution", "Extensions of Fisher's method", "False discovery rate", "International Standard Book Number", "JSTOR", "Meta-analysis", "P-value", "Probabilities", "Ronald Fisher", "Samuel A. Stouffer", "Statistical hypothesis testing", "Statistical independence", "Statistical power", "Statistics", "Test statistic", "Type I and type II errors", "Uniform distribution (continuous)"], "references": ["http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15258/1/224A.pdf", "http://psychclassics.yorku.ca/Fisher/Methods", "http://stats.stackexchange.com/questions/20126/testing-two-tailed-p-values-using-stouffers-approach", "http://doi.org/10.1016/S0167-7152(02)00310-3", "http://doi.org/10.2307/2529826", "http://doi.org/10.2307/2681650", "http://www.jstor.org/stable/2681650", "https://cran.r-project.org/web/packages/metap/index.html"]}, "People v. Collins": {"categories": ["1968 in California", "1968 in United States case law", "California state case law", "Forensic statistics", "Law articles needing an infobox"], "title": "People v. Collins", "method": "People v. Collins", "url": "https://en.wikipedia.org/wiki/People_v._Collins", "summary": "People v. Collins was a 1968 American robbery trial noted for its misuse of probability and as an example of the prosecutor's fallacy.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9a/Johnny-automatic-scales-of-justice.svg", "https://upload.wikimedia.org/wikipedia/en/a/a4/Flag_of_the_United_States.svg"], "links": ["Conditional probability", "Coralie Colmez", "Guilt (law)", "International Standard Book Number", "Jury", "Leila Schneps", "Probability", "Prosecutor", "Prosecutor's fallacy", "Supreme Court of California"], "references": ["https://www.courtlistener.com/c/Cal.2d/68/319/", "https://www.courtlistener.com/opinion/1207456/people-v-collins/", "https://scholar.google.com/scholar_case?case=2393563144534950884"]}, "Algebraic statistics": {"categories": ["Statistical theory"], "title": "Algebraic statistics", "method": "Algebraic statistics", "url": "https://en.wikipedia.org/wiki/Algebraic_statistics", "summary": "Algebraic statistics is the use of algebra to advance statistics. Algebra has been useful for experimental design, parameter estimation, and hypothesis testing.\nTraditionally, algebraic statistics has been associated with the design of experiments and multivariate analysis (especially time series). In recent years, the term \"algebraic statistics\" has been sometimes restricted, sometimes being used to label the use of algebraic geometry and commutative algebra in statistics.", "images": [], "links": ["Abelian group", "Affine geometry", "Akaike information criterion", "Alexander Ostrowski", "Algebra", "Algebraic curve", "Algebraic geometry", "Algebraic variety", "American Mathematical Society", "Anne Penfold Street", "Arne Beurling", "Association scheme", "Bernd Sturmfels", "Binomial random variable", "C. R. Rao", "Commutative algebra", "Contraction mapping", "Contraction mapping theorem", "Damaraju Raghavarao", "Design of experiments", "Discrete random variable", "Estimation", "Finite fields", "Garrett Birkhoff", "Haar measure", "Harmonic analysis", "Henry Mann", "Henry Wynn", "Hilbert metric", "Hypothesis testing", "Image analysis", "Infinite dimensional optimization", "International Standard Book Number", "Invariant subspace", "Jonathan Borwein", "Lattice theory", "Linear programming", "Lior Pachter", "Locally compact group", "Lucien Le Cam", "Multivariate analysis", "Ordered vector space", "Orthogonal array", "Oscar Kempthorne", "Parameter estimation", "Pattern theory", "Perron\u2013Frobenius theorem", "Principle of maximum entropy", "R. A. Bailey", "R. C. Bose", "Random variable", "Riesz space", "Ronald A. Fisher", "Rosemary A. Bailey", "Simplex", "Singular statistical model", "Spatial statistics", "Stationary stochastic process", "Statistical decision theory", "Statistical learning theory", "Statistical theory", "Statistics", "Sumio Watanabe", "Time series", "Ulf Grenander", "Watanabe-Akaike information criterion", "Wold's theorem", "Wold decomposition"], "references": ["http://www.jalgstat.com", "http://watanabe-www.math.dis.titech.ac.jp/users/swatanab/ag-slt-fig.html", "http://www.maths.qmul.ac.uk/~rab/Asbook/", "https://books.google.com/books?id=GiYc5nRVKf8C", "https://web.archive.org/web/20040905100535/http://titles.cambridge.org/catalogue.asp?isbn=052182446X"]}, "Economic epidemiology": {"categories": ["Epidemiology", "Interdisciplinary subfields of economics", "Medical statistics", "Public health"], "title": "Economic epidemiology", "method": "Economic epidemiology", "url": "https://en.wikipedia.org/wiki/Economic_epidemiology", "summary": "Economic epidemiology is a field at the intersection of epidemiology and economics. Its premise is to incorporate incentives for healthy behavior and their attendant behavioral responses into an epidemiological context to better understand how diseases are transmitted. This framework should help improve policy responses to epidemic diseases by giving policymakers and health-care providers clear tools for thinking about how certain actions can influence the spread of disease transmission.\nThe main context through which this field emerged was the idea of prevalence-dependence, or disinhibition, which suggests that individuals change their behavior as the prevalence of a disease changes. However, economic epidemiology also encompasses other ideas, including the role of externalities, global disease commons and how individuals\u2019 incentives can influence the outcome and cost of health interventions.\nStrategic epidemiology is a branch of economic epidemiology that adopts an explicitly game theoretic approach to analyzing the interplay between individual behavior and population wide disease dynamics.\n\n", "images": [], "links": ["Antiretroviral drug", "ArXiv", "Bibcode", "Conflict of interest", "Digital object identifier", "Disinhibition", "Economics", "Emerging Themes in Epidemiology", "Epidemic", "Epidemiology", "Game theory", "HIV", "Human behavior", "Infection", "Infectious disease", "Influenza", "JSTOR", "Malaria", "New Palgrave Dictionary of Economics", "Pathogen", "Prevalence", "PubMed Central", "PubMed Identifier", "Risk perception", "Safe sex", "Severe acute respiratory syndrome", "Sexually transmitted disease", "Side effect", "Smallpox", "Transmission (medicine)", "Unprotected sex", "Vaccine", "Viral load"], "references": ["http://www.dictionaryofeconomics.com/article?id=pde2008_E000261", "http://adsabs.harvard.edu/abs/1994Sci...265.1451B", "http://adsabs.harvard.edu/abs/2000Sci...287..650B", "http://adsabs.harvard.edu/abs/2003PNAS..10010564B", "http://adsabs.harvard.edu/abs/2004PNAS..10113391B", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC193525", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC516577", "http://www.ncbi.nlm.nih.gov/pubmed/10649998", "http://www.ncbi.nlm.nih.gov/pubmed/10691541", "http://www.ncbi.nlm.nih.gov/pubmed/12683957", "http://www.ncbi.nlm.nih.gov/pubmed/12876900", "http://www.ncbi.nlm.nih.gov/pubmed/12920181", "http://www.ncbi.nlm.nih.gov/pubmed/12960827", "http://www.ncbi.nlm.nih.gov/pubmed/14754434", "http://www.ncbi.nlm.nih.gov/pubmed/15249572", "http://www.ncbi.nlm.nih.gov/pubmed/15329411", "http://www.ncbi.nlm.nih.gov/pubmed/15451492", "http://www.ncbi.nlm.nih.gov/pubmed/15627235", "http://www.ncbi.nlm.nih.gov/pubmed/15913667", "http://www.ncbi.nlm.nih.gov/pubmed/18992258", "http://www.ncbi.nlm.nih.gov/pubmed/20149801", "http://www.ncbi.nlm.nih.gov/pubmed/7606144", "http://www.ncbi.nlm.nih.gov/pubmed/8073289", "http://arxiv.org/abs/1309.3327", "http://doi.org/10.1001%2Fjama.292.2.224", "http://doi.org/10.1016%2F0025-5564(94)00066-9", "http://doi.org/10.1016%2FS0167-6296(02)00103-0", "http://doi.org/10.1016%2FS1473-3099(04)01148-X", "http://doi.org/10.1016%2Fj.jtbi.2008.10.005", "http://doi.org/10.1016%2Fj.jtbi.2010.02.007", "http://doi.org/10.1016%2Fj.mbs.2005.03.006", "http://doi.org/10.1017%2Fs1355770x0700383x", "http://doi.org/10.1073%2Fpnas.0403823101", "http://doi.org/10.1073%2Fpnas.1731324100", "http://doi.org/10.1086%2F260352", "http://doi.org/10.1086%2F425267", "http://doi.org/10.1093%2Fwbro%2Flkg011", "http://doi.org/10.1097%2F00002030-200309050-00013", "http://doi.org/10.1097%2F00042560-200202010-00004", "http://doi.org/10.1126%2Fscience.287.5453.601", "http://doi.org/10.1126%2Fscience.287.5453.650", "http://doi.org/10.1126%2Fscience.8073289", "http://doi.org/10.1186%2F1742-7622-3-12", "http://doi.org/10.2174%2F1568005033480999", "http://doi.org/10.2307%2F2527443", "http://www.jstor.org/stable/2527443", "https://doi.org/10.1016%2FS1574-0064(00)80046-3"]}, "F-statistics": {"categories": ["Population genetics", "Wikipedia articles needing clarification from August 2014"], "title": "F-statistics", "method": "F-statistics", "url": "https://en.wikipedia.org/wiki/F-statistics", "summary": "In population genetics, F-statistics (also known as fixation indices) describe the statistically expected level of heterozygosity in a population; more specifically the expected degree of (usually) a reduction in heterozygosity when compared to Hardy\u2013Weinberg expectation.\nF-statistics can also be thought of as a measure of the correlation between genes drawn at different levels of a (hierarchically) subdivided population. This correlation is influenced by several evolutionary processes, such as genetic drift, founder effect, bottleneck, genetic hitchhiking, meiotic drive, mutation, gene flow, inbreeding, natural selection, or the Wahlund effect, but it was originally designed to measure the amount of allelic fixation owing to genetic drift.\nThe concept of F-statistics was developed during the 1920s by the American geneticist Sewall Wright, who was interested in inbreeding in cattle. However, because complete dominance causes the phenotypes of homozygote dominants and heterozygotes to be the same, it was not until the advent of molecular genetics from the 1960s onwards that heterozygosity in populations could be measured.\nF can be used to define effective population size.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/db/F-statistics.png", "https://upload.wikimedia.org/wikipedia/commons/archive/d/db/20161023171755%21F-statistics.png", "https://upload.wikimedia.org/wikipedia/commons/archive/d/db/20161023171751%21F-statistics.png"], "links": ["Allele frequencies", "Balding\u2013Nichols model", "Bibcode", "Binomial expansion", "Cattle", "Coalescent theory", "Coefficient of relationship", "Complete dominance", "Digital object identifier", "E.B. Ford", "Ecological selection", "Effective population size", "Evolution", "Evolutionary game theory", "Expected value", "F-distribution", "F-test", "Fisher's fundamental theorem of natural selection", "Fitness (biology)", "Fitness landscape", "Fixation index", "Founder effect", "Gene flow", "Gene locus", "Genetic drift", "Genetic genealogy", "Genetic hitchhiking", "Genetic linkage", "Hardy\u2013Weinberg law", "Hardy\u2013Weinberg principle", "Heritability", "Heterozygosity", "Identity by descent", "Inbreeding", "Index of evolutionary biology articles", "International Standard Book Number", "J. B. S. Haldane", "JSTOR", "Library of Congress Control Number", "Linkage disequilibrium", "Malecot's method of coancestry", "Meiotic drive", "Microevolution", "Molecular genetics", "Mutation", "Natural selection", "Negative selection (natural selection)", "Neutral theory of molecular evolution", "Observation", "Partition of the sum of squares", "Phenotype", "Population bottleneck", "Population genetics", "Population stratification", "Price equation", "PubMed Central", "PubMed Identifier", "Quantitative genetics", "Ronald Fisher", "Scarlet tiger moth", "Selective breeding", "Sewall Wright", "Sexual selection", "Shifting balance theory", "Small population size", "Wahlund effect", "Zygosity"], "references": ["http://helix.mcmaster.ca/brent/node10.html", "http://adsabs.harvard.edu/abs/1950Natur.166..247W", "http://adsabs.harvard.edu/abs/1991PNAS...88..839B", "http://adsabs.harvard.edu/abs/1997PNAS...94.4516B", "http://adsabs.harvard.edu/abs/2009Natur.461..489R", "http://adsabs.harvard.edu/abs/2009PLoSO...4.5472N", "http://adsabs.harvard.edu/abs/2012PLoSO...749837E", "http://eco-tools.njit.edu/webMathematica/EcoTools/Fstats-1-1/Introduction.html", "http://darwin.eeb.uconn.edu/eeb348/lecture-notes/genetic-structure.pdf", "http://darwin.eeb.uconn.edu/eeb348/lecture-notes/wahlund/wahlund.html", "http://www.uwyo.edu/dbmcd/popecol/Maylects/FST.html", "http://lccn.loc.gov/67025533", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1205020", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1288178", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2038030", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC20754", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2527025", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2675054", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2681007", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2842210", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3504095", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC50909", "http://www.ncbi.nlm.nih.gov/pubmed/10712212", "http://www.ncbi.nlm.nih.gov/pubmed/15439261", "http://www.ncbi.nlm.nih.gov/pubmed/15508000", "http://www.ncbi.nlm.nih.gov/pubmed/1644282", "http://www.ncbi.nlm.nih.gov/pubmed/16957813", "http://www.ncbi.nlm.nih.gov/pubmed/18691889", "http://www.ncbi.nlm.nih.gov/pubmed/18713460", "http://www.ncbi.nlm.nih.gov/pubmed/1933444", "http://www.ncbi.nlm.nih.gov/pubmed/19424496", "http://www.ncbi.nlm.nih.gov/pubmed/19442770", "http://www.ncbi.nlm.nih.gov/pubmed/19687804", "http://www.ncbi.nlm.nih.gov/pubmed/19779445", "http://www.ncbi.nlm.nih.gov/pubmed/1992475", "http://www.ncbi.nlm.nih.gov/pubmed/23185452", "http://www.ncbi.nlm.nih.gov/pubmed/4063030", "http://www.ncbi.nlm.nih.gov/pubmed/9114021", "http://www.library.auckland.ac.nz/subjects/bio/pdfs/733Pop-g-stats2.pdf", "http://doi.org/10.1007%2F978-1-4684-9063-3_14", "http://doi.org/10.1007%2Fs10038-006-0041-1", "http://doi.org/10.1016%2F0735-6757(85)90177-9", "http://doi.org/10.1016%2Fj.ajhg.2009.04.015", "http://doi.org/10.1016%2Fj.cub.2008.07.049", "http://doi.org/10.1038%2F166247a0", "http://doi.org/10.1038%2Fnature08365", "http://doi.org/10.1038%2Fng1435", "http://doi.org/10.1038%2Fnrg2611", "http://doi.org/10.1073%2Fpnas.88.3.839", "http://doi.org/10.1073%2Fpnas.94.9.4516", "http://doi.org/10.1080%2F00071669108417396", "http://doi.org/10.1086%2F302825", "http://doi.org/10.1186%2F1471-2156-9-54", "http://doi.org/10.1371%2Fjournal.pone.0005472", "http://doi.org/10.1371%2Fjournal.pone.0049837", "http://doi.org/10.2307%2F2406450", "http://www.jstor.org/stable/2356081", "http://www.jstor.org/stable/2406450", "http://www.jstor.org/stable/42042", "http://www.stats.ox.ac.uk/~mcvean/slides7.pdf"]}, "Geometric distribution": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from March 2011", "Articles with unsourced statements from May 2012", "Discrete distributions", "Exponential family distributions", "Infinitely divisible probability distributions", "Wikipedia articles needing clarification from May 2012"], "title": "Geometric distribution", "method": "Geometric distribution", "url": "https://en.wikipedia.org/wiki/Geometric_distribution", "summary": "In probability theory and statistics, the geometric distribution is either of two discrete probability distributions:\n\nThe probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...}\nThe probability distribution of the number Y = X \u2212 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... }Which of these one calls \"the\" geometric distribution is a matter of convention and convenience.\nThese two different geometric distributions should not be confused with each other. Often, the name shifted geometric distribution is adopted for the former one (distribution of the number X); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly.\nThe geometric distribution gives the probability that the first occurrence of success requires k independent trials, each with success probability p. If the probability of success on each trial is p, then the probability that the kth trial (out of k trials) is the first success is\n\n \n \n \n Pr\n (\n X\n =\n k\n )\n =\n (\n 1\n \u2212\n p\n \n )\n \n k\n \u2212\n 1\n \n \n p\n \n \n {\\displaystyle \\Pr(X=k)=(1-p)^{k-1}p}\n for k = 1, 2, 3, ....\nThe above form of the geometric distribution is used for modeling the number of trials up to and including the first success. By contrast, the following form of the geometric distribution is used for modeling the number of failures until the first success:\n\n \n \n \n Pr\n (\n Y\n =\n k\n )\n =\n (\n 1\n \u2212\n p\n \n )\n \n k\n \n \n p\n \n \n {\\displaystyle \\Pr(Y=k)=(1-p)^{k}p}\n for k = 0, 1, 2, 3, ....\nIn either case, the sequence of probabilities is a geometric sequence.\nFor example, suppose an ordinary die is thrown repeatedly until the first time a \"1\" appears. The probability distribution of the number of times it is thrown is supported on the infinite set { 1, 2, 3, ... } and is a geometric distribution with p = 1/6.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6f/Geometric_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4b/Geometric_pmf.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian inference", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli trial", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compact space", "Compound Poisson distribution", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Coupon collector's problem", "Cumulant", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dice", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Floor and ceiling functions", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric sequence", "Geometric stable distribution", "Golomb coding", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Indecomposable distribution", "Infinite divisibility (probability)", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "MathWorld", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Memorylessness", "Method of moments (statistics)", "Minimum", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Numeral system", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "PlanetMath", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Posterior distribution", "Power series", "Prefix code", "Prior distribution", "Probability-generating function", "Probability distribution", "Probability mass function", "Probability theory", "Pseudorandom number generator", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Sample (statistics)", "Sample mean", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform convergence", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://mathworld.wolfram.com/GeometricDistribution.html", "http://www.wolframalpha.com/input/?i=inverse+p+=+1+-+e%5E-l", "http://planetmath.org/?op=getobj&from=objects&id=3456"]}, "Inverse-variance weighting": {"categories": ["All articles needing additional references", "Articles needing additional references from September 2012", "Estimation methods", "Meta-analysis"], "title": "Inverse-variance weighting", "method": "Inverse-variance weighting", "url": "https://en.wikipedia.org/wiki/Inverse-variance_weighting", "summary": "In statistics, inverse-variance weighting is a method of aggregating two or more random variables to minimize the variance of the weighted average. Each random variable is weighted in inverse proportion to its variance.\nGiven a sequence of independent observations yi with variances \u03c3i2, the inverse-variance weighted average is given by\n\n \n \n \n \n \n \n y\n ^\n \n \n \n =\n \n \n \n \n \u2211\n \n i\n \n \n \n y\n \n i\n \n \n \n /\n \n \n \u03c3\n \n i\n \n \n 2\n \n \n \n \n \n \u2211\n \n i\n \n \n 1\n \n /\n \n \n \u03c3\n \n i\n \n \n 2\n \n \n \n \n \n .\n \n \n {\\displaystyle {\\hat {y}}={\\frac {\\sum _{i}y_{i}/\\sigma _{i}^{2}}{\\sum _{i}1/\\sigma _{i}^{2}}}.}\n The inverse-variance weighted average has the least variance among all weighted averages, which can be calculated as\n\n \n \n \n \n D\n \n 2\n \n \n (\n \n \n \n y\n ^\n \n \n \n )\n =\n \n \n 1\n \n \n \u2211\n \n i\n \n \n 1\n \n /\n \n \n \u03c3\n \n i\n \n \n 2\n \n \n \n \n \n .\n \n \n {\\displaystyle D^{2}({\\hat {y}})={\\frac {1}{\\sum _{i}1/\\sigma _{i}^{2}}}.}\n If the variances of the measurements are all equal, then the inverse-variance weighted average becomes the simple average.\nInverse-variance weighting is typically used in statistical meta-analysis to combine the results from independent measurements.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Average", "Estimator", "Expectation value", "Gradient", "Gravity of Earth", "International Standard Book Number", "Inverse proportion", "John Wiley & Sons", "Lagrange multiplier", "Meta-analysis", "Projectile motion", "Random variables", "Second partial derivative test", "Simple pendulum", "Statistics", "Variance", "Weighted least squares", "Weighted mean"], "references": []}, "Scoring rule": {"categories": ["CS1 maint: Extra text: editors list", "CS1 maint: Multiple names: editors list", "Decision theory", "Probability assessment"], "title": "Scoring rule", "method": "Scoring rule", "url": "https://en.wikipedia.org/wiki/Scoring_rule", "summary": "In decision theory, a score function, or scoring rule, measures the accuracy of probabilistic predictions. It is applicable to tasks in which predictions must assign probabilities to a set of mutually exclusive outcomes. The set of possible outcomes can be either binary or categorical in nature, and the probabilities assigned to this set of outcomes must sum to one (where each individual probability is in the range of 0 to 1). A score can be thought of as either a measure of the \"calibration\" of a set of probabilistic predictions, or as a \"cost function\" or \"loss function\".\nIf a cost is levied in proportion to a proper scoring rule, the minimal expected cost corresponds to reporting the true set of probabilities. Proper scoring rules are used in meteorology, finance, and pattern classification where a forecaster or algorithm will attempt to minimize the average score to yield refined, calibrated probabilities (i.e. accurate probabilities).", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/55/ExpectedLog.png", "https://upload.wikimedia.org/wikipedia/commons/6/6c/LogScore.png", "https://upload.wikimedia.org/wikipedia/commons/5/53/NormalizedScore.png", "https://upload.wikimedia.org/wikipedia/commons/8/89/RawScore.png"], "links": ["Accuracy and precision", "Affine transformation", "ArXiv", "Bayesian Inference", "Bibcode", "Binary decision", "Brier score", "Calibrated probability assessment", "Decision theory", "Digital object identifier", "Expected value", "Information theory", "Loss function", "Mean absolute error", "Mean squared error", "Personal Probability", "Probabilistic forecasting", "Probability vector", "Self-information", "Social Science Research Network", "Weather forecasting"], "references": ["http://www.decisionsciencenews.com/?p=963", "http://ssrn.com/abstract=2818213", "http://adsabs.harvard.edu/abs/2009QJRMS.135.1512B", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.52.1557&rep=rep1&type=pdf", "http://faculty.engr.utexas.edu/bickel/Papers/QSL_Comparison.pdf", "http://faculty.engr.utexas.edu/bickel/Papers/Scoring_Rules_Education.pdf", "http://www.stat.washington.edu/research/reports/2004/tr463.pdf", "http://docs.lib.noaa.gov/rescue/mwr/078/mwr-078-01-0001.pdf", "http://arxiv.org/abs/0806.0813", "http://doi.org/10.1002%2Fqj.456", "http://doi.org/10.1175%2F1520-0450(1973)012%3C0595:ANVPOT%3E2.0.CO;2", "http://doi.org/10.1175%2F1520-0493(1950)078%3C0001:VOFEIT%3E2.0.CO;2", "http://doi.org/10.1198%2F016214506000001437", "http://doi.org/10.1287%2Fdeca.1070.0089", "http://doi.org/10.2139%2Fssrn.2818213", "http://www.jmlr.org/papers/volume13/hernandez-orallo12a/hernandez-orallo12a.pdf", "http://www.personal.reading.ac.uk/~pt904209/publications/decomposition_qjrms.pdf", "https://www.stat.washington.edu/research/reports/2009/tr551.pdf", "https://dx.doi.org/10.1198/016214506000001437", "https://www.jstor.org/discover/10.2307/1402448?uid=16779064&uid=3737864&uid=2129&uid=2&uid=70&uid=16734048&uid=3&uid=67&uid=62&sid=21101527707467", "https://projecteuclid.org/euclid.aos/1176347398"]}, "Isotonic regression": {"categories": ["All Wikipedia articles needing context", "All pages needing cleanup", "CS1 maint: Multiple names: authors list", "Nonparametric Bayesian statistics", "Nonparametric regression", "Numerical analysis", "Wikipedia articles needing context from February 2012", "Wikipedia introduction cleanup from February 2012"], "title": "Isotonic regression", "method": "Isotonic regression", "url": "https://en.wikipedia.org/wiki/Isotonic_regression", "summary": "In statistics, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations under the following constraints: the fitted free-form line has to be non-decreasing everywhere, and it has to lie as close to the observations as possible.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/30/Isotonic_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational complexity theory", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Directed graph", "Discrete choice", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Embedding", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Euclidean space", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fixed effects model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Iterative algorithm", "Iteratively reweighted least squares", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Joseph Kruskal", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least-angle regression", "Least-squares", "Least absolute deviations", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear least squares", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Mean squared error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monotonic", "Multidimensional scaling", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-decreasing function", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Numerical analysis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order of dissimilarity", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares regression", "Partial order", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial regression", "Pool adjacent violators algorithm", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal component regression", "Prior probability", "Probabilistic design", "Probability distribution", "Probit model", "Proportional hazards model", "Psychometrics", "Quadratic programming", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effects model", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regularized least squares", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Total order", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1007%2FBF01580873", "http://doi.org/10.1007%2FBF02289694", "http://doi.org/10.1093%2Fbiomet%2F88.3.793", "http://doi.org/10.1111%2Fj.1467-9868.2008.00677.x", "http://doi.org/10.18637%2Fjss.v032.i05", "http://www.jstatsoft.org/article/view/v032i05", "http://www.worldcat.org/issn/1548-7660"]}, "Concrete illustration of the central limit theorem": {"categories": ["Central limit theorem"], "title": "Illustration of the central limit theorem", "method": "Concrete illustration of the central limit theorem", "url": "https://en.wikipedia.org/wiki/Illustration_of_the_central_limit_theorem", "summary": "This article gives two concrete illustrations of the central limit theorem. Both involve the sum of independent and identically-distributed random variables and show how the probability distribution of the sum approaches the normal distribution as the number of terms in the sum increases.\nThe first illustration involves a continuous probability distribution, for which the random variables have a probability density function.\nThe second illustration, for which most of the computation can be done by hand, involves a discrete probability distribution, which is characterized by a probability mass function.\nA free full-featured interactive simulation that allows the user to set up various distributions and adjust the sampling parameters is available through the External links section at the bottom of this page.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a6/Central_limit_thm_1.png", "https://upload.wikimedia.org/wikipedia/commons/f/f8/Central_limit_thm_2.png", "https://upload.wikimedia.org/wikipedia/commons/6/69/Central_limit_thm_3.png", "https://upload.wikimedia.org/wikipedia/commons/8/85/Central_limit_thm_4.png", "https://upload.wikimedia.org/wikipedia/commons/7/72/Central_theorem_2.svg"], "links": ["Bar graph", "Central limit theorem", "Continuity correction", "Continuous probability distribution", "Convolution", "Discrete Fourier transform", "Discrete probability distribution", "Discrete random variable", "Independent and identically-distributed random variables", "Independent identically distributed variables", "Monte Carlo method", "Normal distribution", "Piecewise", "Pointwise product", "Polynomial", "Probability density function", "Probability distribution", "Probability mass function", "Square root of 2"], "references": ["http://www.statisticalengineering.com/central_limit_theorem.html", "http://mathworld.wolfram.com/UniformSumDistribution.html", "http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem", "http://blog.vctr.me/posts/central-limit-theorem.html", "http://www.vias.org/simulations/simusoft_cenlimit.html"]}, "Functional data analysis": {"categories": ["Statistical analysis", "Statistical data types"], "title": "Functional data analysis", "method": "Functional data analysis", "url": "https://en.wikipedia.org/wiki/Functional_data_analysis", "summary": "Functional data analysis (FDA) is a branch of statistics that analyses data providing information about curves, surfaces or anything else varying over a continuum. In its most general form, under an FDA framework each sample element is considered to be a function. The physical continuum over which these functions are defined is often time, but may also be spatial location, wavelength, probability, etc.", "images": [], "links": ["Bernard Silverman", "Data analysis", "Differential equation", "Dynamical systems", "Estimation theory", "Functional analysis", "Functional principal component analysis", "International Standard Book Number", "Kernel smoothing", "Measurement error", "Nonparametric statistics", "Precipitation (meteorology)", "Principal components analysis", "Regression model", "Smoothing spline", "Smoothness", "Statistics", "Weather station"], "references": ["http://faculty.bscb.cornell.edu/~hooker/ShortCourseHandout.pdf", "http://anson.ucdavis.edu/~mueller/Review151106.pdf"]}, "Sampling distribution": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2014", "Sampling (statistics)", "Statistical inference", "Use dmy dates from September 2015"], "title": "Sampling distribution", "method": "Sampling distribution", "url": "https://en.wikipedia.org/wiki/Sampling_distribution", "summary": "In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic. If an arbitrarily large number of samples, each involving multiple observations (data points), were separately used in order to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample, then the sampling distribution is the probability distribution of the values that the statistic takes on. In many contexts, only one sample is observed, but the sampling distribution can be found theoretically.\nSampling distributions are important in statistics because they provide a major simplification en route to statistical inference. More specifically, they allow analytical considerations to be based on the probability distribution of a statistic, rather than on the joint probability distribution of all the individual sample values.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli distribution", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Closed-form expression", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monte-Carlo simulation", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random sample", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis test", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://demonstrations.wolfram.com/StatisticsAssociatedWithNormalSamples/", "http://www.indiana.edu/~jkkteach/ExcelSampler/", "http://web.williams.edu/Mathematics/sjmiller/public_html/BrownClasses/162/Handouts/MedianThm04.pdf", "https://books.google.com/books?id=xQRgh4z_5acC"]}, "Sensitivity (tests)": {"categories": ["Accuracy and precision", "All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from June 2017", "Bioinformatics", "Biostatistics", "Cheminformatics", "Medical statistics", "Statistical classification", "Statistical ratios", "Wikipedia articles that are too technical from June 2017"], "title": "Sensitivity and specificity", "method": "Sensitivity (tests)", "url": "https://en.wikipedia.org/wiki/Sensitivity_and_specificity", "summary": "Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as a classification function:\n\nSensitivity (also called the true positive rate, the recall, or probability of detection in some fields) measures the proportion of actual positives that are correctly identified as such (e.g., the percentage of sick people who are correctly identified as having the condition).\nSpecificity (also called the true negative rate) measures the proportion of actual negatives that are correctly identified as such (e.g., the percentage of healthy people who are correctly identified as not having the condition).Equivalently, in medical tests sensitivity is the extent to which actual positives are not overlooked (so false negatives are few), and specificity is the extent to which actual negatives are classified as such (so false positives are few). Thus a highly sensitive test rarely overlooks an actual positive (for example, showing \"nothing bad\" despite something bad existing); a highly specific test rarely registers a positive classification for anything that is not the target of testing (for example, finding one bacterial species and mistaking it for another closely related one that is the true target); and a test that is highly sensitive and highly specific does both, so it \"rarely overlooks a thing that it is looking for\" and it \"rarely mistakes anything else for that thing.\" Because most medical tests do not have sensitivity and specificity values above 99%, \"rarely\" does not equate to certainty. But for practical reasons, tests with sensitivity and specificity values above 90% have high credibility, albeit usually no certainty, in differential diagnosis.\nSensitivity therefore quantifies the avoiding of false negatives and specificity does the same for false positives. For any test, there is usually a trade-off between the measures \u2013 for instance, in airport security, since testing of passengers is for potential threats to safety, scanners may be set to trigger alarms on low-risk items like belt buckles and keys (low specificity) in order to increase the probability of identifying dangerous objects and minimize the risk of missing objects that do pose a threat (high sensitivity). This trade-off can be represented graphically using a receiver operating characteristic curve. A perfect predictor would be described as 100% sensitive, meaning all sick individuals are correctly identified as sick, and 100% specific, meaning no healthy individuals are incorrectly identified as sick. In reality, however, any non-deterministic predictor will possess a minimum error bound known as the Bayes error rate.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e2/HighSensitivity_LowSpecificity_1401x1050.png", "https://upload.wikimedia.org/wikipedia/commons/2/2d/Issoria_lathonia.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a6/LowSensitivity_HighSpecificity_1400x1050.png", "https://upload.wikimedia.org/wikipedia/commons/8/8b/Nuvola_apps_kalzium.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e7/Sensitivity_and_specificity.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d6/WHO_Rod.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Academic clinical trials", "Accuracy", "Accuracy and precision", "Adaptive clinical trial", "Airport security", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Bayes error rate", "Binary classification", "Binomial proportion confidence interval", "Blind experiment", "Bowel cancer", "Brier score", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Certainty", "Classification rule", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Confidence intervals", "Confusion matrix", "Contingency table", "Correlation does not imply causation", "Cross-sectional study", "Cumulative accuracy profile", "Cumulative incidence", "Design of experiments", "Detection theory", "Diagnostic odds ratio", "Differential diagnosis", "Digital object identifier", "Dimensionless", "Discrimination", "Ecological study", "Endoscopy", "Epidemiological methods", "Evidence-based medicine", "Experiment", "F-score", "F1 score", "False alarm", "False discovery rate", "False negative", "False negative rate", "False omission rate", "False positive", "False positive paradox", "False positive rate", "False positives and false negatives", "Fecal occult blood", "First-in-man study", "Glossary of clinical research", "Harmonic mean", "Hazard ratio", "Hit rate", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Information retrieval", "Informedness", "Intention-to-treat analysis", "International Standard Book Number", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Matthews correlation coefficient", "Medical diagnosis", "Medical test", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "NCSS (statistical software)", "Negative likelihood ratio", "Negative predictive value", "Nested case\u2013control study", "Non-deterministic algorithm", "Normal distribution", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "OpenEpi", "Period prevalence", "Point prevalence", "Population Impact Measures", "Positive and negative predictive values", "Positive likelihood ratio", "Positive predictive value", "Pre- and post-test probability", "Precision (information retrieval)", "Precision and recall", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Recall (information retrieval)", "Receiver operating characteristic", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Scientific control", "Seeding trial", "Selection bias", "Sensitivity (test)", "Sensitivity (tests)", "Sensitivity index", "Specificity (tests)", "Specificity and sensitivity", "Statistic", "Statistical classification", "Statistical hypothesis testing", "Statistical population", "Statistical power", "Statistical significance", "Survivorship bias", "Systematic review", "True negative", "True negative rate", "True positive", "True positive rate", "Type II error", "Type I and type II errors", "Type I error", "Uncertainty coefficient", "Vaccine trial", "Virulence", "Youden's J statistic"], "references": ["http://www.flinders.edu.au/science_engineering/fms/School-CSEM/publications/tech_reps-research_artfcts/TRRA_2007.pdf", "http://www.mathworks.com/help/phased/examples/detector-performance-analysis-using-roc-curves.html", "http://www.med.emory.edu/EMAC/curriculum/diagnosis/sensand.htm", "http://omerad.msu.edu/ebm/Diagnosis/Diagnosis4.html", "http://araw.mede.uic.edu/cgi-bin/testcalc.pl", "http://open.umich.edu/education/med/m1/patientspop-decisionmaking/2010/materials", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC200804", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2540489", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2824341", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC487735", "http://www.ncbi.nlm.nih.gov/pubmed/14512479", "http://www.ncbi.nlm.nih.gov/pubmed/15271832", "http://www.ncbi.nlm.nih.gov/pubmed/20089911", "http://www.ncbi.nlm.nih.gov/pubmed/8019315", "http://www.ncbi.nlm.nih.gov/pubmed/8028462", "http://www.ncbi.nlm.nih.gov/pubmed/8028470", "http://people.inf.elte.hu/kiss/11dwhdm/roc.pdf", "http://www.cebm.net/sppin-and-snnout/", "http://vassarstats.net/clin1.html", "http://doi.org/10.1016%2Fj.patrec.2005.10.010", "http://doi.org/10.1136%2Fbmj.308.6943.1552", "http://doi.org/10.1136%2Fbmj.327.7417.716", "http://doi.org/10.1136%2Fbmj.329.7459.209", "http://doi.org/10.1177%2F0272989X9401400202", "http://doi.org/10.1177%2F0272989X9401400210", "http://doi.org/10.1523%2FJNEUROSCI.3585-09.2010", "http://www.medcalc.org/calc/diagnostic_test.php", "https://books.google.com/books?id=hDX65v9bReYC", "https://link.springer.com/referencework/10.1007%2F978-0-387-30164-8", "https://kennis-research.shinyapps.io/Bayes-App/", "https://web.archive.org/web/20130706035232/http://omerad.msu.edu/ebm/Diagnosis/Diagnosis4.html", "https://www.medcalc.org/calc/diagnostic_test.php"]}, "Recurrence quantification analysis": {"categories": ["CS1 maint: Multiple names: authors list", "Chaos theory", "Dynamical systems", "Nonlinear time series analysis", "Signal processing"], "title": "Recurrence quantification analysis", "method": "Recurrence quantification analysis", "url": "https://en.wikipedia.org/wiki/Recurrence_quantification_analysis", "summary": "Recurrence quantification analysis (RQA) is a method of nonlinear data analysis (cf. chaos theory) for the investigation of dynamical systems. It quantifies the number and duration of recurrences of a dynamical system presented by its phase space trajectory.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e3/Logistic_map_rqa.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7d/LogisticMap_BifurcationDiagram.png"], "links": ["Approximate entropy", "ArXiv", "Bibcode", "Chaos theory", "Chemistry", "Complexity", "Correlation sum", "Data analysis", "Deterministic process", "Digital object identifier", "Divergence", "Dynamical system", "Dynamical systems", "Earth sciences", "Engineering", "Frequency distribution", "Intermittency", "Laminar phase", "Lyapunov exponent", "Multiplicative inverse", "Nonlinear", "Phase space", "Physiology", "Predictability", "Probability", "PubMed Identifier", "Recurrence plot", "Shannon entropy", "Synchronisation", "Takens' theorem", "Time series", "White noise"], "references": ["http://www.scitopics.com/Recurrence_Quantification_Analysis.html", "http://adsabs.harvard.edu/abs/1992PhLA..171..199Z", "http://adsabs.harvard.edu/abs/2002PhLA..302..299M", "http://adsabs.harvard.edu/abs/2002PhRvE..66b6702M", "http://adsabs.harvard.edu/abs/2007PhR...438..237M", "http://adsabs.harvard.edu/abs/2008EPJST.164....3M", "http://adsabs.harvard.edu/abs/2016ITPSy..31..581B", "http://www.ncbi.nlm.nih.gov/pubmed/8175612", "http://arxiv.org/abs/1709.09971", "http://arxiv.org/abs/physics/0201061", "http://arxiv.org/abs/physics/0201064", "http://doi.org/10.1016%2F0375-9601(92)90426-M", "http://doi.org/10.1016%2FS0375-9601(02)01170-2", "http://doi.org/10.1016%2Fj.physrep.2006.11.001", "http://doi.org/10.1103%2FPhysRevE.66.026702", "http://doi.org/10.1109%2FTPWRS.2015.2407894", "http://doi.org/10.1140%2Fepjst%2Fe2008-00829-1", "http://www.recurrence-plot.tk/", "https://zenodo.org/record/996840"]}, "Additive model": {"categories": ["Nonparametric regression", "Regression models"], "title": "Additive model", "method": "Additive model", "url": "https://en.wikipedia.org/wiki/Additive_model", "summary": "In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an essential part of the ACE algorithm. The AM uses a one-dimensional smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the curse of dimensionality than e.g. a p-dimensional smoother. Furthermore, the AM is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with AM include model selection, overfitting, and multicollinearity.", "images": [], "links": ["Alternating conditional expectation model", "Backfitting algorithm", "Curse of dimensionality", "Data", "Digital object identifier", "Friedman, J.H.", "Generalized additive model", "Generalized additive model for location, scale, and shape", "JSTOR", "Jerome H. Friedman", "Journal of the American Statistical Association", "Linear regression", "Median polish", "Model selection", "Multicollinearity", "Nonparametric regression", "Overfitting", "Projection pursuit regression", "Robert Tibshirani", "Smooth function", "Smoothing", "Statistical unit", "Statistics", "Trevor Hastie"], "references": ["https://doi.org/10.1080%2F01621459.1981.10477729", "https://doi.org/10.1080%2F01621459.1985.10478157", "https://www.jstor.org/stable/2241560"]}, "Case-control": {"categories": ["CS1 maint: Uses authors parameter", "Design of experiments", "Epidemiology", "Nursing research", "Use dmy dates from April 2011"], "title": "Case\u2013control study", "method": "Case-control", "url": "https://en.wikipedia.org/wiki/Case%E2%80%93control_study", "summary": "A case\u2013control study (also known as case\u2013referent study) is a type of observational study in which two existing groups differing in outcome are identified and compared on the basis of some supposed causal attribute. Case\u2013control studies are often used to identify factors that may contribute to a medical condition by comparing subjects who have that condition/disease (the \"cases\") with patients who do not have the condition/disease but are otherwise similar (the \"controls\"). They require fewer resources but provide less evidence for causal inference than a randomized controlled trial. We only get odds ratio from a case\u2013control study which is an inferior measure of strength of association as compared to relative risk.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b5/ExplainingCaseControlSJW.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Academic clinical trials", "Adaptive clinical trial", "Analysis of clinical trials", "Analysis of variance", "Animal testing", "Animal testing on non-human primates", "Asymptomatic carrier", "Attributable fraction among the exposed", "Attributable fraction for the population", "Austin Bradford Hill", "Auxology", "Bachelor of Science in Public Health", "Behavior change (public health)", "Behavioural change theories", "Biological hazard", "Biostatistics", "Blind experiment", "Carl Rogers Darnall", "Case fatality rate", "Case report", "Case series", "Case study", "Centers for Disease Control and Prevention", "Chief Medical Officer", "Child mortality", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Community health", "Correlation does not imply causation", "Council on Education for Public Health", "Cross-sectional study", "Cultural competence in health care", "Cumulative incidence", "Design of experiments", "Deviance (sociology)", "Diffusion of innovations", "Digital object identifier", "Disease surveillance", "Doctor of Public Health", "Ecological study", "Emergency sanitation", "Environmental health", "Epidemic", "Epidemiological methods", "Epidemiology", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Evidence-based medicine", "Experiment", "Family planning", "Fecal\u2013oral route", "First-in-man study", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Genetically modified food", "George Davey Smith", "Germ theory of disease", "Global health", "Globalization and disease", "Glossary of clinical research", "Good agricultural practice", "Good manufacturing practice", "HACCP", "Hand washing", "Hazard ratio", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Hierarchy of evidence", "Human factors and ergonomics", "Human nutrition", "Hygiene", "ISO 22000", "In vitro", "In vivo", "Incidence (epidemiology)", "Infant mortality", "Infection control", "Infectivity", "Injury prevention", "Intention-to-treat analysis", "International Standard Book Number", "John Snow (physician)", "Joseph Lister", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "List of epidemics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "Longitudinal study", "Margaret Sanger", "Mary Mallon", "Maternal health", "Medical anthropology", "Medical sociology", "Mental health", "Meta-analysis", "Ministry of Health and Family Welfare", "Miquel Porta", "Morbidity", "Mortality rate", "Multicenter trial", "Nested case\u2013control study", "Notifiable disease", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Odds ratio", "Open-label trial", "Open defecation", "Oral hygiene", "PRECEDE-PROCEED model", "Patient safety", "Patient safety organization", "Period prevalence", "Pharmaceutical policy", "Pharmacovigilance", "Point prevalence", "Population Impact Measures", "Population health", "Positive deviance", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Preventive healthcare", "Preventive nutrition", "Professional degrees of public health", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quarantine", "ROC curve", "Race and health", "Randomized controlled trial", "Randomized controlled trials", "Rare disease assumption", "Regression analysis", "Relative risk", "Relative risk reduction", "Reproducibility", "Reproductive health", "Retrospective cohort study", "Richard Doll", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Safe sex", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scientific control", "Seeding trial", "Selection bias", "Sexually transmitted infection", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Sociology of health and illness", "Specificity and sensitivity", "Statistical hypothesis testing", "Statistical power", "Student's t-test", "Survivorship bias", "Systematic review", "Theory of planned behavior", "Transtheoretical model", "Tropical disease", "United States Public Health Service", "Vaccination", "Vaccine trial", "Vector control", "Virulence", "Waterborne diseases", "World Health Organization", "World Toilet Organization", "Z-test"], "references": ["http://emj.bmj.com/content/20/1/54.full.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2035864", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2038856", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC437139", "http://www.ncbi.nlm.nih.gov/pubmed/11844534", "http://www.ncbi.nlm.nih.gov/pubmed/1251836", "http://www.ncbi.nlm.nih.gov/pubmed/13364389", "http://www.ncbi.nlm.nih.gov/pubmed/14772469", "http://www.ncbi.nlm.nih.gov/pubmed/15166201", "http://www.ncbi.nlm.nih.gov/pubmed/15213107", "http://www.ncbi.nlm.nih.gov/pubmed/15836892", "http://www.ncbi.nlm.nih.gov/pubmed/16014596", "http://www.ncbi.nlm.nih.gov/pubmed/16184164", "http://www.ncbi.nlm.nih.gov/pubmed/2190942", "http://www.ncbi.nlm.nih.gov/pubmed/7046823", "http://casestudywriter.org/", "http://doi.org/10.1001%2Fjama.294.2.218", "http://doi.org/10.1016%2FS0140-6736(02)07605-5", "http://doi.org/10.1016%2FS0140-6736(05)66379-9", "http://doi.org/10.1038%2Fsj.ebd.6400355", "http://doi.org/10.1093%2Fije%2F19.1.205", "http://doi.org/10.1093%2Fije%2Fdyh124", "http://doi.org/10.1136%2Fbmj.2.4682.739", "http://doi.org/10.1136%2Fbmj.2.5001.1071", "http://doi.org/10.1136%2Fbmj.38142.554479.AE", "http://doi.org/10.2307%2F2529852", "http://www.wtccc.org.uk/"]}, "Cauchy distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2011", "Articles with unsourced statements from March 2011", "CS1 maint: Uses authors parameter", "Continuous distributions", "Location-scale family probability distributions", "Pages using deprecated image syntax", "Power laws", "Probability distributions with non-finite variance", "Stable distributions"], "title": "Cauchy distribution", "method": "Cauchy distribution", "url": "https://en.wikipedia.org/wiki/Cauchy_distribution", "summary": "The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy\u2013Lorentz distribution, Lorentz(ian) function, or Breit\u2013Wigner distribution. The Cauchy distribution \n \n \n \n f\n (\n x\n ;\n \n x\n \n 0\n \n \n ,\n \u03b3\n )\n \n \n {\\displaystyle f(x;x_{0},\\gamma )}\n is the distribution of the x-intercept of a ray issuing from \n \n \n \n (\n \n x\n \n 0\n \n \n ,\n \u03b3\n )\n \n \n {\\displaystyle (x_{0},\\gamma )}\n with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables if the denominator distribution has mean zero.\nThe Cauchy distribution is often used in statistics as the canonical example of a \"pathological\" distribution since both its expected value and its variance are undefined. (But see the section Explanation of undefined moments below.) The Cauchy distribution does not have finite moments of order greater than or equal to one; only fractional absolute moments exist. The Cauchy distribution has no moment generating function.\nIn mathematics, it is closely related to the Poisson kernel, which is the fundamental solution for the Laplace equation in the upper half-plane. In spectroscopy, it is the description of the shape of spectral lines which are subject to homogeneous broadening in which all atoms interact in the same way with the frequency range contained in the line shape. Many mechanisms cause homogeneous broadening, most notably collision broadening.It is one of the few distributions that is stable and has a probability density function that can be expressed analytically, the others being the normal distribution and the L\u00e9vy distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5b/Cauchy_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/6/61/Cauchy_distribution.png", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Cauchy_pdf.svg"], "links": ["ARGUS distribution", "Addison-Wesley", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Augustin-Louis Cauchy", "Augustin Cauchy", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biometrika", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy principal value", "Cauchy process", "Central Limit Theorem", "Central limit theorem", "Central moment", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular Cauchy distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Confidence belt", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Differentiable function", "Differential entropy", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Distribution fitting", "Elliptical distribution", "Encyclopedia of Mathematics", "Encyclopedia of Statistical Sciences", "Eric W. Weisstein", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fat tails", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fourier transform", "Fr\u00e9chet distribution", "Full width at half maximum", "Fundamental solution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hendrik Lorentz", "Holtsmark distribution", "Homogeneous broadening", "Homogeneous function", "Hotelling's T-squared distribution", "Hydrology", "Hyper-Erlang distribution", "Hyperbolic distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "H\u00f6lder's inequality", "Improper integral", "Independence (probability theory)", "Independent and identically distributed", "Independent and identically distributed random variables", "Indeterminate form", "Infinitely divisible probability distribution", "Infinitesimal", "Information entropy", "International Standard Book Number", "Interquartile range", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverse trigonometric functions", "Irwin\u2013Hall distribution", "Ir\u00e9n\u00e9e-Jules Bienaym\u00e9", "JSTOR", "John Wiley & Sons", "Johnson's 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"Maxwell\u2013J\u00fcttner distribution", "McCullagh's parametrization of the Cauchy distributions", "Mean", "Median", "Michiel Hazewinkel", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Moment (mathematics)", "Moment generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate Student distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "M\u00f6bius transformation", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Newton's method", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal Distribution", "Normal distribution", "Nuclear physics", "Numerical analysis", "Order statistics", "Parabolic fractal distribution", "Pareto distribution", "Particle physics", "Pathological (mathematics)", "Pearson distribution", "Peter McCullagh", "Phase-type distribution", "Physicist", "Pierre-Simon Laplace", "Plotting position", "Poisson binomial distribution", "Poisson distribution", "Poisson kernel", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probable error", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Random vector", "Ratio distribution", "Raw moment", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Resonance", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sim\u00e9on Denis Poisson", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Spectral line", "Spectroscopy", "Stability (probability)", "Stable distribution", "Stable process", "Standardized moment", "Stigler's law of eponymy", "Strong law of large numbers", "Student's t-distribution", "Student's t distribution", "Support (mathematics)", "The Annals of Statistics", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated mean", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "University of Alabama", "Upper half-plane", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Witch of Agnesi", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.econ.yorku.ca/cesg/papers/berapark.pdf", "http://www.springerlink.com/content/3p1430175v4806jq", "http://jeff560.tripod.com/c.html", "http://mathworld.wolfram.com/CauchyDistribution.html", "http://www.math.uah.edu/stat/special/Cauchy.html", "http://www.stat.uchicago.edu/~pmcc/pubs/paper18.pdf", "http://www.statistics4u.info/fundstat_eng/ee_distri_cauchy.html", "http://doi.org/10.1007%2Fs00180-009-0163-y", "http://doi.org/10.1016%2Fj.jspi.2006.05.002", "http://doi.org/10.1080%2F01621459.1964.10482170", "http://doi.org/10.1080%2F01621459.1966.10480912", "http://doi.org/10.1080%2F01621459.1966.10482205", "http://doi.org/10.1080%2F01621459.1974.10480163", "http://doi.org/10.1080%2F01621459.1978.10480031", "http://doi.org/10.1214%2Faoms%2F1177704357", "http://doi.org/10.2307%2F2041858", "http://www.jstatsoft.org/v16/i04/paper", "http://www.jstor.org/stable/2041858", "http://www.jstor.org/stable/2237984", "http://www.jstor.org/stable/2282794", "http://www.jstor.org/stable/2283210", "http://www.jstor.org/stable/2285535", "http://www.jstor.org/stable/2286549", "http://biomet.oxfordjournals.org/cgi/content/abstract/79/2/247", "http://projecteuclid.org/download/pdf_1/euclid.aoms/1177704357", "http://faculty.ksu.edu.sa/69424/USEPAP/Coushy%20dist.pdf", "http://www3.stat.sinica.edu.tw/statistica/oldpdf/A7n310.pdf", "http://www.maths.bath.ac.uk/~ak257/LCSB/part1.pdf", "https://www.waterlog.info/cumfreq.htm", "https://web.archive.org/web/20090914055538/http://www3.stat.sinica.edu.tw/statistica/oldpdf/A7n310.pdf", "https://web.archive.org/web/20110816002255/http://faculty.ksu.edu.sa/69424/USEPAP/Coushy%20dist.pdf", "https://web.archive.org/web/20110930062639/http://www.econ.yorku.ca/cesg/papers/berapark.pdf", "https://arxiv.org/pdf/1505.01957.pdf", "https://doi.org/10.1007/978-94-009-3049-0_4", "https://doi.org/10.1214/aoms/1177706450", "https://www.encyclopediaofmath.org/index.php?title=p/c020850", "https://www.gnu.org/software/gsl/manual/gsl-ref.html#SEC294"]}, "Variance reduction": {"categories": ["Monte Carlo methods", "Variance reduction"], "title": "Variance reduction", "method": "Variance reduction", "url": "https://en.wikipedia.org/wiki/Variance_reduction", "summary": "In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates that can be obtained for a given simulation or computational effort. Every output random variable from the simulation is associated with a variance which limits the precision of the simulation results. In order to make a simulation statistically efficient, i.e., to obtain a greater precision and smaller confidence intervals for the output random variable of interest, variance reduction techniques can be used. The main ones are common random numbers, antithetic variates, control variates, importance sampling and stratified sampling. For simulation with black-box models subset simulation and line sampling can also be used. Under these headings are a variety of specialized techniques; for example, particle transport simulations make extensive use of \"weight windows\" and \"splitting/Russian roulette\" techniques, which are a form of importance sampling.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/18/StratifiedPoints.gif"], "links": ["Antithetic variates", "Black-box", "Confidence interval", "Control variate", "Digital object identifier", "Explained variance", "Importance sampling", "International Standard Book Number", "Journal of the Operational Research Society", "Line sampling", "Mathematics", "Monte Carlo method", "Stratified sampling", "Subset simulation", "Variance"], "references": ["http://demonstrations.wolfram.com/TheMethodOfCommonRandomNumbersAnExample/", "http://doi.org/10.1002%2F9781118445112.stat07975", "http://doi.org/10.1287%2Fopre.1.5.263"]}, "Poisson distribution": {"categories": ["All articles with unsourced statements", "Articles with example pseudocode", "Articles with unsourced statements from April 2012", "Articles with unsourced statements from May 2012", "Articles with unsourced statements from May 2018", "Conjugate prior distributions", "Factorial and binomial topics", "Infinitely divisible probability distributions", "Pages using deprecated image syntax", "Poisson distribution", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers"], "title": "Poisson distribution", "method": "Poisson distribution", "url": "https://en.wikipedia.org/wiki/Poisson_distribution", "summary": "In probability theory and statistics, the Poisson distribution (French pronunciation: \u200b[pwas\u0254\u0303]; in English often rendered ), named after French mathematician Sim\u00e9on Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.\nFor instance, an individual keeping track of the amount of mail they receive each day may notice that they receive an average number of 4 letters per day. If receiving any particular piece of mail does not affect the arrival times of future pieces of mail, i.e., if pieces of mail from a wide range of sources arrive independently of one another, then a reasonable assumption is that the number of pieces of mail received in a day obeys a Poisson distribution. Other examples that may follow a Poisson include the number of phone calls received by a call center per hour and the number of decay events per second from a radioactive source.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fb/Binomial_versus_poisson.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7c/Poisson_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/1/16/Poisson_pmf.svg"], "links": ["ARGUS distribution", "Abraham de Moivre", "Addison Wesley", "Admissible decision rule", "Agner Krarup Erlang", "Anscombe transform", "Arcsine distribution", "Astronomy", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian inference", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli trial", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biology", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "C (programming language)", "Call centre", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Causal Set", "Cell membrane", "Cells (biology)", "Characteristic function (probability theory)", "Chemistry", "Chernoff bound", "Chi-square distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Coefficient of variation", "Combinatorics", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Conjugate prior", "Continuity correction", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation", "Coverage probability", "Cram\u00e9r\u2013Rao lower bound", "Cumulant", "Cumulative distribution function", "DNA", "Dagum distribution", "Data transformation (statistics)", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Dobinski's formula", "Donald Knuth", "E (mathematical constant)", "Earthquake seismology", "Electric current", "Elementary charge", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exact statistics", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Factorial", "Factorial moment", "Finance and insurance", "Fisher's z-distribution", "Fisher information", "Floor function", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fortran", "France", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Generating function", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Guinness", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hermite distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "I. 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"Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Luc Devroye", "L\u00e9vy distribution", "MATLAB", "Management", "Marchenko\u2013Pastur distribution", "Mathematica", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mean absolute deviation", "Median", "Minimax estimator", "Minimum-variance unbiased estimator", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Molar mass distribution", "Moment-generating function", "Moment (mathematics)", "Multinomial distribution", "Multiplicity of infection", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Mutation", "Nakagami 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distribution", "Probability mass function", "Probability theory", "Prussia", "Pseudo-random number sampling", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Queueing theory", "R (programming language)", "Rademacher distribution", "Radioactivity", "Raikov's theorem", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Receptor (biochemistry)", "Reciprocal distribution", "Rectified Gaussian distribution", "Rejection sampling", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Renewal theory", "Rice distribution", "Robbins lemma", "Scale parameter", "Scaled inverse chi-squared distribution", "SciPy", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Shot noise", "Silver", "Sim\u00e9on Denis Poisson", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Space", "Special case", "Stable distribution", "Standard deviation", "Standard normal deviate", "Statistical independence", "Statistics", "Stein's example", "Stigler's law", "Stirling numbers of the second kind", "Student's t-distribution", "Student center", "Sufficient statistic", "Support (mathematics)", "Telecommunication", "The Art of Computer Programming", "Time", "Touchard polynomials", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Unbiased estimator", "Uniform distribution (continuous)", "Upper incomplete gamma function", "V-1 flying bomb", "Variance", "Variance-gamma distribution", "Variance-stabilizing transformation", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Web server", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "William Sealy Gosset", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zero-inflated model", "Zero-truncated Poisson distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.sciencedirect.com/science/article/pii/0167715282900104", "http://www.sciencedirect.com/science/article/pii/S0167668714001279", "http://www.vosesoftware.com/ModelRiskHelp/index.htm#Probability_theory_and_statistics/Stochastic_processes/Some_Poisson_models.htm", "http://reference.wolfram.com/language/ref/MultivariatePoissonDistribution.html", "http://reference.wolfram.com/language/ref/PoissonDistribution.html", "http://www.umass.edu/wsp/resources/poisson/index.html", "http://www.iarc.fr/en/publications/pdfs-online/stat/sp82/index.php", "http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc331.htm", "http://www.sportsbettingonline.net/strategy/football-prediction-model-poisson-distribution/", "http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7266644", "http://cnx.org/content/m13500/latest/?collection=col10343/latest", "http://luc.devroye.org/chapter_ten.pdf", "http://luc.devroye.org/rnbookindex.html", "http://doi.org/10.1007%2FBF02293108", "http://doi.org/10.1016%2F0167-7152(82)90010-4", "http://doi.org/10.1016%2Fj.insmatheco.2014.09.012", "http://doi.org/10.1021%2Fja01863a066", "http://doi.org/10.1080%2F00031305.1984.10483195", "http://doi.org/10.1080%2F01621459.1975.10482497", "http://doi.org/10.1080%2F03610926.2014.901375", "http://doi.org/10.1093%2Fbiomet%2F28.3-4.437", "http://doi.org/10.1112%2Fs0025579300016442", "http://doi.org/10.1137%2F1030059", "http://doi.org/10.1145%2F355993.355997", "http://doi.org/10.1214%2Faoms%2F1177732430", "http://doi.org/10.2307%2F1403045", "http://doi.org/10.2307%2F2340091", "http://doi.org/10.2307%2F2530708", "http://doi.org/10.3844%2Famjbsp.2013.17.29", "http://www.jstor.org/stable/10.2307/2340091", "http://www.jstor.org/stable/1403045", "http://www.jstor.org/stable/2530708", "http://www.proofwiki.org/wiki/Expectation_of_Poisson_Distribution", "http://www.proofwiki.org/wiki/Variance_of_Poisson_Distribution", "http://www.rasch.org/memo1963.pdf", "https://books.google.com/?id=SKUXe_PjtRMC&pg=PA5&dq=%22law+of+rare+events%22+poisson#v=onepage&q=%22law%20of%20rare%20events%22%20poisson&f=false", "https://books.google.com/books?id=o_k3AAAAMAAJ&pg=PA1#v=onepage&q&f=false", "https://books.google.com/books?id=o_k3AAAAMAAJ&pg=PA23#v=onepage&q&f=false", "https://books.google.com/books?id=uovoFE3gt2EC&pg=PA206#v=onepage&q&f=false", "https://www.wired.com/2012/12/what-does-randomness-look-like/", "https://id.loc.gov/authorities/subjects/sh85103956", "https://d-nb.info/gnd/4253010-6", "https://id.ndl.go.jp/auth/ndlna/00569122", "https://arxiv.org/pdf/1502.01975v1.pdf,", "https://www.cambridge.org/core/journals/journal-of-the-institute-of-actuaries/article/an-application-of-the-poisson-distribution/F75111847FDA534103BD4941BD96A78E", "https://cran.r-project.org/web/packages/KFAS/vignettes/KFAS.pdf", "https://www.wikidata.org/wiki/Q205692"]}, "STATISTICA": {"categories": ["CS1 errors: dates", "Science software for Windows", "Statistical software", "Webarchive template archiveis links", "Windows-only software"], "title": "Statistica", "method": "STATISTICA", "url": "https://en.wikipedia.org/wiki/Statistica", "summary": "Statistica is an advanced analytics software package originally developed by StatSoft which was acquired by Dell in March 2014. In November 2016, Dell sold off several pieces of its software group, and Francisco Partners and Elliott Management Corporation acquired Statistica as part of its purchase of Quest Software from Dell. On May 15, 2017, TIBCO Software Inc. announced it entered into an agreement to acquire Statistica.Statistica provides data analysis, data management, statistics, data mining, machine learning, text analytics and data visualization procedures.", "images": [], "links": ["ADMB", "Analyse-it", "Application suite", "Archive.is", "BMDP", "BV4.1 (software)", "COM (hardware interface)", "CSPro", "C Sharp (programming language)", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Data mining", "Data visualization", "Dataplot", "Dell", "Dell Software", "Digital object identifier", "Distributed computing", "EViews", "Elliott Management Corporation", "Epi Info", "Francisco Partners", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "International Standard Book Number", "Internationalization and localization", "JASP", "JMP (statistical software)", "JMulTi", "Java (programming language)", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Machine learning", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Office", "Microsoft Windows", "Minitab", "Multithreading (computer architecture)", "NCSS (statistical software)", "Numerical analysis", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "Outliers", "OxMetrics", "PSPP", "Proprietary software", "Public-domain software", "Quest Software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "Ribbon (computing)", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "Sharepoint", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatSoft", "StatView", "StatXact", "Stata", "Statistica (journal)", "Statistics", "StatsDirect", "TSP (econometrics software)", "The American Statistician", "The Unscrambler", "UNISTAT", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://software.dell.com/products/statistica/", "http://documents.software.dell.com/statistica/12.7/release-notes/", "http://documents.software.dell.com/statistics/current/", "http://www.dell.com/learn/us/en/vn/secure/2014-03-17-dell-acquires-statsoft-data-analytics-software", "http://www.hpcwire.com/topic/developertools/StatSoft-Certifies-REvolution-Computing-R-Language-35773444.html", "http://www.statsoft.com/", "http://www.statsoft.com/company/history/", "http://www.statsoft.com/products/", "http://www.statsoft.com/products/statistica-10-new-features/", "http://www.statsoft.com/products/statistica-12-new-features/", "http://www.statsoft.com/textbook/", "http://doi.org/10.1080%2F00031305.1997.10473593", "http://www.r-project.org/conferences/useR-2008/abstracts/Weiss.pdf", "https://support.software.dell.com/statistica/12.5%20SP1/release-notes-guides", "https://support.software.dell.com/statistica/12.6/release-notes-guides", "https://support.software.dell.com/statistica/release-notes-guides", "https://www.franciscopartners.com/news/francisco-partners-and-elliott-management-complete-acquisition-of-dell-software-group", "https://www.tibco.com/press-releases/2017/tibco-software-acquire-data-science-platform-leader-statistica", "https://www.tibco.com/products/tibco-statistica", "https://archive.is/20130126040323/http://www.hpcwire.com/topic/developertools/StatSoft-Certifies-REvolution-Computing-R-Language-35773444.html"]}, "Statistical hypothesis testing": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2012", "Articles with unsourced statements from December 2015", "CS1 maint: Multiple names: authors list", "CS1 maint: Unfit url", "Commons category link is on Wikidata", "Design of experiments", "Logic and statistics", "Mathematical and quantitative methods (economics)", "Psychometrics", "Statistical hypothesis testing", "Use mdy dates from November 2016", "Webarchive template archiveis links", "Webarchive template wayback links"], "title": "Statistical hypothesis testing", "method": "Statistical hypothesis testing", "url": "https://en.wikipedia.org/wiki/Statistical_hypothesis_testing", "summary": "A statistical hypothesis, sometimes called confirmatory data analysis, is an hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables. A statistical hypothesis test is a method of statistical inference. Commonly, two statistical data sets are compared, or a data set obtained by sampling is compared against a synthetic data set from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis that proposes no relationship between two data sets. The comparison is deemed statistically significant if the relationship between the data sets would be an unlikely realization of the null hypothesis according to a threshold probability\u2014the significance level. Hypothesis tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance. The process of distinguishing between the null hypothesis and the alternative hypothesis is aided by identifying two conceptual types of errors, type 1 and type 2, and by specifying parametric limits on e.g. how much type 1 error will be permitted.\nAn alternative framework for statistical hypothesis testing is to specify a set of statistical models, one for each candidate hypothesis, and then use model selection techniques to choose the most appropriate model. The most common selection techniques are based on either Akaike information criterion or Bayes factor.\nConfirmatory data analysis can be contrasted with exploratory data analysis, which may not have pre-specified hypotheses.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Almost sure hypothesis testing", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Archive.is", "Argument from ignorance", "Arithmetic mean", "Asymptomatic carrier", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Auxology", "Bachelor of Science in Public Health", "Bar chart", "Bayes' Theorem", "Bayes estimator", "Bayes factor", "Bayes factors", "Bayesian decision theory", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bayesian statistics", "Behavior change (public health)", "Behavioural change theories", "Behrens\u2013Fisher problem", "Bias of an estimator", "Bible Analyzer", "Bigfoot", "Binomial regression", "Bioinformatics", "Biological hazard", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Carl Rogers Darnall", "Cartography", "Case\u2013control study", "Categorical data", "Categorical variable", "Census", "Centers for Disease Control and Prevention", "Central limit theorem", "Central tendency", "Checking if a coin is fair", "Chemometrics", "Chi-squared test", "Chi squared test", "Chief Medical Officer", "Child mortality", "Clairvoyance", "Clever Hans effect", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Community health", "Comparing means", "Complete spatial randomness", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlation does not imply causation", "Correlogram", "Council on Education for Public Health", "Count data", "Counternull", "Credible interval", "Crime statistics", "Critical region", "Critical section", "Critical value", "Cross-correlation", "Cross-validation (statistics)", "Cultural competence in health care", "Data collection", "Data mining", "David Hume", "Decision theory", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Detection theory", "Deviance (sociology)", "Dichotomous thinking", "Dickey\u2013Fuller test", "Diffusion of innovations", "Digital object identifier", "Disease surveillance", "Divergence (statistics)", "Doctor of Public Health", "Durbin\u2013Watson statistic", "Econometrics", "Edward Arnold (publisher)", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Emergency sanitation", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental health", "Environmental statistics", "Epidemic", "Epidemiology", "Epistemological", "Error of the first kind", "Error of the second kind", "Errors and residuals in statistics", "Estimating equations", "Estimation statistics", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Exact test", "Experiment", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fallacy", "False discovery rate", "False negative", "False positive", "Falsifiability", "Family planning", "Family wise error rate", "Fan chart (statistics)", "Fecal\u2013oral route", "Fiducial inference", "First-hitting-time model", "Fisher's method", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Forecasting", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Game theory", "Geiger counter", "General linear model", "Generalized linear model", "Genetically modified food", "Geographic information system", "Geometric mean", "Geostatistics", "Germ theory of disease", "Global health", "Globalization and disease", "Good agricultural practice", "Good manufacturing practice", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "HACCP", "Hand washing", "Harmonic mean", "Have one's cake and eat it too", "Hawthorne effect", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "How to Lie with Statistics", "Human factors and ergonomics", "Human nutrition", "Human sex ratio", "Hygiene", "Hypothesis", "ISO 22000", "Index of dispersion", "Infant mortality", "Infection control", "Inferential statistics", "Injury prevention", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "J. Scott Armstrong", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "John Arbuthnot", "John Snow (physician)", "John Tukey", "Jonckheere's trend test", "Joseph Lister", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lady tasting tea", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of epidemics", "List of fields of application of statistics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Look-elsewhere effect", "Loss function", "Lp space", "M-estimator", "M. J. Bayarri", "Mann\u2013Whitney U test", "Margaret Sanger", "Mary Mallon", "Maternal health", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical anthropology", "Medical sociology", "Medical statistics", "Mental health", "Meta-analysis", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Ministry of Health and Family Welfare", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Modifiable areal unit problem", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiple testing", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Muriel Bristol", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Neyman\u2013Pearson lemma", 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tests", "Pharmaceutical policy", "Pharmacovigilance", "Philosophic burden of proof", "Philosophical Transactions of the Royal Society A", "Philosophical Transactions of the Royal Society of London", "Philosophy of science", "Pie chart", "Pierre-Simon Laplace", "Pierre Laplace", "Pivotal quantity", "Placebo effect", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population health", "Population statistics", "Positive deviance", "Posterior probability", "Power (statistics)", "Prediction interval", "Preventive healthcare", "Preventive nutrition", "Principal component analysis", "Principle of indifference", "Prior probability", "Priors", "Probabilistic design", "Probability", "Probability distribution", "Professional degrees of public health", "Proof by contradiction", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Publication bias", "Quality control", "Quarantine", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "ROC curve", "Race and health", "Radar chart", "Radioactive decay", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative risk", "Reliability engineering", "Replication (statistics)", "Reproductive health", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Safe sex", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sensitivity and specificity", "Sexually transmitted infection", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Size (statistics)", "Skewness", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Social statistics", "Sociology of health and illness", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical assumption", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistically significant", "Statistics", "Statistics education", "Stem-and-leaf display", "Stratified sampling", "Strawman", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Student's t distribution", "Subjectivity", "Sufficient statistic", "Suit (cards)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Theory of planned behavior", "Time domain", "Time series", "Tolerance interval", "Transtheoretical model", "Trend estimation", "Trial (law)", "Tropical disease", "Type I and type II errors", "U-statistic", "Uniformly most powerful test", "United States Public Health Service", "V-statistic", "Vaccination", "Vaccine trial", "Variance", "Vector autoregression", "Vector control", "Wald test", "Walter Frank Raphael Weldon", "Waterborne diseases", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "William Sealy Gosset", "World Health Organization", "World Toilet Organization", "Z-test"], "references": ["http://www.schramm.cc/link/Statistics-calculator.php", "http://www.epidemiology.ch/history/PDF%20bg/Cornfield%20J%201976%20recent%20methodological%20contributions.pdf", "http://www.collegeboard.com/student/testing/ap/sub_stats.html", "http://www.jasnh.com/", "http://library.mpib-berlin.mpg.de/ft/gg/GG_Null_2004.pdf", "http://ba.stat.cmu.edu/journal/2008/vol03/issue01/aldrich.pdf", "http://escholarshare.drake.edu/bitstream/handle/2092/413/WhyWeDon't.pdf", "http://ftp.isds.duke.edu/WorkingPapers/03-26.pdf", "http://core.ecu.edu/psyc/wuenschk/StatHelp/NHST-SHIT.htm", "http://mres.gmu.edu/pmwiki/uploads/Main/Meehl1967.pdf", "http://www.indiana.edu/~kruschke/articles/Kruschke2012JEPG.pdf", "http://www.nap.edu/openbook.php?record_id=13163&page=211", "http://rhowell.ba.ttu.edu/meehl1.pdf", "http://www.tufts.edu/~gdallal/LHSP.HTM", "http://www.cs.ucsd.edu/users/goguen/courses/275f00/stat.html", "http://repository.upenn.edu/cgi/viewcontent.cgi?article=1104&context=marketing_papers", "http://www-stat.wharton.upenn.edu/~steele/Publications/PDF/TN148.pdf", "http://www.webapps.cee.vt.edu/ewr/environmental/teach/smprimer/hypotest/ht.html", "http://www.phil.vt.edu/dmayo/PhilStatistics/Triad/Fisher%201955.pdf", "http://www.stat.washington.edu/research/reports/1993/tr254.pdf", "http://cerebro.xu.edu/math/Sources/Laplace/memoir_probabilities.pdf", "http://gallica.bnf.fr/ark:/12148/bpt6k77597p/f386", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC389491", "http://www.ncbi.nlm.nih.gov/pubmed/10383371", "http://www.ncbi.nlm.nih.gov/pubmed/10937333", "http://www.ncbi.nlm.nih.gov/pubmed/17286092", "http://www.mbastats.net", "http://www.stat.auckland.ac.nz/~iase/publications/isr/97.Moore.pdf", "http://annals.org/article.aspx?articleid=712762", "http://www.corestandards.org/the-standards/mathematics/hs-statistics-and-probability/introduction/", "http://doi.org/10.1016%2Fj.edurev.2007.04.001", "http://doi.org/10.1016%2Fj.ijforecast.2007.03.004", "http://doi.org/10.1016%2Fj.socec.2004.09.033", "http://doi.org/10.1037%2F0003-066X.49.12.997", "http://doi.org/10.1037%2F0003-066X.54.8.594", "http://doi.org/10.1037%2F029395", "http://doi.org/10.1037%2F1082-989X.5.2.241", "http://doi.org/10.1037%2Fa0029146", "http://doi.org/10.1037%2Fh0020412", "http://doi.org/10.1037%2Fh0042040", "http://doi.org/10.1073%2Fpnas.68.11.2643", "http://doi.org/10.1080%2F00401706.1960.10489909", "http://doi.org/10.1080%2F01621459.1951.10500764", "http://doi.org/10.1080%2F01621459.1993.10476404", "http://doi.org/10.1080%2F14786440009463897", "http://doi.org/10.1086%2F288135", "http://doi.org/10.1093%2Fbjps%2Faxi152", "http://doi.org/10.1093%2Fbjps%2Faxl003", "http://doi.org/10.1098%2Frsta.1933.0009", "http://doi.org/10.1098%2Frstl.1710.0011", "http://doi.org/10.1126%2Fscience.156.3781.1456", "http://doi.org/10.1177%2F001316446002000401", "http://doi.org/10.1177%2F0273475306288399", "http://doi.org/10.1177%2F0959354314525282", "http://doi.org/10.1177%2F0959354397074006", "http://doi.org/10.1207%2Fs15327965pli0102_1", "http://doi.org/10.1214%2F06-ba115", "http://doi.org/10.1214%2F08-BA306", "http://doi.org/10.1214%2Fss%2F1029963261", "http://doi.org/10.1214%2Fss%2F1032280216", "http://doi.org/10.1214%2Fss%2F1056397485", "http://doi.org/10.1214%2Fss%2F1177012488", "http://doi.org/10.2307%2F1403333", "http://doi.org/10.2307%2F20445367", "http://doi.org/10.4135%2F9781412986311", "http://doi.org/10.7326%2F0003-4819-130-12-199906150-00008", "http://www.icmje.org/publishing_1negative.html", "http://www.jstor.org/stable/20445367", "http://www.jstor.org/stable/2245634", "http://www.jstor.org/stable/2246117", "http://www.randomservices.org/random/hypothesis/Introduction.html", "http://en.wikisource.org/w/index.php?oldid=3592335", "http://www.economics.soton.ac.uk/staff/aldrich/1900.pdf", "http://www.york.ac.uk/depts/maths/histstat/arbuthnot.pdf", "http://www.york.ac.uk/depts/maths/histstat/fisher272.pdf", "http://stats.org.uk/statistical-inference/Rozeboom1960.pdf", "https://lirias.kuleuven.be/bitstream/123456789/136347/1/CastroSotos.pdf", "https://books.google.com/?id=oKZwtLQTmNAC&pg=PA1512&dq=%22mathematics+of+a+lady+tasting+tea%22", "https://books.google.com/books?id=M7yvkERHIIMC&lpg=PA225&ots=Glm4Zj_E6p&pg=PA225#v=onepage", "https://www.ics.uci.edu/~sternh/courses/210/loftus91_tyranny.pdf", "https://archive.is/20120728122912/http://www.corestandards.org/the-standards/mathematics/hs-statistics-and-probability/introduction/", "https://archive.org/details/cu31924003064833", "https://web.archive.org/web/20051124221846/http://www.npwrc.usgs.gov/resource/methods/statsig/stathyp.htm", "https://web.archive.org/web/20060518054857/http://hops.wharton.upenn.edu/ideas/pdf/Armstrong/StatisticalSignificance.pdf", "https://web.archive.org/web/20091029162244/http://www.wiwi.uni-muenster.de/ioeb/en/organisation/pfaff/stat_overview_table.html", "https://web.archive.org/web/20120716211637/http://www.icmje.org/publishing_1negative.html", "https://web.archive.org/web/20130904000350/http://ftp.isds.duke.edu/WorkingPapers/03-26.pdf", "https://web.archive.org/web/20131203010657/http://mres.gmu.edu/pmwiki/uploads/Main/Meehl1967.pdf", "https://web.archive.org/web/20140906190025/http://ba.stat.cmu.edu/journal/2008/vol03/issue01/aldrich.pdf", "https://www.encyclopediaofmath.org/index.php?title=p/s087400"]}, "White noise": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from January 2017", "Commons category link is on Wikidata", "Data compression", "Noise", "Noise (electronics)", "Statistical signal processing"], "title": "White noise", "method": "White noise", "url": "https://en.wikipedia.org/wiki/White_noise", "summary": "In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustic engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band.\n\nIn discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. Depending on the context, one may also require that the samples be independent and have identical probability distribution (in other words independent and identically distributed random variables are the simplest representation of white noise). In particular, if each sample has a normal distribution with zero mean, the signal is said to be Gaussian white noise.The samples of a white noise signal may be sequential in time, or arranged along one or more spatial dimensions. In digital image processing, the pixels of a white noise image are typically arranged in a rectangular grid, and are assumed to be independent random variables with uniform probability distribution over some interval. The concept can be defined also for signals spread over more complicated domains, such as a sphere or a torus.\n\nAn infinite-bandwidth white noise signal is a purely theoretical construction. The bandwidth of white noise is limited in practice by the mechanism of noise generation, by the transmission medium and by finite observation capabilities. Thus, random signals are considered \"white noise\" if they are observed to have a flat spectrum over the range of frequencies that are relevant to the context. For an audio signal, the relevant range is the band of audible sound frequencies (between 20 and 20,000 Hz). Such a signal is heard by the human ear as a hissing sound, resembling the /sh/ sound in \"ash\". In music and acoustics, the term \"white noise\" may be used for any signal that has a similar hissing sound.\nThe term white noise is sometimes used in the context of phylogenetically based statistical methods to refer to a lack of phylogenetic pattern in comparative data. It is sometimes used analogously in nontechnical contexts to mean \"random talk without meaningful contents\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/76/Noise.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f6/White-noise-mv255-240x180.png", "https://upload.wikimedia.org/wikipedia/commons/9/98/White-noise-sound-20sec-mono-44100Hz.ogg", "https://upload.wikimedia.org/wikipedia/commons/c/c1/White_noise.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["AWGN", "Abstract Wiener space", "Acoustic engineering", "Acoustic quieting", "Acoustics", "Active noise control", "Actuarial mathematics", "Additive white Gaussian noise", "American Broadcasting Company", "Amplifier", "Anisotropic diffusion", "Architectural acoustics", "Atmospheric noise", "Attention deficit hyperactivity disorder", "Audio signal", "Audio synthesis", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Background noise", "Bernoulli process", "Bessel process", "Bias of an estimator", "Biased random walk on a graph", "Bilateral filter", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Block-matching and 3D filtering", "Bochner\u2013Minlos theorem", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Brownian noise", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "Burst noise", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Carrier-to-noise ratio", "Carrier-to-receiver noise density", "Cauchy distribution", "Cauchy process", "Central limit theorem", "Channel estimation", "Channel noise level", "Chen model", "Chinese restaurant process", "Circuit noise level", "Claire Shipman", "Classical Wiener space", "Coloring transformation", "Colors of noise", "Compound Poisson process", "Confidence interval", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Continuous uniform distribution", "Contrast-to-noise ratio", "Convergence of random variables", "Correlation", "Correlation and dependence", "Cosmic noise", "Covariance", "Covariance matrix", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Cymbal", "C\u00e0dl\u00e0g", "DBrnC", "DC component", "Data compression", "Dependent and independent variables", "Dependent variable", "Deterministic", "Diagonal matrix", "Diffusion process", "Digital-to-analog converter", "Digital image processing", "Digital object identifier", "Digital signal processor", "Dirac delta function", "Dirichlet process", "Discrete-time stochastic process", "Discrete Fourier transform", "Discrete Hartley transform", "Discrete signal", "Discrete time", "Distortion", "Dol\u00e9ans-Dade exponential", "Don DeLillo", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Eb/N0", "Econometrics", "Effective input noise temperature", "Electronic music", "Electronic noise", "Elliptical distribution", "Empirical process", "Equalization (audio)", "Equivalent noise resistance", "Equivalent pulse code modulation noise", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Fast Fourier transform", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Flicker noise", "Fluid queue", "Fractional Brownian motion", "Frequencies", "Function space", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian", "Gaussian blur", "Gaussian noise", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Good Morning America", "Gradient noise", "Grey noise", "Hardware random number generator", "Health effects from noise", "Heath\u2013Jarrow\u2013Morton framework", "Hertz", "Heston model", "Heteroskedasticity", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Hypothesis testing", "I.i.d.", "Image noise", "Image processing", "Impulse noise (audio)", "Impulse response", "Independent and identically distributed random variables", "Independent component analysis", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "Interference (communication)", "International Standard Book Number", "International Standard Serial Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jitter", "Johnson\u2013Nyquist noise", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Linear model", "List of inequalities", "List of noise topics", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "Low-pass filter", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mean (statistics)", "Median filter", "Microcontroller", "Microprocessor", "Mixing (mathematics)", "Mixing console", "Modulation error ratio", "Moran process", "Moving-average model", "Moving average model", "Multivariate normal distribution", "Music", "Noise", "Noise, vibration, and harshness", "Noise (audio)", "Noise (electronics)", "Noise (physics)", "Noise (radio)", "Noise (video)", "Noise and vibration on maritime vessels", "Noise barrier", "Noise control", "Noise figure", "Noise floor", "Noise generator", "Noise measurement", "Noise pollution", "Noise power", "Noise reduction", "Noise regulation", "Noise shaping", "Noise spectral density", "Noise temperature", "Non-homogeneous Poisson process", "Non-local means", "Normal distribution", "Normally distributed and uncorrelated does not imply independent", "Nuclear space", "Optional stopping theorem", "Ordinary least squares", "Ornstein\u2013Uhlenbeck process", "Orthogonal transformation", "PA system", "Percolation theory", "Phase distortion", "Phase noise", "Phylogenetic comparative methods", "Physics", "Piecewise deterministic Markov process", "Pink noise", "Pitman\u2013Yor process", "Pixel", "Point process", "Poisson distribution", "Poisson point process", "Poisson process", "Potts model", "Power spectral density", "Power spectrum", "Predictable process", "Principal components analysis", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Pseudorandom noise", "PubMed Identifier", "Quadratic variation", "Quantization error", "Queueing model", "Queueing theory", "Radio noise source", "Random.org", "Random dynamical system", "Random element", "Random field", "Random graph", "Random variable", "Random vector", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Regression analysis", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Rhetoric", "Risk process", "Ruin theory", "SABR volatility model", "SINAD", "Sample-continuous process", "Sample (signal)", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sequential", "Serial correlation", "Shot noise", "Shrinkage Fields (image restoration)", "Sigma-martingale", "Signal-to-interference ratio", "Signal-to-noise ratio", "Signal-to-noise ratio (imaging)", "Signal-to-quantization-noise ratio", "Signal (information theory)", "Signal processing", "Signal to noise plus interference", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snare drum", "Snell envelope", "Social Security (United States)", "Sound masking", "Sound reproduction", "Soundproofing", "Sparre\u2013Anderson model", "Spectrogram", "Spectrum analyzer", "Sphere", "Stable process", "Stationary process", "Statistical forecasting", "Statistical independence", "Statistical noise", "Statistically independent", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telecommunication", "Telecommunications", "Telegraph process", "Thermal radiation", "Time reversibility", "Time series", "Time series analysis", "Tinnitus", "Tinnitus masker", "Torus", "Total variation denoising", "Uniform integrability", "Usual hypotheses", "Value noise", "Variance", "Variance gamma process", "Vasicek model", "Wavelet", "White", "White Noise (novel)", "White noise (disambiguation)", "White noise machine", "Whitening transformation", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "Worley noise"], "references": ["http://economics.about.com/od/economicsglossary/g/whitenoise.htm", "http://www.dspguru.com/dsp/howtos/how-to-generate-white-gaussian-noise", "http://eab.sagepub.com/content/24/3/381.abstract", "http://www.biology.ucr.edu/people/faculty/Garland/Fusco_et_al_2011_trilobites.pdf", "http://faculty.washington.edu/ezivot/econ584/notes/timeSeriesConcepts.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/12422383", "http://www.ncbi.nlm.nih.gov/pubmed/12596495", "http://www.ncbi.nlm.nih.gov/pubmed/22276531", "http://andywilliamson.org/_/wp-content/uploads/2010/04/White-Noise.pdf", "http://cogprints.org/5032/1/2002_H.M.J_White-noise_for_PTSD.pdf", "http://doi.org/10.1080%2F00221309.1993.9711152", "http://doi.org/10.1111%2Fj.1469-7610.2007.01749.x", "http://doi.org/10.1111%2Fj.1558-5646.2011.01447.x", "http://doi.org/10.1177%2F0013916592243006", "http://doi.org/10.1186%2F1744-9081-6-55", "http://www.worldcat.org/issn/0016-867X", "http://www.worldcat.org/issn/0021-9630", "http://www.worldcat.org/issn/0022-1309", "https://link.springer.com/10.1007/978-1-4612-1494-6"]}, "Continuity correction": {"categories": ["Computational statistics", "Statistical tests", "Theory of probability distributions"], "title": "Continuity correction", "method": "Continuity correction", "url": "https://en.wikipedia.org/wiki/Continuity_correction", "summary": "In probability theory, a continuity correction is an adjustment that is made when a discrete distribution is approximated by a continuous distribution.", "images": [], "links": ["Bernoulli trial", "Binomial distribution", "Binomial proportion confidence interval", "Binomial test", "Checking whether a coin is fair", "Expected value", "Normal distribution", "Poisson distribution", "Probability distribution", "Probability theory", "Random variable", "Statistical hypothesis test", "Statistical software", "Variance", "Yates's correction for continuity"], "references": []}, "Class membership probabilities": {"categories": ["Probabilistic models", "Statistical classification"], "title": "Probabilistic classification", "method": "Class membership probabilities", "url": "https://en.wikipedia.org/wiki/Probabilistic_classification", "summary": "In machine learning, a probabilistic classifier is a classifier that is able to predict, given an observation of an input, a probability distribution over a set of classes, rather than only outputting the most likely class that the observation should belong to. Probabilistic classifiers provide classification that can be useful in its own right or when combining classifiers into ensembles.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/7b/Calibration_plot.png", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayes' theorem", "Bayes estimator", "Bayesian network", "Bias-variance dilemma", "Bias of an estimator", "Bias\u2013variance tradeoff", "Binary classification", "Binomial regression", "Boosting (machine learning)", "Bootstrap aggregating", "Brier score", "C4.5", "CURE data clustering algorithm", "Calibration (statistics)", "Canonical correlation analysis", "CiteSeerX", "Cluster analysis", "Computational learning theory", "Computer vision", "Conditional probability", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Digital object identifier", "Dimensionality reduction", "Discrete choice", "Document classification", "Econometrics", "Empirical risk minimization", "Ensemble classifier", "Ensemble learning", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature engineering", "Feature learning", "Function (mathematics)", "Gated recurrent unit", "Generative model", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "Independent component analysis", "International Conference on Machine Learning", "International Standard Book Number", "Isotonic regression", "John Platt (computer scientist)", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Log loss", "Logistic regression", "Long short-term memory", "Loss function", "Machine Learning (journal)", "Machine learning", "Mean-shift", "Multiclass classification", "Multilayer perceptron", "Naive Bayes classifier", "Non-negative matrix factorization", "OPTICS algorithm", "Occam learning", "Online machine learning", "Outline of machine learning", "Perceptron", "Platt scaling", "Predictive analytics", "Principal component analysis", "Prior probability", "Probability distribution", "Probably approximately correct learning", "Q-learning", "Random forest", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Scoring rule", "Self-organizing map", "Semi-supervised learning", "Set (mathematics)", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Statistics", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "The Annals of Statistics", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory", "Zentralblatt MATH"], "references": ["http://www.cs.cornell.edu/courses/cs678/2007sp/ZadroznyElkan.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.13.7457", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.6032", "http://statweb.stanford.edu/~tibs/ElemStatLearn/", "http://cseweb.ucsd.edu/~elkan/calibrated.pdf", "http://machinelearning.wustl.edu/mlpapers/paper_files/icml2005_Niculescu-MizilC05.pdf", "http://doi.org/10.1145%2F1102351.1102430", "http://doi.org/10.1145%2F775047.775151", "http://doi.org/10.1214%2Faos%2F1028144844", "http://zbmath.org/?format=complete&q=an:0932.62071", "https://www.researchgate.net/publication/2594015_Probabilistic_Outputs_for_Support_Vector_Machines_and_Comparisons_to_Regularized_Likelihood_Methods/file/504635154cff5262d6.pdf", "https://web.archive.org/web/20140311005243/http://machinelearning.wustl.edu/mlpapers/paper_files/icml2005_Niculescu-MizilC05.pdf", "https://web.archive.org/web/20150126123924/http://statweb.stanford.edu/~tibs/ElemStatLearn/", "https://arxiv.org/list/cs.LG/recent"]}, "Divergence (statistics)": {"categories": ["All articles to be expanded", "All articles with empty sections", "Articles to be expanded from January 2011", "Articles using small message boxes", "Articles with empty sections from January 2011", "F-divergences", "Statistical distance"], "title": "Divergence (statistics)", "method": "Divergence (statistics)", "url": "https://en.wikipedia.org/wiki/Divergence_(statistics)", "summary": "In statistics and information geometry, divergence or a contrast function is a function which establishes the \"distance\" of one probability distribution to the other on a statistical manifold. The divergence is a weaker notion than that of the distance, in particular the divergence need not be symmetric (that is, in general the divergence from p to q is not equal to the divergence from q to p), and need not satisfy the triangle inequality.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Affine connection", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Dual affine connection", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-divergence", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher information metric", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hellinger distance", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Information geometry", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kullback\u2013Leibler divergence", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Manifold", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Positive semi-definite", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Riemannian metric", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shun'ichi Amari", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Torsion of connection", "Trend estimation", "Triangle inequality", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "\u0391-connection", "\u0391-divergence"], "references": ["http://projecteuclid.org/euclid.hmj/1206128255", "http://projecteuclid.org/euclid.hmj/1206128508", "http://projecteuclid.org/euclid.hmj/1206130775"]}, "Predictive intake modelling": {"categories": ["Mathematical modeling"], "title": "Predictive intake modelling", "method": "Predictive intake modelling", "url": "https://en.wikipedia.org/wiki/Predictive_intake_modelling", "summary": "Predictive intake modelling uses mathematical modelling strategies to estimate intake of food, personal care products, and their formulations.", "images": [], "links": ["Absorption (skin)", "Digital object identifier", "European Food Safety Authority", "Exposure Assessment", "Exposure assessment", "Exposure science", "Extrapolation", "Formulations", "Inhalation", "Mathematical model", "Monte Carlo methods", "NHANES", "Personal care", "Phenomenological model", "Predictive modelling", "Public health", "Regression analysis", "Risk assessment", "Sampling (statistics)", "The Food and Drug Administration (FDA or USFDA)"], "references": ["http://ccl.rutgers.edu/ccl-files/presentations/2007-01-26_ORC-Workshop-at-DEP/ShadePamela_ORC-NJDEP_poster_2007.01.26.pdf", "http://www.fda.gov/Food/GuidanceRegulation/GuidanceDocumentsRegulatoryInformation/IngredientsAdditivesGRASPackaging/ucm074725.htm#mode", "http://www.ars.usda.gov/Services/docs.htm?docid=7764", "http://doi.org/10.1080%2F09064702.2011.642000", "http://doi.org/10.1080%2F19440049.2014.955886", "http://doi.org/10.1111%2Fj.1365-2133.2008.08866.x", "http://doi.org/10.2527%2Fjas.2008-1378", "http://www.rifm.org/press-detail.php?id=68"]}, "Point pattern analysis": {"categories": ["Spatial data analysis"], "title": "Point pattern analysis", "method": "Point pattern analysis", "url": "https://en.wikipedia.org/wiki/Point_pattern_analysis", "summary": "Point pattern analysis (PPA) is the study of the spatial arrangements of points in (usually 2-dimensional) space. The simplest formulation is a set X = {x \u2208 D} where D, which can be called the 'study region,' is a subset of Rn, a n-dimensional Euclidean space.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/14/Point_pattern.png"], "links": ["Case control study", "Circle", "Complete spatial randomness", "Contagious disease", "Diffusion", "Ellipse", "Euclidean space", "Goodness of fit", "Infectious disease", "International Standard Book Number", "N-dimensional space", "Poisson process", "Random walk", "Retina", "Retinal mosaic"], "references": []}, "Demography": {"categories": ["Actuarial science", "Articles with Curlie links", "Articles with short description", "Commons category link is on Wikidata", "Demographics", "Demography", "Environmental social science", "Human geography", "Interdisciplinary subfields of sociology", "Market segmentation", "Population", "Use British English Oxford spelling from August 2016", "Use British English Oxford spelling from September 2016", "Use dmy dates from August 2016", "Webarchive template wayback links", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers"], "title": "Demography", "method": "Demography", "url": "https://en.wikipedia.org/wiki/Demography", "summary": "Demography (from prefix demo- from Ancient Greek \u03b4\u1fc6\u03bc\u03bf\u03c2 d\u0113mos meaning \"the people\", and -graphy from \u03b3\u03c1\u03ac\u03c6\u03c9 graph\u014d, implies \"writing, description or measurement\") is the statistical study of populations, especially human beings. As a very general science, it can analyze any kind of dynamic living population, i.e., one that changes over time or space (see population dynamics). Demography encompasses the study of the size, structure, and distribution of these populations, and spatial or temporal changes in them in response to birth, migration, aging, and death. Based on the demographic research of the earth, earth's population up to the year 2050 and 2100 can be estimated by demographers. Demographics are quantifiable characteristics of a given population.\nDemographic analysis can cover whole societies or groups defined by criteria such as education, nationality, religion, and ethnicity. Educational institutions usually treat demography as a field of sociology, though there are a number of independent demography departments.Formal demography limits its object of study to the measurement of population processes, while the broader field of social demography or population studies also analyses the relationships between economic, social, cultural, and biological processes influencing a population.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e4/Social_Network_Diagram_%28segment%29.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b1/World_population.PNG", "https://upload.wikimedia.org/wikipedia/commons/a/ab/World_population_growth_-_time_between_each_billion-person_growth.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["1970 British Cohort Study", "ALLBUS", "Abnormal psychology", "Actuarial table", "Adolphe Qu\u00e9telet", "Aging", "American Philosophical Society", "Ancient Greece", "Ancient Greek", "Ancient Rome", "Anders Nicolas Kaier", "Andrey Korotayev", "Ansley J. Coale", "Anthropology", "Anthrozoology", "Archaeology", "Area studies", "Aristotle", "Augustus de Morgan", "Bartholomew of Lucca", "Behavioral neuroscience", "Ben J. Wattenberg", "Benjamin Franklin", "Benjamin Gompertz", "Bibliography of sociology", "Biodemography", "Biodemography of human longevity", "Biological anthropology", "Birth", "Birth rate", "Brass relational logits", "Brazilian Journal of Population Studies", "Business studies", "Cahiers qu\u00e9b\u00e9cois de d\u00e9mographie", "Cato the Elder", "Census", "China", "Cicero", "Cicred", "Cognitive psychology", "Cognitive science", "Columella", "Communication studies", "Community studies", "Comparative historical research", "Computational sociology", "Conflict theories", "Conway Zirkle", "Country", "Criminology", "Critical theory", "Cultural anthropology", "Cultural assimilation", "Cultural history", "Cultural studies", "Curlie", "Current Population Survey", "Death", "Death rate", "Decrement table", "Demographic analysis", "Demographic and Health Surveys", "Demographic economics", "Demographics of the world", "Demography (album)", "Demography (journal)", "Development studies", "Development theory", "Developmental psychology", "Deviance (sociology)", "Digital object identifier", "Economic history", "Economic sociology", "Economics", "Edmond Halley", "Education", "Environmental social science", "Environmental sociology", "Environmental studies", "Epictetus", "Epicurus", "Epidemiology", "Ethnicity", "Ethnography", "Ethnomethodology", "European Social Survey", "Exponential growth", "Feminist sociology", "Fertility", "Fertility rate", "Food studies", "Geisteswissenschaft", "Gender studies", "General Social Survey", "Geography", "German General Social Survey", "Global Social Change Research Project", "Global studies", "Gompertz curve", "Gompertz\u2013Makeham law of mortality", "Gross reproduction rate", "Hernes model", "Herodotus", "Hippocrates", "Historical Social Research", "Historical demography", "Historical sociology", "History", "History of science", "History of sociology", "History of technology", "Human", "Human ecology", "Human geography", "Human overpopulation", "Human science", "Humanities", "Ibn Khaldun", "Index of sociology articles", "India", "Industrial sociology", "Infant mortality rate", "Information science", "Institut national d'\u00e9tudes d\u00e9mographiques", "Integrated Authority File", "Integrated geography", "International Institute for Applied Systems Analysis", "International Standard Book Number", "International Standard Serial Number", "International relations", "International studies", "JSTOR", "Jacques Bertillon", "John Bongaarts", "John Graunt", "Joseph K\u00f6r\u00f6si", "Jurisprudence", "Land-use planning", "Law", "Lee\u2013Carter model", "Legal history", "Leslie matrix", "Library of Congress Control Number", "Life Table", "Life expectancy", "Life table", "Linguistic demography", "Linguistics", "List of national legal systems", "List of social science journals", "List of sociological associations", "List of sociologists", "List of sociology journals", "Louis-Adolphe Bertillon", "Luigi Bodio", "Macroeconomics", "Malthusian catastrophe", "Marcus Aurelius", "Mathematical sociology", "Max Planck Institute for Demographic Research", "Media studies", "Medical sociology", "Medieval demography", "Microeconomics", "Middle ages", "Migration (human)", "Military history", "Military sociology", "Millennium Cohort Study", "Models of mortality", "Multiple Indicator Cluster Surveys", "Multistate life tables", "NRS social grade", "Nathan Keyfitz", "National Child Development Study", "National Longitudinal Survey", "National Security Study Memorandum 200", "Nationality", "Observations Concerning the Increase of Mankind, Peopling of Countries, etc.", "Office of Population Research", "Organizational theory", "Outline of social science", "Outline of sociology", "PMA2020", "Page model", "Panel Study of Income Dynamics", "Parity progression ratios", "Paul R. Ehrlich", "People's Republic of China", "Personality psychology", "Phillip Longman", "Philosophy and economics", "Philosophy of history", "Philosophy of psychology", "Philosophy of science", "Philosophy of social science", "Pierre Fran\u00e7ois Verhulst", "Plato", "Pliny the elder", "Political demography", "Political ecology", "Political economy", "Political history", "Political science", "Political sociology", "Polus", "Population", "Population Association of America", "Population Council", "Population Reference Bureau", "Population Studies Center at the University of Michigan", "Population and Development Review", "Population biology", "Population dynamics", "Population geography", "Population momentum", "Population projections", "Population reconstruction", "Population statistics", "Positivism", "Proceedings of the American Philosophical Society", "Proportional hazards models", "Protagoras", "Psephology", "Psychology", "PubMed Identifier", "Public administration", "Public health", "Public policy", "Qualitative research", "Quantitative research", "Regional planning", "Regional science", "Religion", "Religious demography", "Replacement migration", "Reproductive health", "Richard B\u00f6ckh", "Richard Price", "Rural sociology", "Science, technology and society", "Science studies", "Seneca the Younger", "Sex ratio", "Social anthropology", "Social change", "Social conflict", "Social construction of technology", "Social constructionism", "Social history", "Social inequality", "Social movement", "Social network analysis", "Social psychology", "Social psychology (sociology)", "Social research", "Social science", "Social stratification", "Social work", "Socio-Economic Panel", "Sociological theory", "Sociology", "Sociology of culture", "Sociology of education", "Sociology of gender", "Sociology of health and illness", "Sociology of immigration", "Sociology of knowledge", "Sociology of law", "Sociology of literature", "Sociology of race and ethnic relations", "Sociology of religion", "Sociology of scientific knowledge", "Sociology of terrorism", "Sociology of the Internet", "Sociology of the family", "Statistics", "Structural functionalism", "Subfields of sociology", "Sullivan's method", "Symbolic interactionism", "The Population Bomb", "Thomas Robert Malthus", "Thucidides", "Timeline of sociology", "Total fertility rate", "Urban planning", "Urban sociology", "Vienna Institute of Demography", "Wayback Machine", "Wilhelm Lexis", "William Farr", "William of Auvergne, Bishop of Paris", "William of Conches", "William of Pagula", "Wittgenstein Centre for Demography and Global Human Capital", "World Values Survey", "\u00c9mile Durkheim"], "references": ["http://www.aetheling.com/NL/sim/population/population1.html", "http://www.merriam-webster.com/dictionary/demography", "http://www.demog.berkeley.edu/", "http://ace1.ma.utexas.edu/users/davis/375/reading/worldbirthrate.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/16155052", "http://www.ncbi.nlm.nih.gov/pubmed/16931528", "http://www.ncbi.nlm.nih.gov/pubmed/9194559", "http://www.amphilsoc.org/sites/default/files/proceedings/5VonValtier1550205.pdf", "http://www.canpopsoc.org", "http://demographicpartitions.org/science-population-determines-population-change/", "http://doi.org/10.1038%2F42935", "http://doi.org/10.1093%2Fije%2Fdyi183", "http://doi.org/10.1093%2Fije%2Fdyl174", "http://www.historicalstatistics.org/", "http://gsociology.icaap.org/basicguide.html", "http://gsociology.icaap.org/report/demsum.html", "http://www.iussp.org", "http://www.jstor.org/stable/984852", "http://www.populationassociation.org", "http://prb.org/pdf07/62.1LivelyIntroduction.pdf", "http://esa.un.org/unpd/ppp/index.htm", "http://esa.un.org/unpd/wup/index.htm", "http://www.unece.org/pau/ffs/ffs.htm", "http://www.unpopulation.org", "http://www.whatwemaybe.org/txt/txt0000/Glad.John.2008.FHE.Meisenberg-abridgement.en.pdf", "http://www.worldcat.org/issn/0003-049X", "http://www.cls.ioe.ac.uk", "https://books.google.com/books?id=LnqlgqeYhwYC&pg=PA312&lpg=PA312&dq=Nicole+Oresme+on+demographics&source=bl&ots=1RB9HPQrvY&sig=RtvI_JuQ4SGR0QYfa7ptB5eDW1w&hl=es&ei=kdLRS8SJBcO78gbWg8jNDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBkQ6AEwAA#v=onepage&q&f=false", "https://books.google.com/books?id=oNcflpmW3BUC&pg=PA1&lpg=PA1&dq=studies+in+demography&source=bl&ots=Y1QFr3LGxP&sig=xJkW1mxVL6XS-Gij0tOpOsFZA9E&hl=es&ei=qdjRS8DjMsGC8gbj4Ii_Dw&sa=X&oi=book_result&ct=result&resnum=2&ved=0CCMQ6AEwAQ#v=onepage&q&f=false", "https://www.cdc.gov/nchs/products/pubs/pubd/lftbls/lftbls.htm", "https://id.loc.gov/authorities/subjects/sh85036659", "https://d-nb.info/gnd/4011412-0", "https://web.archive.org/web/20081216230409/http://ace1.ma.utexas.edu/users/davis/375/reading/worldbirthrate.pdf", "https://web.archive.org/web/20110506065230/http://esa.un.org/unpd/wpp/index.htm", "https://web.archive.org/web/20110626005822/http://www.canpopsoc.org/", "https://web.archive.org/web/20130527141349/http://www.gesis.org/en/hsr/current-issues/current-issues-2010-2012/362-fertility/", "https://web.archive.org/web/20150814023915/http://demographicpartitions.org/science-population-determines-population-change/", "https://web.archive.org/web/20160304072527/https://www.peeparound.com/", "https://curlie.org/Science/Social_Sciences/Demography_and_Population_Studies/", "https://www.un.org/esa/population/unpop.htm", "https://www.wikidata.org/wiki/Q37732"]}, "Box\u2013Cox distribution": {"categories": ["All stub articles", "Continuous distributions", "Statistics stubs"], "title": "Box\u2013Cox distribution", "method": "Box\u2013Cox distribution", "url": "https://en.wikipedia.org/wiki/Box%E2%80%93Cox_distribution", "summary": "In statistics, the Box\u2013Cox distribution (also known as the power-normal distribution) is the distribution of a random variable X for which the Box\u2013Cox transformation on X follows a truncated normal distribution. It is a continuous probability distribution having probability density function (pdf) given by\n\n \n \n \n f\n (\n y\n )\n =\n \n \n 1\n \n \n (\n \n 1\n \u2212\n I\n (\n f\n <\n 0\n )\n \u2212\n sgn\n \u2061\n (\n f\n )\n \u03a6\n (\n 0\n ,\n m\n ,\n \n \n s\n \n \n )\n \n )\n \n \n \n 2\n \u03c0\n \n s\n \n 2\n \n \n \n \n \n \n \n exp\n \u2061\n \n {\n \n \u2212\n \n \n 1\n \n 2\n \n s\n \n 2\n \n \n \n \n \n \n \n (\n \n \n \n \n y\n \n f\n \n \n f\n \n \n \u2212\n m\n \n )\n \n \n 2\n \n \n \n }\n \n \n \n {\\displaystyle f(y)={\\frac {1}{\\left(1-I(f<0)-\\operatorname {sgn} (f)\\Phi (0,m,{\\sqrt {s}})\\right){\\sqrt {2\\pi s^{2}}}}}\\exp \\left\\{-{\\frac {1}{2s^{2}}}\\left({\\frac {y^{f}}{f}}-m\\right)^{2}\\right\\}}\n for y > 0, where m is the location parameter of the distribution, s is the dispersion, \u0192 is the family parameter, I is the indicator function, \u03a6 is the cumulative distribution function of the standard normal distribution, and sgn is the sign function.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Box\u2013Cox transformation", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Indicator function", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign function", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard normal distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.udc.edu/docs/dc_water_resources/technical_reports/report_n_190.pdf"]}, "Decision theory": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from January 2010", "Articles with unsourced statements from July 2017", "Control theory", "Decision theory", "Economics of uncertainty", "Epistemology of science", "Formal sciences", "Mathematical and quantitative methods (economics)", "Risk", "Statistical inference", "Wikipedia articles with GND identifiers"], "title": "Decision theory", "method": "Decision theory", "url": "https://en.wikipedia.org/wiki/Decision_theory", "summary": "Decision theory (or the theory of choice) is the study of the reasoning underlying an agent's choices. Decision theory can be broken into two branches: normative decision theory, which gives advice on how to make the best decisions, given a set of uncertain beliefs and a set of values; and descriptive decision theory, which analyzes how existing, possibly irrational agents actually make decisions.\nClosely related to the field of game theory, decision theory is concerned with the choices of individual agents whereas game theory is concerned with interactions of agents whose decisions affect each other. Decision theory is an interdisciplinary topic, studied by economists,\nstatisticians, psychologists, biologists, political and other social scientists, philosophers, and computer scientists.\nEmpirical applications of this rich theory are usually done with the help of statistical and econometric methods, especially via the so-called choice models, such as probit and logit models. Estimation of such models is usually done via parametric, semi-parametric and non-parametric maximum likelihood methods.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c2/Buridan%27s_bridge.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/22/Deliberations_of_Congress.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f0/PinocchioChiostri22.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/89/Symbol_book_class2.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["AFM Smith", "Abilene paradox", "Abraham Wald", "Adam Smith", "Adaptive expectations", "Admissible decision rule", "Adrian Smith (academic)", "Agent (economics)", "Aggregate demand", "Aggregation problem", "Agricultural economics", "Alabama paradox", "Alexander Lerner", "Alfred Marshall", "Alfred Radcliffe-Brown", "Algorithm", "Algorithm design", "Allais paradox", "Allenna Leonard", "Amartya Sen", "Amos Tversky", "Analysis of algorithms", "Anarchist economics", "Anchoring", "Ancient economic thought", "Annals of Mathematical Statistics", "Anthony Wilden", "Applied economics", "Applied mathematics", "Apportionment paradox", "Approximation theory", "Argument from free will", "Arrow's impossibility theorem", "Arrow information paradox", "Artificial intelligence", "Asia-Pacific Economic Cooperation", "Austrian School", "Average cost", "Axiom", "Balance of payments", "Barber paradox", "Barbershop paradox", "Bayesian probability", "Bayesian statistics", "Behavioral economics", "Berry paradox", "Bertrand paradox (economics)", "Bhartrhari's paradox", "Bilateral monopoly", "Biocybernetics", "Biomedical cybernetics", "Biorobotics", "Biosemiotics", "Black swan theory", "Blaise Pascal", "Bounded rationality", "Braess's paradox", "Brain\u2013computer interface", "Bruno de Finetti", "Buckminster Fuller", "Buddhist economics", "Budget set", "Buridan's ass", "Buridan's bridge", "Business cycle", "Business economics", "Calculus of variations", "Capacity utilization", "Capital flight", "Card paradox", "Catastrophe theory", "Catch-22 (logic)", "Causal decision theory", "Central bank", "Chainstore paradox", "Charles Fran\u00e7ois (systems scientist)", "Charles Sanders Peirce", "Chicago school of economics", "Choice modelling", "Classical economics", "Claude Bernard", "Cliff Joslyn", "Club of Rome", "Coding theory", "Combinatorics", "Competition (economics)", "Computational economics", "Computational mathematics", "Computational neuroscience", "Computational number theory", "Condorcet paradox", "Connectionism", "Constraint satisfaction", "Consumer choice", "Consumer confidence", "Control theory", "Convexity in economics", "Cost\u2013benefit analysis", "Crocodile dilemma", "Cryptography", "Currency", "Curry's paradox", "Cyberneticist", "Cybernetics", "Daniel Bernoulli", "Daniel Ellsberg", "Daniel Kahneman", "David Ricardo", "Deadweight loss", "Decision-making paradox", "Decision analysis", "Decision making", "Decision quality", "Decision support system", "Decision theory", "Deflation", "Demand for money", "Demand shock", "Demographic economics", "Dempster\u2013Shafer theory", "Depression (economics)", "Development economics", "Differential equations", "Differential geometry", "Digital object identifier", "Discrete geometry", "Discrete mathematics", "Distinction bias", "Distribution (economics)", "Donald Davidson (philosopher)", "Downs\u2013Thomson paradox", "Dream argument", "Drinker paradox", "Dutch book", "Dynamic stochastic general equilibrium", "Dynamical systems", "E. L. Lehmann", "Easterlin paradox", "Ecological economics", "Econometrics", "Economic Cooperation Organization", "Economic cost", "Economic equilibrium", "Economic geography", "Economic growth", "Economic history", "Economic indicator", "Economic methodology", "Economic planning", "Economic policy", "Economic rent", "Economic sociology", "Economic statistics", "Economic surplus", "Economic system", "Economic theory", "Economics", "Economies of scale", "Economies of scope", "Economist", "Economy", "Edgeworth paradox", "Education economics", "Effective demand", "Elasticity (economics)", "Ellsberg paradox", "Emergence", "Engineering cybernetics", "Engineering economics", "Environmental economics", "Epicurean paradox", "Epimenides paradox", "Erich von Holst", "Ernst von Glasersfeld", "Estimation theory", "European Free Trade Association", "European paradox", "Evidential decision theory", "Evolutionary economics", "Expected utility", "Expected utility hypothesis", "Expected value", "Experimental economics", "Externality", "Feminist economics", "Fenno's paradox", "Feynman integral", "Financial economics", "Fiscal policy", "Fitch's paradox of knowability", "Fourier analysis", "Francis Heylighen", "Francis Ysidro Edgeworth", "Francisco Varela", "Frank P. Ramsey", "Frederic Vester", "Fredkin's paradox", "Frequentist statistics", "Friedrich Hayek", "Functional analysis", "Functional integration", "Fuzzy logic", "Gambler's fallacy", "Game theory", "Gary Becker", "General equilibrium theory", "Geoffrey Vickers", "Georgism", "Gibson's paradox", "Giffen good", "Gordon Pask", "Gordon S. Brown", "Graph theory", "Great Depression", "Green paradox", "Gregory Bateson", "Grelling\u2013Nelson paradox", "Harmonic analysis (mathematics)", "Harold Hotelling", "Health economics", "Hedgehog's dilemma", "Heinz von Foerster", "Herbert A. Simon", "Heterodox economics", "Heuristic", "Hilbert's paradox of the Grand Hotel", "Historical school of economics", "History of economic thought", "Homeostasis", "Humberto Maturana", "Hyperbolic discounting", "Hyperinflation", "IS\u2013LM model", "I know that I know nothing", "Icarus paradox", "Igor Aleksander", "Income and fertility", "Index of economics articles", "Indifference curve", "Industrial organization", "Inflation", "Info-gap decision theory", "Information theory", "Input\u2013output model", "Institutional economics", "Integrated Authority File", "Interest", "Interest rate", "International Monetary Fund", "International Standard Book Number", "International Standard Serial Number", "International economics", "International organization", "Intertemporal choice", "Inventor's paradox", "Investment (macroeconomics)", "JEL classification codes", "JSTOR", "Jacob Marschak", "Jacque Fresco", "Jakob von Uexk\u00fcll", "James Berger (statistician)", "Jason Jixuan Hu", "Jay Wright Forrester", "Jennifer Wilby", "Jevons paradox", "John Maynard Keynes", "John N. Warfield", "John von Neumann", "Joseph Jastrow", "Joseph Schumpeter", "Jos\u00e9-Miguel Bernardo", "Karl Marx", "Kavka's toxin puzzle", "Kenneth Arrow", "Kevin Warwick", "Keynesian economics", "Kleene\u2013Rosser paradox", "Knowledge economy", "L. J. Savage", "Labour economics", "Lausanne School", "Law and economics", "Leontief paradox", "Liar paradox", "Liberal paradox", "Life expectancy", "List of Ship of Theseus examples", "List of important publications in economics", "List of mathematics topics", "List of paradoxes", "Logic", "Logic in computer science", "Logit", "Loss function", "Lottery paradox", "Lucas paradox", "Ludic fallacy", "Ludwig von Bertalanffy", "L\u00e9on Walras", "M-theory", "Macroeconomics", "Mainstream economics", "Maleyka Abbaszadeh", "Malliavin calculus", "Malthusianism", "Management cybernetics", "Mandeville's paradox", "Manfred Clynes", "Margaret Mead", "Marginal cost", "Marginal utility", "Marginalism", "Marian Mazur", "Market (economics)", "Market failure", "Market structure", "Martin Shubik", "Marxian economics", "Mathematical Reviews", "Mathematical analysis", "Mathematical biology", "Mathematical chemistry", "Mathematical economics", "Mathematical finance", "Mathematical physics", "Mathematical psychology", "Mathematical sociology", "Maurice Allais", "Maximum likelihood", "Mayfield's paradox", "Measures of national income and output", "Mechanism design", "Medical cybernetics", "Meno", "Mercantilism", "Mere addition paradox", "Metzler paradox", "Microeconomics", "Microfoundations", "Milton Friedman", "Minimax", "Monetary economics", "Monetary policy", "Money", "Money supply", "Monopolistic competition", "Monopoly", "Monopsony", "Moore's paradox", "Morton's fork", "Multi-criteria decision making", "Mutualism (economic theory)", "N. Katherine Hayles", "NAIRU", "Natalia Bekhtereva", "National accounts", "Natural resource economics", "Navigation paradox", "Neo-Keynesian economics", "Neo-Marxian economics", "Neoclassical economics", "New Keynesian economics", "New classical macroeconomics", "New institutional economics", "New riddle of induction", "New states paradox", "Newcomb's paradox", "Niklas Luhmann", "No-no paradox", "Non-convexity (economics)", "Norbert Wiener", "Norm (philosophy)", "Normative", "Numerical analysis", "OECD", "Oligopoly", "Oligopsony", "Omnipotence paradox", "Operations research", "Operator algebra", "Operator theory", "Opportunity cost", "Opposite Day", "Optimal decision", "Optimization (mathematics)", "Oskar Morgenstern", "Outline of economics", "Paradox", "Paradox of analysis", "Paradox of competition", "Paradox of entailment", "Paradox of fiction", "Paradox of hedonism", "Paradox of nihilism", "Paradox of prosperity", "Paradox of the Court", "Paradox of thrift", "Paradox of toil", "Paradox of tolerance", "Paradox of value", "Paradox of voting", "Pareto efficiency", "Parrondo's paradox", "Particle physics and representation theory", "Pascal's Wager", "Patrick Suppes", "Paul Krugman", "Paul Samuelson", "Pens\u00e9es", "Perfect competition", "Petro Grigorenko", "Philosophy", "Physiocracy", "Pinocchio paradox", "Plato's beard", "Political economy", "Population paradox", "Positive statement", "Possibility theory", "Post-Keynesian economics", "Preface paradox", "Preference (economics)", "Prevention paradox", "Price", "Price level", "Prior distribution", "Prior probability", "Prisoner's dilemma", "Probability distribution", "Probability theory", "Probit", "Production set", "Productivity paradox", "Profit (economics)", "Prospect theory", "PubMed Identifier", "Public choice", "Public economics", "Public good", "Purchasing power parity", "Qian Xuesen", "Quantum cognition", "Quine's paradox", "Ragnar Frisch", "Random variable", "Ranulph Glanville", "Rate of profit", "Rational expectations", "Rationality", "Rationing", "Raven paradox", "Real business-cycle theory", "Recession", "Regional economics", "Renormalization group", "Resource curse", "Returns to scale", "Richard's paradox", "Richard Thaler", "Richard Threlkeld Cox", "Risk aversion", "Risk function", "Robert Lucas Jr.", "Robert Solow", "Robert Trappl", "Robust statistics", "Ross' paradox", "Russell's paradox", "Saving", "Scarcity", "Schools of economic thought", "Scitovsky paradox", "Second-order cybernetics", "Secretary problem", "Semiotics", "Sensitivity analysis", "Sergei P. Kurdyumov", "Service economy", "Service recovery paradox", "Ship of Theseus", "Shortage", "Shrinkflation", "Sidney Siegel", "Signal detection theory", "Small-numbers game", "Social choice theory", "Social cost", "Socialist economics", "Socio-cognitive", "Sociocybernetics", "Socioeconomics", "Sorites paradox", "St. Petersburg paradox", "Stafford Beer", "Stagflation", "Stanford University Press", "Statistical hypothesis testing", "Statistics", "Stochastic analysis", "Stochastic dominance", "Stochastic process", "Stockholm school (economics)", "Stuart Kauffman", "Stuart Umpleby", "Subjective probability", "Subjectivity", "Sunk cost", "Supply-side economics", "Supply and demand", "Supply shock", "Symbolic computation", "Synergetics (Haken)", "TOTREP", "Talcott Parsons", "The Antitrust Paradox", "The General Theory of Employment, Interest and Money", "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", "Theory of the firm", "Thermoeconomics", "Time inconsistency", "Tjalling Koopmans", "Topic outline of mathematics", "Trade", "Transaction cost", "Transport economics", "Tullock paradox", "Two envelopes problem", "Ulla Mitzdorf", "Uncertainty", "Unemployment", "Unexpected hanging paradox", "Unknown unknowns", "Urban economics", "Utility", "Utility function", "Valentin Turchin", "Valentino Braitenberg", "Value (economics)", "Value (personal and cultural)", "Vilfredo Pareto", "W. Ross Ashby", "Wage", "Walter Bradford Cannon", "Walter Pitts", "Warren Sturgis McCulloch", "Welfare economics", "What the Tortoise Said to Achilles", "When a white horse is not a horse", "William Grey Walter", "Willpower paradox", "Wireless communications", "Wittgenstein on Rules and Private Language", "World Bank", "World Trade Organization", "Yablo's paradox", "Zeno's paradoxes"], "references": ["http://psychclassics.yorku.ca/Peirce/small-diffs.htm", "http://www.sciencedirect.com/science/article/pii/S0167947316302596", "http://plato.stanford.edu/archives/win2015/entries/decision-theory", "http://www.ncbi.nlm.nih.gov/pubmed/4022303", "http://www.ncbi.nlm.nih.gov/pubmed/4022304", "http://www.ams.org/mathscinet-getitem?mr=0000932", "http://www.ams.org/mathscinet-getitem?mr=0804611", "http://www.ams.org/mathscinet-getitem?mr=1274699", "http://www.ams.org/mathscinet-getitem?mr=1835885", "http://doi.org/10.1007%2F0-387-71599-1", "http://doi.org/10.1016%2F0028-3932(85)90022-3", "http://doi.org/10.1016%2F0028-3932(85)90023-5", "http://doi.org/10.1016%2Fj.csda.2016.10.024", "http://doi.org/10.1037%2F0033-295X.108.2.370", "http://doi.org/10.1109%2FTSSC.1968.300114", "http://doi.org/10.1214%2Faoms%2F1177729884", "http://doi.org/10.1214%2Faoms%2F1177732144", "http://doi.org/10.1287%2Fmnsc.31.4.395", "http://doi.org/10.1371%2Fjournal.pcbi.1005436", "http://www.jstor.org/stable/2236552", "http://www.numdam.org/item?id=AIHP_1937__7_1_1_0", "http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005436", "http://www.worldcat.org/issn/1553-7358", "http://www.infra.kth.se/~soh/decisiontheory.pdf", "https://papers.ssrn.com/soL3/papers.cfm?abstract_id=647666", "https://d-nb.info/gnd/4138606-1", "https://notendur.hi.is/ajonsson/kennsla2003/Akerlof_Yellen.pdf", "https://web.archive.org/web/20030605070939/http://cepa.newschool.edu/het/texts/ramsey/ramsess.pdf", "https://web.archive.org/web/20060705052730/http://www.infra.kth.se/~soh/decisiontheory.pdf", "https://www.wikidata.org/wiki/Q177571"]}, "Generalized gamma distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax"], "title": "Generalized gamma distribution", "method": "Generalized gamma distribution", "url": "https://en.wikipedia.org/wiki/Generalized_gamma_distribution", "summary": "The generalized gamma distribution is a continuous probability distribution with three parameters. It is a generalization of the two-parameter gamma distribution. Since many distributions commonly used for parametric models in survival analysis (such as the Exponential distribution, the Weibull distribution and the Gamma distribution) are special cases of the generalized gamma, it is sometimes used to determine which parametric model is appropriate for a given set of data. Another example is the half-normal distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8f/GenGamma.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digamma function", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized integer gamma distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Incomplete gamma function", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kullback-Leibler divergence", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Luigi Amoroso", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "R (programming language)", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Survival analysis", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://threeplusone.com/Crooks-Amoroso.pdf", "https://arxiv.org/abs/1401.6853", "https://arxiv.org/pdf/1401.6853.pdf", "https://www.jstor.org/stable/2237889"]}, "Admissible decision rule": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2010", "Bayesian statistics", "Optimal decisions"], "title": "Admissible decision rule", "method": "Admissible decision rule", "url": "https://en.wikipedia.org/wiki/Admissible_decision_rule", "summary": "In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always \"better\" than it (or at least sometimes better and never worse), in the precise sense of \"better\" defined below. This concept is analogous to Pareto efficiency.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Approximate Bayesian computation", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernstein\u2013von Mises theorem", "Conjugate prior", "Credible interval", "Cromwell's rule", "Decision rule", "Decision theory", "Dominating decision rule", "Empirical Bayes method", "Expected value", "Frequency probability", "Frequentist", "Function (mathematics)", "Hyperparameter", "Hyperprior", "Inequality (mathematics)", "International Standard Book Number", "James\u2013Stein estimator", "Likelihood function", "Loss function", "Markov chain Monte Carlo", "Maximal element", "Maximum a posteriori estimation", "Morris DeGroot", "Normal distribution", "Ordinary least squares", "Pareto efficiency", "Posterior predictive distribution", "Posterior probability", "Principle of indifference", "Principle of maximum entropy", "Prior distribution", "Prior probability", "Probability interpretations", "Radical probabilism", "Risk function", "Sample variance", "Schwarz criterion", "Set (mathematics)", "Statistical decision theory", "Statistics", "Stein's example", "Utility function", "Yadolah Dodge"], "references": []}, "Fr\u00e9chet distribution": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from May 2011", "Articles with unsourced statements from May 2011", "CS1 maint: Uses authors parameter", "Continuous distributions", "Extreme value data", "Location-scale family probability distributions", "Pages using deprecated image syntax"], "title": "Fr\u00e9chet distribution", "method": "Fr\u00e9chet distribution", "url": "https://en.wikipedia.org/wiki/Fr%C3%A9chet_distribution", "summary": "The Fr\u00e9chet distribution, also known as inverse Weibull distribution, is a special case of the generalized extreme value distribution. It has the cumulative distribution function\n\n \n \n \n Pr\n (\n X\n \u2264\n x\n )\n =\n \n e\n \n \u2212\n \n x\n \n \u2212\n \u03b1\n \n \n \n \n \n if \n \n x\n >\n 0.\n \n \n {\\displaystyle \\Pr(X\\leq x)=e^{-x^{-\\alpha }}{\\text{ if }}x>0.}\n where \u03b1 > 0 is a shape parameter. It can be generalised to include a location parameter m (the minimum) and a scale parameter s > 0 with the cumulative distribution function\n\n \n \n \n Pr\n (\n X\n \u2264\n x\n )\n =\n \n e\n \n \u2212\n \n \n (\n \n \n \n x\n \u2212\n m\n \n s\n \n \n )\n \n \n \u2212\n \u03b1\n \n \n \n \n \n if \n \n x\n >\n m\n .\n \n \n {\\displaystyle \\Pr(X\\leq x)=e^{-\\left({\\frac {x-m}{s}}\\right)^{-\\alpha }}{\\text{ if }}x>m.}\n Named for Maurice Fr\u00e9chet who wrote a related paper in 1927, further work was done by Fisher and Tippett in 1928 and by Gumbel in 1958.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8f/FitFrechetDistr.tif", "https://upload.wikimedia.org/wikipedia/commons/d/dd/Frechet_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e0/Frechet_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Confidence belt", "Conway\u2013Maxwell\u2013Poisson distribution", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Emil Julius Gumbel", "Erlang distribution", "Euler\u2013Mascheroni constant", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Fisher\u2013Tippett distribution", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Flory\u2013Schulz distribution", "Folded normal distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hydrology", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "International Standard Book Number", "International Standard Serial Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maurice Fr\u00e9chet", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Oman", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Plotting position", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stability postulate", "Stable distribution", "Standardized moment", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.emeraldinsight.com/Insight/ViewContentServlet?Filename=Published/EmeraldFullTextArticle/Articles/0830160102.html#0830160102006.png", "http://doi.org/10.1007%2Fs00362-009-0271-3", "http://www.worldcat.org/issn/0932-5026", "http://www.maths.lth.se/matstat/wafo/documentation/wafodoc/wafo/wstats/wfrechstat.html", "http://www.wseas.us/e-library/transactions/mathematics/2008/theoretical.pdf", "https://books.google.com/books?id=2nugUEaKqFEC&lpg=PP1&pg=PP1#v=onepage&q=&f=false", "https://dx.doi.org/10.1007/s00362-009-0271-3"]}, "Mat\u00e9rn covariance function": {"categories": ["Covariance and correlation", "Geostatistics", "Spatial data analysis"], "title": "Mat\u00e9rn covariance function", "method": "Mat\u00e9rn covariance function", "url": "https://en.wikipedia.org/wiki/Mat%C3%A9rn_covariance_function", "summary": "In statistics, the Mat\u00e9rn covariance (named after the Swedish forestry statistician Bertil Mat\u00e9rn) is a covariance function used in spatial statistics, geostatistics, machine learning, image analysis, and other applications of multivariate statistical analysis on metric spaces. It is commonly used to define the statistical covariance between measurements made at two points that are d units distant from each other. Since the covariance only depends on distances between points, it is stationary. If the distance is Euclidean distance, the Mat\u00e9rn covariance is also isotropic.", "images": [], "links": ["Bertil Mat\u00e9rn", "Bessel function", "Covariance function", "Digital object identifier", "Euclidean distance", "Gamma function", "Gaussian process", "Geostatistics", "International Standard Book Number", "Isotropic", "Machine learning", "Metric space", "Parameter", "Radial basis function", "Spatial statistics", "Stationary process", "Statistics"], "references": ["http://doi.org/10.1016%2Fj.geoderma.2005.04.003", "http://www.gaussianprocess.org/gpml/chapters/RW4.pdf"]}, "The Long Tail": {"categories": ["All articles that may contain original research", "All articles with specifically marked weasel-worded phrases", "All articles with unsourced statements", "Articles that may contain original research from May 2015", "Articles with specifically marked weasel-worded phrases from January 2018", "Articles with specifically marked weasel-worded phrases from May 2013", "Articles with unsourced statements from April 2011", "Articles with unsourced statements from April 2013", "Articles with unsourced statements from May 2013", "Articles with unsourced statements from November 2011", "E-commerce", "Economics curves", "Statistical laws", "Tails of probability distributions"], "title": "Long tail", "method": "The Long Tail", "url": "https://en.wikipedia.org/wiki/Long_tail", "summary": "In statistics and business, a long tail of some distributions of numbers is the portion of the distribution having a large number of occurrences far from the \"head\" or central part of the distribution. The distribution could involve popularities, random numbers of occurrences of events with various probabilities, etc. The term is often used loosely, with no definition or arbitrary definition, but precise definitions are possible.\nIn statistics, the term long-tailed distribution has a narrow technical meaning, and is a subtype of heavy-tailed distribution. Intuitively, a distribution is (right) long-tailed if, for any fixed amount, when a quantity exceeds a high level, it almost certainly exceeds it by at least that amount: large quantities are probably even larger. Note that there is no sense of the \"long tail\" of a distribution, but only the property of a distribution being long-tailed.\nIn business, the term long tail is applied to rank-size distributions or rank-frequency distributions (primarily of popularity), which often form power laws and are thus long-tailed distributions in the statistical sense. This is used to describe the retailing strategy of selling a large number of unique items with relatively small quantities sold of each (the \"long tail\")\u2014usually in addition to selling fewer popular items in large quantities (the \"head\"). Sometimes an intermediate category is also included, variously called the body, belly, torso, or middle. The specific cutoff of what part of a distribution is the \"long tail\" is often arbitrary, but in some cases may be specified objectively; see segmentation of rank-size distributions.\nThe long tail concept has found some ground for application, research, and experimentation. It is a term used in online business, mass media, micro-finance (Grameen Bank, for example), user-driven innovation (Eric von Hippel), knowledge management, and social network mechanisms (e.g. crowdsourcing, crowdcasting, peer-to-peer), economic models, marketing (viral marketing), and IT Security threat hunting within a SOC (Information security operations center).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8a/Long_tail.svg", "https://upload.wikimedia.org/wikipedia/commons/1/12/Longtail.svg"], "links": ["AdECN", "Ad exchange", "Amazon.com", "Anita Elberse", "Apple Inc.", "Arun Sundararajan", "Asymptotically", "Audible.com", "Banco Azteca", "Bangladesh", "Beno\u00eet Mandelbrot", "Bing (search engine)", "Black swan theory", "Blockbuster Inc.", "Blog", "Business", "Business process overhead", "Chris Anderson (writer)", "Clay Shirky", "Cold start (computing)", "Collaboration", "Collaborative filtering", "Collaborative search engine", "Collective intelligence", "Consumer surplus", "Content discovery platform", "Crowdcasting", "Crowdsourcing", "Culture", "Decision support system", "Demand-side platform", "Demand curve", "Digital object identifier", "Dimensionality reduction", "Display advertising", "E-tailer", "E-tailers", "EBay", "Eric von Hippel", "Erik Brynjolfsson", "Frequency distribution", "Google", "Grameen Bank", "GroupLens Research", "Gutenberg\u2013Richter law", "Harvard Business School", "Heavy-tailed distribution", "IQ", "ITunes Store", "Implicit data collection", "Information security operations center", "Innovation", "International Standard Book Number", "Into Thin Air", "Item-item collaborative filtering", "John Robb (GG theorist)", "Jon Krakauer", "Kiva.org", "Kolmogorov's zero\u2013one law", "Log-normal distribution", "Long-tailed distribution", "Long tail (disambiguation)", "LoveFilm", "L\u00e9vy skew alpha-stable distribution", "MIS Quarterly", "MIT Sloan Management Review", "Malcolm Gladwell", "Marketing", "Mass customization", "Mass media", "Massively multiplayer online game", "Matrix factorization (recommender systems)", "Michael D. Smith (economist)", "Micro-finance", "Microfinance", "Micropublishing", "Microsite", "MovieLens", "Music Genome Project", "Netflix", "Netflix Prize", "New media marketing", "Opportunity cost", "Pareto distribution", "Pareto principle", "Pattern Recognition (novel)", "Pay-per-view", "Pay per click", "Peer-to-Peer (meme)", "Peer-to-peer (meme)", "Podcast", "Politics", "Positive feedback", "Power law", "Preference elicitation", "Preferential attachment", "Probabilities", "Probability distribution", "Product finder", "RSS", "Rank-frequency distribution", "Rank-size distribution", "Recommender system", "Relevance", "Right Media", "Rule of thumb", "Scale-free network", "Search engine marketing", "Search engine optimization", "Search engine technology", "Second Life", "Serguei Netessine", "Similarity search", "Social Science Research Network", "Social innovation", "Social loafing", "Social networks", "Star (classification)", "Statistics", "Swarm intelligence", "Target Corporation", "Television", "Television on demand", "The Long Tail: Why the Future of Business Is Selling Less of More", "The Long Tail (book)", "The Tipping Point", "The Wolfram Demonstrations Project", "Touching the Void (book)", "Trial and error", "User innovation", "Video game", "Viral email", "Viral marketing", "Virtual communities", "Walmart", "Web content", "Wharton School of the University of Pennsylvania", "Wiki", "Wikipedia", "Will Page", "William Gibson", "Wired (magazine)", "Word of mouth", "Yahoo!", "Yahoo! Search", "Yochai Benkler", "YouTube", "Yu (Jeffrey) Hu", "Zipf's law"], "references": ["http://www.longtail.com/the_long_tail/2005/01/long_tail_tv_pa_2.html", "http://www.longtail.com/the_long_tail/2008/06/excellent-hbr-p.html", "http://www.longtail.com/the_long_tail/2008/11/more-long-tail.html", "http://www.mediapost.com/publications/article/142294/long-tail-advertisers-are-back-us-ad-expansio.html", "http://www.roughtype.com/archives/2006/08/the_shape_of_th.php", "http://www.shirky.com/writings/powerlaw_weblog.html", "http://ssrn.com/abstract=1324064", "http://ssrn.com/abstract=1679991", "http://ssrn.com/abstract=400940", "http://ssrn.com/abstract=918142", "http://ssrn.com/abstract=953587", "http://ssrn.com/abstract=955984", "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1742519", "http://longtail.typepad.com/the_long_tail/2005/01/definitions_fin.html#comment-3415583", "http://longtail.typepad.com/the_long_tail/2005/05/the_origins_of_.html", "http://demonstrations.wolfram.com/TheLongTail/", "http://web.mit.edu/evhippel/www/democ1.htm", "http://knowledge.wharton.upenn.edu/article.cfm?articleid=2338", "http://www.benkler.org/", "http://doi.org/10.1007%2F0-387-21525-5_10", "http://doi.org/10.1016%2Fj.evolhumbehav.2006.10.002", "http://doi.org/10.1287%2Fmnsc.1080.0974", "http://www.edge.org/documents/mandelbrot2010/mandelbrot2010_index.html", "http://www.gdrc.org/icm/", "http://hbr.org/2008/07/should-you-invest-in-the-long-tail/ar/1", "http://www.misq.org/forthcoming/", "http://journals.royalsociety.org/content/1n1x17lp0c0q65uj", "http://www.uncdf.org/english/microfinance/", "http://www.worldwidewords.org/turnsofphrase/tp-lon1.htm", "http://www.thetimes.co.uk/tto/arts/music/article2416859.ece", "https://books.google.com/books?id=9qLfsonmwhAC&pg=PT5", "https://books.google.com/books?id=O2k0K1w_bJIC&printsec=frontcover", "https://books.google.com/books?id=RAjNY11rJXIC&pg=PA62", "https://www.wired.com/wired/archive/12.10/tail.html", "https://www.wired.com/wired/archive/14.07/longtail_pr.html", "https://web.archive.org/web/20111231215224/http://www.uncdf.org/english/microfinance/", "https://arxiv.org/abs/0808.1655", "https://www.npr.org/templates/story/story.php?storyId=4156078", "https://www.telegraph.co.uk/connected/main.jhtml?xml=/connected/2004/06/16/ecfpop16.xml&sSheet=/connected/2004/06/14/ixconn.html"]}, "Proxy (statistics)": {"categories": ["All stub articles", "Econometrics stubs", "Statistical analysis", "Statistics stubs"], "title": "Proxy (statistics)", "method": "Proxy (statistics)", "url": "https://en.wikipedia.org/wiki/Proxy_(statistics)", "summary": "In statistics, a proxy or proxy variable is a variable that is not in itself directly relevant, but that serves in place of an unobservable or immeasurable variable. In order for a variable to be a good proxy, it must have a close correlation, not necessarily linear, with the variable of interest. This correlation might be either positive or negative.\nProxy variable must relate to unobserved variable, must correlate with disturbance, and must not correlate with regressors once disturbance is controlled for.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg"], "links": ["Body Mass Index", "Correlation", "Digital object identifier", "Econometrics", "GDP", "Instrumental variable", "International Standard Book Number", "JSTOR", "Operationalization", "Proxy (climate)", "Quality of life", "Race (classification of human beings)", "Social science", "Standard of living", "Statistics", "Variable (mathematics)"], "references": ["http://blog.minitab.com/blog/adventures-in-statistics/proxy-variables-the-good-twin-of-confounding-variables", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.230.7240&rep=rep1&type=pdf", "http://doi.org/10.1016%2F0378-3758(95)00045-3", "http://doi.org/10.2307%2F2110026", "http://www.jstor.org/stable/2110026"]}, "Maximum-entropy Markov model": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2014", "CS1 maint: Multiple names: authors list", "Markov models", "Statistical natural language processing"], "title": "Maximum-entropy Markov model", "method": "Maximum-entropy Markov model", "url": "https://en.wikipedia.org/wiki/Maximum-entropy_Markov_model", "summary": "In machine learning, a maximum-entropy Markov model (MEMM), or conditional Markov model (CMM), is a graphical model for sequence labeling that combines features of hidden Markov models (HMMs) and maximum entropy (MaxEnt) models. An MEMM is a discriminative model that extends a standard maximum entropy classifier by assuming that the unknown values to be learnt are connected in a Markov chain rather than being conditionally independent of each other. MEMMs find applications in natural language processing, specifically in part-of-speech tagging and information extraction.", "images": [], "links": ["Baum\u2013Welch algorithm", "Conditional random field", "Conditionally independent", "Digital object identifier", "Discriminative model", "Forward\u2013backward algorithm", "Generalized iterative scaling", "Graphical model", "Hidden Markov model", "Information extraction", "MEMM", "Machine learning", "Markov chain", "Maximum entropy classifier", "Maximum entropy probability distribution", "Natural language processing", "Part-of-speech tagging", "Semi-supervised learning", "Sequence labeling", "Silvio Memm", "Viterbi algorithm"], "references": ["http://www.ai.mit.edu/courses/6.891-nlp/READINGS/maxent.pdf", "http://leon.bottou.org/papers/bottou-91a", "http://doi.org/10.1214%2Faoms%2F1177692379", "http://projecteuclid.org/download/pdf_1/euclid.aoms/1177692379"]}, "Progressively measurable process": {"categories": ["All stub articles", "Mathematical analysis stubs", "Measure theory", "Probability stubs", "Stochastic processes", "Wikipedia articles needing page number citations from August 2011"], "title": "Progressively measurable process", "method": "Progressively measurable process", "url": "https://en.wikipedia.org/wiki/Progressively_measurable_process", "summary": "In mathematics, progressive measurability is a property in the theory of stochastic processes. A progressively measurable process, while defined quite technically, is important because it implies the stopped process is measurable. Being progressively measurable is a strictly stronger property than the notion of being an adapted process. Progressively measurable processes are important in the theory of It\u00f4 integrals.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c9/Lebesgue_Icon.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg"], "links": ["Adapted process", "Borel sigma algebra", "Brownian motion", "Continuous function", "C\u00e0dl\u00e0g", "Equivalence class", "Filtration (abstract algebra)", "Indicator function", "International Standard Book Number", "It\u00f4 integral", "Mathematical analysis", "Mathematics", "Measurable", "Measurable function", "Measurable space", "Probability", "Probability space", "Sigma algebra", "Stochastic process", "Stochastic processes", "Stopped process"], "references": []}, "Microdata (statistics)": {"categories": ["Censuses", "Sampling (statistics)"], "title": "Microdata (statistics)", "method": "Microdata (statistics)", "url": "https://en.wikipedia.org/wiki/Microdata_(statistics)", "summary": "In the study of survey and census data, microdata is information at the level of individual respondents. For instance, a national census might collect age, home address, educational level, employment status, and many other variables, recorded separately for every person who responds; this is microdata.", "images": [], "links": ["Address (geography)", "Aggregate data", "Census", "Data", "Education", "Employment", "Employment rate", "IPUMS", "Metadata", "Microdata (disambiguation)", "PARIS21", "Region", "Statistical survey", "World Bank"], "references": ["https://web.archive.org/web/20070823010133/http://international.ipums.org/international/confidentiality.html", "https://international.ipums.org/international-action/faq#ques7", "https://international.ipums.org/international/confidentiality.html"]}, "Randomized experiment": {"categories": ["All articles to be expanded", "Articles to be expanded from September 2012", "Articles using small message boxes", "CS1 maint: Multiple names: authors list", "CS1 maint: Uses authors parameter", "Design of experiments", "Experiments"], "title": "Randomized experiment", "method": "Randomized experiment", "url": "https://en.wikipedia.org/wiki/Randomized_experiment", "summary": "In science, randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects. Randomization-based inference is especially important in experimental design and in survey sampling.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/00/Flowchart_of_Phases_of_Parallel_Randomized_Trial_-_Modified_from_CONSORT_2010.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["A/B testing", "ANOVA", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Charles Sanders Peirce", "Chemometrics", "Chi-squared test", "Clinical equipoise", "Clinical study design", "Clinical trial", "Clinical trials", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Consolidated Standards of Reporting Trials", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental design", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "History of experiments", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Ian Hacking", "Ignorability", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "International Standard Serial Number", "Internet bots", "Interquartile range", "Interval estimation", "Isis (journal)", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Joseph Jastrow", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R.A. Fisher", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Rubin Causal Model", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Methods for Research Workers", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen M. Stigler", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survey sampling", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Treatment groups", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Web crawlers", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://psychclassics.yorku.ca/Peirce/small-diffs.htm", "http://www.bmj.com/cgi/content/full/340/mar23_1/c332", "http://www.exp-platform.com/Documents/2015%20Online%20Controlled%20Experiments_EncyclopediaOfMLDM.pdf", "http://www.exp-platform.com/Pages/CUPED.aspx", "http://www.exp-platform.com/Pages/PuzzingOutcomesExplained.aspx", "http://www.exp-platform.com/Pages/SevenRulesofThumbforWebSiteExperimenters.aspx", "http://www.springerlink.com/content/r28m75k77u145115/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1743807", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2844940", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4295227", "http://www.ncbi.nlm.nih.gov/pubmed/15069225", "http://www.ncbi.nlm.nih.gov/pubmed/20332509", "http://www.ncbi.nlm.nih.gov/pubmed/21491415", "http://www.ncbi.nlm.nih.gov/pubmed/24782322", "http://www.ncbi.nlm.nih.gov/pubmed/25490908", "http://www.ncbi.nlm.nih.gov/pubmed/9519574", "http://www.ams.org/mathscinet-getitem?mr=1013489", "http://www.ams.org/mathscinet-getitem?mr=1194407", "http://www.ams.org/mathscinet-getitem?mr=2363107", "http://doi.org/10.1002%2F14651858.MR000012.pub3", "http://doi.org/10.1002%2F14651858.MR000034.pub2", "http://doi.org/10.1007%2Fs10618-008-0114-1", "http://doi.org/10.1086%2F354775", "http://doi.org/10.1086%2F383850", "http://doi.org/10.1086%2F444032", "http://doi.org/10.1136%2Fbmj.c332", "http://doi.org/10.1136%2Fqshc.2003.009480", "http://doi.org/10.1145%2F2487575.2488217", "http://doi.org/10.1145%2F2623330.2623341", "http://doi.org/10.1186%2F1745-6215-15-480", "http://doi.org/10.1214%2Flnms%2F1215458836", "http://www.jstor.org/stable/234674", "http://projecteuclid.org/euclid.lnms/1215458836", "http://www.worldcat.org/issn/1384-5810", "https://books.google.com/?id=T3wWj2kVYZgC&printsec=frontcover", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1743807/pdf/v013p00153.pdf", "https://dx.doi.org/10.1145/2487575.2488217"]}, "Univariate distribution": {"categories": ["All stub articles", "Statistics stubs", "Types of probability distributions"], "title": "Univariate distribution", "method": "Univariate distribution", "url": "https://en.wikipedia.org/wiki/Univariate_distribution", "summary": "In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector (consisting of multiple random variables).", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b7/Binomial_Distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c2/Uniform_distribution.svg"], "links": ["Binomial distribution", "Bivariate distribution", "Chisquare distribution", "Continuous uniform distribution", "Digital object identifier", "Discrete uniform distribution", "Exponential distribution", "F distribution", "Gamma distribution", "Geometric distribution", "International Standard Book Number", "List of probability distributions", "Multivariate distribution", "Negative binomial distribution", "Normal distribution", "Poisson distribution", "Probability distribution", "Random variable", "Random vector", "Statistics", "Student's t distribution", "Uniform distribution (continuous)", "Univariate"], "references": ["http://www.math.wm.edu/~leemis/2008amstat.pdf", "http://doi.org/10.1198%2F000313008X270448"]}, "Standard deviation": {"categories": ["All articles with failed verification", "All articles with unsourced statements", "Articles with failed verification from May 2015", "Articles with unsourced statements from August 2017", "Articles with unsourced statements from January 2012", "Articles with unsourced statements from July 2012", "Statistical deviation and dispersion", "Summary statistics", "Use dmy dates from June 2011", "Wikipedia articles with GND identifiers"], "title": "Standard deviation", "method": "Standard deviation", "url": "https://en.wikipedia.org/wiki/Standard_deviation", "summary": "In statistics, the standard deviation (SD, also represented by the lower case Greek letter sigma \u03c3 or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.\nThe standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.\nA useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data. \nIn addition to expressing the variability of a population, the standard deviation is commonly used to measure confidence in statistical conclusions. For example, the margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times. This derivation of a standard deviation is often called the \"standard error\" of the estimate or \"standard error of the mean\" when referring to a mean. It is computed as the standard deviation of all the means that would be computed from that population if an infinite number of samples were drawn and a mean for each sample were computed.\nIt is very important to note that the standard deviation of a population and the standard error of a statistic derived from that population (such as the mean) are quite different but related (related by the inverse of the square root of the number of observations). The reported margin of error of a poll is computed from the standard error of the mean (or alternatively from the product of the standard deviation of the population and the inverse of the square root of the sample size, which is the same thing) and is typically about twice the standard deviation\u2014the half-width of a 95 percent confidence interval. \nIn science, many researchers report the standard deviation of experimental data, and only effects that fall much farther than two standard deviations away from what would have been expected are considered statistically significant\u2014normal random error or variation in the measurements is in this way distinguished from likely genuine effects or associations. The standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the volatility of the investment.\nWhen only a sample of data from a population is available, the term standard deviation of the sample or sample standard deviation can refer to either the above-mentioned quantity as applied to those data or to a modified quantity that is an unbiased estimate of the population standard deviation (the standard deviation of the entire population).", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Comparison_standard_deviations.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0c/Confidence_interval_by_Standard_deviation.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8b/Metabolic_rates_for_northern_fulmars.svg", "https://upload.wikimedia.org/wikipedia/commons/1/15/Normal-distribution-cumulative-density-function.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d0/SD_of_metabolic_rate_of_fulmars.svg", "https://upload.wikimedia.org/wikipedia/commons/6/67/Standard_deviation_by_Confidence_interval.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["68-95-99.7 rule", "68\u201395\u201399.7 rule", "Accelerated failure time model", "Accumulation/distribution index", "Accuracy and precision", "Actuarial science", "Advance\u2013decline line", "Akaike information criterion", "Algebra", "Algorithms for calculating variance", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "ArXiv", "Arithmetic average", "Arithmetic mean", "Arithmetic overflow", "Arithmetic underflow", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average absolute deviation", "Average directional movement index", "Average human height", "Average true range", "Bar chart", "Basal metabolic rate", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bessel's correction", "Bias of an estimator", "Biased estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bollinger Bands", "Bootstrapping (statistics)", "Bottom (technical analysis)", "Box plot", "Box\u2013Jenkins method", "Breadth of market", "Breakout (technical analysis)", "Breusch\u2013Godfrey test", "Broadening top", "CERN", "Calculus", "Candlestick chart", "Candlestick pattern", "Canonical correlation", "Carl Friedrich Gauss", "Cartography", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central moment", "Central tendency", "Chart pattern", "Chebyshev's inequality", "Chemometrics", "Chi-squared test", "Chi distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Commodity channel index", "Commutative property", "Completeness (statistics)", "Completing the square", "Computational formula for the variance", "Computer program", "Concave function", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous distribution", "Continuous probability distribution", "Control chart", "Coppock curve", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulative distribution function", "Cup and handle", "Data collection", "Data set", "Dead cat bounce", "Decomposition of time series", "Definite integral", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Detrended price oscillator", "Deviation (statistics)", "Dickey\u2013Fuller test", "Digital object identifier", "Dimensionless number", "Distance correlation", "Divergence (statistics)", "Doji", "Donchian channel", "Double top and double bottom", "Dow theory", "Durbin\u2013Watson statistic", "Ease of movement", "Econometrics", "Effect size", "Efficiency (statistics)", "Efficient estimator", "Elliott wave principle", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Error bar", "Error function", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Excess kurtosis", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fibonacci retracement", "First-hitting-time model", "Flag and pennant patterns", "Force index", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "GW150914", "Gamma function", "Gap (chart pattern)", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric standard deviation", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Hammer (candlestick pattern)", "Hanging man (candlestick pattern)", "Harmonic mean", "Head and shoulders (chart pattern)", "Heteroscedasticity", "Higgs boson", "Hikkake pattern", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Ichimoku Kink\u014d Hy\u014d", "Index of dispersion", "Inflection point", "Integrated Authority File", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverted hammer", "Island reversal", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen's inequality", "Johansen test", "Jonckheere's trend test", "Kagi chart", "Kaplan\u2013Meier estimator", "Karl Pearson", "Keltner channel", "Kendall rank correlation coefficient", "Know sure thing oscillator", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line chart", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-normal distribution", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MACD", "Mahalanobis distance", "Mann\u2013Whitney U test", "Margin of error", "Market trend", "Marubozu", "Mass index", "MathWorld", "Maximum a posteriori estimation", "Maximum likelihood", "McClellan oscillator", "McNemar's test", "Mean", "Mean absolute deviation", "Mean absolute error", "Mean squared error", "Measurement", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Modern portfolio theory", "Moment (mathematics)", "Momentum (finance)", "Money flow index", "Monotone likelihood ratio", "Morning star (candlestick pattern)", "Moving average", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Negative volume index", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normalizing constant", "Northern fulmar", "Observational study", "Official statistics", "On-balance volume", "One- and two-tailed tests", "Open-high-low-close chart", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabolic SAR", "Parametric model", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Particle physics", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentage point", "Percentile", "Permutation test", "Philosophical Transactions of the Royal Society A", "Pie chart", "Pivot point (stock market)", "Pivotal quantity", "Plug-in principle", "Point and figure chart", "Point estimation", "Poisson regression", "Pooled standard deviation", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Price channels", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Propagation of uncertainty", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Put/call ratio", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rate of return", "Raw score", "Regression analysis", "Regression model validation", "Relative standard deviation", "Relative strength index", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Risk", "Robust regression", "Robust standard deviation", "Robust statistics", "Root-mean-square deviation", "Root mean square", "Round-off error", "Run chart", "S", "Sample mean", "Sample median", "Sample size", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Samuelson's inequality", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shooting star (candlestick pattern)", "Sigma", "Sign test", "Simple linear regression", "Simultaneous equations model", "Six Sigma", "Skewness", "Smart money index", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spinning top (candlestick pattern)", "Square (algebra)", "Square root", "Squared deviations", "Standard deviation (disambiguation)", "Standard error", "Standard error (statistics)", "Standard error of the mean", "Standard score", "Standardized testing (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistically significant", "Statistics", "Stem-and-leaf display", "Stochastic oscillator", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Summation", "Support and resistance", "Survey methodology", "Survival analysis", "Survival function", "System identification", "TRIN (finance)", "Technical analysis", "Technical indicator", "Three black crows", "Three white soldiers", "Time domain", "Time series", "Tolerance interval", "Top (technical analysis)", "Trend estimation", "Trend line (technical analysis)", "Triangle (chart pattern)", "Triple top and triple bottom", "Trix (technical analysis)", "True strength index", "U-statistic", "Ulcer index", "Ultimate oscillator", "Unbiased estimation of standard deviation", "Unbiased estimator", "Uniformly most powerful test", "United States", "Univariate", "V-statistic", "VIX", "Variance", "Vector autoregression", "Volatility (finance)", "Volume (finance)", "Volume\u2013price trend", "Vortex indicator", "Wald test", "Wavelet", "Wedge pattern", "Whittle likelihood", "Wilcoxon signed-rank test", "Williams %R", "Yamartino method", "YouTube", "Z-test"], "references": ["http://users.monash.edu.au/~murray/BDAR/", "http://press-archive.web.cern.ch/press-archive/PressReleases/Releases2012/PR17.12E.html", "http://public.web.cern.ch/public/", "http://www.edupristine.com/blog/what-is-standard-deviation", "http://www.ifa.com", "http://www.techbookreport.com/tutorials/stddev-30-secs.html", "http://jeff560.tripod.com/mathword.html", "http://mathworld.wolfram.com/BesselsCorrection.html", "http://mathworld.wolfram.com/DistributionFunction.html", "http://zach.in.tu-clausthal.de/teaching/info_literatur/Welford.pdf", "http://adsabs.harvard.edu/abs/1894RSPTA.185...71P", "http://adsabs.harvard.edu/abs/2016PhRvL.116f1102A", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2351401", "http://www.ncbi.nlm.nih.gov/pubmed/26918975", "http://www.ncbi.nlm.nih.gov/pubmed/8664723", "http://arxiv.org/abs/1602.03837", "http://doi.org/10.1080%2F00401706.1962.10490022", "http://doi.org/10.1098%2Frsta.1894.0003", "http://doi.org/10.1103%2FPhysRevLett.116.061102", "http://doi.org/10.1136%2Fbmj.312.7047.1654", "http://doi.org/10.2307%2F2265587", "http://doi.org/10.2307%2F2682923", "https://standard-deviation.appspot.com/", "https://www.youtube.com/watch?v=AUSKTk9ENzg", "https://d-nb.info/gnd/4767332-1", "https://www.encyclopediaofmath.org/index.php?title=p/q076030", "https://www.wikidata.org/wiki/Q159375"]}, "Data Desk": {"categories": ["Plotting software"], "title": "Data Desk", "method": "Data Desk", "url": "https://en.wikipedia.org/wiki/Data_Desk", "summary": "Data Desk is a software program for visual data analysis, visual data exploration, and statistics. It carries out Exploratory Data Analysis (EDA) and standard statistical analyses by means of dynamically linked graphic data displays that update any change simultaneously.", "images": [], "links": ["ADMB", "Analyse-it", "Apple Macintosh", "BMDP", "BV4.1 (software)", "CSPro", "Commercial software", "Comparison of statistical packages", "Cornell University", "Cross-platform", "CumFreq", "DAP (software)", "Data Description Inc.", "Data analysis", "Data visualization", "Dataplot", "Digital object identifier", "EViews", "Epi Info", "Exploratory Data Analysis", "Exploratory data analysis", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "General Linear Model", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "Infoworld", "JASP", "JMP (statistical software)", "JMulTi", "John Tukey", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Macintosh", "Macworld", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Multivariate statistics", "NCSS (statistical software)", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Paul F. Velleman", "Proprietary software", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software", "Software categories", "Software developer", "Software license", "Software release life cycle", "Spreadsheet", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistics", "StatsDirect", "TSP (econometrics software)", "The American Statistician", "The Unscrambler", "UNISTAT", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://datadesk.com/", "http://datadesk.com/company/history.php", "http://www.datadesk.com/", "http://www.infoworld.com/cgi-bin/displayArchive.pl?/97/24/rdataa.dat.htm", "http://www.macworld.com/article/15781/2000/12/06reviewsdatadesk.html", "http://doi.org/10.1080%2F00031305.1997.10473593"]}, "Consensus forecast": {"categories": ["Climate and weather statistics", "Economic forecasting", "Futurology", "Informal estimation", "Macroeconomic forecasting", "Prediction", "Statistical forecasting"], "title": "Consensus forecast", "method": "Consensus forecast", "url": "https://en.wikipedia.org/wiki/Consensus_forecast", "summary": "Used in a number of sciences, ranging from econometrics to meteorology, consensus forecasts are predictions of the future that are created by combining together several separate forecasts which have often been created using different methodologies. Also known as combining forecasts, forecast averaging or model averaging (in econometrics and statistics) and committee machines, ensemble averaging or expert aggregation (in machine learning). Applications can range from forecasting the weather to predicting the annual Gross Domestic Product of a country or the number of cars a company or an individual dealer is likely to sell in a year. While forecasts are often made for future values of a time series, they can also be for one-off events such as the outcome of a presidential election or a football match.", "images": [], "links": ["Arithmetic mean", "Blue Chip Economic Indicators", "Cognitive bias", "Committee machine", "Consensus-based assessment", "Consensus Economics", "Consensus decision-making", "Consensus forecasts", "Delphi method", "Digital object identifier", "Econometrics", "Economic forecasting", "Empirical studies", "Ensemble averaging", "Forecast error", "Forecasting", "Global Energy Forecasting Competition", "Gross Domestic Product", "International Monetary Fund", "International Standard Serial Number", "JSTOR", "Machine learning", "Meteorology", "Organisation for Economic Co-operation and Development", "Prediction interval", "Probabilistic forecasting", "Quantile regression", "Quantile regression averaging", "Reference class forecasting", "Roy Batchelor", "Statistics", "Time series"], "references": ["http://www.consensuseconomics.com", "http://www.sciencedirect.com/science/article/pii/0169207089900125", "http://www.sciencedirect.com/science/article/pii/S1574070605010049", "http://onlinelibrary.wiley.com/doi/10.1002/jae.1192/abstract", "http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0084.2005.00148.x/abstract", "http://www.cnb.cz/miranda2/export/sites/www.cnb.cz/en/research/research_publications/cnb_wp/download/cnbwp_2010_14.pdf", "http://doi.org/10.1002%2Fjae.1192", "http://doi.org/10.1007%2Fs00180-014-0523-0", "http://doi.org/10.1016%2F0169-2070(89)90012-5", "http://doi.org/10.1016%2Fj.ijforecast.2008.05.001", "http://doi.org/10.1016%2Fs0169-2070(00)00057-1", "http://doi.org/10.1016%2Fs1574-0706(05)01004-9", "http://doi.org/10.1057%2Fpalgrave.imfsp.9450007", "http://doi.org/10.1080%2F00036840121785", "http://doi.org/10.1111%2Fj.1468-0084.2005.00148.x", "http://doi.org/10.3905%2Fjpm.2014.40.2.128", "http://www.jstor.org/stable/30036001", "http://www.worldcat.org/issn/0943-4062", "http://www.worldcat.org/issn/1099-1255", "http://www.worldcat.org/issn/1468-0084", "https://link.springer.com/article/10.1007/s00180-014-0523-0"]}, "Content validity": {"categories": ["Validity (statistics)"], "title": "Content validity", "method": "Content validity", "url": "https://en.wikipedia.org/wiki/Content_validity", "summary": "In psychometrics, content validity (also known as logical validity) refers to the extent to which a measure represents all facets of a given construct. For example, a depression scale may lack content validity if it only assesses the affective dimension of depression but fails to take into account the behavioral dimension. An element of subjectivity exists in relation to determining content validity, which requires a degree of agreement about what a particular personality trait such as extraversion represents. A disagreement about a personality trait will prevent the gain of a high content validity.", "images": [], "links": ["Affective", "Behavioral", "Construct validity", "Criterion validity", "Depression (mood)", "Donald Pennington", "Edward Arnold (publisher)", "Extraversion", "Face Validity", "Face validity", "International Standard Book Number", "Personality trait", "Psychometrics", "Statistical test", "Test validity", "Validity (statistics)"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.460.9380&rep=rep1&type=pdf"]}, "Jensen\u2013Shannon divergence": {"categories": ["CS1 Russian-language sources (ru)", "Statistical distance"], "title": "Jensen\u2013Shannon divergence", "method": "Jensen\u2013Shannon divergence", "url": "https://en.wikipedia.org/wiki/Jensen%E2%80%93Shannon_divergence", "summary": "In probability theory and statistics, the Jensen\u2013Shannon divergence is a method of measuring the similarity between two probability distributions. It is also known as information radius (IRad) or total divergence to the average. It is based on the Kullback\u2013Leibler divergence, with some notable (and useful) differences, including that it is symmetric and it is always a finite value. The square root of the Jensen\u2013Shannon divergence is a metric often referred to as Jensen-Shannon distance.", "images": [], "links": ["Advances in Neural Information Processing Systems", "Alexander Holevo", "ArXiv", "Bibcode", "Bioinformatics", "Bures metric", "Claude Shannon", "Density matrices", "Digital object identifier", "Fisher information metric", "Genome comparison", "Holevo's theorem", "International Standard Book Number", "Johan Jensen (mathematician)", "Kullback\u2013Leibler divergence", "Mathematical Reviews", "Metric (mathematics)", "Mixture distribution", "Mutual information", "Probability distribution", "Probability theory", "PubMed Central", "PubMed Identifier", "Pure states", "Quantum information", "Shannon entropy", "Sigma-algebra", "Statistics", "Von Neumann entropy", "Yoshua Bengio"], "references": ["http://www.mdpi.com/1099-4300/15/6/2246", "http://www.math.ku.dk/~topsoe/ISIT2004JSD.pdf", "http://adsabs.harvard.edu/abs/1994PhRvL..72.3439B", "http://adsabs.harvard.edu/abs/2005PhRvA..72e2310M", "http://adsabs.harvard.edu/abs/2009PNAS..106.2677S", "http://adsabs.harvard.edu/abs/2009PhRvA..79e2311B", "http://adsabs.harvard.edu/abs/2013Entrp..15.2246D", "http://adsabs.harvard.edu/abs/2014PNAS..111.9419K", "http://adsabs.harvard.edu/abs/2014arXiv1406.2661G", "http://citeseer.ist.psu.edu/dagan97similaritybased.html", "http://nlp.stanford.edu/fsnlp/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2634796", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2963821", "http://www.ncbi.nlm.nih.gov/pubmed/10056200", "http://www.ncbi.nlm.nih.gov/pubmed/12488102", "http://www.ncbi.nlm.nih.gov/pubmed/14684857", "http://www.ncbi.nlm.nih.gov/pubmed/19188606", "http://www.ncbi.nlm.nih.gov/pubmed/20841429", "http://arxiv.org/abs/0806.4472", "http://arxiv.org/abs/1009.4004", "http://arxiv.org/abs/1302.0907", "http://arxiv.org/abs/1406.2661", "http://arxiv.org/abs/cmp-lg/9708010", "http://arxiv.org/abs/quant-ph/0508138", "http://arxiv.org/archive/cs.CV", "http://doi.org/10.1007%2FBF02517812", "http://doi.org/10.1016%2Fs0022-2836(02)01223-8", "http://doi.org/10.1073%2Fpnas.0813249106", "http://doi.org/10.1073%2Fpnas.1405984111", "http://doi.org/10.1101%2Fgr.105072.110", "http://doi.org/10.1103%2FPhysRevA.72.052310", "http://doi.org/10.1103%2FPhysRevA.79.052311", "http://doi.org/10.1103%2FPhysRevLett.72.3439", "http://doi.org/10.1109%2F18.61115", "http://doi.org/10.1109%2FISIT.2004.1365067", "http://doi.org/10.1109%2FTIT.2003.813506", "http://doi.org/10.3115%2F979617.979625", "http://doi.org/10.3390%2Fe15062246", "http://ieeexplore.ieee.org/document/1365067", "http://www.pnas.org/content/111/26/9419.abstract", "http://thoth-python.org", "https://github.com/evansenter/diverge", "https://github.com/viveksck/langchangetrack/blob/master/langchangetrack/utils/entropy.py", "https://www.cise.ufl.edu/~anand/sp06/jensen-shannon.pdf", "https://mathscinet.ams.org/mathscinet-getitem?mr=456936", "https://arxiv.org/abs/1009.4004", "https://arxiv.org/abs/1406.2661", "https://cran.r-project.org/web/packages/statcomp/"]}, "Mazziotta\u2013Pareto index": {"categories": ["All orphaned articles", "Orphaned articles from February 2016", "Summary statistics"], "title": "Mazziotta\u2013Pareto index", "method": "Mazziotta\u2013Pareto index", "url": "https://en.wikipedia.org/wiki/Mazziotta%E2%80%93Pareto_index", "summary": "The Mazziotta\u2013Pareto index (MPI) is a composite index (OECD, 2008) for summarizing a set of individual indicators that are assumed to be not fully substitutable. It is based on a non-linear function which, starting from the arithmetic mean of the normalized indicators, introduces a penalty for the units with unbalanced values of the indicators (De Muro et al., 2011).\nTwo version of the index have been proposed: (a) MPI, and (b) adjusted MPI (AMPI). The first version is the best solution for a 'static' analysis (e.g., a single-year analysis), whereas the second one is the best solution for a 'dynamic' analysis (e.g., a multi-year analysis). For a comparison between the two versions, see Mazziotta and Pareto (2015).", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/6/6c/Wiki_letter_w.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Composite measure", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human development (humanity)", "Index (statistics)", "Index of dispersion", "Indicator (statistics)", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Matrix (mathematics)", "Maxima and minima", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean (statistics)", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normalization (statistics)", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Poverty", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quality of life", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Well-being", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://edwardbetts.com/find_link?q=Mazziotta%E2%80%93Pareto_index", "http://www.istat.it/it/files/2015/12/Rapporto_BES_2015.pdf"]}, "Skew normal distribution": {"categories": ["Continuous distributions", "Normal distribution", "Pages using deprecated image syntax"], "title": "Skew normal distribution", "method": "Skew normal distribution", "url": "https://en.wikipedia.org/wiki/Skew_normal_distribution", "summary": "In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Skew_normal_cdfs.svg", "https://upload.wikimedia.org/wikipedia/commons/6/63/Skew_normal_densities.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARGUS distribution", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Characteristic function (probability theory)", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Dagum distribution", "Data collection", "Davis distribution", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Error function", "Errors and residuals in statistics", "Estimating equations", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Experiment", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Exponentially modified Gaussian distribution", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "Geostatistics", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment-generating function", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Owen's T function", "Parabolic fractal distribution", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrix", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rice distribution", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Seven states of randomness", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Skellam distribution", "Skewness", "Slash distribution", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable distribution", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Tracy\u2013Widom distribution", "Trend estimation", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.tandfonline.com/doi/pdf/10.1080/02664760050120542", "http://dml.cz/bitstream/handle/10338.dmlcz/124493/Kybernetika_20-1984-2_1.pdf", "http://people.sc.fsu.edu/~burkardt/cpp_src/owens/owens.html", "http://azzalini.stat.unipd.it/SN/", "http://azzalini.stat.unipd.it/SN/Intro/intro.html", "http://dahoiv.net/master/index.html", "http://biomet.oxfordjournals.org/content/83/4/715.full.pdf"]}, "Exponential smoothing": {"categories": ["All articles with minor POV problems", "Articles with minor POV problems from July 2015", "Time series", "Use dmy dates from September 2011", "Wikipedia articles needing page number citations from September 2011"], "title": "Exponential smoothing", "method": "Exponential smoothing", "url": "https://en.wikipedia.org/wiki/Exponential_smoothing", "summary": "Exponential smoothing is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned and easily applied procedure for making some determination based on prior assumptions by the user, such as seasonality. Exponential smoothing is often used for analysis of time-series data.\nExponential smoothing is one of many window functions commonly applied to smooth data in signal processing, acting as low-pass filters to remove high frequency noise. This method is preceded by Poisson's use of recursive exponential window functions in convolutions from the 19th century, as well as Kolmogorov and Zurbenko's use of recursive moving averages from their studies of turbulence in the 1940s.\nThe raw data sequence is often represented by \n \n \n \n {\n \n x\n \n t\n \n \n }\n \n \n {\\displaystyle \\{x_{t}\\}}\n beginning at time \n \n \n \n t\n =\n 0\n \n \n {\\displaystyle t=0}\n , and the output of the exponential smoothing algorithm is commonly written as \n \n \n \n {\n \n s\n \n t\n \n \n }\n \n \n {\\displaystyle \\{s_{t}\\}}\n , which may be regarded as a best estimate of what the next value of \n \n \n \n x\n \n \n {\\displaystyle x}\n will be. When the sequence of observations begins at time \n \n \n \n t\n =\n 0\n \n \n {\\displaystyle t=0}\n , the simplest form of exponential smoothing is given by the formulas:\n \n \n \n \n \n \n \n \n s\n \n 0\n \n \n \n \n \n =\n \n x\n \n 0\n \n \n \n \n \n \n \n s\n \n t\n \n \n \n \n \n =\n \u03b1\n \n x\n \n t\n \n \n +\n (\n 1\n \u2212\n \u03b1\n )\n \n s\n \n t\n \u2212\n 1\n \n \n ,\n \n t\n >\n 0\n \n \n \n \n \n \n {\\displaystyle {\\begin{aligned}s_{0}&=x_{0}\\\\s_{t}&=\\alpha x_{t}+(1-\\alpha )s_{t-1},\\ t>0\\end{aligned}}}\n \nwhere \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n is the smoothing factor, and \n \n \n \n 0\n <\n \u03b1\n <\n 1\n \n \n {\\displaystyle 0<\\alpha <1}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Unbalanced_scales.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive moving average model", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Charles C. Holt", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continued fraction", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometric model", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential function", "F-test", "FIR filter", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forecasting", "Foresight: The International Journal of Applied Forecasting", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric progression", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Hadamard conjecture", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "IIR filter", "Index of dispersion", "Interaction (statistics)", "International Journal of Forecasting", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kolmogorov\u2013Zurbenko filter", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "LibreOffice", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Low-pass filter", "Lp space", "M-estimator", "Management Science: A Journal of the Institute for Operations Research and the Management Sciences", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Microsoft Excel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving average", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Noise", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Prentice Hall", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robert Goodell Brown", "Robust regression", "Robust statistics", "Rule of thumb", "Run chart", "SAP AG", "SPSS", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal processing", "Simple linear regression", "Simple moving average", "Simultaneous equations model", "Sim\u00e9on Denis Poisson", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The Wolfram Demonstrations Project", "Time constant", "Time domain", "Time series", "Tolerance interval", "Trend analysis", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Window function", "Window functions", "Z-test"], "references": ["http://www.real-statistics.com/time-series-analysis/basic-time-series-forecasting/excel-2016-forecasting-functions/", "http://robjhyndman.com/hyndsight/estimation2/", "http://help.sap.com/saphelp_45b/helpdata/en/7d/c27a14454011d182b40000e829fbfe/content.htm", "http://demonstrations.wolfram.com/DataSmoothing/", "http://people.duke.edu/~rnau/411avg.htm", "http://www.duke.edu/~rnau/411avg.htm", "http://legacy.library.ucsf.edu/tid/dae94e00;jsessionid=104A0CEFFA31ADC2FA5E0558F69B3E1D.tobacco03", "http://www.itl.nist.gov/div898/handbook/", "http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc431.htm", "http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc433.htm", "http://www.it.iitb.ac.in/~praj/acads/seminar/04329008_ExponentialSmoothing.pdf", "http://doi.org/10.1287%2Fmnsc.6.3.324", "http://forecasters.org/pdfs/foresight/free/Issue19_goodwin.pdf", "http://babel.hathitrust.org/cgi/pt?id=mdp.39015004514728;view=1up;seq=1", "http://mansci.journal.informs.org/cgi/content/abstract/6/3/324", "http://www.inside-r.org/packages/cran/forecast/docs/ets", "https://stat.ethz.ch/R-manual/R-patched/library/stats/html/HoltWinters.html", "https://labs.omniti.com/people/jesus/papers/holtwinters.pdf", "https://www.stata.com/help.cgi?tssmooth", "https://web.archive.org/web/20150623211648/http://www.eckner.com/papers/ts_alg.pdf", "https://web.archive.org/web/20160716153135/http://www.inside-r.org/packages/cran/forecast/docs/ets", "https://wiki.documentfoundation.org/ReleaseNotes/5.2#New_spreadsheet_functions", "https://doi.org/10.1016/j.ijforecast.2003.09.015", "https://www.otexts.org/fpp/7/1"]}, "Writer invariant": {"categories": ["All stub articles", "CS1 maint: Multiple names: authors list", "Computational linguistics stubs", "Literature stubs", "Statistical natural language processing"], "title": "Writer invariant", "method": "Writer invariant", "url": "https://en.wikipedia.org/wiki/Writer_invariant", "summary": "Writer invariant, also called authorial invariant or author's invariant, is a property of a text which is invariant of its author, that is, it will be similar in all texts of a given author and different in texts of different authors. It can be used to find plagiarism or discover who is real author of anonymously published text. Writer invariant is also an author's pattern of writing a letter in handwritten text recognition.While it is generally recognised that writer invariants exist, it is not agreed what properties of a text should be used. Among the first ones used was distribution of word lengths; other proposed invariants include average sentence length, average word length, noun, verb or adjective usage frequency, vocabulary richness, and frequency of function words, or specific function words.Of these, average sentence lengths can be very similar in works of different authors or vary significantly even within a single work; average word lengths likewise turn out to be very similar in works of different authors. Analysis of function words shows promise because they are used by authors unconsciously.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/91/LampFlowchart.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1d/P_literature.svg"], "links": ["Adjective", "Anatoly Timofeevich Fomenko", "Anonymous work", "Author", "Computational linguistics", "Digital object identifier", "Function word", "Handwriting", "International Standard Book Number", "Noun", "Plagiarism", "Sentence (linguistics)", "Stylometry", "Text recognition", "The American Statistician", "The Semiotic Review of Books", "Verb", "Vocabulary", "Word", "Writeprint"], "references": ["http://www.chass.utoronto.ca/epc/srb/srb/foresem.html", "http://www.biostat.jhsph.edu/~rpeng/papers/archive/authorship-tas2-final.pdf", "http://www.univ-rouen.fr/psi/heutte/download/ewhar98nosary.pdf", "http://doi.org/10.1198/000313002100"]}, "Fourier analysis": {"categories": ["CS1 maint: Explicit use of et al.", "Digital signal processing", "Fourier analysis", "Integral transforms", "Joseph Fourier", "Mathematical physics", "Mathematics of computing", "Time series", "Use dmy dates from April 2012"], "title": "Fourier analysis", "method": "Fourier analysis", "url": "https://en.wikipedia.org/wiki/Fourier_analysis", "summary": "In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer.\nToday, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize the same sound by including the frequency components as revealed in the Fourier analysis. In mathematics, the term Fourier analysis often refers to the study of both operations.\nThe decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends on the domain and other properties of the function being transformed. Moreover, the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, and the general field is often known as harmonic analysis. Each transform used for analysis (see list of Fourier-related transforms) has a corresponding inverse transform that can be used for synthesis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a6/Bass_Guitar_Time_Signal_of_open_string_A_note_%2855_Hz%29.png", "https://upload.wikimedia.org/wikipedia/commons/0/08/Fourier_Transform_of_bass_guitar_time_signal.png", "https://upload.wikimedia.org/wikipedia/commons/c/ca/Fourier_transform%2C_Fourier_series%2C_DTFT%2C_DFT.gif"], "links": ["2 Pallas", "3 Juno", "Abelian group", "Acoustics", "Alexis Clairaut", "Aliasing", "Amplitude", "Anisotropic", "ArXiv", "Asteroid", "Audrey Terras", "Automatic control", "Babylonian mathematics", "Bandpass filter", "Basis vector", "Bibcode", "Bispectrum", "Brady Haran", "Cambridge University Press", "Carl Friedrich Gauss", "Characteristic function (probability theory)", "Chirplet transform", "CiteSeerX", "Coefficients", "Combinatorics", "Complex exponentials", "Constant coefficients", "Continuous time", "Continuous wavelet transform", "Convolution", "Convolution theorem", "Cooley\u2013Tukey FFT algorithm", "Cross correlation", "Cryptography", "Daniel Bernoulli", "Deferent and epicycle", "Derivative", "Dictionary.com", "Differential equation", "Diffraction", "Digital image processing", "Digital object identifier", "Digital signal processing", "Dirac comb", "Dirac delta", "Discrete-time Fourier transform", "Discrete Fourier transform", "Discrete Fourier transform (general)", "Discrete cosine transform", "Discrete sine transform", "Dover Publications", "Eigenfunction", "Ephemerides", "Equalization (audio)", "Exponential function", "FIR filter", "Fast Fourier Transform", "Fast Fourier transform", "Forensics", "Fourier-Bessel series", "Fourier-related transforms", "Fourier series", "Fourier transform", "Fourier transform ion cyclotron resonance", "Fourier transformation", "Fractional Fourier transform", "Frequency", "Frequency spectrum", "Function (mathematics)", "Gabor transform", "Generalized Fourier series", "Geometry", "Gian-Carlo Rota", "Harmonic", "Harmonic analysis", "Heat conduction", "Heat equation", "Heat transfer", "Image processing", "Infrared spectroscopy", "International Standard Book Number", "International Standard Serial Number", "Inverse function", "JPEG", "Jaggies", "Jean le Rond d'Alembert", "Joseph Fourier", "Joseph Louis Lagrange", "LTI system", "Lagrange resolvents", "Laplace transform", "Least-squares spectral analysis", "Leonhard Euler", "Linear operator", "Lis Brack-Bernsen", "List of Fourier-related transforms", "Locally compact", "Magnitude (mathematics)", "Mathematics", "Mellin transform", "Multiplication algorithm", "M\u00e9moire sur la propagation de la chaleur dans les corps solides", "Non-uniform discrete Fourier transform", "Nuclear magnetic resonance", "Number-theoretic transform", "Number theory", "Numerical analysis", "Nyquist\u2013Shannon sampling theorem", "OCLC", "Oceanography", "Optics", "Option pricing", "Orthogonal functions", "Orthogonal system", "Otto E. Neugebauer", "Parseval's theorem", "Partial differential equation", "Periodic summation", "Phase (waves)", "Physics", "Plancherel theorem", "Poisson summation formula", "Polynomial", "Pontryagin duality", "Precision (arithmetic)", "Probability theory", "Protein", "Ptolemaic system", "PubMed Identifier", "Quantum Fourier transform", "Radio frequency interference", "Radio scanner", "Radio wave", "Random House", "Real number", "Representation theory", "Root of unity", "R\u00e9flexions sur la r\u00e9solution alg\u00e9brique des \u00e9quations", "Schwartz space", "Seismic wave", "Short-time Fourier transform", "Signal (information theory)", "Signal processing", "Sine wave", "Sonar", "Sound", "Spectral density", "Spectral density estimation", "Spectral music", "Spectrogram", "Statistics", "Strip aerial photography", "Superheterodyne", "The Art of Computer Programming", "Time series", "Time\u2013frequency analysis", "Topological group", "Transform (mathematics)", "Trigonometric functions", "Trigonometric interpolation", "Trigonometric series", "Two-sided Laplace transform", "Uncertainty principle", "Unitary operator", "University of Nottingham", "Wavelet", "Wavelet transforms", "Whittaker\u2013Shannon interpolation formula", "Window function", "X-ray crystallography"], "references": ["http://www.dictionary.com/browse/Fourier", "http://www.dspguide.com/pdfbook.htm", "http://www.sixtysymbols.com/videos/summation.htm", "http://onlinelibrary.wiley.com/doi/10.1029/1998RG900006/pdf", "http://www.music-processing.de", "http://cns-alumni.bu.edu/~slehar/fourier/fourier.html", "http://adsabs.harvard.edu/abs/1999RvGeo..37..151N", "http://adsabs.harvard.edu/abs/2004IJMPE..13..247B", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.455.4798", "http://www.ncbi.nlm.nih.gov/pubmed/28413352", "http://arxiv.org/abs/physics/0310126", "http://doi.org/10.1007%2F978-3-319-21945-5", "http://doi.org/10.1029%2F1998RG900006", "http://doi.org/10.1142%2FS0218301304002028", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1162257", "http://www.worldcat.org/issn/1944-9208", "http://www.worldcat.org/oclc/5156426043", "http://eqworld.ipmnet.ru/en/auxiliary/aux-inttrans.htm", "https://books.google.com/?id=-B2TA669dJMC&pg=PA30#PPA30,M1", "https://books.google.com/?id=JVhTtVA2zr8C", "https://books.google.com/?id=coq49_LRURUC&pg=PA2#PPA2,M1", "https://books.google.com/books?id=-B2TA669dJMC&pg=PA30#PPA31,M1", "https://books.google.com/books?id=H5smrEExNFUC&pg=PA11", "https://books.google.com/books?id=KVeXG163BggC&pg=PA501", "https://books.google.com/books?id=coq49_LRURUC&pg=PA2#PPA4,M1", "https://books.google.com/books?id=fye--TBu4T0C&pg=PA62", "https://www.audiolabs-erlangen.de/content/05-fau/professor/00-mueller/04-bookFMP/2015_Mueller_FundamentalsMusicProcessing_Springer_Section2-1_SamplePages.pdf", "https://www.ncbi.nlm.nih.gov/pubmed/28413352", "https://archive.org/details/Lectures_on_Image_Processing", "https://pdfs.semanticscholar.org/cc88/4713a9a7b6fe009fbcaaafcf594b9579c586.pdf"]}, "Dilution assay": {"categories": ["Biostatistics", "Drug discovery", "Pharmaceutical industry"], "title": "Dilution assay", "method": "Dilution assay", "url": "https://en.wikipedia.org/wiki/Dilution_assay", "summary": "The term dilution assay is generally used to designate a special type of bioassay in which one or more preparations (e.g. a drug) are administered to experimental units at different dose levels inducing a measurable biological response. The dose levels are prepared by dilution in a diluent that is inert in respect of the response. The experimental units can for example be cell-cultures, tissues, organs or living animals. The biological response may be quantal (e.g. positive/negative) or quantitative (e.g. growth). The goal is to relate the response to the dose, usually by interpolation techniques, and in many cases to express the potency/activity of the test preparation(s) relative to a standard of known potency/activity.\nDilution assays can be direct or indirect. In a direct dilution assay the amount of dose needed to produce a specific (fixed) response is measured, so that the dose is a stochastic variable defining the tolerance distribution. Conversely, in an indirect dilution assay the dose levels are administered at fixed dose levels, so that the response is a stochastic variable.", "images": ["https://upload.wikimedia.org/wikipedia/en/1/16/DilutionAssay.png"], "links": ["Agar", "Antibiotic", "Binomial distribution", "Bioassay", "Continuous function", "Fieller's theorem", "Generalized linear models", "International Standard Book Number", "Interpolation", "Linear function", "Maximum Likelihood", "Microorganism", "Monotone function", "Normal distribution", "Parametric family of functions", "Petri dish", "Probit model"], "references": ["http://www.cambridgesoft.com/software/details/?ds=12&dsv=85", "http://www.unistat.com", "http://www.bioassay.de", "http://combistats.edqm.eu"]}, "Index of dispersion": {"categories": ["Point processes", "Statistical deviation and dispersion", "Statistical randomness", "Statistical ratios"], "title": "Index of dispersion", "method": "Index of dispersion", "url": "https://en.wikipedia.org/wiki/Index_of_dispersion", "summary": "In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.\nIt is defined as the ratio of the variance \n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n {\\displaystyle \\sigma ^{2}}\n to the mean \n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n ,\n\n \n \n \n D\n =\n \n \n \n \u03c3\n \n 2\n \n \n \u03bc\n \n \n .\n \n \n {\\displaystyle D={\\sigma ^{2} \\over \\mu }.}\n It is also known as the Fano factor, though this term is sometimes reserved for windowed data (the mean and variance are computed over a subpopulation), where the index of dispersion is used in the special case where the window is infinite. Windowing data is frequently done: the VMR is frequently computed over various intervals in time or small regions in space, which may be called \"windows\", and the resulting statistic called the Fano factor.\nIt is only defined when the mean \n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n is non-zero, and is generally only used for positive statistics, such as count data or time between events, or where the underlying distribution is assumed to be the exponential distribution or Poisson distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Mathematical Statistics", "Arithmetic mean", "Arthur Roy Clapham", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brownian motion", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Conic sections", "Constant random variable", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Eccentricity (mathematics)", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fano factor", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric distribution", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the Royal Statistical Society, Series C", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Lexis ratio", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Negative binomial distribution", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normalization (statistics)", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Overdispersion", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Paul G. Hoel", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson process", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random walk", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal processing", "Signal to noise ratio", "Signal to noise ratio (image processing)", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standardized moment", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1214%2Faoms%2F1177731457", "http://www.jstor.org/stable/2235818", "http://www.jstor.org/stable/2347079"]}, "Quadrat": {"categories": ["Articles with short description", "Ecology terminology", "Environmental statistics"], "title": "Quadrat", "method": "Quadrat", "url": "https://en.wikipedia.org/wiki/Quadrat", "summary": "A quadrat is a frame, traditionally square, used in ecology and geography to isolate a standard unit of area for study of the distribution of an item over a large area. Modern quadrats can for example be rectangular, circular, or irregular. The quadrat is suitable for sampling plants, slow-moving animals, and some aquatic organisms.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/59/Quadrat_sample.JPG"], "links": ["Arthur Tansley", "Bias", "Differential GPS", "Digital object identifier", "Ecological succession", "Ecologist", "Ecology", "F. E. Clements", "GPS", "Geography", "Habitat", "JSTOR", "Plants", "Quadrat (disambiguation)", "Sampling (statistics)", "Stand level modelling", "Total station"], "references": ["http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2011.00118.x/abstract", "http://doi.org/10.1111%2Fj.2041-210X.2011.00118.x", "http://www.jstor.org/stable/43477708", "http://www.countrysideinfo.co.uk/howto.htm", "http://www.saps.org.uk/secondary/teaching-resources/260-questions-about-quadrats", "https://archive.org/details/cu31924001717820", "https://archive.org/details/newphytologist3190tans", "https://archive.org/details/phytogeographyn00poungoog"]}, "Poly-Weibull distribution": {"categories": ["All stub articles", "Continuous distributions", "Statistics stubs", "Survival analysis"], "title": "Poly-Weibull distribution", "method": "Poly-Weibull distribution", "url": "https://en.wikipedia.org/wiki/Poly-Weibull_distribution", "summary": "In probability theory and statistics, the poly-Weibull distribution is a continuous probability distribution. The distribution is defined to be that of a random variable defined to be the smallest of a number of statistically independent random variables having non-identical Weibull distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the American Statistical Association", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.stat.purdue.edu/research/technical_reports/pdfs/1992/tr92-05c.pdf", "http://doi.org/10.1080%2F01621459.1993.10476426", "http://www.jstor.org/stable/2291285"]}, "Random walk": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from February 2013", "Articles with unsourced statements from April 2012", "Articles with unsourced statements from April 2013", "CS1 maint: Multiple names: authors list", "Stochastic processes", "Use dmy dates from September 2010", "Variants of random walks", "Wikipedia articles with NDL identifiers"], "title": "Random walk", "method": "Random walk", "url": "https://en.wikipedia.org/wiki/Random_walk", "summary": "A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers. An elementary example of a random walk is the random walk on the integer number line, \n \n \n \n \n Z\n \n \n \n {\\displaystyle \\mathbb {Z} }\n , which starts at 0 and at each step moves +1 or \u22121 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be approximated by random walk models, even though they may not be truly random in reality. As illustrated by those examples, random walks have applications to many scientific fields including ecology, psychology, computer science, physics, chemistry, biology as well as economics. Random walks explain the observed behaviors of many processes in these fields, and thus serve as a fundamental model for the recorded stochastic activity. As a more mathematical application, the value of \u03c0 can be approximated by the use of random walk in an agent-based modeling environment. The term random walk was first introduced by Karl Pearson in 1905.Various types of random walks are of interest, which can differ in several ways. The term itself most often refers to a special category of Markov chains or Markov processes, but many time-dependent processes are referred to as random walks, with a modifier indicating their specific properties. Random walks (Markov or not) can also take place on a variety of spaces: commonly studied ones include graphs, others on the integers or the real line, in the plane or higher-dimensional vector spaces, on curved surfaces or higher-dimensional Riemannian manifolds, and also on groups finite, finitely generated or Lie. The time parameter can also be manipulated. In the simplest context the walk is in discrete time, that is a sequence of random variables (Xt) = (X1, X2, ...) indexed by the natural numbers. However, it is also possible to define random walks which take their steps at random times, and in that case, the position Xt has to be defined for all times t \u2208 [0,+\u221e). Specific cases or limits of random walks include the L\u00e9vy flight and diffusion models such as Brownian motion.\nRandom walks are a fundamental topic in discussions of Markov processes. Their mathematical study has been extensive. Several properties, including dispersal distributions, first-passage or hitting times, encounter rates, recurrence or transience, have been introduced to quantify their behavior.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3c/Antony_Gormley_Quantum_Cloud_2000.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a7/Brownian_hierarchical.png", "https://upload.wikimedia.org/wikipedia/commons/2/28/Eight-step_random_walks.png", "https://upload.wikimedia.org/wikipedia/commons/0/05/Flips.svg", "https://upload.wikimedia.org/wikipedia/commons/1/18/Random_walk_2000000.png", "https://upload.wikimedia.org/wikipedia/commons/7/7c/Random_walk_2500.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ea/Random_walk_25000_not_animated.svg", "https://upload.wikimedia.org/wikipedia/commons/b/bd/Walk3d_0.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost surely", "Anomalous diffusion", "Antony Gormley", "ArXiv", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bacterial motility", "Beno\u00eet Mandelbrot", "Bernoulli process", "Bessel process", "Biased random walk (biochemistry)", "Biased random walk on a graph", "Bibcode", "Big O notation", "Biology", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes", "Black\u2013Scholes model", "Boolean network", "Branching process", "Branching random walk", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Cayley graph", "Central limit theorem", "Chemistry", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Combinatorics", "Compound Poisson process", "Computer science", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Coordinate system", "Correlation and dependence", "Coupling (probability)", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Dave Bayer", "Detailed balance", "Diffusion", "Diffusion-limited aggregation", "Diffusion equation", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Ecology", "Econometrics", "Economics", "Electrical networks", "Electrical resistance", "Empirical process", "Entropy rate", "Erd\u0151s\u2013R\u00e9nyi model", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Expected value", "Exploration process", "Extreme value theory", "Factorial", "Feller-continuous process", "Feller process", "Fermi estimation", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Financial economics", "Finitely generated group", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fixational eye movements", "Fleming\u2013Viot process", "Fluid queue", "Foraging", "Fractal", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gambler", "Gambler's ruin", "Gambling", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Genetic drift", "Geometric Brownian motion", "George Herbert Weiss", "George P\u00f3lya", "Gibbs measure", "Girsanov theorem", "Glossary of group theory", "Graph (discrete mathematics)", "Graph theory", "Green's function", "Greg Lawler", "Group (mathematics)", "Group theory", "Harmonic measure", "Hausdorff dimension", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Human brain", "Hunt process", "Ideal chain", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Integer", "Interacting particle system", "International Standard Book Number", "Ising model", "Isoperimetric dimension", "Isoperimetry", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Karl Pearson", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Koml\u00f3s\u2013Major\u2013Tusn\u00e1dy approximation", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Laplace's equation", "Large deviation principle", "Large deviations theory", "Lattice path", "Law of large numbers", "Law of the iterated logarithm", "Lie group", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "London", "Loop-erased random walk", "L\u00e9vy flight", "L\u00e9vy flight foraging hypothesis", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Manifold", "Map-territory relation", "Markov Chain Monte Carlo", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Materials science", "Mathematical", "Mathematical Association of America", "Mathematical Reviews", "Mathematical analysis", "Mathematical finance", "Mathematical statistics", "Mathematische Annalen", "Matrix (mathematics)", "Maximal Entropy Random Walk", "Maximal entropy random walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Molecule", "Molecules", "Moran process", "Motion (physics)", "Moving-average model", "Multiagent random walk", "National Diet Library", "Nira Dyn", "Non-homogeneous Poisson process", "Normal distribution", "Oded Schramm", "Ohm (unit)", "Online social network", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Pascal's triangle", "Percolation theory", "Permanent (mathematics)", "Persi Diaconis", "Physics", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Planar graph", "Plane (mathematics)", "Poincar\u00e9 inequality", "Point process", "Poisson point process", "Poisson process", "Polymer physics", "Polymers", "Population dynamics", "Population genetics", "Potts model", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Psychology", "PubMed Central", "PubMed Identifier", "Quadratic variation", "Quantum Cloud", "Quantum field theory", "Queueing model", "Queueing theory", "Random", "Random Walk", "Random Walk Hypothesis", "Random dynamical system", "Random field", "Random graph", "Random process", "Random variable", "Random walk hypothesis", "Random walker (computer vision)", "Rayleigh distribution", "Reflection principle (Wiener process)", "Regenerative process", "Regular graph", "Reinforced random walk", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Riemannian manifold", "Risk process", "Root mean square", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sampling (statistics)", "Sanov's theorem", "Scaling limit", "Schramm\u2013Loewner evolution", "Segmentation (image processing)", "Self-avoiding walk", "Self-similar process", "Self-similarity", "Semimartingale", "Series (mathematics)", "Share price", "Shlomo Havlin", "Shuffle", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sobolev inequality", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistical independence", "Statistical model", "Statistics", "Stirling formula", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Sum of normally distributed random variables", "Supermartingale", "Superprocess", "Surface (differential geometry)", "Symmetric group", "Symmetry", "System on a chip", "Tanaka equation", "Telegraph process", "Theoretical biology", "Time reversibility", "Time series", "Time series analysis", "Toshikazu Sunada", "Uniform integrability", "Unit root", "Usual hypotheses", "Variance", "Variance gamma process", "Vasicek model", "Vision science", "Wendelin Werner", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "William Feller", "Wireless networking", "Www"], "references": ["http://vlab.infotech.monash.edu.au/simulations/swarms/random-walk/", "http://fr.mathworks.com/matlabcentral/fileexchange/56869-random-walk-estimator", "http://demonstrations.wolfram.com/ElectronConductanceModelsUsingMaximalEntropyRandomWalks/", "http://library.wolfram.com/infocenter/MathSource/9281/", "http://mathworld.wolfram.com/PolyasRandomWalkConstants.html", "http://mathworld.wolfram.com/RandomWalk1-Dimensional.html", "http://www.emis.de/journals/PS/images/getdoc9b04.pdf?id=432&article=94&mode=pdf", "http://www.kyb.mpg.de/fileadmin/user_upload/files/publications/attachments/AlamgirLuxburg2010_%5B0%5D.pdf", "http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0084&DMDID=DMDLOG_0016&L=1", "http://cns-web.bu.edu/~lgrady/grady2006random.pdf", "http://www.math.cornell.edu/~lawler/book.ps", "http://engineering.dartmouth.edu/~d30345d/courses/engs43/Chapter2.pdf", "http://adsabs.harvard.edu/abs/1905Natur..72..294P", "http://adsabs.harvard.edu/abs/1984JChPh..81..584H", "http://adsabs.harvard.edu/abs/1986PCMLD...1..199B", "http://adsabs.harvard.edu/abs/1992Natur.355..396S", "http://adsabs.harvard.edu/abs/1992Natur.355..423L", "http://adsabs.harvard.edu/abs/1992Natur.356..168P", "http://adsabs.harvard.edu/abs/1992PhRvA..45.7128L", "http://adsabs.harvard.edu/abs/1993PhRvL..70.1343P", "http://adsabs.harvard.edu/abs/1997PhyA..245..437L", "http://adsabs.harvard.edu/abs/1998PhRvL..81..729K", "http://adsabs.harvard.edu/abs/2011PNAS..108E.765E", "http://adsabs.harvard.edu/abs/2016ISPAr49B2..491W", "http://adsabs.harvard.edu/abs/2016JPhA...49B5002T", "http://nebula.physics.uakron.edu/dept/faculty/jutta/modeling/diff_eqn.pdf", "http://oz.ss.uci.edu/237/readings/EBRW_nosofsky_1997.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2504494", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3182695", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4385455", "http://www.ncbi.nlm.nih.gov/pubmed/10054352", "http://www.ncbi.nlm.nih.gov/pubmed/1301010", "http://www.ncbi.nlm.nih.gov/pubmed/17063682", "http://www.ncbi.nlm.nih.gov/pubmed/17742050", "http://www.ncbi.nlm.nih.gov/pubmed/21873243", "http://www.ncbi.nlm.nih.gov/pubmed/25698649", "http://www.ncbi.nlm.nih.gov/pubmed/9127583", "http://havlin.biu.ac.il/Publications.php?keyword=Indication+of+a+universal+persistence+law+governing+atmospheric+variability&year=*&match=all", "http://havlin.biu.ac.il/Publications.php?keyword=Long-range+correlations+in+nucleotide+sequences&year=*&match=all", "http://havlin.biu.ac.il/Publications.php?keyword=Long-range+anticorrelations+and+non-gaussian+behavior+of+the+heartbeat&year=*&match=all", "http://havlin.biu.ac.il/Shlomo%20Havlin%20books_d_r.php", "http://www.kisc.meiji.ac.jp/~tz14040/quantumwalk/english/", "http://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XLI-B2/491/2016/", "http://dl.acm.org/citation.cfm?id=2488433", "http://www.ams.org/mathscinet-getitem?mr=0920811", "http://www.ams.org/mathscinet-getitem?mr=1280031", "http://arxiv.org/abs/1603.06613", "http://arxiv.org/abs/cond-mat/9706021", "http://arxiv.org/abs/math.PR/0001057", "http://arxiv.org/abs/math/0610076", "http://doi.org/10.1002%2F9780470142769.ch5", "http://doi.org/10.1007%2F978-94-009-4650-7_5", "http://doi.org/10.1007%2Fs00209-006-0951-9", "http://doi.org/10.1016%2FS0378-4371(97)00368-3", "http://doi.org/10.1016%2Fj.tins.2015.01.005", "http://doi.org/10.1037%2F0033-295x.104.2.266", "http://doi.org/10.1038%2F072294b0", "http://doi.org/10.1038%2F355396a0", "http://doi.org/10.1038%2F355423a0", "http://doi.org/10.1038%2F356168a0", "http://doi.org/10.1051%2Fjphyslet:019820043017062500", "http://doi.org/10.1051%2Fjphyslet:0198300440101300", "http://doi.org/10.1063%2F1.447349", "http://doi.org/10.1073%2Fpnas.1102730108", "http://doi.org/10.1088%2F1751-8113%2F49%2F28%2F285002", "http://doi.org/10.1090%2Fconm%2F338%2F06077", "http://doi.org/10.1098%2Frsif.2008.0014", "http://doi.org/10.1103%2FPhysRevA.45.7128", "http://doi.org/10.1103%2FPhysRevLett.70.1343", "http://doi.org/10.1103%2FPhysRevLett.81.729", "http://doi.org/10.1109%2FTPAMI.2006.233", "http://doi.org/10.1126%2Fscience.290.5498.1883", "http://doi.org/10.1214%2F07-PS094", "http://doi.org/10.2307%2F2332328", "http://doi.org/10.2307%2F2334030", "http://doi.org/10.5194%2Fisprs-archives-xli-b2-491-2016", "http://rsif.royalsocietypublishing.org/content/5/25/813#sec-13", "http://www.sciencemag.org/cgi/content/full/sci;290/5498/1883", "http://upload.wikimedia.org/wikipedia/commons/c/cb/Random_walk_25000.svg", "http://upload.wikimedia.org/wikipedia/commons/f/f3/Random_walk_2500_animated.svg", "https://books.google.com/books?id=sWiyspAjelsC&pg=PP2", "https://www.stat.berkeley.edu/users/aldous/RWG/book.html", "https://id.ndl.go.jp/auth/ndlna/00571555", "https://web.archive.org/web/20040921020230/http://stat-www.berkeley.edu/users/aldous/RWG/book.html", "https://web.archive.org/web/20041210231937/http://oz.ss.uci.edu/237/readings/EBRW_nosofsky_1997.pdf", "https://arxiv.org/abs/0810.4113", "https://arxiv.org/abs/1606.01560", "https://arxiv.org/abs/1611.02861", "https://www.wikidata.org/wiki/Q856741", "https://zenodo.org/record/1233119/files/article.pdf"]}, "Clustering high-dimensional data": {"categories": ["Cluster analysis"], "title": "Clustering high-dimensional data", "method": "Clustering high-dimensional data", "url": "https://en.wikipedia.org/wiki/Clustering_high-dimensional_data", "summary": "Clustering high-dimensional data is the cluster analysis of data with anywhere from a few dozen to many thousands of dimensions. Such high-dimensional spaces of data are often encountered in areas such as medicine, where DNA microarray technology can produce a large number of measurements at once, and the clustering of text documents, where, if a word-frequency vector is used, the number of dimensions equals the size of the vocabulary.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/86/SubspaceClustering.png", "https://upload.wikimedia.org/wikipedia/commons/archive/8/86/20090422154835%21SubspaceClustering.png"], "links": ["Affine subspace", "Association rule learning", "Biclustering", "Bioinformatics", "Cluster analysis", "Correlated", "Correlation clustering", "Curse of dimensionality", "DBSCAN", "DNA microarray", "Digital object identifier", "Dimension", "Distance function", "ELKI", "Hans-Peter Kriegel", "Heaps' law", "Heuristic", "High-dimensional space", "International Standard Book Number", "K-medoid", "Medicine", "Newborn screening", "Partitioning Around Medoids", "Pattern", "SUBCLU", "Text document", "Variance"], "references": ["http://www.dbs.ifi.lmu.de/~zimek/publications/SSDBM2010/SNN-SSDBM2010-preprint.pdf", "http://doi.org/10.1007%2F978-3-642-13818-8_34", "http://doi.org/10.1007%2Fs10618-005-1396-1", "http://doi.org/10.1007%2Fs40708-016-0043-5", "http://doi.org/10.1016%2Fj.patcog.2011.08.012", "http://doi.org/10.1109%2FICDM.2004.10087", "http://doi.org/10.1109%2FICDM.2005.5", "http://doi.org/10.1109%2Fictai.2014.48", "http://doi.org/10.1137%2F1.9781611972740.23", "http://doi.org/10.1145%2F1497577.1497578", "http://doi.org/10.1145%2F304181.304188", "http://doi.org/10.5220%2F0005367106030608", "http://dx.doi.org/10.1109/ictai.2014.48", "http://dx.doi.org/10.5220/0005367106030608"]}, "Weighted median": {"categories": ["All stub articles", "Means", "Robust statistics", "Statistics stubs"], "title": "Weighted median", "method": "Weighted median", "url": "https://en.wikipedia.org/wiki/Weighted_median", "summary": "In statistics, a weighted median of a sample is the 50% weighted percentile. It was first proposed by F. Y. Edgeworth in 1888. Like the median, it is useful as an estimator of central tendency, robust against outliers. It allows for non-uniform statistical weights related to, e.g., varying precision measurements in the sample.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Weighted_median.svg"], "links": ["Central tendency", "Digital object identifier", "F. Y. Edgeworth", "International Standard Book Number", "JSTOR", "Least absolute deviations", "Median filter", "Outliers", "Quickselect", "Robust statistics", "Statistics", "Weighted arithmetic mean", "Weighted percentile"], "references": ["http://doi.org/10.1080/14786448808628170", "http://www.jstor.org/stable/23036355", "https://books.google.com/books?id=AtiDhx2bsiMC&pg=PA313&lpg=PA313&dq=edgeworth+weighted+median&source=bl&ots=SFoKs-I0J4&sig=CimqUDnGiBlYO6BtdxU7s-Xp5B8&hl=en&sa=X&ved=0ahUKEwjr4Py6t-fUAhXDGz4KHdVvBYAQ6AEIMTAD#v=onepage&q=edgeworth%20weighted%20median&f=false", "https://books.google.com/books?id=NLngYyWFl_YC&lpg=PA194&dq=weighted%20median&pg=PA194#v=onepage&q=weighted%20median&f=false", "https://books.google.com/books?id=UM_GCfJe88sC&lpg=PA111&dq=weighted%20median&pg=PA111#v=onepage&q=weighted%20median&f=false", "https://books.google.com/books?id=q1FKJ6l0_zUC&lpg=PA693&dq=weighted%20median&pg=PA693#v=onepage&q=weighted%20median&f=false"]}, "Regression fallacy": {"categories": ["All articles needing additional references", "Articles needing additional references from July 2010", "Causal fallacies", "Cognitive biases", "Misuse of statistics", "Pseudoscience"], "title": "Regression fallacy", "method": "Regression fallacy", "url": "https://en.wikipedia.org/wiki/Regression_fallacy", "summary": "The regression (or regressive) fallacy is an informal fallacy. It assumes that something has returned to normal because of corrective actions taken while it was abnormal. This fails to account for natural fluctuations. It is frequently a special kind of the post hoc fallacy.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["Accident (fallacy)", "Ambiguity", "Anecdotal evidence", "Animistic fallacy", "Argument from analogy", "Base rate fallacy", "Begging the question", "Cherry picking", "Circular reasoning", "Complex question", "Conjunction fallacy", "Continuum fallacy", "Converse accident", "Correlation does not imply causation", "Correlative-based fallacies", "Danny Quah", "Denying the correlative", "Digital object identifier", "Double-barreled question", "Double counting (fallacy)", "Ecological fallacy", "Equivocation", "Fallacies of illicit transference", "Fallacy", "Fallacy of accent", "Fallacy of composition", "Fallacy of division", "Fallacy of the single cause", "False attribution", "False dilemma", "False equivalence", "False precision", "Faulty generalization", "Francis Galton", "Furtive fallacy", "Gambler's fallacy", "Informal fallacy", "International Standard Book Number", "Inverse gambler's fallacy", "JSTOR", "Jinx", "Just-so story", "Leading question", "List of fallacies", "Loaded language", "Loaded question", "Loki's Wager", "McNamara fallacy", "Milton Friedman", "Moving the goalposts", "Nirvana fallacy", "No true Scotsman", "Overwhelming exception", "Post hoc ergo propter hoc", "Post hoc fallacy", "Questionable cause", "Quoting out of context", "Regression toward the mean", "Reification (fallacy)", "Representativeness heuristic", "Sampling bias", "Scott Plous", "Secundum quid", "Slippery slope", "Slothful induction", "Sorites paradox", "Sports Illustrated", "Sports Illustrated cover jinx", "Suppressed correlative", "Syntactic ambiguity", "Texas sharpshooter fallacy", "Thomas Gilovich", "Vagueness"], "references": ["http://www.newyorker.com/reporting/2010/12/13/101213fa_fact_lehrer", "http://doi.org/10.1037%2F0022-3514.48.6.1377", "http://www.fallacyfiles.org/regressf.html", "http://www.jstor.org/stable/2727976", "http://www.jstor.org/stable/3440905"]}, "Kernel smoother": {"categories": ["Nonparametric statistics"], "title": "Kernel smoother", "method": "Kernel smoother", "url": "https://en.wikipedia.org/wiki/Kernel_smoother", "summary": "A kernel smoother is a statistical technique to estimate a real valued function \n \n \n \n f\n :\n \n \n R\n \n \n p\n \n \n \u2192\n \n R\n \n \n \n {\\displaystyle f:\\mathbb {R} ^{p}\\to \\mathbb {R} }\n as the weighted average of neighboring observed data. The weight is defined by the kernel, such that closer points are given higher weights. The estimated function is smooth, and the level of smoothness is set by a single parameter.\nThis technique is most appropriate for low-dimensional (p < 3) data visualization purposes. Actually, the kernel smoother represents the set of irregular data points as a smooth line or surface.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8a/Gaussian_kernel_regression.png", "https://upload.wikimedia.org/wikipedia/commons/9/9f/KernelSmoother.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2d/Localregressionsmoother.svg", "https://upload.wikimedia.org/wikipedia/commons/9/92/NNSmoother.svg"], "links": ["Euclidean norm", "Function (mathematics)", "Gaussian function", "International Standard Book Number", "K-nearest neighbor algorithm", "Kernel (statistics)", "Kernel density estimation", "Kernel methods", "Kernel regression", "Local regression", "Radial basis function kernel", "Savitzky\u2013Golay filter", "Statistics"], "references": ["http://www.mayagupta.org/publications/GuptaGarciaChinTIP2008.pdf", "https://web.stanford.edu/~hastie/ElemStatLearn/"]}, "Seriation (archaeology)": {"categories": ["All articles needing additional references", "Articles needing additional references from August 2016", "CS1 maint: Archived copy as title", "Methods in archaeology"], "title": "Seriation (archaeology)", "method": "Seriation (archaeology)", "url": "https://en.wikipedia.org/wiki/Seriation_(archaeology)", "summary": "In archaeology, seriation is a relative dating method in which assemblages or artifacts from numerous sites, in the same culture, are placed in chronological order. Where absolute dating methods, such as carbon dating, cannot be applied, archaeologists have to use relative dating methods to date archaeological finds and features. Seriation is a standard method of dating in archaeology. It can be used to date stone tools, pottery fragments, and other artifacts. In Europe, it has been used frequently to reconstruct the chronological sequence of graves in a cemetery (e.g. J\u00f8rgensen 1992; M\u00fcssemeier, Nieveler et al. 2003).", "images": ["https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/4/4e/Seriation_Ideal_3Polynom.png", "https://upload.wikimedia.org/wikipedia/en/2/20/Seriation_Ideal_Parabola.png", "https://upload.wikimedia.org/wikipedia/en/a/aa/Seriation_Ideal_Table30.png", "https://upload.wikimedia.org/wikipedia/en/e/e2/Seriation_Parabola.png", "https://upload.wikimedia.org/wikipedia/en/5/59/Seriation_contextual.png", "https://upload.wikimedia.org/wikipedia/en/1/1b/Seriation_simulated_data.png", "https://upload.wikimedia.org/wikipedia/en/8/86/Seriation_simulated_data_raw.png", "https://upload.wikimedia.org/wikipedia/en/0/06/Unsorted_contextual.png", "https://upload.wikimedia.org/wikipedia/en/b/bd/Unsorted_contextual_01.png"], "links": ["ASPRO chronology", "Ab urbe condita", "Absolute dating", "Adoption of the Gregorian calendar", "Amino acid dating", "Anno Domini", "Anno Mundi", "Archaeological association", "Archaeological context", "Archaeological culture", "Archaeological record", "Archaeological site", "Archaeology", "Archaeomagnetic dating", "Artifact (archaeology)", "Assemblage (archaeology)", "Astronomical chronology", "Astronomical year numbering", "Astronomy", "Aztec calendar", "Before Present", "Bimodal distribution", "Biofact (archaeology)", "Byzantine calendar", "Calendar", "Calendar era", "Canon of Kings", "Carbon dating", "Chinese era name", "Chronicle", "Chronological dating", "Chronology", "Chronostratigraphy", "Circa", "Common Era", "Computer simulation", "Contingency table", "Correspondence analysis", "Cosmic Calendar", "David George Kendall", "Deep time", "Dendrochronology", "Detrended correspondence analysis", "Diospolis Parva", "Dual dating", "Egypt", "Egyptian chronology", "Ephemeris", "Epoch (reference date)", "Era", "Flinders Petrie", "Floruit", "Fluorine absorption dating", "Galactic year", "Geochronology", "Geologic Calendar", "Geologic time scale", "Geological history of Earth", "Geology", "Global Boundary Stratotype Section and Point", "Global Standard Stratigraphic Age", "Glottochronology", "Gregorian calendar", "Haab'", "Harris matrix", "Hebrew calendar", "Hindu units of time", "History", "Hoard", "Holocene calendar", "ISO week date", "Ice core", "Incremental dating", "International Standard Book Number", "International Standard Serial Number", "Iranian calendars", "Islamic calendar", "Isotope geochemistry", "Japanese era name", "Julian calendar", "Korean era name", "K\u2013Ar dating", "Law of superposition", "Lichenometry", "Limmu", "Linear transformation", "Luminescence dating", "Lunar calendar", "Lunisolar calendar", "Manuport", "Maya calendar", "Mesoamerican Long Count calendar", "Mesoamerican calendars", "Metonic cycle", "Milankovitch cycles", "Molecular clock", "Multidimensional scaling", "New Chronology (Fomenko)", "Nitrogen dating", "Obsidian hydration dating", "Old Style and New Style dates", "Ordination (statistics)", "Paleomagnetism", "Paleontology", "Parabola", "Periodization", "Polynomial curve", "Proleptic Gregorian calendar", "Proleptic Julian calendar", "Radiocarbon dating", "Radiometric dating", "Regnal year", "Relationship (archaeology)", "Relative dating", "Revised Julian calendar", "Roman calendar", "Samarium\u2013neodymium dating", "Scatterplot", "Seleucid era", "Sexagenary cycle", "Similarity matrix", "Solar calendar", "Sothic cycle", "Spanish era", "Stratification (archaeology)", "Stratigraphy", "Stratigraphy (archaeology)", "Style (visual arts)", "Synchronoptic view", "Tephrochronology", "Terminus post quem", "Thermoluminescence dating", "Time", "Timeline", "Typology (archaeology)", "Tzolk'in", "Uranium\u2013lead dating", "Vietnamese era name", "Winter count", "Year zero", "Yuga"], "references": ["http://archaeology.about.com/od/dating/ss/seriation.htm", "http://www.uni-koeln.de/~al001/", "http://www.archaeoinfo.dk/", "http://publishing.eur.nl/ir/repub/asset/10559/EI2007_40.pdf", "http://folk.uio.no/ohammer/past/", "https://web.archive.org/web/20081003222149/http://publishing.eur.nl/ir/repub/asset/10559/EI2007_40.pdf", "https://cran.r-project.org/package=seriation", "https://www.worldcat.org/search?fq=x0:jrnl&q=n2:0901-6732"]}, "Spatial distribution": {"categories": ["All Wikipedia articles needing context", "All pages needing cleanup", "All stub articles", "Demographics", "Spatial data analysis", "Statistical charts and diagrams", "Statistics stubs", "Wikipedia articles needing context from July 2010", "Wikipedia introduction cleanup from July 2010"], "title": "Spatial distribution", "method": "Spatial distribution", "url": "https://en.wikipedia.org/wiki/Spatial_distribution", "summary": "A spatial distribution is the arrangement of a phenomenon across the Earth's surface and a graphical display of such an arrangement is an important tool in geographical and environmental statistics. A graphical display of a spatial distribution may summarize raw data directly or may reflect the outcome of more sophisticated data analysis. Many different aspects of a phenomenon can be shown in a single graphical display by using a suitable choice of different colours to represent differences.\nOne example of such a display could be observations made to describe the geographic patterns of features, both physical and human across the earth. \nThe information included could be where units of something are, how many units of the thing there are per units of area, and how sparsely or densely packed they are from each other.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["City map", "Data analysis", "Earth's surface", "Environmental statistics", "Graphical display", "Statistics", "Two-step floating catchment area (2SFCA) method"], "references": []}, "Zelen's design": {"categories": ["Clinical research", "Design of experiments"], "title": "Zelen's design", "method": "Zelen's design", "url": "https://en.wikipedia.org/wiki/Zelen%27s_design", "summary": "Zelen's design is an experimental design for randomized clinical trials proposed by Harvard School of Public Health statistician Marvin Zelen (1927-2014). In this design, patients are randomized to either the treatment or control group before giving informed consent. Because the group to which a given patient is assigned is known, consent can be sought conditionally.", "images": [], "links": ["Cluster randomised controlled trial", "Digital object identifier", "Experimental design", "Harvard School of Public Health", "Hawthorne effect", "Informed consent", "International Standard Serial Number", "Marvin Zelen (biostatistician)", "PubMed Central", "PubMed Identifier", "Randomized clinical trials", "Randomized controlled trial", "Resentful demoralization", "Scientific control", "Statistician", "Statistics", "The New England Journal of Medicine"], "references": ["http://www.springerlink.com.ezp-prod1.hul.harvard.edu/content/v78321530508077m/?p=95da6589690a45b0843f86aa63f4df37&pi=1", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1112637", "http://www.ncbi.nlm.nih.gov/pubmed/12357585", "http://www.ncbi.nlm.nih.gov/pubmed/431682", "http://www.ncbi.nlm.nih.gov/pubmed/9518917", "http://doi.org/10.1056%2FNEJM197905313002203", "http://doi.org/10.1136%2Fbmj.316.7131.606", "http://doi.org/10.1191%2F0962280202sm298ra", "http://www.worldcat.org/issn/0962-2802"]}, "Mean value analysis": {"categories": ["Queueing theory"], "title": "Mean value analysis", "method": "Mean value analysis", "url": "https://en.wikipedia.org/wiki/Mean_value_analysis", "summary": "In queueing theory, a discipline within the mathematical theory of probability, mean value analysis (MVA) is a recursive technique for computing expected queue lengths, waiting time at queueing nodes and throughput in equilibrium for a closed separable system of queues. The first approximate techniques were published independently by Schweitzer and Bard, followed later by an exact version by Lavenberg and Reiser published in 1980.It is based on the arrival theorem, which states that when one customer in an M-customer closed system arrives at a service facility he/she observes the rest of the system to be in the equilibrium state for a system with M \u2212 1 customers.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Erlang (unit)", "Erlang distribution", "Expected value", "FIFO (computing and electronics)", "Fixed-point iteration", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "GNU Octave", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "International Standard Book Number", "Jackson network", "Java (programming language)", "Journal of the ACM", "Kelly network", "Kendall's notation", "Key distribution center", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Message queue", "Network congestion", "Network scheduler", "PEPA", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing network", "Queueing theory", "Queuing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "The Computer Journal", "Theory of probability", "Traffic equations"], "references": ["http://www.cs.utexas.edu/users/lam/Vita/Jpapers/Lam83.pdf", "http://www.netlab.tkk.fi/opetus/s383143/kalvot/E_qnets.pdf", "http://www.moreno.marzolla.name/software/queueing/", "http://jmt.sourceforge.net/JMVA.html", "http://jmt.sourceforge.net/Papers/acm09jmt.pdf", "http://doi.org/10.1007/3-540-46506-5_22", "http://doi.org/10.1007/978-1-4419-6472-4_13", "http://doi.org/10.1007/978-3-319-10696-0_14", "http://doi.org/10.1007/BFb0013865", "http://doi.org/10.1016/0166-5316(88)90028-4", "http://doi.org/10.1016/j.peva.2010.12.009", "http://doi.org/10.1093/comjnl/bxq064", "http://doi.org/10.1145/1530873.1530877", "http://doi.org/10.1145/214419.214423", "http://doi.org/10.1145/322186.322195", "http://doi.org/10.2200/S00282ED1V01Y201005CSL002", "http://ieeexplore.ieee.org/document/4641939/", "http://www.doc.ic.ac.uk/~gcasale/peva11mom.pdf", "https://github.com/line-solver/line", "https://books.google.com/books?id=39-jISti_zkC"]}, "Minimum mean square error": {"categories": ["Pages with URL errors", "Point estimation performance", "Signal estimation", "Statistical deviation and dispersion", "Use dmy dates from September 2010"], "title": "Minimum mean square error", "method": "Minimum mean square error", "url": "https://en.wikipedia.org/wiki/Minimum_mean_square_error", "summary": "In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated. Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions. Linear MMSE estimators are a popular choice since they are easy to use, easy to calculate, and very versatile. It has given rise to many popular estimators such as the Wiener\u2013Kolmogorov filter and Kalman filter.\n\n", "images": [], "links": ["Adaptive filter", "Asymptotically unbiased", "Bayes theorem", "Bayesian estimator", "Cholesky decomposition", "Conjugate gradient method", "Covariance matrix", "Dependent variable", "Efficiency (statistics)", "Estimator", "Expected value", "Fisher information", "Gauss elimination", "Gauss\u2013Markov theorem", "Gradient descent", "Gradient descent method", "International Standard Book Number", "Jointly Gaussian", "Kalman filter", "Least mean squares filter", "Least squares", "Levinson recursion", "Linear prediction", "Loss function", "Mean square error", "Mean squared error", "Minimum-variance unbiased estimator", "Monte Carlo methods", "Orthogonality principle", "Pearson's correlation coefficient", "QR decomposition", "Recursive least squares filter", "Scalar (mathematics)", "Signal processing", "Statistics", "Toeplitz matrix", "Trace (linear algebra)", "Uniform distribution (continuous)", "Wide sense stationary", "Wiener filter", "Zero forcing equalizer"], "references": ["http://cnx.rice.edu/content/m11267/latest/", "https://www.probabilitycourse.com/chapter9/9_1_5_mean_squared_error_MSE.php", "https://web.archive.org/web/20080725052939/http://cnx.rice.edu/content/m11267/latest/"]}, "Variance-to-mean ratio": {"categories": ["Point processes", "Statistical deviation and dispersion", "Statistical randomness", "Statistical ratios"], "title": "Index of dispersion", "method": "Variance-to-mean ratio", "url": "https://en.wikipedia.org/wiki/Index_of_dispersion", "summary": "In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.\nIt is defined as the ratio of the variance \n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n {\\displaystyle \\sigma ^{2}}\n to the mean \n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n ,\n\n \n \n \n D\n =\n \n \n \n \u03c3\n \n 2\n \n \n \u03bc\n \n \n .\n \n \n {\\displaystyle D={\\sigma ^{2} \\over \\mu }.}\n It is also known as the Fano factor, though this term is sometimes reserved for windowed data (the mean and variance are computed over a subpopulation), where the index of dispersion is used in the special case where the window is infinite. Windowing data is frequently done: the VMR is frequently computed over various intervals in time or small regions in space, which may be called \"windows\", and the resulting statistic called the Fano factor.\nIt is only defined when the mean \n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n is non-zero, and is generally only used for positive statistics, such as count data or time between events, or where the underlying distribution is assumed to be the exponential distribution or Poisson distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Mathematical Statistics", "Arithmetic mean", "Arthur Roy Clapham", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brownian motion", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Conic sections", "Constant random variable", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Eccentricity (mathematics)", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fano factor", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric distribution", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the Royal Statistical Society, Series C", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Lexis ratio", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Negative binomial distribution", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normalization (statistics)", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Overdispersion", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Paul G. Hoel", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson process", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random walk", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal processing", "Signal to noise ratio", "Signal to noise ratio (image processing)", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standardized moment", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1214%2Faoms%2F1177731457", "http://www.jstor.org/stable/2235818", "http://www.jstor.org/stable/2347079"]}, "Accuracy and precision": {"categories": ["Accuracy and precision", "All articles with unsourced statements", "Articles with unsourced statements from February 2015", "Articles with unsourced statements from July 2009", "Biostatistics", "CS1 maint: Archived copy as title", "Commons category link from Wikidata", "ISO standards", "Metrology", "Psychometrics"], "title": "Accuracy and precision", "method": "Accuracy and precision", "url": "https://en.wikipedia.org/wiki/Accuracy_and_precision", "summary": "Precision is a description of random errors, a measure of statistical variability.\nAccuracy has two definitions:\n\nMore commonly, it is a description of systematic errors, a measure of statistical bias; as these cause a difference between a result and a \"true\" value, ISO calls this trueness.\nAlternatively, ISO defines accuracy as describing a combination of both types of observational error above (random and systematic), so high accuracy requires both high precision and high trueness.In simplest terms, given a set of data points from repeated measurements of the same quantity, the set can be said to be precise if the values are close to each other, while the set can be said to be accurate if their average is close to the true value of the quantity being measured. In the first, more common definition above, the two concepts are independent of each other, so a particular set of data can be said to be either accurate, or precise, or both, or neither.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/92/Accuracy_%28trueness_and_precision%29.svg", "https://upload.wikimedia.org/wikipedia/commons/3/38/Accuracy_and_precision.svg", "https://upload.wikimedia.org/wikipedia/commons/1/10/High_accuracy_Low_precision.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/High_precision_Low_accuracy.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["110 film", "126 film", "135 film", "A440 (pitch standard)", "ALGOL 60", "ANSI escape code", "ASMO 449", "Accepted and experimental value", "Ada Semantic Interface Specification", "Antimagnetic watch", "ArXiv", "ArmSCII", "Bias-variance tradeoff", "Bias (statistics)", "Bias of an estimator", "Binary classification", "British Standard Pipe", "Business Process Model and Notation", "C++", "COBOL", "C (programming language)", "C Sharp (programming language)", "Calibration", "Central limit theorem", "Cloud Infrastructure Management Interface", "Colloquial", "Common Criteria", "Common Language Infrastructure", "Common Logic", "Common Object Request Broker Architecture", "Computer Graphics Metafile", "Confusion matrix", "Cronbach's alpha", "Database", "Delivery Multimedia Integration Framework", "Digital object identifier", "Discounted cumulative gain", "Document Style Semantics and Specification Language", "ECMAScript", "EXPRESS (data modeling language)", "Electronic circuit simulation", "Engineering", "Engineering tolerance", "Envelope", "Equal-loudness contour", "Evaluation measures (information retrieval)", "Evaluation of binary classifiers", "Exactness (disambiguation)", "Experimental uncertainty analysis", "F-score", "FDI World Dental Federation notation", "FTAM", "False precision", "Fiber Distributed Data Interface", "File Allocation Table", "Film speed", "Fuel oil", "Graphical Kernel System", "Ground truth", "Grouping (firearms)", "Guidelines for the Definition of Managed Objects", "H.264/MPEG-4 AVC", "HTML", "Hole punch", "Horsepower", "IS-IS", "ISO-8859-8-I", "ISO-TimeML", "ISO/IEC 10116", "ISO/IEC 10967", "ISO/IEC 11179", "ISO/IEC 11404", "ISO/IEC 11801", "ISO/IEC 12207", "ISO/IEC 14443", "ISO/IEC 15288", "ISO/IEC 15504", "ISO/IEC 15693", "ISO/IEC 17024", "ISO/IEC 17025", "ISO/IEC 18000", "ISO/IEC 18014", "ISO/IEC 19752", "ISO/IEC 19770", "ISO/IEC 19794-5", "ISO/IEC 20000", "ISO/IEC 2022", "ISO/IEC 21827", "ISO/IEC 27000", "ISO/IEC 27000-series", "ISO/IEC 27001", "ISO/IEC 27002", "ISO/IEC 27006", "ISO/IEC 38500", "ISO/IEC 42010", "ISO/IEC 4909", "ISO/IEC 5218", "ISO/IEC 646", "ISO/IEC 6523", "ISO/IEC 7810", "ISO/IEC 7811", "ISO/IEC 7812", "ISO/IEC 7813", "ISO/IEC 7816", "ISO/IEC 80000", "ISO/IEC 8652", "ISO/IEC 8820-5", "ISO/IEC 8859", "ISO/IEC 8859-1", "ISO/IEC 8859-10", "ISO/IEC 8859-11", "ISO/IEC 8859-12", "ISO/IEC 8859-13", "ISO/IEC 8859-14", "ISO/IEC 8859-15", "ISO/IEC 8859-16", "ISO/IEC 8859-2", "ISO/IEC 8859-3", "ISO/IEC 8859-4", "ISO/IEC 8859-5", "ISO/IEC 8859-6", "ISO/IEC 8859-7", "ISO/IEC 8859-8", "ISO/IEC 8859-9", "ISO/IEC 9126", "ISO/IEC 9797-1", "ISO/IEC 9995", "ISO/IEC TR 12182", "ISO/IEEE 11073", "ISO/TR 11941", "ISO/TS 16949", "ISO 1", "ISO 1000", "ISO 10005", "ISO 10006", "ISO 10007", "ISO 10160", "ISO 10161", "ISO 10206", "ISO 10218", "ISO 10303", "ISO 10303-21", "ISO 10303-22", "ISO 10303-28", "ISO 10383", "ISO 10487", "ISO 10962", "ISO 11170", "ISO 11783", "ISO 11784 & 11785", "ISO 11898", "ISO 11940", "ISO 11940-2", "ISO 11992", "ISO 12006", "ISO 128", "ISO 13399", "ISO 13406-2", "ISO 13485", "ISO 13490", "ISO 13567", "ISO 13584", "ISO 14000", "ISO 14031", "ISO 1413", "ISO 14224", "ISO 14644", "ISO 14651", "ISO 14698", "ISO 14750", "ISO 14971", "ISO 15022", "ISO 15189", "ISO 15292", "ISO 15398", "ISO 15686", "ISO 15706-2", "ISO 15897", "ISO 15919", "ISO 15924", "ISO 15926", "ISO 15926 WIP", "ISO 1629", "ISO 16750", "ISO 17100:2015", "ISO 1745", "ISO 18245", "ISO 19011", "ISO 19092-1", "ISO 19092-2", "ISO 19114", "ISO 19115", "ISO 19136", "ISO 19439", "ISO 19600", "ISO 2", "ISO 20022", "ISO 20121", "ISO 2014", "ISO 2015", "ISO 2033", "ISO 20400", "ISO 2047", "ISO 2145", "ISO 2146", "ISO 21500", "ISO 216", "ISO 217", "ISO 22000", "ISO 233", "ISO 25178", "ISO 259", "ISO 25964", "ISO 26000", "ISO 2709", "ISO 2711", "ISO 2788", "ISO 28000", "ISO 2848", "ISO 2852", "ISO 29110", "ISO 31", "ISO 31-0", "ISO 31-1", "ISO 31-10", "ISO 31-11", "ISO 31-12", "ISO 31-13", "ISO 31-2", "ISO 31-3", "ISO 31-4", "ISO 31-5", "ISO 31-6", "ISO 31-7", "ISO 31-8", "ISO 31-9", "ISO 31000", "ISO 3103", "ISO 3166", "ISO 3166-1", "ISO 3166-2", "ISO 3166-3", "ISO 3307", "ISO 361", "ISO 3864", "ISO 3977", "ISO 4", "ISO 4031", "ISO 4157", "ISO 4165", "ISO 4217", "ISO 428", "ISO 5", "ISO 518", "ISO 519", "ISO 5426", "ISO 5427", "ISO 5428", "ISO 55000", "ISO 5775", "ISO 5776", "ISO 5964", "ISO 6344", "ISO 6346", "ISO 6385", "ISO 639", "ISO 639-1", "ISO 639-2", "ISO 639-3", "ISO 639-5", "ISO 639-6", "ISO 6438", "ISO 657", "ISO 668", "ISO 6709", "ISO 690", "ISO 6943", "ISO 7001", "ISO 7002", "ISO 7010", "ISO 7027", "ISO 704", "ISO 7064", "ISO 7200", "ISO 732", "ISO 7637", "ISO 7736", "ISO 8000", "ISO 80000-1", "ISO 80000-2", "ISO 80000-3", "ISO 8178", "ISO 8373", "ISO 843", "ISO 8501-1", "ISO 8583", "ISO 860", "ISO 8601", "ISO 8691", "ISO 898", "ISO 9", "ISO 9000", "ISO 9241", "ISO 9362", "ISO 9529", "ISO 9564", "ISO 965", "ISO 9660", "ISO 9897", "ISO 999", "Independent variable", "International Bank Account Number", "International Organization for Standardization", "International Securities Identification Number", "International Standard Atmosphere", "International Standard Audiovisual Number", "International Standard Book Number", "International Standard Identifier for Libraries and Related Organizations", "International Standard Music Number", "International Standard Musical Work Code", "International Standard Name Identifier", "International Standard Recording Code", "International Standard Serial Number", "International Standard Text Code", "Isofix", "JBIG", "JPEG 2000", "JPEG XR", "Kappa number", "Knowledge Discovery Metamodel", "Kunrei-shiki romanization", "Language Of Temporal Ordering Specification", "Legal Entity Identifier", "Lexical Markup Framework", "Linux Standard Base", "List of IEC standards", "List of ISO romanizations", "List of International Organization for Standardization standards", "Logic simulation", "Longitudinal redundancy check", "MPEG-21", "MPEG-4", "MPEG-4 Part 11", "MPEG-4 Part 12", "MPEG-4 Part 14", "MPEG-4 Part 2", "MPEG-4 Part 3", "Magnetic ink character recognition", "Manufacturing Message Specification", "MaxiCode", "Mean", "Measurement", "Measurement uncertainty", "Meta-Object Facility", "Motion JPEG 2000", "Multibus", "National Institute of Standards and Technology", "Numerical analysis", "O-ring", "OCR-A font", "OSI model", "Object Constraint Language", "Observational error", "Office Open XML", "On-board diagnostics", "OpenDocument", "Open Document Architecture", "Open Systems Interconnection", "Open Virtualization Format", "PDF/A", "PDF/E", "PDF/UA", "PDF/VT", "PDF/X", "PDF417", "PHIGS", "POSIX", "Pascal (programming language)", "Photographic Activity Test", "Pinyin", "Portable Document Format", "Power take-off", "Precision (statistics)", "Precision and recall", "Precision at k", "Probability", "Probability distribution", "Process Specification Language", "Prolog", "Psychometrics", "Psychophysics", "PubMed Identifier", "QR code", "Quantity", "RELAX NG", "RM-ODP", "Rand index", "Random", "Random and systematic errors", "Random errors", "Reliability (statistics)", "Renard series", "Repeatability", "Reproducibility", "Requirements engineering", "Result", "Romanization of Armenian", "Romanization of Georgian", "Ruby (programming language)", "SDMX", "SI", "SQL", "STEP-NC", "Salt spray test", "Sample size", "Science", "Scientific method", "Sensitivity and specificity", "Sensor", "Shoe size", "Significant figures", "Simple feature access", "Software maintenance", "Standard Generalized Markup Language", "Standard error (statistics)", "Standards organization", "Statistical bias", "Statistical significance", "Statistical variability", "Statistics", "Synonymous", "Systematic error", "Systematic errors", "TED (conference)", "Tag Image File Format / Electronic Photography", "Technical standard", "Topic map", "Torx", "Traceability", "Transistor", "Transistor models", "True negative", "True positive", "Unified Modeling Language", "Universal Coded Character Set", "Validity (statistics)", "Value (mathematics)", "Variability (statistics)", "Vicat softening point", "Water Resistant mark", "Web Content Accessibility Guidelines", "Web search engine", "Whirlpool (hash function)", "X.500", "X3D", "XML Metadata Interchange", "Z notation"], "references": ["http://www.alta.asn.au/events/altss_w2003_proc/altss/courses/powers/ALTSS2003-Val+Eval-L3.pdf", "http://digipac.ca/chemical/sigfigs/contents.htm", "http://www.yorku.ca/psycho", "http://img.en25.com/Web/Vaisala/NIST-article.pdf", "http://www.umich.edu/~ners580/ners-bioe_481/lectures/pdfs/1978-10-semNucMed_Metz-basicROC.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/112681", "http://physics.nist.gov/Pubs/guidelines/appd.1.html", "http://www.anthology.aclweb.org/E/E12/E12-1035.pdf", "http://arxiv.org/abs/1503.06410", "http://arxiv.org/archive/cs.IR", "http://www.bipm.org/en/publications/guides/", "http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf", "https://books.google.com/books?id=giFQcZub80oC&pg=PA128", "https://www.youtube.com/watch?v=_LL0uiOgh1E&feature=youtube_gdata_player", "https://www.youtube.com/watch?v=hRAFPdDppzs", "https://web.archive.org/web/20150311073014/http://alta.asn.au/events/altss_w2003_proc/altss/courses/powers/ALTSS2003-Val+Eval-L3.pdf"]}, "Importance sampling": {"categories": ["Monte Carlo methods", "Stochastic simulation", "Variance reduction"], "title": "Importance sampling", "method": "Importance sampling", "url": "https://en.wikipedia.org/wiki/Importance_sampling", "summary": "In statistics, importance sampling is a general technique for estimating properties of a particular distribution, while only having samples generated from a different distribution than the distribution of interest. It is related to umbrella sampling in computational physics. Depending on the application, the term may refer to the process of sampling from this alternative distribution, the process of inference, or both.", "images": [], "links": ["Almost everywhere", "ArXiv", "Auxiliary field Monte Carlo", "Bayesian network", "Bibcode", "Binomial distribution", "Computational physics", "Confidence interval", "Derivative", "Digital communication", "Digital object identifier", "Estimator", "Expected value", "Independent and identically distributed", "International Standard Book Number", "International Standard Serial Number", "Intersymbol interference", "Likelihood-ratio test", "Loss function", "Monte Carlo integration", "Monte Carlo method", "Particle filter", "Probability density function", "Probability distribution", "Probability space", "Radon\u2013Nikodym derivative", "Random variable", "Random variables", "Rejection sampling", "Simulation", "Statistics", "Stratified sampling", "Umbrella sampling", "VEGAS algorithm", "Variance reduction", "Viterbi decoder"], "references": ["http://apps.nrbook.com/empanel/index.html#pg=411", "http://www.sciencedirect.com/science/article/pii/S1051200415001864", "http://www.tandfonline.com/doi/abs/10.1080/01621459.2000.10473909", "http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9469.2011.00756.x/abstract", "http://adsabs.harvard.edu/abs/2015ISPL...22.1757E", "http://adsabs.harvard.edu/abs/2015ITSP...63.4422M", "http://adsabs.harvard.edu/abs/2017ISPM...34...60B", "http://jrxv.net/x/16/ism.pdf", "http://doi.acm.org/10.1145/218380.218498", "http://portal.acm.org/citation.cfm?id=1030470", "http://arxiv.org/abs/0710.4242", "http://arxiv.org/abs/0907.1254", "http://arxiv.org/abs/1505.04732", "http://arxiv.org/abs/1505.05391", "http://arxiv.org/abs/1602.03572", "http://arxiv.org/abs/1607.02758", "http://doi.org/10.1007%2Fs11222-008-9059-x", "http://doi.org/10.1007%2Fs11222-016-9642-5", "http://doi.org/10.1016%2Fj.dsp.2015.05.014", "http://doi.org/10.1016%2Fj.sigpro.2016.07.012", "http://doi.org/10.1016%2Fj.sigpro.2016.08.025", "http://doi.org/10.1080%2F01621459.2000.10473909", "http://doi.org/10.1109%2F49.585771", "http://doi.org/10.1109%2FICC.2001.936655", "http://doi.org/10.1109%2FLSP.2015.2432078", "http://doi.org/10.1109%2FTSP.2015.2440215", "http://doi.org/10.1109%2Fmsp.2017.2699226", "http://doi.org/10.1111%2Fj.1467-9469.2011.00756.x", "http://doi.org/10.1145%2F218380.218498", "http://doi.org/10.1198%2F106186004X12803", "http://doi.org/10.1515%2F156939604323091180", "http://ieeexplore.ieee.org/document/7974876/", "http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7105865", "http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7117437", "http://www.iop.org/EJ/abstract/0143-0807/22/4/315", "http://www.worldcat.org/issn/0162-1459", "http://www.worldcat.org/issn/0960-3174", "http://www.worldcat.org/issn/1053-587X", "http://www.worldcat.org/issn/1053-5888", "http://www.worldcat.org/issn/1061-8600", "http://www.worldcat.org/issn/1070-9908", "http://www.worldcat.org/issn/1467-9469", "http://www-sigproc.eng.cam.ac.uk/smc/", "https://link.springer.com/article/10.1007/s11222-008-9059-x", "https://link.springer.com/article/10.1007/s11222-016-9642-5", "https://doi.org/10.1016/j.sigpro.2016.07.012", "https://doi.org/10.1016/j.sigpro.2016.08.025", "https://dx.doi.org/10.1198/106186004X12803"]}, "Mittag\u2013Leffler distribution": {"categories": ["All articles needing additional references", "Articles needing additional references from October 2013", "Continuous distributions", "Geometric stable distributions", "Probability distributions with non-finite variance"], "title": "Mittag-Leffler distribution", "method": "Mittag\u2013Leffler distribution", "url": "https://en.wikipedia.org/wiki/Mittag-Leffler_distribution", "summary": "The Mittag-Leffler distributions are two families of probability distributions on the half-line \n \n \n \n [\n 0\n ,\n \u221e\n )\n \n \n {\\displaystyle [0,\\infty )}\n . They are parametrized by a real \n \n \n \n \u03b1\n \u2208\n (\n 0\n ,\n 1\n ]\n \n \n {\\displaystyle \\alpha \\in (0,1]}\n or \n \n \n \n \u03b1\n \u2208\n [\n 0\n ,\n 1\n ]\n \n \n {\\displaystyle \\alpha \\in [0,1]}\n . Both are defined with the Mittag-Leffler function, named after G\u00f6sta Mittag-Leffler.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["ARGUS distribution", "Absolute continuity", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution functions", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "G\u00f6sta Mittag-Leffler", "Half-logistic distribution", "Half-normal distribution", "Heavy-tailed distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler function", "Mixture distribution", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Probability distributions", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.sciencedirect.com/science/article/pii/S0378375810001837", "http://www.tandfonline.com/doi/abs/10.1080/03610918.2011.640094#.Vr0c1fkrKM8", "https://www.springer.com/astronomy/extraterrestrial+physics,+space+sciences/book/978-3-642-03323-0"]}, "Le Cam's theorem": {"categories": ["Probabilistic inequalities", "Probability theorems", "Statistical inequalities", "Statistical theorems"], "title": "Le Cam's theorem", "method": "Le Cam's theorem", "url": "https://en.wikipedia.org/wiki/Le_Cam%27s_theorem", "summary": "In probability theory, Le Cam's theorem, named after Lucien le Cam (1924 \u2013 2000), states the following.Suppose:\n\nX1, ..., Xn are independent random variables, each with a Bernoulli distribution (i.e., equal to either 0 or 1), not necessarily identically distributed.\nPr(Xi = 1) = pi for i = 1, 2, 3, ...\n\n \n \n \n \n \u03bb\n \n n\n \n \n =\n \n p\n \n 1\n \n \n +\n \u22ef\n +\n \n p\n \n n\n \n \n .\n \n \n {\\displaystyle \\lambda _{n}=p_{1}+\\cdots +p_{n}.}\n \n\n \n \n \n \n S\n \n n\n \n \n =\n \n X\n \n 1\n \n \n +\n \u22ef\n +\n \n X\n \n n\n \n \n .\n \n \n {\\displaystyle S_{n}=X_{1}+\\cdots +X_{n}.}\n (i.e. \n \n \n \n \n S\n \n n\n \n \n \n \n {\\displaystyle S_{n}}\n follows a Poisson binomial distribution)Then\n\n \n \n \n \n \u2211\n \n k\n =\n 0\n \n \n \u221e\n \n \n \n |\n \n Pr\n (\n \n S\n \n n\n \n \n =\n k\n )\n \u2212\n \n \n \n \n \u03bb\n \n n\n \n \n k\n \n \n \n e\n \n \u2212\n \n \u03bb\n \n n\n \n \n \n \n \n \n k\n !\n \n \n \n \n |\n \n <\n 2\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n p\n \n i\n \n \n 2\n \n \n .\n \n \n {\\displaystyle \\sum _{k=0}^{\\infty }\\left|\\Pr(S_{n}=k)-{\\lambda _{n}^{k}e^{-\\lambda _{n}} \\over k!}\\right|<2\\sum _{i=1}^{n}p_{i}^{2}.}\n In other words, the sum has approximately a Poisson distribution and the above inequality bounds the approximation error in terms of the total variation distance.\nBy setting pi = \u03bbn/n, we see that this generalizes the usual Poisson limit theorem.\nWhen \n \n \n \n \n \u03bb\n \n n\n \n \n \n \n {\\displaystyle \\lambda _{n}}\n is large a better bound is possible: \n \n \n \n \n \u2211\n \n k\n =\n 0\n \n \n \u221e\n \n \n \n |\n \n Pr\n (\n \n S\n \n n\n \n \n =\n k\n )\n \u2212\n \n \n \n \n \u03bb\n \n n\n \n \n k\n \n \n \n e\n \n \u2212\n \n \u03bb\n \n n\n \n \n \n \n \n \n k\n !\n \n \n \n \n |\n \n <\n 2\n (\n 1\n \u2227\n \n \n \n 1\n \u03bb\n \n \n \n n\n \n \n )\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n p\n \n i\n \n \n 2\n \n \n .\n \n \n {\\displaystyle \\sum _{k=0}^{\\infty }\\left|\\Pr(S_{n}=k)-{\\lambda _{n}^{k}e^{-\\lambda _{n}} \\over k!}\\right|<2(1\\wedge {\\frac {1}{\\lambda }}_{n})\\sum _{i=1}^{n}p_{i}^{2}.}\n It is also possible to weaken the independence requirement.\n\n", "images": [], "links": ["Bernoulli distribution", "Digital object identifier", "Eric W. Weisstein", "JSTOR", "Jerzy Neyman", "Lucien le Cam", "MathWorld", "Mathematical Reviews", "Poisson binomial distribution", "Poisson distribution", "Poisson limit theorem", "Probability theory", "Random variable", "Statistical independence", "Total variation distance of probability measures", "Zentralblatt MATH"], "references": ["http://mathworld.wolfram.com/LeCamsInequality.html", "http://www.ams.org/mathscinet-getitem?mr=0142174", "http://www.ams.org/mathscinet-getitem?mr=0199871", "http://doi.org/10.2140%2Fpjm.1960.10.1181", "http://doi.org/10.2307%2F2325124", "http://www.jstor.org/stable/2325124", "http://projecteuclid.org/euclid.pjm/1103038058", "http://zbmath.org/?format=complete&q=an:0118.33601"]}, "Bispectrum": {"categories": ["Complex analysis", "Fourier analysis", "Integral transforms", "Nonlinear time series analysis", "Statistical signal processing", "Time series"], "title": "Bispectrum", "method": "Bispectrum", "url": "https://en.wikipedia.org/wiki/Bispectrum", "summary": "In mathematics, in the area of statistical analysis, the bispectrum is a statistic used to search for nonlinear interactions. \n\n", "images": [], "links": ["Autocorrelation", "Bicoherence", "Bispectral analysis", "Convolution theorem", "Cumulant", "Digital object identifier", "Electroencephalography", "Fourier transform", "MATLAB", "Mathematics", "Power spectrum", "PubMed Identifier", "Seismology", "Signals (biology)", "Statistical analysis", "Trispectrum"], "references": ["http://www.mathworks.com/matlabcentral/fileexchange/3013", "http://www.tandfonline.com/doi/abs/10.1080/09298219708570732#.UvbLW_ZyHh0", "http://meta.wkhealth.com/pt/pt-core/template-journal/lwwgateway/media/landingpage.htm?issn=0003-3022&volume=93&issue=5&spage=1336", "http://www.ncbi.nlm.nih.gov/pubmed/11046224", "http://doi.org/10.1080%2F09298219708570732", "http://doi.org/10.1088%2F0741-3335%2F30%2F5%2F005", "http://doi.org/10.1097%2F00000542-200011000-00029", "http://doi.org/10.1109%2F5.75086", "http://www.iop.org/EJ/abstract/0741-3335/30/5/005"]}, "Matrix population models": {"categories": ["Population models"], "title": "Matrix population models", "method": "Matrix population models", "url": "https://en.wikipedia.org/wiki/Matrix_population_models", "summary": "Population models are used in population ecology to model the dynamics of wildlife or human populations. Matrix population models are a specific type of population model that uses matrix algebra. Matrix algebra, in turn, is simply a form of algebraic shorthand for summarizing a larger number of often repetitious and tedious algebraic computations.\nAll populations can be modeled\n\n \n \n \n \n N\n \n t\n +\n 1\n \n \n =\n \n N\n \n t\n \n \n +\n B\n \u2212\n D\n +\n I\n \u2212\n E\n ,\n \n \n {\\displaystyle N_{t+1}=N_{t}+B-D+I-E,}\n where:\n\nNt+1 = abundance at time t+1\nNt = abundance at time t\nB = number of births within the population between Nt and Nt+1\nD = number of deaths within the population between Nt and Nt+1\nI = number of individuals immigrating into the population between Nt and Nt+1\nE = number of individuals emigrating from the population between Nt and Nt+1This equation is called a BIDE model (Birth, Immigration, Death, Emigration model).\nAlthough BIDE models are conceptually simple, reliable estimates of the 5 variables contained therein (N, B, D, I and E) are often difficult to obtain. Usually a researcher attempts to estimate current abundance, Nt, often using some form of mark and recapture technique. Estimates of B might be obtained via a ratio of immatures to adults soon after the breeding season, Ri. Number of deaths can be obtained by estimating annual survival probability, usually via mark and recapture methods, then multiplying present abundance and survival rate. Often, immigration and emigration are ignored because they are so difficult to estimate.\nFor added simplicity it may help to think of time t as the end of the breeding season in year t and to imagine that one is studying a species that has only one discrete breeding season per year.\nThe BIDE model can then be expressed as:\n\n \n \n \n \n N\n \n t\n +\n 1\n \n \n =\n \n N\n \n t\n ,\n a\n \n \n \u00d7\n \n S\n \n a\n \n \n +\n \n N\n \n t\n ,\n i\n \n \n \u00d7\n \n R\n \n i\n \n \n \u00d7\n \n S\n \n i\n \n \n \n \n {\\displaystyle N_{t+1}=N_{t,a}\\times S_{a}+N_{t,i}\\times R_{i}\\times S_{i}}\n where:\n\nNt,a = number of adult females at time t\nNt,i = number of immature females at time t\nSa = annual survival of adult females from time t to time t+1\nSi = annual survival of immature females from time t to time t+1\nRi = ratio of surviving young females at the end of the breeding season per breeding femaleIn matrix notation this model can be expressed as:\n\n \n \n \n \n \n \n \n \n \n (\n \n \n \n \n N\n \n t\n +\n \n l\n \n i\n \n \n \n \n \n \n \n \n \n N\n \n t\n +\n \n l\n \n a\n \n \n \n \n \n \n \n )\n \n \n \n \n \n =\n \n \n (\n \n \n \n \n S\n \n i\n \n \n \n R\n \n i\n \n \n \n \n \n S\n \n a\n \n \n \n R\n \n i\n \n \n \n \n \n \n \n S\n \n i\n \n \n \n \n \n S\n \n a\n \n \n \n \n \n )\n \n \n \n \n (\n \n \n \n \n N\n \n \n t\n \n i\n \n \n \n \n \n \n \n \n \n N\n \n \n t\n \n a\n \n \n \n \n \n \n \n )\n \n \n \n \n \n \n .\n \n \n {\\displaystyle {\\begin{aligned}{\\begin{pmatrix}N_{t+l_{i}}\\\\N_{t+l_{a}}\\end{pmatrix}}&={\\begin{pmatrix}S_{i}R_{i}&S_{a}R_{i}\\\\S_{i}&S_{a}\\end{pmatrix}}{\\begin{pmatrix}N_{t_{i}}\\\\N_{t_{a}}\\end{pmatrix}}\\end{aligned}}.}\n Suppose that you are studying a species with a maximum lifespan of 4 years. The following is an age-based Leslie matrix for this species. Each row in the first and third matrices corresponds to animals within a given age range (0\u20131 years, 1\u20132 years and 2\u20133 years). In a Leslie matrix the top row of the middle matrix consists of age-specific fertilities: F1, F2 and F3. Note, that F1 = Si\u00d7Ri in the matrix above. Since this species does not live to be 4 years old the matrix does not contain an S3 term.\n\n \n \n \n \n \n \n \n \n \n (\n \n \n \n \n N\n \n t\n +\n \n l\n \n 1\n \n \n \n \n \n \n \n \n \n N\n \n t\n +\n \n l\n \n 2\n \n \n \n \n \n \n \n \n \n N\n \n t\n +\n \n l\n \n 3\n \n \n \n \n \n \n \n )\n \n \n \n \n \n =\n \n \n (\n \n \n \n \n F\n \n 1\n \n \n \n \n \n F\n \n 2\n \n \n \n \n \n F\n \n 3\n \n \n \n \n \n \n \n S\n \n 1\n \n \n \n \n 0\n \n \n 0\n \n \n \n \n 0\n \n \n \n S\n \n 2\n \n \n \n \n 0\n \n \n \n )\n \n \n \n \n (\n \n \n \n \n N\n \n \n t\n \n 1\n \n \n \n \n \n \n \n \n \n N\n \n \n t\n \n 2\n \n \n \n \n \n \n \n \n \n N\n \n \n t\n \n 3\n \n \n \n \n \n \n \n )\n \n \n \n \n \n \n .\n \n \n {\\displaystyle {\\begin{aligned}{\\begin{pmatrix}N_{t+l_{1}}\\\\N_{t+l_{2}}\\\\N_{t+l_{3}}\\end{pmatrix}}&={\\begin{pmatrix}F_{1}&F_{2}&F_{3}\\\\S_{1}&0&0\\\\0&S_{2}&0\\end{pmatrix}}{\\begin{pmatrix}N_{t_{1}}\\\\N_{t_{2}}\\\\N_{t_{3}}\\end{pmatrix}}\\end{aligned}}.}\n These models can give rise to interesting cyclical or seemingly chaotic patterns in abundance over time when fertility rates are high.\nThe terms Fi and Si can be constants or they can be functions of environment, such as habitat or population size. Randomness can also be incorporated into the environmental component.", "images": [], "links": ["International Standard Book Number", "Mark and recapture", "Matrix algebra", "Population dynamics", "Population dynamics of fisheries", "Population ecology", "Populations", "Survival rate"], "references": ["https://web.archive.org/web/20120425152322/http://andrei1606.brinkster.net/MatrixPopulationModel.aspx"]}, "Bayesian linear regression": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from August 2011", "Bayesian inference", "CS1 maint: Uses authors parameter", "Single-equation methods (econometrics)"], "title": "Bayesian linear regression", "method": "Bayesian linear regression", "url": "https://en.wikipedia.org/wiki/Bayesian_linear_regression", "summary": "In statistics, Bayesian linear regression is an approach to linear regression in which the statistical analysis is undertaken within the context of Bayesian inference. When the regression model has errors that have a normal distribution, and if a particular form of prior distribution is assumed, explicit results are available for the posterior probability distributions of the model's parameters.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Admissible decision rule", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrew Gelman", "Approximate Bayesian computation", "Approximation theory", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayes linear statistics", "Bayes theorem", "Bayesian efficiency", "Bayesian estimator", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian interpretation of kernel regularization", "Bayesian model comparison", "Bayesian multivariate linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernstein\u2013von Mises theorem", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calibration curve", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational statistics", "Conditional probability distribution", "Confidence interval", "Confounding", "Conjugate prior", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cromwell's rule", "Cross-correlation", "Cross-validation (statistics)", "Curve fitting", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design matrix", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete choice", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical Bayes method", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Estimation of covariance matrices", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fixed effects model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist", "Frequentist inference", "Friedman test", "G-test", "Gamma function", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "George E. P. Box", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hyperparameter", "Hyperprior", "I.i.d.", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse-gamma distribution", "Isotonic regression", "Iteratively reweighted least squares", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least-angle regression", "Least absolute deviations", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Marginal likelihood", "Markov chain Monte Carlo", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model evidence", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo sampling", "Moore-Penrose pseudoinverse", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normally distributed", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior distribution", "Posterior predictive distribution", "Posterior probability", "Posterior probability distribution", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal component regression", "Principle of indifference", "Principle of maximum entropy", "Prior distribution", "Prior probability", "Prior probability distribution", "Probabilistic design", "Probability distribution", "Probability interpretations", "Probit model", "Proportional hazards model", "Psychometrics", "Python (programming language)", "Quadratic form (statistics)", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Radical probabilism", "Random assignment", "Random effects model", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regularized least squares", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Ridge regression", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Schwarz criterion", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spike and slab variable selection", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Variational Bayes", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://research.microsoft.com/~minka/papers/linear.html", "http://epub.ub.uni-muenchen.de/11050/1/tr069.pdf", "http://doi.org/10.1007%2F978-3-642-01837-4", "http://doi.org/10.1504%2FIJSSS.2015.073223", "https://github.com/AmazaspShumik/sklearn-bayes/blob/master/skbayes/linear_models/bayes_linear.py", "https://github.com/AmazaspShumik/sklearn-bayes/blob/master/ipython_notebooks_tutorials/linear_models/bayesian_linear_regression.ipynb", "https://github.com/AmazaspShumik/sklearn-bayes/blob/master/skbayes/rvm_ard_models/fast_rvm.py", "https://github.com/AmazaspShumik/sklearn-bayes/blob/master/ipython_notebooks_tutorials/rvm_ard/rvm_demo.ipynb"]}, "F-test of equality of variances": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2010", "Statistical deviation and dispersion", "Statistical ratios", "Statistical tests"], "title": "F-test of equality of variances", "method": "F-test of equality of variances", "url": "https://en.wikipedia.org/wiki/F-test_of_equality_of_variances", "summary": "In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance. \nNotionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic used is the ratio of two sample variances . This particular situation is of importance in mathematical statistics since it provides a basic exemplar case in which the F-distribution can be derived. For application in applied statistics, there is concern that the test is so sensitive to the assumption of normality that it would be inadvisable to use it as a routine test for the equality of variances. In other words, this is a case where \"approximate normality\" (which in similar contexts would often be justified using the central limit theorem), is not good enough to make the test procedure approximately valid to an acceptable degree.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Applied statistics", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bartlett's test", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brown\u2013Forsythe test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George E. P. Box", "Geostatistics", "Goldfeld\u2013Quandt test", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hartley's test", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis test", "Independent and identically distributed", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Levene's test", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical statistics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Review of Educational Research", "Robust regression", "Robust statistics", "Run chart", "Sample mean", "Sample median", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical test", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Type I error", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://digitalcommons.wayne.edu/coe_tbf/23", "http://doi.org/10.1093%2Fbiomet%2F40.3-4.318", "http://doi.org/10.2307%2F2684360", "http://doi.org/10.3102%2F00346543051004499", "http://www.jstor.org/stable/2333350", "http://www.jstor.org/stable/2684360"]}, "Genetic epidemiology": {"categories": ["Articles with inconsistent citation formats", "Epidemiology", "Genetic epidemiology", "Genetics", "Human genetics", "Statistical genetics"], "title": "Genetic epidemiology", "method": "Genetic epidemiology", "url": "https://en.wikipedia.org/wiki/Genetic_epidemiology", "summary": "Genetic epidemiology is the study of the role of genetic factors in determining health and disease in families and in populations, and the interplay of such genetic factors with environmental factors. Genetic epidemiology seeks to derive a statistical and quantitative analysis of how genetics work in large groups.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["1000 Genomes Project", "Allele", "Annals of Human Genetics", "BMJ: British Medical Journal", "Behavioural genetics", "Biobank", "Biological database", "Biological specimen", "Chromosome", "De-identification", "Digital object identifier", "Dominance relationship", "Epigenetics", "Etiology", "Familial aggregation", "Framingham Heart Study", "Genetic association", "Genetic disorder", "Genetic linkage", "Genetic polymorphism", "Genetic segregation", "Genetics", "Genome-wide association study", "Genotyping", "Gregor Mendel", "Hardy\u2013Weinberg principle", "Hippocrates", "Human Genome Diversity Project", "Human Genome Project", "Human genetic variation", "Identity by descent", "International HapMap Project", "International Standard Book Number", "International Standard Serial Number", "John Graunt", "John Snow (physician)", "Mendelian randomization", "Molecular epidemiology", "Monogenic disorder", "Multifactorial or multigenic disorder", "Mutation", "Newton Morton", "Personal genomics", "Personalized medicine", "Polygenic disorder", "Population genetics", "Population groups in biomedicine", "Predictive medicine", "PubMed Central", "PubMed Identifier", "SNP array", "Single-nucleotide polymorphisms", "Single nucleotide polymorphism", "Statistical genetics", "Whole genome sequencing"], "references": ["http://www.bmj.com/content/320/7244/1257", "http://www.oup.com/uk/catalogue/?ci=9780195146745", "http://www.oup.com/uk/catalogue/?ci=9780195159394", "http://www3.interscience.wiley.com/journal/35841/home", "http://linkage.rockefeller.edu/wli/reading/morton97.pdf", "http://www.biostat.wustl.edu/gems/definition.shtml", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1117994", "http://www.ncbi.nlm.nih.gov/pubmed/10797040", "http://www.ncbi.nlm.nih.gov/pubmed/4669176", "http://www.dorak.info/epi/genetepi.html", "http://doi.org/10.1002/0470011815.b2a05034", "http://doi.org/10.1017/S0003480096005891", "http://doi.org/10.1093/ije/1.1.25", "http://doi.org/10.1136/bmj.320.7244.1257", "http://www.geneticepi.org/", "http://ije.oxfordjournals.org/content/1/1/25", "http://www.worldcat.org/issn/0300-5771", "http://www.worldcat.org/issn/0959-8138", "https://books.google.com/books?id=VC7BAgAAQBAJ"]}, "Markov chain geostatistics": {"categories": ["Geostatistics", "Interpolation", "Markov models"], "title": "Markov chain geostatistics", "method": "Markov chain geostatistics", "url": "https://en.wikipedia.org/wiki/Markov_chain_geostatistics", "summary": "Markov chain geostatistics uses Markov chain spatial models, simulation algorithms and associated spatial correlation measures (e.g., transiogram) based on the Markov chain random field theory, which extends a single Markov chain into a multi-dimensional random field for geostatistical modeling. A Markov chain random field is still a single spatial Markov chain. The spatial Markov chain moves or jumps in a space and decides its state at any unobserved location through interactions with its nearest known neighbors in different directions. The data interaction process can be well explained as a local sequential Bayesian updating process within a neighborhood. Because single-step transition probability matrices are difficult to estimate from sparse sample data and are impractical in representing the complex spatial heterogeneity of states, the transiogram, which is defined as a transition probability function over the distance lag, is proposed as the accompanying spatial measure of Markov chain random fields.", "images": [], "links": ["Algorithm", "Correlation", "Function (mathematics)", "Geostatistics", "Heterogeneity", "Lag", "Markov chain", "Matrix (mathematics)", "Sample (statistics)", "Simulation", "Transiogram", "Transition probability"], "references": ["http://gis.geog.uconn.edu/weidong/Markov_chain_spatial_statistics.htm"]}, "\u0141ukaszyk\u2013Karmowski metric": {"categories": ["Statistical distance"], "title": "\u0141ukaszyk\u2013Karmowski metric", "method": "\u0141ukaszyk\u2013Karmowski metric", "url": "https://en.wikipedia.org/wiki/%C5%81ukaszyk%E2%80%93Karmowski_metric", "summary": "In mathematics, the \u0141ukaszyk\u2013Karmowski metric is a function defining a distance between two random variables or two random vectors. This function is not a metric as it does not satisfy the identity of indiscernibles condition of the metric, that is for two identical arguments its value is greater than zero. The concept is named after Szymon \u0141ukaszyk and Wojciech Karmowski.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/ae/Equidistant_D2RDx0_ex.png", "https://upload.wikimedia.org/wikipedia/commons/d/dd/Equidistant_d2x0.png", "https://upload.wikimedia.org/wikipedia/commons/4/4b/L-Kmetric_quantum_particle_in_a_box.png", "https://upload.wikimedia.org/wikipedia/commons/7/71/LKmetric_DNN_explanation.png", "https://upload.wikimedia.org/wikipedia/commons/1/13/Probability_metric_DNN.png"], "links": ["Absolute value", "Arithmetic mean", "Digital object identifier", "Dirac delta", "Discrete probability distribution", "Elementary particle", "Error function", "Euclidean distance", "Euclidean metric", "Expected value", "Function (mathematics)", "Identity of indiscernibles", "If and only if", "International Standard Book Number", "Inverse distance weighting", "Joint probability density function", "Joint probability distribution", "Mary E. Thompson", "Mathematics", "Mean", "Metric (mathematics)", "Metric space", "Minkowski inequality", "Non-negative", "Normal distribution", "Particle in a box", "Poisson distribution", "Probabilistic metric space", "Probability", "Probability distribution function", "Quantum mechanics", "Radial basis function network", "Random variable", "Random vector", "Self-organizing map", "Standard deviation", "Statistical distance", "Statistical independence", "Subadditivity", "Symmetry", "Tape measure", "Teuvo Kohonen", "Thomas Landauer", "Triangle inequality", "Uniform distribution (continuous)", "Wavefunction"], "references": ["http://uwspace.uwaterloo.ca/bitstream/10012/5607/1/Meng_Gang.pdf", "http://www.ij-healthgeographics.com/content/9/1/50", "http://www.springerlink.com/content/y4fbdb0m0r12701p", "http://www.met.hu/download.php?id=2&vol=115&no=1-2&a=3", "http://www.sersc.org/journals/IJFGCN/vol3_no4/4.pdf", "http://nauka-polska.pl/dhtml/raporty/praceBadawcze?rtype=opis&lang=pl&objectId=42057", "http://lkmetric.patent.nazwa.pl/PROBABILITY_METRIC_doctoral_dissertation.pdf", "https://books.google.com/books?id=CbCDKLbm_-UC&hl=en", "https://doi.org/10.1007%2Fs00466-003-0532-2", "https://doi.org/10.1186%2F1476-072X-9-50"]}, "Ramaswami's formula": {"categories": ["Markov processes", "Single queueing nodes"], "title": "Matrix analytic method", "method": "Ramaswami's formula", "url": "https://en.wikipedia.org/wiki/Matrix_analytic_method", "summary": "In probability theory, the matrix analytic method is a technique to compute the stationary probability distribution of a Markov chain which has a repeating structure (after some point) and a state space which grows unboundedly in no more than one dimension. Such models are often described as M/G/1 type Markov chains because they can describe transitions in an M/G/1 queue. The method is a more complicated version of the matrix geometric method and is the classical solution method for M/G/1 chains.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "Cyclic reduction", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Embedded Markov chain", "Erlang (unit)", "Erlang distribution", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "International Standard Book Number", "Iterative method", "Jackson network", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/1 type Markov chain", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markov chain", "Markovian arrival process", "Matrix geometric method", "Mean field theory", "Mean value analysis", "Message queue", "Mor Harchol-Balter", "Network congestion", "Network scheduler", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Positive recurrent", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations", "Vaidyanathan Ramaswami"], "references": ["http://www.cs.wm.edu/MAMSolver/", "http://www.cs.wm.edu/~riska/paper-MG1-tutorial.pdf", "http://doi.org/10.1007%2F3-540-45798-4_3", "http://doi.org/10.1007%2F3-540-46029-2_14", "http://doi.org/10.1007%2F978-3-540-78725-9_7", "http://doi.org/10.1016%2F0377-2217(84)90034-1", "http://doi.org/10.1016%2Fj.peva.2005.07.003", "http://doi.org/10.1017%2FCBO9781139226424.028", "http://doi.org/10.1080%2F15326348808807077", "http://doi.org/10.1080%2F15326349708807423", "http://doi.org/10.1080%2F15326349808807483", "http://doi.org/10.1093%2Facprof:oso%2F9780198527688.001.0001", "http://doi.org/10.1145%2F511399.511346"]}, "Bayesian search theory": {"categories": ["Bayesian statistics", "Operations research", "Search algorithms"], "title": "Bayesian search theory", "method": "Bayesian search theory", "url": "https://en.wikipedia.org/wiki/Bayesian_search_theory", "summary": "Bayesian search theory is the application of Bayesian statistics to the search for lost objects. It has been used several times to find lost sea vessels, for example the USS Scorpion. It also played a key role in the recovery of the flight recorders in the Air France Flight 447 disaster of 2009. Currently, it is being used to locate the remains of Malaysia Airlines Flight 370.", "images": [], "links": ["1966 Palomares B-52 crash", "Air France Flight 447", "Azores", "Bathyscaphe", "Bathyscaphe Trieste II", "Bayes' theorem", "Bayesian inference", "Bayesian statistics", "Bernard Koopman", "Civil Air Patrol", "Contour map", "Crush depth", "David Blackwell", "East Coast of the United States", "Gittins index", "Hydroacoustics", "Hydrogen bomb", "Hydrophone", "John Craven USN", "Lanchester Prize", "Lawrence D. Stone", "MV Derbyshire", "Malaysia Airlines Flight 370", "National Museum of the United States Navy", "Naval Research Laboratory", "Norfolk, Virginia", "Nuclear submarine", "Operations Research Society of America", "Probability density function", "Ross, Sheldon M.", "SOSUS", "SS Central America", "Search and rescue", "Search games", "Stone, Lawrence D.", "U.S. Navy", "USNS Mizar (AGOR-11)", "USS Scorpion (SSN-589)", "USS Thresher (SSN-593)", "United States Air Force", "United States Coast Guard"], "references": ["https://www.bloomberg.com/news/articles/2015-12-02/mh370-hunters-say-new-analysis-reaffirms-most-likely-wreck-site", "https://www.bloomberg.com/news/articles/2015-12-03/find-mh370-next-job-for-theory-used-to-show-existence-of-god", "https://books.google.com/books?id=EyoDAAAAMBAJ&pg=PA66", "https://www.informs.org/ORMS-Today/Public-Articles/August-Volume-38-Number-4/In-Search-of-Air-France-Flight-447", "https://www.telegraph.co.uk/news/worldnews/mh370/12030483/MH370-search-narrowed-to-hot-spot-as-analysis-finds-plane-did-not-conduct-controlled-landing.html"]}, "Biometrics (statistics)": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "All pages needing cleanup", "Articles needing additional references from December 2016", "Articles needing cleanup from March 2016", "Articles with sections that need to be turned into prose from March 2016", "Articles with unsourced statements from December 2016", "Bioinformatics", "Biostatistics", "CS1: Julian\u2013Gregorian uncertainty", "CS1 maint: Explicit use of et al.", "Commons category link from Wikidata", "Demography", "Public health"], "title": "Biostatistics", "method": "Biometrics (statistics)", "url": "https://en.wikipedia.org/wiki/Biostatistics", "summary": "Biostatistics are the application of statistics to a wide range of topics in biology. It encompasses the design of biological experiments, especially in medicine, pharmacy, agriculture and fishery; the collection, summarization, and analysis of data from those experiments; and the interpretation of, and inference from, the results. A major branch is medical biostatistics, which is exclusively concerned with medicine and health.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/34/Correlation_coefficient.png", "https://upload.wikimedia.org/wikipedia/commons/1/1d/Example_histogram.png", "https://upload.wikimedia.org/wikipedia/commons/1/15/Examples_of_descriptive_tools.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ANOVA", "ASReml", "Abhaya Indrayan", "Abiogenesis", "Accelerated failure time model", "Accuracy and precision", "Actuarial science", "Agriculture", "Akaike information criterion", "Allele", "Alternative 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"https://www.vsni.co.uk/", "https://www.vsni.co.uk/software/cycdesign/"]}, "Accidental sampling": {"categories": ["CS1 maint: Extra text: authors list", "Sampling techniques"], "title": "Convenience sampling", "method": "Accidental sampling", "url": "https://en.wikipedia.org/wiki/Convenience_sampling", "summary": "Convenience sampling (also known as grab sampling, accidental sampling, or opportunity sampling) is a type of non-probability sampling that involves the sample being drawn from that part of the population that is close to hand. This type of sampling is most useful for pilot testing.", "images": [], "links": ["Bias", "Data collection", "Digital object identifier", "Facebook", "Hypothesis", "International Standard Book Number", "International Standard Serial Number", "Non-probability sampling", "Pilot experiment", "Population", "PubMed Central", "Questionnaire", "Sample (statistics)", "Sampling error", "Statistical power", "Survey (human research)"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4012002", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4286359", "http://doi.org/10.1007%2Fs10488-013-0528-y", "http://doi.org/10.1016%2Fj.dr.2013.08.003", "http://doi.org/10.1177%2F2345678906292430", "http://doi.org/10.4135%2F9781412963909.n68", "http://www.worldcat.org/issn/0273-2297", "https://dx.doi.org/10.4135/9781412963909.n68"]}, "Statistical syllogism": {"categories": ["Arguments", "Logic and statistics", "Syllogism", "Term logic"], "title": "Statistical syllogism", "method": "Statistical syllogism", "url": "https://en.wikipedia.org/wiki/Statistical_syllogism", "summary": "A statistical syllogism (or proportional syllogism or direct inference) is a non-deductive syllogism. It argues, using inductive reasoning, from a generalization true for the most part to a particular case.", "images": [], "links": ["Accident (fallacy)", "Aristotle", "Clinical trials", "Confidence intervals", "Converse accident", "David Stove", "Deductive", "Deductive reasoning", "Dicto simpliciter", "Donald Cary Williams", "Faulty generalization", "Fuzzy logic", "Generalization", "Henry E. Kyburg, Jr.", "Inductive reasoning", "Insurance", "International Standard Book Number", "John Venn", "L. Jonathan Cohen", "Prior Analytics", "Problem of induction", "Qualifier", "Reference class problem", "Statistical inference", "Statistics", "Syllogism", "Talmud"], "references": ["http://plato.stanford.edu/entries/williams-dc/", "http://www.uncg.edu/phi/phi115/induc4.htm", "http://heinonline.org/HOL/LandingPage?collection=journals&handle=hein.journals/arzjl1981&div=29&id=&page=", "https://web.archive.org/web/20070927003210/http://www.uncg.edu/phi/phi115/induc4.htm"]}, "Goodhart's law": {"categories": ["1975 in economics", "Adages", "Economics laws", "Economics of regulation", "Pages containing links to subscription-only content", "Subscription required using via", "Wikipedia articles needing clarification from March 2017"], "title": "Goodhart's law", "method": "Goodhart's law", "url": "https://en.wikipedia.org/wiki/Goodhart%27s_law", "summary": "Goodhart's law is an adage named after economist Charles Goodhart, which has been phrased by Marilyn Strathern as: \"When a measure becomes a target, it ceases to be a good measure.\" One way in which this can occur is individuals trying to anticipate the effect of a policy and then taking actions which alter its outcome.\n\n", "images": [], "links": ["Abilene paradox", "Adage", "Adverse effect", "ArXiv", "Bibcode", "Butterfly effect", "CSI effect", "Campbell's law", "Charles Goodhart", "Citation impact", "Cobra effect", "Counterintuitive", "Digital object identifier", "Economics", "Excess burden of taxation", "Externality", "Failure mode and effects analysis", "Financial risk modeling", "Hawthorne effect", "Hutber's law", "Inverse consequences", "Jevons paradox", "Jon Danielsson", "Lucas critique", "Margaret Thatcher", "Monetarism", "Murphy's law", "Nocebo", "Osborne effect", "Overfitting", "Parable of the broken window", "Perverse incentive", "Policy", "Profit (economics)", "PubMed Identifier", "Rational expectations", "Reflexivity (social theory)", "Reification (fallacy)", "Risk compensation", "ScienceDirect", "Self-defeating prophecy", "Self-refuting idea", "Serendipity", "Social trap", "Streisand effect", "Tragedy of the commons", "Tyranny of small decisions", "Unintended consequences", "United Kingdom"], "references": ["http://conferences.asucollegeoflaw.com/sciencepublicsphere/files/2014/02/Strathern1997-2.pdf", "http://www.nature.com/news/watch-out-for-cheats-in-citation-game-1.20246", "http://www.ribbonfarm.com/2016/09/29/soft-bias-of-underspecified-goals/", "http://www.sciencedirect.com/science/article/pii/S0378426602002637", "http://cyberlibris.typepad.com/blog/files/Goodharts_Law.pdf", "http://adsabs.harvard.edu/abs/2016Natur.535..201B", "http://www.ncbi.nlm.nih.gov/pubmed/27411599", "http://arxiv.org/abs/1803.04585", "http://arxiv.org/archive/cs.AI", "http://doi.org/10.1016%2FS0378-4266(02)00263-7", "http://doi.org/10.1038%2F535201a", "https://www.ribbonfarm.com/2016/06/09/goodharts-law-and-why-measurement-is-hard/", "https://arxiv.org/abs/1803.04585"]}, "Random walk hypothesis": {"categories": ["1964 introductions", "Finance theories", "Stochastic processes", "Wikipedia articles needing clarification from March 2014"], "title": "Random walk hypothesis", "method": "Random walk hypothesis", "url": "https://en.wikipedia.org/wiki/Random_walk_hypothesis", "summary": "The random walk hypothesis is a financial theory stating that stock market prices evolve according to a random walk (so price changes are random) and thus cannot be predicted. It is consistent with the efficient-market hypothesis.\nThe concept can be traced to French broker Jules Regnault who published a book in 1863, and then to French mathematician Louis Bachelier whose Ph.D. dissertation titled \"The Theory of Speculation\" (1900) included some remarkable insights and commentary. The same ideas were later developed by MIT Sloan School of Management professor Paul Cootner in his 1964 book The Random Character of Stock Market Prices. The term was popularized by the 1973 book, A Random Walk Down Wall Street, by Burton Malkiel, a Professor of Economics at Princeton University, and was used earlier in Eugene Fama's 1965 article \"Random Walks In Stock Market Prices\", which was a less technical version of his Ph.D. thesis. The theory that stock prices move randomly was earlier proposed by Maurice Kendall in his 1953 paper, The Analysis of Economic Time Series, Part 1: Prices.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/38/Pi_stock.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/38/20150716173907%21Pi_stock.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/38/20150716173905%21Pi_stock.svg"], "links": ["A Random Walk Down Wall Street", "Adaptive market hypothesis", "Algorithmic trading", "Alok Bhargava", "Alpha (finance)", "Andrew Lo", "Arbitrage pricing theory", "Authorised capital", "Beta (finance)", "Bid\u2013ask spread", "Block trade", "Book value", "Broker-dealer", "Burton Malkiel", "Buy and hold", "Capital asset pricing model", "Capital market", "Capital market line", "Common stock", "Contrarian investing", "Cross listing", "Dark pool", "Day trader", "Day trading", "Digital object identifier", "Dividend", "Dividend discount model", "Dividend yield", "Dollar cost averaging", "DuPont analysis", "Dual-listed company", "Earnings per share", "Earnings yield", "Efficient-market hypothesis", "Efficient frontier", "Electronic communication network", "Eugene Fama", "Finance theory", "Financial law", "Financial market", "Financial regulation", "Flight-to-quality", "Floor broker", "Floor trader", "Fourth market", "Fundamental analysis", "Golden share", "Growth stock", "Haircut (finance)", "Independence (probability theory)", "Initial public offering", "International Standard Book Number", "Investor", "Issued shares", "JSTOR", "Jules Regnault", "List of stock exchange trading hours", "List of stock exchanges", "Long (finance)", "Louis Bachelier", "MIT Press", "MIT Sloan School of Management", "Margin (finance)", "Market anomaly", "Market capitalization", "Market depth", "Market maker", "Market manipulation", "Market price", "Market timing", "Market trend", "Maurice Kendall", "Mean reversion (finance)", "Modern portfolio theory", "Momentum (finance)", "Momentum investing", "Mosaic theory (investments)", "Multilateral trading facility", "Net asset value", "Open outcry", "Over-the-counter (finance)", "Pairs trade", "Paul Cootner", "Pi", "Position (finance)", "Post-modern portfolio theory", "Preferred stock", "Primary market", "Princeton University", "Princeton University Press", "Proprietary trading", "Public float", "Public offering", "Quantitative analyst", "Rally (stock market)", "Random", "Random walk", "Rate of return", "Restricted stock", "Returns-based style analysis", "Reverse stock split", "Secondary market", "Sector rotation", "Security characteristic line", "Security market line", "Share capital", "Share repurchase", "Shares outstanding", "Short (finance)", "Slippage (finance)", "Speculation", "Stock", "Stock dilution", "Stock exchange", "Stock market", "Stock market index", "Stock split", "Stock trader", "Stock valuation", "Style investing", "Swing trading", "T-model", "Technical analysis", "Third market", "Tracking stock", "Trade (financial instrument)", "Trading strategy", "Treasury stock", "Trend following", "Uptick rule", "Value averaging", "Value investing", "Volatility (finance)", "Voting interest", "Yield (finance)"], "references": ["http://www.cfapubs.org/toc/faj/1965/21/5", "http://doi.org/10.2469%2Ffaj.v21.n5.55", "http://www.jstor.org/stable/2980947", "https://books.google.com/books?id=7XGvQgAACAAJ"]}, "Generative model": {"categories": ["Machine learning", "Probabilistic models", "Statistical models"], "title": "Generative model", "method": "Generative model", "url": "https://en.wikipedia.org/wiki/Generative_model", "summary": "In statistical classification, including machine learning, two main approaches are called the generative approach and the discriminative approach. These compute classifiers by different approaches, differing in the degree of statistical modelling. Terminology is inconsistent, but three major types can be distinguished, following Jebara (2004):\n\nGiven an observable variable X and a target variable Y, a generative model is a statistical model of the joint probability distribution on X \u00d7 Y, \n \n \n \n P\n (\n X\n ,\n Y\n )\n \n \n {\\displaystyle P(X,Y)}\n ;\nA discriminative model is a model of the conditional probability of the target Y, given an observation x, symbolically, \n \n \n \n P\n (\n Y\n \n |\n \n X\n =\n x\n )\n \n \n {\\displaystyle P(Y|X=x)}\n ; and\nClassifiers computed without using a probability model are also referred to loosely as \"discriminative\".The distinction between these last two classes is not consistently made; Jebara (2004) refers to these three classes as generative learning, conditional learning, and discriminative learning, but Ng & Jordan (2002) only distinguishes two classes, calling them generative classifiers (joint distribution) and discriminative classifiers (conditional distribution or no distribution), not distinguishing between the latter two classes. Analogously, a classifier based on a generative model is a generative classifier, while a classifier based on a discriminative model is a discriminative classifier, though this term also refers to classifiers that are not based on a model. Standard examples of each, all of which are linear classifiers, are: generative classifiers: naive Bayes classifier and linear discriminant analysis; discriminative model: logistic regression; non-model classifier: perceptron and support vector machine.\nIn application to classification, one wishes to go from an observation x to a label y (or probability distribution on labels). One can compute this directly, without using a probability distribution (distribution-free classifier); one can estimate the probability of a label given an observation, \n \n \n \n P\n (\n Y\n \n |\n \n X\n =\n x\n )\n \n \n {\\displaystyle P(Y|X=x)}\n (discriminative model), and base classification on that; or one can estimate the joint distribution \n \n \n \n P\n (\n X\n ,\n Y\n )\n \n \n {\\displaystyle P(X,Y)}\n (generative model), from that compute the conditional probability \n \n \n \n P\n (\n Y\n \n |\n \n X\n =\n x\n )\n \n \n {\\displaystyle P(Y|X=x)}\n , and then base classification on that. These are increasingly indirect, but increasingly probabilistic, allowing more domain knowledge and probability theory to be applied. In practice different approaches are used, depending on the particular problem, and hybrids can combine strengths of multiple approaches.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrew Ng", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoencoder", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Averaged one-dependence estimators", "Bar chart", "Bayes' rule", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bell System Technical Journal", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Classification (machine learning)", "Classification rule", "Claude Shannon", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional probability", "Conditional random field", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous variable", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Discrete variable", "Discriminative model", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical measure", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian mixture model", "General linear model", "Generalized linear model", "Generative adversarial networks", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Handle System", "Harmonic mean", "Heteroscedasticity", "Hidden Markov model", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latent Dirichlet allocation", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear classifier", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Machine learning", "Mann\u2013Whitney U test", "Marginal distribution", "Massachusetts Institute of Technology", "Maximum-entropy Markov model", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michael I. Jordan", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mixture model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Naive Bayes", "Naive Bayes classifier", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Neural network", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observable variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outcome (probability)", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perceptron", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted Boltzmann machine", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic context-free grammar", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Support Vector Machines", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Target function", "Target variable", "Time domain", "Time series", "Tolerance interval", "Tom M. Mitchell", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.cs.cmu.edu/~tom/mlbook/NBayesLogReg.pdf", "http://www.cs.columbia.edu/~jebara/papers/jebara4.pdf", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.7.513&rep=rep1&type=pdf", "http://robotics.stanford.edu/~ang/papers/nips01-discriminativegenerative.pdf", "http://hdl.handle.net/1721.1%2F8323", "https://books.google.com/books?id=Vh7vAAAAMAAJ&pg=PA3", "https://www.springer.com/us/book/9781402076473", "https://www.tnt.uni-hannover.de/edu/vorlesungen/InfoTheor/download/shannon1948.pdf"]}, "Statistics": {"categories": ["All articles with specifically marked weasel-worded phrases", "All articles with unsourced statements", "Articles with specifically marked weasel-worded phrases from April 2014", "Articles with unsourced statements from April 2015", "Articles with unsourced statements from February 2015", "Articles with unsourced statements from March 2013", "Articles with unsourced statements from September 2018", "CS1 maint: Extra text: authors list", "CS1 maint: Uses editors parameter", "Data", "Formal sciences", "Information", "Mathematical and quantitative methods (economics)", "Research methods", "Statistics", "Wikipedia articles needing clarification from October 2016", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NARA identifiers", "Wikipedia articles with NDL identifiers"], "title": "Statistics", "method": "Statistics", "url": "https://en.wikipedia.org/wiki/Statistics", "summary": "Statistics is a branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation. In applying statistics to, for example, a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as \"all people living in a country\" or \"every atom composing a crystal\". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.\nSee glossary of probability and statistics.\nWhen census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.\nTwo main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.\nA standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a \"false positive\") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a \"false negative\"). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.\nStatistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. In more recent years statistics has relied more on statistical software to produce tests such as descriptive analysis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b9/Gretl_screenshot.png", "https://upload.wikimedia.org/wikipedia/commons/9/97/Jer%C3%B4me_Cardan.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/18/Karl_Pearson%2C_1910.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/75/Linear_least_squares%282%29.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/NYW-confidence-interval.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/P-value_in_statistical_significance_testing.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d8/Scatterplot.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/b8/Simple_Confounding_Case.svg", "https://upload.wikimedia.org/wikipedia/commons/2/25/The_Normal_Distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikibooks-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/2/24/Wikinews-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1b/Wikiversity-logo-en.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1b/Wikiversity-logo-en.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/0/06/Wiktionary-logo-v2.svg"], "links": ["A.W.F. 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"Sample (statistics)", "Sample covariance", "Sample mean", "Sample median", "Sample size determination", "Sample statistic", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set theory", "Sex ratio", "Sexual selection", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social research", "Social science", "Social statistics", "Sociology", "Spatial analysis", "Spatial data analysis", "Spearman's rank correlation coefficient", "Specialized terminology", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Standardized testing (statistics)", "Stanford Encyclopedia of Philosophy", "Stanley Smith Stevens", "Stationary process", "Statistic", "Statistical Methods for Research Workers", "Statistical classification", "Statistical consultant", "Statistical data type", "Statistical decision theory", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical literacy", "Statistical mechanics", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical significance", "Statistical survey", "Statistical theory", "Statistician", "Statisticians", "Statistics (disambiguation)", "Stem-and-leaf display", "Stochastic analysis", "Stochastic music", "Stratified sampling", "Structural break", "Structural equation modeling", "Structural equation modelling", "Structured data analysis (statistics)", "Student's t-distribution", "Student's t-test", "Sufficiency (statistics)", "Sufficient statistic", "Survey methodology", "Survey sampling", "Survival analysis", "Survival function", "System identification", "Systematic error", "T-score", "Temperature", "Test statistic", "The American Statistician", "The Correlation between Relatives on the Supposition of Mendelian Inheritance", "The Design of Experiments", "The Genetical Theory of Natural Selection", "Theory of computation", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Topology", "Trend estimation", "Trigonometry", "Type II error", "Type I and type II errors", "Type I error", "U-statistic", "UMVUE", "Unbiased estimator", "Uniformly most powerful test", "University College London", "V-statistic", "Variable (mathematics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Western Electric Company", "Whittle likelihood", "Wilcoxon signed-rank test", "William Gosset", "Z-score", "Z-test"], "references": ["http://moityca.com.br/pdfs/Cohen_1990.pdf", "http://statistics.about.com/od/Inferential-Statistics/a/Type-I-And-Type-II-Errors.htm", "http://www.merriam-webster.com/dictionary/statistics", "http://onlinestatbook.com/index.html", "http://www.rossmanchance.com/iscam/preface.pdf", "http://www.statsoft.com/textbook/", "http://www.yourstatsguru.com/epar/rp-reviewed/cohen1994/", "http://adsabs.harvard.edu/abs/1877Natur..15..492.", "http://psychstat3.missouristate.edu/Documents/IntroBook3/sbk.htm", "http://www.santafe.edu/news/item/sfnm-wood-big-data/", "http://plato.stanford.edu/entries/statistics/", "http://www.stat.ufl.edu/~aa/articles/agresti_hitchcock_2005.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182327", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1936999", "http://www.ncbi.nlm.nih.gov/pubmed/16060722", "http://www.ncbi.nlm.nih.gov/pubmed/17608932", "http://www.ncbi.nlm.nih.gov/pubmed/18811377", "http://www.economicsdiscussion.net/essays/essay-on-statistics-meaning-and-definition-of-statistics/2315", "http://doi.org/10.1007%2Fs10260-005-0121-y", "http://doi.org/10.1038%2F015492a0", "http://doi.org/10.1080%2F01621459.1938.10502344", "http://doi.org/10.1080%2F14786440009463897", "http://doi.org/10.1086%2F286141", "http://doi.org/10.1177%2F0016986212444122", "http://doi.org/10.1186%2F1471-2288-7-30", "http://doi.org/10.1214%2Fss%2F1177012580", "http://doi.org/10.1371%2Fjournal.pmed.0020124", "http://doi.org/10.1559%2F152304098782383043", "http://doi.org/10.2307%2F2528399", "http://doi.org/10.2307%2F2682986", "http://doi.org/10.3102%2F00028312003003223", "http://www.jstor.org/stable/1161806", "http://www.jstor.org/stable/2342192", "http://www.jstor.org/stable/2528399", "http://www.jstor.org/stable/2682986", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Statistics", "http://www.ucl.ac.uk/stats/department/pearson.html", "https://books.google.com/books?id=jYFRAAAAMAAJ", "https://books.google.com/books?id=mywdBQAAQBAJ", "https://statistics.laerd.com/statistical-guides/descriptive-inferential-statistics.php", "https://plato.stanford.edu/entries/statistics/", "https://catalog.archives.gov/id/10659134", "https://id.loc.gov/authorities/subjects/sh85127580", "https://d-nb.info/gnd/4056995-0", "https://id.ndl.go.jp/auth/ndlna/00573173", "https://web.archive.org/web/20060717201702/http://www.ats.ucla.edu/stat/", "https://web.archive.org/web/20080925065418/http://www.ucl.ac.uk/stats/department/pearson.html", "https://doi.org/10.1016%2Fj.socec.2004.09.033", "https://doi.org/10.1371%2Fjournal.pmed.0040168", "https://www.jstor.org/stable/1400906", "https://www.openintro.org/stat/textbook.php?stat_book=os", "https://openstax.org/details/introductory-statistics", "https://www.wikidata.org/wiki/Q12483", "https://www.answers.org.za/index.php/tutorials"]}, "Forecasting": {"categories": ["All articles with dead external links", "All articles with unsourced statements", "Articles with dead external links from September 2018", "Articles with permanently dead external links", "Articles with unsourced statements from May 2012", "Forecasting", "Pages using web citations with no URL", "Statistical forecasting", "Supply chain analytics", "Supply chain management", "Time series", "Wikipedia articles needing clarification from December 2013"], "title": "Forecasting", "method": "Forecasting", "url": "https://en.wikipedia.org/wiki/Forecasting", "summary": "Forecasting is the process of making predictions of the future based on past and present data and most commonly by analysis of trends. A commonplace example might be estimation of some variable of interest at some specified future date. Prediction is a similar, but more general term. Both might refer to formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods. Usage can differ between areas of application: for example, in hydrology the terms \"forecast\" and \"forecasting\" are sometimes reserved for estimates of values at certain specific future times, while the term \"prediction\" is used for more general estimates, such as the number of times floods will occur over a long period.\nRisk and uncertainty are central to forecasting and prediction; it is generally considered good practice to indicate the degree of uncertainty attaching to forecasts. In any case, the data must be up to date in order for the forecast to be as accurate as possible. In some cases the data used to predict the variable of interest is itself forecasted.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["ARMAX", "Accelerating change", "Algorithm", "Artificial neural networks", "Autoregressive integrated moving average", "Autoregressive\u2013moving-average model", "Average absolute deviation", "Box\u2013Jenkins", "Calculating demand forecast accuracy", "Chaos theory", "Collaborative planning, forecasting, and replenishment", "Confidence interval", "Consensus forecasts", "Correlation", "Credit rating", "Credit score", "Cross-sectional data", "Cross-validation (statistics)", "Customer Demand Planning", "Data", "Data mining", "Decomposition of time series", "Default (finance)", "Delphi method", "Digital object identifier", "Earthquake prediction", "Econometric model", "Economic forecasting", "Edward Lorenz", "Efficient-market hypothesis", "Egain Forecasting", "Egain forecasting", "Energy forecasting", "Ensemble forecasting", "Errors and residuals", "Estimation", "Exchange rate", "Exponential smoothing", "Extrapolation", "Finance", "Flood forecasting", "Fluid dynamics", "Forecast (disambiguation)", "Forecast by analogy", "Forecast error", "Forecast skill", "Forecasting", "Forecasting bias", "Foreign exchange market", "Foresight (future studies)", "Fundamental analysis", "Future", "Futures studies", "Futurology", "GMDH", "Group method of data handling", "Growth curve (statistics)", "Hydrology", "International Journal of Forecasting", "International Standard Book Number", "J. Scott Armstrong", "JSTOR", "Kalman filter", "Kondratiev wave", "Land use forecasting", "Linear prediction", "Longitudinal study", "Machine learning", "Market research", "Mathematical model", "Mean absolute error", "Mean absolute percentage error", "Mean absolute scaled error", "Mean square error", "Mean squared error", "Mean squared prediction error", "Meteorology", "Moving average", "Nicholas Rescher", "Nonparametric regression", "Optimism bias", "PECOTA", "Parametric statistics", "Pattern recognition", "Peter Turchin", "Planning", "Political forecasting", "Predictability", "Prediction", "Prediction interval", "Prediction market", "Probabilistic forecasting", "Probability", "Product forecasting", "Profit margin", "Reference class forecasting", "Regression analysis", "Risk", "Risk management", "Rob J. Hyndman", "Root-mean-square deviation", "Sales", "Sales forecasting", "Scenario building", "Scenario planning", "Seasonality", "Senior management", "Seymour Geisser", "Simple linear regression", "Simulation", "Spending wave", "Statistical survey", "Stochastic drift", "Stock market", "Strategic foresight", "Supply chain management", "Support vector machine", "Survey methodology", "Technology forecasting", "Telecommunications forecasting", "Time Series", "Time series", "Transport planning", "Transportation forecasting", "Trend analysis", "Trend estimation", "Uncertainty", "Weather forecasting", "Weighted moving average", "Wind power forecasting"], "references": ["http://www.forecastingblog.com/?p=134", "http://www.forecastingprinciples.com", "http://www.forecastingprinciples.com/index.php?option=com_content&task=view&id=3&Itemid=3", "http://www.forecastingprinciples.com/index.php?option=com_content&task=view&id=3&Itemid=3#D._Choosing_the_best_method", "http://www.forecastingprinciples.com/index.php?option=com_content&task=view&id=17&Itemid=17", "http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf", "http://www.forecastingprinciples.com/paperpdf/Monetary%20Incentives.pdf", "http://www.mckinsey.com/insights", "http://www.okanduru.com/forecast.htm", "http://www.quakefinder.com", "http://www.robjhyndman.com/papers/mase.pdf", "http://www.statsoft.com/textbook/sttimser.html", "http://www.tandfonline.com/doi/full/10.1080/14445921.2016.1225149", "http://www.tandfonline.com/eprint/pgjIcAMrJBP4WcHIZH7F/full", "http://www.ifs.du.edu", "http://marketing.wharton.upenn.edu/documents/research/Value%20of%20expertise.pdf", "http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/armstrong-errormeasures-empirical.pdf", "http://qbox.wharton.upenn.edu/documents/mktg/research/FAQ.pdf", "http://www.qbox.wharton.upenn.edu/documents/mktg/research/INTFOR3581%20-%20Publication%2015.pdf", "http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm", "http://doi.org/10.1002%2Ffor.3980020411", "http://doi.org/10.1016%2F0169-2070(92)90008-w", "http://doi.org/10.1016%2F0378-7788(91)90028-2", "http://doi.org/10.1016%2Fj.ijforecast.2006.03.001", "http://doi.org/10.1057%2Fs41278-016-0051-7", "http://doi.org/10.1177%2F097206340700900105", "http://doi.org/10.1287%2Fopre.51.3.343.14953", "http://www.forecasters.org", "http://www.jstor.org/stable/2234183", "https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US6098893", "https://www.fidelity.com/viewpoints/investing-ideas/2015-outlook-for-stocks", "https://www.poundsterlinglive.com/euroforecast", "https://link.springer.com/article/10.1057/s41278-016-0051-7", "https://web.archive.org/web/20100620223405/http://marketing.wharton.upenn.edu/documents/research/Value%20of%20expertise.pdf", "https://web.archive.org/web/20120206182744/http://marketing.wharton.upenn.edu/ideas/pdf/armstrong2/armstrong-errormeasures-empirical.pdf", "https://dx.doi.org/10.1109/ICIP.2016.7532978", "https://www.otexts.org/fpp/1/1", "https://www.otexts.org/fpp/2/3", "https://www.otexts.org/fpp/2/5", "https://www.otexts.org/fpp/3/1"]}, "Divisia index": {"categories": ["Economic indicators", "Price index theory", "Time series"], "title": "Divisia index", "method": "Divisia index", "url": "https://en.wikipedia.org/wiki/Divisia_index", "summary": "A Divisia index is a theoretical construct to create index number series for continuous-time data on prices and quantities of goods exchanged. The name comes from Fran\u00e7ois Divisia who first proposed and formally analyzed the indexes in 1926, and discussed in related 1925 and 1928 works.The Divisia index is designed to incorporate quantity and price changes over time from subcomponents that are measured in different units, such as labor hours and equipment investment and materials purchases, and to summarize them in a time series that summarizes the changes in quantities and/or prices. The resulting index number series is unitless, like other index numbers.In practice, economic data are not measured in continuous time. Thus, when a series is said to be a Divisia index, it usually means the series follows a procedure that makes a close analogue in discrete time periods, usually the T\u00f6rnqvist index procedure or the Fisher Ideal Index procedures.", "images": [], "links": ["Bank of England", "Divisia monetary aggregates index", "Fisher Ideal Index", "Fran\u00e7ois Divisia", "Index (economics)", "Price index", "The New Palgrave Dictionary of Economics", "T\u00f6rnqvist index", "Volume index"], "references": ["http://www.economics.ubc.ca/files/2013/06/pdf_paper_erwin-diewert-essays-index-2.pdf", "http://www.dictionaryofeconomics.com/article?id=pde2008_D000174&edition=current&q=Divisia%20index%20&topicid=&result_number=1", "http://research.stlouisfed.org/msi/index.html", "http://moneyterms.co.uk/divisia/"]}, "Probability plot correlation coefficient plot": {"categories": ["Statistical charts and diagrams", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Probability plot correlation coefficient plot", "method": "Probability plot correlation coefficient plot", "url": "https://en.wikipedia.org/wiki/Probability_plot_correlation_coefficient_plot", "summary": "Many statistical analyses are based on distributional assumptions about the population from which the data have been obtained. However, distributional families can have radically different shapes depending on the value of the shape parameter. Therefore, finding a reasonable choice for the shape parameter is a necessary step in the analysis. In many analyses, finding a good distributional model for the data is the primary focus of the analysis.\nThe probability plot correlation coefficient (PPCC) plot is a graphical technique for identifying the shape parameter for a distributional family that best describes the data set. This technique is appropriate for families, such as the Weibull, that are defined by a single shape parameter and location and scale parameters, and it is not appropriate or even possible for distributions, such as the normal, that are defined only by location and scale parameters.\nThe technique is simply \"plot the probability plot correlation coefficients for different values of the shape parameter, and choose whichever value yields the best fit\".", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["Beta distribution", "Cauchy distribution", "Continuous uniform distribution", "Copyright status of work by the U.S. government", "Digital object identifier", "Gamma distribution", "Graphical technique", "Inverse Gaussian distribution", "JSTOR", "Laplace distribution", "Location parameter", "Logistic distribution", "Lognormal distribution", "Long-tailed distribution", "National Institute of Standards and Technology", "Normal distribution", "Pearson product-moment correlation coefficient", "Population (statistics)", "Probability plot", "Probability plot correlation coefficient", "Reliability (statistics)", "Scale parameter", "Shape parameter", "Short-tailed distribution", "Statistical analysis", "Tukey lambda distribution", "Weibull distribution"], "references": ["http://www.itl.nist.gov/div898/handbook/eda/section3/ppccplot.htm", "http://www.nist.gov", "http://doi.org/10.2307%2F1268008", "http://www.jstor.org/stable/1268008"]}, "Lists of statistics topics": {"categories": ["Lists of lists", "Statistics-related lists"], "title": "Lists of statistics topics", "method": "Lists of statistics topics", "url": "https://en.wikipedia.org/wiki/Lists_of_statistics_topics", "summary": "This article itemizes the various lists of statistics topics. Some of these lists link to hundreds of articles; some link only to a few.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Catalog of articles in probability theory", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparison of statistical packages", "Comparison of statistics journals", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Founders of statistics", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Glossary of probability and statistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Index of statistics articles", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of academic statistical associations", "List of actuaries", "List of analyses of categorical data", "List of convolutions of probability distributions", "List of fields of application of statistics", "List of graphical methods", "List of graphing software", "List of important publications in statistics", "List of mathematical probabilists", "List of matrices", "List of national and international statistical services", "List of probability distributions", "List of probability topics", "List of scientific journals in probability", "List of scientific journals in statistics", "List of scientific method topics", "List of statistical software", "List of statisticians", "List of statistics articles", "List of statistics journals", "List of stochastic processes topics", "List of timelines", "List of unsolved problems in statistics", "Lists of countries and territories", "Lists of country-related topics", "Lists of mathematics topics", "Lists of people", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Notation in probability and statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of regression analysis", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Timeline of probability and statistics", "Tolerance interval", "Topic outline of probability", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Structural equation modeling": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from January 2015", "Articles with unsourced statements from November 2009", "Graphical models", "Latent variable models", "Psychometrics", "Regression models", "Structural equation models", "Wikipedia articles with GND identifiers"], "title": "Structural equation modeling", "method": "Structural equation modeling", "url": "https://en.wikipedia.org/wiki/Structural_equation_modeling", "summary": "Structural equation modeling (SEM) is a form of causal modeling that includes a diverse set of mathematical models, computer algorithms, and statistical methods that fit networks of constructs to data. SEM includes confirmatory factor analysis, path analysis, partial least squares path modeling, and latent growth modeling. The concept should not be confused with the related concept of structural models in econometrics, nor with structural models in economics. Structural equation models are often used to assess unobservable 'latent' constructs. They often invoke a measurement model that defines latent variables using one or more observed variables, and a structural model that imputes relationships between latent variables. The links between constructs of a structural equation model may be estimated with independent regression equations or through more involved approaches such as those employed in LISREL.Use of SEM is commonly justified in the social sciences because of its ability to impute relationships between unobserved constructs (latent variables) from observable variables. To provide a simple example, the concept of human intelligence cannot be measured directly as one could measure height or weight. Instead, psychologists develop a hypothesis of intelligence and write measurement instruments with items (questions) designed to measure intelligence according to their hypothesis. They would then use SEM to test their hypothesis using data gathered from people who took their intelligence test. With SEM, \"intelligence\" would be the latent variable and the test items would be the observed variables.\nA simplistic model suggesting that intelligence (as measured by four questions) can predict academic performance (as measured by SAT, ACT, and high school GPA) is shown above (top right). In SEM diagrams, latent variables are commonly shown as ovals and observed variables as rectangles. The diagram above shows how error (e) influences each intelligence question and the SAT, ACT, and GPA scores, but does not influence the latent variables. SEM provides numerical estimates for each of the parameters (arrows) in the model to indicate the strength of the relationships. Thus, in addition to testing the overall theory, SEM therefore allows the researcher to diagnose which observed variables are good indicators of the latent variables.Various methods in structural equation modeling have been used in the sciences, business, and other fields. Criticism of SEM methods often addresses pitfalls in mathematical formulation, weak external validity of some accepted models and philosophical bias inherent to the standard procedures.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b1/Example_Structural_equation_model.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Approximation theory", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavior genetics", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calibration curve", "Cambridge University Press", "Canonical correlation", "Cartography", "Categorical variable", "Causal model", "Census", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparative Fit Index", "Completeness (statistics)", "Computational statistics", "Confidence interval", "Confirmatory factor analysis", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curve fitting", "Data collection", "Data point", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Denis Sargan", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrica", "Econometrics", "Economic model", "Edward Arnold (publisher)", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expectation\u2013maximization algorithm", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "H", "Harmonic mean", "Henri Theil", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human intelligence", "Index of dispersion", "Integrated Authority File", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Item response theory", "Iteratively reweighted least squares", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Judea Pearl", "Kaplan\u2013Meier estimator", "Karl J\u00f6reskog", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kenneth A. Bollen", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "LISREL", "Latent growth modeling", "Latent variables", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear least squares (mathematics)", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Measurement instruments", "Measurement invariance", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Missing data", "Mixed model", "Mixture model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving least squares", "Multilevel models", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-linear least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observable variable", "Observational study", "Official statistics", "One- and two-tailed tests", "OpenMx", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partial least squares path modeling", "Partial least squares regression", "Partition of sums of squares", "Path analysis (statistics)", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter M. Bentler", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychological Bulletin", "Psychometrics", "Quality control", "Quantile regression", "Quasi-experiment", "Quasi-maximum likelihood", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Ridge regression", "Robert Basmann", "Robust regression", "Robust statistics", "Root Mean Square Error of Approximation", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Sewall Wright", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standardized Root Mean Residual", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural Equation Modeling (journal)", "Structural Equations with Latent Variables", "Structural break", "Structural model (econometrics)", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survey sampling", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www-psychology.concordia.ca/fac/kline/sem/qicss/maccallum.pdf", "http://archive.wikiwix.com/cache/20110707224407/http://www2.chass.ncsu.edu/garson/pa765/structur.htm", "http://archive.wikiwix.com/cache/20110707224412/http://afni.nimh.nih.gov/sscc/gangc/PathAna.html", "http://archive.wikiwix.com/cache/20110707224414/http://www.upa.pdx.edu/IOA/newsom/semrefs.htm", "http://www.dgps.de/fachgruppen/methoden/mpr-online/issue20/art2/mpr130_13.pdf", "http://www2.gsu.edu/~mkteer/", "http://bayes.cs.ucla.edu/BOOK-2K/jw.html", "http://disc-nt.cba.uh.edu/chin/ais/", "http://afni.nimh.nih.gov", "http://doi.org/10.1007%2F978-94-007-6094-3_15", "http://doi.org/10.1007%2Fs11135-017-0469-8", "http://doi.org/10.1007%2Fs11747-011-0278-x", "http://doi.org/10.1016%2Fj.elerap.2010.07.003", "http://doi.org/10.1037%2F0033-2909.100.1.107", "http://doi.org/10.1037%2F1082-989X.1.2.130", "http://doi.org/10.1080%2F10705519909540118", "http://doi.org/10.1146%2Fannurev.psych.51.1.201", "http://doi.org/10.1177%2F0011000099274002", "http://doi.org/10.1177%2F0049124187016001004", "http://doi.org/10.22237%2Fjmasm%2F1067644980", "http://doi.org/10.2307%2F1905714", "http://doi.org/10.4135%2F9781412939584.n544", "http://doi.org/10.4135%2F9781412950589.n979", "http://doi.org/10.4135%2F9781412952644.n220", "http://doi.org/10.4135%2F9781412953948.n443", "http://www.jstor.org/stable/1905714", "https://books.google.com/books?id=VcHeAQAAQBAJ&pg=PA57", "https://d-nb.info/gnd/4252999-2", "https://www.wikidata.org/wiki/Q1476639"]}, "Statistical process control": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2014", "Commons category link is on Wikidata", "Statistical process control"], "title": "Statistical process control", "method": "Statistical process control", "url": "https://en.wikipedia.org/wiki/Statistical_process_control", "summary": "Statistical process control (SPC) is a method of quality control which employs statistical methods to monitor and control a process. This helps to ensure that the process operates efficiently, producing more specification-conforming products with less waste (rework or scrap). SPC can be applied to any process where the \"conforming product\" (product meeting specifications) output can be measured. Key tools used in SPC include run charts, control charts, a focus on continuous improvement, and the design of experiments. An example of a process where SPC is applied is manufacturing lines.\nSPC must be practised in 2 phases: The first phase is the initial establishment of the process, and the second phase is the regular production use of the process. In the second phase, a decision of the period to be examined must be made, depending upon the change in 5M&E conditions (Man, Machine, Material, Method, Movement, Environment) and wear rate of parts used in the manufacturing process (machine parts, jigs, and fixtures). \nAn advantage of SPC over other methods of quality control, such as \"inspection\", is that it emphasizes early detection and prevention of problems, rather than the correction of problems after they have occurred.\nIn addition to reducing waste, SPC can lead to a reduction in the time required to produce the product. SPC makes it less likely the finished product will need to be reworked or scrapped.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["5S (methodology)", "ANOVA Gauge R&R", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bell Laboratories", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brownian motion", "Business process mapping", "CMMI", "Canonical correlation", "Capability Maturity Model", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Common cause and special cause (statistics)", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous Improvement Process", "Continuous probability distribution", "Control chart", "Control charts", "Control plan", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "DMAIC", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Designed experiment", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Dr Bill Curtis", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Electronic design automation", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Exchangeability", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure mode and effects analysis", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fred Brooks", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Industrial engineering", "Inspection", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Ishikawa diagram", "Isotonic regression", "Jackknife resampling", "Japan", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaizen", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean absolute difference", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multi-vari chart", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Pareto chart", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Picatinny Arsenal", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Poka-yoke", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Process Window Index", "Process capability", "Process capability index", "Project charter", "Proportional hazards model", "Psychometrics", "Quality assurance", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rework (electronics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Root cause analysis", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Scrap", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Six Sigma", "Six sigma", "Skewness", "Social statistics", "Software Engineering Institute", "Spatial analysis", "Spearman's rank correlation coefficient", "Specification", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic control", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Value stream mapping", "Variance", "Vector autoregression", "Voice of the customer", "W. Edwards Deming", "Wald test", "Walter A. Shewhart", "Wavelet", "Western Electric rules", "Whittle likelihood", "Wilcoxon signed-rank test", "William Ernest Johnson", "William Sealy Gosset", "Z-test"], "references": ["http://ocw.mit.edu/courses/mechanical-engineering/2-830j-control-of-manufacturing-processes-sma-6303-spring-2008/", "http://faculty.salisbury.edu/~xswang/Research/Papers/SERelated/no-silver-bullet.pdf", "http://www.itl.nist.gov/div898/handbook/index2.htm", "http://doi.org/10.1007%2Fbf00485351", "http://doi.org/10.1109%2FMC.1987.1663532"]}, "Path analysis (statistics)": {"categories": ["Graphical models", "Independence (probability theory)", "Structural equation models"], "title": "Path analysis (statistics)", "method": "Path analysis (statistics)", "url": "https://en.wikipedia.org/wiki/Path_analysis_(statistics)", "summary": "In statistics, path analysis is used to describe the directed dependencies among a set of variables. This includes models equivalent to any form of multiple regression analysis, factor analysis, canonical correlation analysis, discriminant analysis, as well as more general families of models in the multivariate analysis of variance and covariance analyses (MANOVA, ANOVA, ANCOVA).\nIn addition to being thought of as a form of multiple regression focusing on causality, path analysis can be viewed as a special case of structural equation modeling (SEM) \u2013 one in which only single indicators are employed for each of the variables in the causal model. That is, path analysis is SEM with a structural model, but no measurement model. Other terms used to refer to path analysis include causal modeling, analysis of covariance structures, and latent variable models.\nPath analysis is considered by Judea Pearl to be a direct ancestor to the techniques of Causal inference.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/3/30/Path_example.JPG", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANCOVA", "ANOVA", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biology", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Canonical correlation analysis", "Cartography", "Categorical variable", "Causal inference", "Causal loop diagram", "Causality", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cycle (graph theory)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Directed acyclic graph", "Directed graph", "Discriminant analysis", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hidden Markov model", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Judea Pearl", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latent variable model", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MANOVA", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiple regression analysis", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Path coefficient", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychology", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sewall Wright", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Sociology", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation model", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://onyx.brandmaier.de/", "http://openmx.psyc.virginia.edu/about-openmx-project", "http://doi.org/10.1214%2Faoms%2F1177732676"]}, "System dynamics": {"categories": ["Articles with French-language external links", "Commons category link is locally defined", "Complex systems theory", "Operations research", "Problem structuring methods", "Scientific modeling", "Systems theory", "Wikipedia articles with GND identifiers"], "title": "System dynamics", "method": "System dynamics", "url": "https://en.wikipedia.org/wiki/System_dynamics", "summary": "System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/98/Adaption_SFD_continuous_time.png", "https://upload.wikimedia.org/wikipedia/commons/e/ea/Adoption_CLD.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3b/Adoption_SFD.png", "https://upload.wikimedia.org/wikipedia/commons/8/8e/Adoption_SFD_ANI.gif", "https://upload.wikimedia.org/wikipedia/commons/7/7c/Adoption_SFD_ANI_s.gif", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f6/Causal_Loop_Diagram_of_a_Model.png", "https://upload.wikimedia.org/wikipedia/commons/0/00/Complex-adaptive-system.jpg", "https://upload.wikimedia.org/wikipedia/commons/5/59/SFDD_VAL.gif", "https://upload.wikimedia.org/wikipedia/commons/0/08/Simple_stock_and_flow_diagram.gif", "https://upload.wikimedia.org/wikipedia/commons/d/df/TRUE_Piston_SFD.png", "https://upload.wikimedia.org/wikipedia/commons/e/e7/TRUE_Procedural_Animation.gif", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ACEGES", "Aerospace engineering", "Alexander Bogdanov", "Alexander Pugh", "Allenna Leonard", "Anatol Rapoport", "Anthony Stafford Beer", "Anthony Wilden", "Arthur David Hall III", "Barbara Grosz", "Barbara J. Grosz", "Benjamin S. Blanchard", "Biological system", "Biological systems engineering", "Bruce Hannon", "Business cycle", "Business dynamics", "Business process", "B\u00e9la H. B\u00e1n\u00e1thy", "C. West Churchman", "Carrying capacity", "Causal loop diagram", "Chaos theory", "Charles A S Hall", "Claude Shannon", "Climate change mitigation scenarios", "Club of Rome", "Comparison of system dynamics software", "Complex adaptive system", "Complex system", "Complex systems", "Computer engineering", "Computer modeling", "Computer simulation", "Conceptual system", "Configuration management", "Control engineering", "Control theory", "Coupled human\u2013environment system", "Cybernetics", "DYNAMO (programming language)", "Database", "Decision-making", "Dennis Meadows", "Derek Hitchins", "Design review", "Digital object identifier", "Discrete time", "Donella Meadows", "Doubling time", "Dynamical system", "Dynamical systems theory", "Earth system science", "Earth systems engineering and management", "Economic system", "Economics", "Ecosystem", "Ecosystem model", "Edsger W. Dijkstra", "Edward Norton Lorenz", "Electric power transmission", "Electrical engineering", "Electricity market", "Energy Modeling Forum", "Energy market", "Energy modeling", "Energy planning", "Energy policy", "Energy system", "Enterprise systems engineering", "Euler method", "Faina Mihajlovna Kirillova", "Feedback loop", "Financial crisis of 2007\u201308", "Formal system", "Francisco Varela", "Function model", "Functional specification", "General Electric", "George Dantzig", "George Klir", "Graeme Snooks", "Graphical user interface", "Great Moderation", "Gregory Bateson", "Grey box model", "Harold Chestnut", "Hartmut Bossel", "Heinz von Foerster", "Holon (philosophy)", "Howard T. Odum", "Human body", "Humberto Maturana", "IDEF", "INEMS", "Ilya Prigogine", "Industrial engineering", "Information system", "Integrated Authority File", "Integrated assessment modelling", "International Standard Book Number", "James Grier Miller", "James J. Kay", "James S. Albus", "Jay Forrester", "Jay Wright Forrester", "Jennifer Wilby", "John A. Laitner", "John F. Collins", "John N. Warfield", "John Sterman", "John Weyant", "Joseph Francis Shea", "Kathleen Carley", "Katia Sycara", "Kenneth E. Boulding", "Kevin Warwick", "Life insurance", "Limiting factor", "Limits to Growth", "List of national legal systems", "List of systems sciences organizations", "List of systems scientists", "Living systems", "Ludwig von Bertalanffy", "Lydia Kavraki", "MARKAL", "MIT Sloan School of Management", "Macroeconomics", "Manfred Clynes", "Manuela M. Veloso", "Margaret Boden", "Margaret Mead", "Mark Z. Jacobson", "Market dynamics", "Mary Cartwright", "Massachusetts Institute of Technology", "Mathematical optimization", "Mental model", "Metric system", "Mihajlo D. Mesarovic", "Minsky (economic simulator)", "Model (abstract)", "Multi-agent system", "Murray Bowen", "National Energy Modeling System", "Negative feedback", "Nervous system", "Niklas Luhmann", "Nonlinear system", "Nonlinearity", "Norbert Wiener", "OpenEI", "Open Energy Modelling Initiative", "Open energy system databases", "Open energy system models", "Operating system", "Operations research", "Performance engineering", "Peter Senge", "Phyllis Fox", "Physical system", "Piston motion equations", "Planetary system", "Plateau Principle", "Political system", "Population dynamics", "Positive feedback", "Predator-prey interaction", "Principia Cybernetica", "Procedural animation", "Project management", "Prospective Outlook on Long-term Energy Systems", "Qian Xuesen", "Quality function deployment", "Quality management", "Radhika Nagpal", "Reegle", "Reliability engineering", "Requirements engineering", "Richard Bennett (computer scientist)", "Richard E. Bellman", "Risk management", "Robert E. Machol", "Runge\u2013Kutta methods", "Russell L. Ackoff", "Ruzena Bajcsy", "Safety engineering", "Scenario analysis", "Sensory system", "Simon Ramo", "Social dynamics", "Social system", "Sociotechnical system", "Software engineering", "Spreadsheet", "Star system", "Stephanie Forrest", "Steve Keen", "Stock and flow", "System", "System Dynamics Society", "System archetype", "System identification", "System integration", "System lifecycle", "System of measurement", "System thinking", "Systemics", "Systems Modeling Language", "Systems analysis", "Systems art", "Systems biology", "Systems development life cycle", "Systems ecology", "Systems engineering", "Systems modeling", "Systems neuroscience", "Systems pharmacology", "Systems psychology", "Systems science", "Systems theory", "Systems theory in anthropology", "Systems theory in archaeology", "Systems theory in political science", "Systems thinking", "TRIZ", "Talcott Parsons", "The Fifth Discipline", "The Limits to Growth", "Twelve leverage points", "United Kingdom", "Urban Dynamics", "Urban metabolism", "V-Model", "Verification and validation", "Viable system phenomena", "Wernher von Braun", "Wicked problem", "William Ross Ashby", "Wolt Fabrycky", "Work breakdown structure", "World-systems theory", "World3", "World Dynamics", "Writing system"], "references": ["http://metasd.com/", "http://web.mit.edu/jsterman/www/DID.html", "http://web.mit.edu/sysdyn/sd-intro/", "http://sourceforge.net/blog/january-2014-potm/%C2%A0SourceForge", "http://doi.org/10.1016%2FS0737-6782(01)00099-6", "http://www.systemdynamics.org/", "http://www.systemdynamics.org/DL-IntroSysDyn/", "http://www.systemdynamics.org/DL-IntroSysDyn/start.htm", "https://d-nb.info/gnd/4058802-6", "https://www.wikidata.org/wiki/Q598451"]}, "F-test": {"categories": ["Analysis of variance", "Statistical ratios", "Statistical tests"], "title": "F-test", "method": "F-test", "url": "https://en.wikipedia.org/wiki/F-test", "summary": "An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis.\nIt is most often used but this occurs when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. Exact \"F-tests\" mainly arise when the models have been fitted to the data using least squares. The name was coined by George W. Snedecor, in honour of Sir Ronald A. Fisher. Fisher initially developed the statistic as the variance ratio in the 1920s.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Bar chart", "Bartlett's test", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brown\u2013Forsythe test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chow test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-distribution", "F-test of equality of variances", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "G. S. Maddala", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George W. Snedecor", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independence (probability theory)", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jan Kmenta", "Jarque\u2013Bera test", "Johansen test", "John Johnston (econometrician)", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lack-of-fit sum of squares", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Levene's test", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mark Thoma", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Residual sum of squares", "Robust regression", "Robust statistics", "Ronald A. Fisher", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scheff\u00e9's method", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical test", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "The American Statistician", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tristan E. P. Box", "Type I error", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "YouTube", "Z-test"], "references": ["http://www.bodowinter.com/tutorial/bw_anova_general.pdf", "http://facweb.cs.depaul.edu/sjost/csc423/documents/f-test-reg.htm", "http://www.public.iastate.edu/~alicia/stat328/Multiple%20regression%20-%20F%20test.pdf", "http://digitalcommons.wayne.edu/jmasm/vol1/iss2/55", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm", "http://www.waterlog.info/f-test.htm", "http://doi.org/10.1093%2Fbiomet%2F40.3-4.318", "http://doi.org/10.2307%2F2684360", "http://www.jstor.org/stable/2333350", "http://www.jstor.org/stable/2684360", "https://books.google.com/books?id=BZtvwZAGyV0C&pg=PA35", "https://books.google.com/books?id=Bxq7AAAAIAAJ&pg=PA147", "https://books.google.com/books?id=V6YrAAAAYAAJ&pg=PA290", "https://books.google.com/books?id=vkQvQgAACAAJ&pg=PA155", "https://www.youtube.com/watch?v=sajXLvfolmg&list=PLD15D38DC7AA3B737&index=2#t=35m01s", "https://web.archive.org/web/20150403095901/http://digitalcommons.wayne.edu/jmasm/vol1/iss2/55/"]}, "Log-Cauchy distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax", "Probability distributions with non-finite variance"], "title": "Log-Cauchy distribution", "method": "Log-Cauchy distribution", "url": "https://en.wikipedia.org/wiki/Log-Cauchy_distribution", "summary": "In probability theory, a log-Cauchy distribution is a probability distribution of a random variable whose logarithm is distributed in accordance with a Cauchy distribution. If X is a random variable with a Cauchy distribution, then Y = exp(X) has a log-Cauchy distribution; likewise, if Y has a log-Cauchy distribution, then X = log(Y) has a Cauchy distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3c/Logcauchycdf.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f3/Logcauchypdf.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential function", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized beta distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "HIV virus", "Half-logistic distribution", "Half-normal distribution", "Harold Jeffreys", "Hazard rate", "Heavy-tailed distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Improper prior", "Infinite divisibility (probability)", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-t distribution", "Logarithm", "Logarithmic distribution", "Logarithmic growth", "Logistic distribution", "Logit-normal distribution", "Lognormal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mathworld", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Median absolute deviation", "Mittag-Leffler distribution", "Mixture distribution", "Moment-generating function", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Natural logarithm", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Outlier", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Pole (complex analysis)", "Poly-Weibull distribution", "Prior distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Robust estimator", "Sample (statistics)", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard deviation", "Student's t-distribution", "Student's t distribution", "Support (mathematics)", "Survival function", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://resources.metapress.com/pdf-preview.axd?code=gn16hw202rxh4q1g&size=largest", "http://www.sciencedirect.com/science/article/pii/089812219390128I", "http://www.sciencedirect.com/science/article/pii/S0304380004005587", "http://onlinelibrary.wiley.com/doi/10.1002/sim.742/abstract", "http://mathworld.wolfram.com/Moment.html", "http://www.math.siu.edu/olive/run.pdf", "http://doi.org/10.1002%2Fsim.742", "http://doi.org/10.1016%2F0898-1221(93)90128-I", "http://doi.org/10.1016%2Fj.ecolmodel.2004.10.011", "http://docentes.deio.fc.ul.pt/fragaalves/SuperHeavy.pdf", "https://web.archive.org/web/20070623175435/http://docentes.deio.fc.ul.pt/fragaalves/SuperHeavy.pdf", "https://web.archive.org/web/20110928191222/http://www.math.siu.edu/olive/run.pdf", "https://web.archive.org/web/20120425064706/http://resources.metapress.com/pdf-preview.axd?code=gn16hw202rxh4q1g&size=largest"]}, "Survey sampling": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "CS1 maint: Archived copy as title", "Mathematical and quantitative methods (economics)", "Public opinion", "Sampling techniques", "Survey methodology"], "title": "Survey sampling", "method": "Survey sampling", "url": "https://en.wikipedia.org/wiki/Survey_sampling", "summary": "In statistics, survey sampling describes the process of selecting a sample of elements from a target population to conduct a survey. \nThe term \"survey\" may refer to many different types or techniques of observation. In survey sampling it most often involves a questionnaire used to measure the characteristics and/or attitudes of people. Different ways of contacting members of a sample once they have been selected is the subject of survey data collection. The purpose of sampling is to reduce the cost and/or the amount of work that it would take to survey the entire target population. A survey that measures the entire target population is called a census.\nSurvey samples can be broadly divided into two types: probability samples and non-probability samples. Probability-based samples implement a sampling plan with specified probabilities (perhaps adapted probabilities specified by an adaptive procedure). Probability-based sampling allows design-based inference about the target population. The inferences are based on a known objective probability distribution that was specified in the study protocol. Inferences from probability-based surveys may still suffer from many types of bias.\nSurveys that are not based on probability sampling have greater difficulty measuring their bias or sampling error. Surveys based on non-probability samples often fail to represent the people in the target population.In academic and government survey research, probability sampling is a standard procedure. In the United States, the Office of Management and Budget's \"List of Standards for Statistical Surveys\" states that federally funded surveys must be performed:\n\nselecting samples using generally accepted statistical methods (e.g., probabilistic methods that can provide estimates of sampling error). Any use of nonprobability sampling methods (e.g., cut-off or model-based samples) must be justified statistically and be able to measure estimation error.\nBesides, random sampling and design-based inference are supplemented by other statistical methods, such as model-assisted sampling and model-based sampling.For example, many surveys have substantial amounts of nonresponse. Even though the units are initially chosen with known probabilities, the nonresponse mechanisms are unknown. For surveys with substantial nonresponse, statisticians have proposed statistical models, with which data sets are analyzed.\nIssues related to survey sampling are discussed in several sources including Salant and Dillman (1994).", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/69/WMF_Strategic_Plan_Survey.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/69/20140903154210%21WMF_Strategic_Plan_Survey.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/69/20140903153556%21WMF_Strategic_Plan_Survey.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/69/20140903153427%21WMF_Strategic_Plan_Survey.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/69/20140903152947%21WMF_Strategic_Plan_Survey.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/69/20140903152812%21WMF_Strategic_Plan_Survey.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/69/20140903152448%21WMF_Strategic_Plan_Survey.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/69/20140903151937%21WMF_Strategic_Plan_Survey.svg"], "links": ["Afrobarometer", "American Association for Public Opinion Research", "American National Election Studies", "Audience measurement", "Categorical data", "Census", "Cluster sampling", "Cognitive psychology", "Comparative Study of Electoral Systems", "Confidence interval", "Contingency table", "Convenience sample", "Couple interview", "Data analysis", "Data collection", "David Freedman (statistician)", "David S. Moore", "Demography", "Descriptive statistics", "Dover Publications", "Eurobarometer", "European Social Survey", "European Society for Opinion and Marketing Research", "European Values Study", "Exploratory data analysis", "Gallup (company)", "General Social Survey", "Graphical model", "Institute for Social Research", "International Social Survey Programme", "International Standard Book Number", "International Statistical Institute", "Interview (research)", "Latinobar\u00f3metro", "Leslie Kish", "Level of measurement", "List of household surveys in the United States", "Margin of error", "Market research", "Multivariate statistics", "National Health and Nutrition Examination Survey", "New York City", "New Zealand Attitudes and Values Study", "Non-response bias", "OCLC", "Office of Management and Budget", "Opinion poll", "Participation bias", "Pew Research Center", "Poisson regression", "Professional association", "Psychometrics", "Public opinion", "Questionnaire", "Quota sampling", "Response bias", "Robert M. Groves", "Sample size determination", "Sampling (statistics)", "Sampling bias", "Sampling error", "Sampling frame", "Self-selection bias", "Semi-structured interview", "Statistical inference", "Statistical model", "Statistical population", "Statistical survey", "Statistical theory", "Statistics", "Stratified sampling", "Structural equation modeling", "Structured interview", "Survey data collection", "Survey research", "Survey weight", "Total survey error", "Unbiased", "University of Michigan", "Unstructured interview", "W. Edwards Deming", "W. W. Norton & Company", "William Gemmell Cochran", "World Association for Public Opinion Research", "World Values Survey"], "references": ["http://www.statcan.gc.ca/edu/power-pouvoir/ch13/nonprob/5214898-eng.htm", "http://www.m-s-g.com/Web/genesys/resources.aspx", "http://www.statpac.com/surveys/sampling.htm", "http://badanalysis.wordpress.com/research-guides/sampling/", "http://www.wwnorton.com/college/titles/math/stat4/comment.htm", "http://nces.ed.gov/StatProg/2002/glossary.asp#nonresponse", "http://www.whitehouse.gov/omb/inforeg/statpolicy/standards_stat_surveys.pdf", "http://whatisasurvey.info", "http://www.aapor.org/Education-Resources/For-Researchers/Poll-Survey-FAQ/Why-Sampling-Works.aspx", "http://www.osra.org/itlpj/bartlettkotrlikhiggins.pdf", "http://www.worldcat.org/oclc/166526", "https://web.archive.org/web/20080706153959/http://www2.wwnorton.com/college/titles/math/stat4/comment.htm", "https://web.archive.org/web/20090612004036/http://www.whitehouse.gov/omb/inforeg/statpolicy/standards_stat_surveys.pdf", "https://web.archive.org/web/20161120041655/http://www.statcan.gc.ca/edu/power-pouvoir/ch13/nonprob/5214898-eng.htm", "https://cran.r-project.org/view=OfficialStatistics"]}, "Biclustering": {"categories": ["All articles with style issues", "Bioinformatics", "Cluster analysis", "Wikipedia articles with style issues from February 2017"], "title": "Biclustering", "method": "Biclustering", "url": "https://en.wikipedia.org/wiki/Biclustering", "summary": "Biclustering, block clustering\n, co-clustering, or two-mode clustering is a data mining technique which allows simultaneous clustering of the rows and columns of a matrix.\nThe term was first introduced by Boris Mirkin to name a technique introduced many years earlier, in 1972, by J. A. Hartigan.Given a set of \n \n \n \n m\n \n \n {\\displaystyle m}\n samples represented by an \n \n \n \n n\n \n \n {\\displaystyle n}\n -dimensional feature vector, the entire dataset can be represented as \n \n \n \n m\n \n \n {\\displaystyle m}\n rows in \n \n \n \n n\n \n \n {\\displaystyle n}\n columns (i.e., an \n \n \n \n m\n \u00d7\n n\n \n \n {\\displaystyle m\\times n}\n matrix). The biclustering algorithm generates biclusters \u2013 a subset of rows which exhibit similar behavior across a subset of columns, or vice versa.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Algorithm", "Algorithms", "Bayesian probability", "Biclique", "BiclustGUI: R package for Biclustering", "Bioinformatics", "Cluster analysis", "Co-clustering", "Computer", "Correlation clustering", "Data mining", "Datatype", "Digital object identifier", "Enumeration", "Formal concept analysis", "Galois connection", "Gene expression", "Gold standard (test)", "Heavy tails", "Heuristics", "Hierarchical clustering", "Information-theoretic", "Information content", "International Standard Book Number", "Iterative", "JSTOR", "Kullback\u2013Leibler divergence", "Latent semantic analysis", "MTBA Toolbox for Biclustering", "Matrix (mathematics)", "Minima", "Mode (statistics)", "Mutual information", "NP-complete", "Non-Gaussianity", "Polynomial", "PubMed Central", "PubMed Identifier", "Sepp Hochreiter", "Singular value decomposition", "Srinivas Aluru", "String processing", "Suffix tree", "Super-majority", "Time-series data", "Tractable problem", "Unsupervised classification", "Vector (mathematics and physics)"], "references": ["http://www.bioinf.jku.at/software/fabia/fabia.html", "http://linkinghub.elsevier.com/retrieve/pii/S0925231206001615", "http://www.sciencedirect.com/science/article/pii/S0166218X03003330", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1502140", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2881408", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC365731", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC430175", "http://www.ncbi.nlm.nih.gov/pubmed/12671006", "http://www.ncbi.nlm.nih.gov/pubmed/14973197", "http://www.ncbi.nlm.nih.gov/pubmed/15516031", "http://www.ncbi.nlm.nih.gov/pubmed/16144809", "http://www.ncbi.nlm.nih.gov/pubmed/16749936", "http://www.ncbi.nlm.nih.gov/pubmed/17048406", "http://www.ncbi.nlm.nih.gov/pubmed/20418340", "http://dl.acm.org/citation.cfm?id=1014111", "http://dl.acm.org/citation.cfm?id=502550", "http://dl.acm.org/citation.cfm?id=956764", "http://doi.acm.org/10.1145/1497577.1497578", "http://doi.org/10.1016%2FS0166-218X(03)00333-0", "http://doi.org/10.1016%2Fj.csda.2007.09.007", "http://doi.org/10.1016%2Fj.neucom.2006.02.018", "http://doi.org/10.1073%2Fpnas.0308661100", "http://doi.org/10.1080%2F01621459.1972.10481214", "http://doi.org/10.1093%2Fbioinformatics%2Fbti641", "http://doi.org/10.1093%2Fbioinformatics%2Fbtq227", "http://doi.org/10.1101%2Fgr.648603", "http://doi.org/10.1109%2FICMLA.2008.103", "http://doi.org/10.1109%2FTCBB.2004.2", "http://doi.org/10.1109%2FTCBB.2008.34", "http://doi.org/10.1145%2F1497577.1497578", "http://doi.org/10.1145%2F99935.99938", "http://doi.org/10.1186%2F1471-2105-7-280", "http://doi.org/10.1191%2F0962280204sm373ra", "http://doi.org/10.2307%2F2284710", "http://www.jstor.org/stable/2284710", "https://www.cs.princeton.edu/courses/archive/fall03/cs597F/Articles/biclustering_of_expression_data.pdf"]}, "Bernoulli sampling": {"categories": ["Sampling techniques"], "title": "Bernoulli sampling", "method": "Bernoulli sampling", "url": "https://en.wikipedia.org/wiki/Bernoulli_sampling", "summary": "In the theory of finite population sampling, Bernoulli sampling is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample. An essential property of Bernoulli sampling is that all elements of the population have equal probability of being included in the sample.\nBernoulli sampling is therefore a special case of Poisson sampling. In Poisson sampling each element of the population may have a different probability of being included in the sample. In Bernoulli sampling, the probability is equal for all the elements.\nBecause each element of the population is considered separately for the sample, the sample size is not fixed but rather follows a binomial distribution.", "images": [], "links": ["Bernoulli process", "Bernoulli trial", "Binomial distribution", "Finite population sampling", "International Standard Book Number", "Poisson sampling", "Sampling design", "Statistical independence", "Statistical population"], "references": ["https://erikerlandson.github.io/blog/2014/09/11/faster-random-samples-with-gap-sampling/"]}, "Good\u2013Turing frequency estimation": {"categories": ["1953 introductions", "Alan Turing", "Categorical data", "Probability assessment"], "title": "Good\u2013Turing frequency estimation", "method": "Good\u2013Turing frequency estimation", "url": "https://en.wikipedia.org/wiki/Good%E2%80%93Turing_frequency_estimation", "summary": "Good\u2013Turing frequency estimation is a statistical technique for estimating the probability of encountering an object of a hitherto unseen species, given a set of past observations of objects from different species. In drawing balls from an urn, the 'objects' would be balls and the 'species' would be the distinct colors of the balls (finite but unknown in number). After drawing \n \n \n \n \n R\n \n red\n \n \n \n \n {\\displaystyle R_{\\text{red}}}\n red balls, \n \n \n \n \n R\n \n black\n \n \n \n \n {\\displaystyle R_{\\text{black}}}\n black balls and \n \n \n \n \n R\n \n green\n \n \n \n \n {\\displaystyle R_{\\text{green}}}\n green balls, we would ask what is the probability of drawing a red ball, a black ball, a green ball or one of a previously unseen color.", "images": [], "links": ["AT&T", "Alan Turing", "Bibcode", "Biometrika", "Bletchley Park", "Cipher", "Digital object identifier", "Empirical Bayes method", "Enigma (novel)", "Enigma machine", "Ewens sampling formula", "Geoffrey Sampson", "Germany", "I.J. Good", "I. J. Good", "JSTOR", "Journal of Quantitative Linguistics", "Marcus Hutter", "Mathematical Reviews", "Multinomial distribution", "Probability", "Pseudocount", "PubMed Identifier", "Robert Harris (novelist)", "Simple linear regression", "Statistical", "World War II"], "references": ["http://www.newswise.com/articles/view/501440/", "http://www.cs.cornell.edu/courses/cs6740/2010sp/guides/lec11.pdf", "http://adsabs.harvard.edu/abs/2003Sci...302..427O", "http://jmlr.csail.mit.edu/papers/v4/mcallester03a.html", "http://people.csail.mit.edu/mcollins/6864/slides/goodturing.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.110.8518", "http://www.ncbi.nlm.nih.gov/pubmed/14564004", "http://www.grsampson.net/D_SGT.c", "http://www.ams.org/mathscinet-getitem?mr=0061330", "http://doi.org/10.1080%2F09296179508590051", "http://doi.org/10.1093%2Fbiomet%2F40.3-4.237", "http://doi.org/10.1126%2Fscience.1088284", "http://www.jstor.org/stable/2333344", "https://papers.nips.cc/paper/5762-competitive-distribution-estimation-why-is-good-turing-good.pdf", "https://dx.doi.org/10.1007/978-3-319-11662-4_17", "https://dx.doi.org/10.1080/01966324.1991.10737313", "https://dx.doi.org/10.1080/09296179508590051"]}, "Clark\u2013Ocone theorem": {"categories": ["Theorems in measure theory", "Theorems regarding stochastic processes"], "title": "Clark\u2013Ocone theorem", "method": "Clark\u2013Ocone theorem", "url": "https://en.wikipedia.org/wiki/Clark%E2%80%93Ocone_theorem", "summary": "In mathematics, the Clark\u2013Ocone theorem (also known as the Clark\u2013Ocone\u2013Haussmann theorem or formula) is a theorem of stochastic analysis. It expresses the value of some function F defined on the classical Wiener space of continuous paths starting at the origin as the sum of its mean value and an It\u014d integral with respect to that path. It is named after the contributions of mathematicians J.M.C. Clark (1970), Daniel Ocone (1984) and U.G. Haussmann (1978).", "images": [], "links": ["Abstract Wiener space", "Adapted process", "Bounded function", "Brownian motion", "Classical Wiener space", "Conditional expectation", "Daniel Ocone", "Derivative", "Divergence", "Expected value", "Filtration (mathematics)", "Fr\u00e9chet derivative", "Function (mathematics)", "H-derivative", "Integral representation theorem for classical Wiener space", "Integration by parts", "Integration by parts operator", "International Standard Book Number", "It\u014d integral", "Malliavin calculus", "Malliavin derivative", "Mathematician", "Mathematics", "Mean", "Sigma algebra", "Skorokhod integral", "Stochastic process", "Theorem", "Vector field"], "references": ["http://www.statslab.cam.ac.uk/~peter/malliavin/Malliavin2005/mall.pdf", "https://web.archive.org/web/20070417205303/http://www.statslab.cam.ac.uk/~peter/malliavin/Malliavin2005/mall.pdf"]}, "Ward's method": {"categories": ["Cluster analysis algorithms"], "title": "Ward's method", "method": "Ward's method", "url": "https://en.wikipedia.org/wiki/Ward%27s_method", "summary": "In statistics, Ward's method is a criterion applied in hierarchical cluster analysis. Ward's minimum variance method is a special case of the objective function approach originally presented by Joe H. Ward, Jr. Ward suggested a general agglomerative hierarchical clustering procedure, where the criterion for choosing the pair of clusters to merge at each step is based on the optimal value of an objective function. This objective function could be \"any function that reflects the investigator's purpose.\" Many of the standard clustering procedures are contained in this very general class. To illustrate the procedure, Ward used the example where the objective function is the error sum of squares, and this example is known as Ward's method or more precisely Ward's minimum variance method.\nThe nearest-neighbor chain algorithm can be used to find the same clustering defined by Ward's method, in time proportional to the size of the input distance matrix and space linear in the number of points being clustered.", "images": [], "links": ["Agglomerative hierarchical clustering", "Anil K. Jain (computer scientist, born 1948)", "Complete-linkage clustering", "Digital object identifier", "Distance matrix", "Euclidean distance", "Hierarchical clustering", "International Standard Book Number", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society", "Lack-of-fit sum of squares", "Nearest-neighbor chain algorithm", "Objective function", "Recursive algorithm", "Single-linkage clustering", "Statistics"], "references": ["http://doi.org/10.1007%2Fs00357-015-9167-1"]}, "Time use survey": {"categories": ["All articles with dead external links", "All articles with unsourced statements", "Articles with dead external links from March 2018", "Articles with permanently dead external links", "Articles with unsourced statements from November 2014", "Survey methodology"], "title": "Time-use survey", "method": "Time use survey", "url": "https://en.wikipedia.org/wiki/Time-use_survey", "summary": "A time-use survey is a statistical survey which aims to report data on how, on average, people spend their time. \n\n", "images": [], "links": ["Metropolitan Travel Survey Archive", "Productive and unproductive labour", "Unpaid work", "Value added"], "references": ["http://www.cev.be/Documents%5CFacts&Figures_UK.pdf", "http://www.bls.gov/news.release/atus.nr0.htm", "http://www.bls.gov/tus/home.htm", "http://www.stat.go.jp/english/data/shakai/1.htm", "http://www.stats.govt.nz/browse_for_stats/people_and_communities/time_use.aspx", "http://www.statistics.gov.uk/STATBASE/ssdataset.asp?vlnk=3720", "https://web.archive.org/web/20050403203203/http://www.statcan.ca/english/sdds/4503.htm", "https://web.archive.org/web/20050403231915/http://iserwww.essex.ac.uk/misoc/timeuse/", "https://web.archive.org/web/20050405090608/http://www.statcan.ca/Daily/English/991109/d991109a.htm", "https://web.archive.org/web/20050406024359/http://www5.cao.go.jp/98/g/19981105g-unpaid-e.html", "https://web.archive.org/web/20050416101455/http://www.newint.org/issue181/facts.htm", "https://web.archive.org/web/20050713081359/http://iserwww.essex.ac.uk/mtus/index.php"]}, "Geodemographic segmentation": {"categories": ["Demography", "Geodemography", "Geostatistics", "Market research", "Market segmentation", "Statistical classification"], "title": "Geodemographic segmentation", "method": "Geodemographic segmentation", "url": "https://en.wikipedia.org/wiki/Geodemographic_segmentation", "summary": "In marketing, geodemographic segmentation is a multivariate statistical classification technique for discovering whether the individuals of a population fall into different groups by making quantitative comparisons of multiple characteristics with the assumption that the differences within any group should be less than the differences between groups.", "images": [], "links": ["ACORN (demographics)", "Australia", "Australian Bureau of Statistics", "Australian Census", "Canadian Census", "Claritas Prizm", "Digital object identifier", "Market segmentation", "Marketing", "Mosaic (geodemography)", "Multivariate statistics", "ONS coding system", "Onomastics", "Quantitative property", "Self-Organizing Map"], "references": ["http://www.esri.com/data/esri_data/tapestry", "http://www.hispanicsegmentos.com", "http://www.paristechreview.com/2013/09/17/onomastics-business/", "http://www.pitneybowes.com/us/location-intelligence/gis-data-sets/psyte-hd-canada.html", "http://www.rdaresearch.com/geosmart", "http://www.sciencedirect.com/science/article/pii/S0143622811002256", "http://www.segmentationportal.com/?hostRegion=UK", "http://doi.org/10.1016%2Fj.apgeog.2011.11.004", "http://doi.org/10.1016%2Fj.compenvurbsys.2005.07.004", "http://doi.org/10.1016%2Fj.compenvurbsys.2007.11.004", "http://www.ccsr.ac.uk/methods/festival/programme/urb/webber.ppt", "http://www.business-strategies.co.uk/sitecore/content/Products%20and%20services/Micromarketing%20data/Consumer%20segmentation/Mosaic.aspx", "http://acorn.caci.co.uk", "http://www.callcredit.co.uk/products-and-services/consumer-marketing-data/segmentation-analysis/cameo-global-classifications", "http://www.callcredit.co.uk/products-and-services/consumer-marketing-data/segmentation-analysis/cameo-global-classifications/cameo-international", "http://www.callcredit.co.uk/products-and-services/consumer-marketing-data/segmentation-analysis", "http://www.callcredit.co.uk/products-and-services/consumer-marketing-data-and-segmentation/cameo-classifications", "http://areaclassification.org.uk/", "https://www.cameodynamic.com/", "https://web.archive.org/web/20160419204522/https://www.pitneybowes.com/us/location-intelligence/gis-data-sets/psyte-hd-canada.html", "https://zenodo.org/record/884484"]}, "Probability theory": {"categories": ["All articles lacking in-text citations", "All articles lacking reliable references", "All articles with unsourced statements", "Articles lacking in-text citations from September 2009", "Articles lacking reliable references from February 2016", "Articles with unsourced statements from December 2015", "Probability theory", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Probability theory", "method": "Probability theory", "url": "https://en.wikipedia.org/wiki/Probability_theory", "summary": "Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of these outcomes is called an event.\nCentral subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes, which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion.\nAlthough it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are the law of large numbers and the central limit theorem.\nAs a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth-century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d2/Gaussian_distribution_2.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/24/NYW-DK-Poisson%285%29.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolutely continuous", "Abstract algebra", "Algebra", "Algebraic geometry", "Algorithm", "Algorithm design", "Almost surely", "Analysis of algorithms", "Analytic geometry", "Andrey Kolmogorov", "Andrey Nikolaevich Kolmogorov", "Applied mathematics", "Approximation theory", "Areas of mathematics", "Arithmetic", "Average", "Axiom system", "Axioms of probability", "Bayes' theorem", "Belmont, California", "Bernoulli distribution", "Berry\u2013Esseen theorem", "Bertrand's paradox (probability)", "Beta distribution", "Binomial distribution", "Blaise Pascal", "Boole's inequality", "Borel algebra", "Brownian motion", "Bruno de Finetti", "Calculus", "Calculus of variations", "Cantor distribution", "Catalog of articles in probability theory", "Category theory", "Central limit theorem", "Christiaan Huygens", "Classical definition of probability", "Coding theory", "Coin", "Coin flipping", "Combinatorics", "Complementary event", "Computational mathematics", "Computational number theory", "Computer science", "Conditional independence", "Conditional probability", "Continuous function", "Continuous probability distribution", "Control theory", "Convergence of random variables", "Countable", "Countable set", "Counting measure", "Cryptography", "Cumulative distribution function", "David Williams (mathematician)", "Decision theory", "Deck of cards", "Determinism", "Dice", "Differential equation", "Differential equations", "Differential geometry", "Digital object identifier", "Dimension", "Dirac delta function", "Discrete geometry", "Discrete mathematics", "Discrete probability distribution", "Dynamical systems", "Dynamical systems theory", "Elementary algebra", "Elementary event", "Event (probability theory)", "Expected value", "Exponential distribution", "Exponential family", "Fat tail", "Feynman integral", "Finite geometry", "Foundations of mathematics", "Fourier analysis", "Function (mathematics)", "Functional analysis", "Functional integration", "Fuzzy logic", "Fuzzy measure theory", "Game of chance", "Game theory", "Gamma distribution", "Geometric distribution", "Geometry", "Gerolamo Cardano", "Glossary of probability and statistics", "Graph theory", "Harmonic analysis (mathematics)", "Heavy tail", "Henk Tijms", "History of mathematics", "History of probability", "Independence (probability theory)", "Information theory", "Integrated Authority File", "International Standard Book Number", "Joint probability distribution", "Kolmogorov axioms", "Law of large numbers", "Law of total probability", "Lebesgue measure", "Likelihood function", "Linear algebra", "List of mathematics topics", "List of probability topics", "List of publications in statistics", "List of statistical topics", "Lists of mathematics topics", "Logic in computer science", "M-theory", "Malliavin calculus", "Marginal distribution", "Mathematical analysis", "Mathematical biology", "Mathematical chemistry", "Mathematical economics", "Mathematical finance", "Mathematical logic", "Mathematical optimization", "Mathematical physics", "Mathematical psychology", "Mathematical sociology", "Mathematical statistics", "Mathematics", "Mathematics and art", "Mathematics education", "Mean", "Measure (mathematics)", "Measure theory", "Monotonic function", "Multilinear algebra", "National Diet Library", "Negative binomial distribution", "Normal distribution", "Notation in probability", "Number theory", "Numerical analysis", "Olav Kallenberg", "Operations research", "Operator algebra", "Operator theory", "Optimization (mathematics)", "Order theory", "Outline of mathematics", "Particle physics and representation theory", "Patrick Billingsley", "Philosophy of mathematics", "Physics", "Pierre-Simon Laplace", "Pierre Simon de Laplace", "Pierre de Fermat", "Poisson distribution", "Power set", "Predictive modelling", "Probabilistic logic", "Probabilistic proofs of non-probabilistic theorems", "Probability", "Probability axioms", "Probability density function", "Probability distribution", "Probability distributions", "Probability interpretations", "Probability mass function", "Probability measure", "Probability space", "Problem of points", "Pure mathematics", "Quantity", "Quantum mechanics", "Radon-Nikodym theorem", "Random variable", "Random walk", "Real number", "Real numbers", "Recreational mathematics", "Renormalization group", "Richard von Mises", "Right-continuous", "Sample space", "Set theory", "Sigma-algebra", "Stable distribution", "Standard normal", "Statistical independence", "Statistical mechanics", "Statistics", "Stochastic analysis", "Stochastic process", "Subjective logic", "Subset", "Symbolic computation", "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", "Theory of computation", "Topic outline of mathematics", "Topology", "Tree diagram (probability theory)", "Trigonometry", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Variance", "Venn diagram", "YouTube"], "references": ["http://www.leithner.com.au/circulars/circular17.htm", "http://www.galtonboard.com", "http://www.probabilityandfinance.com/articles/04.pdf", "http://plato.stanford.edu/archives/sum2012/entries/probability-interpret/", "http://home.ubalt.edu/ntsbarsh/stat-data/Topics.htm", "http://doi.org/10.1007%2F978-3-642-49888-6", "https://books.google.com/books?id=Bc1FAQAAIAAJ&pg=PA26", "https://physics.stackexchange.com/questions/69718/why-is-quantum-mechanics-based-on-probability-theory", "https://www.youtube.com/watch?v=9eaOxgT5ys0", "https://d-nb.info/gnd/4079013-7", "https://id.ndl.go.jp/auth/ndlna/00564753", "https://web.archive.org/web/20140126113323/http://www.leithner.com.au/circulars/circular17.htm", "https://www.wikidata.org/wiki/Q5862903"]}, "Martingale representation theorem": {"categories": ["All articles lacking in-text citations", "All articles with incomplete citations", "Articles lacking in-text citations from October 2011", "Articles with incomplete citations from November 2012", "Martingale theory", "Probability theorems"], "title": "Martingale representation theorem", "method": "Martingale representation theorem", "url": "https://en.wikipedia.org/wiki/Martingale_representation_theorem", "summary": "In probability theory, the martingale representation theorem states that a random variable that is measurable with respect to the filtration generated by a Brownian motion can be written in terms of an It\u00f4 integral with respect to this Brownian motion.\nThe theorem only asserts the existence of the representation and does not help to find it explicitly; it is possible in many cases to determine the form of the representation using Malliavin calculus.\nSimilar theorems also exist for martingales on filtrations induced by jump processes, for example, by Markov chains.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Adapted process", "Augmented filtration", "Brownian motion", "Filtered probability space", "Filtration (probability theory)", "Hedge (finance)", "It\u00f4 integral", "Jump process", "Malliavin calculus", "Markov chain", "Martingale (probability theory)", "Measurable", "Predictable process", "Probability theory", "Robert J. Elliott", "Square integrable", "Volatility (finance)"], "references": []}, "Elston\u2013Stewart algorithm": {"categories": ["All stub articles", "Genetic epidemiology", "Genetic linkage analysis", "Genetics stubs", "Statistical algorithms", "Statistical genetics", "Statistics stubs"], "title": "Elston\u2013Stewart algorithm", "method": "Elston\u2013Stewart algorithm", "url": "https://en.wikipedia.org/wiki/Elston%E2%80%93Stewart_algorithm", "summary": "The Elston\u2013Stewart algorithm is an algorithm for computing the likelihood of observed genotype data given a pedigree. It is due to Robert Elston and John Stewart. It can handle relatively large pedigrees providing they are (almost) outbred. Its computation time is exponential in the number of markers. It is used in the analysis of genetic linkage.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cf/Plain_DNA_icon.svg"], "links": ["Biometrics (journal)", "Digital object identifier", "Genetics", "John Stewart (scientist)", "Lander-Green algorithm", "Likelihood", "Pedigree chart", "Robert Elston", "Statistics"], "references": ["https://doi.org/10.1159%2F000154042", "https://www.jstor.org/stable/2529015"]}, "Process Window Index": {"categories": ["Brazing and soldering", "CS1 errors: external links", "Electronics manufacturing", "Quality control", "Statistical distance"], "title": "Process Window Index", "method": "Process Window Index", "url": "https://en.wikipedia.org/wiki/Process_Window_Index", "summary": "Process Window Index (PWI) is a statistical measure that quantifies the robustness of a manufacturing process, e.g. one which involves heating and cooling, known as a thermal process. In manufacturing industry, PWI values are used to calibrate the heating and cooling of soldering jobs (known as a thermal profile) while baked in a reflow oven.\nPWI measures how well a process fits into a user-defined process limit known as the specification limit. The specification limit is the tolerance allowed for the process and may be statistically determined. Industrially, these specification limits are known as the process window, and values that a plotted inside or outside this window are known as the process window index.\nUsing PWI values, processes can be accurately measured, analyzed, compared, and tracked at the same level of statistical process control and quality control available to other manufacturing processes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f7/ControlChart.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a2/Factory.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Lead_Free_Process_Window_Index.svg", "https://upload.wikimedia.org/wikipedia/commons/5/54/PWI.svg", "https://upload.wikimedia.org/wikipedia/commons/8/80/Process_Window_Index_%28bullseye%29.svg"], "links": ["ANSI/ISA-95", "Arithmetic mean", "B2MML", "Batch production", "Control chart", "Data plot", "Distributed control system", "Enterprise resource planning", "Flow production", "IEC 62264", "ISA-88", "International Standard Book Number", "Job production", "Lean manufacturing", "Manufacturing", "McGraw-Hill", "National Institute of Standards and Technology", "Process capability", "Programmable logic controller", "Quality control", "Quick Response Manufacturing", "Reflow oven", "Reflow soldering", "Reliability centered maintenance", "SAP ERP", "SCADA", "Six Sigma", "Soldering", "Specification (technical standard)", "Standard deviation", "Statistical measure", "Statistical process control", "Theory of constraints", "Thermal shock", "Thermocouple", "Total productive maintenance", "Total quality management", "Value driven maintenance", "Wave soldering", "Worst case analysis", "Zero Defects"], "references": ["http://kicthermal.com/products/solar-industry.html?page=shop.product_details&flypage=flypage.tpl&category_id=6&product_id=16&vmcchk=1", "http://www.kicthermal.com/pwi/PWI--Process%20Optimization%20Made%20Simple%20(CA%202002-02).pdf", "http://www.leadfreemagazine.com/pages/pdf/pain_out_of_reflow.pdf", "http://smt.pennnet.com/display_article/167071/35/ARTCL/none/none/1/Step-2:-Process-Control/", "http://www.itl.nist.gov/div898/handbook/index.htm", "http://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm", "https://www.webcitation.org/5t86JZgab"]}, "GraphPad Prism": {"categories": ["Companies based in San Diego", "Software companies based in California", "Wikipedia articles with possible conflicts of interest from March 2018"], "title": "GraphPad Software", "method": "GraphPad Prism", "url": "https://en.wikipedia.org/wiki/GraphPad_Software", "summary": "GraphPad Software Inc. is a privately held California corporation. They publish scientific software, including:\n\nGraphPad Prism combines 2D scientific graphing, biostatistics with explanations, and curve fitting via nonlinear regression (Windows and Mac).\nGraphPad InStat guides students and scientists through basic biostatistics (Windows).\nGraphPad StatMate performs power and sample size calculations (Windows).\nGraphPad QuickCalcs are a set of statistical calculators (Free, web-based).", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Unbalanced_scales.svg"], "links": ["2D geometric model", "Biostatistics", "Commercial software", "Error bars", "Free content", "GraphPad InStat", "GraphPad Prism", "MacOS", "Mac OS", "Microsoft Windows", "Nonlinear regression", "Operating system", "Proprietary software", "R (programming language)", "SciDAVis", "Software categories", "Software developer", "Software license", "Software release life cycle", "Statistics software", "Windows"], "references": ["http://graphpad.com/prism", "http://www.graphpad.com", "http://www.graphpad.com/instat", "http://www.sciencemag.org/products/bt-statsw.dtl", "https://www.ncbi.nlm.nih.gov/sites/entrez?db=pubmed&cmd=DetailsSearch&term=graphpad&log$=activity", "https://www.google.it/search?q=%22r+software%22+OR+%22r+project%22+OR+%22r+language%22+site:www.ncbi.nlm.nih.gov/pubmed/"]}, "Estimation of covariance matrices": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from January 2015", "Estimation methods", "Statistical deviation and dispersion"], "title": "Estimation of covariance matrices", "method": "Estimation of covariance matrices", "url": "https://en.wikipedia.org/wiki/Estimation_of_covariance_matrices", "summary": "In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix. The sample covariance matrix (SCM) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in Rp\u00d7p; however, measured using the intrinsic geometry of positive-definite matrices, the SCM is a biased and inefficient estimator. In addition, if the random variable has normal distribution, the sample covariance matrix has Wishart distribution and a slightly differently scaled version of it is the maximum likelihood estimate. Cases involving missing data require deeper considerations. Another issue is the robustness to outliers, to which sample covariance matrices are highly sensitive.Statistical analyses of multivariate data often involve exploratory studies of the way in which the variables change in relation to one another and this may be followed up by explicit statistical models involving the covariance matrix of the variables. Thus the estimation of covariance matrices directly from observational data plays two roles:\n\nto provide initial estimates that can be used to study the inter-relationships;\nto provide sample estimates that can be used for model checking.Estimates of covariance matrices are required at the initial stages of principal component analysis and factor analysis, and are also involved in versions of regression analysis that treat the dependent variables in a data-set, jointly with the independent variable as the outcome of a random sample.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Academic Press", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian method", "Bayesian probability", "Bias of an estimator", "Biased estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brian D. Ripley", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Complex number", "Computational Statistics & Data Analysis", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convex combination", "Convex cone", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-covariance", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Determinant", "Diagonal matrix", "Dickey\u2013Fuller test", "Differential geometry", "Digamma function", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation theory", "Estimator", "Estimator bias", "Expected value", "Experiment", "Exponential family", "Exponential map (Lie theory)", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "First order condition", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Frobenius norm", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "IEEE Transactions on Signal Processing", "Identity matrix", "Independent variable", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Intrinsic bias", "Invertible matrix", "Isotonic regression", "JSTOR", "Jackknife resampling", "James\u2013Stein estimator", "Jarque\u2013Bera test", "Johansen test", "John Bibby (mathematician)", "John Kent (statistician)", "Joint probability distribution", "Jonckheere's trend test", "Journal of Multivariate Analysis", "Kanti Mardia", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear algebra", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MATLAB", "Mann\u2013Whitney U test", "Matrix calculus", "Matrix exponential", "Matrix logarithm", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimate", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing at random", "Missing data", "Missing values", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate Analysis", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate random variable", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Observed value", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter J. Huber", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Positive-definite matrix", "Posterior probability", "Power (statistics)", "Precision matrix", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Propagation of uncertainty", "Proportional hazards model", "Psychometrics", "Python programming language", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R programming language", "Radar chart", "Random assignment", "Random variable", "Random vector", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Riemannian curvature", "Riemannian manifold", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample covariance matrix", "Sample mean", "Sample mean and covariance", "Sample mean and sample covariance", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scalar (mathematics)", "Scale parameter", "Scatter matrix", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Single-index model", "Singular matrix", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spectral theorem", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Symmetric space", "System identification", "Tangent space", "The Journal of Portfolio Management", "Time domain", "Time series", "Tolerance interval", "Trace (matrix)", "Trend estimation", "U-statistic", "UCLA Anderson School of Management", "Unbiased estimator", "Uniformly most powerful test", "University of California, Los Angeles", "V-statistic", "Variance", "Variance components", "Vector autoregression", "Vector field", "Vector space", "Wald test", "Wavelet", "Whittle likelihood", "Wide-sense stationary", "Wilcoxon signed-rank test", "William N. Venables", "Wishart distribution", "Z-test"], "references": ["http://www.econ.uzh.ch/dam/jcr:ffffffff-935a-b0d6-0000-00007f64e5b9/cov1para.m.zip", "http://www.econ.uzh.ch/dam/jcr:ffffffff-935a-b0d6-0000-0000648dfc98/covMarket.m.zip", "http://www.econ.uzh.ch/dam/jcr:ffffffff-935a-b0d6-ffff-ffffde5e2d4e/covCor.m.zip", "http://www.econ.uzh.ch/faculty/ledoit/publications/honey.pdf", "http://www.econ.uzh.ch/faculty/wolf/publications/jef.pdf", "http://www.econ.uzh.ch/faculty/wolf/publications/wellCond.pdf", "http://www.anderson.ucla.edu/documents/areas/fac/finance/05-96.pdf", "http://www.anderson.ucla.edu/faculty/finance/working-papers", "http://ledoit.net/cov2para.m", "http://ledoit.net/shrinkDiag.m", "http://doi.org/10.1093%2Fbiomet%2F62.3.531", "http://doi.org/10.1093%2Fimanum%2F22.3.329", "http://doi.org/10.1109%2FTSP.2005.845428", "http://doi.org/10.2307%2F2283988", "http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6935094", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1420804&tag=1", "http://www.jstor.org/stable/2283988", "http://scikit-learn.org/stable/modules/covariance.html", "http://strimmerlab.org/publications/journals/shrinkcov2005.pdf", "https://arxiv.org/pdf/1410.4726.pdf", "https://cran.r-project.org/web/packages/ShrinkCovMat/index.html", "https://cran.r-project.org/web/packages/corpcor/index.html"]}, "Bonferroni correction": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2016", "Multiple comparisons", "Statistical hypothesis testing"], "title": "Bonferroni correction", "method": "Bonferroni correction", "url": "https://en.wikipedia.org/wiki/Bonferroni_correction", "summary": "In statistics, the Bonferroni correction is one of several methods used to counteract the problem of multiple comparisons.", "images": [], "links": ["Annals of Mathematical Statistics", "Annual Review of Psychology", "Behavioral Ecology", "Biometrics (journal)", "Biometrika", "Bonferroni inequalities", "Boole's inequality", "Carlo Emilio Bonferroni", "CiteSeerX", "Confidence intervals", "Digital object identifier", "Expected number", "Familywise error rate", "Genome-wide association study", "Holm\u2013Bonferroni method", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Journal of the American Statistical Association", "Linkage disequilibrium", "Mathematician", "Multiple comparisons problem", "Null hypothesis", "Olive Jean Dunn", "P-value", "PubMed Central", "PubMed Identifier", "Single-nucleotide polymorphism", "Statistical hypothesis testing", "Statistical power", "Statistics", "Statistics in Medicine (journal)", "Type I and type II errors", "Type I error", "\u0160id\u00e1k correction"], "references": ["http://www.quantitativeskills.com/sisa/calculations/bonfer.htm", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.1277", "http://www-stat.wharton.upenn.edu/~steele/Courses/956/Resource/MultipleComparision/Hochberg88.pdf", "http://digitalcommons.wayne.edu/jmasm/vol14/iss1/5", "http://sci2s.ugr.es/keel/pdf/algorithm/articulo/1961-Bonferroni_Dunn-JASA.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3531285", "http://www.ncbi.nlm.nih.gov/pubmed/18618415", "http://www.ncbi.nlm.nih.gov/pubmed/23300413", "http://www.ncbi.nlm.nih.gov/pubmed/24399688", "http://www.ncbi.nlm.nih.gov/pubmed/8014990", "http://doi.org/10.1002%2Fsim.3338", "http://doi.org/10.1002%2Fsim.6082", "http://doi.org/10.1006%2Fjmbi.1994.1407", "http://doi.org/10.1080%2F01621459.1955.10501294", "http://doi.org/10.1080%2F01621459.1961.10482090", "http://doi.org/10.1080%2F01621459.1967.10482935", "http://doi.org/10.1093%2Fbeheco%2Farh107", "http://doi.org/10.1093%2Fbiomet%2F75.4.800", "http://doi.org/10.1146%2Fannurev.ps.46.020195.003021", "http://doi.org/10.1214%2Faoms%2F1177706374", "http://doi.org/10.1371%2Fjournal.pcbi.1002822", "http://doi.org/10.2307%2F2528490", "http://www.jstor.org/stable/2237135", "http://www.jstor.org/stable/2528490", "http://www.worldcat.org/issn/1553-734X", "http://nebc.nerc.ac.uk/courses/GeneSpring/GS_Mar2006/Multiple%20testing%20corrections.pdf", "https://books.google.com/books?id=4C7VBwAAQBAJ&printsec=frontcover#v=onepage&q=Bonferroni&f=false", "https://books.google.com/books?id=fycmsfkK6RQC&pg=PA73", "https://academic.oup.com/beheco/article/15/6/1044/206216", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3531285/"]}, "Optimal discriminant analysis": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2009", "Classification algorithms", "Psychometrics", "Quantitative marketing research", "Statistical classification"], "title": "Optimal discriminant analysis", "method": "Optimal discriminant analysis", "url": "https://en.wikipedia.org/wiki/Optimal_discriminant_analysis", "summary": "Optimal Discriminant Analysis (ODA) and the related classification tree analysis (CTA) are exact statistical methods that maximize predictive accuracy. For any specific sample and exploratory or confirmatory hypothesis, optimal discriminant analysis (ODA) identifies the statistical model that yields maximum predictive accuracy, assesses the exact Type I error rate, and evaluates potential cross-generalizability. Optimal discriminant analysis may be applied to > 0 dimensions, with the one-dimensional case being referred to as UniODA and the multidimensional case being referred to as MultiODA. Classification tree analysis is a generalization of optimal discriminant analysis to non-orthogonal trees. Classification tree analysis has more recently been called \"hierarchical optimal discriminant analysis\". Optimal discriminant analysis and classification tree analysis may be used to find the combination of variables and cut points that best separate classes of objects or events. These variables and cut points may then be used to reduce dimensions and to then build a statistical model that optimally describes the data.\nOptimal discriminant analysis may be thought of as a generalization of Fisher's linear discriminant analysis. Optimal discriminant analysis is an alternative to ANOVA (analysis of variance) and regression analysis, which attempt to express one dependent variable as a linear combination of other features or measurements. However, ANOVA and regression analysis give a dependent variable that is a numerical variable, while optimal discriminant analysis gives a dependent variable that is a class variable.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Analysis of variance", "Annals of Eugenics", "Data mining", "Decision tree", "Dependent variable", "Digital object identifier", "Factor analysis", "Handle System", "IEEE Transactions on Pattern Analysis and Machine Intelligence", "International Standard Book Number", "Linear classifier", "Linear discriminant analysis", "Logistic regression", "Logit", "Machine learning", "Multidimensional scaling", "Perceptron", "Preference regression", "Quadratic classifier", "Regression analysis", "Ronald Fisher", "Statistics", "Type I error"], "references": ["http://people.revoledu.com/kardi/tutorial/LDA/index.html", "http://www.roguewave.com/Portals/0/products/imsl-numerical-libraries/fortran-library/docs/7.0/stat/stat.htm", "http://www.ece.osu.edu/~aleix/pami01f.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.9904", "http://hdl.handle.net/2440%2F15227", "http://books.apa.org/books.cfm?id=4316000", "http://doi.org/10.1109%2F34.908974", "http://doi.org/10.1109%2FNNSP.1999.788121", "http://doi.org/10.1111%2Fj.1469-1809.1936.tb02137.x", "https://dx.doi.org/10.1111/j.1540-5915.1991.tb00362.x"]}, "Spectral clustering": {"categories": ["Algebraic graph theory", "CS1 maint: Multiple names: authors list", "Cluster analysis algorithms"], "title": "Spectral clustering", "method": "Spectral clustering", "url": "https://en.wikipedia.org/wiki/Spectral_clustering", "summary": "In multivariate statistics and the clustering of data, spectral clustering techniques make use of the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality reduction before clustering in fewer dimensions. The similarity matrix is provided as an input and consists of a quantitative assessment of the relative similarity of each pair of points in the dataset.\nIn application to image segmentation, spectral clustering is known as segmentation-based object categorization.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/28/6n-graf2.svg"], "links": ["ARPACK", "Adjacency matrix", "Affinity propagation", "Apache Spark", "Cluster analysis", "Community structure", "Conductance (graph)", "Digital object identifier", "Dimensionality reduction", "Eigenvalue", "Eigenvalues", "Eigenvector", "Hierarchical clustering", "Ill-conditioned", "Kernel principal component analysis", "LOBPCG", "Lanczos algorithm", "Laplacian matrix", "Matrix-free methods", "Multigrid", "Multivariate statistics", "Nonlinear dimensionality reduction", "Power iteration", "Preconditioner", "Preconditioning", "PubMed Central", "PubMed Identifier", "R (programming language)", "Scikit-learn", "Segmentation-based object categorization", "Segmentation (image processing)", "Segmentation based object categorization", "Similarity matrix", "Spectral clustering", "Spectral graph theory", "Spectrum of a matrix"], "references": ["http://www.biomedcentral.com/1471-2105/11/403", "http://www.cs.berkeley.edu/~malik/papers/SM-ncut.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2923634", "http://www.ncbi.nlm.nih.gov/pubmed/20667133", "http://spark.apache.org/docs/latest/mllib-clustering.html#power-iteration-clustering-pic", "http://www.citeulike.org/user/mpotamias/article/498897", "http://doi.org/10.1109%2Ftpami.2007.1115", "http://doi.org/10.1145%2F990308.990313", "http://doi.org/10.1186%2F1471-2105-11-403", "http://doi.org/10.1214%2F11-ejs651", "http://scikit-learn.org/stable/modules/clustering.html#spectral-clustering", "https://people.eecs.berkeley.edu/~demmel/cs267/lecture20/lecture20.html", "https://cran.r-project.org/web/packages/kernlab"]}, "Mixed logit": {"categories": ["All articles needing expert attention", "Articles needing expert attention from February 2009", "Articles needing expert attention with no reason or talk parameter", "Articles needing unspecified expert attention", "Choice modelling"], "title": "Mixed logit", "method": "Mixed logit", "url": "https://en.wikipedia.org/wiki/Mixed_logit", "summary": "Mixed logit is a fully general statistical model for examining discrete choices. The motivation for the mixed logit model arises from the limitations of the standard logit model. The standard logit model has three primary limitations, which mixed logit solves: \"It obviates the three limitations of standard logit by allowing for random taste variation, unrestricted substitution patterns, and correlation in unobserved factors over time.\" Mixed logit can also utilize any distribution for the random coefficients, unlike probit which is limited to the normal distribution. It has been shown that a mixed logit model can approximate to any degree of accuracy any true random utility model of discrete choice, given an appropriate specification of variables and distribution of coefficients.\" The following discussion draws from Ch. 6 of Discrete Choice Methods with Simulation, by Kenneth Train (Cambridge University Press), to which the reader is referred for more details and citations. See also the article on discrete choice for information on how the mixed logit relates to discrete choice analysis in general and to other specific types of choice models.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Cambridge University Press", "Daniel McFadden", "Discrete Choice", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Independence of irrelevant alternatives", "Isotonic regression", "Iteratively reweighted least squares", "Kenneth E. Train", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Mean and predicted response", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probability density function", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Utility", "Weighted least squares"], "references": ["http://elsa.berkeley.edu/wp/mcfadden1198/mcfadden1198.pdf", "http://eml.berkeley.edu/books/choice2.html", "http://eml.berkeley.edu/books/choice2nd/Ch06_p134-150.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.4879", "https://www.jstor.org/stable/pdfplus/2646846.pdf"]}, "Cromwell's rule": {"categories": ["Bayesian statistics", "Statistical principles"], "title": "Cromwell's rule", "method": "Cromwell's rule", "url": "https://en.wikipedia.org/wiki/Cromwell%27s_rule", "summary": "Cromwell's rule, named by statistician Dennis Lindley, states that the use of prior probabilities of 0 (\"the event will definitely not occur\") or 1 (\"the event will definitely occur\") should be avoided, except when applied to statements that are logically true or false, such as 2+2 equaling 4 or 5.\nThe reference is to Oliver Cromwell, who wrote to the General Assembly of the Church of Scotland on 5 August 1650, including a phrase that has become well known and frequently quoted:\nI beseech you, in the bowels of Christ, think it possible that you may be mistaken.\n\nAs Lindley puts it, assigning a probability should \"leave a little probability for the moon being made of green cheese; it can be as small as 1 in a million, but have it there since otherwise an army of astronauts returning with samples of the said cheese will leave you unmoved.\" Similarly, in assessing the likelihood that tossing a coin will result in either a head or a tail facing upwards, there is a possibility, albeit remote, that the coin will land on its edge and remain in that position.\nIf the prior probability assigned to a hypothesis is 0 or 1, then, by Bayes' theorem, the posterior probability (probability of the hypothesis, given the evidence) is forced to be 0 or 1 as well; no evidence, no matter how strong, could have any influence.\nA strengthened version of Cromwell's rule, applying also to statements of arithmetic and logic, alters the first rule of probability, or the convexity rule, 0 \u2264 Pr(A) \u2264 1, to 0 < Pr(A) < 1.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg"], "links": ["Additive smoothing", "Admissible decision rule", "Approximate Bayesian computation", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernstein\u2013von Mises theorem", "Church of Scotland", "Conjugate prior", "Credible interval", "Dennis Lindley", "Empirical Bayes method", "Google Books", "Hyperparameter", "Hyperprior", "International Standard Book Number", "Likelihood function", "Markov chain Monte Carlo", "Maximum a posteriori estimation", "Oliver Cromwell", "Posterior predictive distribution", "Posterior probability", "Principle of indifference", "Principle of maximum entropy", "Prior probability", "Probability interpretations", "Radical probabilism", "Rule of succession", "Schwarz criterion", "Statistics", "The Signal and the Noise"], "references": ["http://www.worldcat.org/title/theory-that-would-not-die-how-bayes-rule-cracked-the-enigma-code-hunted-down-russian-submarines-emerged-triumphant-from-two-centuries-of-controversy/oclc/670481486", "https://books.google.com/books?id=QFqyrNL8yEkC&pg=PA18#v=onepage&q&f=false", "https://books.google.com/books?id=_Kx5xVGuLRIC"]}, "Statistical regularity": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from February 2012", "Statistical laws"], "title": "Statistical regularity", "method": "Statistical regularity", "url": "https://en.wikipedia.org/wiki/Statistical_regularity", "summary": "Statistical regularity is a notion in statistics and probability theory that random events exhibit regularity when repeated enough times or that enough sufficiently similar random events exhibit regularity. It is an umbrella term that covers the law of large numbers, all central limit theorems and ergodic theorems.\nIf one throws a die once, it is difficult to predict the outcome, but if we repeat this experiment many times, we will see that the number of times each result occurs divided by the number of throws will eventually stabilize towards a specific value.\nRepeating a series of trials will produce similar, but not identical, results for each series: the average, the standard deviation and other distributional characteristics will be around the same for each series of trials.\nThe notion is used in games of chance, demographic statistics, quality control of a manufacturing process, and in many other parts of our lives.\nObservations of this phenomenon provided the initial motivation for the concept of what is now known as frequency probability.\nThis phenomenon should not be confused with the gambler's fallacy, because regularity only refers to the (possibly very) long run. The gambler's fallacy does not apply to statistical regularity because the latter considers the whole rather than individual cases.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Central limit theorem", "Demographic statistics", "Ergodic theorem", "Frequency probability", "Gambler's fallacy", "Games of chance", "Impossibility of a gambling system", "International Standard Book Number", "Law of large numbers", "Probability theory", "Quality control", "Stationarity (statistics)", "Statistics", "Umbrella term"], "references": ["http://www.columbia.edu/~ww2040/scalingchno.pdf"]}, "Mauchly's sphericity test": {"categories": ["Analysis of variance", "CS1 maint: Multiple names: authors list", "Statistical tests"], "title": "Mauchly's sphericity test", "method": "Mauchly's sphericity test", "url": "https://en.wikipedia.org/wiki/Mauchly%27s_sphericity_test", "summary": "Mauchly's sphericity test is a statistical test used to validate a repeated measures analysis of variance (ANOVA).", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Epsilon", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent variable", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Mauchly", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MANOVA", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "SPSS", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Type I error", "U-statistic", "Uniformly most powerful test", "Univariate", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.wjh.harvard.edu/~moulton/mauchly_test.pdf", "http://oak.ucc.nau.edu/rh232/courses/EPS625/Handouts/RM-ANOVA/Sphericity.pdf", "http://doi.org/10.1007%2Fbf02289596", "http://doi.org/10.1037%2F0033-2909.97.2.316", "http://doi.org/10.1214%2Faoms%2F1177731915", "http://www.jstor.org/stable/2235878", "https://statistics.laerd.com/statistical-guides/sphericity-statistical-guide.php"]}, "Transect": {"categories": ["All articles with failed verification", "Articles with failed verification from April 2016", "Articles with short description", "Ecological techniques", "Environmental statistics", "Pages with login required references or sources", "Scientific observation", "Webarchive template wayback links", "Wikipedia articles needing page number citations from April 2016"], "title": "Transect", "method": "Transect", "url": "https://en.wikipedia.org/wiki/Transect", "summary": "A transect is a path along which one counts and records occurrences of the species of study (e.g. plants).It requires an observer to move along a fixed path and to count occurrences along the path and, at the same time (in some procedures), obtain the distance of the object from the path. This results in an estimate of the area covered and an estimate of the way in which detectability increases from probability 0 (far from the path) towards 1 (near the path). Using the raw count and this probability function, one can arrive at an estimate of the actual density of objects.\n\nThe estimation of the abundance of populations (such as terrestrial mammal species) can be achieved using a number of different types of transect methods, such as strip transects, line transects, belt transects, point transects and curved line transects.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/24/Transect_Gillmore_Hill_Wyoming.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a6/Transects_of_fire_boundary_above_Backhouse_Tarn.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg"], "links": ["Belt transect", "Census", "Curved line transect", "Distance sampling", "International Standard Book Number", "Line-intercept sampling", "Mark and recapture", "MegaTransect", "Point transect", "Strip transect", "Transect (urban)", "Wayback Machine"], "references": ["http://www.colostate.edu/Dept/coopunit/download.html", "http://www.creem.st-and.ac.uk/tiago/webpages/pdfs/Hiby&Krishna2001.pdf", "https://www.academia.edu/17269986/Physico-chemical_Parameters_and_Macrobenthic_Invertebrates_of_the_Intertidal_Zone_of_Gusa_Cagayan_de_Oro_City_Philippines", "https://web.archive.org/web/20070930121723/http://www.creem.st-and.ac.uk/tiago/webpages/pdfs/Hiby&Krishna2001.pdf"]}, "Weibull modulus": {"categories": ["All Wikipedia articles needing clarification", "Engineering statistics", "Materials science", "Wikipedia articles needing clarification from August 2008"], "title": "Weibull modulus", "method": "Weibull modulus", "url": "https://en.wikipedia.org/wiki/Weibull_modulus", "summary": "The Weibull modulus is a dimensionless parameter of the Weibull distribution which is used to describe variability in measured material strength of brittle materials. \nFor ceramics and other brittle materials, the maximum stress that a sample can be measured to withstand before failure may vary from specimen to specimen, even under identical testing conditions. This is related to the distribution of physical flaws present in the surface or body of the brittle specimen, since brittle failure processes originate at these weak points. When flaws are consistent and evenly distributed, samples will behave more uniformly than when flaws are clustered inconsistently. This must be taken into account when describing the strength of the material, so strength is best represented as a distribution of values rather than as one specific value. The Weibull modulus is a shape parameter for the Weibull distribution model which, in this case, maps the probability of failure of a component at varying stresses.\nConsider strength measurements made on many small samples of a brittle ceramic material. If the measurements show little variation from sample to sample, the calculated Weibull modulus will be high and a single strength value would serve as a good description of the sample-to-sample performance. It may be concluded that its physical flaws, whether inherent to the material itself or resulting from the manufacturing process, are distributed uniformly throughout the material. If the measurements show high variation, the calculated Weibull modulus will be low; this reveals that flaws are clustered inconsistently and the measured strength will be generally weak and variable. Products made from components of low Weibull modulus will exhibit low reliability and their strengths will be broadly distributed.\nTest procedures for determining the Weibull modulus are specified in DIN EN 843-5 and DIN 51 110-3.\nA further method to determine the strength of brittle materials has been described by the Wikibook contribution Weakest link determination by use of three parameter Weibull statistics.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Ceramic materials", "Digital object identifier", "Dimensionless quantity", "Probability density function", "Probability distribution", "Statistical dispersion", "Strength of materials", "Stress (physics)", "Weibull distribution"], "references": ["http://www.keramverband.de/brevier_engl/5/3/3/5_3_3_4.htm", "https://doi.org/10.1016%2Fj.ijsolstr.2005.08.002", "https://doi.org/10.1117%2F1.3265716"]}, "Plot (graphics)": {"categories": ["CS1 maint: Multiple names: authors list", "Charts", "Commons category link is on Wikidata", "Plots (graphics)", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Plot (graphics)", "method": "Plot (graphics)", "url": "https://en.wikipedia.org/wiki/Plot_(graphics)", "summary": "A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a mechanical or electronic plotter. Graphs are a visual representation of the relationship between variables, very useful for humans who can quickly derive an understanding which would not come from lists of values. Graphs can also be used to read off the value of an unknown variable plotted as a function of a known one. Graphs of functions are used in mathematics, sciences, engineering, technology, finance, and other areas.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f6/Biplot_of_Anderson%27s_Iris_data_set.svg", "https://upload.wikimedia.org/wikipedia/commons/b/bc/Bland-altman_plot.png", "https://upload.wikimedia.org/wikipedia/commons/1/16/Comet_plot_1.gif", "https://upload.wikimedia.org/wikipedia/commons/5/50/Comet_plot_2.gif", "https://upload.wikimedia.org/wikipedia/commons/1/1d/Contour-plot.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/bc/Dotplot_of_random_values_2.png", "https://upload.wikimedia.org/wikipedia/commons/7/73/Forestplot01.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/7a/Four_variable_carpet_plot.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2c/Funnelplot.png", "https://upload.wikimedia.org/wikipedia/commons/0/09/MER_Star_Plot.gif", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Michelsonmorley-boxplot.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f6/NO2_Arrhenius_k_against_T.svg", "https://upload.wikimedia.org/wikipedia/commons/b/ba/Nichols_plot.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2c/Normal_probability_plot.gif", "https://upload.wikimedia.org/wikipedia/commons/4/44/Nov192001h5spaghetti5640m.png", "https://upload.wikimedia.org/wikipedia/commons/0/06/Nyquist_plot.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Oldfaithful3.png", "https://upload.wikimedia.org/wikipedia/commons/c/c5/Probability_Plot.gif", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Qqnormexp.png", "https://upload.wikimedia.org/wikipedia/commons/c/c4/Scatter_plot.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a3/Surface-plot.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/44/Ternary.example.1.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Violin_plot.gif", "https://upload.wikimedia.org/wikipedia/commons/3/33/Zinc-finger-dot-plot.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["Abscissa", "Ade Olufeko", "Adolphe Quetelet", "Alan MacEachren", "Antenna (radio)", "Arrhenius plot", "Arthur Bowley", "Arthur H. Robinson", "Assay", "August Kekul\u00e9", "Automatic control", "BMJ", "Bang Wong", "Barycentric coordinates (mathematics)", "Ben Shneiderman", "Biological data visualization", "Biplot", "Bland-Altman plot", "Bode plot", "Box plot", "Bruce H. McCormick", "Carpet plot", "Cartography", "Charles Joseph Minard", "Chart", "Chartjunk", "Chemical imaging", "Christopher R. Johnson", "Clifford A. Pickover", "Comet plot", "Computer graphics", "Computer graphics (computer science)", "Confidence interval", "Continuous function", "Contour line", "Contour plot", "Control theory", "Copyright status of work by the U.S. government", "Crime mapping", "Dalitz plot", "Data", "Data analysis", "Data set", "Data visualization", "De Finetti diagram", "Device under test", "Diagram", "Digital object identifier", "Dot plot (bioinformatics)", "Dot plot (statistics)", "Economic equilibrium", "Edward Tufte", "Engineering", "Engineering drawing", "Environmental epidemiology", "Enzyme kinetics", "Equilateral", "Exploratory data analysis", "Feedback", "Fernanda Vi\u00e9gas", "Finance", "Five-number summary", "Florence Nightingale", "Flow visualization", "Forest plot", "Fraser Stoddart", "Frequency response", "Funnel plot", "Galbraith plot", "Game theory", "Gaspard Monge", "George Davey Smith", "George Furnas", "George G. Robertson", "Geovisualization", "Geyser", "Gradient", "Graph drawing", "Graph of a function", "Graphic design", "Graphic organizer", "Graphical technique", "Hanspeter Pfister", "Heat map", "Histogram", "Howard Wainer", "Hypothesis", "Ideogram", "Imaging science", "Infographic", "Information science", "Information visualization", "International Standard Book Number", "JSTOR", "Jacques Bertin", "Jock D. Mackinlay", "Karl Wilhelm Pohlke", "Kernel density estimation", "Lawrence J. Rosenblum", "Least squares regression", "Line-line intersection", "Line chart", "Lineweaver\u2013Burk plot", "List of graphical methods", "List of information graphics software", "Location parameter", "Logarithm", "Manuel Lima", "Map", "Martin M. Wattenberg", "Mathematical diagram", "Mathematical equations", "Mathematics", "Matthias Egger", "Medical imaging", "Mental image", "Meta-analysis", "Metallurgy", "Michael Friendly", "Michael Maltz", "Mineralogy", "Miriah Meyer", "Misleading graph", "Molecular graphics", "National Institute of Standards and Technology", "Neuroimaging", "Nichols plot", "Nigel Holmes", "Non-parametric statistics", "Normal distribution", "Normal probability plot", "Nyquist plot", "Old Faithful", "Ordinate", "Otto Neurath", "Outlier", "Partial regression plot", "Partial residual plot", "Pat Hanrahan", "Patent drawing", "Petrology", "Phase space", "Photograph", "Pictogram", "Plotter", "Polar coordinates", "Population genetics", "Probability density function", "Probability distribution", "Probability plot", "Psychrometric chart", "PubMed Central", "PubMed Identifier", "Q-Q plot", "Quantile", "Quantitative data", "Radiation pattern", "Random sample", "Randomized controlled trials", "Rectangular coordinates", "Recurrence plot", "Regression analysis", "Rudolf Modley", "Scale parameter", "Scatter plot", "Scatterplot", "Schematic", "Science", "Scientific modelling", "Scientific visualization", "Shape", "Shmoo plot", "Signal processing", "Skeletal formula", "Software visualization", "Spaghetti plot", "Spaghetti plots", "Spatial analysis", "Spectrum", "Standard error", "Star plot", "Statistical graphics", "Statistical population", "Statistics", "Stemplot", "Stuart Card", "Study heterogeneity", "Supply and demand", "Surface plot", "Table (information)", "Tamara Munzner", "Technical drawing", "Technical illustration", "Technology", "Ternary plot", "Thomas A. DeFanti", "Triangle", "Tukey mean-difference plot", "Univariate", "User interface", "User interface design", "Variable (mathematics)", "Vector field", "Violin plot", "Visual analytics", "Visual culture", "Visual perception", "Visualization (computer graphics)", "Visualization (graphics)", "Volume cartography", "Volume rendering", "Weibull distribution", "William Playfair"], "references": ["http://www.bmj.com/cgi/content/full/315/7109/629", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2127453", "http://www.ncbi.nlm.nih.gov/pubmed/2868172", "http://www.ncbi.nlm.nih.gov/pubmed/9310563", "http://www.itl.nist.gov/div898/handbook/eda/section1/eda15.htm", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda33.htm", "http://www.nist.gov", "http://doi.org/10.1016%2FS0140-6736(86)90837-8", "http://doi.org/10.1080%2F00031305.1998.10480559", "http://doi.org/10.1136%2Fbmj.315.7109.629", "http://doi.org/10.2307%2F1270081", "http://doi.org/10.2307%2F2987937", "http://www.jstor.org/stable/1270081", "http://www.jstor.org/stable/2987937", "https://books.google.com/books?id=ev54lAwS2KIC&pg=PA128&dq=spaghetti+diagram+book#v=onepage&q=spaghetti%20diagram%20book&f=false"]}, "Rayleigh distribution": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from April 2013", "Articles with unsourced statements from April 2013", "Continuous distributions", "Exponential family distributions", "Pages using deprecated image syntax", "Wikipedia articles needing page number citations from April 2013"], "title": "Rayleigh distribution", "method": "Rayleigh distribution", "url": "https://en.wikipedia.org/wiki/Rayleigh_distribution", "summary": "In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for positive-valued random variables. It is a chi distribution in two degrees of freedom.\nA Rayleigh distribution is often observed when the overall magnitude of a vector is related to its directional components. One example where the Rayleigh distribution naturally arises is when wind velocity is analyzed in two dimensions.\nAssuming that each component is uncorrelated, normally distributed with equal variance, and zero mean, then the overall wind speed (vector magnitude) will be characterized by a Rayleigh distribution. \nA second example of the distribution arises in the case of random complex numbers whose real and imaginary components are independently and identically distributed Gaussian with equal variance and zero mean. In that case, the absolute value of the complex number is Rayleigh-distributed.\nThe distribution is named after Lord Rayleigh ().", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a9/Rayleigh_distributionCDF.svg", "https://upload.wikimedia.org/wikipedia/commons/6/61/Rayleigh_distributionPDF.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["ARGUS distribution", "Animal husbandry", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular error probable", "Circular uniform distribution", "Complex numbers", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degrees of freedom", "Delaporte distribution", "Diet (nutrition)", "Differential entropy", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Error function", "Euclidean vector", "Euler\u2013Mascheroni constant", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Fundamental theorem of calculus", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hoyt distribution", "Human", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent and identically distributed", "Information entropy", "International Standard Book Number", "International Standard Serial Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverse transform sampling", "Irwin\u2013Hall distribution", "John Strutt, 3rd Baron Rayleigh", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Magnetic resonance imaging", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood estimation", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Moment (mathematics)", "Moment generating function", "Multinomial distribution", "Multiple integral", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Nutrient", "Nutrition", "Parabolic fractal distribution", "Parameter", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Plane (geometry)", "Poisson binomial distribution", "Poisson distribution", "Polar coordinate system", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh fading", "Rayleigh mixture distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uncorrelated", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wind", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://adsabs.harvard.edu/abs/2011PhRvD..84l2004R", "http://adsabs.harvard.edu/abs/2017PLoSO..1287292A", "http://nvlpubs.nist.gov/nistpubs/jres/66D/jresv66Dn2p167_A1b.pdf", "http://arxiv.org/abs/1109.0442", "http://doi.org/10.1002%2F(sici)1098-1098(1999)10:2%3C109::aid-ima2%3E3.0.co;2-r", "http://doi.org/10.1016%2Fj.ejmp.2014.05.002", "http://doi.org/10.1103%2Fphysrevd.84.122004", "http://doi.org/10.1371%2Fjournal.pone.0187292", "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0187292", "http://www.worldcat.org/issn/1932-6203", "https://archive.org/details/jresv68Dn9p1005", "https://web.archive.org/web/20131105232146/http://home.kpn.nl/jhhogema1966/skeetn/ballist/sgs/sgs.htm#_Toc96439743"]}, "Specification (regression)": {"categories": ["All articles to be expanded", "Articles to be expanded from June 2018", "Articles using small message boxes", "Regression variable selection"], "title": "Model specification", "method": "Specification (regression)", "url": "https://en.wikipedia.org/wiki/Model_specification", "summary": "In regression analysis, model specification is the process of developing a regression model. This process consists of selecting an appropriate functional form for the model and choosing which variables to include. For instance, one may specify the functional relationship \n \n \n \n y\n =\n f\n (\n s\n ,\n x\n )\n \n \n {\\displaystyle y=f(s,x)}\n between personal income \n \n \n \n y\n \n \n {\\displaystyle y}\n and human capital, with the latter proxied by schooling \n \n \n \n s\n \n \n {\\displaystyle s}\n and on-the-job experience \n \n \n \n x\n ,\n \n \n {\\displaystyle x,}\n as\n\n \n \n \n ln\n \u2061\n y\n =\n ln\n \u2061\n \n y\n \n 0\n \n \n +\n \u03c1\n s\n +\n \n \u03b2\n \n 1\n \n \n x\n +\n \n \u03b2\n \n 2\n \n \n \n x\n \n 2\n \n \n +\n \u03b5\n \n \n {\\displaystyle \\ln y=\\ln y_{0}+\\rho s+\\beta _{1}x+\\beta _{2}x^{2}+\\varepsilon }\n where \n \n \n \n \u03b5\n \n \n {\\displaystyle \\varepsilon }\n is the unexplained error term that is supposed to be independent and identically distributed. If assumptions of the regression model are correct, the least squares estimates of the parameters \n \n \n \n \u03c1\n \n \n {\\displaystyle \\rho }\n and \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n will be efficient and unbiased. Hence specification diagnostics usually involve testing the first to fourth moment of the residuals.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128143823%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128140726%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110427033551%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110424212543%21Wiki_letter_w_cropped.svg"], "links": ["Bias (statistics)", "Cross-validation (statistics)", "Damodar N. Gujarati", "Dependent variable", "Digital object identifier", "Edward E. Leamer", "Efficiency (statistics)", "Errors and residuals in statistics", "Expected value", "Function (mathematics)", "G. S. Maddala", "Human capital", "Independent and identically distributed random variables", "Independent variable", "International Standard Book Number", "J. Scott Long", "JSTOR", "Jan Kmenta", "Journal of Economic Literature", "Least squares", "Measurement errors", "Mincer earnings function", "Model risk", "Moment (mathematics)", "Omitted-variable bias", "Overfitting", "Parameter", "Personal income", "Ramsey RESET test", "Regression analysis", "Regression validation", "Scientific theory", "Simultaneous equations model"], "references": ["http://economicsbulletin.vanderbilt.edu/2005/volume3/EB-04C50033A.pdf", "http://cemood.people.wm.edu/603.html", "http://doi.org/10.1080%2F01621459.1977.10480627", "http://www.jstor.org/stable/2286231", "http://www.jstor.org/stable/2727880"]}, "Graphical models for protein structure": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from August 2010", "Articles lacking in-text citations from June 2010", "Computational chemistry", "Graphical models", "Protein methods"], "title": "Graphical models for protein structure", "method": "Graphical models for protein structure", "url": "https://en.wikipedia.org/wiki/Graphical_models_for_protein_structure", "summary": "Graphical models have become powerful frameworks for protein structure prediction, protein\u2013protein interaction and free energy calculations for protein structures. Using a graphical model to represent the protein structure allows the solution of many problems including secondary structure prediction, protein protein interactions, protein-drug interaction, and free energy calculations.\nThere are two main approaches to use graphical models in protein structure modeling. The first approach uses discrete variables for representing coordinates or dihedral angles of the protein structure. The variables are originally all continuous values and, to transform them into discrete values, a discretization process is typically applied. The second approach uses continuous variables for the coordinates or dihedral angles.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Approximation", "Backbone chain", "Boltzmann constant", "Bond length", "Clique (graph theory)", "Closed-form expression", "Conditional independence", "Covariance matrix", "Digital object identifier", "Dihedral angle", "Dihedral angles", "Discrete mathematics", "Expectation propagation", "Function (mathematics)", "Generalized belief propagation", "Goblin System", "Graphical model", "Inference", "L-1 regularization", "Markov random field", "Mean values", "Multivariate Gaussian distribution", "Multivariate probability distribution", "Neighborhood selection", "Particle filtering", "Partition function (mathematics)", "Precision matrix", "Probability density function", "Protein structure", "Protein structure prediction", "Protein\u2013protein interaction", "PubMed Identifier", "Random variable", "Rotamer", "Thermodynamic free energy", "Undirected graph"], "references": ["http://www.liebertonline.com/doi/pdf/10.1089/cmb.2007.0131", "http://www.cs.cmu.edu/~jgc/publication/Predicting_Protein_Folds_ICML_2005.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/19432536", "http://doi.org/10.1089%2Fcmb.2008.0176", "http://www.learningtheory.org/colt2008/81-Zhou.pdf"]}, "Information gain ratio": {"categories": ["All articles lacking sources", "All articles to be merged", "Articles lacking sources from November 2008", "Articles to be merged from April 2018", "Classification algorithms", "Decision trees", "Entropy and information", "Statistical ratios"], "title": "Information gain ratio", "method": "Information gain ratio", "url": "https://en.wikipedia.org/wiki/Information_gain_ratio", "summary": "In decision tree learning, Information gain ratio is a ratio of information gain to the intrinsic information. It was proposed by Ross Quinlan, to reduce a bias towards multi-valued attributes by taking the number and size of branches into account when choosing\nan attribute.Information Gain is also known as Mutual Information.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/aa/Merge-arrow.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Credit card number", "Decision tree learning", "Entropy (information theory)", "Information gain in decision trees", "Mutual information", "Ross Quinlan", "Training set"], "references": ["http://stats.stackexchange.com/questions/13389/information-gain-mutual-information-and-related-measures", "http://www.ke.tu-darmstadt.de/lehre/archiv/ws0809/mldm/dt.pdf", "https://link.springer.com/article/10.1007/BF00116251"]}, "Gittins index": {"categories": ["CS1 maint: Multiple names: authors list", "Decision theory", "Design of experiments", "Sequential methods"], "title": "Gittins index", "method": "Gittins index", "url": "https://en.wikipedia.org/wiki/Gittins_index", "summary": "The Gittins index is a measure of the reward that can be achieved through a given stochastic process with certain properties, namely: the process has an ultimate termination state and evolves with an option, at each intermediate state, of terminating. Upon terminating at a given state, the reward achieved is the sum of the probabilistic expected rewards associated with every state from the actual terminating state to the ultimate terminal state, inclusive. The index is a real scalar.", "images": [], "links": ["Bernoulli process", "Digital object identifier", "Don Berry (statistician)", "Dynamic programming", "Gaussian elimination", "International Standard Book Number", "JSTOR", "John C. Gittins", "Journal of the Royal Statistical Society, Series B", "Lagrangian multiplier", "Linear programming", "Markov chain", "Markov decision process", "Michael Katehakis", "Multi-armed bandit", "NP (complexity)", "Optimal stopping", "Peter Whittle (mathematician)", "Range (mathematics)", "Real number", "Richard R. Weber", "Scalar (mathematics)", "Scheduling (computing)", "Slot machine", "Stochastic process", "Stochastic scheduling"], "references": ["http://sites.google.com/site/lorenzodigregorio/gittins-index", "http://doi.org/10.1016/j.spl.2008.01.049", "http://doi.org/10.1017/S0269964814000217", "http://doi.org/10.1214/aoap/1177005588", "http://doi.org/10.1287/ijoc.1060.0206", "http://doi.org/10.1287/moor.11.1.180", "http://doi.org/10.1287/moor.11.1.184", "http://doi.org/10.1287/moor.12.2.262", "http://doi.org/10.2307/2233856", "http://www.jstor.org/stable/2959678", "http://www.jstor.org/stable/3689689", "https://www.jstor.org/stable/2233856", "https://www.jstor.org/stable/2335176", "https://www.jstor.org/stable/2985029"]}, "Lewontin's Fallacy": {"categories": ["Biology papers", "Human population genetics", "Race (human categorization)", "Scientific controversies", "Taxonomy (biology)"], "title": "Human Genetic Diversity: Lewontin's Fallacy", "method": "Lewontin's Fallacy", "url": "https://en.wikipedia.org/wiki/Human_Genetic_Diversity:_Lewontin%27s_Fallacy", "summary": "\"Human Genetic Diversity: Lewontin's Fallacy\" is a 2003 paper by A. W. F. Edwards. He criticises an argument first made by Richard Lewontin in his 1972 article \"The Apportionment of Human Diversity\", which argued that division of humanity into races is taxonomically invalid. Edwards' critique is discussed in a number of academic and popular science books, with varying degrees of support.", "images": [], "links": ["A. W. F. Edwards", "Allele", "American Anthropological Association", "Cambridge University Press", "Cluster analysis", "Digital object identifier", "Evolutionary biology", "Fixation index", "Genetic similarity", "Houghton Mifflin Harcourt", "Human genetic clustering", "International Standard Book Number", "Jonathan Marks (anthropologist)", "Locus (genetics)", "Luigi Luca Cavalli-Sforza", "Neven Sesardic", "Ordination (statistics)", "Popular science", "Population groups in biomedicine", "PubMed Central", "PubMed Identifier", "Race (classification of human beings)", "Race and genetics", "Richard Dawkins", "Richard Lewontin", "Springer Science+Business Media", "Taxonomy (general)", "The American Naturalist", "University of California Press"], "references": ["http://gutengroup.mcb.arizona.edu/Publications/Ramachandran2010.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1893020", "http://www.ncbi.nlm.nih.gov/pubmed/12879450", "http://www.ncbi.nlm.nih.gov/pubmed/17339205", "http://www.aaanet.org/resources/A-Public-Education-Program.cfm", "http://www.aaanet.org/stmts/racepp.htm", "http://doi.org/10.1002%2Fbies.10315", "http://doi.org/10.1002%2Fevan.20079", "http://doi.org/10.1007%2F978-1-4684-9063-3_14", "http://doi.org/10.1007%2F978-3-540-37654-5", "http://doi.org/10.1007%2Fs10539-009-9193-7", "http://doi.org/10.1086%2F283155", "http://doi.org/10.1086%2F283359", "http://doi.org/10.1534%2Fgenetics.106.067355", "https://books.google.com/books?id=3NRf_8gwmO8C&pg=PA270", "https://books.google.com/books?id=KKrsBcU_DikC&pg=PA76&dq=%22Lewontin's+Fallacy%22&hl=en&ei=JQIeTo-DBcXXiALGhe3-CA&sa=X&oi=book_result&ct=result&resnum=6&ved=0CEQQ6AEwBQ#v=onepage&q=%22Lewontin's%20Fallacy%22&f=false", "https://books.google.com/books?id=OKSL_N0tybsC&pg=PA115", "https://books.google.com/books?id=rR9XPnaqvCMC&pg=PA406", "https://www.springer.com/biomed/human+genetics/book/978-3-540-37653-8", "https://web.archive.org/web/20131203115416/http://gutengroup.mcb.arizona.edu/Publications/Ramachandran2010.pdf"]}, "NCSS (statistical software)": {"categories": ["Regression and curve fitting software", "Time series software", "Wikipedia articles with possible conflicts of interest from May 2016", "Windows-only software"], "title": "NCSS (statistical software)", "method": "NCSS (statistical software)", "url": "https://en.wikipedia.org/wiki/NCSS_(statistical_software)", "summary": "NCSS is a statistics package produced and distributed by NCSS, LLC. Created in 1981 by Jerry L. Hintze, NCSS, LLC specializes in providing statistical analysis software to researchers, businesses, and academic institutions. It also produces PASS Sample Size Software which is used in scientific study planning and evaluation.\nThe NCSS package includes over 250 documented statistical and plot procedures. NCSS imports and exports all major spreadsheet, database, and statistical file formats.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Unbalanced_scales.svg"], "links": ["ADMB", "Analyse-it", "BMDP", "BV4.1 (software)", "CSPro", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "EViews", "Epi Info", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "International Standard Book Number", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Numerical analysis", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PASS Sample Size Software", "PSPP", "Proprietary software", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.ncss.com/about/", "http://www.ncss.com/software/ncss", "http://www.ncss.com/software/ncss/", "http://www.ncss.com/software/ncss/ncss-documentation", "http://www.ncss.com/software/ncss/upgrade/", "https://www.apponfly.com/en/application/ncss10"]}, "An Essay towards solving a Problem in the Doctrine of Chances": {"categories": ["1763 documents", "18th-century essays", "Bayesian inference", "History of probability and statistics", "Probability books"], "title": "An Essay towards solving a Problem in the Doctrine of Chances", "method": "An Essay towards solving a Problem in the Doctrine of Chances", "url": "https://en.wikipedia.org/wiki/An_Essay_towards_solving_a_Problem_in_the_Doctrine_of_Chances", "summary": "An Essay towards solving a Problem in the Doctrine of Chances is a work on the mathematical theory of probability by the Reverend Thomas Bayes, published in 1763, two years after its author's death, and containing multiple amendments and additions due to his friend Richard Price. The title comes from the contemporary use of the phrase \"doctrine of chances\" to mean the theory of probability, which had been introduced via the title of a book by Abraham de Moivre. Contemporary reprints of the Essay carry a more specific and significant title: A Method of Calculating the Exact Probability of All Conclusions founded on Induction.The Essay includes theorems of conditional probability which form the basis of what is now called Bayes's Theorem, together with a detailed treatment of the problem of setting a prior probability.\nBayes supposed a sequence of independent experiments, each having as its outcome either success or failure, the probability of success being some number p between 0 and 1. But then he supposed p to be an uncertain quantity, whose probability of being in any interval between 0 and 1 is the length of the interval. In modern terms, p would be considered a random variable uniformly distributed between 0 and 1. Conditionally on the value of p, the trials resulting in success or failure are independent, but unconditionally (or \"marginally\") they are not. That is because if a large number of successes are observed, then p is more likely to be large, so that success on the next trial is more probable. The question Bayes addressed was: what is the conditional probability distribution of p, given the numbers of successes and failures so far observed. The answer is that its probability density function is\n\n \n \n \n f\n (\n p\n )\n =\n \n \n \n (\n n\n +\n 1\n )\n !\n \n \n k\n !\n (\n n\n \u2212\n k\n )\n !\n \n \n \n \n p\n \n k\n \n \n (\n 1\n \u2212\n p\n \n )\n \n n\n \u2212\n k\n \n \n \n for \n \n 0\n \u2264\n p\n \u2264\n 1\n \n \n {\\displaystyle f(p)={\\frac {(n+1)!}{k!(n-k)!}}p^{k}(1-p)^{n-k}{\\text{ for }}0\\leq p\\leq 1}\n (and \u0192(p) = 0 for p < 0 or p > 1) where k is the number of successes so far observed, and n is the number of trials so far observed. This is what today is called the Beta distribution with parameters k + 1 and n \u2212 k + 1.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["Abraham de Moivre", "ArXiv", "Bayes's Theorem", "Bayesian inference", "Beta distribution", "Biometrika", "Conditional distribution", "Conditional probability", "Deity", "Digital object identifier", "George Alfred Barnard", "Isaac Todhunter", "Marginal distribution", "Parameter", "Philosophical Transactions of the Royal Society of London", "Prior distribution", "Prior probability", "Probability", "Probability density function", "Random variable", "Richard Price", "Teleological argument", "The Doctrine of Chances", "Theory of probability", "Thomas Bayes", "UCLA", "Uniform distribution (continuous)"], "references": ["http://www.stat.ucla.edu/history/essay.pdf", "http://arxiv.org/abs/1310.0173", "http://doi.org/10.1093/biomet/45.3-4.293", "http://doi.org/10.1098/rstl.1763.0053", "http://doi.org/10.1214/13-STS438"]}, "Imprecise probability": {"categories": ["Probability theory", "Statistical approximations"], "title": "Imprecise probability", "method": "Imprecise probability", "url": "https://en.wikipedia.org/wiki/Imprecise_probability", "summary": "Imprecise probability generalizes probability theory to allow for partial probability specifications, and is applicable when information is scarce, vague, or conflicting, in which case a unique probability distribution may be hard to identify. Thereby, the theory aims to represent the available knowledge more accurately. Imprecision is useful for dealing with expert elicitation, because:\n\nPeople have a limited ability to determine their own subjective probabilities and might find that they can only provide an interval.\nAs an interval is compatible with a range of opinions, the analysis ought to be more convincing to a range of different people.\n\n", "images": [], "links": ["A Treatise on Probability", "Ambiguity aversion", "Andrey Kolmogorov", "ArXiv", "Artificial intelligence", "Asymmetric information", "Bayesian probability", "Belief functions", "Bibcode", "Bruno de Finetti", "Capacity (statistics)", "Choquet integral", "Cox's theorem", "Dempster\u2013Shafer theory", "Dennis Lindley", "Digital object identifier", "Expert elicitation", "Fair price", "Frank P. Ramsey", "Game-theoretic probability", "George Boole", "Glenn Shafer", "Henry Kyburg", "Hurwicz", "Illiquid", "Imprecise Dirichlet process", "International Standard Book Number", "Isaac Levi", "JSTOR", "John Maynard Keynes", "Lower and upper previsions", "Non-parametric statistics", "Pierre-Simon Laplace", "Possibility theory", "Prediction market", "Previsions", "Probability", "Probability box", "Probability distribution", "Probability interpretations", "Probability theory", "Robust Bayes analysis", "Robust decision making", "Robust statistics", "Set function", "Upper and lower probabilities", "Vladik Kreinovich"], "references": ["http://ipg.idsia.ch", "http://www.idsia.ch/~giorgio/jncc2.html", "http://www.ramas.com/unabridged.zip", "http://adsabs.harvard.edu/abs/2008JMAA..347..143D", "http://arxiv.org/abs/0801.1962", "http://doi.org/10.1016%2F0165-0114(78)90029-5", "http://doi.org/10.1016%2FS0888-613X(00)00032-3", "http://doi.org/10.1016%2Fj.artint.2008.03.001", "http://doi.org/10.1016%2Fj.ijar.2006.07.019", "http://doi.org/10.1016%2Fj.jmaa.2008.05.071", "http://doi.org/10.1016%2Fj.jspi.2003.07.003", "http://doi.org/10.1214%2Faoms%2F1177698950", "http://doi.org/10.1214%2Faos%2F1176342363", "http://doi.org/10.1214%2Fss%2F1177013611", "http://www.gutenberg.org/etext/15114", "http://www.jstor.org/stable/2239146", "http://www.sipta.org/", "http://www.maths.dur.ac.uk/users/matthias.troffaes/jstpip/improb.html", "https://archive.org/details/treatiseonprobab007528mbp"]}, "Sampling fraction": {"categories": ["All stub articles", "Sampling (statistics)", "Statistical ratios", "Statistics stubs"], "title": "Sampling fraction", "method": "Sampling fraction", "url": "https://en.wikipedia.org/wiki/Sampling_fraction", "summary": "In sampling theory, the sampling fraction is the ratio of sample size to population size or, in the context of stratified sampling, the ratio of the sample size to the size of the stratum.\nThe formula for the sampling fraction is\n\n \n \n \n f\n =\n \n \n n\n N\n \n \n ,\n \n \n {\\displaystyle f={\\frac {n}{N}},}\n where n is the sample size and N is the population size. A sampling fraction value close to 1 will occur if the sample size is relatively close to the population size. When sampling from a finite population without replacement, this may cause dependence between individual samples. To correct for this dependence when calculating the sample variance, a finite population correction (or finite population multiplier) of (N-n)/(N-1) may be used. If the sampling fraction is small, less than 0.05, then the sample variance is not appreciably affected by dependence, and the finite population correction may be ignored.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Correlation and dependence", "Finite population correction", "International Standard Book Number", "OCLC", "Sample (statistics)", "Sampling with replacement", "Statistical population", "Statistical sampling", "Statistics", "Stratified sampling", "Variance"], "references": ["http://www.worldcat.org/oclc/24142279", "http://www.worldcat.org/oclc/58425200"]}, "Multinomial distribution": {"categories": ["Discrete distributions", "Exponential family distributions", "Factorial and binomial topics", "Multivariate discrete distributions"], "title": "Multinomial distribution", "method": "Multinomial distribution", "url": "https://en.wikipedia.org/wiki/Multinomial_distribution", "summary": "In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for rolling a k-sided die n times. For n independent trials each of which leads to a success for exactly one of k categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories.\nWhen k is 2 and n is 1, the multinomial distribution is the Bernoulli distribution. When k is 2 and n is bigger than 1, it is the binomial distribution. When k is bigger than 2 and n is 1, it is the categorical distribution.\nThe Bernoulli distribution models the outcome of a single Bernoulli trial. In other words, it models whether flipping a (possibly biased) coin one time will result in either a success (obtaining a head) or failure (obtaining a tail). The binomial distribution generalizes this to the number of heads from performing n independent flips (Bernoulli trials) of the same coin. The multinomial distribution models the outcome of n experiments, where the outcome of each trial has a categorical distribution, such as rolling a k-sided die n times.\nLet k be a fixed finite number. Mathematically, we have k possible mutually exclusive outcomes, with corresponding probabilities p1, ..., pk, and n independent trials. Since the k outcomes are mutually exclusive and one must occur we have pi \u2265 0 for i = 1, ..., k and \n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n k\n \n \n \n p\n \n i\n \n \n =\n 1\n \n \n {\\displaystyle \\sum _{i=1}^{k}p_{i}=1}\n . Then if the random variables Xi indicate the number of times outcome number i is observed over the n trials, the vector X = (X1, ..., Xk) follows a multinomial distribution with parameters n and p, where p = (p1, ..., pk). While the trials are independent, their outcomes X are dependent because they must be summed to n.\nIn some fields such as natural language processing, categorical and multinomial distributions are synonymous and it is common to speak of a multinomial distribution when a categorical distribution is actually meant. This stems from the fact that it is sometimes convenient to express the outcome of a categorical distribution as a \"1-of-K\" vector (a vector with one element containing a 1 and all other elements containing a 0) rather than as an integer in the range \n \n \n \n 1\n \u2026\n K\n \n \n {\\displaystyle 1\\dots K}\n ; in this form, a categorical distribution is equivalent to a multinomial distribution over a single trial.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli trial", "Beta-binomial distribution", "Beta-binomial model", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Centering matrix", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation matrix", "Covariance", "Covariance matrix", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fair coin", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hardy\u2013Weinberg principle", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Integer", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Moment-generating function", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Natural language processing", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pascal's pyramid", "Pascal's triangle", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Positive-definite matrix", "Probability-generating function", "Probability distribution", "Probability mass function", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Range (mathematics)", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Simplex", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://mathworld.wolfram.com/MultinomialDistribution.html", "https://onlinecourses.science.psu.edu/stat504/node/40"]}, "Quantile function": {"categories": ["CS1 maint: Archived copy as title", "CS1 maint: Multiple names: authors list", "Functions related to probability distributions", "Webarchive template wayback links"], "title": "Quantile function", "method": "Quantile function", "url": "https://en.wikipedia.org/wiki/Quantile_function", "summary": "In probability and statistics, the quantile function, associated with a probability distribution of a random variable, specifies the value of the random variable such that the probability of the variable being less than or equal to that value equals the given probability. It is also called the percent-point function or inverse cumulative distribution function.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9b/Probit_plot.png", "https://upload.wikimedia.org/wikipedia/commons/5/55/Quantile_distribution_function.svg"], "links": ["Beta distribution", "Bisection method", "Cauchy distribution", "Central moment", "Characteristic function (probability theory)", "Closed-form expression", "Combinant", "Computational finance", "Copula (statistics)", "Cumulant", "Cumulative distribution function", "Differential equation", "Digital object identifier", "Expected value", "Exponential distribution", "Galois connection", "Gamma distribution", "Infimum and supremum", "Integral of inverse functions", "International Standard Book Number", "Inverse function", "Inverse transform sampling", "JSTOR", "Kurtosis", "L-moment", "Location-scale family", "Log-logistic distribution", "Logistic distribution", "Mean", "Median", "Mixture distribution", "Moment-generating function", "Monte Carlo method", "Monte Carlo methods in finance", "Multivariate analysis", "Normal distribution", "Numerical Recipes", "Numerical methods", "Ordinary differential equation", "Percent point", "Probability", "Probability-generating function", "Probability density function", "Probability distribution", "Probability mass function", "Probit", "Pseudorandom number", "Quantile", "Quartile", "Random variable", "Rank-size distribution", "Raw moment", "Root-finding algorithm", "Skewness", "Standard deviation", "Statistical significance", "Statistical software", "Statistics", "Student's t-distribution", "Student t-distribution", "Tukey lambda distribution", "Uniform distribution (continuous)", "Variance", "Wayback Machine", "Weibull distribution"], "references": ["http://course.shufe.edu.cn/jpkc/jrjlx/ref/StaTable.pdf", "http://home.online.no/~pjacklam/notes/invnorm/", "http://portal.acm.org/citation.cfm?id=168387", "http://portal.acm.org/citation.cfm?id=355600", "http://doi.org/10.1016%2Fj.csda.2005.09.014", "http://doi.org/10.1017%2FS0956792508007341", "http://doi.org/10.2307%2F2347330", "http://www.jstor.org/stable/2347330", "https://web.archive.org/web/20070505093933/http://home.online.no/~pjacklam/notes/invnorm/", "https://web.archive.org/web/20070508022437/http://www.mth.kcl.ac.uk/~shaww/web_page/papers/Tdistribution06.pdf", "https://web.archive.org/web/20070609171237/http://www.mth.kcl.ac.uk/~shaww/web_page/papers/NormalQuantile1.pdf", "https://web.archive.org/web/20120324042025/http://course.shufe.edu.cn/jpkc/jrjlx/ref/StaTable.pdf", "https://arxiv.org/abs/0901.0638", "https://doi.org/10.1145%2F168173.168387"]}, "Multivariate probit": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2017", "Regression models"], "title": "Multivariate probit model", "method": "Multivariate probit", "url": "https://en.wikipedia.org/wiki/Multivariate_probit_model", "summary": "In statistics and econometrics, the multivariate probit model is a generalization of the probit model used to estimate several correlated binary outcomes jointly. For example, if it is believed that the decisions of sending at least one child to public school and that of voting in favor of a school budget are correlated (both decisions are binary), then the multivariate probit model would be appropriate for jointly predicting these two choices on an individual-specific basis. This approach was initially developed by Siddhartha Chib and Edward Greenberg.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Bivariate normal distribution", "Cumulative distribution function", "Digital object identifier", "Discrete choice", "Econometrics", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "GHK algorithm", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Isotonic regression", "Iteratively reweighted least squares", "Latent variable", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Maximum likelihood", "Mean and predicted response", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Weighted least squares"], "references": ["http://doi.org/10.1007%2Fs10994-017-5652-6", "https://academic.oup.com/biomet/article-abstract/85/2/347/298820", "https://link.springer.com/content/pdf/10.1007%2Fs10994-017-5652-6.pdf"]}, "Treynor ratio": {"categories": ["All stub articles", "Finance stubs", "Financial ratios", "Statistical ratios"], "title": "Treynor ratio", "method": "Treynor ratio", "url": "https://en.wikipedia.org/wiki/Treynor_ratio", "summary": "The Treynor reward to volatility model (sometimes called the reward-to-volatility ratio or Treynor measure), named after Jack L. Treynor, is a measurement of the returns earned in excess of that which could have been earned on an investment that has no diversifiable risk (e.g., Treasury bills or a completely diversified portfolio), per each unit of market risk assumed.\nThe Treynor ratio relates excess return over the risk-free rate to the additional risk taken; however, systematic risk is used instead of total risk. The higher the Treynor ratio, the better the performance of the portfolio under analysis.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/29/ThreeCoins.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/2/29/20180705065644%21ThreeCoins.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/2/29/20081006162233%21ThreeCoins.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/2/29/20081006161859%21ThreeCoins.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/2/29/20081006153702%21ThreeCoins.svg"], "links": ["Active management", "Beta (finance)", "Beta coefficient", "Bias ratio (finance)", "CROCI", "Capital asset pricing model", "Capitalization rate", "Cyclically adjusted price-to-earnings ratio", "Debt-to-equity ratio", "Dividend cover", "Dividend payout ratio", "EV/EBITDA", "EV/GCI", "EV/Sales", "Excess return", "Finance", "Financial ratio", "Hansen-Jagannathan bound", "Investment", "Jack L. Treynor", "Jensen's alpha", "Loan-to-value ratio", "Modern portfolio theory", "Modigliani risk-adjusted performance", "Omega ratio", "Operating margin", "P/B ratio", "PEG ratio", "Price/cash flow ratio", "Price\u2013earnings ratio", "Price\u2013sales ratio", "Profit margin", "Return on assets", "Return on capital", "Return on capital employed", "Return on equity", "Return on net assets", "Return on tangible equity", "Risk-adjusted return on capital", "Risk free rate", "Risk return ratio", "Security market line", "Sharpe ratio", "Short interest ratio", "Sortino ratio", "Sustainable growth rate", "Systematic risk", "United States Treasury security", "Upside potential ratio", "V2 ratio"], "references": ["http://www.investopedia.com/terms/t/treynorratio.asp"]}, "Fieller's theorem": {"categories": ["Normal distribution", "Statistical approximations", "Statistical theorems"], "title": "Fieller's theorem", "method": "Fieller's theorem", "url": "https://en.wikipedia.org/wiki/Fieller%27s_theorem", "summary": "In statistics, Fieller's theorem allows the calculation of a confidence interval for the ratio of two means.", "images": [], "links": ["Arithmetic mean", "Bias of an estimator", "Biometrika", "Boots UK", "Bootstrapping (statistics)", "Confidence interval", "Correlation", "Digital object identifier", "Expected value", "International Standard Book Number", "JSTOR", "Journal of the Royal Statistical Society", "Journal of the Royal Statistical Society, Series B", "Karl Pearson", "King's College, Cambridge", "National Physical Laboratory (United Kingdom)", "Operational research", "PharmacoEconomics (journal)", "PubMed Identifier", "QJM: An International Journal of Medicine", "RAF Fighter Command", "Ratio distribution", "Sample mean", "Second World War", "Standard error", "Statistics", "Statistics in Medicine (journal)", "Student's t-distribution", "The American Statistician", "University College London"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/10947489", "http://doi.org/10.1093%2Fqjmed%2F92.3.177", "http://doi.org/10.1198%2Ftast.2010.08130", "http://doi.org/10.2165%2F00019053-200017040-00004", "http://www.jstor.org/stable/2984043", "http://www.jstor.org/stable/2984155", "https://doi.org/10.1002%2Fsim.1450", "https://doi.org/10.1093%2Fbiomet%2F24.3-4.428", "https://www.jstor.org/stable/2983630"]}, "Kolmogorov's inequality": {"categories": ["Accuracy disputes from November 2017", "All accuracy disputes", "All articles needing additional references", "All articles with unsourced statements", "Articles containing proofs", "Articles needing additional references from November 2017", "Articles with multiple maintenance issues", "Articles with unsourced statements from May 2007", "Probabilistic inequalities", "Stochastic processes", "Wikipedia articles incorporating text from PlanetMath"], "title": "Kolmogorov's inequality", "method": "Kolmogorov's inequality", "url": "https://en.wikipedia.org/wiki/Kolmogorov%27s_inequality", "summary": "In probability theory, Kolmogorov's inequality is a so-called \"maximal inequality\" that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound. The inequality is named after the Russian mathematician Andrey Kolmogorov.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/1/17/System-search.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Andrey Kolmogorov", "Bernstein inequalities (probability theory)", "Chebyshev's inequality", "Doob's martingale inequality", "Etemadi's inequality", "Expected value", "Finite set", "Independent random variables", "Inequality (mathematics)", "International Standard Book Number", "Kareem Amin", "Landau\u2013Kolmogorov inequality", "Markov's inequality", "Martingale (probability theory)", "Mathematician", "Partial sum", "PlanetMath", "Probability space", "Probability theory", "Random variable", "Random walk", "Russia", "Statistical independence", "Variance", "William Feller", "Without loss of generality"], "references": []}, "Path coefficient": {"categories": ["Structural equation models"], "title": "Path coefficient", "method": "Path coefficient", "url": "https://en.wikipedia.org/wiki/Path_coefficient", "summary": "Path coefficients are standardized versions of linear regression weights which can be used in examining the possible causal linkage between statistical variables in the structural equation modeling approach. The standardization involves multiplying the ordinary regression coefficient by the standard deviations of the corresponding explanatory variable: these can then be compared to assess the relative effects of the variables within the fitted regression model. The idea of standardization can be extended to apply to partial regression coefficients.\nThe term \"path coefficient\" derives from Wright (1921), where a particular diagram-based approach was used to consider the relations between variables in a multivariate system.", "images": [], "links": ["International Standard Book Number", "Linear regression", "Path analysis (statistics)", "Sewall Wright", "Statistical variable", "Structural equation modeling"], "references": []}, "Fuzzy measure theory": {"categories": ["Exotic probabilities", "Fuzzy logic", "Measure theory"], "title": "Fuzzy measure theory", "method": "Fuzzy measure theory", "url": "https://en.wikipedia.org/wiki/Fuzzy_measure_theory", "summary": "In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. The central concept of fuzzy measure theory is the fuzzy measure (also capacity, see ) which was introduced by Choquet in 1953 and independently defined by Sugeno in 1974 in the context of fuzzy integrals. There exists a number of different classes of fuzzy measures including plausibility/belief measures; possibility/necessity measures; and probability measures which are a subset of classical measures.", "images": [], "links": ["Choquet integral", "Class (mathematics)", "Dempster-Shafer theory", "Digital object identifier", "Function (mathematics)", "Game", "George J. Klir", "Gustave Choquet", "Lebesgue integral", "Mathematics", "Measure (mathematics)", "Monotone class", "Multi-criteria decision analysis", "Ordered weighted averaging aggregation operator", "Polynomial", "Possibility theory", "Power set", "Probability measure", "Probability theory", "Semiring", "Shapley value", "Submodular", "Subset", "Sugeno integral", "Universe of discourse"], "references": ["http://pami.uwaterloo.ca/tizhoosh/measure.htm", "http://doi.org/10.1016%2FS0165-0114(97)00168-1", "http://doi.org/10.1109%2F21.57289"]}, "Generalized linear model": {"categories": ["Actuarial science", "All articles with unsourced statements", "Articles with unsourced statements from November 2011", "Generalized linear models", "Regression models"], "title": "Generalized linear model", "method": "Generalized linear model", "url": "https://en.wikipedia.org/wiki/Generalized_linear_model", "summary": "In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.\nGeneralized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. They proposed an iteratively reweighted least squares method for maximum likelihood estimation of the model parameters. Maximum-likelihood estimation remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian approaches and least squares fits to variance stabilized responses, have been developed.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bayesian statistics", "Bernoulli distribution", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Canonical form", "Cartography", "Categorical distribution", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Closed-form expression", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparison of general and generalized linear models", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Density function", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete choice", "Discrete distribution", "Divergence (statistics)", "Domain of a function", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Eta (letter)", "Expected value", "Experiment", "Exponential dispersion model", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher information", "Fixed effects model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "GLIM (software)", "Gamma distribution", "Gauss\u2013Markov theorem", "General linear model", "Generalized additive model", "Generalized estimating equation", "Generalized least squares", "Generalized linear array model", "Generalized linear mixed model", "Geographic information system", "Geometric mean", "Geostatistics", "Gibbs sampling", "Goodness of fit", "Granger causality", "Graphical model", "Greek alphabet", "Grouped data", "Harmonic mean", "Hessian matrix", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Huber-White standard errors", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse Gaussian distribution", "Isotonic regression", "Iterative method", "Iteratively reweighted least squares", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Nelder", "Jonckheere's trend test", "Joseph Hilbe", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laplace approximation", "Least-angle regression", "Least-squares", "Least absolute deviations", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear least squares", "Linear probability model", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-linear model", "Log-rank test", "Logarithm", "Logistic regression", "Logit", "Longitudinal studies", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Markov chain Monte Carlo", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multilevel model", "Multinomial distribution", "Multinomial logistic regression", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multiplicative inverse", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural exponential family", "Natural logarithm", "Nelson\u2013Aalen estimator", "Newton\u2013Raphson method", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Observed information", "Odds ratio", "Official statistics", "One- and two-tailed tests", "One-to-one function", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Outline of statistics", "Overdispersion", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares regression", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter McCullagh", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior distribution", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal component regression", "Prior distribution", "Prior probability", "Probabilistic design", "Probability distribution", "Probability distributions", "Probability mass function", "Probit model", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Quality control", "Quantile regression", "Quasi-experiment", "Quasi-likelihood", "Quasi-variance", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effects", "Random effects model", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (mathematics)", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regularized least squares", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response variable", "Robert Wedderburn (statistician)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score (statistics)", "Score test", "Scoring algorithm", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smoothing", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficiency (statistics)", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Trend estimation", "Tweedie distributions", "U-statistic", "Uncorrelated", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-stabilizing transformation", "Variance function", "Vector autoregression", "Vector generalized linear model", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/3233245", "http://doi.org/10.1214%2Fss%2F1056397489", "http://doi.org/10.2307%2F2344614", "http://doi.org/10.2307%2F2531734", "http://www.jstor.org/stable/2344614", "http://www.jstor.org/stable/2531734"]}, "Sethi model": {"categories": ["Advertising", "Mathematical economics", "Optimal control", "Stochastic models"], "title": "Sethi model", "method": "Sethi model", "url": "https://en.wikipedia.org/wiki/Sethi_model", "summary": "The Sethi model was developed by Suresh P. Sethi and describes the process of how sales evolve over time in response to advertising. The rate of change in sales depend on three effects: response to advertising that acts positively on the unsold portion of the market, the loss due to forgetting or possibly due to competitive factors that act negatively on the sold portion of the market, and a random effect that can go either way.\nSuresh Sethi published his paper \"Deterministic and Stochastic Optimization of a Dynamic Advertising Model\" in 1983. The Sethi model is a modification as well as a stochastic extension of the Vidale-Wolfe advertising model. The model and its competitive extensions have been used extensively in the literature. Moreover, some of these extensions have been also tested empirically.\n\n", "images": [], "links": ["Advertising", "Bass diffusion model", "Brownian motion", "Differential game", "Diffusion of innovations", "Digital object identifier", "Dipak C. Jain", "International Standard Book Number", "Nash equilibrium", "Optimal control", "Social Science Research Network", "Stackleberg competition", "Stochastic differential equation", "Suresh P. Sethi", "White noise", "Wiener process"], "references": ["http://ssrn.com/abstract=1069063", "http://ssrn.com/abstract=1069162", "http://www.utdallas.edu/~sethi/OPRE7320presentation.html", "http://doi.org/10.1002%2Foca.4660040207", "http://doi.org/10.1007%2Fs10957-008-9472-5", "http://doi.org/10.1007%2Fs11518-007-5058-2", "http://doi.org/10.1016%2F0165-1889(89)90011-0", "http://doi.org/10.1016%2Fj.automatica.2008.09.018", "http://doi.org/10.1023%2FB:JOTA.0000043996.62867.20", "http://doi.org/10.1111%2Fj.1430-9134.1995.00109.x", "http://doi.org/10.1111%2Fj.1937-5956.2009.01006.x", "http://doi.org/10.1287%2Fmksc.1050.0119", "http://doi.org/10.1287%2Fmnsc.1070.0755", "http://doi.org/10.1287%2Fmnsc.38.9.1230", "http://doi.org/10.1287%2Fopre.1080.0663", "http://doi.org/10.1287%2Fopre.5.3.370"]}, "Sample standard deviation (disambiguation)": {"categories": ["All articles with failed verification", "All articles with unsourced statements", "Articles with failed verification from May 2015", "Articles with unsourced statements from August 2017", "Articles with unsourced statements from January 2012", "Articles with unsourced statements from July 2012", "Statistical deviation and dispersion", "Summary statistics", "Use dmy dates from June 2011", "Wikipedia articles with GND identifiers"], "title": "Standard deviation", "method": "Sample standard deviation (disambiguation)", "url": "https://en.wikipedia.org/wiki/Standard_deviation", "summary": "In statistics, the standard deviation (SD, also represented by the lower case Greek letter sigma \u03c3 or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.\nThe standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.\nA useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data. \nIn addition to expressing the variability of a population, the standard deviation is commonly used to measure confidence in statistical conclusions. For example, the margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times. This derivation of a standard deviation is often called the \"standard error\" of the estimate or \"standard error of the mean\" when referring to a mean. It is computed as the standard deviation of all the means that would be computed from that population if an infinite number of samples were drawn and a mean for each sample were computed.\nIt is very important to note that the standard deviation of a population and the standard error of a statistic derived from that population (such as the mean) are quite different but related (related by the inverse of the square root of the number of observations). The reported margin of error of a poll is computed from the standard error of the mean (or alternatively from the product of the standard deviation of the population and the inverse of the square root of the sample size, which is the same thing) and is typically about twice the standard deviation\u2014the half-width of a 95 percent confidence interval. \nIn science, many researchers report the standard deviation of experimental data, and only effects that fall much farther than two standard deviations away from what would have been expected are considered statistically significant\u2014normal random error or variation in the measurements is in this way distinguished from likely genuine effects or associations. The standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the volatility of the investment.\nWhen only a sample of data from a population is available, the term standard deviation of the sample or sample standard deviation can refer to either the above-mentioned quantity as applied to those data or to a modified quantity that is an unbiased estimate of the population standard deviation (the standard deviation of the entire population).", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Comparison_standard_deviations.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0c/Confidence_interval_by_Standard_deviation.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8b/Metabolic_rates_for_northern_fulmars.svg", "https://upload.wikimedia.org/wikipedia/commons/1/15/Normal-distribution-cumulative-density-function.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d0/SD_of_metabolic_rate_of_fulmars.svg", "https://upload.wikimedia.org/wikipedia/commons/6/67/Standard_deviation_by_Confidence_interval.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["68-95-99.7 rule", "68\u201395\u201399.7 rule", "Accelerated failure time model", "Accumulation/distribution index", "Accuracy and precision", "Actuarial science", "Advance\u2013decline line", "Akaike information criterion", "Algebra", "Algorithms for calculating variance", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "ArXiv", "Arithmetic average", "Arithmetic mean", "Arithmetic overflow", "Arithmetic underflow", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average absolute deviation", "Average directional movement index", "Average human height", "Average true range", "Bar chart", "Basal metabolic rate", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bessel's correction", "Bias of an estimator", "Biased estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bollinger Bands", "Bootstrapping (statistics)", "Bottom (technical analysis)", "Box plot", "Box\u2013Jenkins method", "Breadth of market", "Breakout (technical analysis)", "Breusch\u2013Godfrey test", "Broadening top", "CERN", "Calculus", "Candlestick chart", "Candlestick pattern", "Canonical correlation", "Carl Friedrich Gauss", "Cartography", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central moment", "Central tendency", "Chart pattern", "Chebyshev's inequality", "Chemometrics", "Chi-squared test", "Chi distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Commodity channel index", "Commutative property", "Completeness (statistics)", "Completing the square", "Computational formula for the variance", "Computer program", "Concave function", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous distribution", "Continuous probability distribution", "Control chart", "Coppock curve", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulative distribution function", "Cup and handle", "Data collection", "Data set", "Dead cat bounce", "Decomposition of time series", "Definite integral", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Detrended price oscillator", "Deviation (statistics)", "Dickey\u2013Fuller test", "Digital object identifier", "Dimensionless number", "Distance correlation", "Divergence (statistics)", "Doji", "Donchian channel", "Double top and double bottom", "Dow theory", "Durbin\u2013Watson statistic", "Ease of movement", "Econometrics", "Effect size", "Efficiency (statistics)", "Efficient estimator", "Elliott wave principle", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. 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"Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Negative volume index", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normalizing constant", "Northern fulmar", "Observational study", "Official statistics", "On-balance volume", "One- and two-tailed tests", "Open-high-low-close chart", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabolic SAR", "Parametric model", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Particle physics", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentage point", "Percentile", "Permutation 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analysis", "Regression model validation", "Relative standard deviation", "Relative strength index", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Risk", "Robust regression", "Robust standard deviation", "Robust statistics", "Root-mean-square deviation", "Root mean square", "Round-off error", "Run chart", "S", "Sample mean", "Sample median", "Sample size", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Samuelson's inequality", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shooting star (candlestick pattern)", "Sigma", "Sign test", "Simple linear regression", "Simultaneous equations model", "Six Sigma", "Skewness", "Smart money index", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spinning top (candlestick pattern)", "Square (algebra)", "Square root", "Squared deviations", "Standard deviation (disambiguation)", "Standard error", "Standard error (statistics)", "Standard error of the mean", "Standard score", "Standardized testing (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistically significant", "Statistics", "Stem-and-leaf display", "Stochastic oscillator", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Summation", "Support and resistance", "Survey methodology", "Survival analysis", "Survival function", "System identification", "TRIN (finance)", "Technical analysis", "Technical indicator", "Three black crows", "Three white soldiers", "Time domain", "Time series", "Tolerance interval", "Top (technical analysis)", "Trend estimation", "Trend line (technical analysis)", "Triangle (chart pattern)", "Triple top and triple bottom", "Trix (technical analysis)", "True strength index", "U-statistic", "Ulcer index", "Ultimate oscillator", "Unbiased estimation of standard deviation", "Unbiased estimator", "Uniformly most powerful test", "United States", "Univariate", "V-statistic", "VIX", "Variance", "Vector autoregression", "Volatility (finance)", "Volume (finance)", "Volume\u2013price trend", "Vortex indicator", "Wald test", "Wavelet", "Wedge pattern", "Whittle likelihood", "Wilcoxon signed-rank test", "Williams %R", "Yamartino method", "YouTube", "Z-test"], "references": ["http://users.monash.edu.au/~murray/BDAR/", "http://press-archive.web.cern.ch/press-archive/PressReleases/Releases2012/PR17.12E.html", "http://public.web.cern.ch/public/", "http://www.edupristine.com/blog/what-is-standard-deviation", "http://www.ifa.com", "http://www.techbookreport.com/tutorials/stddev-30-secs.html", "http://jeff560.tripod.com/mathword.html", "http://mathworld.wolfram.com/BesselsCorrection.html", "http://mathworld.wolfram.com/DistributionFunction.html", "http://zach.in.tu-clausthal.de/teaching/info_literatur/Welford.pdf", "http://adsabs.harvard.edu/abs/1894RSPTA.185...71P", "http://adsabs.harvard.edu/abs/2016PhRvL.116f1102A", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2351401", "http://www.ncbi.nlm.nih.gov/pubmed/26918975", "http://www.ncbi.nlm.nih.gov/pubmed/8664723", "http://arxiv.org/abs/1602.03837", "http://doi.org/10.1080%2F00401706.1962.10490022", "http://doi.org/10.1098%2Frsta.1894.0003", "http://doi.org/10.1103%2FPhysRevLett.116.061102", "http://doi.org/10.1136%2Fbmj.312.7047.1654", "http://doi.org/10.2307%2F2265587", "http://doi.org/10.2307%2F2682923", "https://standard-deviation.appspot.com/", "https://www.youtube.com/watch?v=AUSKTk9ENzg", "https://d-nb.info/gnd/4767332-1", "https://www.encyclopediaofmath.org/index.php?title=p/q076030", "https://www.wikidata.org/wiki/Q159375"]}, "Varadhan's lemma": {"categories": ["Asymptotic analysis", "Large deviations theory", "Lemmas", "Probability theorems", "Statistical theorems"], "title": "Varadhan's lemma", "method": "Varadhan's lemma", "url": "https://en.wikipedia.org/wiki/Varadhan%27s_lemma", "summary": "In mathematics, Varadhan's lemma is a result from large deviations theory named after S. R. Srinivasa Varadhan. The result gives information on the asymptotic distribution of a statistic \u03c6(Z\u03b5) of a family of random variables Z\u03b5 as \u03b5 becomes small in terms of a rate function for the variables.", "images": [], "links": ["Asymptotic analysis", "Continuous function", "Indicator function", "International Standard Book Number", "Laplace principle (large deviations theory)", "Large deviation principle", "Large deviations theory", "Mathematical Reviews", "Mathematics", "Moment (mathematics)", "Probability measure", "Random variable", "Rate function", "Regular space", "S. R. Srinivasa Varadhan"], "references": ["http://www.ams.org/mathscinet-getitem?mr=1619036"]}, "Inverse relationship": {"categories": ["Independence (probability theory)", "Negative concepts"], "title": "Negative relationship", "method": "Inverse relationship", "url": "https://en.wikipedia.org/wiki/Negative_relationship", "summary": "In statistics, there is a negative relationship or inverse relationship between two variables if higher values of one variable tend to be associated with lower values of the other. A negative relationship between two variables usually implies that the correlation between them is negative, or \u2014 what is in some contexts equivalent \u2014 that the slope in a corresponding graph is negative. A negative correlation between variables is also called anticorrelation or inverse correlation.\nNegative correlation can be seen geometrically when two normalized random vectors are viewed as points on a sphere, and the correlation between them is the cosine of the arc of separation of the points on the sphere. When this arc is more than a quarter-circle (\u03b8 > \u03c0/2), then the cosine is negative. Diametrically opposed points represent a correlation of \u20131 = cos(\u03c0). Any two points not in the same hemisphere have negative correlation.\nAn example would be a negative cross-sectional relationship between illness and vaccination, if it is observed that where the incidence of one is higher than average, the incidence of the other tends to be lower than average. Similarly, there would be a negative temporal relationship between illness and vaccination if it is observed in one location that times with a higher-than-average incidence of one tend to coincide with a lower-than-average incidence of the other.\nA particular inverse relationship is called inverse proportionality, and is given by \n \n \n \n y\n =\n k\n \n /\n \n x\n \n \n {\\displaystyle y=k/x}\n where k > 0 is a constant. In a Cartesian plane this relationship is displayed as a hyperbola with y decreasing as x increases.In finance, an inverse correlation between the returns on two different assets enhances the risk-reduction effect of diversifying by holding them both in the same portfolio.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/IdempotentCosineAngle.jpg"], "links": ["Cartesian plane", "Constant (mathematics)", "Correlation", "Cosine", "Cross-sectional", "Derivative", "Diametrically opposed", "Diminishing returns", "Diversification (finance)", "Finance", "Financial risk", "Hyperbola", "Oklahoma State University\u2013Stillwater", "Pearson correlation coefficient", "Positive real numbers", "Proportionality (mathematics)", "Random vector", "Rate of return", "Singular point of a curve", "Slope", "Statistics", "Time series", "University of Hawaii"], "references": ["http://www.hawaii.edu/powerkills/UC.HTM", "http://ordination.okstate.edu/STATS.htm"]}, "Vector autoregression": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from February 2012", "Articles with unsourced statements from April 2010", "Articles with unsourced statements from February 2012", "Multivariate time series", "Time series models"], "title": "Vector autoregression", "method": "Vector autoregression", "url": "https://en.wikipedia.org/wiki/Vector_autoregression", "summary": "Vector autoregression (VAR) is a stochastic process model used to capture the linear interdependencies among multiple time series. VAR models generalize the univariate autoregressive model (AR model) by allowing for more than one evolving variable. All variables in a VAR enter the model in the same way: each variable has an equation explaining its evolution based on its own lagged values, the lagged values of the other model variables, and an error term. VAR modeling does not require as much knowledge about the forces influencing a variable as do structural models with simultaneous equations: The only prior knowledge required is a list of variables which can be hypothesized to affect each other intertemporally.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute value", "Accelerated failure time model", "Actuarial science", "Adam Smith", "Adaptive expectations", "Aggregate demand", "Aggregation problem", "Agricultural economics", "Akaike information criterion", "Alfred Marshall", "Amartya Sen", "Analysis of covariance", "Analysis of variance", "Anarchist economics", "Ancient economic thought", "Anderson\u2013Darling test", "Applied Economics (journal)", "Applied economics", "Arithmetic mean", "Arnold Zellner", "Asia-Pacific Economic Cooperation", "Asymptotic theory (statistics)", "Austrian School", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive model", "Autoregressive\u2013moving-average model", "Average cost", "Balance of payments", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bayesian vector autoregression", "Behavioral economics", "Bias of an estimator", "Bilateral monopoly", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Buddhist economics", "Budget set", "Business cycle", "Business economics", "Canonical correlation", "Capacity utilization", "Capital flight", "Cartography", "Categorical variable", "Census", "Central bank", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Chicago school of economics", "Christopher A. 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family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "L\u00e9on Walras", "M-estimator", "Macroeconomic", "Macroeconomics", "Main diagonal", "Mainstream economics", "Malthusianism", "Mann\u2013Whitney U test", "Marginal cost", "Marginal utility", "Marginalism", "Market (economics)", "Market failure", "Market structure", "Marxian economics", "Mathematical economics", "Mathematical finance", "Mathematical induction", "Matlab", "Matrix (mathematics)", "Matrix difference equation", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimator", "McNemar's test", "Mean", "Measures of national income and output", "Mechanism design", "Median", "Median-unbiased estimator", "Medical statistics", "Mercantilism", "Method of moments (statistics)", "Methods engineering", "Microeconomics", "Microfoundations", "Milton Friedman", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monetary economics", "Monetary policy", "Money", "Money supply", "Monopolistic competition", "Monopoly", "Monopsony", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate regression", "Multivariate statistics", "Mutualism (economic theory)", "NAIRU", "National accounts", "Natural experiment", "Natural resource economics", "Nelson\u2013Aalen estimator", "Neo-Keynesian economics", "Neo-Marxian economics", "Neoclassical economics", "New Keynesian economics", "New classical macroeconomics", "New institutional economics", "Non-convexity (economics)", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "OECD", "Observational study", "Official statistics", "Oligopoly", "Oligopsony", "One- and two-tailed tests", "Operations research", "Opinion poll", "Opportunity cost", "Optimal decision", "Optimal design", "Order of integration", "Order statistic", "Ordinary least squares", "Outline of economics", "Outline of statistics", "Panel data", "Panel vector autoregression", "Parameter identification problem", "Parametric statistics", "Pareto efficiency", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Paul Krugman", "Paul Samuelson", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perfect competition", "Permutation test", "Physiocracy", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Political economy", "Population (statistics)", "Population statistics", "Positive-definite matrix", "Post-Keynesian economics", "Posterior probability", "Power (statistics)", "Prediction interval", "Preference (economics)", "Price", "Price level", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Production set", "Profit (economics)", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Public choice", "Public economics", "Public good", "Purchasing power parity", "Python (programming language)", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Ragnar Frisch", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rate of profit", "Rational expectations", "Rationing", "Real business-cycle theory", "Recession", "Regional economics", "Regression analysis", "Regression analysis of time series", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Returns to scale", "Richard Thaler", "Right hand side", "Risk aversion", "Robert Lucas Jr.", "Robert Solow", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Saving", "Scale parameter", "Scarcity", "Scatter plot", "Schools of economic thought", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Serial correlation", "Service economy", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shortage", "Shrinkflation", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social choice theory", "Social cost", "Social statistics", "Socialist economics", "Socioeconomics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stagflation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic", "Stochastic process", "Stockholm school (economics)", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sunk cost", "Supply-side economics", "Supply and demand", "Supply shock", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Tax revenues", "The General Theory of Employment, Interest and Money", "Theory of the firm", "Thermoeconomics", "Time domain", "Time series", "Tjalling Koopmans", "Tolerance interval", "Trade", "Transaction cost", "Transport economics", "Trend estimation", "U-statistic", "Uncertainty", "Unemployment", "Uniformly most powerful test", "Urban economics", "Utility", "V-statistic", "Value (economics)", "Var (disambiguation)", "Variance", "Variance decomposition", "Variance decomposition of forecast errors", "Vector space", "Vectorization (mathematics)", "Vilfredo Pareto", "Wage", "Wald test", "Wavelet", "Welfare economics", "Whittle likelihood", "Wilcoxon signed-rank test", "World Bank", "World Trade Organization", "Y-intercept", "Z-test"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.163.5425", "http://www.ncbi.nlm.nih.gov/pubmed/27551988", "http://doi.org/10.1016%2Fj.econmod.2003.09.005", "http://doi.org/10.1080%2F01621459.1962.10480664", "http://doi.org/10.1080%2F02664760801920473", "http://doi.org/10.1097%2FPSY.0000000000000378", "http://doi.org/10.1111%2Fj.1467-6419.2010.00637.x", "http://doi.org/10.2307%2F1912017", "http://www.jstor.org/stable/1912017", "https://cran.r-project.org/web/packages/vars/vignettes/vars.pdf", "https://ideas.repec.org/a/eee/ecmode/v21y2004i4p661-683.html", "https://ideas.repec.org/a/taf/applec/v41y2009i9p1121-1125.html", "https://ideas.repec.org/a/taf/japsta/v35y2008i6p601-615.html"]}, "Chi-squared test": {"categories": ["All articles lacking in-text citations", "All articles with incomplete citations", "Articles lacking in-text citations from November 2014", "Articles with incomplete citations from January 2013", "Nonparametric statistics", "Statistical tests for contingency tables"], "title": "Chi-squared test", "method": "Chi-squared test", "url": "https://en.wikipedia.org/wiki/Chi-squared_test", "summary": "A chi-squared test, also written as \u03c72 test, is any statistical hypothesis test where the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. Without other qualification, 'chi-squared test' often is used as short for Pearson's chi-squared test. The chi-squared test is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.\nIn the standard applications of the test, the observations are classified into mutually exclusive classes, and there is some theory, or say null hypothesis, which gives the probability that any observation falls into the corresponding class. The purpose of the test is to evaluate how likely the observations that are made would be, assuming the null hypothesis is true.\nChi-squared tests are often constructed from a sum of squared errors, or through the sample variance. Test statistics that follow a chi-squared distribution arise from an assumption of independent normally distributed data, which is valid in many cases due to the central limit theorem. A chi-squared test can be used to attempt rejection of the null hypothesis that the data are independent.\nAlso considered a chi-squared test is a test in which this is asymptotically true, meaning that the sampling distribution (if the null hypothesis is true) can be made to approximate a chi-squared distribution as closely as desired by making the sample size large enough.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8e/Chi-square_distributionCDF-English.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bibcode", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Cindy Greenwood", "Ciphertext", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran\u2013Mantel\u2013Haenszel statistics", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Collar workers", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cryptanalysis", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete probability distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's exact test", "Forest plot", "Fourier analysis", "Frank Yates", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lack-of-fit sum of squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mansfield Merriman", "MathWorld", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum chi-square estimation", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nomogram", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plaintext", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Portmanteau test", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald A. Fisher", "Run chart", "Sample median", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Sir George Airy", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Time-series analysis", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tukey's test of additivity", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William G. Cochran", "Yates's correction for continuity", "Z-test"], "references": ["http://ibmathsresources.com/2014/06/15/using-chi-squared-to-crack-codes/", "http://practicalcryptography.com/cryptanalysis/text-characterisation/chi-squared-statistic/", "http://mathworld.wolfram.com/Chi-SquaredTest.html", "http://adsabs.harvard.edu/abs/1895RSPTA.186..343P", "http://adsabs.harvard.edu/abs/1901RSPTA.197..443P", "http://adsabs.harvard.edu/abs/1916RSPTA.216..429P", "http://adsabs.harvard.edu/abs/2008PNAS..105.4323F", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2393821", "http://boris.ryabko.net/jspi.pdf", "http://doi.org/10.1016%2Fs0378-3758(03)00149-6", "http://doi.org/10.1073%2Fpnas.0701722105", "http://doi.org/10.1080%2F14786440009463897", "http://doi.org/10.1098%2Frspl.1893.0079", "http://doi.org/10.1098%2Frsta.1895.0010", "http://doi.org/10.1098%2Frsta.1901.0023", "http://doi.org/10.1098%2Frsta.1916.0009", "http://doi.org/10.1214%2Faoms%2F1177729380", "http://doi.org/10.2307%2F2340521", "http://www.jstor.org/stable/115538", "http://www.jstor.org/stable/2236678", "http://www.jstor.org/stable/2340521", "http://www.jstor.org/stable/2341149", "http://www.jstor.org/stable/2983604", "http://www.jstor.org/stable/90649", "http://www.jstor.org/stable/90841", "http://www.jstor.org/stable/91092", "http://www.pnas.org/content/105/11/4323", "http://www.economics.soton.ac.uk/staff/aldrich/1900.pdf", "https://visa.pharmacy.wsu.edu/bioinformatics/documents/chi-square-tests.pdf"]}, "Maximal information coefficient": {"categories": ["All articles lacking reliable references", "All articles needing expert attention", "Articles lacking reliable references from May 2012", "Articles needing expert attention from January 2012", "Articles needing expert attention with no reason or talk parameter", "Articles needing unspecified expert attention", "Articles with multiple maintenance issues", "Covariance and correlation", "Information theory"], "title": "Maximal information coefficient", "method": "Maximal information coefficient", "url": "https://en.wikipedia.org/wiki/Maximal_information_coefficient", "summary": "In statistics, the maximal information coefficient (MIC) is a measure of the strength of the linear or non-linear association between two variables X and Y.\nThe MIC belongs to the maximal information-based nonparametric exploration (MINE) class of statistics. In a simulation study, MIC outperformed some selected low power tests, however concerns have been raised regarding reduced statistical power in detecting some associations in settings with low sample size when compared to powerful methods such as distance correlation and Heller\u2013Heller\u2013Gorfine (HHG). Comparisons with these methods, in which MIC was outperformed, were made in Simon and Tibshirani and in Gorfine, Heller, and Heller. It is claimed that MIC approximately satisfies a property called equitability which is illustrated by selected simulation studies. It was later proved that no non-trivial coefficient can exactly satisfy the equitability property as defined by Reshef et al., although this result has been challenged. Some criticisms of MIC are addressed by Reshef et al. in further studies published on arXiv.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Data binning", "Digital object identifier", "Distance correlation", "Eric Lander", "Gilean McVean", "Mutual Information", "Pardis Sabeti", "PubMed Central", "PubMed Identifier", "Statistical power", "Statistics"], "references": ["http://www-stat.stanford.edu/~tibs/reshef/comment.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3325791", "http://www.ncbi.nlm.nih.gov/pubmed/22174245", "http://ie.technion.ac.il/~gorfinm/files/science6.pdf", "http://doi.org/10.1103/PhysRevA.33.1134", "http://doi.org/10.1126/science.1205438", "http://biomet.oxfordjournals.org/content/100/2/503", "http://www.pnas.org/content/111/21/E2160.extract", "https://link.aps.org/doi/10.1103/PhysRevA.33.1134", "https://web.archive.org/web/20170808213131/https://ie.technion.ac.il/~gorfinm/files/science6.pdf", "https://arxiv.org/abs/1301.6314v1", "https://arxiv.org/abs/1301.7745v1"]}, "Approximate entropy": {"categories": ["Entropy and information", "Time series"], "title": "Approximate entropy", "method": "Approximate entropy", "url": "https://en.wikipedia.org/wiki/Approximate_entropy", "summary": "In statistics, an approximate entropy (ApEn) is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time-series data.For example, there are two series of data:\n\nseries 1: (10,20,10,20,10,20,10,20,10,20,10,20...), which alternates 10 and 20.series 2: (10,10,20,10,20,20,20,10,10,20,10,20,20...), which has either a value of 10 or 20, chosen randomly, each with probability 1/2.Moment statistics, such as mean and variance, will not distinguish between these two series. Nor will rank order statistics distinguish between these series. Yet series 1 is \"perfectly regular\"; knowing one term has the value of 20 enables one to predict with certainty that the next term will have the value of 10. Series 2 is randomly valued; knowing one term has the value of 20 gives no insight into what value the next term will have.\nRegularity was originally measured by exact regularity statistics, which has mainly centered on various entropy measures.\nHowever, accurate entropy calculation requires vast amounts of data, and the results will be greatly influenced by system noise, therefore it is not practical to apply these methods to experimental data. ApEn was developed by Steve M. Pincus to handle these limitations by modifying an exact regularity statistic, Kolmogorov\u2013Sinai entropy. ApEn was initially developed to analyze medical data, such as heart rate, and later spread its applications in finance, psychology, and human factors engineering.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ca/Heartrate.jpg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg"], "links": ["American Journal of Physiology. Heart and Circulatory Physiology", "Artificial Intelligence in Medicine", "Circulation (journal)", "Digital object identifier", "Epilepsy Research", "Finance", "Human Factors (journal)", "Human factors engineering", "Integer", "Journal of Clinical Monitoring and Computing", "Kolmogorov\u2013Sinai entropy", "Mean", "Moment (mathematics)", "Positive number", "Proceedings of the National Academy of Sciences", "Psychiatry Research: Neuroimaging", "Psychology", "PubMed Central", "PubMed Identifier", "Rank order", "Real number", "Recurrence quantification analysis", "Sample entropy", "Scalar (mathematics)", "Statistics", "Steve M. Pincus", "The American Journal of Physiology", "Time-series", "Unpredictability", "Variance", "Vector (mathematics and physics)"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC51218", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC518821", "http://www.ncbi.nlm.nih.gov/pubmed/10843903", "http://www.ncbi.nlm.nih.gov/pubmed/11607165", "http://www.ncbi.nlm.nih.gov/pubmed/15358860", "http://www.ncbi.nlm.nih.gov/pubmed/19403281", "http://www.ncbi.nlm.nih.gov/pubmed/21616643", "http://www.ncbi.nlm.nih.gov/pubmed/22445216", "http://www.ncbi.nlm.nih.gov/pubmed/8184944", "http://www.ncbi.nlm.nih.gov/pubmed/9264491", "http://doi.org/10.1007/BF01619355", "http://doi.org/10.1016/j.artmed.2009.03.003", "http://doi.org/10.1016/j.eplepsyres.2011.04.013", "http://doi.org/10.1016/j.pscychresns.2011.07.009", "http://doi.org/10.1073/pnas.0405168101", "http://doi.org/10.1073/pnas.88.6.2297", "http://doi.org/10.1161/01.cir.96.3.842", "http://doi.org/10.1177/0018720811411297", "http://physionet.org/physiotools/ApEn/"]}, "Partial regression plot": {"categories": ["CS1 maint: Multiple names: authors list", "Regression diagnostics", "Statistical charts and diagrams", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Partial regression plot", "method": "Partial regression plot", "url": "https://en.wikipedia.org/wiki/Partial_regression_plot", "summary": "In applied statistics, a partial regression plot attempts to show the effect of adding another variable to a model that already has one or more independent variables. Partial regression plots are also referred to as added variable plots, adjusted variable plots, and individual coefficient plots.\nWhen performing a linear regression with a single independent variable, a scatter plot of the response variable against the independent variable provides a good indication of the nature of the relationship. If there is more than one independent variable, things become more complicated. Although it can still be useful to generate scatter plots of the response variable against each of the independent variables, this does not take into account the effect of the other independent variables in the model.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["Applied statistics", "Copyright status of work by the U.S. government", "Digital object identifier", "Heteroscedasticity", "Independent variable", "International Standard Book Number", "JSTOR", "Leverage (statistics)", "Linear regression", "National Institute of Standards and Technology", "Partial correlation", "Partial leverage plot", "Partial residual plot", "Response variable", "Scatter plot", "Simple correlation", "Variance inflation factor"], "references": ["http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partregr.htm", "http://www.nist.gov", "http://doi.org/10.2307%2F2683296", "http://www.jstor.org/stable/2683296"]}, "Internal validity": {"categories": ["Causal inference", "Validity (statistics)"], "title": "Internal validity", "method": "Internal validity", "url": "https://en.wikipedia.org/wiki/Internal_validity", "summary": "Internal validity is the extent to which a piece of evidence supports a claim about cause and effect, within the context of a particular study. It is one of the most important properties of scientific studies, and is an important concept in reasoning about evidence more generally. Internal validity is determined by how well a study can rule out alternative explanations for its findings (usually, sources of systematic error or 'bias'). It contrasts with external validity, the extent to which results can justify conclusions about other contexts (that is, the extent to which results can be generalized).", "images": [], "links": ["Causality", "Confounding variable", "Construct validity", "Content validity", "Dependent variable", "Digital object identifier", "Double blind", "Ecological validity", "Effect size", "Evidence", "External validity", "Generalization", "Independent variable", "Mnemonic", "Regression toward the mean", "Spurious relationship", "Statistical conclusion validity", "Statistical power", "Survivorship bias", "Systematic error", "Validity (statistics)", "Variable and attribute (research)"], "references": ["http://www.socialresearchmethods.net/kb/intval.php", "http://doi.org/10.1146%2Fannurev.ps.34.020183.001255"]}, "Floor effect": {"categories": ["All articles lacking sources", "Articles lacking sources from February 2017", "Psychological testing", "Psychometrics"], "title": "Floor effect", "method": "Floor effect", "url": "https://en.wikipedia.org/wiki/Floor_effect", "summary": "In statistics, a floor effect (also known as a basement effect) arises when a data-gathering instrument has a lower limit to the data values it can reliably specify. This lower limit is known as the \"floor\".\nFloor effects are occasionally encountered in psychological testing, when a test designed to estimate some psychological trait has a minimum standard score that may not distinguish some test-takers who differ in their responses on the test item content. Giving preschool children an IQ test designed for adults would likely show many of the test-takers with scores near the lowest standard score for adult test-takers (IQ 40 on most tests that were currently normed as of 2010). To indicate differences in current intellectual functioning among young children, IQ tests specifically for young children are developed, on which many test-takers can score well above the floor score. An IQ test designed to help assess intellectually disabled persons might intentionally be designed with easier item content and a lower floor score to better distinguish among individuals taking the test as part of an assessment process.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Ceiling effect (statistics)", "IQ", "Intellectual disability", "International Standard Book Number", "Psychological testing", "Robert Sternberg", "Statistics"], "references": ["http://www.elsevier.com/wps/find/bookdescription.cws_home/722906/description#description", "http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470083581.html", "http://psycnet.apa.org/psycinfo/2000-07612-000"]}, "Wrapped exponential distribution": {"categories": ["Continuous distributions", "Directional statistics", "Pages using deprecated image syntax"], "title": "Wrapped exponential distribution", "method": "Wrapped exponential distribution", "url": "https://en.wikipedia.org/wiki/Wrapped_exponential_distribution", "summary": "In probability theory and directional statistics, a wrapped exponential distribution is a wrapped probability distribution that results from the \"wrapping\" of the exponential distribution around the unit circle.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fd/WrappedExponentialCDF.png", "https://upload.wikimedia.org/wikipedia/commons/8/86/WrappedExponentialPDF.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Lerch transcendent", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unit circle", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.pstat.ucsb.edu/faculty/jammalam/html/Some%20Publications/2004_WrappedSkewFamilies_Comm..pdf", "http://doi.org/10.1081%2FSTA-200026570"]}, "Randomized block design": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from January 2018", "CS1 maint: Multiple names: authors list", "Design of experiments", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Blocking (statistics)", "method": "Randomized block design", "url": "https://en.wikipedia.org/wiki/Blocking_(statistics)", "summary": "In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algebraic statistics", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anne Penfold Street", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Block design", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinatorial design", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Control group", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Damaraju Raghavarao", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Double blind", "Drug", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Francis J. Anscombe", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Holger Rootz\u00e9n", "Homoscedasticity", "Hyper-Graeco-Latin square design", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "Paired difference test", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Placebo", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R.A. Bailey", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized complete block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sidney Addelman", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Treatment group", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://itfeature.com/design-of-experiment-doe/randomized-complete-block-design", "http://www.nist.gov", "http://www.isid.ac.in/~rbb/", "http://www.ams.org/mathscinet-getitem?mr=0030181", "http://www.ams.org/mathscinet-getitem?mr=1994124", "http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521683579", "http://doi.org/10.1214%2Faoms%2F1177703889", "http://doi.org/10.2307%2F2284277", "http://doi.org/10.2307%2F2333423", "http://doi.org/10.2307%2F2681737", "http://doi.org/10.2307%2F2684574", "http://doi.org/10.2307%2F2984159", "http://www.jstor.org/stable/2238364", "http://www.jstor.org/stable/2284277", "http://www.jstor.org/stable/2333423", "http://www.jstor.org/stable/2681737", "http://www.jstor.org/stable/2684574", "http://www.jstor.org/stable/2984159", "http://www.maths.qmul.ac.uk/~rab/DOEbook/", "http://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm", "https://books.google.com/books?id=T5dsExIP3aAC", "https://www.springer.com/series/694"]}, "XploRe": {"categories": ["All articles lacking reliable references", "All articles with topics of unclear notability", "Articles lacking reliable references from December 2015", "Articles with multiple maintenance issues", "Articles with topics of unclear notability from December 2015", "Discontinued software", "Official website different in Wikidata and Wikipedia", "Statistical programming languages", "Windows-only freeware"], "title": "XploRe", "method": "XploRe", "url": "https://en.wikipedia.org/wiki/XploRe", "summary": "XploRe was a commercial statistics software package, developed by the German software company MD*Tech around Prof. Dr. Wolfgang H\u00e4rdle. XploRe has been discontinued in 2008, the last version, 4.8, is available for download at no cost. The user interacted with the software via the XploRe programming language, which is derived from the C programming language. Individual XploRe programs were called Quantlets.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ADMB", "Analyse-it", "BMDP", "BV4.1 (software)", "CSPro", "C (programming language)", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "EViews", "Epi Info", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "Germany", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "International Standard Book Number", "JASP", "JMP (statistical software)", "JMulTi", "Java applet", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Open-source software", "OpenBUGS", "Orange (software)", "OxMetrics", "PSPP", "Programming language", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "Web browser", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat"], "references": ["http://scholar.google.com/scholar?q=%22XploRe%22", "http://www.google.com/search?&q=%22XploRe%22+site:news.google.com/newspapers&source=newspapers", "http://www.google.com/search?as_eq=wikipedia&q=%22XploRe%22&num=50", "http://www.google.com/search?tbm=nws&q=%22XploRe%22+-wikipedia", "http://www.google.com/search?tbs=bks:1&q=%22XploRe%22+-wikipedia", "http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore.php", "https://www.jstor.org/action/doBasicSearch?Query=%22XploRe%22&acc=on&wc=on"]}, "Classifier (mathematics)": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from January 2010", "Classification algorithms", "Commons category link from Wikidata", "Machine learning", "Statistical classification"], "title": "Statistical classification", "method": "Classifier (mathematics)", "url": "https://en.wikipedia.org/wiki/Statistical_classification", "summary": "In machine learning and statistics, classification is the problem of identifying to which of a set of categories (sub-populations) a new observation belongs, on the basis of a training set of data containing observations (or instances) whose category membership is known. Examples are assigning a given email to the \"spam\" or \"non-spam\" class, and assigning a diagnosis to a given patient based on observed characteristics of the patient (sex, blood pressure, presence or absence of certain symptoms, etc.). Classification is an example of pattern recognition.\nIn the terminology of machine learning, classification is considered an instance of supervised learning, i.e., learning where a training set of correctly identified observations is available. The corresponding unsupervised procedure is known as clustering, and involves grouping data into categories based on some measure of inherent similarity or distance.\nOften, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features. These properties may variously be categorical (e.g. \"A\", \"B\", \"AB\" or \"O\", for blood type), ordinal (e.g. \"large\", \"medium\" or \"small\"), integer-valued (e.g. the number of occurrences of a particular word in an email) or real-valued (e.g. a measurement of blood pressure). Other classifiers work by comparing observations to previous observations by means of a similarity or distance function.\nAn algorithm that implements classification, especially in a concrete implementation, is known as a classifier. The term \"classifier\" sometimes also refers to the mathematical function, implemented by a classification algorithm, that maps input data to a category.\nTerminology across fields is quite varied. In statistics, where classification is often done with logistic regression or a similar procedure, the properties of observations are termed explanatory variables (or independent variables, regressors, etc.), and the categories to be predicted are known as outcomes, which are considered to be possible values of the dependent variable. In machine learning, the observations are often known as instances, the explanatory variables are termed features (grouped into a feature vector), and the possible categories to be predicted are classes. Other fields may use different terminology: e.g. in community ecology, the term \"classification\" normally refers to cluster analysis, i.e., a type of unsupervised learning, rather than the supervised learning described in this article.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Accuracy", "Actuarial science", "Akaike information criterion", "Algorithm", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anomaly detection", "ArXiv", "Arithmetic mean", "Artificial intelligence", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Asymptotic theory (statistics)", "Autocorrelation", "Autoencoder", "Automated machine learning", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "BIRCH", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bias-variance dilemma", "Bias of an estimator", "Binary classification", "Binary data", "Binomial regression", "Bioinformatics", "Biological classification", "Biometric", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Blood pressure", "Blood type", "Boosting (machine learning)", "Boosting (meta-algorithm)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "C. R. Rao", "CURE data clustering algorithm", "Canonical correlation", "Canonical correlation analysis", "Cartography", "Categorical data", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Class membership probabilities", "Classification rule", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Community ecology", "Completeness (statistics)", "Compound term processing", "Computational learning theory", "Computer vision", "Conditional random field", "Conference on Neural Information Processing Systems", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convolutional neural network", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Credit scoring", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "DBSCAN", "Data collection", "Data mining", "Data warehouse", "Decision tree learning", "Decomposition of time series", "DeepDream", "Deep learning", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimensionality reduction", "Discrete choice", "Distance", "Divergence (statistics)", "Document classification", "Dot product", "Drug development", "Drug discovery", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Email", "Empirical distribution function", "Empirical risk minimization", "Engineering statistics", "Ensemble learning", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expectation\u2013maximization algorithm", "Experiment", "Explanatory variable", "Explanatory variables", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feature (pattern recognition)", "Feature engineering", "Feature learning", "Feature vector", "First-hitting-time model", "Fisher's linear discriminant", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Function (mathematics)", "Fuzzy logic", "G-test", "Gated recurrent unit", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of artificial intelligence", "Goodness of fit", "Grammar induction", "Granger causality", "Graphical model", "Grouped data", "Handwriting recognition", "Harmonic mean", "Heteroscedasticity", "Hidden Markov model", "Hierarchical clustering", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent component analysis", "Independent variable", "Index of dispersion", "Information retrieval", "Integer", "Interaction (statistics)", "International Conference on Machine Learning", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbor algorithm", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Learning to rank", "Learning vector quantization", "Least squares support vector machine", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear", "Linear classifier", "Linear combination", "Linear discriminant analysis", "Linear function", "Linear predictor function", "Linear regression", "List of datasets for machine-learning research", "List of datasets for machine learning research", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local outlier factor", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Long short-term memory", "Loss function", "Lp space", "M-estimator", "Machine Learning (journal)", "Machine learning", "Mahalanobis distance", "Mann\u2013Whitney U test", "Markov chain Monte Carlo", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean-shift", "Median", "Median-unbiased estimator", "Medical imaging", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Metric (mathematics)", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiclass classification", "Multilayer perceptron", "Multinomial logistic regression", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Naive Bayes classifier", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "No free lunch in search and optimization", "Non-negative matrix factorization", "Nonlinear", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "OPTICS algorithm", "Observation", "Observational study", "Occam learning", "Official statistics", "One- and two-tailed tests", "Online machine learning", "Opinion poll", "Optical character recognition", "Optimal decision", "Optimal design", "Order statistic", "Ordinal data", "Ordinary least squares", "Outline of machine learning", "Outline of statistics", "Parametric statistics", "Parse tree", "Parsing", "Part of speech", "Part of speech tagging", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pattern recognition", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perceptron", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Precision and recall", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic classification", "Probabilistic design", "Probability", "Probability distribution", "Probably approximately correct learning", "Probit regression", "Proportional hazards model", "Psychometrics", "Q-learning", "Quadratic classifier", "Quality control", "Quantitative structure-activity relationship", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R. A. Fisher", "Radar chart", "Random assignment", "Random forest", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real number", "Receiver operating characteristic", "Recommender system", "Recurrent neural network", "Regression analysis", "Regression model validation", "Reinforcement learning", "Relevance vector machine", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted Boltzmann machine", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sariel Har-Peled", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Search engines", "Seasonal adjustment", "Self-organizing map", "Semi-supervised learning", "Semiparametric regression", "Sequence labeling", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Similarity function", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spam filtering", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Speech recognition", "Standard deviation", "Standard error", "State\u2013action\u2013reward\u2013state\u2013action", "Stationary process", "Statistic", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical natural language processing", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistically independent", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Structured prediction", "Student's t-test", "Sufficient statistic", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "Syntactic structure", "System identification", "T-distributed stochastic neighbor embedding", "T. W. Anderson", "Temporal difference learning", "Time domain", "Time series", "Tolerance interval", "Toxicogenomics", "Training set", "Trend estimation", "U-Net", "U-statistic", "Uncertainty coefficient", "Uniformly most powerful test", "Unsupervised learning", "Utility", "V-statistic", "Vapnik\u2013Chervonenkis theory", "Variable kernel density estimation", "Variance", "Vector autoregression", "Video tracking", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://arxiv.org/abs/1202.2194", "http://doi.org/10.1080%2F01431161.2010.507795", "https://books.google.com/books?id=7f5bBAAAQBAJ&printsec=frontcover#v=onepage&q=classification&f=false", "https://academic.oup.com/biomet/article-abstract/68/1/275/237691", "https://towardsdatascience.com/a-tour-of-the-top-10-algorithms-for-machine-learning-newbies-dde4edffae11", "https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1469-1809.1938.tb02189.x", "https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1469-1809.1936.tb02137.x", "https://arxiv.org/list/cs.LG/recent", "https://deepai.org/machine-learning-glossary-and-terms/classifier"]}, "Least trimmed squares": {"categories": ["Robust regression", "Robust statistics"], "title": "Least trimmed squares", "method": "Least trimmed squares", "url": "https://en.wikipedia.org/wiki/Least_trimmed_squares", "summary": "Least trimmed squares (LTS), or least trimmed sum of squares, is a robust statistical method that fits a function to a set of data whilst not being unduly affected by the presence of outliers. It is one of a number of methods for robust regression.", "images": [], "links": ["Dependent and independent variables", "Digital object identifier", "Errors and residuals in statistics", "International Standard Book Number", "JSTOR", "Journal of Applied Statistics", "Journal of the American Statistical Association", "Least squares", "Outlier", "Peter Rousseeuw", "Residual sum of squares", "Robust regression", "Robust statistics"], "references": ["http://doi.org/10.1002%2F0471725382", "http://doi.org/10.1016%2Fj.csda.2004.04.003", "http://doi.org/10.1023%2FA:1008942604045", "http://doi.org/10.1080%2F01621459.1984.10477105", "http://doi.org/10.1080%2F02664760601004973", "http://www.jstor.org/stable/2288718"]}, "Jackson network": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from June 2012", "Queueing theory", "Wikipedia articles needing clarification from January 2013"], "title": "Jackson network", "method": "Jackson network", "url": "https://en.wikipedia.org/wiki/Jackson_network", "summary": "In queueing theory, a discipline within the mathematical theory of probability, a Jackson network (sometimes Jacksonian network) is a class of queueing network where the equilibrium distribution is particularly simple to compute as the network has a product-form solution. It was the first significant development in the theory of networks of queues, and generalising and applying the ideas of the theorem to search for similar product-form solutions in other networks has been the subject of much research, including ideas used in the development of the Internet. The networks were first identified by James R. Jackson and his paper was re-printed in the journal Management Science\u2019s \u2018Ten Most Influential Titles of Management Sciences First Fifty Years.\u2019Jackson was inspired by the work of Burke and Reich, though Jean Walrand notes \"product-form results \u2026 [are] a much less immediate result of the output theorem than Jackson himself appeared to believe in his fundamental paper\".An earlier product-form solution was found by R. R. P. Jackson for tandem queues (a finite chain of queues where each customer must visit each queue in order) and cyclic networks (a loop of queues where each customer must visit each queue in order).A Jackson network consists of a number of nodes, where each node represents a queue in which the service rate can be both node-dependent (different nodes have different service rates) and state-dependent (service rates change depending on queue lengths). Jobs travel among the nodes following a fixed routing matrix. All jobs at each node belong to a single \"class\" and jobs follow the same service-time distribution and the same routing mechanism. Consequently, there is no notion of priority in serving the jobs: all jobs at each node are served on a first-come, first-served basis.\nJackson networks where a finite population of jobs travel around a closed network also have a product-form solution described by the Gordon\u2013Newell theorem.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/Open_jackson_network_%28final%29.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Annals of Mathematical Statistics", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Equilibrium distribution", "Erlang (unit)", "Erlang distribution", "F. P. Kelly", "FIFO (computing and electronics)", "First-come, first-served", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid network", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Geometric distribution", "Gordon F. Newell", "Gordon\u2013Newell network", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "IEEE Transactions on Information Theory", "Information system", "International Standard Book Number", "JSTOR", "James R. Jackson", "Jean Walrand", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 model", "M/M/1 queue", "M/M/c model", "M/M/c queue", "M/M/\u221e queue", "Management Science: A Journal of the Institute for Operations Research and the Management Sciences", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Operations Research (journal)", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability mass function", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Renewal process", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations", "Unit vector", "Utilization"], "references": ["http://www.dtic.mil/dtic/tr/fulltext/u2/296776.pdf", "http://doi.org/10.1093%2Fimaman%2F6.4.382", "http://doi.org/10.1109%2FTIT.1983.1056762", "http://doi.org/10.1214%2Faoms%2F1177706889", "http://doi.org/10.1287%2Fmnsc.1040.0268", "http://doi.org/10.1287%2Fopre.15.2.254", "http://doi.org/10.1287%2Fopre.5.4.518", "http://doi.org/10.2307%2F1425912", "http://doi.org/10.2307%2F1426753", "http://doi.org/10.2307%2F3213702", "http://www.jstor.org/stable/1425912", "http://www.jstor.org/stable/1426753", "http://www.jstor.org/stable/167249", "http://www.jstor.org/stable/168557", "http://www.jstor.org/stable/2237237", "http://www.jstor.org/stable/2627213", "http://www.jstor.org/stable/30046149", "http://www.jstor.org/stable/30046150"]}, "Longstaff\u2013Schwartz model": {"categories": ["All articles with dead external links", "Articles with dead external links from December 2017", "Articles with permanently dead external links", "CS1 maint: Multiple names: authors list", "CS1 maint: Uses authors parameter", "Interest rates", "Short-rate models", "Webarchive template wayback links"], "title": "Short-rate model", "method": "Longstaff\u2013Schwartz model", "url": "https://en.wikipedia.org/wiki/Short-rate_model", "summary": "A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written \n \n \n \n \n r\n \n t\n \n \n \n \n \n {\\displaystyle r_{t}\\,}\n .", "images": [], "links": ["Alan White (economist)", "American option", "Amortising swap", "Andrew Kalotay", "Arbitrage", "Asian option", "Asset swap", "Backspread", "Barrier option", "Basis swap", "Basket option", "Bear spread", "Binary option", "Binomial options pricing model", "Black model", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Bond option", "Box spread (options)", "Brace\u2013Gatarek\u2013Musiela model", "Bull spread", "Butterfly (options)", "CFA Institute", "Calendar spread", "Call option", "Cambridge University Press", "Chen model", "Chooser option", "CiteSeerX", "Cliquet", "Collar (finance)", "Collateralized debt obligation", "Columbia University", "Commodore option", "Compound interest", "Compound option", "Conditional variance swap", "Constant maturity swap", "Constant proportion portfolio insurance", "Consumer debt", "Contango", "Contract for difference", "Corporate bond", "Correlation swap", "Covered call", "Cox\u2013Ingersoll\u2013Ross model", "Credit-linked note", "Credit default option", "Credit default swap", "Credit derivative", "Credit spread (options)", "Currency future", "Currency swap", "Debit spread", "Derivative (finance)", "Derivatives market", "Diagonal spread", "Digital object identifier", "Dividend future", "Dividend swap", "Econometrica", "Eduardo Schwartz", "Emanuel Derman", "Employee stock option", "Energy derivative", "Equity-linked note", "Equity derivative", "Equity swap", "European option", "Exercise (options)", "Exotic derivative", "Exotic option", "Expiration (options)", "Farshid Jamshidian", "Fence (finance)", "Financial Analysts Journal", "Finite difference methods for option pricing", "Fischer Black", "Fixed-income attribution", "Fixed income", "Foreign-exchange option", "Foreign exchange derivative", "Foreign exchange swap", "Forward contract", "Forward market", "Forward price", "Forward rate", "Forward rate agreement", "Forward start option", "Francis Longstaff", "Frank J. Fabozzi", "Fran\u00e7ois-Serge Lhabitant", "Free parameter", "Freight derivative", "Fund derivative", "Futures contract", "Government debt", "Great Recession", "Greeks (finance)", "Heath\u2013Jarrow\u2013Morton framework", "Ho\u2013Lee model", "Hull\u2013White model", "Inflation derivative", "Inflation swap", "Instantaneous", "Interest rate", "Interest rate derivative", "Interest rate derivatives", "Interest rate future", "Interest rate option", "Interest rate swap", "Intermarket Spread", "International Standard Book Number", "Iron butterfly (options strategy)", "Iron condor", "John C. Hull", "John Carrington Cox", "John Wiley & Sons", "John Wiley and Sons", "Jonathan E. Ingersoll", "Journal of Finance", "Journal of Financial Economics", "Journal of Financial and Quantitative Analysis", "Kalotay\u2013Williams\u2013Fabozzi model", "Lattice model (finance)", "Lognormal", "Longstaff\u2013Schwartz model", "Lookback option", "Manchester Business School", "Margin (finance)", "Margrabe's formula", "Market model", "Martingale measure", "Mathematical model", "Mean reversion (finance)", "Moneyness", "Monte Carlo methods for option pricing", "Monte Carlo methods in finance", "Mortgage-backed security", "Mountain range (options)", "Municipal debt", "NYU", "Natural filtration", "Normal backwardation", "Oldrich Vasicek", "Open interest", "Option (finance)", "Option style", "Options spread", "Options strategy", "Ornstein\u2013Uhlenbeck process", "Overnight indexed swap", "Parameter", "Pin risk (options)", "Piotr Karasinski", "Power reverse dual-currency note", "Princeton University Press", "Property derivative", "Protective put", "Put option", "Put\u2013call parity", "Rainbow option", "Ratio spread", "Real options valuation", "Rendleman\u2013Bartter model", "Review of Financial Studies", "Riccardo Rebonato", "Risk-free interest rate", "Risk-neutral measure", "Risk reversal", "Robert C. Merton", "Robert Jarrow", "Salomon Brothers", "Sang Bin Lee", "Single-stock futures", "Slippage (finance)", "Spot rate", "Springer Science+Business Media", "State variable", "Stephen Ross (economist)", "Stochastic", "Stochastic differential equation", "Stochastic process", "Stock market index future", "Straddle", "Strangle (options)", "Strike price", "Swap (finance)", "Swaption", "Tax policy", "Thomas Ho (finance)", "Total return swap", "Trinomial tree", "University of Twente", "Valuation of options", "Vanilla option", "Vanna\u2013Volga pricing", "Variance swap", "Vasicek model", "Vertical spread", "Volatility (finance)", "Volatility swap", "Warrant (finance)", "Wayback Machine", "Weather derivative", "Wiener process", "William Toy", "Year-on-Year Inflation-Indexed Swap", "Yield curve", "Zero-Coupon Inflation-Indexed Swap", "Zero-coupon bond", "Zero coupon swap"], "references": ["http://efinance.org.cn/cn/FEshuo/19920901Interest%20Rate%20Volatility%20and%20the%20Term%20Structure%20A%20Two-Factor%20General%20Equilibrium%20Model,%20pp.%201259-1282.pdf", "http://www.defaultrisk.com/pa_related_24.htm", "http://www.defaultrisk.com/pa_related_29.htm", "http://www.kamakuraco.com/Blog/tabid/231/EntryId/347/Pitfalls-in-Asset-and-Liability-Management-One-Factor-Term-Structure-Models.aspx", "http://simonbenninga.com/wiener/MiER73.pdf", "http://simonbenninga.com/wiener/leippold-wiener2003.pdf", "http://eu.wiley.com/legacy/wileychi/eoas/contents.html", "http://www.columbia.edu/~mh2078/cts_shortrate_models.pdf", "http://www.math.nyu.edu/~alberts/spring07/Lecture5.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.456.1407", "http://faculty.maxwell.syr.edu/cdkao/teaching/taiwan/2003/TSMRS.pdf", "http://personal.anderson.ucla.edu/francis.longstaff/empiricalcomparison.pdf", "http://savage.wharton.upenn.edu/FNCE-934/syllabus/papers/Black_Derman_Toy_FAJ_90.pdf", "http://www.cmpr.co.kr/asset/research_material/implementing_interest_rate_models.pdf", "http://wwwhome.math.utwente.nl/~jamshidianf/pdf/Overview%20of%20interest%20%20rate%20modeling.pdf", "http://www.cfapubs.org/doi/abs/10.2469/faj.v49.n3.35", "http://doi.org/10.1007%2Fs11147-004-4810-8", "http://doi.org/10.1016%2F0304-405X(77)90016-2", "http://doi.org/10.1093%2Frfs%2F3.4.573", "http://doi.org/10.1111%2Fj.1540-6261.1992.tb04657.x", "http://doi.org/10.2307%2F1911242", "http://doi.org/10.2307%2F2328161", "http://doi.org/10.2307%2F2979016", "http://doi.org/10.2307%2F3003143", "http://doi.org/10.2469%2Ffaj.v49.n3.35", "http://econpapers.repec.org/article/anrrefeco/v_3a1_3ay_3a2009_3ap_3a69-96.htm", "http://www.worldcat.org/title/effective-duration-of-callable-bonds-the-salomon-brothers-term-structure-based-option-pricing-model/oclc/16187107", "http://www.ma.hw.ac.uk/~andrewc/papers/ajgc33.pdf", "http://www.mth.kcl.ac.uk/finmath/articles/LPH_risk.pdf", "http://php.portals.mbs.ac.uk/Portals/49/docs/spoon/IRD/Ch5_ShortRateNOTE.pdf", "https://books.google.com/books?id=OlfyQX31bEkC&pg=PT218", "https://web.archive.org/web/20080910041743/http://savage.wharton.upenn.edu/FNCE-934/syllabus/papers/Black_Derman_Toy_FAJ_90.pdf", "https://web.archive.org/web/20100816021705/http://www.cmpr.co.kr/asset/research_material/implementing_interest_rate_models.pdf", "https://web.archive.org/web/20120123191444/http://www.columbia.edu/~mh2078/cts_shortrate_models.pdf", "https://web.archive.org/web/20120406191436/http://wwwhome.math.utwente.nl/~jamshidianf/pdf/Overview%20of%20interest%20%20rate%20modeling.pdf"]}, "Somers' D": {"categories": ["Independence (probability theory)", "Nonparametric statistics"], "title": "Somers' D", "method": "Somers' D", "url": "https://en.wikipedia.org/wiki/Somers%27_D", "summary": "In statistics, Somers\u2019 D, sometimes incorrectly referred to as Somer\u2019s D, is a measure of ordinal association between two possibly dependent random variables X and Y. Somers\u2019 D takes values between \n \n \n \n \u2212\n 1\n \n \n {\\displaystyle -1}\n when all pairs of the variables disagree and \n \n \n \n 1\n \n \n {\\displaystyle 1}\n when all pairs of the variables agree. Somers\u2019 D is named after Robert H. Somers, who proposed it in 1962.Somers\u2019 D plays a central role in rank statistics and is the parameter behind many nonparametric methods. It is also used as a quality measure of binary choice or ordinal regression (e.g., logistic regressions) and credit scoring models.\n\n", "images": [], "links": ["Binary choice", "Binary choice model", "Binary classification", "Binary variable", "Concordant pair", "Continuous probability distribution", "Credit score", "Dependent variable", "Digital object identifier", "Discrete variable", "Goodman and Kruskal's gamma", "JSTOR", "Kendall tau rank correlation coefficient", "Logistic regression", "Ordinal association", "Ordinal regression", "Probit regression", "Receiver operating characteristic"], "references": ["http://www.stata-journal.com/article.html?article=st0007", "http://doi.org/10.2307%2F2090408", "http://www.jstor.org/stable/2090408"]}, "Homoscedasticity": {"categories": ["All articles needing additional references", "Articles needing additional references from October 2011", "Statistical deviation and dispersion"], "title": "Homoscedasticity", "method": "Homoscedasticity", "url": "https://en.wikipedia.org/wiki/Homoscedasticity", "summary": "In statistics, a sequence or a vector of random variables is homoscedastic if all random variables in the sequence or vector have the same finite variance. This is also known as homogeneity of variance. The complementary notion is called heteroscedasticity. The spellings homoskedasticity and heteroskedasticity are also frequently used.The assumption of homoscedasticity simplifies mathematical and computational treatment. Serious violations in homoscedasticity (assuming a distribution of data is homoscedastic when in reality it is heteroscedastic ) may result in overestimating the goodness of fit as measured by the Pearson coefficient.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/93/Homoscedasticity.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bartlett's test", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Best linear unbiased estimator", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Breusch\u2013Pagan test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlation matrix", "Correlogram", "Count data", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrica", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gauss\u2013Markov theorem", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goldfeld\u2013Quandt test", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heterogeneous", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homogeneity (statistics)", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Machine learning", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pattern recognition", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequence", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://reocities.com/Heartland/4205/SPSS/HeteroscedasticityTestingAndCorrectingInSPSS1.pdf", "http://jmlr.csail.mit.edu/papers/volume8/hamsici07a/hamsici07a.pdf", "http://www.jstor.org/stable/1911250", "https://books.google.com/books?id=AEXUlWus4K4C&pg=PA47"]}, "Carpet plot": {"categories": ["Statistical charts and diagrams"], "title": "Carpet plot", "method": "Carpet plot", "url": "https://en.wikipedia.org/wiki/Carpet_plot", "summary": "A carpet plot is any of a few different specific types of plot. The more common plot referred to as a carpet plot is one that illustrates the interaction between two or more independent variables and one or more dependent variables in a two-dimensional plot. Besides the ability to incorporate more variables, another feature that distinguishes a carpet plot from an equivalent contour plot or 3D surface plot is that a carpet plot can be used to more accurately interpolate data points. A conventional carpet plot can capture the interaction of up to three independent variables and three dependent variables and still be easily read and interpolated.\nCarpet plots have common applications within areas such as material science for showing elastic modulus in laminates, and within aeronautics.Another plot sometimes referred to as a carpet plot is the temporal raster plot.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/98/Cheater_plot_aligned.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c8/Cheater_plot_filled_contour.svg", "https://upload.wikimedia.org/wikipedia/commons/2/26/Four_variable_carpet_plot_interpolation.png", "https://upload.wikimedia.org/wikipedia/commons/c/c0/Lattice_carpet_plot.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Aeronautics", "Contour line", "Contour plot", "Daniel Raymer", "Elastic modulus", "Laminates", "Material science", "Plot (graphics)", "Rug plot", "Temporal Raster Plot"], "references": ["http://www.esdu.com/cgi-bin/ps.pl?sess=unlicensed_1100107121229jld&t=di&p=di_04008", "http://math.materials-sciences.com/webMathematica/MSC/JSP/carpet.jsp", "http://www.mathworks.com/matlabcentral/fileexchange/40831-carpet-plot-toolkit", "http://www.mathworks.com/matlabcentral/fileexchange/41467-the-carpetplot-class/", "http://www.gasturb.de/Gtb12Tutorials/GasTurb12DesignParametric.ppt", "http://www.dept.aoe.vt.edu/~mason/Mason_f/SD1CarpetsbySAP.pdf", "https://books.google.com/books?id=9jBsLgEACAAJ", "https://plot.ly/javascript/carpet-plots", "https://plot.ly/python/carpet-plot", "https://plot.ly/r/carpet-plot", "https://web.archive.org/web/20081120214946/http://math.materials-sciences.com/webMathematica/MSC/JSP/carpet.jsp"]}, "Bimodal distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2017", "CS1 maint: Archived copy as title", "Continuous distributions"], "title": "Multimodal distribution", "method": "Bimodal distribution", "url": "https://en.wikipedia.org/wiki/Multimodal_distribution", "summary": "In statistics, a bimodal distribution is a continuous probability distribution with two different modes. These appear as distinct peaks (local maxima) in the probability density function, as shown in Figures 1 and 2.\nMore generally, a multimodal distribution is a continuous probability distribution with two or more modes, as illustrated in Figure 3.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/12/Bimodal-bivariate-small.png", "https://upload.wikimedia.org/wikipedia/commons/e/e2/Bimodal.png", "https://upload.wikimedia.org/wikipedia/commons/b/bc/Bimodal_geological.PNG"], "links": ["ARGUS distribution", "Acrophase", "Amplitude", "Ann E. Watkins", "Antimode", "ArXiv", "Arcsine distribution", "Astronomy", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bandwidth test (multimodal)", "Bates distribution", "Batiphase", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bimodal", "Bimodality", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Catastrophe theory", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circadian rhythm", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Confluent hypergeometric function", "Continuous probability distribution", "Conway-Maxwell-Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Crepuscular", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dip test", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Distribution of fitness effects", "Econometrics", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Excess mass test", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Galaxy color-magnitude diagram", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Gene", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Genome", "Geometric distribution", "Geometric stable distribution", "Geyser", "Gompertz distribution", "Grain size", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hodgkin's lymphoma", "Holtsmark distribution", "Homoscedastic", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "If and only if", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isoniazid", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "MAP test", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Mode existence test", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Mutations", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Nova", "Otsu's method", "Overdispersion", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Periodogram", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Polynomial", "Probability density function", "Probability distribution", "PubMed Central", "PubMed Identifier", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "R (programming language)", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Runt test", "SAS language", "Saddle test", "Sample skewness", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Span test", "Stable distribution", "Standard deviation", "Statistics", "Student's t-distribution", "The American Statistician", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Unimodal", "Unimodality", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weaver ant", "Weaver ants", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.cirano.qc.ca/realisations/grandes_conferences/methodes_econometriques/white.pdf", "http://www.uni-marburg.de/fb12/stoch/research/rpackage/manualbimodlilitytest.pdf", "http://adsabs.harvard.edu/abs/1894RSPTA.185...71P", "http://adsabs.harvard.edu/abs/1916RSPTA.216..429P", "http://adsabs.harvard.edu/abs/1957JSedR..27....3F", "http://adsabs.harvard.edu/abs/1982ApJ...263..835S", "http://adsabs.harvard.edu/abs/1994AJ....108.2348A", "http://adsabs.harvard.edu/abs/1997WRR....33.1179S", "http://adsabs.harvard.edu/abs/2003QJRMS.129.2847Z", "http://adsabs.harvard.edu/abs/2008SoPh..249....1S", "http://adsabs.harvard.edu/abs/2011PNAS..108.7896H", "http://adsabs.harvard.edu/abs/2014PLoSO...991195D", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1380036", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2730180", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2880115", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3093508", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3963849", "http://www.ncbi.nlm.nih.gov/pubmed/17637733", "http://www.ncbi.nlm.nih.gov/pubmed/20478892", "http://www.ncbi.nlm.nih.gov/pubmed/21464309", "http://www.ncbi.nlm.nih.gov/pubmed/24663432", "http://www.amstat.org/sections/srms/Proceedings/y2002/Files/JSM2002-000150.pdf", "http://antbase.org/ants/publications/10434/10434.pdf", "http://arxiv.org/abs/0711.0216", "http://arxiv.org/abs/astro-ph/9408030", "http://arxiv.org/abs/math/0602238", "http://doi.org/10.1007%2FBF01201021", "http://doi.org/10.1007%2Fbf02514796", "http://doi.org/10.1007%2Fbf02618468", "http://doi.org/10.1007%2Fs10182-008-0057-2", "http://doi.org/10.1007%2Fs11207-008-9170-3", "http://doi.org/10.1023%2Fa:1010374114305", "http://doi.org/10.1029%2F97wr00365", "http://doi.org/10.1038%2Fnrg2146", "http://doi.org/10.1046%2Fj.1466-822x.2003.00018.x", "http://doi.org/10.1061%2F(asce)0733-9429(1993)119:4(491)", "http://doi.org/10.1073%2Fpnas.1016024108", "http://doi.org/10.1080%2F00401706.1964.10490199", "http://doi.org/10.1080%2F01621459.1991.10475103", "http://doi.org/10.1080%2F02724634.1992.10011472", "http://doi.org/10.1080%2F03461238.1969.10404590", "http://doi.org/10.1086%2F117248", "http://doi.org/10.1086%2F160554", "http://doi.org/10.1093%2Faesa%2F39.1.7", "http://doi.org/10.1093%2Fbiomet%2F24.3-4.428", "http://doi.org/10.1098%2Frsta.1894.0003", "http://doi.org/10.1098%2Frsta.1916.0009", "http://doi.org/10.1098%2Frstb.2010.0063", "http://doi.org/10.1111%2Fj.1365-2125.1989.tb03558.x", "http://doi.org/10.1111%2Fj.1368-423X.2010.00315.x", "http://doi.org/10.1111%2Fj.1469-1809.1951.tb02488.x", "http://doi.org/10.1155%2Fs1173912601000013", "http://doi.org/10.1177%2F0013164491512001", "http://doi.org/10.1198%2F00031300265", "http://doi.org/10.1214%2F009053605000000417", "http://doi.org/10.1214%2Faoms%2F1177733063", "http://doi.org/10.1214%2Faos%2F1031594735", "http://doi.org/10.1214%2Faos%2F1176346577", "http://doi.org/10.1256%2Fqj.02.166", "http://doi.org/10.1306%2F74D71FE6-2B21-11D7-8648000102C1865D", "http://doi.org/10.1306%2F74d70646-2b21-11d7-8648000102c1865d", "http://doi.org/10.1371%2Fjournal.pone.0091195", "http://doi.org/10.14429%2Fdsj.60.356", "http://doi.org/10.2307%2F1267357", "http://doi.org/10.2307%2F2444163", "http://doi.org/10.3758%2FBF03205709", "http://doi.org/10.4067%2Fs0716-09172010000300006", "http://doi.org/10.4137%2FCIN.S2846", "http://www.fao.org/docrep/W5449E/w5449e05.htm.%7CFAO:", "http://www.jstor.org/stable/2290406", "http://www.jstor.org/stable/2985156", "http://www.jstor.org/stable/91092", "https://engineering.purdue.edu/~bouman/software/cluster/", "https://web.archive.org/web/20131103100209/http://www.uni-marburg.de/fb12/stoch/research/rpackage/manualbimodlilitytest.pdf", "https://cran.r-project.org/web/packages/diptest/index.html", "https://cran.r-project.org/web/packages/discrimARTs/discrimARTs.pdf", "https://cran.r-project.org/web/packages/flexmix/index.html", "https://cran.r-project.org/web/packages/mclust/index.html", "https://cran.r-project.org/web/packages/mixdist/index.html", "https://cran.r-project.org/web/packages/mixtools/index.html", "https://cran.r-project.org/web/packages/nor1mix/index.html"]}, "BV4.1 (software)": {"categories": ["All articles lacking sources", "Articles lacking sources from August 2016", "Econometrics software", "Time series software", "Windows-only freeware"], "title": "BV4.1 (software)", "method": "BV4.1 (software)", "url": "https://en.wikipedia.org/wiki/BV4.1_(software)", "summary": "The application software BV4.1 is an easy-to-use tool for decomposing and seasonally adjusting monthly or quarterly economic time series by version 4.1 of the Berlin procedure. It is being developed by the Federal Statistical Office of Germany. The software is released as freeware for non-commercial purposes.", "images": ["https://upload.wikimedia.org/wikipedia/en/0/0b/BV41_Menues_E_new.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ADMB", "Analyse-it", "Application software", "BMDP", "Berlin procedure", "CSPro", "Comma-separated values", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "Decomposing of time series", "EViews", "English language", "Epi Info", "Federal Statistical Office of Germany", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "German language", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Access", "Microsoft Excel", "Microsoft SQL Server", "Microsoft Windows", "Microsoft Windows 98", "Microsoft Windows NT", "Minitab", "NCSS (statistical software)", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "Seasonal adjustment", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistics", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "Time series", "Time series analysis", "UNISTAT", "WinBUGS", "Windows nt 4.0", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.destatis.de/EN/Methods/TimeSeries/SoftwareBV41.html", "http://www.destatis.de/EN/Methods/TimeSeries/TimeSeriesBV41.pdf?__blob=publicationFile"]}, "Mean-reverting process": {"categories": ["All articles lacking in-text citations", "All articles to be expanded", "All articles with empty sections", "All articles with unsourced statements", "Articles lacking in-text citations from January 2011", "Articles to be expanded from March 2014", "Articles using small message boxes", "Articles with empty sections from March 2014", "Articles with unsourced statements from January 2012", "Articles with unsourced statements from July 2011", "Articles with unsourced statements from June 2011", "Markov processes", "Stochastic differential equations", "Variants of random walks", "Wikipedia articles needing clarification from July 2011"], "title": "Ornstein\u2013Uhlenbeck process", "method": "Mean-reverting process", "url": "https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process", "summary": "In mathematics, the Ornstein\u2013Uhlenbeck process (named after Leonard Ornstein and George Eugene Uhlenbeck), is a stochastic process that, roughly speaking, describes the velocity of a massive Brownian particle under the influence of friction. The process is a stationary Gauss\u2013Markov process, which means that it is a Gaussian process, a Markov process, and is temporally homogeneous. The Ornstein\u2013Uhlenbeck process is the only nontrivial process that satisfies these three conditions, up to allowing linear transformations of the space and time variables. Over time, the process tends to drift towards its long-term mean: such a process is called mean-reverting.\nThe process can be considered to be a modification of the random walk in continuous time, or Wiener process, in which the properties of the process have been changed so that there is a tendency of the walk to move back towards a central location, with a greater attraction when the process is further away from the center. The Ornstein\u2013Uhlenbeck process can also be considered as the continuous-time analogue of the discrete-time AR(1) process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f2/OrnsteinUhlenbeckProcess2D.svg", "https://upload.wikimedia.org/wikipedia/commons/3/34/OrnsteinUhlenbeckProcess3D.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/c/cb/OrnsteinUhlenbeck4.png"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost surely", "Annals of Mathematics", "ArXiv", "Autoregressive", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Bibcode", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Continuous time", "Convergence of random variables", "Covariance function", "Cox-Ingersoll-Ross model", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Discrete time", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Equipartition theorem", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fokker\u2013Planck equation", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian distribution", "Gaussian noise", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "George Eugene Uhlenbeck", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hooke's law", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "Interest rates", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "It\u014d isometry", "JSTOR", "Joseph Leo Doob", "Journal of Finance", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Langevin equation", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Leonard Ornstein", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "Maximum likelihood estimation", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moment (mathematics)", "Moran process", "Moving-average model", "Neil Shephard", "Non-homogeneous Poisson process", "Ole Barndorff-Nielsen", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck operator", "Overdamped", "Pairs trade", "Percolation theory", "Physical Review", "Piecewise deterministic Markov process", "Pink noise", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "PubMed Identifier", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Random walks", "Reflection principle (Wiener process)", "Regenerative process", "Regression toward the mean", "Relaxation (physics)", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Scaling limit", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Short rate model", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stokes\u2013Einstein equation", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Temperature", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance", "Variance gamma process", "Variation of parameters", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "World Scientific Publishing Co."], "references": ["http://www.ms.unimelb.edu.au/publications/RampertshammerStefan.pdf", "http://www.investmentscience.com/Content/howtoArticles/MLE_for_OR_mean_reverting.pdf", "http://www.sitmo.com/article/calibrating-the-ornstein-uhlenbeck-model/", "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1109160", "http://www.symmys.com/node/132", "http://turingfinance.com/interactive-stochastic-processes/", "http://adsabs.harvard.edu/abs/1930PhRv...36..823U", "http://adsabs.harvard.edu/abs/1996PhRvE..54.2084G", "http://adsabs.harvard.edu/abs/2008Metro..45S.117B", "http://www.cs.sunysb.edu/~skiena/691/lectures/lecture23.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/9965289", "http://arxiv.org/abs/1411.5062", "http://doi.org/10.1088%2F0026-1394%2F45%2F6%2FS17", "http://doi.org/10.1103%2FPhysRev.36.823", "http://doi.org/10.1103%2FPhysRevE.54.2084", "http://doi.org/10.1111%2Fj.1540-6261.1992.tb04011.x", "http://doi.org/10.1142%2FS021902491550020X", "http://doi.org/10.2307%2F1968873", "http://www.jstor.org/stable/1968873"]}, "Inferential statistics": {"categories": ["All articles to be expanded", "All articles with incomplete citations", "All articles with unsourced statements", "Articles to be expanded from November 2017", "Articles using small message boxes", "Articles with incomplete citations from November 2012", "Articles with unsourced statements from April 2012", "Articles with unsourced statements from December 2016", "Articles with unsourced statements from February 2012", "Articles with unsourced statements from March 2010", "Commons category link is on Wikidata", "Deductive reasoning", "Inductive reasoning", "Logic and statistics", "Philosophy of science", "Psychometrics", "Statistical inference", "Wikipedia articles needing page number citations from June 2011", "Wikipedia articles with GND identifiers"], "title": "Statistical inference", "method": "Inferential statistics", "url": "https://en.wikipedia.org/wiki/Statistical_inference", "summary": "Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.\nInferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abraham Wald", "Absolute value", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algorithmic inference", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrei N. 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"Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Summarizing statistical data", "Survey methodology", "Survey sampling", "Survival analysis", "Survival function", "System identification", "Test statistic", "Theoretical Computer Science (journal)", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Upper and lower probabilities", "Utility function", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Walter de Gruyter", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Kruskal", "World Scientific", "Z-test"], "references": ["http://e-collection.library.ethz.ch/eserv/eth:26403/eth-26403-01.pdf", "http://www.springerreference.com/docs/html/chapterdbid/372458.html", "http://www.stat.berkeley.edu/webmastr/users/binyu/ps/mdl.ps", "http://dspace.mit.edu/handle/1721.1/45587", "http://www.nptel.ac.in/courses/111105043/", "http://www.ams.org/mathscinet-getitem?mr=0178484", "http://www.ams.org/mathscinet-getitem?mr=0443141", "http://www.ams.org/mathscinet-getitem?mr=1082556", "http://www.ams.org/mathscinet-getitem?mr=1291393", "http://www.ams.org/mathscinet-getitem?mr=1643414", "http://www.ams.org/mathscinet-getitem?mr=1825292", "http://www.ams.org/mathscinet-getitem?mr=1939352", "http://www.ams.org/mathscinet-getitem?mr=2489600", "http://doi.org/10.1016%2FS0304-3975(98)00075-9", "http://doi.org/10.1080%2F01621459.2000.10474346", "http://doi.org/10.1093%2Fbjps%2Faxi152", "http://doi.org/10.1098%2Frsta.1937.0005", "http://doi.org/10.1111%2Finsr.12067", "http://doi.org/10.1198%2F016214501753168398", "http://doi.org/10.1214%2Fss%2F1177011233", "http://doi.org/10.2307%2F2290117", "http://doi.org/10.2307%2F270939", "http://www.jstor.org/stable/2246073", "http://www.jstor.org/stable/2290117", "http://www.jstor.org/stable/2669786", "http://www.jstor.org/stable/2670311", "http://www.jstor.org/stable/270939", "http://www.jstor.org/stable/2983716", "http://www.jstor.org/stable/91337", "http://www.stats.org.uk/statistical-inference/Lenhard2006.pdf", "https://books.google.com/?id=T3wWj2kVYZgC&printsec=frontcover", "https://books.google.com/books?id=V7oIAAAAQAAJ&pg=PA126", "https://books.google.com/books?id=ZKMVAAAAYAAJ&jtp=604", "https://books.google.com/books?id=ZKMVAAAAYAAJ&jtp=705", "https://books.google.com/books?id=hkWK8kFzXWIC&printsec=frontcover#v=onepage&q=%22descriptive%20statistics%22&f=false", "https://books.google.com/books?id=u8sWAQAAIAAJ&jtp=203", "https://books.google.com/books?id=u8sWAQAAIAAJ&jtp=470", "https://www.youtube.com/playlist?list=PLbMVogVj5nJRkNUH5v9qNEJvW7r2A7rEY", "https://www.academia.edu/3247833/", "https://d-nb.info/gnd/4182963-3", "https://archive.org/stream/popscimonthly12yoummiss#page/612/mode/1up", "https://archive.org/stream/popscimonthly12yoummiss#page/715/mode/1up", "https://archive.org/stream/popularsciencemo13newy#page/203/mode/1up", "https://archive.org/stream/popularsciencemo13newy#page/470/mode/1up", "https://web.archive.org/web/20041116080440/http://www.stat.berkeley.edu/webmastr/users/binyu/ps/mdl.ps", "https://www.jstor.org/stable/1403482", "https://www.jstor.org/stable/2342192", "https://www.wikidata.org/wiki/Q938438"]}, "Histogram": {"categories": ["All articles with unsourced statements", "Articles containing Ancient Greek-language text", "Articles with unsourced statements from August 2010", "Articles with unsourced statements from June 2011", "Commons category link is on Wikidata", "Estimation of densities", "Frequency distribution", "Nonparametric statistics", "Quality control tools", "Statistical charts and diagrams", "Statistics articles needing expert attention"], "title": "Histogram", "method": "Histogram", "url": "https://en.wikipedia.org/wiki/Histogram", "summary": "A histogram is an accurate representation of the distribution of numerical data. It is an estimate of the probability distribution of a continuous variable (quantitative variable) and was first introduced by Karl Pearson. It differs from a bar graph, in the sense that a bar graph relates two variables, but a histogram relates only one. To construct a histogram, the first step is to \"bin\" (or \"bucket\") the range of values\u2014that is, divide the entire range of values into a series of intervals\u2014and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent, and are often (but are not required to be) of equal size.If the bins are of equal size, a rectangle is erected over the bin with height proportional to the frequency\u2014the number of cases in each bin. A histogram may also be normalized to display \"relative\" frequencies. It then shows the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1.\nHowever, bins need not be of equal width; in that case, the erected rectangle is defined to have its area proportional to the frequency of cases in the bin. The vertical axis is then not the frequency but frequency density\u2014the number of cases per unit of the variable on the horizontal axis. Examples of variable bin width are displayed on Census bureau data below.\nAs the adjacent bins leave no gaps, the rectangles of a histogram touch each other to indicate that the original variable is continuous.Histograms give a rough sense of the density of the underlying distribution of the data, and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot.\nA histogram can be thought of as a simplistic kernel density estimation, which uses a kernel to smooth frequencies over the bins. This yields a smoother probability density function, which will in general more accurately reflect distribution of the underlying variable. The density estimate could be plotted as an alternative to the histogram, and is usually drawn as a curve rather than a set of boxes. Histograms are nevertheless preferred in applications, when their statistical properties need to be modeled. The correlated variation of a kernel density estimate is very difficult to describe mathematically, while it is simple for a histogram where each bin varies independently.\nAn alternative to kernel density estimation is the average shifted histogram,\nwhich is fast to compute and gives a smooth curve estimate of the density without using kernels.\nThe histogram is one of the seven basic tools of quality control.Histograms are sometimes confused with bar charts. A histogram is used for continuous data, where the bins represent ranges of data, while a bar chart is a plot of categorical variables. Some authors recommend that bar charts have gaps between the rectangles to clarify the distinction.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/7a/Bimodal-histogram.png", "https://upload.wikimedia.org/wikipedia/commons/d/d9/Black_cherry_tree_histogram.svg", "https://upload.wikimedia.org/wikipedia/commons/5/53/Cumulative_vs_normal_histogram.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1d/Example_histogram.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/5/56/Gumbel_distribtion.png", "https://upload.wikimedia.org/wikipedia/commons/c/c3/Histogram_of_arrivals_per_minute.svg", "https://upload.wikimedia.org/wikipedia/commons/3/39/Multimodal.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7b/Skewed-left.png", "https://upload.wikimedia.org/wikipedia/commons/1/12/Skewed-right.png", 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probability distribution", "Continuous variable", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data binning", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Entropy estimation", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", 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density estimation", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Milwaukee", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normalization (statistics)", "OCLC", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Pareto chart", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Prunus serotina", "Psychometrics", "PubMed Identifier", "Quality (business)", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative frequency", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Risk function", "Robust regression", "Robust statistics", "Round number", "Run chart", "SOCR", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter diagram", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Seven Basic Tools of Quality", "Seven basic tools of quality", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smooth function", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Unit interval", "United States Census Bureau", "V-optimal histograms", "V-statistic", "Variance", "Vector autoregression", "Vertical direction", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://excelandfinance.com/histogram-in-excel/", "http://www.mathworks.com/matlabcentral/fileexchange/27388-plot-and-compare-nice-histograms-by-default", "http://www.mathworks.com/matlabcentral/fileexchange/30480-histconnect", "http://onlinestatbook.com/", "http://digitalassets.lib.berkeley.edu/sdtr/ucb/text/34.pdf", "http://adsabs.harvard.edu/abs/1895RSPTA.186..343P", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.6404", "http://cameron.econ.ucdavis.edu/excel/ex11histogram.html", "http://www.socr.ucla.edu/htmls/SOCR_Charts.html", "http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_ModelerActivities_MixtureModel_1", "http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_PowerTransformFamily_Graphs", "http://bayes.wustl.edu/Manual/FreedmanDiaconis1_1981.pdf", "http://quarknet.fnal.gov/toolkits/ati/histograms.html", "http://www.ncbi.nlm.nih.gov/pubmed/17444758", "http://2000.jukuin.keio.ac.jp/shimazaki/res/histogram.html", "http://www.ton.scphys.kyoto-u.ac.jp/~shino/histograms/", "http://www.asq.org/learn-about-quality/seven-basic-quality-tools/overview/overview.html", "http://www.astroml.org/user_guide/density_estimation.html", "http://cnx.org/content/m16298/1.11/", "http://doi.org/10.1002%2Fwics.54", "http://doi.org/10.1007%2FBF01025868", "http://doi.org/10.1080%2F01621459.1926.10502161", "http://doi.org/10.1093%2Fbiomet%2F66.3.605", "http://doi.org/10.1098%2Frsta.1895.0010", "http://doi.org/10.1162%2Fneco.2007.19.6.1503", "http://www.jstor.org/stable/2965501", "http://www.mitpressjournals.org/doi/abs/10.1162/neco.2007.19.6.1503", "http://www.rutherfordjournal.org/article010107.html", "http://www.shodor.org/interactivate/activities/histogram/", "http://www.worldcat.org/oclc/682200824", "https://www.forbes.com/sites/naomirobbins/2012/01/04/a-histogram-is-not-a-bar-chart/#345b9c746d77", "https://www.census.gov/population/www/socdemo/journey.html", "https://www.census.gov/prod/2004pubs/c2kbr-33.pdf", "https://www.waterlog.info/cumfreq.htm", "https://www.waterlog.info/density.htm", "https://www.researchgate.net/publication/229760716_Averaged_shifted_histogram", "https://web.archive.org/web/20150501071703/http://www.stat.rice.edu/~scottdw/stat550/HW/hw3/c03.pdf", "https://tinlizzie.org/histograms/"]}, "Hierarchical hidden Markov model": {"categories": ["Hidden Markov models"], "title": "Hierarchical hidden Markov model", "method": "Hierarchical hidden Markov model", "url": "https://en.wikipedia.org/wiki/Hierarchical_hidden_Markov_model", "summary": "The hierarchical hidden Markov model (HHMM) is a statistical model derived from the hidden Markov model (HMM). In an HHMM each state is considered to be a self-contained probabilistic model. More precisely each state of the HHMM is itself an HHMM. \nHHMMs and HMMs are useful in many fields, including pattern recognition.", "images": ["https://upload.wikimedia.org/wikipedia/en/1/16/Hierarchical_hidden_Markov_model_%28diagram%29.png", "https://upload.wikimedia.org/wikipedia/en/1/16/Hierarchical_hidden_Markov_model_%28diagram%29.png"], "links": ["Hidden Markov model", "Hierarchical temporal memory", "Layered hidden Markov model", "Pattern recognition", "Probabilistic model", "Statistical model"], "references": []}, "Prosecutor's fallacy": {"categories": ["All articles needing expert attention", "Articles needing expert attention from September 2009", "Articles needing expert attention with no reason or talk parameter", "Articles with short description", "Bayesian statistics", "Forensic statistics", "Informal fallacies", "Misuse of statistics", "Philosophy/Logic articles needing expert attention"], "title": "Prosecutor's fallacy", "method": "Prosecutor's fallacy", "url": "https://en.wikipedia.org/wiki/Prosecutor%27s_fallacy", "summary": "The prosecutor's fallacy is a fallacy of statistical reasoning, typically used by the prosecution to argue for the guilt of a defendant during a criminal trial. Although it is named after prosecutors, it is not specific to them, and some variants of the fallacy can be used by defense lawyers arguing for the innocence of their client.\nThe following demonstrates the fallacy in the context of a prosecutor questioning an expert witness: \u201cthe odds of finding this evidence on an innocent man are so small that the jury can safely disregard the possibility that this defendant is innocent\u201d. The fallacy obscures that the odds of a defendant being innocent given said evidence in fact depends on the likely higher prior odds of the defendant being innocent, the explicitly lesser odds of the evidence in the case that he was innocent as mentioned, as well as the underlying cumulative odds of the evidence being on the defendant.\nAt its heart, the fallacy involves assuming that the prior probability of a random match is equal to the probability that the defendant is innocent. For instance, if a perpetrator is known to have the same blood type as a defendant and 10% of the population share that blood type, then to argue on that basis alone that the probability of the defendant being guilty is 90% makes the prosecutor's fallacy (in a very simple form).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["A priori and a posteriori", "Abuse of process", "Actual innocence", "Admissible evidence", "Adversarial system", "ArXiv", "Attorney misconduct", "Base rate fallacy", "Batson v. Kentucky", "Bayes' theorem", "Bayesian inference", "Berkson's paradox", "Bias", "Bibcode", "Binary classification", "Brady disclosure", "Capital punishment in the United States", "Cheating", "Conditional probability", "Confidence (statistics)", "Cross-race effect", "DNA", "DNA profiling", "Data dredging", "Database", "Digital object identifier", "Discretion", "Ecological fallacy", "Entrapment", "Epidemiology", "Equal Protection Clause", "Equality (mathematics)", "Estimation theory", "Ethics in mathematics", "Evidence (law)", "Exculpatory evidence", "Expert witness", "Eyewitness identification", "Eyewitness memory", "Fallacy", "False accusation", "False accusation of rape", "False allegation of child sexual abuse", "False arrest", "False positive", "False positive paradox", "Forced confession", "Forensic evidence", "Gaming the system", "Genetic predisposition", "Gerd Gigerenzer", "Harmless error", "Howland will forgery trial", "Ineffective assistance of counsel", "Innocence Project", "Innocence Protection Act", "Innocent prisoner's dilemma", "Investigating Innocence", "JSTOR", "Jury instructions", "Jury tampering", "Kangaroo court", "Lawyer", "Legal ethics", "Legal malpractice", "Likelihood function", "List of United States death row inmates", "List of exonerated death row inmates", "List of miscarriage of justice cases", "List of wrongful convictions in the United States", "Loophole", "Los Angeles", "Lucia de Berk", "Malicious prosecution", "Meadow's law", "Miscarriage of justice", "Misinformation effect", "Mislead", "Mistaken identity", "Mosaic", "M\u00fcnchausen syndrome by proxy", "National Registry of Exonerations", "Null hypothesis", "O. J. Simpson", "O. J. Simpson murder case", "Odds", "Overturned convictions in the United States", "People v. Collins", "Police misconduct", "Police perjury", "Posterior probability", "Prior probability", "Probability", "Prosecutor", "Prosecutorial misconduct", "PubMed Central", "PubMed Identifier", "Race in the United States criminal justice system", "Racial profiling", "Recidivism", "Relevance (law)", "Representativeness heuristic", "Right to a fair trial", "Roy Meadow", "Royal Statistical Society", "Sally Clark", "Selective enforcement", "Selective prosecution", "Sharp practice", "Show trial", "Simpson's paradox", "Social Science Research Network", "Spoliation of evidence", "Statistical independence", "Statistical significance", "Sudden infant death syndrome", "Tampering with evidence", "The Guardian", "Type I and type II errors", "Type I error", "Uncorrelated", "University of Canterbury", "University of Salford", "Witness tampering", "Wrongful execution"], "references": ["http://dna-view.com/profile.htm", "http://www.mrbartonmaths.com/resources/a%20level/s1/Beyond%20reasonable%20doubt.doc", "http://ssrn.com/abstract=1539107", "http://www.ted.com/index.php/talks/peter_donnelly_shows_how_stats_fool_juries.html", "http://adsabs.harvard.edu/abs/2016AnRSA...3...51F", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4934658", "http://www.ncbi.nlm.nih.gov/pubmed/27398389", "http://uctv.canterbury.ac.nz/viewfile.php/4/sharing/55/74/74/NZEPVersionofImpreciseProbabilitiespaperVersi.pdf", "http://arxiv.org/abs/math/0607340", "http://www.bailii.org/ew/cases/EWCA/Crim/2003/1020.html", "http://www.denverda.org/DNA_Documents/DNA%20in%20Australia.pdf", "http://doi.org/10.1007%2FBF01044641", "http://doi.org/10.1093%2Flpr%2Fmgm003", "http://doi.org/10.1111%2Fj.1365-3016.2004.00560.x", "http://doi.org/10.1146%2Fannurev-statistics-041715-033428", "http://www.jstor.org/stable/1393631", "http://plus.maths.org/issue21/features/clark/", "http://policechiefmagazine.org/magazine/index.cfm?fuseaction=display_arch&article_id=1922&issue_id=102009", "http://understandinguncertainty.org/node/545#notes", "http://reporter.leeds.ac.uk/428/mead.htm", "http://www.cse.salford.ac.uk/staff/RHill/ppe_5601.pdf", "http://news.bbc.co.uk/1/hi/england/essex/7082411.stm", "http://observer.guardian.co.uk/print/0,,4221973-102285,00.html", "http://www.rss.org.uk/uploadedfiles/documentlibrary/744.pdf", "https://www.theguardian.com/science/2006/oct/28/uknews1", "https://www.theguardian.com/society/2007/mar/17/childrensservices.uknews", "https://web.archive.org/web/20030528061717/http://www.colchsfc.ac.uk/maths/dna/discuss.htm", "https://web.archive.org/web/20110824151124/http://www.rss.org.uk/uploadedfiles/documentlibrary/744.pdf"]}, "Questionnaire": {"categories": ["Commons category link is defined as the pagename", "Pages using web citations with no URL", "Questionnaire construction", "Types of polling", "Wikipedia articles with GND identifiers", "Wikipedia articles with NARA identifiers", "Wikipedia articles with NDL identifiers"], "title": "Questionnaire", "method": "Questionnaire", "url": "https://en.wikipedia.org/wiki/Questionnaire", "summary": "A questionnaire is a research instrument consisting of a series of questions (or other types of prompts) for the purpose of gathering information from respondents. The questionnaire was invented by the Statistical Society of London in 1838.Although questionnaires are often designed for statistical analysis of the responses, this is not always the case.\nQuestionnaires have advantages over some other types of surveys in that they are cheap, do not require as much effort from the questioner as verbal or telephone surveys, and often have standardized answers that make it simple to compile data. However, such standardized answers may frustrate users. Questionnaires are also sharply limited by the fact that respondents must be able to read the questions and respond to them. Thus, for some demographic groups conducting a survey by questionnaire may not be concrete.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/3/38/Multi-item_psychometric_scale.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d0/Questionaire_in_Thai.png", "https://upload.wikimedia.org/wikipedia/commons/6/69/WMF_Strategic_Plan_Survey.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Acrylamide", "Actuarial science", "Afrobarometer", "Akaike information criterion", "American Association for Public Opinion Research", "American National Election Studies", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Audience measurement", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavioral Risk Factor Surveillance System", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical data", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparative Study of Electoral Systems", "Completeness (statistics)", "Computer-assisted personal interviewing", "Confidence interval", "Confounding", "Construct validity", "Content validity", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Couple interview", "Credible interval", "Crime statistics", "Criterion validity", "Cross-correlation", "Cross-validation (statistics)", "Data analysis", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic group", "Demographic statistics", "Demography", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Enterprise Feedback Management", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Eurobarometer", "European Social Survey", "European Society for Opinion and Marketing Research", "European Values Study", "Experiment", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Food frequency questionnaire", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "G.J. Mellenbergh", "Gallup (company)", "General Social Survey", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Gideon J. Mellenbergh", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "H.J. Ad\u00e8r", "H. J. Ad\u00e8r", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Information", "Integrated Authority File", "Interaction (statistics)", "Internal consistency", "International Social Survey Programme", "International Statistical Institute", "Interquartile range", "Interval estimation", "Interview (research)", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latinobar\u00f3metro", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likert scale", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of household surveys in the United States", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Market research", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multitrait-multimethod matrix", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Myers-Briggs Type Indicator", "National Archives and Records Administration", "National Diet Library", "National Health and Nutrition Examination Survey", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New Zealand Attitudes and Values Study", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Office for National Statistics", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pew Research Center", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Position analysis questionnaire", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Professional association", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Public opinion", "Quality control", "Quantitative marketing research", "Quantitative research", "Quasi-experiment", "Question", "Questionnaire (horse)", "Questionnaire construction", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rating scale", "Regression analysis", "Regression model validation", "Reliability (statistics)", "Reliability engineering", "Repeatability", "Replication (statistics)", "Resampling (statistics)", "Research", "Response rate (survey)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale (social sciences)", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semi-structured interview", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social science", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Society of London", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical survey", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Structured interview", "Structured interviewing", "Student's t-test", "Sufficient statistic", "Survey data collection", "Survey methodology", "Survey research", "Survey sampling", "Survival analysis", "Survival function", "System identification", "Thai language", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Unstructured interview", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Web-based experiments", "Whittle likelihood", "Wilcoxon signed-rank test", "World Association for Public Opinion Research", "World Values Survey", "Z-test"], "references": ["http://sqp.upf.edu", "http://www.ncbi.nlm.nih.gov/pubmed/19187374", "http://essedunet.nsd.uib.no/cms/topics/measurement/", "http://cebp.aacrjournals.org/cgi/content/abstract/16/11/2304", "http://doi.org/10.1007%2Fs11205-015-1002-x", "http://doi.org/10.1080%2F08919402.1907.10532551", "http://doi.org/10.1111%2Fj.1471-0528.2008.01957.x", "http://www.jstor.org/stable/i315562", "http://www.ons.gov.uk/ons/guide-method/harmonisation/harmonisation-index-page/index.html", "https://catalog.archives.gov/id/10643040", "https://d-nb.info/gnd/4128271-1", "https://id.ndl.go.jp/auth/ndlna/00571296", "https://dx.doi.org/10.1002/hrm.21852", "https://www.wikidata.org/wiki/Q747810"]}, "Nicholson\u2013Bailey model": {"categories": ["Mathematical and theoretical biology", "Population models", "Predation"], "title": "Nicholson\u2013Bailey model", "method": "Nicholson\u2013Bailey model", "url": "https://en.wikipedia.org/wiki/Nicholson%E2%80%93Bailey_model", "summary": "The Nicholson\u2013Bailey model was developed in the 1930s to describe the population dynamics of a coupled host-parasitoid system.a It is named after Alexander John Nicholson and Victor Albert Bailey. Host-parasite and prey-predator systems can also be represented with the Nicholson-Bailey model. The model is closely related to the Lotka\u2013Volterra model, which describes the dynamics of antagonistic populations (preys and predators) using differential equations.\nThe model uses (discrete time) difference equations to describe the population growth of host-parasite populations. The model assumes that parasitoids search for hosts at random, and that both parasitoids and hosts are assumed to be distributed in a non-contiguous (\"clumped\") fashion in the environment. In its original form, the model does not allow for stable coexistence. Subsequent refinements of the model, notably adding density dependence on several terms, allowed this coexistence to happen.", "images": [], "links": ["Alexander John Nicholson", "Difference equation", "Differential equation", "Digital object identifier", "International Standard Book Number", "Lotka\u2013Volterra equation", "Lotka\u2013Volterra inter-specific competition equations", "Parasitoid", "Population dynamics", "Population growth", "Predator-prey", "Victor Albert Bailey"], "references": ["http://www.publish.csiro.au/paper/HR9880720179.htm", "http://www.biosym.uzh.ch/modules/models/ETHZ/Nicholson-BaileyModel/nicholson_bailey.xhtml", "http://wikis.swarthmore.edu/mathbio/index.php/Nicholson-Bailey_Model", "http://www.inhs.uiuc.edu/research/biocontrol/theoriesmodels/nbmodel.html", "http://doi.org/10.1071%2Fhr9880720179", "https://books.google.com/books?id=6GGyquH8kLcC&pg=PA214"]}, "BA model": {"categories": ["Graph algorithms", "Random graphs", "Social networks"], "title": "Barab\u00e1si\u2013Albert model", "method": "BA model", "url": "https://en.wikipedia.org/wiki/Barab%C3%A1si%E2%80%93Albert_model", "summary": "The Barab\u00e1si\u2013Albert (BA) model is an algorithm for generating random scale-free networks using a preferential attachment mechanism. Several natural and human-made systems, including the Internet, the world wide web, citation networks, and some social networks are thought to be approximately scale-free and certainly contain few nodes (called hubs) with unusually high degree as compared to the other nodes of the network. The BA model tries to explain the existence of such nodes in real networks. The algorithm is named for its inventors Albert-L\u00e1szl\u00f3 Barab\u00e1si and R\u00e9ka Albert and is a special case of a more general model called Price's model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a8/Barabasi-albert_model_degree_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2e/Barabasi_Albert_generated_network.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/48/Barabasi_Albert_model.gif", "https://upload.wikimedia.org/wikipedia/commons/4/40/Barabasi_albert_graph.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e9/Data_collapse_m1.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/7b/ScaledDegreeDistribution-multiplot.jpg", "https://upload.wikimedia.org/wikipedia/commons/d/d2/Internet_map_1024.jpg"], "links": ["A. Korn", "A. Schubert", "A. Telcs", "Adjacency list", "Adjacency matrix", "Agent-based model", "Albert-L\u00e1szl\u00f3 Barab\u00e1si", "ArXiv", "Artificial neural network", "Assortativity", "Autocatalysis", "Average path length", "Balance theory", "Betweenness centrality", "Bianconi\u2013Barab\u00e1si model", "Bibcode", "Biological network", "Biometrika", "Bipartite graph", "Boolean network", "Centrality", "Chinese restaurant process", "Citation analysis", "CiteSeerX", "Clique (graph theory)", "Closeness (graph theory)", "Clustering coefficient", "Combinatorial optimization", "Community structure", "Complete graph", "Complex contagion", "Complex network", "Complex networks", "Computer network", "Connected component (graph theory)", "Cut (graph theory)", "Cycle (graph theory)", "Degree (graph theory)", "Degree distribution", "Dependency network", "Derek J. de Solla Price", "Digital object identifier", "Directed graph", "Distance (graph theory)", "Dynamic scaling", "Edge (graph theory)", "Efficiency (network science)", "Epidemic model", "Erd\u0151s\u2013R\u00e9nyi model", "Evolving networks", "Exponential random graph models", "Fitness model (network theory)", "Flow network", "Google", "Graph (abstract data type)", "Graph (discrete mathematics)", "Graph drawing", "H-index", "Handle System", "Herbert A. Simon", "Hierarchical network model", "Homophily", "Hyperbolic geometric graph", "Hypergraph", "Incidence list", "Incidence matrix", "Interdependent networks", "International Standard Serial Number", "Internet", "JSTOR", "Journal of the American Society for Information Science", "Lancichinetti\u2013Fortunato\u2013Radicchi benchmark", "Link analysis", "List of algorithms", "List of network scientists", "List of network theory topics", "Loop (graph theory)", "Matthew effect (sociology)", "Metrics (networking)", "Modularity (networks)", "Multigraph", "Neighbourhood (graph theory)", "Network controllability", "Network effect", "Network motif", "Network on a chip", "Network science", "Network theory", "PageRank", "Path (graph theory)", "Percolation theory", "Physical Review E", "Positive feedback", "Power law", "Preferential attachment", "Price's model", "PubMed Identifier", "Random geometric graph", "Random graph", "Reciprocity (network science)", "Reviews of Modern Physics", "Rich get richer", "R\u00e9ka Albert", "SIR model", "Scale-free network", "Scale-free networks", "Science (journal)", "Scientific collaboration network", "Semantic network", "Small-world network", "Social capital", "Social influence", "Social network", "Social network analysis software", "Social networks", "Spatial network", "Spectral properties", "Stochastic block model", "Telecommunications network", "Transitive relation", "Transport network", "Triadic closure", "Udny Yule", "Vertex (graph theory)", "Watts and Strogatz model", "Weighted network", "World wide web"], "references": ["http://www.hpl.hp.com/research/idl/papers/scalingcomment/", "http://www.popsci.com/science/article/2011-10/man-could-rule-world", "http://adsabs.harvard.edu/abs/1999Sci...286..509B", "http://adsabs.harvard.edu/abs/2001PhRvE..64b6704F", "http://adsabs.harvard.edu/abs/2002PhRvE..65e7102K", "http://adsabs.harvard.edu/abs/2002PhRvE..65f6122D", "http://adsabs.harvard.edu/abs/2002RvMP...74...47A", "http://adsabs.harvard.edu/abs/2003PhRvL..90e8701C", "http://adsabs.harvard.edu/abs/2009PhyA..388.2221K", "http://adsabs.harvard.edu/abs/2013EPJB...86..510F", "http://www.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/StatisticalMechanics_Rev%20of%20Modern%20Physics%2074,%2047%20(2002).pdf", "http://www.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/EmergenceRandom_Science%20286,%20509-512%20(1999).pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.114", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.176.6988", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.176.6988", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.242.4753", "http://www.ncbi.nlm.nih.gov/pubmed/10521342", "http://www.ncbi.nlm.nih.gov/pubmed/11497741", "http://www.ncbi.nlm.nih.gov/pubmed/12059755", "http://www.ncbi.nlm.nih.gov/pubmed/12188798", "http://www.ncbi.nlm.nih.gov/pubmed/12633404", "http://www.ncbi.nlm.nih.gov/pubmed/14683021", "http://hdl.handle.net/10261%2F15314", "http://hdl.handle.net/2047%2Fd20000692", "http://arxiv.org/abs/0809.0514", "http://arxiv.org/abs/1308.5169", "http://arxiv.org/abs/cond-mat/0102335", "http://arxiv.org/abs/cond-mat/0106096", "http://arxiv.org/abs/cond-mat/0107607", "http://arxiv.org/abs/cond-mat/0112143", "http://arxiv.org/abs/cond-mat/0205476", "http://arxiv.org/abs/cond-mat/0306255", "http://arxiv.org/abs/cond-mat/9910332", "http://doi.org/10.1002%2Fasi.4630270505", "http://doi.org/10.1016%2Fj.physa.2009.02.013", "http://doi.org/10.1093%2Fbiomet%2F42.3-4.425", "http://doi.org/10.1103%2FPhysRevE.64.026704", "http://doi.org/10.1103%2FPhysRevE.65.057102", "http://doi.org/10.1103%2FPhysRevE.65.066122", "http://doi.org/10.1103%2FPhysRevE.68.046126", "http://doi.org/10.1103%2FPhysRevLett.90.058701", "http://doi.org/10.1103%2FRevModPhys.74.47", "http://doi.org/10.1126%2Fscience.286.5439.509", "http://doi.org/10.1140%2Fepjb%2Fe2013-40920-6", "http://doi.org/10.2307%2F2341419", "http://www.e-publications.org/ims/submission/index.php/BEJ/user/submissionFile/10315?confirm=c40442a0", "http://www.jstor.org/stable/2341419", "http://www.worldcat.org/issn/0031-9007", "http://www.worldcat.org/issn/0034-6861", "https://github.com/alihadian/ROLL", "https://compuzzle.wordpress.com/2015/02/03/generating-barabasi-albert-model-graphs-in-clojure/", "https://web.archive.org/web/20120417112354/http://www.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/EmergenceRandom_Science%20286,%20509-512%20(1999).pdf", "https://web.archive.org/web/20150824235818/http://www3.nd.edu/~networks/Publication%20Categories/03%20Journal%20Articles/Physics/StatisticalMechanics_Rev%20of%20Modern%20Physics%2074,%2047%20(2002).pdf", "https://dx.doi.org/10.1088/1751-8113/44/17/175101"]}, "Uniformly most powerful test": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "Statistical hypothesis testing"], "title": "Uniformly most powerful test", "method": "Uniformly most powerful test", "url": "https://en.wikipedia.org/wiki/Uniformly_most_powerful_test", "summary": "In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n among all possible tests of a given size \u03b1. For example, according to the Neyman\u2013Pearson lemma, the likelihood-ratio test is UMP for testing simple (point) hypotheses.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Exponential family", "International Standard Book Number", "Likelihood-ratio test", "Neyman\u2013Pearson lemma", "Parametrized family", "Probability density function", "Probability mass function", "Statistical hypothesis testing", "Statistical power", "Sufficiency (statistics)", "Type I and type II errors"], "references": []}, "Heckman correction": {"categories": ["Econometric modeling", "Regression analysis", "Sampling (statistics)"], "title": "Heckman correction", "method": "Heckman correction", "url": "https://en.wikipedia.org/wiki/Heckman_correction", "summary": "The Heckman correction (the two-stage method, Heckman's lambda or the Heckit method) is any of a number of related statistical methods developed by James Heckman at the University of Chicago in 1976 to 1979 which allow the researcher to correct for selection bias. Selection bias problems are endemic to applied econometric problems, which make Heckman\u2019s original technique, and subsequent refinements by both himself and others, indispensable to applied econometricians. Heckman received the Economics Nobel Prize in 2000 for this achievement.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "American Economic Review", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Approximation theory", "Arithmetic mean", "Arthur Goldberger", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrap (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calibration curve", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational statistics", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Control function (econometrics)", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Curve fitting", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrician", "Econometrics", "Economic theory", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "H. Gregg Lewis", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Instrumental variable", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse Mills ratio", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jackknife resampling", "James G. MacKinnon", "James Heckman", "Jarque\u2013Bera test", "Jeffrey Wooldridge", "Johansen test", "Jonckheere's trend test", "Journal of Political Economy", "Journal of Statistical Software", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lambda", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Leo Goodman", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear least squares (mathematics)", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Logit", "Loss function", "Lp space", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving least squares", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nobel Memorial Prize in Economic Sciences", "Non-linear least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observational study", "Official statistics", "Omitted-variables bias", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probit", "Propensity score matching", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Reuben Gronau", "Ridge regression", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Karlin", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Selection bias", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Takeshi Amemiya", "Time domain", "Time series", "Tobit model", "Tolerance interval", "Total least squares", "Trend estimation", "U-statistic", "Uniformly most powerful test", "University of Chicago", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "William Greene (economist)", "Z-test"], "references": ["http://www.britannica.com/eb/topic-734492/Heckman-correction", "http://www.columbia.edu/~ap2231/ET/et18-oct00.htm", "http://doi.org/10.1002%2F9780470996249.ch19", "http://doi.org/10.1086%2F260267", "http://doi.org/10.1086%2F260268", "http://doi.org/10.1111%2F1467-6419.00104", "http://doi.org/10.18637%2Fjss.v027.i07", "http://doi.org/10.2307%2F1912352", "http://www.jstatsoft.org/v27/i07/", "http://www.jstor.org/stable/1830664", "http://www.jstor.org/stable/1830665", "http://www.jstor.org/stable/1912352", "https://books.google.com/books?id=UkKQRAAACAAJ&pg=PA556", "https://books.google.com/books?id=VplRX78ZQgsC&pg=PA227", "https://books.google.com/books?id=Zf0gCwxC9ocC&pg=PA546", "https://books.google.com/books?id=cdBPOJUP4VsC&pg=PA562", "https://books.google.com/books?id=ou0xxPriEGYC&pg=PA61", "https://books.google.com/books?id=vqkap8AwAy0C&pg=PA486", "https://www.stata.com/manuals13/rheckman.pdf", "https://www.nobelprize.org/nobel_prizes/economics/laureates/2000/heckman.html", "https://cran.r-project.org/web/packages/sampleSelection/index.html"]}, "Natural exponential family": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from June 2012", "Articles with unsourced statements from July 2012", "Exponentials", "Types of probability distributions", "Wikipedia articles needing clarification from July 2012"], "title": "Natural exponential family", "method": "Natural exponential family", "url": "https://en.wikipedia.org/wiki/Natural_exponential_family", "summary": "In probability and statistics, a natural exponential family (NEF) is a class of probability distributions that is a special case of an exponential family (EF). Every distribution possessing a moment-generating function is a member of a natural exponential family, and the use of such distributions simplifies the theory and computation of generalized linear models.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian inference", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Carl Morris (statistician)", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conjugate prior distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulant generating function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear models", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gradient", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hessian matrix", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent identically distributed", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lognormal", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mathematical statistics", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Moment-generating function", "Moment generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Posterior probability distribution", "Probability", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Variance function", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": []}, "Natural experiment": {"categories": ["Epidemiology", "Experiments", "Observational study", "Use dmy dates from September 2010"], "title": "Natural experiment", "method": "Natural experiment", "url": "https://en.wikipedia.org/wiki/Natural_experiment", "summary": "A natural experiment is an empirical study in which individuals (or clusters of individuals) are exposed to the experimental and control conditions that are determined by nature or by other factors outside the control of the investigators. The process governing the exposures arguably resembles random assignment. Thus, natural experiments are observational studies and are not controlled in the traditional sense of a randomized experiment. Natural experiments are most useful when there has been a clearly defined exposure involving a well defined subpopulation (and the absence of exposure in a similar subpopulation) such that changes in outcomes may be plausibly attributed to the exposure. In this sense, the difference between a natural experiment and a non-experimental observational study is that the former includes a comparison of conditions that pave the way for causal inference, but the latter does not.\nNatural experiments are employed as study designs when controlled experimentation is extremely difficult to implement or unethical, such as in several research areas addressed by epidemiology (like evaluating the health impact of varying degrees of exposure to ionizing radiation in people living near Hiroshima at the time of the atomic blast) and economics (like estimating the economic return on amount of schooling in US adults).", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/2/27/Snow-cholera-map-1.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["1854 Broad Street cholera outbreak", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "American Economic Review", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Atmospheric pollution", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "British Medical Journal", "Canonical correlation", "Cartography", "Categorical variable", "Causal inference", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Cholera", "Clinical study design", "Clinical trial", "Cluster (epidemiology)", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Common garden experiment", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "David A. Freedman", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Draft lottery (1969)", "Durbin\u2013Watson statistic", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Helena, Montana", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Industrial Revolution", "Industrial melanism", "Instrumental variable", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Isotope", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Snow (physician)", "Jonckheere's trend test", "Joshua Angrist", "Journal of Economic Literature", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lambeth Waterworks Company", "Lawrence E. Blume", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "London", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Myocardial infarction", "National accounts", "Natural selection", "Nelson\u2013Aalen estimator", "New Palgrave", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuclear weapons testing", "Observational studies", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial Nuclear Test Ban Treaty", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Peppered moth", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Pulse-chase experiment", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "River Thames", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sewage", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smoking ban", "Social Science Research Network", "Social statistics", "Soho", "Soot", "Southwark and Vauxhall Waterworks Company", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Steven N. Durlauf", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Study design", "Sufficient statistic", "Sulphur dioxide", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.dictionaryofeconomics.com/article?id=pde2008_N000142", "http://www.nature.com/hdy/journal/v101/n6/full/hdy2008105a.html", "http://www.spiked-online.com/newsite/article/7451", "http://ssrn.com/abstract=1592456", "http://ssrn.com/abstract=636508", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC404491", "http://www.ncbi.nlm.nih.gov/pubmed/15066887", "http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521671057", "http://doi.org/10.1038%2Fhdy.2008.105", "http://doi.org/10.1057%2F9780230226203.1162", "http://doi.org/10.1136%2Fbmj.38055.715683.55", "http://doi.org/10.1257%2Faer.98.1.38", "http://doi.org/10.1257%2Fjel.38.4.827", "http://doi.org/10.1287%2Fmnsc.1110.1413", "http://www.jstor.org/stable/116844", "http://www.jstor.org/stable/2006669", "http://www.jstor.org/stable/29729963", "https://www.youtube.com/watch?v=OUN6Gp_H3q4"]}, "Convex hull": {"categories": ["CS1 maint: Uses editors parameter", "Closure operators", "Computational geometry", "Convex analysis", "Convex hulls", "Geometry processing"], "title": "Convex hull", "method": "Convex hull", "url": "https://en.wikipedia.org/wiki/Convex_hull", "summary": "In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X.Formally, the convex hull may be defined either as the intersection of all convex sets containing X, or as the set of all convex combinations of points in X. With the latter definition, convex hulls may be extended from Euclidean spaces to arbitrary real vector spaces; they may also be generalized further, to oriented matroids.The algorithmic problem of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces is one of the fundamental problems of computational geometry.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/7a/3D_Convex_Hull.tiff", "https://upload.wikimedia.org/wikipedia/commons/d/de/ConvexHull.svg", "https://upload.wikimedia.org/wikipedia/commons/0/01/Convex_hull.png", "https://upload.wikimedia.org/wikipedia/commons/8/8e/Extreme_points.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Minkowski_sum_graph_-_vector_version.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9d/Truncated_cuboctahedron%2C_ball-and-stick%2C_triangles.png", "https://upload.wikimedia.org/wikipedia/commons/c/c8/Truncated_cuboctahedron%2C_ball-and-stick.png", "https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg"], "links": ["Absolutely convex set", "Absorbing set", "Abstract Wiener space", "Abstract interpretation", "Affine hull", "Affine space", "Algebraic interior", "Algorithm", "Alpha shape", "Balanced set", "Banach algebra", "Banach lattice", "Banach space", "Banach\u2013Alaoglu theorem", "Banach\u2013Mazur theorem", "Banach\u2013Saks theorem", "Barrelled space", "Bernard Chazelle", "Bessel's inequality", "Bilinear form", "Bilinear map", "Bochner integral", "Bochner space", "Borel functional calculus", "Bornological space", "Bounded operator", "Bounded set", "Bounded set (topological vector space)", "Bounding point", "Branko Gr\u00fcnbaum", "Brauner space", "C*-algebra", "Carath\u00e9odory's theorem (convex hull)", "Cauchy\u2013Schwarz inequality", "Chan's algorithm", "Choquet theory", "Closed graph theorem", "Closed linear operator", "Closed range theorem", "Closed set", "Closure operator", "Commutativity", "Compact operator", "Compact set", "Computational geometry", "Concave set", "Cone (linear algebra)", "Continuous functional calculus", "Continuous linear operator", "Convex combination", "Convex cone", "Convex hull algorithms", "Convex layers", "Convex polygon", "Convex polytope", "Convex set", "Convex skull", "Coplanarity", "Data structure", "Delaunay triangulation", "Densely defined", "Derivative", "Diameter", "Differentiation in Fr\u00e9chet spaces", "Digital object identifier", "Discontinuous linear map", "Discrete and Computational Geometry", "Donald Knuth", "Dual (mathematics)", "Dual norm", "Dual space", "Dual topology", "Dunford integral", "Eberlein\u2013\u0160mulian theorem", "Empty set", "Eric W. Weisstein", "Ethology", "Euclidean geometry", "Euclidean plane", "Euclidean space", "Extreme point", "F-space", "Facet (geometry)", "Finite set", "Fredholm operator", "Freudenthal spectral theorem", "Fr\u00e9chet derivative", "Fr\u00e9chet space", "Functional analysis", "Functional calculus", "Functional derivative", "GRASS GIS", "Game theory", "Gelfand\u2013Mazur theorem", "Gelfand\u2013Naimark theorem", "Geographic information system", "Gift wrapping algorithm", "Goldstine theorem", "Graham scan", "G\u00e2teaux derivative", "Hahn\u2013Banach theorem", "Half-space (geometry)", "Helly's theorem", "Hermitian adjoint", "Hilbert space", "Hilbert\u2013Schmidt operator", "Holomorphic functional calculus", "Holomorphically convex hull", "Home range", "Hyperplane separation theorem", "Idempotence", "Image processing", "Infinite-dimensional Lebesgue measure", "Infinite-dimensional holomorphy", "Inner product space", "Integral", "Interior (topology)", "International Standard Book Number", "Invariant subspace problem", "Inverse function theorem", "JSTOR", "Join and meet", "Kakutani fixed-point theorem", "Kirkpatrick\u2013Seidel algorithm", "Krein\u2013Milman theorem", "LF-space", "Lattice (order)", "Line (geometry)", "Line segment", "Linear form", "Linear hull", "Linear map", "List of functional analysis topics", "Locally convex topological vector space", "M. Riesz extension theorem", "Mackey space", "Mackey topology", "Mackey\u2013Arens theorem", "Mark Krein", "Mark Overmars", "MathWorld", "Mathematical Reviews", "Mathematics", "Mazur's lemma", "Measure (mathematics)", "Minkowski addition", "Minkowski functional", "Minkowski sum", "Monotone function", "Montel space", "Nash\u2013Moser theorem", "Norm (mathematics)", "Normal operator", "Normed space", "Nuclear operator", "Nuclear space", "Oloid", "Open mapping theorem (functional analysis)", "Open set", "Operation (mathematics)", "Operator theory", "Operator topologies", "Oriented matroid", "Orthogonal convex hull", "Outlier", "Output-sensitive algorithm", "Paley\u2013Wiener integral", "Parseval's identity", "Pattern recognition", "Pettis integral", "Phase diagrams", "Polar decomposition", "Polar set", "Polarization identity", "Positive linear functional", "Projection-valued measure", "Quasinorm", "Quickhull", "R (programming language)", "Radial set", "Real vector space", "Reflexive space", "Regulated integral", "Riesz representation theorem", "Riesz space", "Rotating calipers", "Rubber band", "Schauder fixed-point theorem", "SciPy", "Self-adjoint operator", "Sesquilinear form", "Set theory", "Shapley\u2013Folkman lemma", "Simplex", "Singular value decomposition", "Smith space", "Spectral radius", "Spectral theorem", "Spectral theory", "Spectral theory of ordinary differential equations", "Spectrum (functional analysis)", "Spectrum of a C*-algebra", "Star domain", "Static code analysis", "Statistics", "Stereotype space", "Strictly convex space", "Strictly singular operator", "Strong operator topology", "Strong topology", "Strong topology (polar topology)", "Subset", "Sumset", "Symmetric set", "Tensor product of Hilbert spaces", "Topological tensor product", "Topological vector space", "Topology of uniform convergence", "Trace class", "Transpose of a linear map", "Triangle", "Truncated cuboctahedron", "Two-dimensional", "Ultrastrong topology", "Ultraweak topology", "Unbounded operator", "Union (set theory)", "Unitary operator", "Upper half-plane", "Vector measure", "Vertex (geometry)", "Voronoi diagram", "Weak operator topology", "Weak topology", "Weak topology (polar topology)", "Weakly measurable function", "Webbed space", "Weighted average", "Width", "Wolfram Demonstrations Project", "Zonotope"], "references": ["http://demonstrations.wolfram.com/ConvexHull/", "http://mathworld.wolfram.com/ConvexHull.html", "http://www.cs.princeton.edu/~chazelle/pubs/ConvexHullAlgorithm.pdf", "http://www-cs-faculty.stanford.edu/~uno/aah.html", "http://www.ams.org/mathscinet-getitem?mr=0002009", "http://www.ams.org/mathscinet-getitem?mr=1216521", "http://www.ams.org/mathscinet-getitem?mr=1226891", "http://doi.org/10.1007%2F3-540-55611-7", "http://doi.org/10.1007%2FBF02573985", "http://doi.org/10.1016%2F0020-0190(79)90072-3", "http://doi.org/10.1016%2F0020-0190(79)90074-7", "http://doi.org/10.1017%2FCBO9780511526282", "http://doi.org/10.2307%2F1968735", "http://www.jstor.org/stable/1968735", "http://grass.osgeo.org/grass64/manuals/addons/v.adehabitat.mcp.html", "https://books.google.com/books?hl=en&lr=&id=tkyG8W2163YC&oi=fnd&pg=PA2", "https://cran.r-project.org/web/packages/adehabitatHR/adehabitatHR.pdf", "https://docs.scipy.org/doc/scipy-0.19.0/reference/generated/scipy.spatial.ConvexHull.html"]}, "Stochastic differential equation": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from July 2013", "Articles with unsourced statements from August 2011", "CS1 maint: Extra text: authors list", "Differential equations", "Stochastic calculus", "Stochastic differential equations", "Stochastic processes", "Wikipedia articles with NDL identifiers"], "title": "Stochastic differential equation", "method": "Stochastic differential equation", "url": "https://en.wikipedia.org/wiki/Stochastic_differential_equation", "summary": "A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as unstable stock prices or physical systems subject to thermal fluctuations. Typically, SDEs contain a variable which represents random white noise calculated as the derivative of Brownian motion or the Wiener process. However, other types of random behaviour are possible, such as jump processes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Navier_Stokes_Laminar.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Adapted process", "Almost surely", "Annus Mirabilis Papers", "Applied mathematics", "Astronomy", "Asymptotic stability", "Augustin-Louis Cauchy", "Autonomous differential equation", "Bachelier", "Bernt \u00d8ksendal", "Bibcode", "Biology", "Black\u2013Scholes model", "Brownian motion", "Butterfly effect", "C. W. Gardiner", "Carl David Tolm\u00e9 Runge", "Chaos theory", "Chemistry", "CiteSeerX", "Complex differential equation", "Continuous time", "Continuum mechanics", "Crackling noise", "Crank\u2013Nicolson method", "Delay differential equation", "Dependent and independent variables", "Difference equation", "Differential algebraic equation", "Differential equation", "Differential form", "Differential operator", "Diffusion equation", "Diffusion process", "Digital object identifier", "Dimension", "Dirac delta function", "Dynamical systems", "Dynamical systems theory", "Economics", "Einstein", "Engineering", "Ernst Lindel\u00f6f", "Euclidean space", "Euler method", "Euler\u2013Maruyama method", "Exact differential equation", "Expected value", "Exponential response formula", "Exponential stability", "Filtration (abstract algebra)", "Finite difference method", "Finite element method", "Finite volume method", "Fokker\u2013Planck equation", "Fractional differential equations", "Galerkin method", "Generalized function", "Geology", "Geometric Brownian motion", "Goldstone theorem", "Gottfried Leibniz", "Heuristic", "Homogeneous differential equations", "Infinite element method", "Integral equation", "Integral transform", "Integrating factor", "Integro-differential equation", "International Standard Book Number", "International Standard Serial Number", "Isaac Newton", "It\u00f4 calculus", "John Crank", "Jump process", "J\u00f3zef Maria Hoene-Wro\u0144ski", "Kiyoshi It\u00f4", "Langevin dynamics", "Langevin equation", "Lebesgue integral", "Leonhard Euler", "Linear differential equation", "Local volatility", "Lyapunov stability", "Marian Smoluchowski", "Markov property", "Martin Kutta", "Mathematical finance", "Mathematical model", "Measurable function", "Method of characteristics", "Method of undetermined coefficients", "Milstein method", "Moment (mathematics)", "Monte Carlo Method", "National Diet Library", "Natural science", "Navier\u2013Stokes equations", "Non-homogeneous differential equation", "Non-linear differential equation", "Normal distribution", "Notation for differentiation", "Numerical integration", "Numerical methods", "Ordinary differential equation", "Ordinary differential equations", "Partial differential equation", "Path integral formulation", "Paul Langevin", "Perturbation theory", "Petrov\u2013Galerkin method", "Phase portrait", "Phase space", "Phyllis Nicolson", "Physics", "Picard\u2013Lindel\u00f6f theorem", "Pink noise", "Population dynamics", "Power series solution of differential equations", "Probability distribution function", "Probability space", "Probability theory", "Quantitative finance", "Quantum mechanics", "Rate of convergence", "Rudolf Lipschitz", "Runge\u2013Kutta method (SDE)", "Runge\u2013Kutta methods", "Ruslan L. Stratonovich", "Schr\u00f6dinger equation", "Self-organized criticality", "Separation of variables", "Smoluchowski equation", "Social science", "Stochastic difference equation", "Stochastic partial differential equations", "Stochastic process", "Stochastic volatility", "Stock", "Stock price", "Stratonovich integral", "Stratonovich stochastic calculus", "Supersymmetric quantum mechanics", "Supersymmetric theory of stochastic dynamics", "Supersymmetry", "Thermal fluctuations", "Turbulence", "Variance", "White noise", "Wiener process", "Wronskian", "\u00c9mile Picard"], "references": ["http://linkinghub.elsevier.com/retrieve/pii/S0022247X13000449", "http://adsabs.harvard.edu/abs/1979PhRvL..43..744P", "http://adsabs.harvard.edu/abs/2001SIAMR..43..525H", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.6375", "http://doi.org/10.1016%2Fj.jmaa.2013.01.027", "http://doi.org/10.1103%2FPhysRevLett.43.744", "http://doi.org/10.1137%2FS0036144500378302", "http://www.worldcat.org/issn/1109-2769", "https://id.ndl.go.jp/auth/ndlna/00575718", "https://www.wikidata.org/wiki/Q1545585"]}, "Tag cloud": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2008", "Commons category link is on Wikidata", "Visualization (web)", "Web 2.0 neologisms", "Webarchive template wayback links"], "title": "Tag cloud", "method": "Tag cloud", "url": "https://en.wikipedia.org/wiki/Tag_cloud", "summary": "A tag cloud (word cloud, or weighted list in visual design) is a novelty visual representation of text data, typically used to depict keyword metadata (tags) on websites, or to visualize free form text. Tags are usually single words, and the importance of each tag is shown with font size or color. This format is useful for quickly perceiving the most prominent terms and for locating a term alphabetically to determine its relative prominence. When used as website navigation aids, the terms are hyperlinked to items associated with the tag.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9e/Foundation-l_word_cloud_without_headers_and_quotes.png", "https://upload.wikimedia.org/wikipedia/commons/d/d9/State_of_the_union_word_clouds.png", "https://upload.wikimedia.org/wikipedia/commons/7/79/Top_500_by_volume_on_the_NYSE.png", "https://upload.wikimedia.org/wikipedia/commons/a/a7/Web_2.0_Map.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0d/Wikipedia_Wordle_-_Top_1000_vital_article_hits.png", "https://upload.wikimedia.org/wikipedia/commons/e/ec/Word_population_tagcloud_2011.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["2002 State of the Union Address", "2011 State of the Union Address", "Adobe Flex", "ArXiv", "Collocation", "Concordance (publishing)", "Country population", "Del.icio.us", "Democracy", "Digital object identifier", "Douglas Coupland", "Flickr", "Folksonomy", "HTML", "Heuristics", "Index term", "International Standard Book Number", "Logarithm", "Mentimeter", "Metadata", "Microserfs", "PageRank", "Page layout", "Popularity", "Power law", "R (programming language)", "Search engine marketing", "Search engine optimization", "Social software", "Stewart Butterfield", "Stock market", "T-distributed stochastic neighbor embedding", "Tag (metadata)", "Technorati", "Text corpus", "Tf-idf", "Wayback Machine", "Web 2.0", "Word embedding"], "references": ["http://chir.ag/phernalia/preztags/", "http://www.austria-lexikon.at/attach/User/Trattner%20Christoph/ctrattner_IADIS_WWW_journal.pdf", "http://www.austria-lexikon.at/attach/User/Trattner%20Christoph/ht076-trattner.pdf", "http://www.37signals.com/svn/archives/000937.php", "http://www.echochamberproject.com/node/247", "http://services.alphaworks.ibm.com/manyeyes/view/SIk76IsOtha6qFGgix3cI2-", "http://services.alphaworks.ibm.com/manyeyes/view/Sh3S9FsOtha6OdUrBNWFF2-", "http://www.joelamantia.com/blog/archives/tag_clouds/text_clouds_a_new_form_of_tag_cloud.html", "http://www.joelamantia.com/ideas/tag-clouds-evolve-understanding-tag-clouds", "http://research.microsoft.com/en-us/um/people/nath/docs/sparkclouds_infovis2010.pdf", "http://www.nosolousabilidad.com/hassan/improving_tagclouds.pdf", "http://www.onlamp.com/pub/a/onlamp/2006/06/08/designing-tag-clouds.html", "http://www.readwriteweb.com/archives/tag_clouds_rip.php", "http://www.sciencedirect.com/science/article/pii/S0952197617301422", "http://www.smashingapps.com/2011/12/15/nine-excellent-yet-free-online-word-cloud-generators.html", "http://www.tagcrowd.com/blog/2011/03/05/state-of-the-union-2002-vs-2011/", "http://www.webbyawards.com/press/archived-speeches.php#2006", "http://wikistics.falsikon.de/latest/wikipedia/en/topics/Vital_articles.htm", "http://www.uni-due.de/~s400268/Lohmann09-interact.pdf", "http://www.phil-fak.uni-duesseldorf.de/fileadmin/Redaktion/Institute/Informationswissenschaft/stock/Knautz_Soubusta_Stock.pdf", "http://www.vis.uni-stuttgart.de/uploads/tx_vispublications/PrefixTagClouds-IV2013.pdf", "http://matriisi.ee.tut.fi/hypermedia/julkaisut/2007-salonen-som-clouds.pdf", "http://bielenberg.info/thesis.pdf", "http://www.markusstrohmaier.info/documents/2011_JoSCCPS-socialcom2010_extended.pdf", "http://www.wordle.net/show/wrdl/3017653/WikipediaTop1000VitalArticleHits", "http://arxiv.org/abs/0710.2156", "http://arxiv.org/abs/1708.03569", "http://arxiv.org/abs/cs/0604036", "http://arxiv.org/abs/cs/0703109", "http://arxiv.org/archive/cs.DB", "http://arxiv.org/archive/cs.IR", "http://doi.org/10.1504%2FIJSCCPS.2011.043603", "http://ieeexplore.ieee.org/abstract/document/8017641/", "http://wordclouds.visualdataweb.org/", "http://www2007.org/htmlposters/poster988/", "http://www.scottishcorpus.ac.uk/corpus/search/collocatecloud.php", "https://www.mentimeter.com/features/word-cloud", "https://static1.squarespace.com/static/5502f56fe4b0aa4bfbdae0a8/t/599a547af9a61eee6b38cf72/1503286395089/infovis17-word-clouds-apart.pdf", "https://web.archive.org/web/20041204231120/http://twiki.tensegrity.net/bin/view/Main/SearchReferralZeitgeist", "https://web.archive.org/web/20060426191534/http://www.37signals.com/svn/archives/000937.php", "https://web.archive.org/web/20060703183324/http://www.webbyawards.com/press/archived-speeches.php#2006", "https://web.archive.org/web/20060813162618/http://www.nosolousabilidad.com/hassan/improving_tagclouds.pdf", "https://web.archive.org/web/20071008061841/http://bielenberg.info/thesis.pdf", "https://web.archive.org/web/20071019035301/http://chir.ag/phernalia/preztags/", "https://web.archive.org/web/20071029115347/http://services.alphaworks.ibm.com/manyeyes/view/SIk76IsOtha6qFGgix3cI2-", "https://web.archive.org/web/20080214102610/http://services.alphaworks.ibm.com/manyeyes/view/Sh3S9FsOtha6OdUrBNWFF2-", "https://web.archive.org/web/20080910235655/http://www.joelamantia.com/blog/archives/tag_clouds/text_clouds_a_new_form_of_tag_cloud.html", "https://web.archive.org/web/20081224093118/http://matriisi.ee.tut.fi/hypermedia/julkaisut/2007-salonen-som-clouds.pdf", "https://web.archive.org/web/20091007173622/http://www.uni-due.de/~s400268/Lohmann09-interact.pdf", "https://web.archive.org/web/20110411071238/http://www.tagcrowd.com/blog/2011/03/05/state-of-the-union-2002-vs-2011/", "https://web.archive.org/web/20110717203420/http://www.phil-fak.uni-duesseldorf.de/fileadmin/Redaktion/Institute/Informationswissenschaft/stock/Knautz_Soubusta_Stock.pdf", "https://web.archive.org/web/20110719002236/http://www.alphaworks.ibm.com/tech/wordcloud", "https://web.archive.org/web/20120319093314/http://www.readwriteweb.com/archives/tag_clouds_rip.php", "https://web.archive.org/web/20120615114901/http://www.austria-lexikon.at/attach/User/Trattner%20Christoph/ctrattner_IADIS_WWW_journal.pdf", "https://web.archive.org/web/20120615160853/http://www.austria-lexikon.at/attach/User/Trattner%20Christoph/ht076-trattner.pdf", "https://web.archive.org/web/20130419181926/http://wikistics.falsikon.de/latest/wikipedia/en/topics/Vital_articles.htm", "https://web.archive.org/web/20130927181437/http://www.vis.uni-stuttgart.de/uploads/tx_vispublications/PrefixTagClouds-IV2013.pdf", "https://web.archive.org/web/20130927221723/http://www.wordle.net/show/wrdl/3017653/WikipediaTop1000VitalArticleHits", "https://web.archive.org/web/20130928054952/http://research.microsoft.com/en-us/um/people/nath/docs/sparkclouds_infovis2010.pdf", "https://web.archive.org/web/20131002095156/http://www.echochamberproject.com/node/247", "https://web.archive.org/web/20140223032659/http://wordclouds.visualdataweb.org/", "https://web.archive.org/web/20170514121504/http://www2007.org/htmlposters/poster988/"]}, "Case-control study": {"categories": ["CS1 maint: Uses authors parameter", "Design of experiments", "Epidemiology", "Nursing research", "Use dmy dates from April 2011"], "title": "Case\u2013control study", "method": "Case-control study", "url": "https://en.wikipedia.org/wiki/Case%E2%80%93control_study", "summary": "A case\u2013control study (also known as case\u2013referent study) is a type of observational study in which two existing groups differing in outcome are identified and compared on the basis of some supposed causal attribute. Case\u2013control studies are often used to identify factors that may contribute to a medical condition by comparing subjects who have that condition/disease (the \"cases\") with patients who do not have the condition/disease but are otherwise similar (the \"controls\"). They require fewer resources but provide less evidence for causal inference than a randomized controlled trial. We only get odds ratio from a case\u2013control study which is an inferior measure of strength of association as compared to relative risk.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b5/ExplainingCaseControlSJW.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Academic clinical trials", "Adaptive clinical trial", "Analysis of clinical trials", "Analysis of variance", "Animal testing", "Animal testing on non-human primates", "Asymptomatic carrier", "Attributable fraction among the exposed", "Attributable fraction for the population", "Austin Bradford Hill", "Auxology", "Bachelor of Science in Public Health", "Behavior change (public health)", "Behavioural change theories", "Biological hazard", "Biostatistics", "Blind experiment", "Carl Rogers Darnall", "Case fatality rate", "Case report", "Case series", "Case study", "Centers for Disease Control and Prevention", "Chief Medical Officer", "Child mortality", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Community health", "Correlation does not imply causation", "Council on Education for Public Health", "Cross-sectional study", "Cultural competence in health care", "Cumulative incidence", "Design of experiments", "Deviance (sociology)", "Diffusion of innovations", "Digital object identifier", "Disease surveillance", "Doctor of Public Health", "Ecological study", "Emergency sanitation", "Environmental health", "Epidemic", "Epidemiological methods", "Epidemiology", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Evidence-based medicine", "Experiment", "Family planning", "Fecal\u2013oral route", "First-in-man study", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Genetically modified food", "George Davey Smith", "Germ theory of disease", "Global health", "Globalization and disease", "Glossary of clinical research", "Good agricultural practice", "Good manufacturing practice", "HACCP", "Hand washing", "Hazard ratio", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Hierarchy of evidence", "Human factors and ergonomics", "Human nutrition", "Hygiene", "ISO 22000", "In vitro", "In vivo", "Incidence (epidemiology)", "Infant mortality", "Infection control", "Infectivity", "Injury prevention", "Intention-to-treat analysis", "International Standard Book Number", "John Snow (physician)", "Joseph Lister", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "List of epidemics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "Longitudinal study", "Margaret Sanger", "Mary Mallon", "Maternal health", "Medical anthropology", "Medical sociology", "Mental health", "Meta-analysis", "Ministry of Health and Family Welfare", "Miquel Porta", "Morbidity", "Mortality rate", "Multicenter trial", "Nested case\u2013control study", "Notifiable disease", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Odds ratio", "Open-label trial", "Open defecation", "Oral hygiene", "PRECEDE-PROCEED model", "Patient safety", "Patient safety organization", "Period prevalence", "Pharmaceutical policy", "Pharmacovigilance", "Point prevalence", "Population Impact Measures", "Population health", "Positive deviance", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Preventive healthcare", "Preventive nutrition", "Professional degrees of public health", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quarantine", "ROC curve", "Race and health", "Randomized controlled trial", "Randomized controlled trials", "Rare disease assumption", "Regression analysis", "Relative risk", "Relative risk reduction", "Reproducibility", "Reproductive health", "Retrospective cohort study", "Richard Doll", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Safe sex", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scientific control", "Seeding trial", "Selection bias", "Sexually transmitted infection", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Sociology of health and illness", "Specificity and sensitivity", "Statistical hypothesis testing", "Statistical power", "Student's t-test", "Survivorship bias", "Systematic review", "Theory of planned behavior", "Transtheoretical model", "Tropical disease", "United States Public Health Service", "Vaccination", "Vaccine trial", "Vector control", "Virulence", "Waterborne diseases", "World Health Organization", "World Toilet Organization", "Z-test"], "references": ["http://emj.bmj.com/content/20/1/54.full.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2035864", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2038856", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC437139", "http://www.ncbi.nlm.nih.gov/pubmed/11844534", "http://www.ncbi.nlm.nih.gov/pubmed/1251836", "http://www.ncbi.nlm.nih.gov/pubmed/13364389", "http://www.ncbi.nlm.nih.gov/pubmed/14772469", "http://www.ncbi.nlm.nih.gov/pubmed/15166201", "http://www.ncbi.nlm.nih.gov/pubmed/15213107", "http://www.ncbi.nlm.nih.gov/pubmed/15836892", "http://www.ncbi.nlm.nih.gov/pubmed/16014596", "http://www.ncbi.nlm.nih.gov/pubmed/16184164", "http://www.ncbi.nlm.nih.gov/pubmed/2190942", "http://www.ncbi.nlm.nih.gov/pubmed/7046823", "http://casestudywriter.org/", "http://doi.org/10.1001%2Fjama.294.2.218", "http://doi.org/10.1016%2FS0140-6736(02)07605-5", "http://doi.org/10.1016%2FS0140-6736(05)66379-9", "http://doi.org/10.1038%2Fsj.ebd.6400355", "http://doi.org/10.1093%2Fije%2F19.1.205", "http://doi.org/10.1093%2Fije%2Fdyh124", "http://doi.org/10.1136%2Fbmj.2.4682.739", "http://doi.org/10.1136%2Fbmj.2.5001.1071", "http://doi.org/10.1136%2Fbmj.38142.554479.AE", "http://doi.org/10.2307%2F2529852", "http://www.wtccc.org.uk/"]}, "Cochran's Q test": {"categories": ["Nonparametric statistics", "Statistical tests", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Cochran's Q test", "method": "Cochran's Q test", "url": "https://en.wikipedia.org/wiki/Cochran%27s_Q_test", "summary": "In statistics, in the analysis of two-way randomized block designs where the response variable can take only two possible outcomes (coded as 0 and 1), Cochran's Q test is a non-parametric statistical test to verify whether k treatments have identical effects. It is named after William Gemmell Cochran. Cochran's Q test should not be confused with Cochran's C test, which is a variance outlier test. Put in simple technical terms, Cochran's Q test requires that there only be a binary response (e.g. success/failure or 1/0) and that there be more than 2 groups of the same size. The test assesses whether the proportion of successes is the same between groups. Often it is used to assess if different observers of the same phenomenon have consistent results (interobserver variability).", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["Blocking (statistics)", "Chi-squared distribution", "Cochran's C test", "Copyright status of work by the U.S. government", "Digital object identifier", "Durbin test", "Friedman test", "International Standard Book Number", "JSTOR", "McNemar's test", "Multiple comparisons", "National Institute of Standards and Technology", "Non-parametric", "OCLC", "Quantile", "Randomized block design", "Sign test", "Significance level", "Statistical test", "Statistics", "William Gemmell Cochran"], "references": ["http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/cochran.htm", "http://www.nist.gov", "http://doi.org/10.1093%2Fbiomet%2F37.3-4.256", "http://www.jstor.org/stable/2332378", "http://www.worldcat.org/oclc/61365784", "https://www.worldcat.org/oclc/61365784"]}, "World Programming System": {"categories": ["All articles lacking reliable references", "Articles lacking reliable references from September 2014", "Business intelligence", "Data warehousing", "Incomplete lists from August 2010", "Pages using deprecated image syntax", "Proprietary commercial software for Linux", "Statistical software"], "title": "World Programming System", "method": "World Programming System", "url": "https://en.wikipedia.org/wiki/World_Programming_System", "summary": "The World Programming System, also known as WPS Analytics or WPS, is a software product developed by a company called World Programming. WPS allows users to create, edit and run programs written in the language of SAS.The program was the subject of a lawsuit by SAS Institute. The EU Court of Justice ruled in favor of World Programming, stating that the copyright protection does not extend to the software functionality, the programming language used and the format of the data files used by the program. It stated that there is no copyright infringement when a company which does not have access to the source code of a program studies, observes and tests that program to create another program with the same functionality.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/d/da/WPS_Workbench.png"], "links": ["AArch64", "Apache Hadoop", "Comma-separated values", "Computer programs", "Data (computing)", "Data compression", "Direct access storage device", "Eclipse (software)", "European Court of Justice", "Gartner", "Graphical user interface", "Greenplum", "HTML", "IBM AIX", "IBM DB2", "IBM Informix", "Integrated development environment", "Linux", "Linux on zSeries", "Linux on z Systems", "MacOS", "Microsoft SQL Server", "Microsoft Windows", "MySQL", "Netezza", "OLE DB", "Open Database Connectivity", "Operating system", "Oracle Database", "PDF", "PSPP", "ParAccel", "PostgreSQL", "PowerLinux", "Proprietary software", "Python (programming language)", "R (programming language)", "SAND CDBMS", "SAS Institute Inc. v World Programming Ltd", "SAS Institute Inc v World Programming Ltd", "SAS language", "SPSS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Solaris (operating system)", "Statistics", "Sybase", "Sybase IQ", "Teradata", "Vertica", "Virtual storage access method", "Windows 10", "World Programming", "XML", "Z/OS"], "references": ["http://www.gartner.com/doc/2716417", "http://www.kognitio.com/analyticalplatform", "http://www.worldprogramming.com/", "http://www.bailii.org/ew/cases/EWHC/Ch/2010/1829.html", "https://www.bloomberg.com/news/2012-05-02/copyright-can-t-block-software-reverse-engineering-court.html", "https://www.worldprogramming.com/", "https://www.worldprogramming.com/information/sas-language/modules/language/machine_learning", "https://www.worldprogramming.com/products/wps/modules/interface/cli", "https://www.worldprogramming.com/products/wps/modules/interface/workbench", "https://www.worldprogramming.com/products/wps/modules/interface/link", "https://www.worldprogramming.com/products/wps/modules/interface/communicate", "https://www.worldprogramming.com/products/wps/modules/language/core", "https://www.worldprogramming.com/products/wps/modules/language/graphing", "https://www.worldprogramming.com/products/wps/modules/language/statistics", "https://www.worldprogramming.com/products/wps/modules/language/time_series", "https://www.worldprogramming.com/products/wps/modules/language/interop_for_hadoop", "https://www.worldprogramming.com/products/wps/modules/language/interop_for_r", "https://www.worldprogramming.com/products/wps/modules/language/matrix_programming", "https://www.worldprogramming.com/products/wps/modules/language/interop_for_python", "https://www.worldprogramming.com/products/wps/overview", "https://www.worldprogramming.com/products/wps/platforms", "https://www.worldprogramming.com/products/wps/your-apps/data-support", "https://www.worldprogramming.com/products/wps/your-apps/language-support"]}, "Ecological correlation": {"categories": ["All articles needing additional references", "Articles needing additional references from November 2014", "Covariance and correlation"], "title": "Ecological correlation", "method": "Ecological correlation", "url": "https://en.wikipedia.org/wiki/Ecological_correlation", "summary": "In statistics, an ecological correlation (also spatial correlation) is a correlation between two variables that are group means, in contrast to a correlation between two variables that describe individuals. For example, one might study the correlation between physical activity and weight among sixth-grade children. A study at the individual level might make use of 100 children, then measure both physical activity and weight; the correlation between the two variables would be at the individual level. By contrast, another study might make use of 100 classes of sixth-grade students, then measure the mean physical activity and the mean weight of each of the 100 classes. A correlation between these group means would be an example of an ecological correlation.\nBecause a correlation describes the measured strength of a relationship, correlations at the group level can be much higher than those at the individual level. Thinking both are equal is an example of ecological fallacy.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Complete spatial randomness", "Correlation", "Ecological fallacy", "Ecological regression", "Geographic information science", "International Standard Book Number", "Mean", "Modifiable Areal Unit Problem", "Spatial autocorrelation", "Spatial econometrics", "Spatial epidemiology", "Statistics"], "references": ["https://books.google.com/books?id=9jHYSm_8Fz4C&pg=PA119"]}, "Dependent and independent variables": {"categories": ["Design of experiments", "Independence (probability theory)", "Mathematical terminology", "Regression analysis", "Webarchive template wayback links"], "title": "Dependent and independent variables", "method": "Dependent and independent variables", "url": "https://en.wikipedia.org/wiki/Dependent_and_independent_variables", "summary": "In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables. The dependent variables represent the output or outcome whose variation is being studied. The independent variables, also known in a statistical context as regressors, represent inputs or causes, that is, potential reasons for variation. In an experiment, any variable that the experimenter manipulates can be called an independent variable. Models and experiments test the effects that the independent variables have on the dependent variables. Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential confounding effect.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f8/Polynomialdeg2.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg"], "links": ["Abscissa", "Bias (statistics)", "Blocking (statistics)", "Calculus", "Cartesian product", "Confounding", "Control variable", "Covariance", "Data mining", "Dependent variable", "Design of experiments", "Digital object identifier", "Econometrics", "Errors and residuals", "Experimental science", "Feature (machine learning)", "Function (mathematics)", "Goodness of fit", "Graph of a function", "Horizontal axis", "Hypothesis", "Independence (probability theory)", "International Standard Book Number", "Linear model", "Machine learning", "Manifold (mathematics)", "Mathematical modeling", "Medical statistics", "Multivariable calculus", "Multivariate statistics", "Omitted variable bias", "Ordinate", "Pattern recognition", "Prediction", "RapidMiner", "Reliability theory", "Risk factor", "Set (mathematics)", "Set theory", "Simulation", "Statistical model", "Stochastic", "Subset", "Supervised learning", "Test data", "Variable and attribute (research)", "Vector-valued functions", "Vertical axis", "Wayback Machine"], "references": ["http://1xltkxylmzx3z8gd647akcdvov.wpengine.netdna-cdn.com/wp-content/uploads/2013/10/rapidminer-5.0-manual-english_v1.0.pdf", "http://onlinestatbook.com/2/introduction/variables.html", "http://doi.org/10.1080%2F15210608709379549", "https://web.archive.org/web/20140210002634/http://1xltkxylmzx3z8gd647akcdvov.wpengine.netdna-cdn.com/wp-content/uploads/2013/10/rapidminer-5.0-manual-english_v1.0.pdf"]}, "Dot plot (statistics)": {"categories": ["Statistical charts and diagrams"], "title": "Dot plot (statistics)", "method": "Dot plot (statistics)", "url": "https://en.wikipedia.org/wiki/Dot_plot_(statistics)", "summary": "A dot chart or dot plot is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles. There are two common, yet very different, versions of the dot chart. The first has been used in hand-drawn (pre-computer era) graphs to depict distributions going back to 1884. The other version is described by William S. Cleveland as an alternative to the bar chart, in which dots are used to depict the quantitative values (e.g. counts) associated with categorical variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/bc/Dotplot_of_random_values_2.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Box plot", "Continuous function", "Digital object identifier", "Handle System", "Histogram", "International Standard Book Number", "JSTOR", "Kernel density estimation", "Outlier", "Paul Murrell", "Peter Dalgaard", "Quantitative data", "R (programming language)", "Statistics", "Stemplot", "Univariate", "William S. Cleveland"], "references": ["http://www.b-eye-network.com/view/2468", "http://hdl.handle.net/2027%2Fmdp.39015026891187", "http://www.stat.auckland.ac.nz/~paul/RGraphics/rgraphics.html", "http://doi.org/10.2307%2F2686111", "http://www.jstor.org/stable/2686111"]}, "Ancestral graph": {"categories": ["Extensions and generalizations of graphs", "Graphical models"], "title": "Ancestral graph", "method": "Ancestral graph", "url": "https://en.wikipedia.org/wiki/Ancestral_graph", "summary": "In statistics and Markov modeling, an ancestral graph is a type of mixed graph to provide a graphical representation for the result of marginalizing one or more vertices in a graphical model that takes the form of a directed acyclic graph.\n\n", "images": [], "links": ["CiteSeerX", "Digital object identifier", "Directed acyclic graph", "Graphical model", "Markov model", "Mathematical Reviews", "Mixed graph", "Mixed graphs", "Statistics"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.4906", "http://www.ams.org/mathscinet-getitem?mr=1926166", "http://doi.org/10.1214%2Faos%2F1031689015"]}, "Bregman divergence": {"categories": ["Geometric algorithms", "Statistical distance"], "title": "Bregman divergence", "method": "Bregman divergence", "url": "https://en.wikipedia.org/wiki/Bregman_divergence", "summary": "In mathematics, a Bregman divergence or Bregman distance is similar to a metric, but satisfies neither the triangle inequality nor symmetry.\nBregman divergences are named after Lev M. Bregman, who introduced the concept in 1967.", "images": [], "links": ["ArXiv", "Bibcode", "Computational geometry", "Conference on Neural Information Processing Systems", "Convex conjugate", "Convex function", "Convex set", "Delaunay triangulation", "Digital object identifier", "Discrete and Computational Geometry", "Hamming distance", "IEEE Signal Processing Letters", "IEEE Transactions on Information Theory", "Itakura\u2013Saito distance", "Jensen\u2013Shannon divergence", "Journal of Machine Learning Research", "Kullback\u2013Leibler divergence", "Lev M. Bregman", "Mahalanobis distance", "Mathematics", "Metric (mathematics)", "Mutual information", "Precision and recall", "Projective duality", "Stein's loss", "Submodular set function", "Taylor expansion", "Triangle inequality", "Von Neumann entropy", "Voronoi diagram"], "references": ["http://www.mdpi.com/1099-4300/19/5/206", "http://www.springerlink.com/index/10.1007/978-3-642-30232-9", "http://adsabs.harvard.edu/abs/2017Entrp..19..206H", "http://adsabs.harvard.edu/abs/2017ISPL...24.1123N", "http://jmlr.csail.mit.edu/papers/v6/banerjee05b.html", "http://www.ee.washington.edu/research/guptalab/publications/FrigyikSrivastavaGupta.pdf", "http://hal.archives-ouvertes.fr/hal-00488441/en/", "http://www.lix.polytechnique.fr/~nielsen/ISVD09-GenBregmanVD.pdf", "http://www1.univ-ag.fr/~rnock/Articles/Drafts/book12-nmbn.pdf", "http://www.csl.sony.co.jp/person/nielsen/PT/SoCG07/", "http://arxiv.org/abs/0711.3242", "http://arxiv.org/abs/1004.5049", "http://arxiv.org/abs/1701.01010", "http://arxiv.org/abs/1702.04877", "http://arxiv.org/abs/cs/0611123", "http://arxiv.org/archive/cs.CG", "http://doi.org/10.1007%2Fs00454-010-9256-1", "http://doi.org/10.1016%2F0041-5553(67)90040-7", "http://doi.org/10.1109%2FISVD.2009.15", "http://doi.org/10.1109%2FLSP.2017.2712195", "http://doi.org/10.1109%2FTIT.2008.929943", "http://doi.org/10.1109%2FTIT.2011.2159046", "http://doi.org/10.1145%2F1137856.1137931", "http://doi.org/10.1145%2F1247069.1247089", "http://doi.org/10.3390%2Fe19050206", "https://www.ee.washington.edu/techsite/papers/documents/UWEETR-2008-0001.pdf", "https://web.archive.org/web/20100812221422/http://www.ee.washington.edu/research/guptalab/publications/FrigyikSrivastavaGupta.pdf", "https://arxiv.org/abs/1810.09113"]}, "FLAME clustering": {"categories": ["Cluster analysis algorithms", "Wikipedia articles with possible conflicts of interest from August 2010"], "title": "FLAME clustering", "method": "FLAME clustering", "url": "https://en.wikipedia.org/wiki/FLAME_clustering", "summary": "Fuzzy clustering by Local Approximation of MEmberships (FLAME) is a data clustering algorithm that defines clusters in the dense parts of a dataset and performs cluster assignment solely based on the neighborhood relationships among objects. The key feature of this algorithm is that the neighborhood relationships among neighboring objects in the feature space are used to constrain the memberships of neighboring objects in the fuzzy membership space.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Unbalanced_scales.svg", "https://upload.wikimedia.org/wikipedia/en/2/26/FLAME_Demo.png"], "links": ["Data clustering", "Fuzzy clustering"], "references": ["http://www.biomedcentral.com/1471-2105/8/3", "http://flame-clustering.googlecode.com/svn/trunk/"]}, "Banburismus": {"categories": ["Alan Turing", "Banbury", "Bletchley Park", "Cryptographic attacks", "Statistical algorithms", "Use British English from April 2018", "Use dmy dates from April 2018"], "title": "Banburismus", "method": "Banburismus", "url": "https://en.wikipedia.org/wiki/Banburismus", "summary": "Banburismus was a cryptanalytic process developed by Alan Turing at Bletchley Park in Britain during the Second World War. It was used by Bletchley Park's Hut 8 to help break German Kriegsmarine (naval) messages enciphered on Enigma machines. The process used sequential conditional probability to infer information about the likely settings of the Enigma machine. It gave rise to Turing's invention of the ban as a measure of the weight of evidence in favour of a hypothesis. This concept was later applied in Turingery and all the other methods used for breaking the Lorenz cipher.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/Enigma-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ed/Part_of_a_Banbury_Sheet_as_used_in_Banburismus.jpg"], "links": ["Alan Turing", "Alan Turing: The Enigma", "Andrew Hodges", "Anthony Sale", "Ban (unit)", "Banbury", "Bayesian inference", "Bigram", "Biometrika", "Biuro Szyfr\u00f3w", "Bletchley Park", "Bomba (cryptography)", "Bombe", "Cadix", "Clock (cryptography)", "Conditional probability", "Conel Hugh O'Donel Alexander", "Cryptanalysis", "Cryptanalysis of the Enigma", "Cyclometer", "Digital object identifier", "Enigma machine", "Enigma procedures", "Enigma rotor details", "Grill (cryptology)", "HMS Griffin (H31)", "Harry Hinsley", "Hugh Foss", "Hugh Sebag-Montefiore", "Hut 3", "Hut 6", "Hut 8", "I. J. Good", "Index of Coincidence", "International Standard Book Number", "Jack Copeland", "Jerzy R\u00f3\u017cycki", "Joan Clarke", "John Herivel", "Karl Popper", "Known-plaintext attack", "Kriegsmarine", "Lorenz cipher", "Mathematical Reviews", "Military intelligence", "Narvik", "Naval trawler", "North Sea", "Norway", "PC Bruno", "Polish Enigma double", "Second World War", "Sequential analysis", "Tabulating machine", "Trigram", "Turingery", "Ultra", "United Kingdom", "Wheels of the Enigma", "Zygalski sheets"], "references": ["http://www.ellsbury.com/gne/gne-000.htm", "http://www.ellsbury.com/hut8/hut8-000.htm", "http://www.naval-history.net/xGM-Chrono-10DD-25G-Griffin.htm", "http://www.ams.org/mathscinet-getitem?mr=0548210", "http://doi.org/10.1093%2Fbiomet%2F66.2.393", "http://www.gap-system.org/~history/Printonly/Clarke_Joan.html", "http://www.inference.phy.cam.ac.uk/mackay/itila/", "http://www.codesandciphers.org.uk/documents/cryptdict/page05.htm", "http://stoneship.org.uk/~steve/banburismus.html", "https://web.archive.org/web/20110607183723/http://www.gap-system.org/~history/Printonly/Clarke_Joan.html", "https://web.archive.org/web/20160217105359/http://www.inference.phy.cam.ac.uk/mackay/itila/book.html"]}, "Hannan\u2013Quinn information criterion": {"categories": ["Model selection", "Regression variable selection"], "title": "Hannan\u2013Quinn information criterion", "method": "Hannan\u2013Quinn information criterion", "url": "https://en.wikipedia.org/wiki/Hannan%E2%80%93Quinn_information_criterion", "summary": "In statistics, the Hannan\u2013Quinn information criterion (HQC) is a criterion for model selection. It is an alternative to Akaike information criterion (AIC) and Bayesian information criterion (BIC). It is given as\n\n \n \n \n \n H\n Q\n C\n \n =\n \u2212\n 2\n \n L\n \n m\n a\n x\n \n \n +\n 2\n k\n ln\n \u2061\n (\n ln\n \u2061\n (\n n\n )\n )\n ,\n \n \n \n {\\displaystyle \\mathrm {HQC} =-2L_{max}+2k\\ln(\\ln(n)),\\ }\n where \n \n \n \n \n L\n \n m\n a\n x\n \n \n \n \n {\\displaystyle L_{max}}\n is the log-likelihood, k is the number of parameters, and n is the number of observations.\nBurnham & Anderson (2002, p. 287) say that HQC, \"while often cited, seems to have seen little use in practice\". They also note that HQC, like BIC, but unlike AIC, is not an estimator of Kullback\u2013Leibler divergence. Claeskens & Hjort (2008, ch. 4) note that HQC, like BIC, but unlike AIC, is not asymptotically efficient; however, it misses the optimal estimation rate by a very small ln ln n factor. They further point out that whatever method is being used for fine-tuning the criterion will be more important in practice than the term ln ln n, since this latter number is small even for very large n; however, the \n \n \n \n ln\n \u2061\n ln\n \u2061\n n\n \n \n {\\displaystyle \\ln \\ln n}\n term ensures that, unlike AIC, HQC is strongly consistent. It follows from the law of the iterated logarithm that any strongly consistent method must miss efficiency by at least a ln ln n factor, so in this sense HQC is asymptotically very well-behaved. Van der Pas and Gr\u00fcnwald prove that model selection based on a modified Bayesian estimator, the so-called switch distribution, in many cases behaves asymptotically like HQC, while retaining the advantages of Bayesian methods such as the use of priors etc.", "images": [], "links": ["Akaike information criterion", "Barry Gerard Quinn", "Bayesian information criterion", "Deviance information criterion", "Edward J. Hannan", "Efficiency (statistics)", "Focused information criterion", "Gerda Claeskens", "International Standard Book Number", "Journal of the Royal Statistical Society", "Kullback\u2013Leibler divergence", "Law of the iterated logarithm", "Model selection", "Nils Lid Hjort", "Observations", "Parameters", "Statistics"], "references": ["http://www3.stat.sinica.edu.tw/statistica/", "http://www3.stat.sinica.edu.tw/statistica/oldpdf/A3n214.pdf"]}, "Round robin test": {"categories": ["Design of experiments", "Statistical hypothesis testing"], "title": "Round robin test", "method": "Round robin test", "url": "https://en.wikipedia.org/wiki/Round_robin_test", "summary": "In experimental methodology, a round robin test is an interlaboratory test (measurement, analysis, or experiment) performed independently several times. This can involve multiple independent scientists performing the test with the use of the same method in different equipment, or a variety of methods and equipment. In reality it is often a combination of the two, for example if a sample is analysed, or one (or more) of its properties is measured by different laboratories using different methods, or even just by different units of equipment of identical construction. \nA round robin program is a Measurement Systems Analysis technique which uses Analysis of Variance (ANOVA) random effects model to assess a measurement system.\n\n", "images": [], "links": ["ANOVA", "ASTM", "Experiment", "Experimental design", "Measurement Systems Analysis", "Random effects model", "Reproducibility", "Standard Reference Material", "Test method"], "references": ["http://www.itl.nist.gov/div898/handbook/", "http://www.proficiency-test.info/", "http://www.iupac.org/projects/1999/1999-021-1-400.html", "http://www.pri-network.org/PRI/IPT-vs-Round-Robin.id.27.htm"]}, "Realization (probability)": {"categories": ["Statistical data types"], "title": "Realization (probability)", "method": "Realization (probability)", "url": "https://en.wikipedia.org/wiki/Realization_(probability)", "summary": "In probability and statistics, a realization, observation, or observed value, of a random variable is the value that is actually observed (what actually happened). The random variable itself is the process dictating how the observation comes about. Statistical quantities computed from realizations without deploying a statistical model are often called \"empirical\", as in empirical distribution function or empirical probability.\nConventionally, to avoid confusion, upper case letters denote random variables; the corresponding lower case letters denote their realizations.In more formal probability theory, a random variable is a function X defined from a sample space \u03a9 to a measurable space called the state space. If an element in \u03a9 is mapped to an element in state space by X, then that element in state space is a realization. (In fact, a random variable cannot be an arbitrary function and it needs to satisfy another condition: it needs to be measurable.) Elements of the sample space can be thought of as all the different possibilities that could happen; while a realization (an element of the state space) can be thought of as the value X attains when one of the possibilities did happen. Probability is a mapping that assigns numbers between zero and one to certain subsets of the sample space. Subsets of the sample space that contain only one element are called elementary events. The value of the random variable (that is, the function) X at a point \u03c9 \u2208 \u03a9,\n\n \n \n \n x\n =\n X\n (\n \u03c9\n )\n \n \n {\\displaystyle x=X(\\omega )}\n is called a realization of X.\n\n", "images": [], "links": ["Elementary event", "Empirical", "Empirical distribution function", "Empirical probability", "Function (mathematics)", "Map (mathematics)", "Measurable", "Probability", "Probability theory", "Random variable", "Random variate", "Sample space", "Statistics", "Subset"], "references": []}, "SCORUS": {"categories": ["All stub articles", "Official statistics", "Statistical organizations", "Statistics stubs"], "title": "SCORUS", "method": "SCORUS", "url": "https://en.wikipedia.org/wiki/SCORUS", "summary": "An acronym for \"Standing Committee of Regional and Urban Statistics\", SCORUS is a sub-committee of the International Association for Official Statistics (IAOS) which is a section of the International Statistical Institute. The sub-committee has specific responsibility for regional and urban statistics and research. Its members form a dedicated international network of persons interested in regional and urban statistical issues.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["International Association for Official Statistics", "International Statistical Institute", "Statistics"], "references": ["http://www.scorus.org"]}, "Beta-binomial distribution": {"categories": ["Compound probability distributions", "Conjugate prior distributions", "Discrete distributions", "Pages using deprecated image syntax"], "title": "Beta-binomial distribution", "method": "Beta-binomial distribution", "url": "https://en.wikipedia.org/wiki/Beta-binomial_distribution", "summary": "In probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random. The beta-binomial distribution is the binomial distribution in which the probability of success at each trial is fixed but randomly drawn from a beta distribution prior to n Bernoulli trials. It is frequently used in Bayesian statistics, empirical Bayes methods and classical statistics to capture overdispersion in binomial type distributed data.\nIt reduces to the Bernoulli distribution as a special case when n = 1. For \u03b1 = \u03b2 = 1, it is the discrete uniform distribution from 0 to n. It also approximates the binomial distribution arbitrarily well for large \u03b1 and \u03b2. The beta-binomial is a one-dimensional version of the Dirichlet-multinomial distribution, as the binomial and beta distributions are univariate versions of the multinomial and Dirichlet distributions, respectively.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Beta-binomial_cdf.png", "https://upload.wikimedia.org/wikipedia/commons/e/e1/Beta-binomial_distribution_pmf.png"], "links": ["ARGUS distribution", "Akaike information criterion", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli trial", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Burstiness", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Classical statistics", "Compound Poisson distribution", "Compound distribution", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Empirical Bayes methods", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized hypergeometric series", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Integer", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "Law of total expectation", "Law of total variance", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Mammal", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Method of moments (statistics)", "Mittag-Leffler distribution", "Mixture distribution", "Moment-generating function", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Natural numbers", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Overdispersion", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Polya urn model", "Posterior distribution", "Probability distribution", "Probability mass function", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "R (programming language)", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Sample moments", "Saxony", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Trivers\u2013Willard hypothesis", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Urn model", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://research.microsoft.com/~minka/papers/dirichlet/", "http://research.microsoft.com/~minka/software/fastfit/", "http://it.stlawu.edu/~msch/biometrics/papers.htm", "http://www.math.wm.edu/~leemis/chart/UDR/UDR.html", "http://foundry.sandia.gov/releases/latest/javadoc-api/gov/sandia/cognition/statistics/distribution/BetaBinomialDistribution.html", "https://cran.r-project.org/web/packages/VGAM/index.html"]}, "Equipossible": {"categories": ["All articles lacking in-text citations", "All articles lacking sources", "All articles needing expert attention", "Articles lacking in-text citations from June 2012", "Articles lacking sources from July 2017", "Articles needing expert attention from February 2009", "Articles needing expert attention with no reason or talk parameter", "Philosophy articles needing expert attention", "Possibility", "Probability interpretations"], "title": "Equipossibility", "method": "Equipossible", "url": "https://en.wikipedia.org/wiki/Equipossibility", "summary": "Equipossibility is a philosophical concept in possibility theory that is a precursor to the notion of equiprobability in probability theory. It is used to distinguish what can occur in a probability experiment. For example, when considering rolling a six-sided die, why do we typically view the possible outcomes as {1,2,3,4,5,6} rather than, say, {6, not 6}? The former set contains equally possible alternatives, while the latter does not because there are five times as many alternatives inherent in 'not 6' as in 6. This is true even if the die is biased so that 6 and 'not 6' are equally likely to occur.\nBy the Principle of Indifference of Laplace, equipossible alternatives may be accorded equal probabilities if nothing more is known about the underlying probability distribution.\nIt is a matter of contention whether the concept of equipossibility, also called equispecificity (from equispecific), can truly be distinguished from the concept of equiprobability.\nIn Bayesian inference, a widely used definition of equipossibility is \"a transformation group which leaves invariant one's state of knowledge\". Equiprobability is then defined by normalizing the Haar measure of this symmetry group. This is known as the principle of transformation groups.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayesian inference", "Equiprobability", "Haar measure", "Laplace", "Philosophy", "Possibility theory", "Principle of Indifference", "Principle of transformation groups", "Probability distribution", "Probability theory", "Transformation group"], "references": ["http://socrates.berkeley.edu/~fitelson/148/kyburg_3.pdf", "http://www.stats.org.uk/probability/classical.html"]}, "Monte Carlo method": {"categories": ["All articles with dead external links", "Articles with dead external links from October 2017", "Articles with short description", "Commons category link is on Wikidata", "Computational physics", "Monte Carlo methods", "Numerical analysis", "Randomized algorithms", "Risk analysis methodologies", "Sampling techniques", "Statistical approximations", "Statistical mechanics", "Stochastic simulation", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Monte Carlo method", "method": "Monte Carlo method", "url": "https://en.wikipedia.org/wiki/Monte_Carlo_method", "summary": "Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. Their essential idea is using randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.\nIn physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean-Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of risk in business and, in math, evaluation of multidimensional definite integrals with complicated boundary conditions. In application to systems engineering problems (space, oil exploration, aircraft design, etc.) problems, Monte Carlo\u2013based predictions of failure, cost overruns and schedule overruns are routinely better than human intuition or alternative \"soft\" methods.In principle, Monte Carlo methods can be used to solve any problem having a probabilistic interpretation. By the law of large numbers, integrals described by the expected value of some random variable can be approximated by taking the empirical mean (a.k.a. the sample mean) of independent samples of the variable. When the probability distribution of the variable is parametrized, mathematicians often use a Markov chain Monte Carlo (MCMC) sampler. The central idea is to design a judicious Markov chain model with a prescribed stationary probability distribution. That is, in the limit, the samples being generated by the MCMC method will be samples from the desired (target) distribution. By the ergodic theorem, the stationary distribution is approximated by the empirical measures of the random states of the MCMC sampler.\nIn other problems, the objective is generating draws from a sequence of probability distributions satisfying a nonlinear evolution equation. These flows of probability distributions can always be interpreted as the distributions of the random states of a Markov process whose transition probabilities depend on the distributions of the current random states (see McKean-Vlasov processes, nonlinear filtering equation). In other instances we are given a flow of probability distributions with an increasing level of sampling complexity (path spaces models with an increasing time horizon, Boltzmann-Gibbs measures associated with decreasing temperature parameters, and many others). These models can also be seen as the evolution of the law of the random states of a nonlinear Markov chain. A natural way to simulate these sophisticated nonlinear Markov processes is to sample a large number of copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled empirical measures. In contrast with traditional Monte Carlo and MCMC methodologies these mean field particle techniques rely on sequential interacting samples. The terminology mean field reflects the fact that each of the samples (a.k.a. particles, individuals, walkers, agents, creatures, or phenotypes) interacts with the empirical measures of the process. 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group(s). In comparative experiments, members of the complementary group, the control group, receive either no treatment or a standard treatment.A placebo control group can be used to support a double-blind study, where a portion of patients are given a placebo medication (typically, sugar pill), in order to observe the patients are taking their medications in the manner as proscribed, with no major procedural differences between the treatment group(s) versus the placebo control group(s). In such cases, a 3rd, nontreatment control group can be used to measure the placebo effect, as the difference between placebo subjects and the non-treatment subjects, perhaps paired by age group, twin/triplet or other related factors.\nFor the conclusions drawn from the results of an experiment to have validity, it is essential that the items or patients assigned to treatment and control groups be representative of the same population. In some experiments, such as many in agriculture or psychology, this can be achieved by randomly assigning items from a common population to one of the treatment and control groups. In studies of twins involving just one treatment group and a control group, it is statistically efficient to do this random assignment separately for each pair of twins, so that one is in the treatment group and one in the control group.\nIn some medical studies, where it may be unethical not to treat patients who present with symptoms, controls may be given a standard treatment, rather than no treatment at all. An alternative is to select controls from a wider population, provided that this population is well-defined and that those presenting with symptoms at the clinic are representative of those in the wider population. Another method to reduce ethical concerns would be to test early-onset symptoms, with enough time later to offer real treatments to the control subjects, and let those subjects know the first treatments are \"experimental\" and might not be as effective as later treatments, again with the understanding there would be ample time to try other remedies.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Blocking (statistics)", "Cgroups", "Control variable", "Design of experiments", "Digital object identifier", "Dorota Dabrowska", "Double-blind study", "Efficiency (statistics)", "Experimental unit", "Hawthorne effect", "Ian Hacking", "Internal validity", "International Standard Book Number", "Isis (journal)", "Jerzy Neyman", "Mathematical Reviews", "Placebo", "Placebo effect", "PubMed Identifier", "Random assignment", "Scientific control", "Statistical population", "Statistics", "Stephen M. Stigler", "Sugar pill", "Terence Speed", "Wait list control group"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/9519574", "http://www.ams.org/mathscinet-getitem?mr=1092986", "http://www.ams.org/mathscinet-getitem?mr=2363107", "http://www.ams.org/mathscinet-getitem?mr=2422352", "http://doi.org/10.1002%2Fpsb.344", "http://doi.org/10.1086%2F354775", "http://doi.org/10.1086%2F383850", "http://doi.org/10.1086%2F444032", "http://doi.org/10.1214%2Fss%2F1177012031", "http://www.maths.qmul.ac.uk/~rab/DOEbook/", "https://books.google.com/?id=T3wWj2kVYZgC&printsec=frontcover", "https://books.google.com/books?id=RvJeBwAAQBAJ&pg=PA13&lpg=PA13&dq=placebo+healthier+choices&source=bl"]}, "Predictive modelling": {"categories": ["All articles with unsourced statements", "Articles needing POV-check from April 2016", "Articles with unsourced statements from March 2013", "Business intelligence", "CS1 errors: dates", "Regression models", "Statistical classification", "Wikipedia articles needing page number citations from September 2016"], "title": "Predictive modelling", "method": "Predictive modelling", "url": "https://en.wikipedia.org/wiki/Predictive_modelling", "summary": "Predictive modelling uses statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place.In many cases the model is chosen on the basis of detection theory to try to guess the probability of an outcome given a set amount of input data, for example given an email determining how likely that it is spam.\nModels can use one or more classifiers in trying to determine the probability of a set of data belonging to another set, say spam or 'ham'.\nDepending on definitional boundaries, predictive modelling is synonymous with, or largely overlapping with, the field of machine learning, as it is more commonly referred to in academic or research and development contexts. When deployed commercially, predictive modelling is often referred to as predictive analytics.\nPredictive modelling is often contrasted with causal modelling/analysis. In the former, one may be entirely satisfied to make use of indicators of, or proxies for, the outcome of interest. In the latter, one seeks to determine true cause-and-effect relationships. This distinction has given rise to a burgeoning literature in the fields of research methods and statistics and to the common statement that \"correlation is not the same as causation.\"", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5c/Ambox_scales.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1e/Artificial_Neural_Network.jpg"], "links": ["Accelerometer", "Alan Greenspan", "Archaeology", "Artificial neural network", "Biostatistics", "Churn rate", "Classifier (mathematics)", "Collateralized debt obligation", "Covariance", "Cross-sell", "Customer attrition", "Customer relationship management", "Data mining", "Decision tree learning", "Detection theory", "Digital object identifier", "Discrete variable", "E-mail spam", "Email", "Explanatory variable", "Federal Reserve", "Financial crisis of 2008", "GPS", "Generalized additive model", "Generalized linear model", "Gordon Willey", "Gradient boosting", "Group method of data handling", "International Standard Book Number", "K-nearest neighbor algorithm", "Logistic regression", "Long Term Capital Management", "Machine learning", "Macroeconomic", "Multinomial regression", "Multivariate adaptive regression splines", "Naive Bayes classifier", "Nobel Memorial Prize in Economic Sciences", "Non-parametric models", "Ordinary least squares", "Parametric model", "Parkland Health & Hospital System", "Poisson regression", "Prediction interval", "Predictive analytics", "Probability of default", "Random forest", "Regression model", "Robust regression", "Semi-parametric model", "Semiparametric regression", "Seymour Geisser.", "Statistical model", "Support vector machine", "Uplift modelling", "Upselling", "Usage-based insurance", "Vehicle insurance", "Wall Street"], "references": ["http://systemtradersuccess.com/predictive-model-based-trading-systems-2/", "http://forteconsultancy.wordpress.com/2010/05/17/wondering-what-lies-ahead-the-power-of-predictive-modeling/", "http://doi.org/10.1007%2Fbf00058655", "http://doi.org/10.1038%2Fs41598-018-27946-5", "https://www.nature.com/articles/s41598-018-27946-5", "https://www.quantinsti.com/blog/predictive-modeling-algorithmic-trading/", "https://link.springer.com/article/10.1023%2FA:1018054314350", "https://innovations.ahrq.gov/profiles/hospital-uses-data-analytics-and-predictive-modeling-identify-and-allocate-scarce-resources"]}, "ViSta, The Visual Statistics system": {"categories": ["Statistical software"], "title": "ViSta, The Visual Statistics system", "method": "ViSta, The Visual Statistics system", "url": "https://en.wikipedia.org/wiki/ViSta,_The_Visual_Statistics_system", "summary": "ViSta, the Visual Statistics system is a freeware statistical system developed by Forrest W. Young of the University of North Carolina. ViSta current version maintained by Pedro M. Valero-Mora of the University of Valencia and can be found at [1]. Old versions of ViSta and of the documentation can be found at [2].\nViSta incorporates a number of special features that are of both theoretical and practical interest: The workmap keeps record of the datasets opened by the user and the subsequent statistical transformations and analysis applied to them. Spreadplots show all the relevant plots for a dataset with a given combination of types of variables. Graphics are the primary way of output in contrast with traditional statistics packages where the textual output is more important.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/archive/4/4a/20160405223351%21Commons-logo.svg"], "links": ["Forrest W. Young", "Freeware", "International Standard Book Number", "Michael Friendly", "University of North Carolina"], "references": ["http://www.uv.es/visualstats/Book", "http://www.visualstats.org", "http://www.visualstats.org/", "https://www.uv.es/visualstats/Book/ViSta%207.9.2.8.zip", "https://web.archive.org/web/20090323151854/http://www.mdp.edu.ar/psicologia/vista/vista.htm", "https://web.archive.org/web/20100324032203/http://www.math.yorku.ca/SCS/Gallery/milestone/sec9.html"]}, "Combinatorial design": {"categories": ["CS1 maint: Multiple names: authors list", "Design of experiments", "Design theory", "Set families"], "title": "Combinatorial design", "method": "Combinatorial design", "url": "https://en.wikipedia.org/wiki/Combinatorial_design", "summary": "Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in sudoku grids.\nCombinatorial design theory can be applied to the area of design of experiments. Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including; Finite geometry, tournament scheduling, lotteries, mathematical biology, algorithm design and analysis, networking, group testing and cryptography.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/af/Fano_plane.svg"], "links": ["1-factorization", "15 schoolgirl problem", "Algebraic statistics", "Algorithm design", "Analysis of covariance", "Analysis of variance", "Annals of Eugenics", "Annals of Mathematical Statistics", "Anne Penfold Street", "Association scheme", "Bayesian experimental design", "Bayesian linear regression", "Bent function", "Bhat-Nayak Vasanti N.", "Blind experiment", "Block design", "Blocking (statistics)", "Box\u2013Behnken design", "Bruck\u2013Ryser theorem", "Bruck\u2013Ryser\u2013Chowla theorem", "Cambridge University Press", "Cardinality", "Central composite design", "Cochran's theorem", "Combinatorics", "Commutative", "Comparing means", "Completely randomized design", "Computer network", "Confounding", "Contrast (statistics)", "Costas array", "Covariate", "Crossover study", "Cryptography", "Damaraju Raghavarao", "De Bruijn\u2013Erd\u0151s theorem (incidence geometry)", "Design of experiments", "Difference set", "Distributive property", "Effect size", "Error-correcting code", "Experiment", "Experimental unit", "External validity", "Factorial design", "Factorial experiment", "Fano plane", "Finite field", "Finite geometry", "Fisher's inequality", "Fractional factorial design", "Generalized randomized block design", "Glossary of experimental design", "Graeco-Latin square", "Group (mathematics)", "Group testing", "Hadamard matrix", "Hall's marriage theorem", "Hierarchical Bayes model", "Hierarchical linear modeling", "Hypergraph", "Idempotent", "Incidence matrix", "Integral", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Journal of Combinatorial Theory", "Kirkman's schoolgirl problem", "Latin hypercube sampling", "Latin rectangle", "Latin square", "Linear regression", "Linear space (geometry)", "List of statistics articles", "Lo Shu Square", "Lottery", "Magic square", "Mathematical biology", "Mathematics", "Matrix (mathematics)", "Mixed model", "Modulo operation", "Multiple comparison", "Multiset", "Multivariate analysis of variance", "Nuisance variable", "Optimal design", "Order of a group", "Ordinary least squares", "Orthogonal Latin squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Plackett-Burman design", "Polynomial and rational function modeling", "Prime power", "Projective geometry", "Projective plane", "Quadratic form", "Quasigroup", "R. C. Bose", "Random assignment", "Random effect", "Randomization", "Randomized block design", "Randomized controlled trial", "Recreational mathematics", "Repeated measures design", "Replication (statistics)", "Response surface methodology", "Restricted randomization", "Ronald Fisher", "Room square", "Round-robin tournament", "S. S. Shrikhande", "Sample size", "Scientific control", "Scientific method", "Sequential analysis", "Sequential probability ratio test", "Set system", "Sphere", "Spherical design", "Square numbers", "Statistical inference", "Statistical model", "Steiner system", "Strongly regular graph", "Subset", "Sudoku", "Taguchi methods", "Tournament", "Transylvanian lottery", "Tur\u00e1n system", "Validity (statistics)"], "references": ["https://link.springer.com/referenceworkentry/10.1007%2F978-1-4020-4425-0_9778#howtocite"]}, "Classic data sets": {"categories": ["Computer data", "Statistical data sets"], "title": "Data set", "method": "Classic data sets", "url": "https://en.wikipedia.org/wiki/Data_set", "summary": "A data set (or dataset) is a collection of data. Most commonly a data set corresponds to the contents of a single database table, or a single statistical data matrix, where every column of the table represents a particular variable, and each row corresponds to a given member of the data set in question. The data set lists values for each of the variables, such as height and weight of an object, for each member of the data set. Each value is known as a datum. The data set may comprise data for one or more members, corresponding to the number of rows.\nThe term data set may also be used more loosely, to refer to the data in a collection of closely related tables, corresponding to a particular experiment or event. Less used names for this kind of data sets are data corpus and data stock. An example of this type is the data sets collected by space agencies performing experiments with instruments aboard space probes. Data sets that are so large that traditional data processing applications are inadequate to deal with them are known as big data.In the open data discipline, data set is the unit to measure the information released in a public open data repository. The European Open Data portal aggregates more than half a million data sets. In this field other definitions have been proposed but currently there is not an official one. Some other issues (real-time data sources, non-relational data sets, etc.) increases the difficulty to reach a consensus about it.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/10/Crystal_Clear_device_cdrom_unmount.png", "https://upload.wikimedia.org/wikipedia/commons/d/d7/Desktop_computer_clipart_-_Yellow_theme.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg"], "links": ["Algorithms", "Andrew Gelman", "Annals of Eugenics", "Anscombe's quartet", "Big data", "Categorical data analysis", "Column (database)", "Data", "Data (computing)", "Data blending", "Data collection system", "Data matrix (multivariate statistics)", "Data processing", "Data set (IBM mainframe)", "Data store", "Digital object identifier", "Imputation (statistics)", "Integer", "International Standard Book Number", "Interoperability", "Iris flower data set", "Kurtosis", "Level of measurement", "MNIST database", "Missing values", "Modem", "Nominal data", "Number", "Open data", "Peter Rousseeuw", "Real number", "Robust statistics", "Ronald Fisher", "Row (database)", "SPSS", "Sampling (statistics)", "Software", "Space probe", "Standard deviation", "Statistical", "Statistical measure", "Statistical population", "Statistics", "Table (database)", "Time series"], "references": ["http:ftp://ftp.ics.uci.edu/pub/machine-learning-databases/liver-disorders", "http://duweb.donau-uni.ac.at/imperia/md/content/department/gpa/zeg/bilder/cedem/cedem14/cedem14_proceedings.pdf#page=258", "http://digital.library.adelaide.edu.au/coll/special//fisher/138.pdf", "http://www.researchpipeline.com/mediawiki/index.php?title=Main_Page", "http://www.uni-koeln.de/themen/statistik/data/rousseeuw/", "http://lib.stat.cmu.edu/jasadata/", "http://lib.stat.cmu.edu/modules.php?op=modload&name=PostWrap&file=index&page=datasets/", "http://www.stat.columbia.edu/~gelman/book/data/", "http://archive.ics.uci.edu/ml/", "http://www.europeandataportal.eu/data/en/dataset", "http://data.gov", "http://gcmd.nasa.gov", "http://datahub.io/", "http://www.ijis.net/ijis7_1/ijis7_1_editorial.html", "http://doi.org/10.1111%2Fj.1469-1809.1936.tb02137.x", "http://www.meloda.org/dataset-definition/", "http://data.gov.uk", "https://books.google.com.au/books?id=X0wtLo2XY9gC", "https://books.google.com/books?id=uTzeRZFmaBgC&pg=PA100", "https://relational.fit.cvut.cz/", "https://web.archive.org/web/20060910161517/http://homes.stat.unipd.it/coles/public_html/ismev/ismev.dat"]}, "Barnard's test": {"categories": ["Statistical tests for contingency tables", "Use dmy dates from March 2011"], "title": "Barnard's test", "method": "Barnard's test", "url": "https://en.wikipedia.org/wiki/Barnard%27s_test", "summary": "In statistics, Barnard's test is an exact test used in the analysis of contingency tables. It examines the association of two categorical variables and is a more powerful alternative than Fisher's exact test for 2\u00d72 contingency tables. While first published in 1945 by George Alfred Barnard, the test did not gain popularity due to the computational difficulty of calculating the p-value, and Fisher's disapproval. Nowadays, for small/moderate sample sizes ( n < 1000 ), computers can often implement Barnard's test in a few seconds.", "images": [], "links": ["Ancillary statistic", "Binomial distribution", "Case-control study", "Categorical variable", "Contingency table", "Cross-sectional study", "Digital object identifier", "Exact test", "Fisher's exact test", "George Alfred Barnard", "Hypergeometric distribution", "Lady tasting tea", "Multinomial distribution", "Nuisance parameter", "Placebo", "Ronald Fisher", "Statistical power", "Statistics", "Type I and type II errors", "Uniformly most powerful test"], "references": ["http://doi.org/10.1038%2F156177a0", "http://doi.org/10.1080%2F00031305.1993.10475946", "http://doi.org/10.1093%2Fbiomet%2F34.1-2.123", "http://doi.org/10.1111%2Fj.1467-9574.1970.tb00104.x", "https://cran.r-project.org/web/packages/Exact/Exact.pdf"]}, "File drawer problem": {"categories": ["Academic publishing", "Academic terminology", "Bias", "CS1 maint: Multiple names: authors list", "Criticism of academia", "Meta-analysis", "Publishing", "Systematic review", "Use dmy dates from April 2017"], "title": "Publication bias", "method": "File drawer problem", "url": "https://en.wikipedia.org/wiki/Publication_bias", "summary": "Publication bias is a type of bias that occurs in published academic research. It occurs when the outcome of an experiment or research study influences the decision whether to publish or otherwise distribute it. Publication bias matters because literature reviews regarding support for a hypothesis can be biased if the original literature is contaminated by publication bias. Publishing only results that show a significant finding disturbs the balance of findings.Studies with significant results can be of the same standard as studies with a null result with respect to quality of execution and design. However, statistically significant results are three times more likely to be published than papers with null results.Multiple factors contribute to publication bias. For instance, once a scientific finding is well established, it may become newsworthy to publish reliable papers that fail to reject the null hypothesis. It has been found that the most common reason for non-publication is simply that investigators decline to submit results, leading to non-response bias. Factors cited as underlying this effect include investigators assuming they must have made a mistake, failure to support a known finding, loss of interest in the topic, or anticipation that others will be uninterested in the null results. The nature of these issues and the problems that have been triggered, have been referred to as the 5 diseases that threaten science, which include: \"significosis, an inordinate focus on statistically significant results; neophilia, an excessive appreciation for novelty; theorrhea, a mania for new theory; arigorium, a deficiency of rigor in theoretical and empirical work; and finally, disjunctivitis, a proclivity to produce large quantities of redundant, trivial, and incoherent works.\" Attempts to identify unpublished studies often prove difficult or are unsatisfactory. In an effort to combat this problem, some journals require that studies submitted for publication are pre-registered (registering a study prior to collection of data and analysis) with organizations like the Center for Open Science.\nOther proposed strategies to detect and control for publication bias include p-curve analysis and disfavoring small and non-randomised studies because of their demonstrated high susceptibility to error and bias.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a2/FloreAndWicherts2015_meta_analysis_sex_stereotype_threat.png", "https://upload.wikimedia.org/wikipedia/commons/7/77/Open_Access_logo_PLoS_transparent.svg", "https://upload.wikimedia.org/wikipedia/commons/6/6c/Psi2.svg"], "links": ["Academic bias", "Acquiescence bias", "Adversarial collaboration", "AllTrials", "Anchoring", "Annals of Internal Medicine", "Antidepressant", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "Bad Pharma", "Belief bias", "Ben Goldacre", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Center for Open Science", "Choice-supportive bias", "Clinical trial protocol", "Clinical trials registry", "Cochrane Library", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Confirmation bias", "Congruence bias", "Controlled Clinical Trials", "Counternull", "Cultural bias", "Debiasing", "Design of experiments", "Digital object identifier", "Distinction bias", "Dunning\u2013Kruger effect", "Effect size", "Egocentric bias", "Emotional bias", "Evidence-based medicine", "Experiment", "Experimenter's bias", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Forecast bias", "Fundamental attribution error", "Funding bias", "Funnel plot", "Halo effect", "Healthy user bias", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "Hypothesis", "Impact bias", "In-group favoritism", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "International Standard Serial Number", "JAMA (journal)", "JNCI", "John P.A. Ioannidis", "John P. A. Ioannidis", "Journal of Chronic Diseases", "Journal of Personality and Social Psychology", "Journal of Scientific Exploration", "Journal of the American Medical Association", "Kay Dickersin", "Lancet (journal)", "Lead time bias", "Length time bias", "List of cognitive biases", "List of memory biases", "Literature review", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Meta-analyses", "Negativity bias", "Net bias", "New England Journal of Medicine", "Non-response bias", "Normalcy bias", "Null result", "Omission bias", "Omitted-variable bias", "Open access", "Optimism bias", "Outcome bias", "Overton window", "P-curve", "PLoS Medicine", "Parapsychology", "Participation bias", "Peer review", "Personality and Social Psychology Review", "Peter Wilmshurst", "Pfizer", "Precision bias", "Pro-innovation bias", "Proteus phenomenon", "PubMed Central", "PubMed Identifier", "Reboxetine", "Recall bias", "Replication crisis", "Reporting bias", "Research", "Response bias", "Restraint bias", "Robert Rosenthal (psychologist)", "Sampling bias", "Selection bias", "Self-selection bias", "Self-serving bias", "Smh.com.au", "Social comparison bias", "Social desirability bias", "Spectrum bias", "Statistical significance", "Status quo bias", "Stereotype threat", "Survivorship bias", "Systematic error", "Systematic review", "Systemic bias", "The Lancet", "The Washington Post", "Time-saving bias", "Trait ascription bias", "Trials (journal)", "United States news media and the Vietnam War", "Verification bias", "Von Restorff effect", "Wet bias", "White hat bias", "Woozle effect", "World Health Organization", "Zero-risk bias"], "references": ["http://www.smh.com.au/articles/2004/09/09/1094530773888.html", "http://www.arjournals.com/", "http://www.jasnh.com/", "http://www.jnrbm.com/", "http://www.newyorker.com/reporting/2010/12/13/101213fa_fact_lehrer", "http://www.newyorker.com/reporting/2010/12/13/101213fa_fact_lehrer?currentPage=all", "http://journals.sagepub.com/doi/10.1177/1745691616662243", "http://www.sciencedirect.com/science/article/pii/S104898431730070X", "http://skepdic.com/filedrawer.html", "http://skepdic.com/posoutbias.html", "http://www.ted.com/talks/ben_goldacre_what_doctors_don_t_know_about_the_drugs_they_prescribe.html", "http://www.trialsjournal.com/info/instructions/?txt_jou_id=10096&txt_mst_id=61789", "http://marcorlitzky.webs.com/Papers/Orlitzky2011beq_preprint.pdf", "http://onlinelibrary.wiley.com/doi/10.1002/bimj.201000151/abstract", "http://onlinelibrary.wiley.com/doi/10.1002/jrsm.1266/abstract", "http://onlinelibrary.wiley.com/doi/10.1002/sim.6342/abstract", "http://www.clinicaltrials.gov/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182327", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3241511", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4156818", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC555875", "http://www.ncbi.nlm.nih.gov/pubmed/15026468", "http://www.ncbi.nlm.nih.gov/pubmed/15647155", "http://www.ncbi.nlm.nih.gov/pubmed/15681569", "http://www.ncbi.nlm.nih.gov/pubmed/16060722", "http://www.ncbi.nlm.nih.gov/pubmed/1672966", "http://www.ncbi.nlm.nih.gov/pubmed/20181324", "http://www.ncbi.nlm.nih.gov/pubmed/22179297", "http://www.ncbi.nlm.nih.gov/pubmed/2406472", "http://www.ncbi.nlm.nih.gov/pubmed/25168036", "http://www.ncbi.nlm.nih.gov/pubmed/25636259", "http://www.ncbi.nlm.nih.gov/pubmed/25988604", "http://www.ncbi.nlm.nih.gov/pubmed/3442991", "http://www.ncbi.nlm.nih.gov/pubmed/447779", "http://www.ncbi.nlm.nih.gov/pubmed/8306005", "http://doi.apa.org/getdoi.cfm?doi=10.1037/a0033242", "http://psycnet.apa.org/?fa=main.doiLanding&uid=1960-05032-001", "http://doi.org/10.1001%2Fjama.263.10.1385", "http://doi.org/10.1002%2Fbimj.201000151", "http://doi.org/10.1002%2Fjrsm.1266", "http://doi.org/10.1002%2Fsim.6342", "http://doi.org/10.1002%2Fsim.6525", "http://doi.org/10.1016%2F0021-9681(79)90012-2", "http://doi.org/10.1016%2F0140-6736(91)90201-Y", "http://doi.org/10.1016%2F0197-2456(87)90155-3", "http://doi.org/10.1016%2Fj.jclinepi.2011.06.022", "http://doi.org/10.1016%2Fj.jsp.2014.10.002", "http://doi.org/10.1016%2Fj.leaqua.2017.01.006", "http://doi.org/10.1037%2F0033-2909.86.3.638", "http://doi.org/10.1037%2Fa0033242", "http://doi.org/10.1080%2F01621459.1997.10474047", "http://doi.org/10.1093%2Fjnci%2Fdjh075", "http://doi.org/10.1136%2Fbmj.38356.424606.8f", "http://doi.org/10.1136%2Fbmj.38488.385995.8f", "http://doi.org/10.1136%2Fbmjopen-2014-004831", "http://doi.org/10.1177%2F1745691616662243", "http://doi.org/10.1186%2F1471-2288-9-79", "http://doi.org/10.1191%2F096228000701555244", "http://doi.org/10.1207%2Fs15327957pspr0203_4", "http://doi.org/10.1258%2Fjrsm.2011.11k042", "http://doi.org/10.1371%2Fjournal.pmed.0020124", "http://doi.org/10.1371%2Fjournal.pmed.0020334", "http://doi.org/10.1371%2Fjournal.pmed.0020409", "http://doi.org/10.1371%2Fjournal.pmed.1001566", "http://doi.org/10.1371%2Fjournal.pone.0081823", "http://doi.org/10.2307%2F2282137", "http://doi.org/10.3102%2F10769986021004299", "http://doi.org/10.3310%2Fhta14080", "http://jnci.oxfordjournals.org/cgi/content/full/96/6/434", "http://www.plosone.org/article/info:doi%2F10.1371%2Fjournal.pone.0081823", "http://psychfiledrawer.org/", "http://www.scientificexploration.org/journal/jse_14_1_scargle.pdf", "http://www.worldcat.org/issn/1097-0258", "http://www.worldcat.org/issn/1521-4036", "http://www.worldcat.org/issn/1759-2887", "http://direct.bl.uk/bld/PlaceOrder.do?UIN=048343521&ETOC=RN&from=searchengine", "http://www.medico-legalsociety.org.uk/articles/dishonesty_in_medical_research.pdf", "https://www.theguardian.com/commentisfree/2011/apr/23/ben-goldacre-bad-science", "https://web.archive.org/web/20130521050439/http://www.medico-legalsociety.org.uk/articles/dishonesty_in_medical_research.pdf"]}, "Gaussian process": {"categories": ["Kernel methods for machine learning", "Nonparametric Bayesian statistics", "Normal distribution", "Stochastic processes", "Wikipedia articles with NDL identifiers"], "title": "Gaussian process", "method": "Gaussian process", "url": "https://en.wikipedia.org/wiki/Gaussian_process", "summary": "In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g. time or space.\nA machine-learning algorithm that involves a Gaussian process uses lazy learning and a measure of the similarity between points (the kernel function) to predict the value for an unseen point from training data. The prediction is not just an estimate for that point, but also has uncertainty information\u2014it is a one-dimensional Gaussian distribution (which is the marginal distribution at that point).For some kernel functions, matrix algebra can be used to calculate the predictions using the technique of kriging. When a parameterised kernel is used, optimisation software is typically used to fit a Gaussian process model.\nThe concept of Gaussian processes is named after Carl Friedrich Gauss because it is based on the notion of the Gaussian distribution (normal distribution). Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions.\nGaussian processes are useful in statistical modelling, benefiting from properties inherited from the normal. For example, if a random process is modelled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly. Such quantities include the average value of the process over a range of times and the error in estimating the average using sample values at a small set of times.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7f/Gaussian_Process_Regression.png", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Gaussian_process_draws_from_prior_distribution.png", "https://upload.wikimedia.org/wikipedia/commons/a/a7/Regressions_sine_demo.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bayes linear statistics", "Bayesian inference", "Bayesian interpretation of regularization", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cambridge University Press", "Cameron\u2013Martin formula", "Carl Friedrich Gauss", "Cauchy process", "Central limit theorem", "Characteristic function (probability theory)", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Covariance", "Covariance function", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "David J.C. MacKay", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical Bayes", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Finite set", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "Function (mathematics)", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma function", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian free field", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Gradient-Enhanced Kriging (GEK)", "Gram matrix", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Homogeneous", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "If and only if", "Independent and identically distributed random variables", "Indexed family", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Interpolation", "Ising model", "Isotropy", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "John Wiley & Sons", "Joint distribution", "Jump diffusion", "Jump process", "Karhunen\u2013Lo\u00e8ve theorem", "Kernel methods for vector output", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kriging", "Kronecker delta", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Lazy learning", "Linear combination", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "MIT Press", "Machine learning", "Malliavin calculus", "Manifold learning", "Marginal distribution", "Marginal likelihood", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Matrix (mathematics)", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "Maximum a posteriori", "McKean\u2013Vlasov process", "Mean (mathematics)", "Mixing (mathematics)", "Modified Bessel function", "Moran process", "Moving-average model", "Multivariate Gaussian", "Multivariate normal distribution", "National Diet Library", "Non-homogeneous Poisson process", "Normal distribution", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Oxford University Press", "Percolation theory", "Periodic function", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Prior probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random process", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sampling (mathematics)", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Scikit-learn", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Smoothness", "Snell envelope", "Sparre\u2013Anderson model", "Springer Science+Business Media", "Stable process", "Standard deviation", "Stationary process", "Statistical independence", "Statistical model", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic kernel", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "Supervised learning", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Unsupervised learning", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://www.sumo.intec.ugent.be/ooDACE", "http://au.mathworks.com/matlabcentral/fileexchange/38880:", "http://www.sciencedirect.com/science/article/pii/S0925231213005523", "http://www.uqlab.com/", "http://www.cnel.ufl.edu/~weifeng/publication.htm", "http://becs.aalto.fi/en/research/bayes/gpstuff/", "http://www.tmpl.fi/gp/", "http://sourceforge.net/projects/kriging", "http://videolectures.net/epsrcws08_rasmussen_lgp", "http://videolectures.net/gpip06_mackay_gpb", "http://videolectures.net/mlss07_rasmussen_bigp", "http://publications.nr.no/917_Rapport.pdf", "http://doi.org/10.1142%2Fs0129065704001899", "http://doi.org/10.1162%2F089976602317250933", "http://www.GaussianProcess.org", "http://www.gaussianprocess.org/gpml/", "http://ieeexplore.ieee.org/document/6613486/", "http://scikit-learn.org", "http://scikit-learn.org/stable/auto_examples/gaussian_process/plot_compare_gpr_krr.html", "http://www.inference.phy.cam.ac.uk/itprnn/book.pdf", "http://web4.cs.ucl.ac.uk/staff/D.Barber/pmwiki/pmwiki.php?n=Brml.HomePage", "http://platypusinnovation.blogspot.co.uk/2016/05/a-simple-intro-to-gaussian-processes.html", "https://github.com/ChristophJud/GPR", "https://github.com/SheffieldML/GPy", "https://github.com/Yelp/MOE", "https://github.com/modsim/KriKit", "https://id.ndl.go.jp/auth/ndlna/01180243", "https://arxiv.org/abs/1505.02965", "https://pdfs.semanticscholar.org/c9f2/1b84149991f4d547b3f0f625f710750ad8d9.pdf", "https://www.wikidata.org/wiki/Q1496376"]}, "Exact statistics": {"categories": ["Statistical inference"], "title": "Exact statistics", "method": "Exact statistics", "url": "https://en.wikipedia.org/wiki/Exact_statistics", "summary": "Exact statistics, such as that described in exact test, is a branch of statistics that was developed to provide more accurate results pertaining to statistical testing and interval estimation by eliminating procedures based on asymptotic and approximate statistical methods. The main characteristic of exact methods is that statistical tests and confidence intervals are based on exact probability statements that are valid for any sample size. \nExact statistical methods help avoid some of the unreasonable assumptions of traditional statistical methods, such as the assumption of equal variances in classical ANOVA. They also allow exact inference on variance components of mixed models.\nWhen exact p-values and confidence intervals are computed under a certain distribution, such as the normal distribution, then the underlying methods are referred to as exact parametric methods. The exact methods that do not make any distributional assumptions are referred to as exact nonparametric methods. The latter has the advantage of making fewer assumptions whereas, the former tend to yield more powerful tests when the distributional assumption is reasonable. For advanced methods such as higher-way ANOVA regression analysis, and mixed models, only exact parametric methods are available.\nWhen the sample size is small, asymptotic results given by some traditional methods may not be valid. In such situations, the asymptotic p-values may differ substantially from the exact p-values. Hence asymptotic and other approximate results may lead to unreliable and misleading conclusions.", "images": [], "links": ["ANOVA", "Asymptotic theory (statistics)", "Bayesian statistics", "Classification tree analysis", "Confidence interval", "Exact test", "Fisher's exact test", "Generalized p-value", "Interval estimation", "John Wiley & Sons", "Journal of the American Statistical Association", "Mixed model", "Optimal discriminant analysis", "P-Value", "Prentice Hall", "Regression analysis", "Sample size", "Springer-Verlag", "Statistical Methods for Research Workers", "Statistical test", "Statistics", "Variance component"], "references": ["http://www.weerahandi.org", "https://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-40621-3"]}, "Multiple-indicator kriging": {"categories": ["All articles with failed verification", "All articles with unsourced statements", "Articles with failed verification from December 2015", "Articles with unsourced statements from August 2018", "Articles with unsourced statements from March 2016", "Commons category link is on Wikidata", "Geostatistics", "Interpolation", "Multivariate interpolation", "Webarchive template wayback links", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from November 2014"], "title": "Kriging", "method": "Multiple-indicator kriging", "url": "https://en.wikipedia.org/wiki/Kriging", "summary": "In statistics, originally in geostatistics, kriging or Gaussian process regression is a method of interpolation for which the interpolated values are modeled by a Gaussian process governed by prior covariances. Under suitable assumptions on the priors, kriging gives the best linear unbiased prediction of the intermediate values. Interpolating methods based on other criteria such as smoothness (e.g., smoothing spline) need not yield the most likely intermediate values. The method is widely used in the domain of spatial analysis and computer experiments. The technique is also known as Wiener\u2013Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov.\n\nThe theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the Master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes. The English verb is to krige and the most common noun is kriging; both are often pronounced with a hard \"g\", following the pronunciation of the name \"Krige\". The word is sometimes capitalized as Kriging in the literature.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f5/Example_of_kriging_interpolation_in_1D.png", "https://upload.wikimedia.org/wikipedia/commons/1/1d/Information_icon4.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Andrey Kolmogorov", "Astronomy", "Bayes linear statistics", "Bayesian inference", "Best linear unbiased estimator", "Best linear unbiased prediction", "Bibcode", "Carol A. Gotway Crawford", "Computer experiment", "Covariance", "Covariance function", "Covariance matrix", "Covariogram", "Curve fitting", "Danie G. Krige", "Digital object identifier", "Engineering", "Environmental science", "Expected value", "Finite element method", "Function (mathematics)", "Gaussian process", "Gauss\u2013Markov theorem", "Generalized least squares", "Geographic coordinate system", "Georges Matheron", "Geostatistics", "Gradient-Enhanced Kriging (GEK)", "Hard and soft g", "Hydrogeology", "Indicator function", "Integrated Circuit Analysis and Optimization", "International Standard Book Number", "Interpolation", "JSTOR", "Kernel (set theory)", "Lagrange multiplier", "Lagrange multipliers", "Likelihood function", "Log-normal distribution", "Logarithm", "Mathematical Geology", "Metal forming", "Metamodeling", "Mining", "Modelling of Microwave Devices", "Moment (mathematics)", "Multivariate interpolation", "Natural resource", "Nonparametric regression", "Norbert Wiener", "Normal distribution", "Optimization", "Polynomial", "Posterior probability", "Prior probability distribution", "Probability distribution", "PubMed Identifier", "Radial basis function", "Random field", "Random variable", "Real estate appraisal", "Regression-kriging", "Regression analysis", "Remote sensing", "Reproducing kernel Hilbert space", "Saraju Mohanty", "Set (mathematics)", "Smoothing spline", "Smoothness", "South Africa", "Space mapping", "Spatial analysis", "Spatial dependence", "Spline (mathematics)", "Stationary process", "Statistics", "Stochastic process", "Surrogate model", "Variogram", "Wayback Machine", "Witwatersrand"], "references": ["http://www.sumo.intec.ugent.be/ooDACE", "http://apps.nrbook.com/empanel/index.html?pg=144", "http://apps.nrbook.com/empanel/index.html?pg=836", "http://www.pykriging.com", "http://www.uqlab.com", "http://adsabs.harvard.edu/abs/1998WRR....34.1373Z", "http://web.mit.edu/dennism/www/Publications/M25_1998_Zimmerman_etal_WRR.pdf", "http://www.cse.unt.edu/~smohanty/Publications_Journals/2013/Mohanty_IET-CDS-2013Sep_Thermal-Sensor-Geostatistical.pdf", "http://press3.mcs.anl.gov/scala-gauss/", "http://www.ncbi.nlm.nih.gov/pubmed/11916123", "http://sourceforge.net/projects/kriging", "http://mgstat.sourceforge.net/", "http://doi.org/10.1002%2Fjnm.803", "http://doi.org/10.1007%2F0-306-47647-9_6", "http://doi.org/10.1007%2F978-94-011-5014-9_23", "http://doi.org/10.1007%2Fs00477-005-0234-8", "http://doi.org/10.1007%2Fs11004-005-1560-6", "http://doi.org/10.1007%2Fs12289-008-0001-8", "http://doi.org/10.1023%2FA:1023239606028", "http://doi.org/10.1029%2F98WR00003", "http://doi.org/10.1093%2Fmnras%2Fstu937", "http://doi.org/10.1093%2Fmnras%2Fstv2947", "http://doi.org/10.1093%2Fmnras%2Fstx418", "http://doi.org/10.1111%2Fj.1745-6584.2002.tb02503.x", "http://doi.org/10.1137%2F1.9781611970128", "http://www.gaussianprocess.org/gpml/code/matlab/", "http://www.jstor.org/stable/2245858", "http://www.openturns.org/", "http://scikit-learn.org/stable/", "http://scikit-learn.org/stable/modules/generated/sklearn.gaussian_process.GaussianProcessRegressor.html#sklearn.gaussian_process.GaussianProcessRegressor", "https://github.com/SMTorg/SMT", "https://github.com/bsmurphy/PyKrige", "https://github.com/modsim/KriKit", "https://web.archive.org/web/20050604080848/http://www2.imm.dtu.dk/~hbn/dace/", "https://web.archive.org/web/20140714173450/http://www.cse.unt.edu/~smohanty/Publications_Journals/2013/Mohanty_IET-CDS-2013Sep_Thermal-Sensor-Geostatistical.pdf"]}, "Confidence and prediction bands": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "CS1 maint: Archived copy as title", "Estimation theory"], "title": "Confidence and prediction bands", "method": "Confidence and prediction bands", "url": "https://en.wikipedia.org/wiki/Confidence_and_prediction_bands", "summary": "A confidence band is used in statistical analysis to represent the uncertainty in an estimate of a curve or function based on limited or noisy data. Similarly, a prediction band is used to represent the uncertainty about the value of a new data-point on the curve, but subject to noise. Confidence and prediction bands are often used as part of the graphical presentation of results of a regression analysis.\nConfidence bands are closely related to confidence intervals, which represent the uncertainty in an estimate of a single numerical value. \"As confidence intervals, by construction, only refer to a single point, they are narrower (at this point) than a confidence band which is supposed to hold simultaneously at many points.\"", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b6/Binomial_confidence_band.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/0/01/Regression_confidence_band.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bonferroni correction", "Bonferroni method", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "CDF-based nonparametric confidence interval", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Characteristic function (probability theory)", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Familywise error rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov-Smirnov test", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scheff\u00e9's method", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smoothing", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode17.html", "http://doi.org/10.1093%2Fbiomet%2Fasn005", "http://doi.org/10.1111%2Fj.1751-5823.2007.00027.x", "http://doi.org/10.2307%2F2291062", "http://www.jstor.org/stable/2291062", "https://books.google.com/books?id=qPCmAOS-CoMC&lpg=PA65&vq=As%20confidence%20intervals,%20by%20construction,%20only%20refer%20to%20a%20single%20point,%20they%20are%20narrower%20(at%20this%20point)%20than%20a%20confidence%20band%20which%20is%20supposed%20to%20hold%20simultaneously%20at%20many%20points&pg=PA65#v=snippet&q=As%20confidence%20intervals,%20by%20construction,%20only%20refer%20to%20a%20single%20point,%20they%20are%20narrower%20(at%20this%20point)%20than%20a%20confidence%20band%20which%20is%20supposed%20to%20hold%20simultaneously%20at%20many%20points&f=false", "https://archive.is/20130412073504/http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode17.html"]}, "Birnbaum\u2013Saunders distribution": {"categories": ["Continuous distributions", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Birnbaum\u2013Saunders distribution", "method": "Birnbaum\u2013Saunders distribution", "url": "https://en.wikipedia.org/wiki/Birnbaum%E2%80%93Saunders_distribution", "summary": "The Birnbaum\u2013Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. There are several alternative formulations of this distribution in the literature. It is named after Z. W. Birnbaum and S. C. Saunders.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Copyright status of work by the U.S. government", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "National Institute of Standards and Technology", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Reliability (statistics)", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard normal distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z. W. Birnbaum", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.itl.nist.gov/div898/handbook/eda/section3/eda366a.htm", "http://www.nist.gov", "http://www.dtic.mil/get-tr-doc/pdf?AD=AD0677586", "http://doi.org/10.1016%2Fj.csda.2006.08.016", "http://doi.org/10.1016%2Fj.csda.2010.10.007", "http://doi.org/10.1080%2F10629360600903882", "http://doi.org/10.1214%2F11-BJPS160", "http://doi.org/10.2307%2F3212003", "http://doi.org/10.2307%2F3315148", "http://www.jstor.org/stable/3212003", "http://www.jstor.org/stable/3315148"]}, "List of convolutions of probability distributions": {"categories": ["Mathematics-related lists", "Statistics-related lists", "Theory of probability distributions"], "title": "List of convolutions of probability distributions", "method": "List of convolutions of probability distributions", "url": "https://en.wikipedia.org/wiki/List_of_convolutions_of_probability_distributions", "summary": "In probability theory, the probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of random variables is the convolution of their corresponding probability mass functions or probability density functions respectively. Many well known distributions have simple convolutions. The following is a list of these convolutions. Each statement is of the form\n\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n X\n \n i\n \n \n \u223c\n Y\n \n \n {\\displaystyle \\sum _{i=1}^{n}X_{i}\\sim Y}\n where \n \n \n \n \n X\n \n 1\n \n \n ,\n \n X\n \n 2\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n \n \n {\\displaystyle X_{1},X_{2},\\dots ,X_{n}}\n are independent random variables, and \n \n \n \n Y\n \n \n {\\displaystyle Y}\n is the distribution that results from the convolution of \n \n \n \n \n X\n \n 1\n \n \n ,\n \n X\n \n 2\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n \n \n {\\displaystyle X_{1},X_{2},\\dots ,X_{n}}\n . In place of \n \n \n \n \n X\n \n i\n \n \n \n \n {\\displaystyle X_{i}}\n and \n \n \n \n Y\n \n \n {\\displaystyle Y}\n the names of the corresponding distributions and their parameters have been indicated.", "images": [], "links": ["Algebra of random variables", "Convolution", "Independent (probability)", "Infinite divisibility (probability)", "International Standard Book Number", "Mathematical Reviews", "Mixture distribution", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Product distribution", "Random variable", "Relationships among probability distributions", "Robert V. Hogg", "Stable distribution", "Sum of normally distributed random variables"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0467974", "https://www.pearson.com/us/higher-education/product/Hogg-Introduction-to-Mathematical-Statistics-6th-Edition/9780130085078.html"]}, "Kaplan\u2013Meier estimator": {"categories": ["Actuarial science", "Estimator", "Hidden templates using styles", "Pages with citations having bare URLs", "Pages with citations lacking titles", "Reliability engineering", "Survival analysis"], "title": "Kaplan\u2013Meier estimator", "method": "Kaplan\u2013Meier estimator", "url": "https://en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator", "summary": "The Kaplan\u2013Meier estimator, also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure the fraction of patients living for a certain amount of time after treatment. In other fields, Kaplan\u2013Meier estimators may be used to measure the length of time people remain unemployed after a job loss, the time-to-failure of machine parts, or how long fleshy fruits remain on plants before they are removed by frugivores. The estimator is named after Edward L. Kaplan and Paul Meier, who each submitted similar manuscripts to the Journal of the American Statistical Association. The journal editor, John Tukey, convinced them to combine their work into one paper, which has been cited about 50,000 times since its publication.The estimator is given by:\n\n \n \n \n \n \n \n S\n ^\n \n \n \n (\n t\n )\n =\n \n \u220f\n \n i\n :\n \n \n t\n \n i\n \n \n \u2264\n t\n \n \n \n (\n \n 1\n \u2212\n \n \n \n d\n \n i\n \n \n \n n\n \n i\n \n \n \n \n \n )\n \n ,\n \n \n {\\displaystyle {\\widehat {S}}(t)=\\prod \\limits _{i:\\ t_{i}\\leq t}\\left(1-{\\frac {d_{i}}{n_{i}}}\\right),}\n with \n \n \n \n \n t\n \n i\n \n \n \n \n {\\displaystyle t_{i}}\n a time when at least one event happened, di the number of events (i.e., deaths) that happened at time \n \n \n \n \n t\n \n i\n \n \n \n \n {\\displaystyle t_{i}}\n and \n \n \n \n \n n\n \n i\n \n \n \n \n {\\displaystyle n_{i}}\n the individuals known to survive (have not yet had an event or been censored) at time \n \n \n \n \n t\n \n i\n \n \n \n \n {\\displaystyle t_{i}}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Km_plot.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli random variable", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Censoring (statistics)", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Delta method", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "ETH Zurich", "Econometrica", "Econometrics", "Edward L. Kaplan", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequency of exceedance", "Frequentist inference", "Friedman test", "Frugivore", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hazard function", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Tukey", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Log rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MATLAB", "Major Greenwood", "Mann\u2013Whitney U test", "Martingale central limit theorem", "Mathematica", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Median lethal dose", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Paul Meier (statistician)", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Proportional hazards models", "Psychometrics", "PubMed Central", "PubMed Identifier", "Python (programming language)", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "SAS (software)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "StatsDirect(software)", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Greene (economist)", "YouTube", "Z-test"], "references": ["http://stat.ethz.ch/education/semesters/ss2011/seminar/contents/presentation_2.pdf", "http://stat.ethz.ch/education/semesters/ss2011/seminar/contents/handout_2.pdf", "http://articles.chicagotribune.com/2011-08-18/news/ct-met-meier-obit-20110818_1_clinical-trials-research-experimental-treatment", "http://mathworks.com/help/stats/ecdf.html", "http://reference.wolfram.com/language/ref/SurvivalModelFit.html", "http://www.garfield.library.upenn.edu/classics1983/A1983QS51100001.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3932959", "http://www.ncbi.nlm.nih.gov/pubmed/20723767", "http://www.cancerguide.org/scurve_km.html", "http://doi.org/10.1007%2F978-3-319-08383-4_6", "http://doi.org/10.1016%2Fj.otohns.2010.05.007", "http://doi.org/10.2307%2F2281868", "http://doi.org/10.2307%2F2938349", "http://www.jstor.org/stable/2281868", "https://books.google.com/books?id=-WFPYgEACAAJ&pg=PA909", "https://books.google.com/books?id=7tdcCol9mNEC&pg=PA141", "https://books.google.com/books?id=Cd2CBAAAQBAJ&pg=PA135", "https://books.google.com/books?id=PpnA1M8VwR8C&pg=PA483", "https://books.google.com/books?id=fGnRBQAAQBAJ&pg=PA99", "https://books.google.com/books?id=xttbn0a-QR8C&pg=PA93", "https://scholar.google.com/scholar?cites=14181649205747775124&as_sdt=5,28&sciodt=0,28&hl=en", "https://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/viewer.htm#statug_lifetest_overview.htm", "https://www.stata.com/manuals13/ststs.pdf", "https://www.youtube.com/watch?v=5C_zzD1pOAg", "https://web.stanford.edu/~lutian/coursepdf/STAT331unit3.pdf", "https://www.math.wustl.edu/~sawyer/handouts/greenwood.pdf", "https://lifelines.readthedocs.io/en/latest/", "https://cran.r-project.org/web/packages/survival/index.html", "https://www.statsdirect.co.uk/help/Default.htm#survival_analysis/kaplan_meier.htm"]}, "Image denoising": {"categories": ["All articles with dead external links", "Articles with dead external links from January 2016", "Articles with hAudio microformats", "Audio engineering", "CS1 German-language sources (de)", "Image noise reduction techniques", "Interlanguage link template link number", "Noise reduction", "Pages with citations having bare URLs", "Pages with citations lacking titles", "Sound recording", "Wikipedia articles needing page number citations from January 2016"], "title": "Noise reduction", "method": "Image denoising", "url": "https://en.wikipedia.org/wiki/Noise_reduction", "summary": "Noise reduction is the process of removing noise from a signal.\nAll signal processing devices, both analog and digital, have traits that make them susceptible to noise. Noise can be random or white noise with an even frequency distribution, or frequency dependent noise introduced by a device's mechanism or signal processing algorithms.\nIn electronic recording devices, a major type of noise is hiss created by random electron motion due to thermal agitation at all temperatures above absolute zero. These agitated electrons rapidly add and subtract from the voltage of the output signal and thus create detectable noise.\nIn the case of photographic film and magnetic tape, noise (both visible and audible) is introduced due to the grain structure of the medium. In photographic film, the size of the grains in the film determines the film's sensitivity, more sensitive film having larger sized grains. In magnetic tape, the larger the grains of the magnetic particles (usually ferric oxide or magnetite), the more prone the medium is to noise.\nTo compensate for this, larger areas of film or magnetic tape may be used to lower the noise to an acceptable level.\nMany noise reduction algorithms tend to alter signals to a greater or lesser degree. The local signal-and-noise orthogonalization algorithm can be used to avoid changes to the signals.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/87/Gnome-mime-sound-openclipart.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Noise_reduction_in_Audacity_%280%2C_5%2C_12%2C_30_dB%29_%28150Hz%29_%280.15_sec%29.ogg"], "links": ["AEG-Telefunken", "Academic Press", "Acoustic quieting", "Acoustics", "Active noise control", "Additive white Gaussian noise", "Adobe Photoshop", "Aesthetics", "Algorithm", "Analog (signal)", "Analog electronics", "Anisotropic diffusion", "ArXiv", "Architectural acoustics", "Art", "Atmospheric noise", "Audacity (audio editor)", "Audio (magazine)", "Automatic Dynamic Range Expansion System", "Automatic Noise Reduction System", "Background noise", "Bibcode", "Bilateral filter", "Block-matching algorithm", "Block-matching and 3D filtering", "Brownian noise", "Burst noise", "Burwen (noise reduction)", "CEDAR Audio Ltd", "Car stereo", "Carrier-to-noise ratio", "Carrier-to-receiver noise density", "Cassette deck", "Central limit theorem", "Channel noise level", "Charge-coupled device", "Circuit noise level", "Color grading", "Colors of noise", "Compander", "Computer vision", "Conditional distribution", "Contrast-to-noise ratio", "Convolution", "Convolutional neural network", "Cosmic noise", "DBrnC", "Dark frame", "Darktable", "David E. 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"Gradient noise", "Grey noise", "Health effects from noise", "Heat equation", "Helicon Filter", "Henry Kloss", "Hertz", "High Com", "High Com II", "Image noise", "Image restoration", "Image scaling", "Impulse noise (audio)", "Independent and identically distributed", "Interference (communication)", "International Standard Book Number", "Inverse telecine", "JSTOR", "JVC", "Jeep", "Jeep Cherokee (XJ)", "Jitter", "Johnson\u2013Nyquist noise", "List of noise topics", "Low-pass filter", "Machine learning", "Macroblocks", "Magnetic tape", "Magnetite", "Marketing", "Median", "Median filter", "Modulation error ratio", "Nakamichi", "National Semiconductor", "Neat Image", "Netpbm", "Noise", "Noise, vibration, and harshness", "Noise-cancelling headphones", "Noise (audio)", "Noise (electronics)", "Noise (radio)", "Noise (video)", "Noise Ninja", "Noise and vibration on maritime vessels", "Noise barrier", "Noise control", "Noise figure", "Noise floor", "Noise generator", "Noise measurement", "Noise pollution", "Noise power", "Noise print", "Noise regulation", "Noise shaping", "Noise spectral density", "Noise temperature", "Noiseless", "Noiseware", "Non-local means", "Normal distribution", "Paint Shop Pro", "Partial differential equation", "Phase distortion", "Phase noise", "Philips", "Phonograph records", "Photographic film", "Pink noise", "Pixel", "Pixel art scaling algorithms", "Proceedings of the IEEE", "Pseudorandom noise", "Quantization error", "Radio noise source", "Random field", "Ray Dolby", "SINAD", "Salt and pepper noise", "Sanyo", "Semiconductor", "Shot noise", "Shrinkage Fields (image restoration)", "Signal-to-interference ratio", "Signal-to-noise ratio", "Signal-to-noise ratio (imaging)", "Signal-to-quantization-noise ratio", "Signal (electronics)", "Signal (information theory)", "Signal processing", "Signal subspace", "Signal to noise plus interference", "Sound masking", "Soundproofing", "Spectrum analyzer", "Statistical noise", "Super-resolution imaging", "Super D (noise reduction)", "Tape head", "Tape hiss", "Taylor & Francis", "Telcom c4", "Telecine", "Telefunken", "Telephony", "Thermal radiation", "Toshiba", "Total variation denoising", "U401BR", "Ulead Systems", "Uncompressed video", "Value noise", "Video denoising", "Video post-processing", "Video processing", "Video recording", "Voltage", "Wavelet", "White noise", "Worley noise"], "references": ["http://audiotools.com/noise.html", "http://www.burwenaudio.com/110_DB_DYNAMIC_RANGE_FOR_TAPE_-_AUDIO_JUNE_1971.pdf", "http://www.compolinc.com/dynamic.htm", "http://www.hellodirect.com/catalog/Product.jhtml?PRODID=11127&CATID=15295", "http://www.national.com/company/pressroom/history80.html", "http://www.national.com/pf/LM/LM1894.html", "http://www.triadspeakers.com/education_avterms.html", "http://www.ernstschroeder.de/u401br.pdf", "http://gimps.de/en/tutorials/gimp/picture-photo-image/pixel-noise/", "http://adsabs.harvard.edu/abs/2007ITIP...16.2080D", "http://adsabs.harvard.edu/abs/2015JAG...114...32C", "http://adsabs.harvard.edu/abs/2016GeoJI.204..768G", "http://adsabs.harvard.edu/abs/2016GeoJI.206..457C", "http://adsabs.harvard.edu/abs/2016GeoJI.207.1313C", "http://adsabs.harvard.edu/abs/2016Geop...81S..11X", "http://adsabs.harvard.edu/abs/2016Geop...81V.193C", "http://adsabs.harvard.edu/abs/2016Geop...81V.261H", "http://adsabs.harvard.edu/abs/2017GeoJI.209...21C", "http://www.cs.tut.fi/~foi/GCF-BM3D", "http://www.cs.tut.fi/~foi/SA-DCT/#ref_software", "http://www.ipol.im/pub/algo/bcm_non_local_means_denoising/", "http://freespace.virgin.net/ljmayes.mal/comp/philips.htm", "http://arxiv.org/abs/1711.10925v2", "http://arxiv.org/archive/Computer", "http://www.darktable.org/2012/12/profiling-sensor-and-photon-noise/", "http://doi.org/10.1016%2Fj.jappgeo.2015.01.004", "http://doi.org/10.1093%2Fgji%2Fggv484", "http://doi.org/10.1093%2Fgji%2Fggw165", "http://doi.org/10.1093%2Fgji%2Fggw343", "http://doi.org/10.1093%2Fgji%2Fggw492", "http://doi.org/10.1109%2F5.135376", "http://doi.org/10.1109%2FCVPR.2014.349", "http://doi.org/10.1109%2FTIP.2007.901238", "http://doi.org/10.1190%2FGEO2014-0227.1", "http://doi.org/10.1190%2FINT-2016-0030.1", "http://doi.org/10.1190%2Fgeo2014-0524.1", "http://doi.org/10.1190%2Fgeo2014-0525.1", "http://doi.org/10.1190%2Fgeo2015-0264.1", "http://www.jstor.org/stable/2345426", "http://www.rivowners.org/features/evolution/evpt83.html", "http://research.uweschmidt.org/pubs/cvpr14schmidt.pdf", "https://books.google.com/books?id=6p8fCgT0QNMC&pg=PA13", "https://web.archive.org/web/20070927190856/http://www.national.com/company/pressroom/history80.html", "https://web.archive.org/web/20081105073059/http://freespace.virgin.net/ljmayes.mal/comp/philips.htm", "https://web.archive.org/web/20081220022234/http://www.national.com/pf/LM/LM1894.html", "https://web.archive.org/web/20081220145857/http://triadspeakers.com/education_avterms.html", "https://web.archive.org/web/20111118001653/http://www.stanford.edu/~slansel/tutorial/summary.htm", "https://web.archive.org/web/20160416153706/http://www.ernstschroeder.de/u401br.pdf", "https://web.archive.org/web/20171113211531/http://www.burwenaudio.com/110_DB_DYNAMIC_RANGE_FOR_TAPE_-_AUDIO_JUNE_1971.pdf", "https://www.radiomuseum.org/r/gyar_mk42mk_4.html"]}, "Graeco-Latin square": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from November 2010", "Articles with unsourced statements from August 2017", "CS1 maint: Multiple names: authors list", "Design of experiments", "Latin squares"], "title": "Graeco-Latin square", "method": "Graeco-Latin square", "url": "https://en.wikipedia.org/wiki/Graeco-Latin_square", "summary": "In combinatorics, a Graeco-Latin square or Euler square or orthogonal Latin squares of order n over two sets S and T, each consisting of n symbols, is an n\u00d7n arrangement of cells, each cell containing an ordered pair (s,t), where s is in S and t is in T, such that every row and every column contains each element of S and each element of T exactly once, and that no two cells contain the same ordered pair.\n\nOrthogonal Latin squares\n\t\t\n\t\t\n\t\t\nThe arrangement of the s-coordinates by themselves (which may be thought of as Latin characters) and of the t-coordinates (the Greek characters) each forms a Latin square. A Graeco-Latin square can therefore be decomposed into two \"orthogonal\" Latin squares. Orthogonality here means that every pair (s, t) from the Cartesian product S\u00d7T occurs exactly once.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/80/GraecoLatinSquare-Order3.svg", "https://upload.wikimedia.org/wikipedia/commons/8/88/GraecoLatinSquare-Order5.png", "https://upload.wikimedia.org/wikipedia/commons/f/fa/GrecoLatinSquare-Order4.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anne Penfold Street", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Black", "Blind experiment", "Block design", "Blocking (statistics)", "Blue", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartesian product", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinatorial design", "Combinatorics", "Comic Sans", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Constraint propagation", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Courier New", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Cut-the-knot", "Damaraju Raghavarao", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital computer", "Divergence (statistics)", "Donald Knuth", "Durbin\u2013Watson statistic", "E. T. Parker", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Equivalence class", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "Exponentiation", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finite projective plane", "First-hitting-time model", "Fjord", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaston Tarry", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Georges Perec", "Georgia (typeface)", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Granger causality", "Graphical model", "Greek alphabet", "Grouped data", "Harmonic mean", "Helvetica", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hyper-Graeco-Latin square design", "Impact (typeface)", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jacques Ozanam", "Jarque\u2013Bera test", "Jawbox", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kathleen Ollerenshaw", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin alphabet", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Leonhard Euler", "Life: A User's Manual", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Lime (color)", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Magic square", "Mann\u2013Whitney U test", "Maroon", "Martin Gardner", "Mathematical Games column", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Modular arithmetic", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Navy blue", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "On-Line Encyclopedia of Integer Sequences", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordered pair", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phlegm", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Playing card", "Playoff format", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Prime number", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proof by exhaustion", "Proportional hazards model", "Psychometrics", "Qiviut", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Raj Chandra Bose", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Red", "Regression analysis", "Regression model validation", "Reliability engineering", "Remington Rand", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Rouse Ball", "Run chart", "S. S. Shrikhande", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Set (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Silver", "Simple linear regression", "Simultaneous equations model", "Singly and doubly even", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "TAOCP", "Taguchi methods", "Teal", "Thirty-six officers problem", "Time domain", "Time series", "Times Roman", "Tolerance interval", "Trend estimation", "U-statistic", "UNIVAC", "UNIVAC 1206", "Uniformly most powerful test", "Up to", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Verdana", "Wald test", "Wavelet", "White", "Whittle likelihood", "Wilcoxon signed-rank test", "Without loss of generality", "Yellow", "Z-test", "Zinc"], "references": ["http://www.cut-the-knot.org/Curriculum/Algebra/OrthoLatin.shtml", "http://eulerarchive.maa.org/date-publish.html", "http://eulerarchive.maa.org/date-write.html", "http://eulerarchive.maa.org/pages/E530.html", "http://plus.maths.org/issue38/features/aiden/", "https://github.com/OMerkel/eulersquare", "https://omerkel.github.io/eulersquare/src/", "https://web.archive.org/web/20070713214718/http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=1434&bodyId=1597", "https://books.google.com.tw/books?id=6JP6Hz5EHYQC&pg=PA434", "https://books.google.com.tw/books?id=6JP6Hz5EHYQC&pg=PA476", "https://books.google.com.tw/books?id=IkuEBAAAQBAJ&pg=PT28"]}, "Saturated array": {"categories": ["All stub articles", "Design of experiments", "Statistics stubs"], "title": "Saturated array", "method": "Saturated array", "url": "https://en.wikipedia.org/wiki/Saturated_array", "summary": "In experiments in which additional factors are not likely to interact with any of the other factors, a saturated array can be used. In a saturated array, a controllable factor is substituted for the interaction of two or more by-products. Using a saturated array, a two-factor test matrix could be used to test three factors. Using the saturated array allows three factors to be tested in four tests rather than in eight, as would be required by a standard orthogonal array.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Design of experiments", "Matrix (mathematics)", "Orthogonal array", "Statistics"], "references": []}, "Brownian motion": {"categories": ["Albert Einstein", "All articles needing expert attention", "All articles that are too technical", "All articles with dead external links", "All articles with unsourced statements", "Articles containing Ancient Greek-language text", "Articles containing video clips", "Articles needing expert attention from June 2011", "Articles with dead external links from November 2018", "Articles with permanently dead external links", "Articles with unsourced statements from February 2018", "Articles with unsourced statements from July 2012", "Articles with unsourced statements from October 2012", "CS1 French-language sources (fr)", "CS1 German-language sources (de)", "Colloidal chemistry", "Commons category link is on Wikidata", "Fractals", "L\u00e9vy processes", "Robert Brown (botanist)", "Statistical mechanics", "Use dmy dates from July 2012", "Wiener process", "Wikipedia articles needing clarification from April 2010", "Wikipedia articles that are too technical from June 2011", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers", "Wikipedia articles with NKC identifiers"], "title": "Brownian motion", "method": "Brownian motion", "url": "https://en.wikipedia.org/wiki/Brownian_motion", "summary": "Brownian motion or pedesis (from Ancient Greek: \u03c0\u03ae\u03b4\u03b7\u03c3\u03b9\u03c2 /p\u03ad\u02d0d\u03b5\u02d0sis/ \"leaping\") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving molecules in the fluid.This pattern of motion typically alternates random fluctuations in a particle's position inside a fluid sub-domain with a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such fluid there exists no preferential direction of flow as in transport phenomena. More specifically the fluid's overall linear and angular momenta remain null over time. It is important also to note that the kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations sum up to the caloric component of a fluid\u2019s internal energy.\nThis motion is named after the botanist Robert Brown, who was the most eminent microscopist of his time. In 1827, while looking through a microscope at pollen of the plant Clarkia pulchella immersed in water, the triangular shaped pollen burst at the corners, emitting particles which he noted jiggled around in the water in random fashion. He was not able to determine the mechanisms that caused this motion. Atoms and molecules had long been theorized as the constituents of matter, and Albert Einstein published a paper in 1905 that explained in precise detail how the motion that Brown had observed was a result of the pollen being moved by individual water molecules, making one of his first big contributions to science. This explanation of Brownian motion served as convincing evidence that atoms and molecules exist, and was further verified experimentally by Jean Perrin in 1908. Perrin was awarded the Nobel Prize in Physics in 1926 \"for his work on the discontinuous structure of matter\". The direction of the force of atomic bombardment is constantly changing, and at different times the particle is hit more on one side than another, leading to the seemingly random nature of the motion.\nThe many-body interactions that yield the Brownian pattern cannot be solved by a model accounting for every involved molecule. In consequence only probabilistic models applied to molecular populations can be employed to describe it. Two such models of the statistical mechanics, due to Einstein and Smoluchowski are presented below. Another, pure probabilistic class of models is the class of the stochastic process models. There exist both simpler and more complicated stochastic processes which in extreme (\"taken to the limit\") may describe the Brownian Motion (see random walk and Donsker's theorem).", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a9/2D_Random_Walk_400x400.ogv", "https://upload.wikimedia.org/wikipedia/commons/9/97/2d_random_walk_ag_adatom_ag111.gif", "https://upload.wikimedia.org/wikipedia/commons/4/4e/BMonSphere.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cc/Brownian_Motion.ogv", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Brownian_motion_gamboge.jpg", "https://upload.wikimedia.org/wikipedia/commons/c/c2/Brownian_motion_large.gif", "https://upload.wikimedia.org/wikipedia/commons/5/51/Brownianmotion5particles150frame.gif", "https://upload.wikimedia.org/wikipedia/commons/7/7d/Diffusion_of_Brownian_particles.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4b/Fractal_fern_explained.png", "https://upload.wikimedia.org/wikipedia/commons/4/44/PerrinPlot2.svg", "https://upload.wikimedia.org/wikipedia/commons/8/89/Symbol_book_class2.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f8/Wiener_process_3d.png", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Affine transformation", "Albert Einstein", "Albert Einstein's brain", "Albert Einstein: Creator and Rebel", "Albert Einstein Award", "Albert Einstein House", "Albert Einstein Medal", "Albert Einstein Peace Prize", "Albert Einstein World Award of Science", "Albert Einstein in popular culture", "Aleksandr Lyapunov", "Almost surely", "American Journal of Physics", "Ancient Greek language", "Angular momentum", "Annalen der Physik", "Annales de chimie et de physique", "Annus Mirabilis papers", "ArXiv", "Arnold Sommerfeld", "Assouad dimension", "Atomic theory", "Avogadro's law", "Avogadro constant", "Barnsley fern", "Barometric formula", "Basic Books", "Benoit Mandelbrot", "Bernhard Caesar Einstein", "Bibcode", "Binomial distribution", "Black hole", "Bohr\u2013Einstein debates", "Boltzmann's constant", "Boltzmann constant", "Bose\u2013Einstein condensate", "Bose\u2013Einstein correlations", "Bose\u2013Einstein statistics", "Brownian bridge", "Brownian covariance", "Brownian dynamics", "Brownian motion of sol particles", "Brownian motor", "Brownian noise", "Brownian ratchet", "Brownian surface", "Brownian tree", "Brownian web", "Buddhabrot", "Bulletin International de l'Acad\u00e9mie des Sciences de Cracovie", "Burning Ship fractal", "Cantor set", "Chaos: Making a New Science", "Charged particle", "CiteSeerX", "Clarkia pulchella", "Classical Wiener measure", "Coal", "Coastline paradox", "Complex system", "Comptes Rendus", "Computer vision", "Concentration gradient", "Continuity equation", "Correlation dimension", "Cosmological constant", "C\u00e0dl\u00e0g", "Die Grundlagen der Einsteinschen Relativit\u00e4ts-Theorie", "Diffusion-limited aggregation", "Diffusion equation", "Digital object identifier", "Dirac delta function", "Donsker's theorem", "Dragon curve", "Dust", "Dynamic equilibrium", "Dynamic viscosity", "EPR paradox", "Economy", "Edge detection", "Edward Nelson", "Einstein's Gift", "Einstein's awards and honors", "Einstein's thought experiments", "Einstein's unsuccessful investigations", "Einstein Papers Project", "Einstein Prize (APS)", "Einstein Prize for Laser Science", "Einstein and Eddington", "Einstein and Religion", "Einstein coefficients", "Einstein family", "Einstein field equations", "Einstein for Beginners", "Einstein radius", "Einstein refrigerator", "Einstein relation (kinetic theory)", "Einstein solid", "Einsteinium", "Einstein\u2013Cartan theory", "Einstein\u2013Infeld\u2013Hoffmann equations", "Einstein\u2013de Haas effect", "Electric field", "Electrostatic force", "Elsa Einstein", "Equipartition theorem", "Equivalence principle", "Ethanol", "Evelyn Einstein", "Expected value", "Felix Hausdorff", "Fick's laws of diffusion", "Filled Julia set", "Fluid", "Fractal", "Fractal art", "Fractal canopy", "Fractal dimension", "Fractal landscape", "Free will in antiquity", "Friction", "Gamboge", "Gas", "Gaston Julia", "General relativity", "Genius (U.S. TV series)", "Geometric Brownian motion", "Georg Cantor", "Gravitational", "Gravity", "H tree", "Hans Albert Einstein", "Hausdorff dimension", "Helge von Koch", "Hermann Einstein", "How Long Is the Coast of Britain? 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Thiele", "Torus", "Transport phenomena", "Tricorn (mathematics)", "Tyndall effect", "Ultramicroscope", "Universal gas constant", "Van 't Hoff factor", "Variance", "Wac\u0142aw Sierpi\u0144ski", "Walther Nernst", "Wave\u2013particle duality", "White noise", "Why Socialism?", "Wiener process", "Wikisource", "William Ellery Leonard", "Zeitschrift f\u00fcr Physikalische Chemie", "\u00dcber die von der molekularkinetischen Theorie der W\u00e4rme geforderte Bewegung von in ruhenden Fl\u00fcssigkeiten suspendierten Teilchen"], "references": ["http://rdcohen.50megs.com/BrownianMotion.pdf", "http://www.gizmag.com/einsteins-prediction-finally-witnessed/16212/", "http://users.physik.fu-berlin.de/~kleinert/files/eins_brownian.pdf", "http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_549-560.pdf", "http://www.feynmanlectures.caltech.edu/I_41.html", "http://www.csun.edu/~dchoudhary/Physics-Year_files/ed_diss.pdf", "http://physerver.hamilton.edu/Research/Brownian/index.html", "http://adsabs.harvard.edu/abs/1905AnP...322..549E", "http://adsabs.harvard.edu/abs/1906AnP...326..756V", "http://adsabs.harvard.edu/abs/1986JChEd..63..933C", "http://adsabs.harvard.edu/abs/2004ApJ...616..872R", "http://adsabs.harvard.edu/abs/2010AmJPh..78.1278P", "http://adsabs.harvard.edu/abs/2010Sci...328.1673L", "http://adsabs.harvard.edu/abs/2011PhLA..375.4113M", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.167.8245", "http://onlinebooks.library.upenn.edu/webbin/gutbook/lookup?num=785", "http://chaos.utexas.edu/wp-uploads/2010/06/science.1189403v1.pdf", "http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/applet.html", "http://gallica.bnf.fr/ark:/12148/bpt6k15328k/f770.chemindefer", "http://cafemath.fr/mathblog/article.php?page=BrownianMotion.php", "http://www.ncbi.nlm.nih.gov/pubmed/20488989", "http://xxx.imsc.res.in/abs/physics/0412132", "http://www.fisicateorica.me/repositorio/howto/artigoshistoricosordemcronologica/1905%20-Einstein%201905%20Investigations%20on%20the%20Theory%20of%20the%20Brownian%20Movement.pdf", "http://arxiv.org/abs/1008.0039", "http://arxiv.org/abs/astro-ph/0408107", "http://doi.org/10.1002%2Fandp.19053220806", "http://doi.org/10.1002%2Fandp.19063261405", "http://doi.org/10.1016%2Fj.physleta.2011.10.001", "http://doi.org/10.1021%2Fed063p933", "http://doi.org/10.1086%2F424960", "http://doi.org/10.1119%2F1.3475685", "http://doi.org/10.1126%2Fscience.1189403", "http://iwant2study.org/ospsg/index.php/interactive-resources/physics/03-thermal-physics/01-kinetic-model/105-brownianmotionwee", "http://sciweb.nybg.org/science2/pdfs/dws/Brownian.pdf", "http://openlibrary.org/works/OL16802359W", "https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph195850&CON_LNG=ENG", "https://web.math.princeton.edu/~nelson/books/bmotion.pdf", "https://d-nb.info/gnd/4128328-4", "https://tritemio.github.io/PyBroMo/", "https://id.ndl.go.jp/auth/ndlna/00560924", "https://pubs.acs.org/doi/abs/10.1021/acs.jchemed.6b01008", "https://archive.org/stream/atomsper00perruoft#page/115/mode/1up", "https://archive.org/stream/bulletininternat1906pols#page/202/mode/2up", "https://archive.org/stream/bulletininternat1906pols#page/577/mode/2up", "https://web.archive.org/web/20010222031055/http://www.bun.kyoto-u.ac.jp/~suchii/einsteinBM.html", "https://web.archive.org/web/20140106194631/http://www.fisicateorica.me/repositorio/howto/artigoshistoricosordemcronologica/1905%20-Einstein%201905%20Investigations%20on%20the%20Theory%20of%20the%20Brownian%20Movement.pdf#", "https://arxiv.org/abs/0705.1951", "https://www.wikidata.org/wiki/Q178036"]}, "Chronux": {"categories": ["All articles needing additional references", "All articles with topics of unclear notability", "All articles with unsourced statements", "Articles needing additional references from September 2008", "Articles with topics of unclear notability from May 2017", "Articles with unsourced statements from May 2017", "Free mathematics software", "Signal processing"], "title": "Chronux", "method": "Chronux", "url": "https://en.wikipedia.org/wiki/Chronux", "summary": "Chronux is an open-source software package developed for the loading, visualization and analysis of a variety of modalities / formats of neurobiological time series data. Usage of this tool enables neuroscientists to perform a variety of analysis on multichannel electrophysiological data such as LFP (local field potentials), EEG, MEG, Neuronal spike times and also on spatiotemporal data such as FMRI and dynamic optical imaging data. The software consists of a set of MATLAB routines interfaced with C libraries that can be used to perform the tasks that constitute a typical study of neurobiological data. These include local regression and smoothing, spike sorting and spectral analysis - including multitaper spectral analysis, a powerful nonparametric method to estimate power spectrum. The package also includes some GUIs for time series visualization and analysis. Chronux is GNU GPL v2 licensed (and MATLAB is proprietary).\nThe most recent version of Chronux is version 2.12.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Command line", "Confidence intervals", "EEG", "FMRI", "Frequency spectrum", "Likelihood", "Local regression", "MATLAB", "Marine Biological Laboratory", "Multitaper", "Neurobiological", "Neuroinformatics", "Neuroscience", "Neuroscientist", "Nonparametric", "Plug-in (computing)", "Probability distributions", "Resampling (statistics)", "Smoothing", "Time-series analysis", "Time series", "XML"], "references": ["http://scholar.google.com/scholar?q=%22Chronux%22", "http://www.google.com/search?&q=%22Chronux%22+site:news.google.com/newspapers&source=newspapers", "http://www.google.com/search?as_eq=wikipedia&q=%22Chronux%22&num=50", "http://www.google.com/search?tbm=nws&q=%22Chronux%22+-wikipedia", "http://www.google.com/search?tbs=bks:1&q=%22Chronux%22+-wikipedia", "http://chronux.org/downloads/chronux/chronux/manual.pdf", "https://web.archive.org/web/20080920024725/http://www.chronux.org/", "https://web.archive.org/web/20110525190303/http://www.us.oup.com/us/catalog/general/subject/Medicine/Neuroscience/?view=usa&ci=9780195178081", "https://arxiv.org/abs/q-bio/0309028", "https://www.jstor.org/action/doBasicSearch?Query=%22Chronux%22&acc=on&wc=on"]}, "Kullback\u2013Leibler divergence": {"categories": ["All articles with unsourced statements", "Articles with inconsistent citation formats", "Articles with unsourced statements from August 2017", "Articles with unsourced statements from May 2018", "Entropy and information", "F-divergences", "Information geometry", "Thermodynamics", "Wikipedia articles needing clarification from May 2018"], "title": "Kullback\u2013Leibler divergence", "method": "Kullback\u2013Leibler divergence", "url": "https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence", "summary": "In mathematical statistics, the Kullback\u2013Leibler divergence (also called relative entropy) is a measure of how one probability distribution is different from a second, reference probability distribution. Applications include characterizing the relative (Shannon) entropy in information systems, randomness in continuous time-series, and information gain when comparing statistical models of inference. In contrast to variation of information, it is a distribution-wise asymmetric measure and thus does not qualify as a statistical metric of spread. In the simple case, a Kullback\u2013Leibler divergence of 0 indicates that the two distributions in question are identical. In simplified terms, it is a measure of surprise, with diverse applications such as applied statistics, fluid mechanics, neuroscience, basketball analytics, and machine learning.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c2/ArgonKLdivergence.png", "https://upload.wikimedia.org/wikipedia/commons/8/8e/Kullback%E2%80%93Leibler_distributions_example_1.svg", "https://upload.wikimedia.org/wikipedia/en/a/a8/KL-Gauss-Example.png"], "links": ["Absolute continuity", "Absolutely continuous measure", "Additive map", "Akaike information criterion", "Alfr\u00e9d R\u00e9nyi", "Almost everywhere", "Annals of Mathematical Statistics", "Approximation", "ArXiv", "Asymmetry", "Base (exponentiation)", "Basketball analytics", "Bayes' theorem", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian statistics", "Bibcode", "Binomial distribution", "Bit", "Bregman divergence", "Chain rule", "Change of variables", "Chapman & Hall", "Chi-squared test", "Coding theory", "Conditional entropy", "Conference on Neural Information Processing Systems", "Continuous random variable", "Convex function", "Covariance matrix", "Cross-entropy", "Cross entropy", "Data compression", "Data differencing", "Density matrix", "Deviance information criterion", "Differential entropy", "Digital object identifier", "Dimensional analysis", "Discrete probability distribution", "Discrete random variable", "Divergence", "Divergence (statistics)", "Dover Publications", "E.T. 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The use of the forward measure was pioneered by Farshid Jamshidian (1987), and later used as a means of calculating the price of options on bonds.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Bond option", "Damiano Brigo", "Digital object identifier", "Fabio Mercurio", "Farshid Jamshidian", "Finance", "Forward price", "International Standard Book Number", "Martingale (probability theory)", "Numeraire", "Radon\u2013Nikodym derivative", "Risk-neutral measure"], "references": ["http://doi.org/10.1111%2Fj.1540-6261.1989.tb02413.x"]}, "Mortality rate": {"categories": ["Actuarial science", "All articles containing potentially dated statements", "All articles with dead external links", "Articles containing potentially dated statements from 2017", "Articles with dead external links from February 2018", "Articles with permanently dead external links", "Commons category link is locally defined", "Demography", "Epidemiology", "Medical aspects of death", "Medical statistics", "Population", "Population ecology", "Temporal rates", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Mortality rate", "method": "Mortality rate", "url": "https://en.wikipedia.org/wiki/Mortality_rate", "summary": "Mortality rate, or death rate, is a measure of the number of deaths (in general, or due to a specific cause) in a particular population, scaled to the size of that population, per unit of time. Mortality rate is typically expressed in units of deaths per 1,000 individuals per year; thus, a mortality rate of 9.5 (out of 1,000) in a population of 1,000 would mean 9.5 deaths per year in that entire population, or 0.95% out of the total. It is distinct from \"morbidity\", which is either the prevalence or incidence of a disease, and also from the incidence rate (the number of newly appearing cases of the disease per unit of time).\nIn the generic form, mortality rates are calculated as:\n\n \n \n \n d\n \n /\n \n p\n \u2217\n \n 10\n \n n\n \n \n \n \n {\\displaystyle d/p*10^{n}}\n \nwhere d represents the deaths occurring within a given time period and p represents the size of the population in which the deaths occur.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d7/Death_rate_world_map.PNG", "https://upload.wikimedia.org/wikipedia/commons/9/9a/Flag_of_Afghanistan.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9a/Flag_of_Bulgaria.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4b/Flag_of_Chad.svg", "https://upload.wikimedia.org/wikipedia/commons/0/01/Flag_of_Guinea-Bissau.svg", "https://upload.wikimedia.org/wikipedia/commons/8/84/Flag_of_Latvia.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4a/Flag_of_Lesotho.svg", "https://upload.wikimedia.org/wikipedia/commons/1/11/Flag_of_Lithuania.svg", "https://upload.wikimedia.org/wikipedia/commons/f/ff/Flag_of_Serbia.svg", "https://upload.wikimedia.org/wikipedia/commons/4/49/Flag_of_Ukraine.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2b/Income_death_in_logs_graph.JPG", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f3/Flag_of_Russia.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abortion", "Abortion law", "Academic clinical trials", "Accidental death", "Activation-induced cell death", "Adaptive clinical trial", "Administration (probate law)", "Afghanistan", "Afterlife", "Age-specific mortality rate", "Algor mortis", "Alkaline hydrolysis (body disposal)", "Alzheimer's disease", "Analysis of clinical trials", "Animal sacrifice", "Animal testing", "Animal testing on non-human primates", "Anoikis", "Apoptosis", "Apparent death", "Assisted suicide", "Attributable fraction among the exposed", "Attributable fraction for the population", "Aubrey de Grey", "Autolysis (biology)", "Autophagy", "Autopsy", "Autoschizis", "Avascular necrosis", "Beating heart cadaver", "Bed burial", "Biodemography", "Biological immortality", "Biostratinomy", "Birthday effect", "Blind experiment", "Body donation", "Brain death", "Brainstem death", "Bronchus cancer", "Bulgaria", "Burial", "Burial at sea", "CIA World Factbook", "Cadaver", "Cadaveric spasm", "Capital punishment", "Case fatality rate", "Case report", "Case series", "Case study", "Caseous necrosis", "Case\u2013control study", "Cause of death", "Cell death", "Cemetery", "Censoring (statistics)", "Chad", "Chariot burial", "Child mortality", "Christmas and holiday season", "Chronic obstructive pulmonary disease", "Civil death", "Clinical death", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cluster sampling", "Coagulative necrosis", "Coffin birth", "Cohort study", "Compensation law of mortality", "Consciousness after death", "Coroner", "Correlation does not imply causation", "Cremation", "Cross-sectional study", "Cryonics", "Cryopreservation", "Cumulative incidence", "Dark tourism", "Darwin Awards", "Dead on arrival", "Dead pool", "Death", "Death-positive movement", "Death-qualified jury", "Death (personification)", "Death and culture", "Death and the Internet", "Death anniversary", "Death anxiety (psychology)", "Death by natural causes", "Death certificate", "Death drive", "Death education", "Death erection", "Death from laughter", "Death hoax", "Death knell", "Death march", "Death mask", "Death messenger", "Death notification", "Death panel", "Death poem", "Death pose", "Death rattle", "Death row", "Death squad", "Death threat", "Death trajectory", "Declared death in absentia", "Decomposition", "Dementias", "Demography", "Design of experiments", "Developed countries", "Diabetes mellitus", "Diarrhoeal diseases", "Digital immortality", "Digital object identifier", "Dignified death", "Dismemberment", "Disposal of human corpses", "Dissection", "Dying-and-rising deity", "Dying declaration", "Dysthanasia", "Ecological study", "Embalming", "End-of-life care", "Epidemiological methods", "Eschar", "Eternal oblivion", "Euthanasia", "Evidence-based medicine", "Excarnation", "Experiment", "Extermination camp", "Extinction", "Faked death", "Fan death", "Fascination with death", "Fat necrosis", "Festival of the Dead", "Fibrinoid necrosis", "First-in-man study", "Forensic pathology", "Fossil", "Funeral", "Funeral director", "Gangrene", "Ghost", "Gibbeting", "Glossary of clinical research", "Gompertz\u2013Makeham law of mortality", "Grief", "Guinea-Bissau", "Hazard ratio", "Homicide", "Human cannibalism", "Human sacrifice", "Immortality", "Immunogenic cell death", "In vitro", "In vivo", "Incidence (epidemiology)", "Incidence rate", "Infant mortality", "Infectivity", "Information-theoretic death", "Inquest", "Integrated Authority File", "Intention-to-treat analysis", "Intermediate state", "International Standard Book Number", "International Standard Serial Number", "Intrinsic apoptosis", "Ischaemic heart disease", "Ischemic cell death", "JSTOR", "Jar burial", "Jean Ziegler", "Karyolysis", "Karyorrhexis", "Kar\u014dshi", "Last rites", "Latvia", "Lazarus sign", "Lazarus syndrome", "Legal death", "Lesotho", "Likelihood ratios in diagnostic testing", "Liquefactive necrosis", "List of causes of death by rate", "List of clinical research topics", "List of countries by birth rate", "List of countries by death rate", "List of countries by life expectancy", "List of countries by number of deaths", "List of death deities", "List of expressions related to death", "List of natural disasters by death toll", "List of premature obituaries", "List of sovereign states and dependent territories by mortality rate", "List of television actors who died during production", "List of unusual deaths", "Lists of deaths by year", "Lists of people by cause of death", "Lithuania", "Livor mortis", "Longitudinal study", "Lower respiratory infections", "Lung cancer", "Maceration (bone)", "Malnutrition", "Martyr", "Maternal death", "Maternal mortality", "Maternal mortality in fiction", "Maternal mortality ratio", "Maximum life span", "Measurement", "Medical condition", "Medical definition of death", "Medical examiner", "Medical statistics", "Megadeath", "Memento mori", "Meta-analysis", "Micromort", "Micronutrients", "Missing data", "Mitotic catastrophe", "Morbidity", "Mortality displacement", "Mortality salience", "Mortuary science", "Mourning", "Multicenter trial", "Multistage sampling", "Mummy", "Murder", "Museum of Death", "National Diet Library", "Natural burial", "Natural logarithm", "Near-death experience", "Near-death studies", "Necromancy", "Necronym", "Necrophilia", "Necrophobia", "Necroptosis", "Necrosis", "Nested case\u2013control study", "Neuropreservation", "Null result", "Number needed to harm", "Number needed to treat", "Obituary", "Observational study", "Odds ratio", "Open-label trial", "Organ donation", "Out-of-body experience", "Outline of death", "Pallor mortis", "Paraptosis", "Parthanatos", "Perinatal mortality", "Period prevalence", "Phenoptosis", "Plastination", "Point prevalence", "Population Impact Measures", "Post-mortem chemistry", "Post-mortem interval", "Post-mortem photography", "Postmortem caloricity", "Pre- and post-test probability", "Predation", "Premature burial", "Prevalence", "Preventable causes of death", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Programmed cell death", "Prohibition of death", "Promession", "Proportionality (mathematics)", "Prosection", "Prospective cohort study", "Protocol (science)", "Pseudoapoptosis", "Psychopomp", "PubMed Central", "PubMed Identifier", "Putrefaction", "Pyknosis", "Pyroptosis", "Randomized controlled trial", "Reincarnation", "Relative risk reduction", "Reproducibility", "Resurrection", "Retrospective cohort study", "Right to die", "Rigor mortis", "Risk adjusted mortality rate", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Road traffic accidents", "Russia", "Sacrifice", "Sampling error", "Scientific control", "Secondary burial", "Seeding trial", "Selection bias", "Serbia", "Ship burial", "Skeletonization", "Sky burial", "Space burial", "Specificity and sensitivity", "Spiritual death", "Standardized mortality ratio", "Statistical population", "Stillbirth and Neonatal Death Society", "Stroke", "Suicide", "Suicide gene", "Survivorship bias", "Suspicious death", "Systematic review", "S\u00e9ance", "Taboo on the dead", "Taphonomy", "Taxidermy", "Temporal lobe necrosis", "Terminal illness", "Thanatology", "Thanatosensitivity", "The Order of the Good Death", "Trachea cancer", "Trust law", "Tuberculosis", "US Centers for Disease Control", "Ukraine", "Undead", "United Nations", "United Nations Special Rapporteur", "Unnatural death", "Vaccine trial", "Vigil", "Virulence", "Vital statistics (government records)", "Voodoo death", "Weekend effect", "Will and testament", "World Health Organization"], "references": ["http://www.google.com/publicdata/overview?ds=j0r9lucsi4q1d_", "http://www.medterms.com/script/main/art.asp?articlekey=19649", "http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198229971.001.0001/acprof-9780198229971", "http://www.pierre-marteau.com/editions/1693-mortality.html", "http://journals.sagepub.com/doi/10.1177/1352458516688954", "http://doi.wiley.com/10.1111/jog.13445", "http://webapp.cdc.gov/sasweb/ncipc/leadcaus10.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5589409", "http://www.ncbi.nlm.nih.gov/pubmed/2734809", "http://www.ncbi.nlm.nih.gov/pubmed/28888247", "http://www.who.int/gho/mortality_burden_disease/causes_death/top_10/en/", "http://www.cedat.org/", "http://www.data360.org/graph_group.aspx?Graph_Group_Id=347", "http://www.deathriskrankings.org/", "http://doi.org/10.1016%2Fj.jaip.2017.06.031", "http://doi.org/10.1093%2Facprof:oso%2F9780198229971.001.0001%2Facprof-9780198229971", "http://doi.org/10.1111%2Fjog.13445", "http://doi.org/10.1177%2F1352458516688954", "http://doi.org/10.2202%2F1941-6008.1011", "http://doi.org/10.2307%2F1966567", "http://doi.org/10.2307%2F3644262", "http://www.jstor.org/stable/3644262", "http://www.mortality.org/", "http://www.sens.org/files/pdf/ENHANCE-PP.pdf", "http://data.un.org/Data.aspx?d=PopDiv&f=variableID:65", "http://www.worldcat.org/issn/0039-3665", "http://www.worldcat.org/issn/1341-8076", "http://www.worldcat.org/issn/1352-4585", "https://books.google.com/books?id=okf1AwAAQBAJ&pg=PA189", "https://books.google.com/books?id=okf1AwAAQBAJ&pg=PA36", "https://books.google.com/books?id=okf1AwAAQBAJ&pg=PA64", "https://books.google.com/books?id=okf1AwAAQBAJ&pg=PA69", "https://www.cdc.gov/ophss/csels/dsepd/ss1978/lesson3/section3.html", "https://www.cia.gov/library/publications/the-world-factbook/geos/xx.html", "https://www.cia.gov/library/publications/the-world-factbook/rankorder/2066rank.html", "https://www.ncbi.nlm.nih.gov/books/NBK220916/", "https://d-nb.info/gnd/4057312-6", "https://id.ndl.go.jp/auth/ndlna/00570879", "https://web.archive.org/web/20090215000125/http://esa.un.org/unpp/index.asp?panel=2", "https://www.wikidata.org/wiki/Q58702"]}, "Epps effect": {"categories": ["All stub articles", "Multivariate time series", "Statistics stubs"], "title": "Epps effect", "method": "Epps effect", "url": "https://en.wikipedia.org/wiki/Epps_effect", "summary": "In econometrics and time series analysis, the Epps effect, named after T. W. Epps, is the phenomenon that the empirical correlation between the returns of two different stocks decreases with the length of the interval for which the price changes are measured. The phenomenon is caused by non-synchronous/asynchronous trading\n and discretization effects. However, a current study shows that the effect originates in investors' herd behaviour.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Cross correlation", "Econometrics", "Herd behaviour", "Statistics", "Time series analysis"], "references": ["http://iopscience.iop.org/1367-2630/16/5/053040", "https://arxiv.org/abs/1001.5124", "https://www.jstor.org/stable/2286325"]}, "Mixed model": {"categories": ["Analysis of variance", "Regression models"], "title": "Mixed model", "method": "Mixed model", "url": "https://en.wikipedia.org/wiki/Mixed_model", "summary": "A mixed model is a statistical model containing both fixed effects and random effects. These models are useful in a wide variety of disciplines in the physical, biological and social sciences.\nThey are particularly useful in settings where repeated measurements are made on the same statistical units (longitudinal study), or where measurements are made on clusters of related statistical units. Because of their advantage in dealing with missing values, mixed effects models are often preferred over more traditional approaches such as repeated measures ANOVA.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["ANOVA", "ASReml-R", "Applied Longitudinal Analysis (textbook)", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian statistics", "Best linear unbiased prediction", "Charles Roy Henderson", "Conditional variance", "Covariance matrix", "Design matrix", "Digital object identifier", "Discrete choice", "EM algorithm", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effect", "Fixed effects model", "Garrett M. Fitzmaurice", "Gauss\u2013Markov theorem", "GenStat", "General linear model", "Generalized least squares", "Generalized linear mixed model", "Generalized linear model", "Goodness of fit", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "James H. Ware", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Longitudinal study", "Matrix notation", "Maximum likelihood estimate", "Mean and predicted response", "Mixed-design analysis of variance", "Mixed logit", "Mixture model", "Multilevel model", "Multinomial logit", "Multinomial probit", "NCSS (statistical software)", "Nan M. Laird", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Nuisance parameter", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "PubMed Identifier", "Quantile regression", "R (programming language)", "Random effect", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Repeated measures design", "Robust regression", "Ronald Fisher", "SAS (software)", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Stata", "Statistical model", "Statistical unit", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "United States National Academy of Sciences", "Weighted least squares"], "references": ["http://www.cbssports.com/mlb/news/mlb-analytics-guru-who-could-be-the-next-nate-silver-has-a-revolutionary-new-stat/", "http://www.lexjansen.com/mwsug/1993/MWSUG93035.pdf", "http://books.nap.edu/html/biomems/chenderson.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/7168798", "http://doi.org/10.1017%2FS0080456800012163", "http://doi.org/10.1080%2F01621459.1988.10478693", "http://doi.org/10.1214%2Fss%2F1177011926", "http://doi.org/10.2307%2F2527669", "http://doi.org/10.2307%2F2529876", "http://doi.org/10.2307%2F2685241", "http://www.journalofanimalscience.org/content/1973/Symposium/10.full.pdf", "http://www.jstor.org/stable/2245695", "http://www.jstor.org/stable/2527669", "http://www.jstor.org/stable/2529876", "http://www.jstor.org/stable/2685241"]}, "Scott's Pi": {"categories": ["Inter-rater reliability"], "title": "Scott's Pi", "method": "Scott's Pi", "url": "https://en.wikipedia.org/wiki/Scott%27s_Pi", "summary": "Scott's pi (named after William A. Scott) is a statistic for measuring inter-rater reliability for nominal data in communication studies. Textual entities are annotated with categories by different annotators, and various measures are used to assess the extent of agreement between the annotators, one of which is Scott's pi. Since automatically annotating text is a popular problem in natural language processing, and goal is to get the computer program that is being developed to agree with the humans in the annotations it creates, assessing the extent to which humans agree with each other is important for establishing a reasonable upper limit on computer performance.\nScott's pi is similar to Cohen's kappa in that they improve on simple observed agreement by factoring in the extent of agreement that might be expected by chance. However, in each statistic, the expected agreement is calculated slightly differently. Scott's pi makes the assumption that annotators have the same distribution of responses, which makes Cohen's kappa slightly more informative. Scott's pi is extended to more than two annotators in the form of Fleiss' kappa.\nThe equation for Scott's pi, as in Cohen's kappa, is:\n\n \n \n \n \u03c0\n =\n \n \n \n Pr\n (\n a\n )\n \u2212\n Pr\n (\n e\n )\n \n \n 1\n \u2212\n Pr\n (\n e\n )\n \n \n \n ,\n \n \n {\\displaystyle \\pi ={\\frac {\\Pr(a)-\\Pr(e)}{1-\\Pr(e)}},}\n However, Pr(e) is calculated using joint proportions. A worked example is given below.\nConfusion matrix for two annotators, three categories {Yes, No, Maybe} and 45 items rated (90 ratings for 2 annotators):\n\nTo calculate the expected agreement, sum marginals across annotators and divide by the total number of ratings to obtain joint proportions. Square and total these:\n\nTo calculate observed agreement, divide the number of items on which annotators agreed by the total number of items. In this case,\n\n \n \n \n Pr\n (\n a\n )\n =\n \n \n \n 1\n +\n 5\n +\n 9\n \n 45\n \n \n =\n 0.333.\n \n \n {\\displaystyle \\Pr(a)={\\frac {1+5+9}{45}}=0.333.}\n Given that Pr(e) = 0.369, Scott's pi is then\n\n \n \n \n \u03c0\n =\n \n \n \n 0.333\n \u2212\n 0.369\n \n \n 1\n \u2212\n 0.369\n \n \n \n =\n \u2212\n 0.059.\n \n \n {\\displaystyle \\pi ={\\frac {0.333-0.369}{1-0.369}}=-0.059.}", "images": [], "links": ["Cohen's kappa", "Communication studies", "Fleiss' kappa", "Inter-rater reliability", "Krippendorff's alpha", "Natural language processing", "Nominal data", "William A. Scott"], "references": []}, "Complete-linkage clustering": {"categories": ["All articles needing additional references", "All articles to be expanded", "Articles needing additional references from September 2010", "Articles to be expanded from October 2011", "Articles using small message boxes", "Articles with short description", "Bioinformatics algorithms", "Cluster analysis algorithms", "Computational phylogenetics"], "title": "Complete-linkage clustering", "method": "Complete-linkage clustering", "url": "https://en.wikipedia.org/wiki/Complete-linkage_clustering", "summary": "Complete-linkage clustering is one of several methods of agglomerative hierarchical clustering. At the beginning of the process, each element is in a cluster of its own. The clusters are then sequentially combined into larger clusters until all elements end up being in the same cluster. The method is also known as farthest neighbour clustering. The result of the clustering can be visualized as a dendrogram, which shows the sequence of cluster fusion and the distance at which each fusion took place.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a2/Complete_linkage_Dendrogram_5S_data.svg", "https://upload.wikimedia.org/wikipedia/commons/4/43/Simple_linkage-5S.svg", "https://upload.wikimedia.org/wikipedia/commons/4/43/UPGMA_Dendrogram_5S_data.svg", "https://upload.wikimedia.org/wikipedia/commons/3/39/WPGMA_Dendrogram_5S_data.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["5S ribosomal RNA", "Acholeplasma", "Bacillus stearothermophilus", "Bacillus subtilis", "Cluster analysis", "Complete linkage", "Dendrogram", "Digital object identifier", "Hierarchical clustering", "International Standard Book Number", "Micrococcus luteus", "Models of DNA evolution", "Molecular clock", "Neighbor-joining", "PubMed Central", "PubMed Identifier", "Sabine Landau", "Single-linkage clustering", "Single linkage clustering", "UPGMA", "Ultrametricity", "WPGMA", "Weissella"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC341310", "http://www.ncbi.nlm.nih.gov/pubmed/2422630", "http://www.ncbi.nlm.nih.gov/pubmed/3241556", "http://doi.org/10.1093%2Fcomjnl%2F20.4.364", "http://comjnl.oxfordjournals.org/content/20/4/364.full.pdf"]}, "Borel\u2013Cantelli lemma": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2009", "Covering lemmas", "Lemmas", "Probability theorems", "Theorems in measure theory"], "title": "Borel\u2013Cantelli lemma", "method": "Borel\u2013Cantelli lemma", "url": "https://en.wikipedia.org/wiki/Borel%E2%80%93Cantelli_lemma", "summary": "In probability theory, the Borel\u2013Cantelli lemma is a theorem about sequences of events. In general, it is a result in measure theory. It is named after \u00c9mile Borel and Francesco Paolo Cantelli, who gave statement to the lemma in the first decades of the 20th century. A related result, sometimes called the second Borel\u2013Cantelli lemma, is a partial converse of the first Borel\u2013Cantelli lemma. The lemma states that, under certain conditions, an event will have probability of either zero or one. Accordingly, it is the best-known of a class of similar theorems, known as zero-one laws. Other examples include Kolmogorov's zero\u2013one law and the Hewitt\u2013Savage zero\u2013one law.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Almost surely", "Compact set", "Converse (logic)", "Elias M. Stein", "Encyclopedia of Mathematics", "Event (probability theory)", "Francesco Paolo Cantelli", "Franz Thomas Bruss", "Hewitt\u2013Savage zero\u2013one law", "Infinite monkey theorem", "International Standard Book Number", "Iverson bracket", "Kolmogorov's zero\u2013one law", "Kuratowski convergence", "Lebesgue measure", "L\u00e9vy's zero\u2013one law", "Measure (mathematics)", "Measure space", "Measure theory", "Michiel Hazewinkel", "Pairwise independence", "Probability space", "Probability theory", "Random variable", "Sequence", "Set-theoretic limit", "Sigma-algebra", "Statistical independence", "Stochastic process", "Theorem", "William Feller", "\u00c9mile Borel"], "references": ["http://terrytao.wordpress.com/2008/06/18/the-strong-law-of-large-numbers/", "http://www.math.ucdavis.edu/~romik/teaching/lectures.pdf", "https://web.archive.org/web/20081007200246/http://planetmath.org/encyclopedia/BorelCantelliLemma.html", "https://web.archive.org/web/20100614024007/http://www.math.ucdavis.edu/~romik/teaching/lectures.pdf", "https://www.encyclopediaofmath.org/index.php?title=B/b017040"]}, "Shifting baseline": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from January 2011", "Biostatistics", "Environmental terminology", "Fisheries science", "Measurement"], "title": "Shifting baseline", "method": "Shifting baseline", "url": "https://en.wikipedia.org/wiki/Shifting_baseline", "summary": "A shifting baseline (also known as sliding baseline) is a type of change to how a system is measured, usually against previous reference points (baselines), which themselves may represent significant changes from an even earlier state of the system. \nThe concept arose in landscape architect Ian McHarg's 1969 manifesto Design With Nature in which the modern landscape is compared to that on which ancient people once lived. The concept was then considered by the fisheries scientist Daniel Pauly in his paper \"Anecdotes and the shifting baseline syndrome of fisheries\". Pauly developed the concept in reference to fisheries management where fisheries scientists sometimes fail to identify the correct \"baseline\" population size (e.g. how abundant a fish species population was before human exploitation) and thus work with a shifted baseline. He describes the way that radically depleted fisheries were evaluated by experts who used the state of the fishery at the start of their careers as the baseline, rather than the fishery in its untouched state. Areas that swarmed with a particular species hundreds of years ago, may have experienced long term decline, but it is the level of decades previously that is considered the appropriate reference point for current populations. In this way large declines in ecosystems or species over long periods of time were, and are, masked. There is a loss of perception of change that occurs when each generation redefines what is \"natural\". \nMost modern fisheries stock assessments do not ignore historical fishing and account for it by either including the historical catch or use other techniques to reconstruct the depletion level of the population at the start of the period for which adequate data is available. Anecdotes about historical populations levels can be highly unreliable and result in severe mismanagement of the fishery.The concept was further refined and applied to the ecology of kelp forests by Paul Dayton and others from the Scripps Institution of Oceanography. They used a slightly different version of the term in their paper, \"Sliding baselines, ghosts, and reduced expectations in kelp forest communities\". Both terms refer to a shift over time in the expectation of what a healthy ecosystem baseline looks like.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/81/Great_Barracuda_off_the_Netherland_Antilles.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/1e/Trawer_Hauling_Nets.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Yellowfin_tuna_nurp.jpg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Acoustic tag", "Age class structure", "Algal bloom", "Angling", "Aquaculture", "Aquaculture Stewardship Council", "Aquatic ecosystem", "Artificial fly", "Artisanal fishing", "Bias of an estimator", "Big-game fishing", "Bioeconomics (fisheries)", "Biomass (ecology)", "Bite indicator", "Bycatch", "CalCOFI", "Catch and release", "Catch per unit effort", "Catch reporting", "Catch share", "Census of Marine Life", "Cetacean bycatch", "Coastal fish", "Cod fisheries", "Coded wire tag", "Commercial fishing", "Common Fisheries Policy", "Condition index", "Conservation movement", "Coral reef", "Coral reef fish", "Crab fisheries", "Daniel Pauly", "Data storage tag", "Dead zone (ecology)", "Defying Ocean's End", "Demersal fish", "Destructive fishing practices", "Discards", "Diversity of fish", "EcoSCOPE", "Ecologist", "Ecology", "EconMult", "Ecopath", "Eel ladder", "Eel life history", "Environmental effects of fishing", "European Fishery MLS", "Exclusive economic zone", "Filmmaker", "FishBase", "Fish counter", "Fish diseases and parasites", "Fish farming", "Fish hook", "Fish kill", "Fish ladder", "Fish market", "Fish marketing", "Fish measurement", "Fish migration", "Fish mortality", "Fish pond", "Fish processing", "Fish products", "Fish screen", "Fish slaughter", "Fish stock", "Fish trap", "Fisheries acoustics", "Fisheries and climate change", "Fisheries law", "Fisheries management", "Fisheries observer", "Fisheries science", "Fisherman", "Fishery", "Fishery Resources Monitoring System", "Fishfinder", "Fishing", "Fishing bait", "Fishing down the food web", "Fishing industry", "Fishing industry by country", "Fishing line", "Fishing lure", "Fishing net", "Fishing rod", "Fishing sinker", "Fishing tackle", "Fishing techniques", "Fishing tournament", "Fishing vessel", "Fishing village", "Fly fishing", "Forage fish", "Friend of the Sea", "Future of Marine Animal Populations", "GIS and aquatic science", "Gathering seafood by hand", "Generation", "Glossary of fisheries", "Glossary of fishery terms", "Greenpeace", "Grey nurse shark conservation", "Handline fishing", "History of fishing", "Hotspot Ecosystem Research and Man's Impact On European Seas", "Humboldt Current", "Ian McHarg", "Illegal, unreported and unregulated fishing", "Incidental catch", "Index of fishing articles", "Individual fishing quota", "International Seafood Sustainability Foundation", "Jeremy Jackson (scientist)", "Kelp", "Kelp forest", "Krill fishery", "List of fishing topics by subject", "List of harvested aquatic animals by weight", "List of threatened rays", "List of threatened sharks", "Lobster fishing", "Los Angeles Times", "Magnuson\u2013Stevens Fishery Conservation and Management Act", "Marine Protected Area", "Marine Stewardship Council", "Marine biologist", "Marine biology", "Marine conservation", "Marine conservation activism", "Marine habitats", "Marine pollution", "Marine reserve", "Marine snow", "Match/mismatch", "Maximum sustainable yield", "Mercury in fish", "Minimum landing size", "Mongabay.com", "Monitoring control and surveillance", "Observer effect (disambiguation)", "Ocean Conservancy", "Ocean Outcomes", "Ocean Surface Topography Mission", "Ocean bank (topography)", "Ocean fisheries", "Oceana (non-profit group)", "Op-ed", "Otolith microchemical analysis", "Outline of fishing", "Overfishing", "Overton window", "PROFISH", "Pelagic fish", "Perception", "Pop-up satellite archival tag", "Population dynamics of fisheries", "Public service announcements", "Pulse fishing", "Recreational fishing", "Salmon conservation", "Salmon run", "Sardine run", "Scripps Institution of Oceanography", "SeaChoice", "Sea Around Us (organization)", "Sea Around Us Project", "Sea Shepherd Conservation Society", "Seafood", "Seafood Watch", "Seed (magazine)", "Shark finning", "Shark sanctuary", "Shoaling and schooling", "Shrimp-Turtle Case", "Shrimp fishery", "Slot limit", "Spearfishing", "Standard weight in fish", "Stock assessment", "Surfrider Foundation", "Sustainable fisheries", "Sustainable fishery", "Sustainable seafood", "Syndrome", "The Black Fish", "The End of the Line (book)", "The Ocean Conservancy", "The Sunken Billions", "Trawling", "Trolling (fishing)", "Trophic cascade", "Trophic level", "Turtle excluder device", "Upwelling", "Vessel monitoring system", "Water column", "Wild fisheries", "WorldFish Center"], "references": ["http://www.fisheries.ubc.ca/members/dpauly/chaptersInBooksReports/2001/ImportanceHistoricalDimensionPolicyMngtNaturalResourceSystems.pdf", "http://news.mongabay.com/2009/0623-hance_shiftingbaselines.html", "http://www.scienceblogs.com/shiftingbaselines", "http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VJ1-40W0T2R-7Y&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=313bda126ec2c8cba56b51a0c83d6e6d", "http://www.ted.com/talks/daniel_pauly_the_ocean_s_shifting_baseline.html", "http://www3.interscience.wiley.com/journal/122200416/abstract?CRETRY=1&SRETRY=0", "http://www.psp.wa.gov/shiftingbaselines.php", "http://www.conservationinstitute.org/ocean_change/Fisheries/shiftingbaselines.htm", "http://www.esajournals.org/doi/abs/10.1890/1051-0761(1998)008%5B0309:SBGARE%5D2.0.CO;2", "http://seaaroundus.org/magazines/2006/ShiftingBaselines_Canright.pdf", "http://www.shiftingbaselines.org"]}, "Engset calculation": {"categories": ["Queueing theory"], "title": "Engset formula", "method": "Engset calculation", "url": "https://en.wikipedia.org/wiki/Engset_formula", "summary": "In queueing theory, the Engset formula is used to determine the blocking probability of an M/M/c/c/N queue (in Kendall's notation).\nThe formula is named after its developer, T. O. Engset.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["ArXiv", "Bisection", "Digital object identifier", "Erlang (unit)", "Fixed-point iteration", "Hypergeometric function", "International Standard Serial Number", "Kendall's notation", "Limit of a sequence", "MATLAB", "Newton's method", "Probability", "Python (programming language)", "Queueing theory", "SciPy", "T. O. Engset"], "references": ["http://www.mathworks.com/products/symbolic/", "http://www.ee.cityu.edu.hk/~zukerman/classnotes.pdf", "http://arxiv.org/abs/1511.00291", "http://doi.org/10.1002%2F047001363X", "http://doi.org/10.1016%2Fj.orl.2016.02.011", "http://www.worldcat.org/issn/0167-6377", "https://github.com/parsiad/fast-engset/releases"]}, "Event study": {"categories": ["Valuation (finance)"], "title": "Event study", "method": "Event study", "url": "https://en.wikipedia.org/wiki/Event_study", "summary": "An event study is a statistical method to assess the impact of an event on the value of a firm. For example, the announcement of a merger between two business entities can be analyzed to see whether investors believe the merger will create or destroy value. The basic idea is to find the abnormal return attributable to the event being studied by adjusting for the return that stems from the price fluctuation of the market as a whole. The event study was invented by Fama, Fisher, Jensen, and Roll (1969).As the event methodology can be used to elicit the effects of any type of event on the direction and magnitude of stock price changes, it is very versatile. Event studies are thus common to various research areas, such as accounting and finance, management, economics, marketing, information technology, law, political science, operations and supply chain management.\nOne aspect often used to structure the overall body of event studies is the breadth of the studied event types. On the one hand, there is research investigating the stock market responses to economy-wide events (i.e., market shocks, such as regulatory changes, or catastrophic events). On the other hand, event studies are used to investigate the stock market responses to corporate events, such as mergers and acquisitions, earnings announcements, debt or equity issues, corporate reorganisations, investment decisions and corporate social responsibility (MacKinlay 1997; McWilliams & Siegel, 1997).", "images": [], "links": ["Abnormal return", "Capital asset pricing model", "Center for Research in Securities Prices", "Corporate social responsibility", "Debt", "Digital object identifier", "Federal Trade Commission", "Financial crisis of 2007\u20132008", "International Standard Serial Number", "Jerold Warner", "Long-horizon", "MS Excel", "Matlab", "Merger", "Office Depot", "Post earnings announcement drift", "Regression analysis", "S.P. Kothari", "STATA", "Short-horizon", "Staples, Inc.", "Statistics", "Stock", "Student's t-distribution", "T-test"], "references": ["http://linkinghub.elsevier.com/retrieve/pii/S0925527318301610", "http://www.eventstudy.com", "http://www.eventstudymetrics.com", "http://www.eventstudytools.com", "http://www.law360.com/articles/142884/testing-for-materiality-in-volatile-markets", "http://ssrn.com/abstract=2534446", "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=608601", "http://doi.org/10.1016%2Fj.ijpe.2018.04.006", "http://www.worldcat.org/issn/0925-5273", "https://www.jstor.org/stable/257056", "https://www.jstor.org/stable/2729691", "https://www.jstor.org/stable/41798368"]}, "Inter-rater reliability": {"categories": ["Comparison of assessments", "Inter-rater reliability", "Statistical data types"], "title": "Inter-rater reliability", "method": "Inter-rater reliability", "url": "https://en.wikipedia.org/wiki/Inter-rater_reliability", "summary": "In statistics, inter-rater reliability (also called by various similar names, such as inter-rater agreement, inter-rater concordance, interobserver reliability, and so on) is the degree of agreement among raters. It is a score of how much homogeneity, or consensus, there is in the ratings given by various judges. In contrast, intra-rater reliability is a score of the consistency in ratings given by the same person across multiple instances. Inter-rater and intra-rater reliability are aspects of test validity. Assessments of them are useful in refining the tools given to human judges, for example by determining if a particular scale is appropriate for measuring a particular variable. If various raters do not agree, either the scale is defective or the raters need to be re-trained.\nThere are a number of statistics that can be used to determine inter-rater reliability. Different statistics are appropriate for different types of measurement. Some options are: joint-probability of agreement, Cohen's kappa, Scott's pi and the related Fleiss' kappa, inter-rater correlation, concordance correlation coefficient, intra-class correlation, and Krippendorff's alpha.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/18/Bland-Altman-Plot.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Bland\u2013Altman plot", "Cohen's kappa", "Computational linguistics", "Concordance correlation coefficient", "Consensus", "Content analysis", "Cronbach's alpha", "Experimenter's bias", "Fleiss' kappa", "Generalizability theory", "International Standard Book Number", "Intra-class correlation", "Intra-class correlation coefficient", "Intra-rater reliability", "Kendall rank correlation coefficient", "Krippendorff's alpha", "Mean", "Nominal data", "Observational studies", "Pearson product-moment correlation coefficient", "Psychometrics", "Rasch model", "Rating (pharmaceutical industry)", "Scott's pi", "Spearman's rank correlation coefficient", "Standard deviation", "Statistics", "Survey research", "Test validity"], "references": ["http://www.agreestat.com/agreestat.html", "http://www.agreestat.com/blog_irr/chance_agreement_correction.html", "http://www.agreestat.com/book4/", "http://www.agreestat.com/book_excerpts.html", "http://www.agreestat.com/research_papers/bjmsp2008_interrater.pdf", "http://www.crcpress.com/product/isbn/9781439810804", "http://john-uebersax.com/stat/agree.htm", "http://onlinelibrary.wiley.com/doi/10.1111/j.1440-1681.2009.05288.x/full", "http://justus.randolph.name/kappa", "http://www.med-ed-online.org/rating/reliability.html", "https://nlp-ml.io/jg/software/ira"]}, "Discrete choice analysis": {"categories": ["Choice modelling", "Economics models", "Mathematical and quantitative methods (economics)"], "title": "Discrete choice", "method": "Discrete choice analysis", "url": "https://en.wikipedia.org/wiki/Discrete_choice", "summary": "In economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives, such as entering or not entering the labor market, or choosing between modes of transport. Such choices contrast with standard consumption models in which the quantity of each good consumed is assumed to be a continuous variable. In the continuous case, calculus methods (e.g. first-order conditions) can be used to determine the optimum amount chosen, and demand can be modeled empirically using regression analysis. On the other hand, discrete choice analysis examines situations in which the potential outcomes are discrete, such that the optimum is not characterized by standard first-order conditions. Thus, instead of examining \u201chow much\u201d as in problems with continuous choice variables, discrete choice analysis examines \u201cwhich one.\u201d However, discrete choice analysis can also be used to examine the chosen quantity when only a few distinct quantities must be chosen from, such as the number of vehicles a household chooses to own and the number of minutes of telecommunications service a customer decides to purchase. Techniques such as logistic regression and probit regression can be used for empirical analysis of discrete choice.\nEstimation of such models is usually done via parametric, semi-parametric and non-parametric maximum likelihood methods.Discrete choice models theoretically or empirically model choices made by people among a finite set of alternatives. The models have been used to examine, e.g., the choice of which car to buy, where to go to college, which mode of transport (car, bus, rail) to take to work among numerous other applications. Discrete choice models are also used to examine choices by organizations, such as firms or government agencies. In the discussion below, the decision-making unit is assumed to be a person, though the concepts are applicable more generally. Daniel McFadden won the Nobel prize in 2000 for his pioneering work in developing the theoretical basis for discrete choice.\nDiscrete choice models statistically relate the choice made by each person to the attributes of the person and the attributes of the alternatives available to the person. For example, the choice of which car a person buys is statistically related to the person\u2019s income and age as well as to price, fuel efficiency, size, and other attributes of each available car. The models estimate the probability that a person chooses a particular alternative. The models are often used to forecast how people\u2019s choices will change under changes in demographics and/or attributes of the alternatives.\nDiscrete choice models specify the probability that an individual chooses an option among a set of alternatives. The probabilistic description of discrete choice behavior is used not to reflect individual behavior that is viewed as intrinsically probabilistic. Rather, it is the lack of information that leads us to describe choice in a probabilistic fashion. In practice, we cannot know all factors affecting individual choice decisions as their determinants are partially observed or imperfectly measured. Therefore, discrete choice models rely on stochastic assumptions and specifications to account for unobserved factors related to a) choice alternatives, b) taste variation over people (interpersonal heterogeneity) and over time (intra-individual choice dynamics), and c) heterogeneous choice sets. The different formulations have been summarized and classified into groups of models.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Artelys Knitro", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bellman equation", "Charles F. Manski", "Collectively exhaustive events", "Constrained optimization", "Consumer theory", "Continuous variable", "Counterfactual conditional", "Cumulative normal", "Daniel McFadden", "Demand curve", "Digital object identifier", "Discounting", "Discrete variable", "Dynamic programming", "Econometrica", "Economics", "Errors-in-variables models", "Errors and residuals in statistics", "Extreme value distribution", "Fixed effects model", "G. S. Maddala", "Gauss\u2013Markov theorem", "General linear model", "Generalized extreme value distribution", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Gumbel distribution", "Heteroscedasticity", "Iid", "Independence of irrelevant alternatives", "Initial condition", "International Economic Review", "International Standard Book Number", "International Standard Serial Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jerry Hausman", "John Rust", "Journal of Applied Econometrics", "Journal of Econometrics", "Journal of Human Resources", "Kenneth E. Train", "Kenneth Judd", "Kronecker delta", "Labor market", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic distribution", "Logistic function", "Logistic regression", "Markov chain", "Markov decision process", "Maximum likelihood estimation", "Mean and predicted response", "Method of simulated moments", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Mutual exclusivity", "New product development", "Nobel Memorial Prize in Economic Sciences", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Normal distribution", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Plackett\u2013Luce model", "Poisson regression", "Polynomial regression", "Polytomous choice", "Present value", "Pricing", "Principal component regression", "Probit model", "Probit regression", "Quantile regression", "Random effects model", "Rapid transit", "Regression analysis", "Regression model validation", "Regularized least squares", "Review of Economics and Statistics", "Robust regression", "Scion (automobile)", "Segmented regression", "Semiparametric regression", "Simple linear regression", "State variable", "Statistics", "Structural estimation", "Studentized residual", "Tikhonov regularization", "Time horizon", "Total least squares", "Transport", "Utility theory", "Weighted least squares", "William Greene (economist)"], "references": ["http://roso.epfl.ch/mbi/handbook-final.pdf", "http://trb.metapress.com/content/126847136p81w0p3/", "http://trb.metapress.com/content/l341607q38j850j7/", "http://www.sciencedirect.com/science/article/pii/S0167947316302596", "http://www2.informatik.hu-berlin.de/alkox/lehre/lvws0809/verkehr/logit.pdf", "http://elsa.berkeley.edu/choice2/ch5.pdf", "http://elsa.berkeley.edu/choice2/ch6.pdf", "http://elsa.berkeley.edu/reprints/misc/multinomial.pdf", "http://elsa.berkeley.edu/wp/mcfadden1198/mcfadden1198.pdf", "http://elsa.berkeley.edu/~train/valtrb.pdf", "http://emlab.berkeley.edu/books/choice.html", "http://dspace.mit.edu/handle/1721.1/49797", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.4879", "http://cowles.econ.yale.edu/P/cd/d04b/d0477.pdf", "http://doi.org/10.1002%2F1099-1255(200009%2F10)15:5%3C447::AID-JAE570%3E3.0.CO;2-1", "http://doi.org/10.1016%2F0041-1647(78)90120-x", "http://doi.org/10.1016%2F0304-4076(81)90056-7", "http://doi.org/10.1016%2FS0148-2963(99)00058-2", "http://doi.org/10.1016%2Fj.csda.2016.10.024", "http://doi.org/10.1016%2Fj.labeco.2007.04.003", "http://doi.org/10.1016%2Fj.red.2008.07.001", "http://doi.org/10.1016%2Fj.ssci.2013.10.004", "http://doi.org/10.1111%2Fj.1468-2354.2007.00471.x", "http://doi.org/10.1162%2F003465398557735", "http://doi.org/10.2307%2F1911259", "http://doi.org/10.2307%2F2298122", "http://doi.org/10.2307%2F3147053", "http://doi.org/10.3141%2F1805-10", "http://doi.org/10.3982%2FECTA12605", "http://doi.org/10.3982%2FECTA7925", "http://dx.doi.org/10.2307/2298122", "http://www.jstor.org/stable/145612", "http://www.jstor.org/stable/1911259", "http://www.jstor.org/stable/1913909", "http://www.jstor.org/stable/2346567", "http://www.jstor.org/stable/2555538", "http://www.jstor.org/stable/2646846", "http://www.worldcat.org/issn/0012-9682", "http://www.worldcat.org/issn/1468-0262", "https://editorialexpress.com/jrust/nfxp.html", "https://archive.is/20120717185534/http://trb.metapress.com/content/126847136p81w0p3/", "https://archive.is/20130129010708/http://trb.metapress.com/content/l341607q38j850j7/", "https://doi.org/10.3982/ECTA12605", "https://dx.doi.org/10.3982/ECTA7925"]}, "EMG distribution": {"categories": ["Compound probability distributions", "Continuous distributions", "Pages using deprecated image syntax"], "title": "Exponentially modified Gaussian distribution", "method": "EMG distribution", "url": "https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution", "summary": "In probability theory, an exponentially modified Gaussian (EMG) distribution (exGaussian distribution) describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Gaussian with mean \u03bc and variance \u03c32, and Y is exponential of rate \u03bb. It has a characteristic positive skew from the exponential component.\nIt may also be regarded as a weighted function of a shifted exponential with the weight being a function of the normal distribution.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/66/EMG_Distribution_CDF.png", "https://upload.wikimedia.org/wikipedia/en/1/1c/EMG_Distribution_PDF.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Cell cycle", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Chromatography", "Circular distribution", "Circular uniform distribution", "Complementary error function", "Compound Poisson distribution", "Compound probability distribution", "Convolution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Double-precision floating-point format", "Elliptical distribution", "Erlang distribution", "Error function", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential decay", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Method of moments (statistics)", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonparametric skew", "Normal-Wishart distribution", "Normal-exponential-gamma distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "PubMed Central", "PubMed Identifier", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard deviation", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Vincent average", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3459330", "http://www.ncbi.nlm.nih.gov/pubmed/19825376", "http://www.ncbi.nlm.nih.gov/pubmed/22324584", "http://www.ncbi.nlm.nih.gov/pubmed/22886092", "http://doi.org/10.1002%2Fcem.1343", "http://doi.org/10.1016%2Fj.jtbi.2009.10.005", "http://doi.org/10.1021%2Fac00279a094", "http://doi.org/10.1021%2Fac60276a013", "http://doi.org/10.1021%2Fac60319a011", "http://doi.org/10.1037%2F0033-2909.86.3.446", "http://doi.org/10.1037%2F0096-3445.123.1.34", "http://doi.org/10.1037%2Fa0020747", "http://doi.org/10.1038%2Fnmeth.2138", "http://doi.org/10.1116%2F1.2335433", "http://doi.org/10.3758%2FBF03198390", "http://doi.org/10.3758%2Fbf03200523", "https://books.google.co.uk/books?id=x8tGby300QMC"]}, "Multicollinearity": {"categories": ["Design of experiments", "Regression analysis", "Use dmy dates from November 2010"], "title": "Multicollinearity", "method": "Multicollinearity", "url": "https://en.wikipedia.org/wiki/Multicollinearity", "summary": "In statistics, multicollinearity (also collinearity) is a phenomenon in which one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy. In this situation the coefficient estimates of the multiple regression may change erratically in response to small changes in the model or the data. Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least within the sample data set; it only affects calculations regarding individual predictors. That is, a multivariate regression model with collinear predictors can indicate how well the entire bundle of predictors predicts the outcome variable, but it may not give valid results about any individual predictor, or about which predictors are redundant with respect to others.\nIn the case of perfect multicollinearity (in which one independent variable is an exact linear combination of the others) the design matrix \n \n \n \n X\n \n \n {\\displaystyle X}\n has less than full rank, and therefore the moment matrix \n \n \n \n \n X\n \n \n T\n \n \n \n X\n \n \n {\\displaystyle X^{\\mathsf {T}}X}\n cannot be inverted. Under these circumstances, for a general linear model \n \n \n \n y\n =\n X\n \u03b2\n +\n \u03f5\n \n \n {\\displaystyle y=X\\beta +\\epsilon }\n , the ordinary least-squares estimator \n \n \n \n \n \n \n \n \u03b2\n ^\n \n \n \n \n O\n L\n S\n \n \n =\n (\n \n X\n \n \n T\n \n \n \n X\n \n )\n \n \u2212\n 1\n \n \n \n X\n \n \n T\n \n \n \n y\n \n \n {\\displaystyle {\\hat {\\beta }}_{OLS}=(X^{\\mathsf {T}}X)^{-1}X^{\\mathsf {T}}y}\n does not exist.\nNote that in statements of the assumptions underlying regression analyses such as ordinary least squares, the phrase \"no multicollinearity\" is sometimes used to mean the absence of perfect multicollinearity, which is an exact (non-stochastic) linear relation among the regressors.", "images": [], "links": ["Arthur Goldberger", "Coefficient of determination", "Collinearity (geometry)", "Collinearity (statistics)", "Condition number", "Damodar N. Gujarati", "Dependent and independent variables", "Dependent variable", "Design matrix", "Digital object identifier", "Distributed lag", "Double-precision floating-point format", "Dummy variable (statistics)", "Edwin Kuh", "Eigenvalue", "Explanatory variable", "F-test", "Frisch\u2013Waugh\u2013Lovell theorem", "G. S. Maddala", "Ill-conditioned matrix", "International Standard Book Number", "JSTOR", "Jan Kmenta", "John Johnston (econometrician)", "Journal of the Association for Information Systems", "Linear independence", "Mark Thoma", "Matrix inversion", "Moment matrix", "Multiple regression", "Ordinary least squares", "Orthogonality", "Overfitting", "Partial least squares regression", "Principal component regression", "R (programming language)", "Rank (linear algebra)", "Regression analysis", "Regression coefficient", "Review of Economics and Statistics", "Ridge regression", "Shapley value", "Simple linear regression", "Single-precision floating-point format", "Standard error (statistics)", "Statistics", "Survival analysis", "Type II error", "University of Oregon", "Variable (mathematics)", "Variance inflation factor", "YouTube"], "references": ["http://www.scriptwarp.com/warppls/pubs/Kock_Lynn_2012.pdf", "http://jeff560.tripod.com/m.html", "http://doi.org/10.1002%2F9780470996249.ch13", "http://doi.org/10.1002%2Fasmb.446", "http://doi.org/10.1007%2Fs11135-006-9018-6", "http://doi.org/10.1016%2FS0377-2217(03)00069-9", "http://www.jstor.org/stable/1923925", "http://www.jstor.org/stable/1923926", "http://www.jstor.org/stable/1923927", "http://www.jstor.org/stable/1937887", "https://books.google.com/books?id=mHmxNGKRlQsC&pg=PA245", "https://www.youtube.com/watch?v=K8eFiMIb8qo&list=PLD15D38DC7AA3B737&index=16#t=25m09s", "https://cran.r-project.org/web/packages/perturb/index.html"]}, "Quantitative marketing research": {"categories": ["All articles lacking in-text citations", "Applied statistics", "Articles lacking in-text citations from January 2010", "Business intelligence", "Market research", "Psychometrics", "Quantitative marketing research", "Quantitative research"], "title": "Quantitative marketing research", "method": "Quantitative marketing research", "url": "https://en.wikipedia.org/wiki/Quantitative_marketing_research", "summary": "Quantitative marketing research is the application of quantitative research techniques to the field of marketing. It has roots in both the positivist view of the world, and the modern marketing viewpoint that marketing is an interactive process in which both the buyer and seller reach a satisfying agreement on the \"four Ps\" of marketing: Product, Price, Place (location) and Promotion.\nAs a social research method, it typically involves the construction of questionnaires and scales. People who respond (respondents) are asked to complete the survey. Marketers use the information to obtain and understand the needs of individuals in the marketplace, and to create strategies and marketing plans.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/6/69/WMF_Strategic_Plan_Survey.svg"], "links": ["Afrobarometer", "American Association for Public Opinion Research", "American National Election Studies", "Audience measurement", "Automated computer telephone interviewing", "Brand strength analysis", "Bureau of Labor Statistics", "Categorical data", "Census", "Choice Modelling", "Cluster sampling", "Comparative Study of Electoral Systems", "Computer-assisted personal interviewing", "Computer-assisted telephone interviewing", "Contingency table", "Couple interview", "Cronbach's alpha", "DIY research", "Data Mining", "Data analysis", "Data collection", "Demography", "Descriptive statistics", "Enterprise Feedback Management", "Errors and residuals in statistics", "Eurobarometer", "European Social Survey", "European Society for Opinion and Marketing Research", "European Values Study", "Experimental design", "Exploratory data analysis", "Gallup (company)", "General Social Survey", "Graphical model", "Hypothesis", "International Social Survey Programme", "International Statistical Institute", "Interview (research)", "Latinobar\u00f3metro", "Level of measurement", "List of household surveys in the United States", "List of statistical packages", "Market research", "Marketing", "Marketing mix", "Marketing plan", "Marketing research", "Master of Marketing Research", "Maximum Difference Preference Scaling", "Multistage sampling", "Multivariate statistics", "NIPO Software", "National Health and Nutrition Examination Survey", "New Zealand Attitudes and Values Study", "Nonprobability sampling", "Official statistics", "Online panel", "Opinion poll", "Paid survey", "Pearson product-moment correlation coefficient", "Pew Research Center", "Poisson regression", "Positivism", "Professional association", "Psychometrics", "Public opinion", "Qualitative marketing research", "Qualtrics", "Quantitative research", "Questionnaire", "Questionnaire construction", "Questionnaires", "Rating scale", "Reliability (psychometric)", "Report writing", "SPSS", "Sampling (statistics)", "Scale (social sciences)", "Semi-structured interview", "Simple random sampling", "Social research", "Spearman\u2013Brown prediction formula", "Statistical analysis", "Statistical inference", "Statistical model", "Statistical survey", "Strategic planning", "Stratified sampling", "Structural equation modeling", "Structured interview", "Survey data collection", "Survey research", "Survey sampling", "Systematic sampling", "Type I and type II errors", "Unstructured interview", "Urtak", "Validity (psychometric)", "World Association for Public Opinion Research", "World Values Survey"], "references": ["https://www.questia.com/PM.qst?a=o&d=100501261", "https://www.questia.com/PM.qst?a=o&d=104829752", "https://www.questia.com/PM.qst?a=o&d=59669912"]}, "Antithetic variates": {"categories": ["Computational statistics", "Monte Carlo methods", "Variance reduction"], "title": "Antithetic variates", "method": "Antithetic variates", "url": "https://en.wikipedia.org/wiki/Antithetic_variates", "summary": "In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods. Considering that the error reduction in the simulated signal (using Monte Carlo methods) has a square root convergence, a very large number of sample paths is required to obtain an accurate result. The antithetic variates method reduces the variance of the simulation results.", "images": [], "links": ["Limit of a sequence", "Monte Carlo methods", "Normal distribution", "Sample (statistics)", "Square root", "Statistics", "Uniform distribution (continuous)", "Variance", "Variance reduction"], "references": []}, "Craps principle": {"categories": ["Probability theorems", "Statistical principles", "Statistical theorems"], "title": "Craps principle", "method": "Craps principle", "url": "https://en.wikipedia.org/wiki/Craps_principle", "summary": "In probability theory, the craps principle is a theorem about event probabilities under repeated iid trials. Let \n \n \n \n \n E\n \n 1\n \n \n \n \n {\\displaystyle E_{1}}\n and \n \n \n \n \n E\n \n 2\n \n \n \n \n {\\displaystyle E_{2}}\n denote two mutually exclusive events which might occur on a given trial. Then the probability that \n \n \n \n \n E\n \n 1\n \n \n \n \n {\\displaystyle E_{1}}\n occurs before \n \n \n \n \n E\n \n 2\n \n \n \n \n {\\displaystyle E_{2}}\n equals the conditional probability that \n \n \n \n \n E\n \n 1\n \n \n \n \n {\\displaystyle E_{1}}\n occurs given that \n \n \n \n \n E\n \n 1\n \n \n \n \n {\\displaystyle E_{1}}\n or \n \n \n \n \n E\n \n 2\n \n \n \n \n {\\displaystyle E_{2}}\n occur on the next trial, which is\n\n \n \n \n P\n \u2061\n [\n \n E\n \n 1\n \n \n \n \n \n before\n \n \n \n \n E\n \n 2\n \n \n ]\n =\n P\n \u2061\n \n [\n \n \n E\n \n 1\n \n \n \u2223\n \n E\n \n 1\n \n \n \u222a\n \n E\n \n 2\n \n \n \n ]\n \n =\n \n \n \n P\n \u2061\n [\n \n E\n \n 1\n \n \n ]\n \n \n P\n \u2061\n [\n \n E\n \n 1\n \n \n ]\n +\n P\n \u2061\n [\n \n E\n \n 2\n \n \n ]\n \n \n \n \n \n {\\displaystyle \\operatorname {P} [E_{1}\\,\\,{\\text{before}}\\,\\,E_{2}]=\\operatorname {P} \\left[E_{1}\\mid E_{1}\\cup E_{2}\\right]={\\frac {\\operatorname {P} [E_{1}]}{\\operatorname {P} [E_{1}]+\\operatorname {P} [E_{2}]}}}\n The events \n \n \n \n \n E\n \n 1\n \n \n \n \n {\\displaystyle E_{1}}\n and \n \n \n \n \n E\n \n 2\n \n \n \n \n {\\displaystyle E_{2}}\n need not be collectively exhaustive (if they are, the result is trivial).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["Advantage gambling", "Boxcars (slang)", "Collectively exhaustive", "Conditional probability", "Craps", "Dice", "Dice control", "Draw (tie)", "Event (probability theory)", "Floating craps", "Frank Scoblete", "Geometric series", "Glossary of craps terms", "Hazard (game)", "Independent and identically-distributed random variables", "Infinite series", "International Standard Book Number", "Jerry L. Patterson", "Mutually exclusive", "Probabilities", "Probability theory", "Snake eyes", "Stanford Wong", "Yo-leven"], "references": ["http://statweb.stanford.edu/~susan/courses/s116/node63.html", "https://books.google.com/books?id=fQzJoqBwtT4C&pg=PT50"]}, "Uniform distribution (continuous)": {"categories": ["Continuous distributions", "Location-scale family probability distributions", "Pages using deprecated image syntax"], "title": "Uniform distribution (continuous)", "method": "Uniform distribution (continuous)", "url": "https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)", "summary": "In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values. The distribution is often abbreviated U(a,b). It is the maximum entropy probability distribution for a random variate X under no constraint other than that it is contained in the distribution's support.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/96/Uniform_Distribution_PDF_SVG.svg", "https://upload.wikimedia.org/wikipedia/commons/6/63/Uniform_cdf.svg"], "links": ["ARGUS distribution", "Almost everywhere", "Antithetic variates", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli number", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Borel set", "Box\u2013Muller transform", "Box\u2013Muller transformation", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central moment", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulant", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Efficiency (statistics)", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fourier analysis", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "German tank problem", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heaviside step function", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "I.i.d.", "Information entropy", "Integral transform", "International Standard Book Number", "Interval (mathematics)", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverse transform sampling", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Journal of Econometrics", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Least significant bit", "Lebesgue measure", "Library of Congress Control Number", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maximum likelihood estimate", "Maximum spacing estimation", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Measure theory", "Median", "Method of moments (statistics)", "Mid-range", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Null hypothesis", "Order statistic", "P-value", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability distributions", "Probability plot", "Probability theory", "Programming language", "Pseudorandom number sequence", "Q-Gaussian distribution", "Q-Q plot", "Q-Weibull distribution", "Q-exponential distribution", "Quantization error", "Q\u2013Q plot", "RMS error", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Raw moments", "Rayleigh distribution", "Reciprocal distribution", "Rectangle function", "Rectangular function", "Rectified Gaussian distribution", "Rejection sampling", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Roger L. Berger", "Sample maximum", "Sample size", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign function", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Symmetric distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "UMVU", "Unbiased estimator", "Uniform distribution (discrete)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "World War II", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.elektro-energetika.cz/calculations/ro.php?language=english", "http://lccn.loc.gov/2001025794", "http://doi.org/10.1016%2Fj.jeconom.2008.12.014", "https://galton.uchicago.edu/~wichura/Stat304/Handouts/L18.cumulants.pdf"]}, "Transmission risks and rates": {"categories": ["All articles lacking sources", "Articles lacking sources from November 2009", "Epidemiology", "Medical statistics"], "title": "Transmission risks and rates", "method": "Transmission risks and rates", "url": "https://en.wikipedia.org/wiki/Transmission_risks_and_rates", "summary": "Transmission of an infection requires three conditions:\n\nan infectious individual\na susceptible individual\nan effective contact between themAn effective contact is defined as any kind of contact between two individuals such that, if one individual is infectious and the other susceptible, then the first individual infects the second. Whether or not a particular kind of contact will be effective depends on the infectious agent and its route of transmission.\nThe effective contact rate (denoted \u03b2) in a given population for a given infectious disease is measured in effective contacts per unit time. This may be expressed as the total contact rate (the total number of contacts, effective or not, per unit time, denoted \u03b3), multiplied by the risk of infection, given contact between an infectious and a susceptible individual. This risk is called the transmission risk and is denoted p. Thus:\n\n \n \n \n \u03b2\n =\n \u03b3\n \u00d7\n p\n \n \n \n {\\displaystyle \\beta =\\gamma \\times p\\,}\n The total contact rate, \u03b3, will generally be greater than the effective contact rate, \u03b2, since not all contacts result in infection. That is to say, p is almost always less than 1 and it can never be greater than 1, since it is effectively the probability of transmission occurring.\nThis relation formalises the fact that the effective contact rate depends not only on the social patterns of contact in a particular society (\u03b3) but also on the specific types of contact and the pathology of the infectious organism (p). For example, it has been shown that a concurrent sexually transmitted infection can substantially increase the probability (p) of infecting a susceptible with HIV. Therefore, one way to reduce the value of p (and hence lower HIV transmission rates) might be to treat other sexually transmitted infections.\nThere are a number of difficulties in using this relation. The first is that it is very difficult to measure contact rates because they vary widely between individuals and groups, and within the same group at different times. For sexually transmitted infections, large scale studies of sexual behaviour have been set up to estimate the contact rate. In developed countries for serious diseases such as AIDS or tuberculosis, contact tracing is often carried out when a patient is diagnosed (the patient and medical authorities try to inform every possible contact the patient may have made since infection). This, however, is not so much a research tool and more to alert the contacts to the possibility that they may be infected and so can seek medical treatment and avoiding passing on the disease if they have contracted it. \nA second consideration is that it is generally thought unethical to carry out direct experiments to establish per-contact infection risks as this would require the deliberate exposure of individuals to infectious agents. The Common Cold Unit that researched cold transmission in the UK between 1946 and 1989 was a notable exception. It is also possible to estimate the transmission risk in certain circumstances where exposures to infection have been documented, for example the rate of infection among nurses who have accidentally pricked their fingers with a needle that had previously been used with contaminated blood.\nA more direct assessment of transmission risks can be provided by a contact study, which is often carried out because of an outbreak (such a study was carried out during the SARS outbreak of 2002\u20133). The first (or primary) case within a defined group (such as a school or family) is identified and people infected by this individual (called secondary cases) are documented. If the number of susceptibles in the group is n and the number of secondary cases is x, then an estimation of the transmission risk is\n\n \n \n \n p\n =\n \n \n x\n n\n \n \n .\n \n \n {\\displaystyle p={\\frac {x}{n}}.}\n Here, p is the same parameter as before but it has been calculated in a different way. To reflect this, it is called the secondary attack rate (it is really a risk, of course, and not a rate, but the term is still commonly used).\nEven if the whole group in question is susceptible, x is generally smaller than the basic reproduction number for the disease. That is defined as the number of individuals each infected individual will go on to infect themselves, in a population with no resistance to the disease. The basic reproduction number includes all secondary cases infected by a primary case, while x is only the number of secondary cases within the group in question.\nSecondary attack rates are useful for comparisons between vaccinated and unvaccinated groups and hence assessing the efficacy of vaccinations against the disease under inspection. However, there are inevitably complications with such contact studies. It is not always obvious which members of the group are susceptible and distinguishing between secondary and subsequent cases (for example, those infected by the secondary cases are tertiary cases and so on) can be difficult. Also, the possibility of infection from an outsider must be ignored.\nDespite these problems, the parameters p and \u03b2 are powerful tools in the mathematical modelling of epidemics. But it should always be remembered that a model is only as good as the assumptions on which it is based and the data from which its parameters are calculated.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["AIDS", "Basic reproduction number", "Bugchasing and giftgiving", "Common Cold Unit", "Contact study", "Epidemic model", "HIV", "Infection", "Infectious disease", "Mathematical modelling in epidemiology", "Medical ethics", "Parameter", "Population", "Probability", "Risk factor", "Risk of infection", "SARS", "Sexual network", "Sexually transmitted disease", "Susceptible", "Transmission (medicine)", "Tuberculosis", "Vaccination"], "references": []}, "Ziggurat algorithm": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from September 2011", "Non-uniform random numbers", "Pseudorandom number generators", "Statistical algorithms"], "title": "Ziggurat algorithm", "method": "Ziggurat algorithm", "url": "https://en.wikipedia.org/wiki/Ziggurat_algorithm", "summary": "The ziggurat algorithm is an algorithm for pseudo-random number sampling. Belonging to the class of rejection sampling algorithms, it relies on an underlying source of uniformly-distributed random numbers, typically from a pseudo-random number generator, as well as precomputed tables. The algorithm is used to generate values from a monotone decreasing probability distribution. It can also be applied to symmetric unimodal distributions, such as the normal distribution, by choosing a value from one half of the distribution and then randomly choosing which half the value is considered to have been drawn from. It was developed by George Marsaglia and others in the 1960s.\nA typical value produced by the algorithm only requires the generation of one random floating-point value and one random table index, followed by one table lookup, one multiply operation and one comparison. Sometimes (2.5% of the time, in the case of a normal or exponential distribution when using typical table sizes) more computations are required. Nevertheless, the algorithm is computationally much faster than the two most commonly used methods of generating normally distributed random numbers, the Marsaglia polar method and the Box\u2013Muller transform, which require at least one logarithm and one square root calculation for each pair of generated values. However, since the ziggurat algorithm is more complex to implement it is best used when large quantities of random numbers are required.\nThe term ziggurat algorithm dates from Marsaglia's paper with Wai Wan Tsang in 2000; it is so named because it is conceptually based on covering the probability distribution with rectangular segments stacked in decreasing order of size, resulting in a figure that resembles a ziggurat.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e1/Ziggurat_method.gif"], "links": ["Algorithm", "ArXiv", "Bibcode", "Bisection method", "Box\u2013Muller transform", "Defense Technical Information Center", "Digital object identifier", "Error function", "Exponential distribution", "Gaussian distribution", "George Marsaglia", "IEEE 754", "Inline function", "International Standard Serial Number", "MATLAB", "Marsaglia polar method", "Monotonic function", "Normal distribution", "Normalizing constant", "Numerical integration", "Probability distribution", "Pseudo-random number generator", "Pseudo-random number sampling", "Recursion", "Rejection sampling", "Root-finding algorithm", "Round-off error", "Sanity test", "Symmetric function", "The Journal of Business", "Unimodal distribution", "Ziggurat"], "references": ["http://www.doornik.com/research/ziggurat.pdf", "http://www.oalib.com/paper/3786042", "http://www.ee.cooper.edu/~nummey/ersa2009.pdf", "http://adsabs.harvard.edu/abs/2006math......3058N", "http://www.dtic.mil/docs/citations/AD0423993", "http://arxiv.org/abs/math/0603058v1", "http://doi.org/10.1145%2F1287620.1287622", "http://heliosphan.org/zigguratalgorithm/zigguratalgorithm.html", "http://www.jstatsoft.org/v05/i08/paper", "http://www.worldcat.org/issn/0360-0300", "http://www.doc.ic.ac.uk/~wl/papers/07/csur07dt.pdf", "https://au.mathworks.com/company/newsletters/articles/normal-behavior.html", "https://blogs.mathworks.com/cleve/2015/05/18/the-ziggurat-random-normal-generator/", "https://www.jstatsoft.org/article/downloadSuppFile/v005i08/rnorrexp.c"]}, "Mixture (probability)": {"categories": ["All stub articles", "Compound probability distributions", "Probability theory", "Statistical classification", "Statistics stubs"], "title": "Mixture (probability)", "method": "Mixture (probability)", "url": "https://en.wikipedia.org/wiki/Mixture_(probability)", "summary": "In probability theory and statistics, a mixture is a probabilistic combination of two or more probability distributions. The concept arises mostly in two contexts:\n\nA mixture defining a new probability distribution from some existing ones, as in a mixture distribution or a compound distribution. Here a major problem often is to derive the properties of the resulting distribution.\nA mixture used as a statistical model such as is often used for statistical classification. The model may represent the population from which observations arise as a mixture of several components, and the problem is that of a mixture model, in which the task is to infer from which of a discrete set of sub-populations each observation originated.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Cluster analysis", "Compound distribution", "Mixture (disambiguation)", "Mixture distribution", "Mixture model", "Probability distribution", "Probability theory", "Statistical classification", "Statistical model", "Statistics"], "references": []}, "Mathematical statistics": {"categories": ["Actuarial science", "All articles with unsourced statements", "Articles with unsourced statements from March 2018", "CS1 maint: Extra text: authors list", "Statistical theory"], "title": "Mathematical statistics", "method": "Mathematical statistics", "url": "https://en.wikipedia.org/wiki/Mathematical_statistics", "summary": "Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abraham Wald", "Abstract algebra", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algebra", "Algebraic geometry", "Algebraic statistics", "Analysis of covariance", "Analysis of variance", "Analytic geometry", "Anderson\u2013Darling test", "Applied mathematics", "Areas of mathematics", "Arithmetic", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average value", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli distribution", "Beta distribution", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calculus", "Canonical correlation", "Cartography", "Categorical distribution", "Categorical variable", "Category theory", "Census", "Central limit theorem", "Central tendency", "Charles Sanders Peirce", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi squared distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinatorial design", "Completeness (statistics)", "Computational mathematics", "Computer science", "Conditional expectation", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous time", "Continuous uniform distribution", "Control chart", "Control theory", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data", "Data analysis", "Data collection", "David A. Freedman (statistician)", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Differential equation", "Differential equations", "Differential geometry", "Dimension", "Discrete geometry", "Discrete mathematics", "Discrete uniform distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dynamical systems theory", "Econometrics", "Effect size", "Efficiency (statistics)", "Elementary algebra", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experiment (probability theory)", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finite geometry", "First-hitting-time model", "Forest plot", "Foundations of mathematics", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Function (mathematics)", "Functional analysis", "G-test", "Game theory", "Gamma distribution", "Gauss", "General linear model", "Generalized linear model", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometry", "Geostatistics", "Goodness of fit", "Granger causality", "Graph theory", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "History of mathematics", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypergeometric distribution", "Independent (statistics)", "Independent variable", "Index of dispersion", "Inductive reasoning", "Inference", "Inferential statistics", "Information theory", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laplace", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear algebra", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Lists of mathematics topics", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "Lucien Le Cam", "M-estimator", "Mann\u2013Whitney U test", "Mathematical analysis", "Mathematical logic", "Mathematical optimization", "Mathematical physics", "Mathematics", "Mathematics and art", "Mathematics education", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measure (mathematics)", "Measure theory", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multilinear algebra", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural experiments", "Negative binomial distribution", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Number theory", "Numerical analysis", "Observational studies", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Optimization (mathematics)", "Order statistic", "Order theory", "Ordinary least squares", "Outline of mathematics", "Outline of statistics", "Parameter", "Parametric statistics", "Parametrization", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter J. Bickel", "Philosophy of mathematics", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Preferences", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability density function", "Probability distribution", "Probability mass function", "Probability measure", "Probability theory", "Proportional hazards model", "Psychometrics", "Pure mathematics", "Quality control", "Quantile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random sampling", "Random variable", "Random variables", "Random vector", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Ranking", "Rao\u2013Blackwell theorem", "Recreational mathematics", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sample space", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific computing", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set theory", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard normal", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical survey", "Statistical theory", "Statisticians", "Statistics", "Stem-and-leaf display", "Stochastic analysis", "Stochastic processes", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Student's t distribution", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Theory of computation", "Time domain", "Time series", "Tolerance interval", "Topology", "Trend estimation", "Trigonometry", "U-statistic", "Uniformly most powerful test", "Univariate distribution", "Utility function", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.trigonella.ch/statibot/english/", "http://www.math.uah.edu/stat/"]}, "DataDetective": {"categories": ["Business intelligence"], "title": "Sentient Information Systems", "method": "DataDetective", "url": "https://en.wikipedia.org/wiki/Sentient_Information_Systems", "summary": "Sentient Information Systems BV is a Dutch software provider specialized in data mining. The company was founded in 2001 out of the former Sentient Machine Research (SMR) and is located in Amsterdam.\nSentient's flagship product is DataDetective, a data mining platform capable of analyzing information from various domains. Users of this tool include several Dutch police departments, hospitals, insurance and media companies.", "images": [], "links": ["Amsterdam", "Business Intelligence", "DataDetective", "Data mining", "List of legal entity types by country", "Netherlands", "Private Company"], "references": ["http://www.doelgroepdetector.nl/", "http://www.sentient.nl", "http://www.sentient.nl/"]}, "Pseudoreplication": {"categories": ["All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from March 2016", "Design of experiments", "Wikipedia articles that are too technical from March 2016"], "title": "Pseudoreplication", "method": "Pseudoreplication", "url": "https://en.wikipedia.org/wiki/Pseudoreplication", "summary": "Pseudoreplication is the process of artificially inflating the number of samples or replicates. As a result, statistical tests performed on the data are rendered invalid. Pseudoreplication is originally defined as a special case of inadequate specification of random factors where both random and fixed factors are present.\nThe problem of inadequate specification arises when treatments are assigned to units that are subsampled and the treatment F-ratio in an analysis of variance (ANOVA) table is formed with respect to the residual mean square rather than with respect to the among unit mean square. The F-ratio relative to the within unit mean square is vulnerable to the confounding of treatment and unit effects, especially when experimental unit number is small (e.g. four tank units, two tanks treated, two not treated, several subsamples per tank). The problem is eliminated by forming the F-ratio relative to the correct mean square in the ANOVA table (tank by treatment MS in the example above), where this is possible. The problem is addressed by the use of mixed models.Hurlbert reported \"pseudoreplication\" in 48% of the studies he examined, that used inferential statistics. Several studies examining scientific papers published up to 2016 similarly found about half of the papers were suspected of pseudoreplication. When time and resources limit the number of experimental units, and unit effects cannot be eliminated statistically by testing over the unit variance, it is important to use other sources of information to evaluate the degree to which an F-ratio is confounded by unit effects.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["ANOVA", "Confounding", "Digital object identifier", "JSTOR", "Replication (statistics)", "Statistical hypothesis testing", "Statistical significance", "Statistical unit", "Student's t-test"], "references": ["http://people.stat.sfu.ca/~cschwarz/Stat-650/Notes/Handouts.readings/Hurlbert-1984-pseudorep.pdf", "http://doi.org/10.1016%2Fj.fishres.2004.08.016", "http://doi.org/10.1186%2F1471-2202-11-5", "http://doi.org/10.2307%2F1942661", "http://www.jstor.org/stable/1942661", "https://spectrumnews.org/news/statistical-errors-may-taint-many-half-mouse-studies/"]}, "Moderation (statistics)": {"categories": ["CS1 maint: Multiple names: authors list", "Psychometrics", "Regression analysis"], "title": "Moderation (statistics)", "method": "Moderation (statistics)", "url": "https://en.wikipedia.org/wiki/Moderation_(statistics)", "summary": "In statistics and regression analysis, moderation occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator variable or simply the moderator. The effect of a moderating variable is characterized statistically as an interaction; that is, a categorical (e.g., sex, ethnicity, class) or quantitative (e.g., level of reward) variable that affects the direction and/or strength of the relation between dependent and independent variables. Specifically within a correlational analysis framework, a moderator is a third variable that affects the zero-order correlation between two other variables, or the value of the slope of the dependent variable on the independent variable. In analysis of variance (ANOVA) terms, a basic moderator effect can be represented as an interaction between a focal independent variable and a factor that specifies the appropriate conditions for its operation.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c1/Two-way_interaction_effect_example.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavioral sciences", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Personality and Social Psychology", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Life satisfaction", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multicollinearity", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "Omitted-variable bias", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variable (mathematics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.psy.mq.edu.au/psystat/documents/interaction.pdf", "http://www.jeremydawson.co.uk/slopes.htm"]}, "MCAR": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2016", "CS1 maint: Archived copy as title", "Missing data", "Statistical data types"], "title": "Missing data", "method": "MCAR", "url": "https://en.wikipedia.org/wiki/Missing_data", "summary": "In statistics, missing data, or missing values, occur when no data value is stored for the variable in an observation. Missing data are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data.\nMissing data can occur because of nonresponse: no information is provided for one or more items or for a whole unit (\"subject\"). Some items are more likely to generate a nonresponse than others: for example items about private subjects such as income. Attrition is a type of missingness that can occur in longitudinal studies\u2014for instance studying development where a measurement is repeated after a certain period of time. Missingness occurs when participants drop out before the test ends and one or more measurements are missing.\nData often are missing in research in economics, sociology, and political science because governments or private entities choose not to, or fail to, report critical statistics, or because the information is not available. Sometimes missing values are caused by the researcher\u2014for example, when data collection is done improperly or mistakes are made in data entry.These forms of missingness take different types, with different impacts on the validity of conclusions from research: Missing completely at random, missing at random, and missing not at random. Missing data can be handled similarly as censored data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9e/Missing_not_at_random.png"], "links": ["ArXiv", "Attrition (epidemiology)", "Bias", "Censored data", "Censoring (statistics)", "Data", "Data analysis", "Digital object identifier", "Economics", "Expectation-maximization algorithm", "Expectation\u2013maximization algorithm", "Imputation (statistics)", "Indicator variable", "International Standard Book Number", "International Standard Serial Number", "Interpolation", "Inverse probability weighting", "Latent variable", "Listwise deletion", "London School of Hygiene & Tropical Medicine", "Markov chain", "Matrix completion", "Maximum likelihood", "Pieter Abbeel", "Political science", "PubMed Central", "PubMed Identifier", "Robust statistics", "Sociology", "Statistical power", "Statistics", "Unit of observation", "Value (mathematics)", "Variable (mathematics)"], "references": ["http://onbiostatistics.blogspot.com/2012/10/missingness-mechanism-mcar-mar-and-mnar.html", "http://www-03.ibm.com/software/products/en/spss-missing-values", "http://www.psychwiki.com/wiki/Dealing_with_Missing_Data", "http://www.psychwiki.com/wiki/Identifying_Missing_Data", "http://www.psychwiki.com/wiki/Missing_Values", "http://support.sas.com/onlinedoc/913/docMainpage.jsp", "http://www.statmodel.com/features5.shtml", "http://www3.interscience.wiley.com/journal/118686888/abstract", "http://www.cs.hmc.edu/~fleck/envision/user-manual/missing.html", "http://ftp.cs.ucla.edu/pub/stat_ser/r417.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1198040", "http://www.ncbi.nlm.nih.gov/pubmed/12090408", "http://www.ncbi.nlm.nih.gov/pubmed/16138788", "http://www.ncbi.nlm.nih.gov/pubmed/18652544", "http://dl.acm.org/citation.cfm?id=1390681.1390682", "http://arxiv.org/abs/1211.2958", "http://arxiv.org/abs/1604.00627", "http://doi.org/10.1007%2Fbf01066742", "http://doi.org/10.1007%2Fs11121-007-0070-9", "http://doi.org/10.1016%2Fj.compbiomed.2016.06.004", "http://doi.org/10.1037%2F1082-989X.7.2.147", "http://doi.org/10.1093%2Fbiomet%2F63.3.581", "http://doi.org/10.1109%2FICSMC.2006.385265", "http://doi.org/10.1111%2Fj.1741-3737.2005.00191.x", "http://doi.org/10.1111%2Fsjos.12110", "http://doi.org/10.1146%2Fannurev.psych.58.110405.085530", "http://doi.org/10.1191%2F0962280206sm448oa", "http://doi.org/10.1371%2Fjournal.pmed.0020267", "http://doi.org/10.22237%2Fjmasm%2F1493597280", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?tp=&arnumber=4274271&isnumber=4274116", "http://biomet.oxfordjournals.org/content/63/3/581.short", "http://www.worldcat.org/issn/1532-4435", "http://missingdata.lshtm.ac.uk/index.php?option=com_content&view=article&id=76:missing-at-random-mar&catid=40:missingness-mechanisms&Itemid=96", "http://missingdata.org.uk/", "https://www.researchgate.net/publication/300400110_Handling_missing_data_in_large_healthcare_dataset_A_case_study_of_unknown_trauma_outcomes", "https://web.archive.org/web/20150910180057/http://missingdata.lshtm.ac.uk/index.php?option=com_content&view=article&id=76:missing-at-random-mar&catid=40:missingness-mechanisms&Itemid=96", "https://web.archive.org/web/20160315011709/http://onbiostatistics.blogspot.com/2012/10/missingness-mechanism-mcar-mar-and-mnar.html", "https://web.archive.org/web/20160805184827/https://www.researchgate.net/publication/300400110_Handling_missing_data_in_large_healthcare_dataset_A_case_study_of_unknown_trauma_outcomes"]}, "Littlewood's law": {"categories": ["Miracles", "Pages containing links to subscription-only content", "Probability theory paradoxes", "Skepticism", "Statistical laws"], "title": "Littlewood's law", "method": "Littlewood's law", "url": "https://en.wikipedia.org/wiki/Littlewood%27s_law", "summary": "Littlewood's law states that a person can expect to experience events with odds of one in a million (defined by the law as a \"miracle\") at the rate of about one per month.", "images": [], "links": ["A Mathematician's Miscellany", "B. Bollob\u00e1s", "Bart K. Holland", "Cambridge University Press", "Coincidence", "Confirmation bias", "Freeman J. Dyson", "Georges Charpak", "Henri Broch", "International Standard Book Number", "John Edensor Littlewood", "Johns Hopkins University Press", "Law of truly large numbers", "List of eponymous laws", "Miracle", "New York Review of Books", "Phenomenology (psychology)", "Supernatural", "Synchronicity", "University of Cambridge"], "references": ["http://www.nybooks.com/articles/16991"]}, "Periodic variation": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from November 2008", "Articles needing additional references from November 2010", "Articles with multiple maintenance issues", "Inventory", "Pages with citations having bare URLs", "Pages with citations lacking titles", "Seasonality", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Seasonality", "method": "Periodic variation", "url": "https://en.wikipedia.org/wiki/Seasonality", "summary": "In time series data, seasonality is the presence of variations that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly. Seasonality may be caused by various factors, such as weather, vacation, and holidays and consists of periodic, repetitive, and generally regular and predictable patterns in the levels of a time series.\nSeasonal fluctuations in a time series can be contrasted with cyclical patterns. The latter occur when the data exhibits rises and falls that are not of a fixed period. Such non-seasonal fluctuations are usually due to economic conditions and are often related to the \"business cycle\"; their period usually extends beyond a single year, and the fluctuations are usually of at least two years.Organisations facing seasonal variations, such as ice-cream vendors, are often interested in knowing their performance relative to the normal seasonal variation. Seasonal variations in the labour market can be attributed to the entrance of school leavers into the job market as they aim to contribute to the workforce upon the completion of their schooling. These regular changes are of less interest to those who study employment data than the variations that occur due to the underlying state of the economy; their focus is on how unemployment in the workforce has changed, despite the impact of the regular seasonal variations.It is necessary for organisations to identify and measure seasonal variations within their market to help them plan for the future. This can prepare them for the temporary increases or decreases in labour requirements and inventory as demand for their product or service fluctuates over certain periods. This may require training, periodic maintenance, and so forth that can be organized in advance. Apart from these considerations, the organisations need to know if variation they have experienced has been more or less than the expected amount, beyond what the usual seasonal variations account for.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6a/Acfbeer.png", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/SeasonalplotUS.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARIMA", "Autocorrelation plot", "Box plot", "Copyright status of work by the U.S. government", "Cycle count", "Cyclostationary process", "Decomposition of time series", "Dependent variable", "Dummy variable (statistics)", "Frequency", "Graphical technique", "Independent variable", "International Standard Book Number", "Inventory", "Moving average", "National Institute of Standards and Technology", "Ordinary least squares", "Oscillation", "Periodic function", "Periodicity (disambiguation)", "Photoperiodism", "Regression analysis", "Run sequence plot", "Safety stock", "Seasonal adjustment", "Seasonal subseries plot", "Sine wave", "Sinusoidal model", "Spectral density estimation", "Time-series", "Time series", "Time series analysis", "Trend estimation", "X-12-ARIMA"], "references": ["http://www.allbusiness.com/barrons_dictionary/dictionary-seasonality-4946957-1.html", "http://www.businessdictionary.com/definition/seasonality.html", "http://stats.stackexchange.com/questions/16117/what-method-can-be-used-to-detect-seasonality-in-data", "http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc443.htm", "https://www.otexts.org/fpp/2/1", "https://www.otexts.org/fpp/6/1"]}, "Difference in differences": {"categories": ["Causal inference", "Design of experiments", "Econometric modeling", "Observational study", "Regression analysis", "Subtraction"], "title": "Difference in differences", "method": "Difference in differences", "url": "https://en.wikipedia.org/wiki/Difference_in_differences", "summary": "Difference in differences (DID or DD) is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differential effect of a treatment on a 'treatment group' versus a 'control group' in a natural experiment. It calculates the effect of a treatment (i.e., an explanatory variable or an independent variable) on an outcome (i.e., a response variable or dependent variable) by comparing the average change over time in the outcome variable for the treatment group, compared to the average change over time for the control group. Although it is intended to mitigate the effects of extraneous factors and selection bias, depending on how the treatment group is chosen, this method may still be subject to certain biases (e.g., mean regression, reverse causality and omitted variable bias).\nIn contrast to a time-series estimate of the treatment effect on subjects (which analyzes differences over time) or a cross-section estimate of the treatment effect (which measures the difference between treatment and control groups), difference in differences uses panel data to measure the differences, between the treatment and control group, of the changes in the outcome variable that occur over time.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/da/Illustration_of_Difference_in_Differences.png", "https://upload.wikimedia.org/wikipedia/en/f/fb/Parallel_Trend_Assumption.png"], "links": ["Alan Krueger", "American Economic Review", "Ashenfelter dip", "Autocorrelation", "Average treatment effect", "Control group", "David Card", "Dependent variable", "Design of experiments", "Difference in differences", "Digital object identifier", "Dummy variable (statistics)", "Econometrics", "Errors and residuals in statistics", "Esther Duflo", "Experiment", "Fast food", "Full-time equivalent", "Independent variable", "International Standard Book Number", "JSTOR", "Journal of Economic Literature", "Minimum wage", "Natural experiment", "New Jersey", "Observational study", "Omitted-variable bias", "Omitted variable bias", "Ordinary least squares", "Panel data", "Pennsylvania", "Quantitative research", "Quarterly Journal of Economics", "Regression to the mean", "Reverse causality bias", "Review of Economic Studies", "Sampling (statistics)", "Selection bias", "Statistics", "Time series", "Unemployment", "Without loss of generality"], "references": ["http://healthcare-economist.com/2006/02/11/difference-in-difference-estimation/", "http://doi.org/10.1111%2F0034-6527.00321", "http://doi.org/10.1162%2F003355304772839588", "http://doi.org/10.1257%2Fjel.47.1.5", "http://doi.org/10.3386%2Ft0312", "http://doi.org/10.3386%2Fw14237", "http://www.jstor.org/stable/2118030", "https://books.google.com/books?id=ztXL21Xd8v8C&pg=PA227"]}, "Sample maximum and minimum": {"categories": ["Summary statistics"], "title": "Sample maximum and minimum", "method": "Sample maximum and minimum", "url": "https://en.wikipedia.org/wiki/Sample_maximum_and_minimum", "summary": "In statistics, the sample maximum and sample minimum, also called the largest observation and smallest observation, are the values of the greatest and least elements of a sample. They are basic summary statistics, used in descriptive statistics such as the five-number summary and Bowley's seven-figure summary and the associated box plot.\nThe minimum and the maximum value are the first and last order statistics (often denoted X(1) and X(n) respectively, for a sample size of n).\nIf the sample has outliers, they necessarily include the sample maximum or sample minimum, or both, depending on whether they are extremely high or low. However, the sample maximum and minimum need not be outliers, if they are not unusually far from other observations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ce/1755_Lisbon_earthquake.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Michelsonmorley-boxplot.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg"], "links": ["1755 Lisbon earthquake", "Black swan theory", "Box plot", "Complete statistic", "Decile", "Deciles", "Descriptive statistics", "Efficiency (statistics)", "Estimators", "Exchangeable sequence", "Extreme value theory", "Five-number summary", "German tank problem", "Heavy-tailed distribution", "Kurtosis risk", "Maxima and minima", "Maximum absolute deviation", "Michelson\u2013Morley experiment", "Mid-range", "Non-stationary", "Normal distribution", "Normality test", "Order statistic", "Outliers", "Percentiles", "Platykurtic", "Prediction interval", "Quantiles", "Range (statistics)", "Robust statistics", "Sample (statistics)", "Sample mean", "Sample standard deviation", "Seven-number summary", "Smooth maximum", "Statistics", "Student's t-distribution", "Sufficient statistic", "Summary statistics", "T-statistic", "Three sigma rule", "UMVU", "Uniform distribution (discrete)"], "references": []}, "Quantile regression": {"categories": ["All articles with unsourced statements", "All pages needing cleanup", "Articles needing cleanup from December 2010", "Articles with unsourced statements from August 2015", "Cleanup tagged articles without a reason field from December 2010", "Regression analysis", "Wikipedia articles needing page number citations from December 2010", "Wikipedia pages needing cleanup from December 2010"], "title": "Quantile regression", "method": "Quantile regression", "url": "https://en.wikipedia.org/wiki/Quantile_regression", "summary": "Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares results in estimates of the conditional mean of the response variable given certain values of the predictor variables, quantile regression aims at estimating either the conditional median or other quantiles of the response variable. Essentially, quantile regression is the extension of linear regression and we use it when the conditions of linear regression are not applicable.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Annals of Statistics", "ArXiv", "Asymptotic normality", "Bayesian linear regression", "Bayesian multivariate linear regression", "Central tendency", "Complexity", "Cumulative distribution function", "Data", "Digital object identifier", "Discrete choice", "Ecology", "Equator", "Equivariance", "Errors-in-variables models", "Errors and residuals in statistics", "Eviews", "Fixed effects model", "Francis Ysidro Edgeworth", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Gretl", "Huixia Judy Wang", "Indicator function", "Inner product space", "Interior point method", "International Standard Book Number", "International Statistical review", "Invariant estimator", "Isotonic regression", "Iteratively reweighted least squares", "Joshua Angrist", "Journal of Computational and Graphical Statistics", "Journal of Econometrics", "Journal of Statistical Computation and Simulation", "Journal of the American Statistical Association", "Least-angle regression", "Least absolute deviations", "Least squares", "Legendre polynomials", "Linear least squares", "Linear programming", "Linear regression", "Local regression", "Logistic regression", "Loss function", "MATLAB", "Mathematica", "Mean", "Mean and predicted response", "Median", "Method of least squares", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Numerical linear algebra", "Observation", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Pierre-Simon Laplace", "Planet", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Projection (mathematics)", "Python (programming language)", "Quantiles", "R (programming language)", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Roger Joseph Boscovich", "Roger Koenker", "SAS System", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Simplex algorithm", "Simplex method", "Society of Jesus", "Stata", "Statistical dispersion", "Statistics", "Statistics in Medicine (journal)", "Statsmodels", "Studentized residual", "Tikhonov regularization", "Total least squares", "Vowpal Wabbit", "Weighted least squares", "Xuming He"], "references": ["http://www.mathworks.com/matlabcentral/fileexchange/32115-quantreg-x-y-tau-order-nboot-", "http://www2.sas.com/proceedings/sugi30/213-30.pdf", "http://www.econ.uiuc.edu/~roger/research/galton/Galton.pdf", "http://www.econ.uiuc.edu/~roger/research/rq/QReco.pdf", "http://ricardo.ecn.wfu.edu/pub//gretl/manual/en/gretl-ref.pdf", "http://statsmodels.sourceforge.net/devel/examples/notebooks/generated/quantile_regression.html", "http://arxiv.org/abs/1207.5378", "http://doi.org/10.1002%2Fsim.2271", "http://doi.org/10.1016%2F0304-4076(86)90016-3", "http://doi.org/10.1080%2F00949655.2010.496117", "http://doi.org/10.1093%2Fbiomet%2F71.3.615", "http://doi.org/10.1111%2Finsr.12114", "http://doi.org/10.1198%2F016214502388618663", "http://doi.org/10.1198%2F016214503000000954", "http://doi.org/10.1198%2F106186005X27563", "http://doi.org/10.1198%2Fjasa.2009.tm08230", "http://doi.org/10.1214%2F009053606000000623", "http://doi.org/10.1214%2F12-AOS1005", "http://doi.org/10.2307%2F3868138", "https://github.com/JohnLangford/vowpal_wabbit/wiki/Loss-functions", "https://github.com/antononcube/MathematicaForPrediction/blob/master/QuantileRegression.m", "https://books.google.com/books?id=UkKQRAAACAAJ&pg=PA211", "https://books.google.com/books?id=hdkt7V4NXsgC", "https://books.google.com/books?id=ztXL21Xd8v8C&pg=PA269", "https://www.stata.com/manuals13/rqreg.pdf", "https://scikit-garden.github.io/examples/QuantileRegressionForests/", "https://cran.r-project.org/web/packages/gbm/", "https://cran.r-project.org/web/packages/qrnn/index.html", "https://cran.r-project.org/web/packages/quantreg/index.html", "https://cran.r-project.org/web/packages/quantregForest/index.html"]}, "Data assimilation": {"categories": ["All Wikipedia articles needing clarification", "All articles needing additional references", "All articles to be expanded", "All articles with incomplete citations", "All articles with unsourced statements", "Articles needing additional references from September 2011", "Articles to be expanded from June 2008", "Articles using small message boxes", "Articles with incomplete citations from January 2018", "Articles with multiple maintenance issues", "Articles with unsourced statements from January 2018", "Bayesian statistics", "Climate and weather statistics", "Control theory", "Estimation theory", "Numerical climate and weather models", "Statistical forecasting", "Weather forecasting", "Wikipedia articles needing clarification from October 2013"], "title": "Data assimilation", "method": "Data assimilation", "url": "https://en.wikipedia.org/wiki/Data_assimilation", "summary": "Data assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations. There may be a number of different goals sought, for example\u2014to determine the optimal state estimate of a system, to determine initial conditions for a numerical forecast model, to interpolate sparse observation data using (e.g. physical) knowledge of the system being observed, to train numerical model parameters based on observed data. Depending on the goal, different solution methods may be used. Data assimilation is distinguished from other forms of machine learning, image analysis, and statistical methods in that it utilizes a dynamical model of the system being analyzed.\nData assimilation initially developed in the field of numerical weather prediction. Numerical weather prediction models are equations describing the dynamical behavior of the atmosphere, typically coded into a computer program. In order to use these models to make forecasts, initial conditions are needed for the model that closely resemble the current state of the atmosphere. Simply inserting point-wise measurements into the numerical models did not provide a satisfactory solution. Real world measurements contain errors both due to the quality of the instrument and how accurately the position of the measurement is known. These errors can cause instabilities in the models that eliminate any level of skill in a forecast. Thus, more sophisticated methods were needed in order to initialize a model using all available data while making sure to maintain stability in the numerical model. Such data typically includes the measurements as well as a previous forecast valid at the same time the measurements are made. If applied iteratively, this process begins to accumulate information from past observations into all subsequent forecasts.\nBecause data assimilation developed out of the field of numerical weather prediction, it initially gained popularity amongst the geosciences. In fact, one of the most cited publication in all of the geosciences is an application of data assimilation to reconstruct the observed history of the atmosphere.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7e/Lewis_Fry_Richardson.png", "https://upload.wikimedia.org/wikipedia/commons/3/3a/ReSeDAssimilationDiagram.png", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Alpilles", "Apollo program", "Atmosphere", "Atmospheric pressure", "Autochem", "Bar (unit)", "Bayes' theorem", "Bibcode", "Butterfly effect", "Cambridge University Press", "Computational power", "Conjugate gradient method", "Convection", "Covariance", "Deterministic", "Digital object identifier", "ECMWF", "Ensemble Kalman filter", "Eugenia Kalnay", "Finite differences", "Fluid", "Fluid dynamics", "Fokker-Planck equation", "Forecast skill", "GPS", "Generalized minimal residual method", "Hurricane Hunters", "Hydrology", "Hydrostatic equilibrium", "Inch of mercury", "Initial condition", "Initial value problem", "International Standard Book Number", "Inverse problem", "Kalman-Bucy filter", "Kalman filter", "Kalman filtering", "Lee wave", "Lewis Fry Richardson", "Loss function", "METAR", "MM5 (weather model)", "Mars Global Surveyor", "Mars Reconnaissance Orbiter", "Met Office", "National Climatic Data Center", "National Oceanic and Atmospheric Administration", "Nonlinear system", "Numerical weather prediction", "Optimal control", "Particle filter", "Pilot report", "Primitive equations", "Probability distribution function", "Radar", "Radiosonde", "Recursive Bayesian estimation", "Regression analysis", "Representation (mathematics)", "Roger Daley", "SYNOP", "Satellite", "Sea surface temperature", "Sodar", "Spectral methods", "State space (controls)", "Stratosphere", "Temperature", "Thermodynamics", "Tropical cyclone", "Troposphere", "UNISYS", "University Corporation for Atmospheric Research", "Vilhelm Bjerknes", "Weather reconnaissance", "Weather satellite", "World Meteorological Organization"], "references": ["http://ams.confex.com/ams/91Annual/webprogram/Paper181664.html", "http://www.hurricanehunters.com", "http://www.marsclimatecenter.com", "http://weather.unisys.com/wxp/Appendices/Formats/SYNOP.html", "http://pdaf.awi.de", "http://adsabs.harvard.edu/abs/1986BAMS...67..138A", "http://adsabs.harvard.edu/abs/1995AnRFM..27..195K", "http://adsabs.harvard.edu/abs/1997JHyd..188....4G", "http://adsabs.harvard.edu/abs/2008BAMS...89.1689B", "http://adsabs.harvard.edu/abs/2008JCoPh.227.3431L", "http://www.eps.jhu.edu/~mjhoffman/pages/research.html", "http://hfip.psu.edu/EDA2010/MZhang.pdf", "http://www.meted.ucar.edu/nwp/pcu1/ic6/frameset.htm", "http://www.mmm.ucar.edu/mm5/", "http://www.mmm.ucar.edu/wrf/WG4/wrfvar/wrfvar-tutorial.htm", "http://w3.avignon.inra.fr/reseda/base/documents/reseda-report/00reseda-report.pdf", "http://www.aero.jussieu.fr/~sparc/News12/Radiosondes.html", "http://www.ncdc.noaa.gov/oa/climate/conversion/swometardecoder.html", "http://www.noaanews.noaa.gov/stories2010/20100112_plane.html", "http://www.vos.noaa.gov/vos_scheme.shtml", "http://www.data-assimilation.net/", "http://doi.org/10.1016%2FS0022-1694(96)03308-2", "http://doi.org/10.1016%2Fj.jcp.2007.02.034", "http://doi.org/10.1080%2F16000870.2018.1445364", "http://doi.org/10.1109%2FIGARSS.1998.702226", "http://doi.org/10.1146%2Fannurev.fl.27.010195.001211", "http://doi.org/10.1175%2F1520-0477(1986)067%3C0138:HAHAEF%3E2.0.CO;2", "http://doi.org/10.1175%2F1520-0477(1996)077%3C0437:TNYRP%3E2.0.CO;2", "http://doi.org/10.1175%2F2008BAMS2332.1", "http://doi.org/10.2151%2Fjmsj1965.75.1B_181", "http://www.openda.org/joomla/index.php", "http://badc.nerc.ac.uk/home/", "http://www.atm.ox.ac.uk/group/gpfd/research.html#marsgcm", "http://www.metoffice.gov.uk/research/modelling-systems/unified-model/weather-forecasting", "https://books.google.com/books?id=BQ_7vh5SrHQC&pg=PA223", "https://books.google.com/books?id=SV04AAAAIAAJ&pg=PA38&dq=sea+surface+temperature+importance+use+numerical+weather+prediction+book#v=onepage&q=sea%20surface%20temperature%20importance%20use%20numerical%20weather%20prediction%20book&f=false", "https://books.google.com/books?id=lMXSpRwKNO8C&pg=PA137&dq=sea+ice+use+numerical+weather+prediction+book#v=onepage&q=sea%20ice%20use%20numerical%20weather%20prediction%20book&f=false", "https://books.google.com/books?id=lMXSpRwKNO8C&pg=PA56&dq=radiation+mountain+parameterization+book#v=onepage&q=radiation%20mountain%20parameterization%20book&f=false", "https://www.washingtonpost.com/wp-dyn/content/article/2007/10/07/AR2007100700971_pf.html", "https://www.dwd.de", "https://www.eol.ucar.edu/field_projects/hapex-mobilhy", "https://software.ecmwf.int/wiki/display/OPTR/Data+Assimilation+Lecture+Notes", "https://www.ecmwf.int/en/elibrary/9231-part-ii-data-assimilation", "https://www.ecmwf.int/sites/default/files/elibrary/2011/14950-hybrid-variationalensemble-data-assimilation.pdf", "https://web.archive.org/web/20060717223237/http://www.cdacentral.info/", "https://web.archive.org/web/20070223072036/http://www.pdfcentral.info/", "https://web.archive.org/web/20070607142822/http://www.aero.jussieu.fr/~sparc/News12/Radiosondes.html", "https://web.archive.org/web/20070814044336/http://www.mmm.ucar.edu/wrf/WG4/wrfvar/wrfvar-tutorial.htm", "https://web.archive.org/web/20071230100059/http://weather.unisys.com/wxp/Appendices/Formats/SYNOP.html", "https://www.metoffice.gov.uk/research/weather/data-assimilation"]}, "Hartley's test": {"categories": ["Analysis of variance", "Statistical tests"], "title": "Hartley's test", "method": "Hartley's test", "url": "https://en.wikipedia.org/wiki/Hartley%27s_test", "summary": "In statistics, Hartley's test, also known as the Fmax test or Hartley's Fmax, is used in the analysis of variance to verify that different groups have a similar variance, an assumption needed for other statistical tests. It was developed by H. O. Hartley, who published it in 1950.The test involves computing the ratio of the largest group variance, max(sj2) to the smallest group variance, min(sj2). The resulting ratio, Fmax, is then compared to a critical value from a table of the sampling distribution of Fmax. If the computed ratio is less than the critical value, the groups are assumed to have similar or equal variances.\nHartley's test assumes that data for each group are normally distributed, and that each group has an equal number of members. This test, although convenient, is quite sensitive to violations of the normality assumption. Alternatives to Hartley's test that are robust to violations of normality are O'Brien's procedure, and the Brown\u2013Forsythe test.", "images": [], "links": ["Analysis of variance", "Bartlett's test", "Brown\u2013Forsythe test", "Cochran's C test", "Herman Otto Hartley", "International Standard Book Number", "Normal distribution", "Ratio", "Sampling distribution", "Statistics", "Variance"], "references": ["http://www.csulb.edu/~acarter3/course-biostats/tables/table-Fmax-values.pdf"]}, "Stochastic ordering": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from February 2012", "Articles with unsourced statements from February 2012", "Probability theory"], "title": "Stochastic ordering", "method": "Stochastic ordering", "url": "https://en.wikipedia.org/wiki/Stochastic_ordering", "summary": "In probability theory and statistics, a stochastic order quantifies the concept of one random variable being \"bigger\" than another. These are usually partial orders, so that one random variable \n \n \n \n A\n \n \n {\\displaystyle A}\n may be neither stochastically greater than, less than nor equal to another random variable \n \n \n \n B\n \n \n {\\displaystyle B}\n . Many different orders exist, which have different applications.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Convergence in distribution", "Coupling (probability)", "Cumulative distribution function", "Decision theory", "Hazard rate", "International Standard Book Number", "Order statistic", "Partial order", "Probability theory", "Random variable", "State of nature", "Statistics", "Stochastic", "Stochastic dominance", "Variance"], "references": ["https://www.mcgill.ca/files/economics/stochasticdominance.pdf", "https://www.jstor.org/stable/2691998"]}, "Noncentral F-distribution": {"categories": ["CS1 maint: Uses authors parameter", "Continuous distributions"], "title": "Noncentral F-distribution", "method": "Noncentral F-distribution", "url": "https://en.wikipedia.org/wiki/Noncentral_F-distribution", "summary": "In probability theory and statistics, the noncentral F-distribution is a continuous probability distribution that is a generalization of the (ordinary) F-distribution. It describes the distribution of the quotient (X/n1)/(Y/n2), where the numerator X has a noncentral chi-squared distribution with n1 degrees of freedom and the denominator Y has a central chi-squared distribution with n2 degrees of freedom. It is also required that X and Y are statistically independent of each other.\nIt is the distribution of the test statistic in analysis of variance problems when the null hypothesis is false. The noncentral F-distribution is used to find the power function of such a test.", "images": [], "links": ["ARGUS distribution", "Analysis of variance", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Boost C++ Libraries", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Eric W. Weisstein", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "MATLAB", "Marchenko\u2013Pastur distribution", "MathWorld", "Mathematica", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Null hypothesis", "NumPy", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "R (programming language)", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Regularized incomplete beta function", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Statistical independence", "Statistical power", "Statistics", "Student's t-distribution", "Test statistic", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://mathworld.wolfram.com/NoncentralF-Distribution.html", "http://mars.wiwi.hu-berlin.de/mediawiki/slides/index.php/Comparison_of_noncentral_and_central_distributions", "http://www.boost.org/doc/libs/1_39_0/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html"]}, "Single equation methods (econometrics)": {"categories": ["All stub articles", "Econometrics stubs", "Mathematical and quantitative methods (economics)", "Single-equation methods (econometrics)"], "title": "Single-equation methods (econometrics)", "method": "Single equation methods (econometrics)", "url": "https://en.wikipedia.org/wiki/Single-equation_methods_(econometrics)", "summary": "A variety of methods are used in econometrics to estimate models consisting of a single equation. The oldest and still the most commonly used is the ordinary least squares method used to estimate linear regressions.\nA variety of methods are available to estimate non-linear models. A particularly important class of non-linear models are those used to estimate relationships where the dependent variable is discrete, truncated or censored. These include logit, probit and Tobit models. \nSingle equation methods may be applied to time-series, cross section or panel data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170527191524%21Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170519203409%21Emoji_u1f4c8.svg"], "links": ["Dependent variable", "Econometrics", "Equation", "Linear regression", "Logit", "Model (economics)", "Non-linear", "Ordinary least squares", "Probit", "Time-series", "Tobit model", "Truncated dependent variable"], "references": []}, "Three-point estimation": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2010", "Informal estimation", "Project management techniques", "Statistical approximations", "Wikipedia articles needing clarification from February 2017"], "title": "Three-point estimation", "method": "Three-point estimation", "url": "https://en.wikipedia.org/wiki/Three-point_estimation", "summary": "The three-point estimation technique is used in management and information systems applications for the construction of an approximate probability distribution representing the outcome of future events, based on very limited information. While the distribution used for the approximation might be a normal distribution, this is not always so and, for example a triangular distribution might be used, depending on the application.\nIn three-point estimation, three figures are produced initially for every distribution that is required, based on prior experience or best-guesses:\n\na = the best-case estimate\nm = the most likely estimate\nb = the worst-case estimateThese are then combined to yield either a full probability distribution, for later combination with distributions obtained similarly for other variables, or summary descriptors of the distribution, such as the mean, standard deviation or percentage points of the distribution. The accuracy attributed to the results derived can be no better than the accuracy inherent in the 3 initial points, and there are clear dangers in using an assumed form for an underlying distribution that itself has little basis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["68-95-99.7 rule", "Asymptotic distribution", "Confidence interval", "Correlation", "Cost estimate", "Expected value", "Five-number summary", "Information systems", "L-estimator", "Mean", "Monte Carlo Method", "Normal distribution", "PERT", "PERT distribution", "Parametric estimating", "Percentile", "Probability distribution", "Program Evaluation and Review Technique", "Project management software", "Quality costs", "Reserve study", "Seven-number summary", "Standard deviation", "Standard error", "Triangular distribution", "Vendor bid analysis", "Weighted average", "Work breakdown structure"], "references": ["http://www.4pm.com/articles/PERT_program_evaluation_&_review_technique.pdf", "http://www.aof.mod.uk/aofcontent/tactical/risk/content/tpe.htm", "http://www.aof.mod.uk/aofcontent/tactical/risk/downloads/3pepracgude.pdf"]}, "Structured data analysis (statistics)": {"categories": ["All stub articles", "CS1 maint: Multiple names: authors list", "Statistical analysis", "Statistics stubs", "Structure"], "title": "Structured data analysis (statistics)", "method": "Structured data analysis (statistics)", "url": "https://en.wikipedia.org/wiki/Structured_data_analysis_(statistics)", "summary": "Structured data analysis is the statistical data analysis of structured data. This can arise either in the form of an a priori structure such as multiple-choice questionnaires or in situations with the need to search for structure that fits the given data, either exactly or approximately. This structure can then be used for making comparisons, predictions, manipulations etc.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Cluster analysis", "Combinatorial data analysis", "Data analysis", "Decision tree learning", "Formal concept analysis", "Functional data analysis", "Geometric data analysis", "Hierarchical Bayes model", "International Standard Book Number", "Jacqueline Meulman", "Regression analysis", "Statistical shape analysis", "Statistics", "Structure", "Structured data analysis (disambiguation)", "Topological data analysis"], "references": ["http://bus.utk.edu/stat/DataMining/Tree%20Structured%20Data%20Analysis%20(SPSS).pdf", "http://www.ams.org/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf"]}, "Generalized Pareto distribution": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2012", "Continuous distributions", "Pages using deprecated image syntax", "Power laws", "Probability distributions with non-finite variance"], "title": "Generalized Pareto distribution", "method": "Generalized Pareto distribution", "url": "https://en.wikipedia.org/wiki/Generalized_Pareto_distribution", "summary": "In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another distribution. It is specified by three parameters: location \n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n , scale \n \n \n \n \u03c3\n \n \n {\\displaystyle \\sigma }\n , and shape \n \n \n \n \u03be\n \n \n {\\displaystyle \\xi }\n . Sometimes it is specified by only scale and shape and sometimes only by its shape parameter. Some references give the shape parameter as \n \n \n \n \u03ba\n =\n \u2212\n \u03be\n \n \n \n {\\displaystyle \\kappa =-\\xi \\,}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/55/Gpdcdf.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d7/Gpdpdf.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Differential equation", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Laurens de Haan", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Pickands\u2013Balkema\u2013de Haan theorem", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real numbers", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.mathworks.com/help/stats/generalized-pareto-distribution.html", "http://doi.org/10.1007%2FBF00894450", "http://doi.org/10.1080%2F03610926.2018.1441418", "http://doi.org/10.1214%2Faop%2F1176996548", "http://doi.org/10.1214%2Faos%2F1176343003", "http://doi.org/10.2307%2F1269343", "http://projecteuclid.org/euclid.aop/1176996548", "http://projecteuclid.org/euclid.aos/1176343003", "https://books.google.com/books?id=2nugUEaKqFEC", "https://books.google.com/books?id=6M03_6rm8-oC&pg=PA462", "https://books.google.com/books?id=BXOI2pICfJUC", "https://books.google.com/books?id=fUJZZLj1kbwC&lpg=PR1&pg=PA119#v=onepage&q&f=false", "https://www.tandfonline.com/doi/abs/10.1080/03610926.2018.1441418", "https://www.tandfonline.com/doi/pdf/10.1080/03610926.2018.1441418?needAccess=true"]}, "Compound Poisson process": {"categories": ["All articles needing additional references", "Articles needing additional references from September 2014", "L\u00e9vy processes", "Poisson point processes"], "title": "Compound Poisson process", "method": "Compound Poisson process", "url": "https://en.wikipedia.org/wiki/Compound_Poisson_process", "summary": "A compound Poisson process is a continuous-time (random) stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution. A compound Poisson process, parameterised by a rate \n \n \n \n \u03bb\n >\n 0\n \n \n {\\displaystyle \\lambda >0}\n and jump size distribution G, is a process \n \n \n \n {\n \n Y\n (\n t\n )\n :\n t\n \u2265\n 0\n \n }\n \n \n {\\displaystyle \\{\\,Y(t):t\\geq 0\\,\\}}\n given by\n\n \n \n \n Y\n (\n t\n )\n =\n \n \u2211\n \n i\n =\n 1\n \n \n N\n (\n t\n )\n \n \n \n D\n \n i\n \n \n \n \n {\\displaystyle Y(t)=\\sum _{i=1}^{N(t)}D_{i}}\n where, \n \n \n \n {\n \n N\n (\n t\n )\n :\n t\n \u2265\n 0\n \n }\n \n \n {\\displaystyle \\{\\,N(t):t\\geq 0\\,\\}}\n is a Poisson process with rate \n \n \n \n \u03bb\n \n \n {\\displaystyle \\lambda }\n , and \n \n \n \n {\n \n \n D\n \n i\n \n \n :\n i\n \u2265\n 1\n \n }\n \n \n {\\displaystyle \\{\\,D_{i}:i\\geq 1\\,\\}}\n are independent and identically distributed random variables, with distribution function G, which are also independent of \n \n \n \n {\n \n N\n (\n t\n )\n :\n t\n \u2265\n 0\n \n }\n .\n \n \n \n {\\displaystyle \\{\\,N(t):t\\geq 0\\,\\}.\\,}\n \nWhen \n \n \n \n \n D\n \n i\n \n \n \n \n {\\displaystyle D_{i}}\n are non-negative integer-valued random variables, then this compound Poisson process is known as a stuttering Poisson process which has the feature that two or more events occur in a very short time .", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Borel set", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Campbell's formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson distribution", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Convolution", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Expected value", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "Fractional Poisson process", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Law of total probability", "Law of total variance", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moment generating function", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson distribution", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Real number", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance", "Variance gamma process", "Vasicek model", "Wald's equation", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": []}, "Flood risk assessment": {"categories": ["Articles with limited geographic scope from May 2008", "Environmental policy in the United Kingdom", "Extreme value data", "Flood control", "Natural hazards", "United Kingdom-centric", "Webarchive template wayback links"], "title": "Flood risk assessment", "method": "Flood risk assessment", "url": "https://en.wikipedia.org/wiki/Flood_risk_assessment", "summary": "A flood risk assessment (FRA) is an assessment of the risk of flooding from all flooding mechanisms, the identification of flood mitigation measures and should provide advice on actions to be taken before and during a flood.\nThe sources of water which produce floods include:\n\nGroundwater (saturated groundwater)\nVadose (water flowing the ground in an unsaturated state)\nSurface water\nArtificial water (burst water mains, canals or reservoirs)\nRivers, streams or watercourses\nSewers and drains\nFlooding of low-lying coastal regions due to sea level riseFor each of the sources of water, different hydraulic intensities occur. Floods can occur because of a combination of sources of flooding, such as high groundwater and an inadequate surface water drainage system. The topography, hydrogeology and physical attributes of the existing or proposed development need to be considered. A flood risk assessment should be an evaluation of the flood risk and the consequences and impact and vulnerability.\nNon-professional flood risk assessments can be produced by members of the public, Architects, environment assessors, or others who are not specifically professionally qualified in this field. However, it is a complex evaluation and such assessments they can be rejected by Authorities as inadequate, or could be considered as negligent in the event of a flooding event, damage and a claim to insurers being made.\nIn the UK, the writing of professional flood risk assessments is undertaken by Civil Engineering Consultants. They will have membership of the Institution of Civil Engineers and are bound by their rules of professional conduct. A key requirement is to ensure such professional flood risk assessments are independent to all parties by carrying out their professional duties with complete objectivity and impartiality. Their professional advice should be supported by professional indemnity insurance for such specific professional advice ultimately held with a Lloyd's of London underwriter.\nProfessional flood risk assessments can cover single buildings, or whole regions. They can part of a due-diligence process for existing householders or businesses, or can be required in England and Wales to provide independent evidence to a planning application on the flood risk.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/bd/Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20120912112036%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20090504090119%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20090429055401%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081116011312%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081116010712%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081114061656%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112053306%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112013744%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112013034%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112012748%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20081112012546%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20080503023049%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20080503022818%21Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bd/20080503022500%21Ambox_globe_content.svg"], "links": ["Department of the Environment, Community and Local Government", "Department of the Environment (Northern Ireland)", "Environment Agency", "Flood", "Flood Modeller Pro", "Flood warning", "Floods directive", "Groundwater", "Institution of Civil Engineers", "International Standard Book Number", "Lloyd's of London", "Northern Ireland", "Office of Public Works", "PPS 25", "Planning Policy Statement", "Planning Service", "Planning permission", "Professional indemnity insurance", "Risk assessment", "Rivers Agency", "Sea level rise", "Vadose zone", "Wayback Machine"], "references": ["http://www.environ.ie/en/Publications/DevelopmentandHousing/Planning/FileDownLoad,21708,en.pdf", "http://www.communities.gov.uk/documents/planningandbuilding/pdf/planningpolicystatement25.pdf", "http://www.environment-agency.gov.uk/subjects/flood/", "http://webarchive.nationalarchives.gov.uk/20080306200436/http://www.communities.gov.uk/documents/planningandbuilding/pdf/153740", "http://webarchive.nationalarchives.gov.uk/20100408000121/http://www.communities.gov.uk/statements/corporate/planning-policy-flooding", "http://www.planningni.gov.uk/index/policy/policy_publications/planning_statements/pps15-flood-risk.pdf", "http://planningguidance.planningportal.gov.uk/blog/guidance/flood-risk-and-coastal-change/flood-zone-and-flood-risk-tables/table-2-flood-risk-vulnerability-classification/", "https://web.archive.org/web/20100215083945/http://www.communities.gov.uk/documents/planningandbuilding/pdf/planningpolicystatement25.pdf", "https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/6077/2116950.pdf", "https://www.ice.org.uk/ICEDevelopmentWebPortal/media/Documents/About%20Us/ice-code-of-professional-conduct.pdf"]}, "Multilinear principal-component analysis": {"categories": ["All Wikipedia articles needing context", "All pages needing cleanup", "Dimension reduction", "Machine learning", "Webarchive template wayback links", "Wikipedia articles needing context from June 2012", "Wikipedia introduction cleanup from June 2012"], "title": "Multilinear principal component analysis", "method": "Multilinear principal-component analysis", "url": "https://en.wikipedia.org/wiki/Multilinear_principal_component_analysis", "summary": "Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA). MPCA is employed in the analysis of n-way arrays, i.e. a cube or hyper-cube of numbers, also informally referred to as a \"data tensor\". N-way arrays may be decomposed, analyzed, or modeled by \n\nlinear tensor models such as CANDECOMP/Parafac, or\nmultilinear tensor models, such as multilinear principal component analysis (MPCA), or multilinear independent component analysis (MICA), etc.The origin of MPCA can be traced back to the Tucker decomposition and Peter Kroonenberg's \"M-mode PCA/3-mode PCA\" work. In 2000, De Lathauwer et al. restated Tucker and Kroonenberg's work in clear and concise numerical computational terms in their SIAM paper entitled \"Multilinear Singular Value Decomposition\", (HOSVD) and in their paper \"On the Best Rank-1 and Rank-(R1, R2, ..., RN ) Approximation of Higher-order Tensors\".Circa 2001, Vasilescu reframed the data analysis, recognition and synthesis problems as multilinear tensor problems based on the insight that most observed data are the compositional consequence of several causal factors of data formation, and are well suited for multi-modal data tensor analysis. The power of the tensor framework was showcased by analyzing human motion joint angles, facial images or textures in terms of their causal factors of data formation in the following works: Human Motion Signatures\n(CVPR 2001, ICPR 2002), face recognition \u2013 TensorFaces,\n(ECCV 2002, CVPR 2003, etc.) and computer graphics \u2013 TensorTextures (Siggraph 2004).\nHistorically, MPCA has been referred to as \"M-mode PCA\", a terminology which was coined by Peter Kroonenberg in 1980. In 2005, Vasilescu and Terzopoulos introduced the Multilinear PCA terminology as a way to better differentiate between linear and multilinear tensor decomposition, as well as, to better differentiate between the work that computed 2nd order statistics associated with each data tensor mode(axis), and subsequent work on Multilinear Independent Component Analysis that computed higher order statistics associated with each tensor mode/axis.\nMultilinear PCA may be applied to compute the causal factors of data formation, or as signal processing tool on data tensors whose individual observation have either been vectorized, or whose observations are treated as matrix and concatenated into a data tensor.\nMPCA computes a set of orthonormal matrices associated with each mode of the data tensor which are analogous to the orthonormal row and column space of a matrix computed by the matrix SVD. This transformation aims to capture as high a variance as possible, accounting for as much of the variability in the data associated with each data tensor mode(axis).", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["ArXiv", "Boosting (meta-algorithm)", "Demetri Terzopoulos", "Digital object identifier", "International Standard Serial Number", "Ledyard R Tucker", "M. Alex O. Vasilescu", "Multilinear", "Multilinear Singular Value Decomposition", "Principal component analysis", "Psychometrika", "TensorFaces", "TensorTextures", "Tucker decomposition", "Wayback Machine"], "references": ["http://www.dsp.utoronto.ca/~haiping/Publication/CrowdMPCA_CIKM2010.pdf", "http://www.dsp.utoronto.ca/~haiping/Publication/MPCA_TNN08_rev2010.pdf", "http://www.dsp.utoronto.ca/~haiping/Publication/SurveyMSL_PR2011.pdf", "http://www.dsp.utoronto.ca/~haiping/Publication/UMPCA_TNN09.pdf", "http://www.hindawi.com/journals/ivp/2009/713183.html", "http://www.mathworks.com/matlabcentral/fileexchange/26168", "http://www.mathworks.com/matlabcentral/fileexchange/35432", "http://www.springerlink.com/content/c8551t1p31236776/", "http://www.media.mit.edu/~maov/mica/mica05.pdf", "http://www.media.mit.edu/~maov/motionsignatures/hms_icpr02_corrected.pdf", "http://www.media.mit.edu/~maov/tensorfaces/cvpr03.pdf", "http://www.media.mit.edu/~maov/tensorfaces/eccv02_corrected.pdf", "http://www.media.mit.edu/~maov/tensortextures/Vasilescu_siggraph04.pdf", "http://www.cs.toronto.edu/~maov/tensorfaces/cvpr03.pdf", "http://research.cs.aalto.fi/pml/software/mtf/", "http://portal.acm.org/citation.cfm?id=354398", "http://portal.acm.org/citation.cfm?id=354405", "http://arxiv.org/abs/1412.4679", "http://doi.org/10.1007%2FBF02289464", "http://doi.org/10.1007%2Fs10994-016-5563-y", "http://doi.org/10.1016%2Fj.patcog.2011.01.004", "http://www.worldcat.org/issn/0885-6125", "https://link.springer.com/article/10.1007/s10994-016-5563-y", "https://web.archive.org/web/20101022214324/http://www.hindawi.com/journals/ivp/2009/713183.html", "https://doi.org/10.1155%2F2009%2F713183"]}, "Poisson sampling": {"categories": ["All stub articles", "Sampling techniques", "Statistics stubs"], "title": "Poisson sampling", "method": "Poisson sampling", "url": "https://en.wikipedia.org/wiki/Poisson_sampling", "summary": "In the theory of finite population sampling, Poisson sampling is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample.\nEach element of the population may have a different probability of being included in the sample. The probability of being included in a sample during the drawing of a single sample is denoted as the first-order inclusion probability of that element. If all first-order inclusion probabilities are equal, Poisson sampling becomes equivalent to Bernoulli sampling, which can therefore be considered to be a special case of Poisson sampling.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Bernoulli sampling", "Bernoulli trial", "Finite population sampling", "Inclusion probability", "International Standard Book Number", "Poisson disk sampling", "Poisson distribution", "Poisson process", "Sampling (statistics)", "Sampling design", "Statistical independence", "Statistical population", "Statistics"], "references": []}, "PSPP": {"categories": ["Commons category link is on Wikidata", "Free educational software", "Free software programmed in C", "Free statistical software", "GNU Project software", "Science software that uses GTK+"], "title": "PSPP", "method": "PSPP", "url": "https://en.wikipedia.org/wiki/PSPP", "summary": "PSPP is a free software application for analysis of sampled data, intended as a free alternative for IBM SPSS Statistics. It has a graphical user interface and conventional command-line interface. It is written in C and uses GNU Scientific Library for its mathematical routines. The name has \"no official acronymic expansion\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/3/31/Free_and_open-source_software_logo_%282009%29.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7a/GNU_PSPP.png", "https://upload.wikimedia.org/wikipedia/commons/1/1a/PSPP.png", "https://upload.wikimedia.org/wikipedia/commons/6/6d/Pspplogo.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["ADMB", "ASCII", "Alexandre Oliva", "Analyse-it", "BMDP", "BV4.1 (software)", "Bash (Unix shell)", "Benjamin Mako Hill", "Bradley M. Kuhn", "CSPro", "C (programming language)", "Comma-separated values", "Command-line interface", "Commercial software", "Comparison of statistical packages", "Cronbach's alpha", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Database", "Dataplot", "Defective by Design", "Digital restrictions management", "EViews", "Eben Moglen", "Electric (software)", "Epi Info", "Federico Heinz", "For Dummies", "Free Software Directory", "Free Software Foundation", "Free Software Foundation Europe", "Free Software Foundation Latin America", "Free Software Foundation anti-Windows campaigns", "Free Software Foundation of India", "Free software", "Free statistical software", "Freeware", "GAUSS (software)", "GIMP", "GNOME", "GNU", "GNU/Linux naming controversy", "GNU Affero General Public License", "GNU Archimedes", "GNU Binutils", "GNU Build System", "GNU C Library", "GNU Chess", "GNU Compiler Collection", "GNU Core Utilities", "GNU Debugger", "GNU Emacs", "GNU Find Utilities", "GNU Free Documentation License", "GNU GRUB", "GNU General Public License", "GNU Go", "GNU Guix", "GNU Health", "GNU Hurd", "GNU IceCat", "GNU Lesser General Public License", "GNU Manifesto", "GNU Multiple Precision Arithmetic Library", "GNU Octave", "GNU Privacy Guard", "GNU Project", "GNU Savannah", "GNU Scientific Library", "GNU TeXmacs", "GNU variants", "GNUmed", "GNUnet", "GNUstep", "GPL linking exception", "GenStat", "Georg C. F. Greve", "Gnash (software)", "Gnumeric", "Gnuzilla", "GraphPad InStat", "GraphPad Prism", "Graphical user interface", "Gretl", "Guix System Distribution", "H2O (software)", "HTML", "Histogram", "History of free and open-source software", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "LilyPond", "Linux", "Linux-libre", "List of GNU packages", "List of statistical packages", "Lo\u00efc Dachary", "MATLAB", "MLwiN", "MacOS", "Maple (software)", "Mathcad", "Mathematica", "Matt Lee (artist)", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Nagarjuna G.", "Np-chart", "One-way analysis of variance", "Open-source software", "OpenBUGS", "OpenDocument", "Operating system", "Orange (software)", "OxMetrics", "PDF", "PPSSPP", "Pie-chart", "PostScript", "Postgres", "Proprietary software", "Public-domain software", "Public/social/private partnership", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Repository (version control)", "Revolution Analytics", "Revolution OS", "Ricardo Galli", "Richard Stallman", "Ring (software)", "Robert J. Chassell", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Inc.", "SPSS Modeler", "SUDAAN", "SVG", "SYSTAT (software)", "SageMath", "Scree plot", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Spreadsheet", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistics", "StatsDirect", "Student's t-test", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "Ubuntu (operating system)", "Weibull modulus", "William John Sullivan", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://freestatisticalsoftware.com/pspp-overview/", "http://www.linux.com/archive/articles/150363", "http://slo-tech.com/clanki/09006/", "http://media.wiley.com/product_data/excerpt/48/04701134/0470113448-2.pdf", "http://www.communicationresearch.info/software/PSPP/basic.html", "http://search.cpan.org/~pdonelan/PSPP-Perl-0.7.2.20090730/lib/PSPP.pm", "http://savannah.gnu.org/forum/forum.php?forum_id=9283", "http://git.savannah.gnu.org/cgit/pspp.git", "http://www.spssusers.co.uk/Newsletter/1998/pspp.html", "https://translate.google.com/translate?prev=hp&hl=sl&js=n&u=http://slo-tech.com/clanki/09006/&sl=sl&tl=en", "https://directory.fsf.org/wiki/PSPP", "https://savannah.gnu.org/git/?group=pspp", "https://www.gnu.org/s/pspp/", "https://www.gnu.org/software/pspp/faq.html", "https://www.wikidata.org/wiki/Q1848165#P1324", "https://www.wikidata.org/wiki/Q1848165#P856", "https://archive.today/20080514022548/http://research.gc.cuny.edu/wiki/index.php/Importing_SPSS_syntax_data_files_into_R_under_Linux_using_PSPP"]}, "Noncentral beta distribution": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from August 2011", "Continuous distributions"], "title": "Noncentral beta distribution", "method": "Noncentral beta distribution", "url": "https://en.wikipedia.org/wiki/Noncentral_beta_distribution", "summary": "In probability theory and statistics, the noncentral beta distribution is a continuous probability distribution that is a generalization of the (central) beta distribution.\nThe noncentral beta distribution (Type I) is the distribution of the ratio\n\n \n \n \n X\n =\n \n \n \n \n \u03c7\n \n m\n \n \n 2\n \n \n (\n \u03bb\n )\n \n \n \n \u03c7\n \n m\n \n \n 2\n \n \n (\n \u03bb\n )\n +\n \n \u03c7\n \n n\n \n \n 2\n \n \n \n \n \n ,\n \n \n {\\displaystyle X={\\frac {\\chi _{m}^{2}(\\lambda )}{\\chi _{m}^{2}(\\lambda )+\\chi _{n}^{2}}},}\n where \n \n \n \n \n \u03c7\n \n m\n \n \n 2\n \n \n (\n \u03bb\n )\n \n \n {\\displaystyle \\chi _{m}^{2}(\\lambda )}\n is a \nnoncentral chi-squared random variable with degrees of freedom m and noncentrality parameter \n \n \n \n \u03bb\n \n \n {\\displaystyle \\lambda }\n , and \n \n \n \n \n \u03c7\n \n n\n \n \n 2\n \n \n \n \n {\\displaystyle \\chi _{n}^{2}}\n is a central chi-squared random variable with degrees of freedom n, independent of \n \n \n \n \n \u03c7\n \n m\n \n \n 2\n \n \n (\n \u03bb\n )\n \n \n {\\displaystyle \\chi _{m}^{2}(\\lambda )}\n .\nIn this case, \n \n \n \n X\n \u223c\n \n \n Beta\n \n \n \n (\n \n \n \n m\n 2\n \n \n ,\n \n \n n\n 2\n \n \n ,\n \u03bb\n \n )\n \n \n \n {\\displaystyle X\\sim {\\mbox{Beta}}\\left({\\frac {m}{2}},{\\frac {n}{2}},\\lambda \\right)}\n \nA Type II noncentral beta distribution is the distribution\nof the ratio \n\n \n \n \n Y\n =\n \n \n \n \u03c7\n \n n\n \n \n 2\n \n \n \n \n \u03c7\n \n n\n \n \n 2\n \n \n +\n \n \u03c7\n \n m\n \n \n 2\n \n \n (\n \u03bb\n )\n \n \n \n ,\n \n \n {\\displaystyle Y={\\frac {\\chi _{n}^{2}}{\\chi _{n}^{2}+\\chi _{m}^{2}(\\lambda )}},}\n where the noncentral chi-squared variable is in the denominator only. If \n \n \n \n Y\n \n \n {\\displaystyle Y}\n follows \nthe type II distribution, then \n \n \n \n X\n =\n 1\n \u2212\n Y\n \n \n {\\displaystyle X=1-Y}\n follows a type I distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["ARGUS distribution", "Abramowitz and Stegun", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biometrika", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Confluent hypergeometric function", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irene Stegun", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Milton Abramowitz", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral F-distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Noncentrality parameter", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Regularized incomplete beta function", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://amstat.tandfonline.com/doi/abs/10.1080/00031305.1995.10476151#.UhpzB3_3Oy8", "http://doi.org/10.1080%2F00031305.1993.10475957", "http://doi.org/10.1080%2F00031305.1995.10476151", "http://doi.org/10.1093%2Fbiomet%2F50.3-4.542", "http://doi.org/10.1214%2Faoms%2F1177728424", "http://www.jstor.org/stable/2685195"]}, "Schuette\u2013Nesbitt formula": {"categories": ["Articles containing proofs", "Enumerative combinatorics", "Probability theorems", "Statistical theorems"], "title": "Schuette\u2013Nesbitt formula", "method": "Schuette\u2013Nesbitt formula", "url": "https://en.wikipedia.org/wiki/Schuette%E2%80%93Nesbitt_formula", "summary": "In mathematics, the Schuette\u2013Nesbitt formula is a generalization of the inclusion\u2013exclusion principle. It is named after Donald R. Schuette and Cecil J. Nesbitt.\nThe probabilistic version of the Schuette\u2013Nesbitt formula has practical applications in actuarial science, where it is used to calculate the net single premium for life annuities and life insurances based on the general symmetric status.", "images": [], "links": ["Actuarial mathematics", "Actuarial notation", "Actuarial science", "Binomial coefficient", "Binomial formula", "Binomial theorem", "Cecil J. Nesbitt", "Combinatorial proof", "Complement (set theory)", "Complex number", "Convergence in distribution", "Convex combination", "Curriculum vitae", "Difference operator", "Discrete probability distribution", "Donald R. Schuette", "Edward Waring", "Empty set", "Euclidean space", "Event (probability theory)", "Expected value", "Exponential function", "Field (mathematics)", "Finite measure", "Fixed point (mathematics)", "Formula", "Function composition", "Identity matrix", "Identity operator", "Inclusion\u2013exclusion principle", "Indeterminate (variable)", "Indicator function", "Infinity", "Institute for Advanced Study", "International Standard Book Number", "Intersection (set theory)", "Kronecker delta", "Life annuity", "Life insurance", "Life table", "Linear map", "Lp space", "Mathematical education", "Mathematics", "Mathematics Genealogy Project", "Matrix (mathematics)", "Module (mathematics)", "Multiplicative identity", "Net premium valuation", "Partial sum", "PhD", "Poisson distribution", "Polynomial", "Polynomial ring", "Power (mathematics)", "Princeton, New Jersey", "Probability-generating function", "Probability distribution", "Probability space", "Probability theory", "Random permutation", "Random variable", "Real number", "Rencontres numbers", "Ring (mathematics)", "Sequence space", "Set (mathematics)", "Shift operator", "Society of Actuaries", "Statistical independence", "Subsets", "Support (measure theory)", "Transpose", "Unital algebra", "University of Michigan", "University of Toronto", "University of Wisconsin\u2013Madison", "Vector component", "Vector space", "William Feller", "Zentralblatt MATH"], "references": ["http://www.soa.org/library/research/actuarial-research-clearing-house/1978-89/1979/arch-1/arch79v16.pdf", "http://www.soa.org/library/research/transactions-of-society-of-actuaries/1959/january/tsa59v11n29ab7.pdf", "http://zbmath.org/?format=complete&q=an:0155.23101", "http://zbmath.org/?format=complete&q=an:0634.62107", "http://zbmath.org/?format=complete&q=an:0825.62745", "http://zbmath.org/?format=complete&q=an:0869.62072", "https://www.genealogy.math.ndsu.nodak.edu/id.php?id=5022", "https://www.genealogy.math.ndsu.nodak.edu/id.php?id=7749"]}, "Separation test": {"categories": ["All stub articles", "Statistical tests", "Statistics stubs"], "title": "Separation test", "method": "Separation test", "url": "https://en.wikipedia.org/wiki/Separation_test", "summary": "A separation test is a statistical procedure for early-phase research, to decide whether to pursue further research. It is designed to avoid the prevalent situation in early-phase research, when a statistically underpowered test gives a negative result.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Statistical power", "Statistics"], "references": ["http://www.ergologic.us"]}, "Robust regression": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2017", "Articles with unsourced statements from September 2017", "CS1 errors: invisible characters", "Robust regression"], "title": "Robust regression", "method": "Robust regression", "url": "https://en.wikipedia.org/wiki/Robust_regression", "summary": "In robust statistics, robust regression is a form of regression analysis designed to overcome some limitations of traditional parametric and non-parametric methods. Regression analysis seeks to find the relationship between one or more independent variables and a dependent variable. Certain widely used methods of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results if those assumptions are not true; thus ordinary least squares is said to be not robust to violations of its assumptions. Robust regression methods are designed to be not overly affected by violations of assumptions by the underlying data-generating process.\nIn particular, least squares estimates for regression models are highly sensitive to (i.e. not robust against) outliers. While there is no precise definition of an outlier, outliers are observations which do not follow the pattern of the other observations. This is not normally a problem if the outlier is simply an extreme observation drawn from the tail of a normal distribution, but if the outlier results from non-normal measurement error or some other violation of standard ordinary least squares assumptions, then it compromises the validity of the regression results if a non-robust regression technique is used.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/e/ee/OLSandMM.JPG", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/2/24/ResidualPlots.JPG"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Approximation theory", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "BUPA", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Cox transformation", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brian D. Ripley", "Calibration curve", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Classic data sets", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational statistics", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curve fitting", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete choice", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Ernest Burgess", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fixed effects model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedastic", "Homoscedasticity", "Howard Wainer", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least-angle regression", "Least absolute deviations", "Least squares", "Least trimmed squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-linear least squares", "Non-negative least squares", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Outliers", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Rousseeuw", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal component regression", "Prior probability", "Probabilistic design", "Probability distribution", "Probit model", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "RANSAC", "R (programming language)", "Radar chart", "Random assignment", "Random effects model", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model", "Regression model validation", "Regularized least squares", "Relaxed intersection", "Reliability engineering", "Repeated median regression", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Ridge regression", "Robust statistics", "Robyn Dawes", "Run chart", "S-PLUS", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel S. Wilks", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social Science Research Network", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Statsmodels", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Theil\u2013Sen estimator", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Trend estimation", "Type I and type II errors", "U-statistic", "Uniformly most powerful test", "Unit-weighted regression", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://ssrn.com/abstract=1406472", "http://users.cms.caltech.edu/~jtropp/papers/LMTZ12-Robust-Computation.pdf", "http://www.cmu.edu/dietrich/sds/docs/dawes/the-robust-beauty-of-improper-linear-models-in-decision-making.pdf", "http://webmining.spd.louisville.edu/wp-content/uploads/2014/05/A-Brief-Overview-of-Robust-Statistics.pdf", "http://webmining.spd.louisville.edu/wp-content/uploads/2014/05/A-Brief-Overview-of-Robust-Clustering-Techniques.pdf", "http://www.eng.tau.ac.il/~bengal/outlier.pdf", "http://www.sourceforge.net/projects/l1-norm-robust-regression", "http://doi.org/10.1214%2F088342304000000549", "http://doi.org/10.1214%2Fss%2F1009213725", "http://doi.org/10.1214%2Fss%2F1177012915", "http://doi.org/10.1504%2FIJSSS.2015.073223", "http://doi.org/10.2139%2Fssrn.1406472", "http://doi.org/10.2307%2F2290063", "http://www.jstatsoft.org/v10/a05/paper", "http://www.jstor.org/stable/2245578", "http://www.jstor.org/stable/2290063", "http://www.jstor.org/stable/2676681", "http://www.jstor.org/stable/4144426", "http://www.nickfieller.staff.shef.ac.uk/sheff-only/StatModall05.pdf", "https://github.com/gsubramani/robust-nonlinear-regression", "https://books.google.com/books/about/The_Workings_of_the_Indeterminate_senten.html?id=V6xCAAAAIAAJ", "https://web.archive.org/web/20121021081319/http://www.stats.ox.ac.uk/pub/StatMeth/Robust.pdf", "https://doi.org/10.1007%2FBF02287917", "https://doi.org/10.1007%2FBF02291695", "https://doi.org/10.1037%2F0003-066X.34.7.571", "https://doi.org/10.1177%2F1094428106294734", "https://doi.org/10.1177%2F109442819814003"]}, "Multi-armed bandit": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2015", "CS1 maint: Multiple names: authors list", "Machine learning", "Sequential experiments", "Sequential methods", "Stochastic optimization"], "title": "Multi-armed bandit", "method": "Multi-armed bandit", "url": "https://en.wikipedia.org/wiki/Multi-armed_bandit", "summary": "In probability theory, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is a problem in which a fixed limited set of resources must be allocated between competing (alternative) choices in a way that maximizes their expected gain, when each choice's properties are only partially known at the time of allocation, and may become better understood as time passes or by allocating resources to the choice. The name comes from imagining a gambler at a row of slot machines (sometimes known as \"one-armed bandits\"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. The multi-armed bandit problem also falls into the broad category of stochastic scheduling.\nIn the problem, each machine provides a random reward from a probability distribution specific to that machine. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between \"exploitation\" of the machine that has the highest expected payoff and \"exploration\" to get more information about the expected payoffs of the other machines. The trade-off between exploration and exploitation is also faced in machine learning. In practice, multi-armed bandits have been used to model problems such as managing research projects in a large organization like a science foundation or a pharmaceutical company. In early versions of the problem, the gambler begins with no initial knowledge about the machines.\nHerbert Robbins in 1952, realizing the importance of the problem, constructed convergent population selection strategies in \"some aspects of the sequential design of experiments\". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal policy for maximizing the expected discounted reward.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b2/Framework_of_UCB-ALP_for_Constrained_Contextual_Bandits.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/82/Las_Vegas_slot_machines.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/26/The_Jet_Propulsion_Laboratory_%289416811752%29.jpg"], "links": ["Adaptive routing", "Annals of Applied Probability", "Annals of Statistics", "ArXiv", "Asymptotic", "Bayes' theorem", "Bibcode", "Bulletin of the American Mathematical Society", "CiteSeerX", "Clinical trial", "Condorcet winner", "Digital object identifier", "Don Berry (statistician)", "Gambler", "Germany", "Gittins index", "Greedy algorithm", "Herbert Robbins", "International Standard Book Number", "Iterated prisoner's dilemma", "JSTOR", "John C. Gittins", "Journal of the Royal Statistical Society", "Lecture Notes in Computer Science", "Machine learning", "Markov decision process", "Mathematical Reviews", "Medical ethics", "Michael Katehakis", "Michael N. Katehakis", "Nonparametric regression", "Open-Source", "Operations Research (journal)", "Optimal stopping", "Peter Whittle (mathematician)", "Pharmaceutical industry", "Portfolio (finance)", "Probability distribution", "Probability theory", "PubMed Central", "PubMed Identifier", "Regret (decision theory)", "Ridge regression", "SIAM Journal on Computing", "Search theory", "Singular-value decomposition", "Slot machines", "Softmax function", "Stochastic scheduling", "Thompson sampling", "Voting paradoxes", "World War II"], "references": ["http://webdocs.cs.ualberta.ca/~sutton/book/the-book.html", "http://books.nips.cc/papers/files/nips20/NIPS2007_0673.pdf", "http://papers.nips.cc/paper/3178-the-epoch-greedy-algorithm-for-multi-armed-bandits-with-side-information", "http://www.chrisstucchio.com/blog/2012/bandit_algorithms_vs_ab.html", "http://www.sciencedirect.com/science/article/pii/S0022000012000281", "http://www.tokic.com/www/tokicm/publikationen/papers/AdaptiveEpsilonGreedyExploration.pdf", "http://www.tokic.com/www/tokicm/publikationen/papers/KI2011.pdf", "http://adsabs.harvard.edu/abs/1995PNAS...92.8584K", "http://adsabs.harvard.edu/abs/2009PNAS..10622387P", "http://adsabs.harvard.edu/abs/2010arXiv1009.5419B", "http://adsabs.harvard.edu/abs/2013arXiv1309.6869V", "http://adsabs.harvard.edu/abs/2014arXiv1401.8257G", "http://adsabs.harvard.edu/abs/2015arXiv150203473L", "http://adsabs.harvard.edu/abs/2015arXiv150600312Z", "http://adsabs.harvard.edu/abs/2016arXiv160407101W", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.380.6983&rep=rep1&type=pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.5482", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2793317", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC41010", "http://www.ncbi.nlm.nih.gov/pubmed/11607577", "http://www.ncbi.nlm.nih.gov/pubmed/20018711", "http://www.feynmanlectures.info/exercises/Feynmans_restaurant_problem.html", "http://homes.di.unimi.it/~cesabian/Pubblicazioni/banditSurvey.pdf", "http://bandit.sourceforge.net", "http://bandit.sourceforge.net/Vermorel2005poker.pdf", "http://www.aaai.org/ocs/index.php/IJCAI/IJCAI15/paper/viewPDFInterstitial/10972/10798", "http://www.ams.org/mathscinet-getitem?mr=0974588", "http://arxiv.org/abs/0711.3861", "http://arxiv.org/abs/0905.2776", "http://arxiv.org/abs/1009.5419", "http://arxiv.org/abs/1110.6084", "http://arxiv.org/abs/1309.6869", "http://arxiv.org/abs/1401.8257", "http://arxiv.org/abs/1409.8191", "http://arxiv.org/abs/1502.03473", "http://arxiv.org/abs/1506.00312", "http://arxiv.org/abs/1604.07101", "http://doi.org/10.1002%2Fasmb.874", "http://doi.org/10.1006%2Faama.1996.0007", "http://doi.org/10.1007%2F978-3-319-12637-1_47", "http://doi.org/10.1007%2F978-3-642-16111-7_23", "http://doi.org/10.1007%2F978-3-642-34487-9_40", "http://doi.org/10.1007%2Fs10994-011-5257-4", "http://doi.org/10.1016%2F0196-8858(85)90002-8", "http://doi.org/10.1016%2Fj.jcss.2011.12.028", "http://doi.org/10.1016%2Fj.tcs.2010.04.005", "http://doi.org/10.1023%2FA:1013689704352", "http://doi.org/10.1073%2Fpnas.0912378106", "http://doi.org/10.1073%2Fpnas.92.19.8584", "http://doi.org/10.1090%2FS0002-9904-1952-09620-8", "http://doi.org/10.1109%2Fsfcs.2000.892116", "http://doi.org/10.1109%2Ftaai.2011.59", "http://doi.org/10.1137%2FS0097539701398375", "http://doi.org/10.1145%2F1870103.1870106", "http://doi.org/10.1214%2F13-aos1101", "http://doi.org/10.1214%2Faoap%2F1177005588", "http://doi.org/10.1214%2Faop%2F1176994469", "http://doi.org/10.1214%2Flnms%2F1215540286", "http://doi.org/10.1239%2Faap%2F1214950209", "http://doi.org/10.1287%2Fmoor.12.2.262", "http://doi.org/10.1287%2Fmoor.22.1.222", "http://doi.org/10.1287%2Fopre.1100.0891", "http://doi.org/10.2307%2F3214163", "http://jmlr.org/proceedings/papers/v37/gajane15.pdf", "http://jmlr.org/proceedings/papers/v40/Komiyama15.pdf", "http://jmlr.org/proceedings/papers/v51/feraud16.html", "http://www.jmlr.org/proceedings/papers/v28/urvoy13.pdf", "http://www.jmlr.org/proceedings/papers/v32/zoghi14.pdf", "http://www.jstor.org/stable/2959678", "http://www.jstor.org/stable/2985029", "http://www.jstor.org/stable/3689689", "http://www.jstor.org/stable/4355518", "http://mloss.org/software/view/415/", "http://www.pnas.org/content/106/52/22387", "http://www.scitepress.org/DigitalLibrary/PublicationsDetail.aspx?ID=Dx2xXEB0PJE=&t=1", "http://techtalks.tv/talks/54451/", "http://techtalks.tv/talks/54455/", "https://papers.nips.cc/paper/6008-algorithms-with-logarithmic-or-sublinear-regret-for-constrained-contextual-bandits", "https://github.com/jkomiyama/banditlib", "https://link.springer.com/chapter/10.1007%2F978-3-642-34487-9_40", "https://mpatacchiola.github.io/blog/2017/08/14/dissecting-reinforcement-learning-6.html", "https://archive.is/20121212095047/http://www.cs.washington.edu/research/jair/volume4/kaelbling96a-html/node6.html", "https://web.archive.org/web/20131211192714/http://webdocs.cs.ualberta.ca/~sutton/book/the-book.html", "https://arxiv.org/abs/0805.3415", "https://arxiv.org/abs/1508.03326", "https://dx.doi.org/10.1109/sfcs.2000.892116", "https://dx.doi.org/10.1109/taai.2011.59"]}, "Soliton distribution": {"categories": ["Coding theory", "Discrete distributions"], "title": "Soliton distribution", "method": "Soliton distribution", "url": "https://en.wikipedia.org/wiki/Soliton_distribution", "summary": "A soliton distribution is a type of discrete probability distribution that arises in the theory of erasure correcting codes. A paper by Luby introduced two forms of such distributions, the ideal soliton distribution and the robust soliton distribution.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "CiteSeerX", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erasure correcting code", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Luby transform code", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Probability mass function", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.8104", "http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1181950"]}, "Bioinformatics": {"categories": ["All articles with unsourced statements", "All articles with vague or ambiguous time", "Articles including recorded pronunciations (English)", "Articles with hAudio microformats", "Articles with unsourced statements from July 2015", "Bioinformatics", "CS1 maint: Multiple names: authors list", "Spoken articles", "Use dmy dates from July 2012", "Vague or ambiguous time from September 2018", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Bioinformatics", "method": "Bioinformatics", "url": "https://en.wikipedia.org/wiki/Bioinformatics", "summary": "Bioinformatics (listen) is an interdisciplinary field that develops methods and software tools for understanding biological data. As an interdisciplinary field of science, bioinformatics combines biology, computer science, information engineering, mathematics and statistics to analyze and interpret biological data. Bioinformatics has been used for in silico analyses of biological queries using mathematical and statistical techniques.\nBioinformatics is both an umbrella term for the body of biological studies that use computer programming as part of their methodology, as well as a reference to specific analysis \"pipelines\" that are repeatedly used, particularly in the field of genomics. Common uses of bioinformatics include the identification of candidates genes and single nucleotide polymorphisms (SNPs). Often, such identification is made with the aim of better understanding the genetic basis of disease, unique adaptations, desirable properties (esp. in agricultural species), or differences between populations. In a less formal way, bioinformatics also tries to understand the organisational principles within nucleic acid and protein sequences, called proteomics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/50/1kqf_opm.png", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/43/En-Bioinformatics.ogg", "https://upload.wikimedia.org/wikipedia/commons/7/76/En-us-bioinformatics.ogg", "https://upload.wikimedia.org/wikipedia/commons/4/43/Genome_viewer_screenshot_small.png", "https://upload.wikimedia.org/wikipedia/commons/d/d8/Image_DNA_sequence_-_png.png", "https://upload.wikimedia.org/wikipedia/commons/2/2d/Issoria_lathonia.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/8a/Loudspeaker.svg", "https://upload.wikimedia.org/wikipedia/commons/6/60/Myoglobin.png", "https://upload.wikimedia.org/wikipedia/commons/9/92/Open_book_nae_02.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/47/Sound-icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/89/Symbol_book_class2.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b4/The_protein_interaction_network_of_Treponema_pallidum.png", "https://upload.wikimedia.org/wikipedia/commons/0/09/Tree_of_life.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a7/WPP_domain_alignment.PNG", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": [".NET Bio", "2-D electrophoresis", "ACM Computing Classification System", "Abiogenesis", "Accuracy", "Adaptation", "Adaptive radiation", "African Society for Bioinformatics and Computational Biology", "Algorithm", "Algorithm design", "Algorithmic efficiency", "Alzheimer's Disease", "American Medical Informatics Association", "Amino acid", "Amino acid sequence", "Analysis of algorithms", "Anatomy", "Anduril (workflow engine)", "Apache Taverna", "Application security", "Applications of evolution", "Approximation algorithms", "Archival informatics", "Artificial intelligence", "Artificial life", "Astrobiology", "Astroinformatics", "Australasian College of Health Informatics", "Automata theory", "Automated planning and scheduling", "BLAST", "Barcode of Life Data System", "Base calling", "Basel Computational Biology Conference", "Bayesian analysis", "Ben Hesper", "Bernd Sturmfels", "Bibcode", "BioCompute Object", "BioCyc database collection", "BioJS", "BioJava", "BioPerl", "BioRuby", "BioRxiv", "Biochemistry", "Biochip", "Bioclipse", "Bioconductor", "Biodiversity", "Biodiversity informatics", "Bioengineering", "Biogeography", "Biohistory", "Bioimage informatics", "Bioinformatics", "Bioinformatics (journal)", "Bioinformatics Open Source Conference", "Bioinformatics companies", "Bioinformatics workflow management systems", "Biological Data Visualization", "Biological classification", "Biological computation", "Biological database", "Biological network", "Biology", "Biomarkers in Medicine", "Biomechanics", "Biomedical text mining", "Biomolecule", "Biophysics", "Biopython", "Biosocial criminology", "Biostatistics", "Botany", "Bovine spongiform encephalopathy", "Bowtie (sequence analysis)", "Brazilian Society of Health Informatics", "Breast cancer", "Briefings in Functional Genomics", "Broad Institute", "Business informatics", "Call-map proteomics", "Canadian Bioinformatics Workshops", "Cancer", "Cell (biology)", "Cell biology", "Cell cycle", "Cell nucleus", "Cellular microbiology", "Cellular model", "Cellular respiration", "ChIA-PET", "Charles Darwin", "Chemical Reviews", "Chemical biology", "Cheminformatics", "Chemogenomics", "Chromosome conformation capture", "Chronobiology", "Cladistics", "Clinic management system", "Clustal", "Cluster analysis", "Co-operation (evolution)", "Coevolution", "Coextinction", "Cognitive genomics", "Common descent", "Community informatics", "Comparative genomic hybridization", "Comparative genomics", "Compiler construction", "Computational biology", "Computational biomodeling", "Computational chemistry", "Computational complexity theory", "Computational engineering", "Computational genomics", "Computational geometry", "Computational informatics", "Computational linguistics", "Computational mathematics", "Computational phylogenetics", "Computational physics", "Computational social science", "Computational systems biology", "Computer", "Computer accessibility", "Computer animation", "Computer architecture", "Computer data storage", "Computer graphics", "Computer hardware", "Computer network", "Computer program", "Computer programming", "Computer science", "Computer security", "Computer security compromised by hardware failure", "Computer simulation", "Computer vision", "Computerized physician order entry", "Computing platform", "Concurrency (computer science)", "Concurrent computing", "Connectomics", "Consensus clustering", "Conservation biology", "Consumer health informatics", "Continuity of Care Record", "Control theory", "Convergent evolution", "Copy number variation", "Coursera", "Creation\u2013evolution controversy", "Creative Commons", "Cross-validation (statistics)", "Cryptography", "Current Opinion in Structural Biology", "Current Protocols", "Cyberwarfare", "Cytogenetics", "DICOM", "DNA", "DNA Data Bank of Japan", "DNA barcoding", "DNA microarray", "DNA sequence", "DNA sequencing", "Data mining", "Data warehouse", "Database management system", "De facto", "Decision support system", "Dependability", "Development informatics", "Developmental biology", "Diagnostics", "Digital art", "Digital library", "Digital marketing", "Digital object identifier", "Discrete mathematics", "Disease 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Russell", "Subjective logic", "Sufficient statistic", "Sven Erik J\u00f8rgensen", "Tetration", "Thomas Bayes", "Topological ordering", "Treewidth", "Variable-order Bayesian network", "Variable elimination", "Variational Bayes", "WinBUGS", "Yale University Press"], "references": ["http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2005", "http://www.csse.monash.edu.au/~dld/David.Dowe.publications.html#ComleyDowe2003", "http://www.csse.monash.edu.au/~dld/MML.html", "http://www.csse.monash.edu.au/~dld/Publications/2010/Dowe2010_MML_HandbookPhilSci_Vol7_HandbookPhilStat_MML+hybridBayesianNetworkGraphicalModels+StatisticalConsistency+InvarianceAndUniqueness_pp901-982.pdf", "http://www.niedermayer.ca/papers/bayesian/bayes.html", "http://papers.nips.cc/paper/6232-learning-treewidth-bounded-bayesian-networks-with-thousands-of-variables", "http://www.agenarisk.com/resources/apps_bayesian_networks.pdf", "http://www.biomedcentral.com/1471-2105/7/514/abstract", "http://www.kamran-karimi.com/pubs/khISMIS2000.pdf", "http://online.liebertpub.com/doi/abs/10.1089/106652700750050961", "http://research.microsoft.com/research/pubs/view.aspx?msr_tr_id=MSR-TR-95-06", "http://princesofserendib.com/", "http://fuzzy.cs.uni-magdeburg.de/books/gm/", "http://aima.cs.berkeley.edu/", "http://icsi.berkeley.edu/~luby/PAPERS/bayesian.ps", "http://www.andrew.cmu.edu/user/scheines/tutor/d-sep.html", "http://repository.cmu.edu/cgi/viewcontent.cgi?article=1316&context=philosophy", "http://adsabs.harvard.edu/abs/2013arXiv1302.6835P", "http://cogcomp.cs.illinois.edu/page/publication_view/5", "http://cogcomp.cs.illinois.edu/papers/hardJ.pdf", "http://robotics.stanford.edu/~nodelman/papers/ctbn.pdf", "http://bayes.cs.ucla.edu/BOOK-09/ch11-1-2-final.pdf", "http://bayes.cs.ucla.edu/BOOK-2K/ch3-3.pdf", "http://ftp.cs.ucla.edu/pub/stat_ser/r116.pdf", "http://ftp.cs.ucla.edu/tech-report/198_-reports/850017.pdf", "http://pages.cs.wisc.edu/~dyer/cs540/handouts/charniak.pdf", "http://www.tiny-clues.eu/Research/Petitjean2013-ICDM.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/11108481", "http://www.ncbi.nlm.nih.gov/pubmed/16268944", "http://www.ncbi.nlm.nih.gov/pubmed/19630097", "http://www.eng.tau.ac.il/~bengal/BN.pdf", "http://videolectures.net/kdd07_neapolitan_lbn/", "http://dl.acm.org/ft_gateway.cfm?id=2074452&ftid=1062250&dwn=1&CFID=161588115&CFTOKEN=10243006", "http://arxiv.org/abs/1302.6835", "http://www.cambridge.org/9780521884389", "http://doi.org/10.1002%2F9780470061572.eqr089", "http://doi.org/10.1002%2Fsim.3680", "http://doi.org/10.1007%2Fs10044-004-0214-5", "http://doi.org/10.1016%2F0004-3702(86)90072-X", "http://doi.org/10.1016%2F0004-3702(90)90060-d", "http://doi.org/10.1016%2F0004-3702(93)90036-b", "http://doi.org/10.1016%2Fs0004-3702(97)00013-1", "http://doi.org/10.1023%2FA:1007465528199", "http://doi.org/10.1023%2FA:1009730122752", "http://doi.org/10.1089%2F106652700750050961", "http://doi.org/10.1098%2Frstl.1763.0053", "http://doi.org/10.1111%2Fj.1539-6924.2005.00641.x", "http://doi.org/10.1177%2F089443939100900106", "http://www.labmedinfo.org/download/lmi339.pdf", "http://www.worldcat.org/oclc/42291253", "http://www.dcs.qmul.ac.uk/~norman/papers/oprisk.pdf", "http://www.dcs.qmw.ac.uk/~norman/BBNs/BBNs.htm", "https://papers.nips.cc/paper/5803-learning-bayesian-networks-with-thousands-of-variables", "https://books.google.com/books?id=7X5KLwEACAAJP", "https://books.google.com/books?id=Av6qWhtw0-EC", "https://books.google.com/books?id=AvNID7LyMusC", "https://books.google.com/books?id=I8Fa-LKDpF0C", "https://books.google.com/books?id=LLkhAwAAQBAJ", "https://books.google.com/books?id=LxXOBQAAQBAJ", "https://books.google.com/books?id=OlMZAQAAIAAJ", "https://books.google.com/books?id=TNYhnkXQSjAC", "https://books.google.com/books?id=TNYhnkXQSjAC&pg=PA120", "https://books.google.com/books?id=VkawQgAACAAJ", "https://books.google.com/books?id=cWLaBwAAQBAJ", "https://books.google.com/books?id=etXXsgEACAAJ", "https://books.google.com/books?id=ikuuHAAACAAJ", "https://books.google.com/books?id=mPG5RupkTX0C", "https://books.google.com/books?id=mn2jBQAAQBAJ", "https://link.springer.com/article/10.1023%2FA:1007465528199", "https://stat.duke.edu/~sayan/npcomplete.pdf", "https://www.researchgate.net/publication/222479046_Approximating_probabilistic_inference_in_Bayesian_belief_networks_is_NP-hard", "https://web.archive.org/web/20060719171558/http://research.microsoft.com/research/pubs/view.aspx?msr_tr_id=MSR-TR-95-06", "https://web.archive.org/web/20070927153751/https://www.dcs.qmul.ac.uk/~norman/papers/Combining%20evidence%20in%20risk%20analysis%20using%20BNs.pdf", "https://web.archive.org/web/20090923200511/http://wiki.syncleus.com/index.php/DANN:Bayesian_Network", "https://arxiv.org/abs/1206.6876", "https://arxiv.org/abs/1208.5160", "https://arxiv.org/abs/1304.2736", "https://dslpitt.org/papers/11/p153-cussens.pdf", "https://www.dcs.qmul.ac.uk/~norman/papers/Combining%20evidence%20in%20risk%20analysis%20using%20BNs.pdf"]}, "Anchor test": {"categories": ["Comparison of assessments", "Psychometrics"], "title": "Anchor test", "method": "Anchor test", "url": "https://en.wikipedia.org/wiki/Anchor_test", "summary": "In psychometrics, an anchor test is a common set of test items administered in combination with two or more alternative forms of the test with the aim of establishing the equivalence of the test scores on the alternative forms. The purpose of the anchor test is to provide a baseline for an equating analysis between different forms of a test.Anchor test is one type of psychological assessment tool to measure an individual's knowledge or cognitive ability by testing the same areas in different ways. In psychometrics, to develop assessment tools that are reliable for testing certain skills and abilities are what most Psychometricists are interested in. Anchor tests are not intended to test the subject's ability to take tests, interpret questions, or understand a concept that is unrelated to the test questions. Instead, it eliminates the incongruency between what the test is designed to assess and what it actually assesses. Subjects will be tested on the same knowledge and skills in multiple ways in an anchor test. Compared with traditional tests in both education and psychology, anchor tests are intended to find out what an individual is able to do rather than what an individual is unable to do. A study examined that higher anchor test to total test correlation leads to better equating then implies that an anchor test with items of medium difficulty may lead to better equating.\n\n", "images": [], "links": ["Equating", "Psychometrics", "Test (student assessment)", "Test score"], "references": ["http://www.wisegeek.com/what-is-an-anchor-test.htm", "http://www.ets.org/Media/Research/pdf/RR-12-14.pdf"]}, "Nonlinear autoregressive exogenous model": {"categories": ["Nonlinear time series analysis", "Time series models"], "title": "Nonlinear autoregressive exogenous model", "method": "Nonlinear autoregressive exogenous model", "url": "https://en.wikipedia.org/wiki/Nonlinear_autoregressive_exogenous_model", "summary": "In time series modeling, a nonlinear autoregressive exogenous model (NARX) is a nonlinear autoregressive model which has exogenous inputs. This means that the model relates the current value of a time series to both:\n\npast values of the same series; and\ncurrent and past values of the driving (exogenous) series \u2014 that is, of the externally determined series that influences the series of interest.In addition, the model contains:\n\nan \"error\" termwhich relates to the fact that knowledge of the other terms will not enable the current value of the time series to be predicted exactly.\nSuch a model can be stated algebraically as\n\n \n \n \n \n y\n \n t\n \n \n =\n F\n (\n \n y\n \n t\n \u2212\n 1\n \n \n ,\n \n y\n \n t\n \u2212\n 2\n \n \n ,\n \n y\n \n t\n \u2212\n 3\n \n \n ,\n \u2026\n ,\n \n u\n \n t\n \n \n ,\n \n u\n \n t\n \u2212\n 1\n \n \n ,\n \n u\n \n t\n \u2212\n 2\n \n \n ,\n \n u\n \n t\n \u2212\n 3\n \n \n ,\n \u2026\n )\n +\n \n \u03b5\n \n t\n \n \n \n \n {\\displaystyle y_{t}=F(y_{t-1},y_{t-2},y_{t-3},\\ldots ,u_{t},u_{t-1},u_{t-2},u_{t-3},\\ldots )+\\varepsilon _{t}}\n Here y is the variable of interest, and u is the externally determined variable. In this scheme, information about u helps predict y, as do previous values of y itself. Here \u03b5 is the error term (sometimes called noise). For example, y may be air temperature at noon, and u may be the day of the year (day-number within year).\nThe function F is some nonlinear function, such as a polynomial. F can be a neural network, a wavelet network, a sigmoid network and so on. To test for non-linearity in a time series, the BDS test (Brock-Dechert-Scheinkman test) developed for econometrics can be used.", "images": [], "links": ["Autoregressive model", "BDS test", "Econometrics", "Errors and residuals in statistics", "Exogenous", "International Standard Book Number", "Neural network", "Nonlinear", "Polynomial", "Sigmoid network", "Time series", "Wavelet network"], "references": ["http://sourceforge.net/projects/narxsim"]}, "Area compatibility factor": {"categories": ["Actuarial science", "All articles lacking sources", "All articles needing expert attention", "All articles that are too technical", "All stub articles", "Articles lacking sources from October 2018", "Articles needing expert attention from May 2016", "Articles with multiple maintenance issues", "Demography", "Epidemiology", "Statistics stubs", "Wikipedia articles that are too technical from May 2016"], "title": "Area compatibility factor", "method": "Area compatibility factor", "url": "https://en.wikipedia.org/wiki/Area_compatibility_factor", "summary": "In survival analysis, the area compatibility factor, F, is used in indirect standardisation of population mortality rates.\n\n \n \n \n F\n =\n \n \n \n \n \u2211\n \n x\n \n \n \n \n\n \n \n s\n \n \n \n E\n \n x\n ,\n t\n \n \n c\n \n \n \n \n\n \n \n s\n \n \n \n m\n \n x\n ,\n t\n \n \n \n \n \n \u2211\n \n x\n \n \n \n \n\n \n \n s\n \n \n \n E\n \n x\n ,\n t\n \n \n c\n \n \n \n \n \n \n /\n \n \n \n \n \u2211\n \n x\n \n \n \n E\n \n x\n ,\n t\n \n \n c\n \n \n \n \n\n \n \n s\n \n \n \n m\n \n x\n ,\n t\n \n \n \n \n \n \u2211\n \n x\n \n \n \n E\n \n x\n ,\n t\n \n \n c\n \n \n \n \n \n \n \n \n \n {\\displaystyle F={\\frac {\\sum _{x}{}^{s}E_{x,t}^{c}{}^{s}m_{x,t}}{\\sum _{x}{}^{s}E_{x,t}^{c}}}\\left/{\\frac {\\sum _{x}E_{x,t}^{c}{}^{s}m_{x,t}}{\\sum _{x}E_{x,t}^{c}}}\\right.}\n where:\n\n \n \n \n \n \n\n \n \n s\n \n \n \n E\n \n x\n ,\n t\n \n \n c\n \n \n \n \n {\\displaystyle {}^{s}E_{x,t}^{c}}\n is the standardised central exposed-to risk from age x to x + t for the standard population,\n \n \n \n \n E\n \n x\n ,\n t\n \n \n c\n \n \n \n \n {\\displaystyle E_{x,t}^{c}}\n is the central exposed-to risk from age x to x + t for the population under study and\n \n \n \n \n \n\n \n \n s\n \n \n \n m\n \n x\n ,\n t\n \n \n \n \n {\\displaystyle {}^{s}m_{x,t}}\n is the mortality rate in the standard population for ages x to x + t.The expression can be thought of as the crude mortality rate for the standard population divided by what the crude mortality rate is for the region being studied, assuming the mortality rates are the same as for the standard population.\nF is then multiplied by the crude mortality rate to arrive at the indirectly standardised mortality rate.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Mortality rate", "Population (statistics)", "Statistics", "Survival analysis"], "references": []}, "X-12-ARIMA": {"categories": ["All stub articles", "Free econometrics software", "Free statistical software", "Linux stubs", "Pages using Infobox software with unknown parameters", "Public-domain software with source code", "Science software for Linux", "Science software for Windows", "Statistics stubs", "Time series software", "United States Census Bureau", "Unix stubs", "Windows software stubs"], "title": "X-12-ARIMA", "method": "X-12-ARIMA", "url": "https://en.wikipedia.org/wiki/X-12-ARIMA", "summary": "X-12-ARIMA was the U.S. Census Bureau's software package for seasonal adjustment.\nX-12-ARIMA can be used together with many statistical packages, such as Gretl or EViews which provides a graphical user interface for X-12-ARIMA, and NumXL which avails X-12-ARIMA functionality in Microsoft Excel.\nNotable statistical agencies presently using X-12-ARIMA for seasonal adjustment include Statistics Canada and the U.S. Bureau of Labor Statistics. The Brazilian Institute of Geography and Statistics uses X-13-ARIMA.X-12-ARIMA was the successor to X-11-ARIMA; the current version is X-13ARIMA-SEATS.X-13-ARIMA-SEATS's source code can be found on the Census Bureau's website.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b0/NewTux.svg", "https://upload.wikimedia.org/wikipedia/commons/1/13/Poundexclam.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ee/Windows_logo_%E2%80%93_2012_%28dark_blue%29.svg"], "links": ["ADMB", "ARIMA", "Analyse-it", "Autoregressive integrated moving average", "BMDP", "BV4.1 (software)", "Brazilian Institute of Geography and Statistics", "Bureau of Labor Statistics", "CSPro", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "EViews", "Epi Info", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Graphical user interface", "Gretl", "H2O (software)", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Linux", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "NumXL", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Public-domain software", "Public domain", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Repository (version control)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "Seasonal adjustment", "Seasonality", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software", "Software categories", "Software developer", "Software license", "Software release life cycle", "Source code", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistics", "Statistics Canada", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "U.S. Census Bureau", "UNISTAT", "Unix", "WinBUGS", "World Programming System", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http:ftp://ftp.ibge.gov.br/Contas_Nacionais/Contas_Nacionais_Trimestrais/Ajuste_Sazonal/X13_NasContasTrimestrais.pdf", "http://www.statcan.gc.ca/pub/12-539-x/2009001/seasonal-saisonnal-eng.htm", "http://www.bls.gov/cpi/cpisahoma.htm", "https://www.census.gov/srd/www/disclaimer.html", "https://www.census.gov/srd/www/x12a/", "https://www.census.gov/srd/www/x13as/", "https://www.census.gov/srd/www/x13as/x13down_unix.html", "https://web.archive.org/web/20160205235259/http://www.census.gov/srd/www/x12a/", "https://www.wikidata.org/wiki/Q640173#P1324"]}, "Epi Info": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2014", "Centers for Disease Control and Prevention", "Free healthcare software", "Free statistical software", "Pages using deprecated image syntax", "Public-domain software"], "title": "Epi Info", "method": "Epi Info", "url": "https://en.wikipedia.org/wiki/Epi_Info", "summary": "Epi Info is statistical software for epidemiology developed by Centers for Disease Control and Prevention (CDC) in Atlanta, Georgia (US) and licensed as public domain.\nEpi Info has been in existence for over 20 years and is currently available for Microsoft Windows. The program allows for electronic survey creation, data entry, and analysis. Within the analysis module, analytic routines include t-tests, ANOVA, nonparametric statistics, cross tabulations and stratification with estimates of odds ratios, risk ratios, and risk differences, logistic regression (conditional and unconditional), survival analysis (Kaplan Meier and Cox proportional hazard), and analysis of complex survey data. The software is in the public domain, free, and can be downloaded from https://www.cdc.gov/epiinfo. Limited support is available.\nAn analysis conducted in 2003 documented over 1,000,000 downloads of Epi Info from 180 countries.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/1/14/Epiinfoanalisis.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/31/Free_and_open-source_software_logo_%282009%29.svg", "https://upload.wikimedia.org/wikipedia/commons/0/03/Green_check.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/e/ef/EpiInfoIcon.png", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/b/ba/Red_x.svg"], "links": ["ADMB", "Analyse-it", "Analysis of variance", "Asymptomatic carrier", "Atlanta", "Auxology", "BMDP", "BV4.1 (software)", "Bachelor of Science in Public Health", "Batch file", "Behavior change (public health)", "Behavioural change theories", "Biological hazard", "Biostatistics", "CSPro", "C Sharp (programming language)", "Carl Rogers Darnall", "Case\u2013control study", "Centers for Disease Control and Prevention", "Chief Medical Officer", "Child mortality", "Codeplex", "Commercial software", "Community health", "Comparison of statistical packages", "Council on Education for Public Health", "Cross-platform", "Cultural competence in health care", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "Deviance (sociology)", "Diffusion of innovations", "Disease surveillance", "Doctor of Public Health", "EViews", "Emergency sanitation", "Environmental health", "Epi Map", "Epidemic", "Epidemiology", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Family planning", "Fecal\u2013oral route", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Free statistical software", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "Genetically modified food", "Germ theory of disease", "Global health", "Globalization and disease", "Good agricultural practice", "Good manufacturing practice", "GraphPad InStat", "GraphPad Prism", "Gretl", "Growth chart", "H2O (software)", "HACCP", "Hand washing", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Human factors and ergonomics", "Human nutrition", "Hygiene", "ISO 22000", "Infant mortality", "Infection control", "Injury prevention", "JASP", "JMP (statistical software)", "JMulTi", "Jeff Dean (computer scientist)", "John Snow (physician)", "Joseph Lister", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of epidemics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "MATLAB", "MLwiN", "MS-DOS", "Maple (software)", "Margaret Sanger", "Mary Mallon", "Maternal health", "Mathcad", "Mathematica", "MedCalc", "Medical anthropology", "Medical sociology", "Mental health", "Microfit", "Microsoft Access", "Microsoft Excel", "Microsoft Windows", "Ministry of Health and Family Welfare", "Minitab", "NCSS (statistical software)", "National Electronic Telecommunications System for Surveillance", "Notifiable disease", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Open-source software", "OpenBUGS", "OpenEpi", "Open defecation", "Operating system", "Oral hygiene", "Orange (software)", "OxMetrics", "PRECEDE-PROCEED model", "PSPP", "Patient safety", "Patient safety organization", "Pharmaceutical policy", "Pharmacovigilance", "Population health", "Positive deviance", "Preventive healthcare", "Preventive nutrition", "Professional degrees of public health", "Public-domain software", "Public domain", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quarantine", "RATS (software)", "RExcel", "ROC curve", "RStudio", "R (programming language)", "Race and health", "Randomized controlled trial", "Regression analysis", "Relative risk", "Repository (version control)", "Reproductive health", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "Safe sex", "SageMath", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "SegReg", "Sexually transmitted infection", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Sociology of health and illness", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistical hypothesis testing", "StatsDirect", "Student's t-test", "TSP (econometrics software)", "The Unscrambler", "Theory of planned behavior", "Transtheoretical model", "Tropical disease", "UNISTAT", "United States Public Health Service", "Vaccination", "Vaccine trial", "Vector control", "Waterborne diseases", "WinBUGS", "World Health Organization", "World Programming System", "World Toilet Organization", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe", "Z-test"], "references": ["http:ftp://ftp.cdc.gov/pub/software/epi_info/EpiInfoReadMe3_5_1.txt", "http://epiinfo.codeplex.com/", "http://epiinfo.codeplex.com/SourceControl/list/changesets", "http://www.openepi.com/", "http://forums.myepi.info/", "http://www.phconnect.org/group/epiinfo", "https://www.youtube.com/playlist?list=PL9B9157E47AB3FDFA", "https://www.cdc.gov/EpiInfo/", "https://www.cdc.gov/epiinfo", "https://www.cdc.gov/epiinfo/", "https://www.cdc.gov/epiinfo/about.htm", "https://www.cdc.gov/epiinfo/epiinfo1.htm", "https://www.cdc.gov/epiinfo/epiinfo5.htm", "https://www.wikidata.org/wiki/Q2601695#P1324"]}, "Qualitative comparative analysis": {"categories": ["Causal inference", "Comparisons", "Data analysis"], "title": "Qualitative comparative analysis", "method": "Qualitative comparative analysis", "url": "https://en.wikipedia.org/wiki/Qualitative_comparative_analysis", "summary": "In statistics, qualitative comparative analysis (QCA) is a data analysis technique for determining which logical conclusions a data set supports. The analysis begins with listing and counting all the combinations of variables observed in the data set, followed by applying the rules of logical inference to determine which descriptive inferences or implications the data supports. The technique was originally developed by Charles Ragin in 1987.", "images": [], "links": ["Boolean algebra (logic)", "Charles Ragin", "CsQCA", "Data analysis", "Data set", "Dichotomous", "Digital object identifier", "FsQCA", "International Standard Serial Number", "Logical inference", "Monte Carlo simulations", "MvQCA", "Null hypothesis", "Social science", "Statistics", "Type I error", "University of California Press"], "references": ["http://www.encyclopedia.com/doc/1O88-qualitativecomparatvnlyss.html", "http://jtr.sagepub.com/content/early/2016/09/22/0047287516667850.long", "http://www.sciencedirect.com/science/article/pii/S0148296315006256", "http://www.sciencedirect.com/science/article/pii/S0148296317300760", "http://www.tandfonline.com/doi/abs/10.1080/08276331.2013.876765#.U0UIwvl_t8E", "http://doi.org/10.1016%2Fj.jbusres.2015.11.015", "http://doi.org/10.1016%2Fj.jbusres.2016.08.022", "http://doi.org/10.1016%2Fj.jbusres.2017.02.015", "http://doi.org/10.1093%2Fpan%2Fmps061", "http://doi.org/10.1093%2Fpan%2Fmpu016", "http://doi.org/10.1093%2Fpan%2Fmpv017", "http://doi.org/10.1177%2F0047287516667850", "http://doi.org/10.1177%2F0047287517751676", "http://doi.org/10.1177%2F0268580906067836", "http://doi.org/10.1177%2F1065912912468269", "http://pan.oxfordjournals.org/content/21/2/252", "http://pan.oxfordjournals.org/content/23/1/21", "http://pan.oxfordjournals.org/content/early/2015/07/24/pan.mpv017", "http://www.worldcat.org/issn/0148-2963", "http://www.worldcat.org/issn/1047-1987", "https://www.sciencedirect.com/science/article/abs/pii/S0148296316305239", "https://cran.r-project.org/web/packages/QCAfalsePositive/index.html"]}, "Sample size determination": {"categories": ["Sampling (statistics)", "Webarchive template wayback links"], "title": "Sample size determination", "method": "Sample size determination", "url": "https://en.wikipedia.org/wiki/Sample_size_determination", "summary": "Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is determined based on the expense of data collection, and the need to have sufficient statistical power. In complicated studies there may be several different sample sizes involved in the study: for example, in a stratified survey there would be different sample sizes for each stratum. In a census, data are collected on the entire population, hence the sample size is equal to the population size. In experimental design, where a study may be divided into different treatment groups, this may be different sample sizes for each group.\nSample sizes may be chosen in several different ways:\n\nexperience \u2013 A choice of small sample sizes, though sometimes necessary, can result in wide confidence intervals or risks of errors in statistical hypothesis testing.\nusing a target variance for an estimate to be derived from the sample eventually obtained, i.e. if a high precision is required (narrow confidence interval) this translates to a low target variance of the estimator.\nusing a target for the power of a statistical test to be applied once the sample is collected.\nusing a confidence level, i.e. the larger the required confidence level, the larger the sample size (given a constant precision requirement).", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ASTM", "Accelerated failure time model", "Accuracy and precision", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli distribution", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's d", "Cohen's h", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Control group", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decision rule", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Experimental design", "Experimental group", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent (statistics)", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laboratory animal", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Leslie Kish", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "NIST", "National accounts", "Natural experiment", "Negative binomial distribution", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population proportion", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Proportionality (mathematics)", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "SEMATECH", "Sample (statistics)", "Sample median", "Sample survey", "Sampling (statistics)", "Sampling distribution", "Sampling rate", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical estimation", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survey sampling", "Survival analysis", "Survival function", "System identification", "Systematic error", "Thematic analysis", "Theoretical sampling", "Time domain", "Time series", "Tolerance interval", "Treatment group", "Treatment groups", "Trend estimation", "Two-sample t-test", "Type I error", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.biomedcentral.com/1472-6947/11/36", "http://fmx.sagepub.com/content/18/1/59", "http://www.tandfonline.com/doi/full/10.1080/13645579.2015.1005453", "http://nebula.deanza.fhda.edu/~bloom/Math10/M10ConfIntNotes.pdf", "http://www.utdallas.edu/~ammann/stat3355/node25.html", "http://www.itl.nist.gov/div898/handbook/ppc/section3/ppc333.htm", "http://www.itl.nist.gov/div898/handbook/prc/section2/prc242.htm", "http://www.isogenic.info/html/resource_equation.html", "http://davidakenny.net/doc/statbook/chapter_13.pdf", "http://www.qualitative-research.net/index.php/fqs/article/view/1428/3027", "http://doi.org/10.1080%2F13645579.2015.1005453", "http://www.osra.org/itlpj/bartlettkotrlikhiggins.pdf", "https://books.google.com/books?id=Wjr9u1AAht4C&pg=PA29", "https://www.qualtrics.com/experience-management/research/determine-sample-size/", "https://link.springer.com/article/10.1007%2Fs11135-005-1098-1", "https://web.archive.org/web/20110823021440/http://nebula.deanza.fhda.edu/~bloom/Math10/M10ConfIntNotes.pdf"]}, "Random effects model": {"categories": ["All articles needing expert attention", "All articles with unsourced statements", "Analysis of variance", "Articles needing expert attention from January 2011", "Articles needing expert attention with no reason or talk parameter", "Articles with unsourced statements from July 2018", "Articles with unsourced statements from September 2017", "Regression models", "Statistics articles needing expert attention"], "title": "Random effects model", "method": "Random effects model", "url": "https://en.wikipedia.org/wiki/Random_effects_model", "summary": "In statistics, a random effects model, also called a variance components model, is a statistical model where the model parameters are random variables. It is a kind of hierarchical linear model, which assumes that the data being analysed are drawn from a hierarchy of different populations whose differences relate to that hierarchy. In econometrics, random effects models are used in the analysis of hierarchical or panel data when one assumes no fixed effects (it allows for individual effects). The random effects model is a special case of the fixed effects model.\nContrast this to the biostatistics definitions, as biostatisticians use \"fixed\" and \"random\" effects to respectively refer to the population-average and subject-specific effects (and where the latter are generally assumed to be unknown, latent variables).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Biometrics (journal)", "Biostatistics", "B\u00fchlmann model", "Conditional variance", "Consistency (statistics)", "Covariance estimation", "Digital object identifier", "Discrete choice", "Dummy variable (statistics)", "Econometrics", "Efficiency (statistics)", "Errors-in-variables models", "Errors and residuals in statistics", "Estimation", "Expected mean square", "Fixed effects", "Fixed effects estimator", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Grand average", "Hausman specification test", "Hierarchical linear model", "Hierarchical linear modeling", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Latent variables", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "MINQUE", "Mean and predicted response", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Panel data", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random sample", "Random variable", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistical model", "Statistics", "Statistics in Medicine (journal)", "Studentized residual", "Tikhonov regularization", "Total least squares", "Unobserved heterogeneity", "Weighted least squares"], "references": ["http://www.pitt.edu/~SUPER1/lecture/lec1171/012.htm", "http://teaching.sociology.ul.ie/DCW/confront/node45.html", "http://doi.org/10.1002%2Fsim.3478", "http://www.jstor.org/stable/2529876"]}, "Lumpability": {"categories": ["Markov processes"], "title": "Lumpability", "method": "Lumpability", "url": "https://en.wikipedia.org/wiki/Lumpability", "summary": "In probability theory, lumpability is a method for reducing the size of the state space of some continuous-time Markov chains, first published by Kemeny and Snell.\n\n", "images": [], "links": ["Continuous-time Markov chain", "Digital object identifier", "International Standard Book Number", "Jane Hillston", "John George Kemeny", "Markov chain", "Michael Katehakis", "Michael N. Katehakis", "Nearly completely decomposable Markov chain", "Partition of a set", "Performance Evaluation", "Peter Harrison (computer scientist)", "Probability theory", "Stochastic matrix"], "references": ["http://doi.org/10.1016/0166-5316(94)90015-9", "http://doi.org/10.1017/S0269964812000150", "http://www.dcs.ed.ac.uk/pepa/compositional.ps.gz"]}, "EWMA chart": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2010", "CS1 errors: external links", "Quality control tools", "Statistical charts and diagrams"], "title": "EWMA chart", "method": "EWMA chart", "url": "https://en.wikipedia.org/wiki/EWMA_chart", "summary": "In statistical quality control, the EWMA chart (or exponentially weighted moving average chart) is a type of control chart used to monitor either variables or attributes-type data using the monitored business or industrial process's entire history of output. While other control charts treat rational subgroups of samples individually, the EWMA chart tracks the exponentially-weighted moving average of all prior sample means. EWMA weights samples in geometrically decreasing order so that the most recent samples are weighted most highly while the most distant samples contribute very little.Although the normal distribution is the basis of the EWMA chart, the chart is also relatively robust in the face of non-normally distributed quality characteristics. There is, however, an adaptation of the chart that accounts for quality characteristics that are better modeled by the Poisson distribution. The chart monitors only the process mean; monitoring the process variability requires the use of some other technique.The EWMA control chart requires a knowledgeable person to select two parameters before setup:\n\nThe first parameter is \u03bb, the weight given to the most recent rational subgroup mean. \u03bb must satisfy 0 < \u03bb \u2264 1, but selecting the \"right\" value is a matter of personal preference and experience. One source recommends 0.05 \u2264 \u03bb \u2264 0.25, while another recommends 0.2 \u2264 \u03bb \u2264 0.3.\nThe second parameter is L, the multiple of the rational subgroup standard deviation that establishes the control limits. L is typically set at 3 to match other control charts, but it may be necessary to reduce L slightly for small values of \u03bb.Instead of plotting rational subgroup averages directly, the EWMA chart computes successive observations zi by computing the rational subgroup average, \n \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n i\n \n \n \n \n {\\displaystyle {\\bar {x}}_{i}}\n , and then combining that new subgroup average with the running average of all preceding observations, zi - 1, using the specially\u2013chosen weight, \u03bb, as follows:\n\n \n \n \n \n z\n \n i\n \n \n =\n \u03bb\n \n \n \n \n x\n \u00af\n \n \n \n \n i\n \n \n +\n \n (\n \n 1\n \u2212\n \u03bb\n \n )\n \n \n z\n \n i\n \u2212\n 1\n \n \n \n \n {\\displaystyle z_{i}=\\lambda {\\bar {x}}_{i}+\\left(1-\\lambda \\right)z_{i-1}}\n .The control limits for this chart type are \n \n \n \n T\n \u00b1\n L\n \n \n S\n \n n\n \n \n \n \n \n \n \n \u03bb\n \n 2\n \u2212\n \u03bb\n \n \n \n [\n 1\n \u2212\n \n \n (\n \n 1\n \u2212\n \u03bb\n \n )\n \n \n 2\n i\n \n \n ]\n \n \n \n \n {\\displaystyle T\\pm L{\\frac {S}{\\sqrt {n}}}{\\sqrt {{\\frac {\\lambda }{2-\\lambda }}\\lbrack 1-\\left(1-\\lambda \\right)^{2i}\\rbrack }}}\n where T and S are the estimates of the long-term process mean and standard deviation established during control-chart setup and n is the number of samples in the rational subgroup. Note that the limits widen for each successive rational subgroup, approaching \n \n \n \n \u00b1\n L\n \n \n \n \n \u03c3\n ^\n \n \n \n n\n \n \n \n \n \n \n \u03bb\n \n 2\n \u2212\n \u03bb\n \n \n \n \n \n \n {\\displaystyle \\pm L{\\frac {\\hat {\\sigma }}{\\sqrt {n}}}{\\sqrt {\\frac {\\lambda }{2-\\lambda }}}}\n .The EWMA chart is sensitive to small shifts in the process mean, but does not match the ability of Shewhart-style charts (namely the \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n and R and \n \n \n \n \n \n \n x\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {x}}}\n and s charts) to detect larger shifts. One author recommends superimposing the EWMA chart on top of a suitable Shewhart-style chart with widened control limits in order to detect both small and large shifts in the process mean.Exponentially weighted moving variance (EWMVar) can be used to obtain a significance score or limits that automatically adjust to the observed data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a7/MATLABEWMAChart.png"], "links": ["Business process", "Control chart", "Digital object identifier", "EWMA", "Hans-Peter Kriegel", "Hoboken, New Jersey", "International Standard Book Number", "John Wiley & Sons", "List of industrial processes", "National Institute of Standards and Technology", "Normal distribution", "OCLC", "Poisson distribution", "Statistical process control", "Variable and attribute (research)", "Xbar and R chart", "Xbar and s chart"], "references": ["http://www.eas.asu.edu/~masmlab/montgomery/", "http://www.itl.nist.gov/div898/handbook/index.htm", "http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc324.htm", "http://doi.org/10.1145%2F2623330.2623740", "http://www.worldcat.org/oclc/56729567"]}, "Sigma-algebra": {"categories": ["Boolean algebra", "Experiment (probability theory)", "Measure theory", "Set families"], "title": "Sigma-algebra", "method": "Sigma-algebra", "url": "https://en.wikipedia.org/wiki/Sigma-algebra", "summary": "In mathematical analysis and in probability theory, a \u03c3-algebra (also \u03c3-field) on a set X is a collection \u03a3 of subsets of X that\nincludes X itself,\nis closed under complement, and is closed under\ncountable unions\n(the definition implies that it also includes \nthe empty subset and that it is closed under countable intersections). \nThe pair (X, \u03a3) is called a measurable space or Borel space.\nA \u03c3-algebra is a type of algebra of sets. An algebra of sets needs only to be closed under the union or intersection of finitely many subsets, which is a weaker condition.The main use of \u03c3-algebras is in the definition of measures; specifically, the collection of those subsets for which a given measure is defined is necessarily a \u03c3-algebra. This concept is important in mathematical analysis as the foundation for Lebesgue integration, and in probability theory, where it is interpreted as the collection of events which can be assigned probabilities. Also, in probability, \u03c3-algebras are pivotal in the definition of conditional expectation.\nIn statistics, (sub) \u03c3-algebras are needed for the formal mathematical definition of a sufficient statistic, particularly when the statistic is a function or a random process and the notion of conditional density is not applicable.\nIf X = {a, b, c, d}, one possible \u03c3-algebra on X is \u03a3 = {\u2009\u2205, {a, b}, {c, d}, {a, b, c, d}\u2009}, where \u2205 is the empty set. In general, a finite algebra is always a \u03c3-algebra.\nIf {A1, A2, A3, \u2026} is a countable partition of X then the collection of all unions of sets in the partition (including the empty set) is a \u03c3-algebra.\nA more useful example is the set of subsets of the real line formed by starting with all open intervals and adding in all countable unions, countable intersections, and relative complements and continuing this process (by transfinite iteration through all countable ordinals) until the relevant closure properties are achieved (a construction known as the Borel hierarchy).", "images": [], "links": ["Abuse of notation", "Algebra of sets", "Axiom of choice", "Borel algebra", "Borel hierarchy", "Borel set", "Calligraphic", "Category (mathematics)", "Closed set", "Closure (mathematics)", "Complement (set theory)", "Complete measure", "Conditional expectation", "Conditional probability distribution", "Convergence of random variables", "Countable", "Countable ordinal", "Cumulative distribution function", "Cylinder set", "De Morgan's laws", "Digital object identifier", "Disjoint sets", "Dynkin system", "Empty set", "Encyclopedia of Mathematics", "Equivalence class", "Euclidean space", "Filtration (probability theory)", "Fraktur (typeface)", "Function (mathematics)", "Fundamenta Mathematicae", "Generated \u03c3-algebra (by sets)", "If and only if", "Integral", "International Standard Book Number", "Intersection (set theory)", "Join (sigma algebra)", "Kenneth Kunen", "Lebesgue-Stieltjes integral", "Lebesgue integration", "Lebesgue measure", "Mathematical analysis", "McGraw-Hill", "Measurable function", "Measurable set", "Measurable space", "Measure (mathematics)", "Metric (mathematics)", "Metric space", "Michiel Hazewinkel", "Monotone class theorem", "Morphism", "Olav Kallenberg", "Open interval", "Open set", "Partition of a set", "Patrick Billingsley", "Pi-system", "Power set", "Preimage", "Probability measure", "Probability space", "Probability theory", "Product space", "Product topology", "Pseudometric space", "Random variable", "Real line", "Real number", "Ring of sets", "Sample space", "Separable space", "Set-theoretic limit", "Set (mathematics)", "Sigma-algebra", "Sigma-ring", "Sigma additivity", "Sigma ring", "Singleton (mathematics)", "Springer Publishing", "Standard Borel space", "Statistics", "Stochastic process", "Stopping time", "Subset", "Sufficient statistic", "Symmetric difference", "Topological space", "Transfinite iteration", "Union (set theory)", "Universal algebra", "Universal set", "Vitali set", "Walter Rudin", "\u03a3-Algebra of \u03c4-past", "\u03a3-algebra"], "references": ["http://www.math.uah.edu/stat/foundations/Measure.html", "http://doi.org/10.1016%2Fj.spl.2012.09.024", "https://dx.doi.org/10.1016/j.spl.2012.09.024", "https://www.encyclopediaofmath.org/index.php?title=p/a011400", "https://archive.uea.ac.uk/~h020/fundamenta.pdf"]}, "SDMX": {"categories": ["ISO standards", "Statistical data coding"], "title": "SDMX", "method": "SDMX", "url": "https://en.wikipedia.org/wiki/SDMX", "summary": "SDMX, which stands for Statistical Data and Metadata eXchange is an international initiative that aims at standardising and modernising (\u201cindustrialising\u201d) the mechanisms and processes for the exchange of statistical data and metadata among international organisations and their member countries.The SDMX sponsoring institutions are the Bank for International Settlements (BIS), the European Central Bank (ECB), Eurostat (the statistical office of the European Union), the International Monetary Fund (IMF), the Organisation for Economic Co-operation and Development (OECD), the United Nations Statistics Division (UNSD), and the World Bank.\nThese organisations are the main players at world and regional levels in the collection of official statistics in a large variety of domains (agriculture statistics, economic and financial statistics, social statistics, environment statistics etc.).\nThe latest version of the SDMX \u2013 SDMX 2.1 \u2013 was released in May 2011, and was approved by ISO as International Standard (ISO 17369:2013) in 2013.\nPeople who are new to SDMX are invited to consult the \u201cLearning about SDMX Basics\u201d page which will provide them with the necessary basic material for understanding SDMX.\nUsers who are already familiar with the SDMX standard will find on the SDMX.org website all material, such as the technical standards and guidelines necessary for properly implementing SDMX in a statistical domain.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["110 film", "126 film", "135 film", "A440 (pitch standard)", "ALGOL 60", "ANSI escape code", "ASMO 449", "Accuracy and precision", "Ada Semantic Interface Specification", "Antimagnetic watch", "ArmSCII", "Bank for International Settlements", "British Standard Pipe", "Business Process Model and Notation", "C++", "COBOL", "C (programming language)", "C Sharp (programming language)", "Cloud Infrastructure Management Interface", "Common Criteria", "Common Language Infrastructure", "Common Logic", "Common Object Request Broker Architecture", "Computer Graphics Metafile", "Data", "Delivery Multimedia Integration Framework", "Digital object identifier", "Document Style Semantics and Specification Language", "ECMAScript", "EDIFACT", "EXPRESS (data modeling language)", "Economic statistics", "Envelope", "Equal-loudness contour", "European Central Bank", "Eurostat", "FDI World Dental Federation notation", "FTAM", "Fiber Distributed Data Interface", "File Allocation Table", "Film speed", "Fuel oil", "GESMES/TS", "Graphical Kernel System", "Guidelines for the Definition of Managed Objects", "H.264/MPEG-4 AVC", "HTML", "Hole punch", "Horsepower", "IS-IS", "ISO-8859-8-I", "ISO-TimeML", "ISO/IEC 10116", "ISO/IEC 10967", "ISO/IEC 11179", "ISO/IEC 11404", "ISO/IEC 11801", "ISO/IEC 12207", "ISO/IEC 14443", "ISO/IEC 15288", "ISO/IEC 15504", "ISO/IEC 15693", "ISO/IEC 17024", "ISO/IEC 17025", "ISO/IEC 18000", "ISO/IEC 18014", "ISO/IEC 19752", "ISO/IEC 19770", "ISO/IEC 19794-5", "ISO/IEC 20000", "ISO/IEC 2022", "ISO/IEC 21827", "ISO/IEC 27000", "ISO/IEC 27000-series", "ISO/IEC 27001", "ISO/IEC 27002", "ISO/IEC 27006", "ISO/IEC 38500", "ISO/IEC 42010", "ISO/IEC 4909", "ISO/IEC 5218", "ISO/IEC 646", "ISO/IEC 6523", "ISO/IEC 7810", "ISO/IEC 7811", "ISO/IEC 7812", "ISO/IEC 7813", "ISO/IEC 7816", "ISO/IEC 80000", "ISO/IEC 8652", "ISO/IEC 8820-5", "ISO/IEC 8859", "ISO/IEC 8859-1", "ISO/IEC 8859-10", "ISO/IEC 8859-11", "ISO/IEC 8859-12", "ISO/IEC 8859-13", "ISO/IEC 8859-14", "ISO/IEC 8859-15", "ISO/IEC 8859-16", "ISO/IEC 8859-2", "ISO/IEC 8859-3", "ISO/IEC 8859-4", "ISO/IEC 8859-5", "ISO/IEC 8859-6", "ISO/IEC 8859-7", "ISO/IEC 8859-8", "ISO/IEC 8859-9", "ISO/IEC 9126", "ISO/IEC 9797-1", "ISO/IEC 9995", "ISO/IEC TR 12182", "ISO/IEEE 11073", "ISO/TR 11941", "ISO/TS 16949", "ISO 1", "ISO 1000", "ISO 10005", "ISO 10006", "ISO 10007", "ISO 10160", "ISO 10161", "ISO 10206", "ISO 10218", "ISO 10303", "ISO 10303-21", "ISO 10303-22", "ISO 10303-28", "ISO 10383", "ISO 10487", "ISO 10962", "ISO 11170", "ISO 11783", "ISO 11784 & 11785", "ISO 11898", "ISO 11940", "ISO 11940-2", "ISO 11992", "ISO 12006", "ISO 128", "ISO 13399", "ISO 13406-2", "ISO 13485", "ISO 13490", "ISO 13567", "ISO 13584", "ISO 14000", "ISO 14031", "ISO 1413", "ISO 14224", "ISO 14644", "ISO 14651", "ISO 14698", "ISO 14750", "ISO 14971", "ISO 15022", "ISO 15189", "ISO 15292", "ISO 15398", "ISO 15686", "ISO 15706-2", "ISO 15897", "ISO 15919", "ISO 15924", "ISO 15926", "ISO 15926 WIP", "ISO 1629", "ISO 16750", "ISO 17100:2015", "ISO 1745", "ISO 18245", "ISO 19011", "ISO 19092-1", "ISO 19092-2", "ISO 19114", "ISO 19115", "ISO 19136", "ISO 19439", "ISO 19600", "ISO 2", "ISO 20022", "ISO 20121", "ISO 2014", "ISO 2015", "ISO 2033", "ISO 20400", "ISO 2047", "ISO 2145", "ISO 2146", "ISO 21500", "ISO 216", "ISO 217", "ISO 22000", "ISO 233", "ISO 25178", "ISO 259", "ISO 25964", "ISO 26000", "ISO 2709", "ISO 2711", "ISO 2788", "ISO 28000", "ISO 2848", "ISO 2852", "ISO 29110", "ISO 31", "ISO 31-0", "ISO 31-1", "ISO 31-10", "ISO 31-11", "ISO 31-12", "ISO 31-13", "ISO 31-2", "ISO 31-3", "ISO 31-4", "ISO 31-5", "ISO 31-6", "ISO 31-7", "ISO 31-8", "ISO 31-9", "ISO 31000", "ISO 3103", "ISO 3166", "ISO 3166-1", "ISO 3166-2", "ISO 3166-3", "ISO 3307", "ISO 361", "ISO 3864", "ISO 3977", "ISO 4", "ISO 4031", "ISO 4157", "ISO 4165", "ISO 4217", "ISO 428", "ISO 5", "ISO 518", "ISO 519", "ISO 5426", "ISO 5427", "ISO 5428", "ISO 55000", "ISO 5775", "ISO 5776", "ISO 5964", "ISO 6344", "ISO 6346", "ISO 6385", "ISO 639", "ISO 639-1", "ISO 639-2", "ISO 639-3", "ISO 639-5", "ISO 639-6", "ISO 6438", "ISO 657", "ISO 668", "ISO 6709", "ISO 690", "ISO 6943", "ISO 7001", "ISO 7002", "ISO 7010", "ISO 7027", "ISO 704", "ISO 7064", "ISO 7200", "ISO 732", "ISO 7637", "ISO 7736", "ISO 8000", "ISO 80000-1", "ISO 80000-2", "ISO 80000-3", "ISO 8178", "ISO 8373", "ISO 843", "ISO 8501-1", "ISO 8583", "ISO 860", "ISO 8601", "ISO 8691", "ISO 898", "ISO 9", "ISO 9000", "ISO 9241", "ISO 9362", "ISO 9529", "ISO 9564", "ISO 965", "ISO 9660", "ISO 9897", "ISO 999", "International Bank Account Number", "International Monetary Fund", "International Organization for Standardization", "International Securities Identification Number", "International Standard Atmosphere", "International Standard Audiovisual Number", "International Standard Book Number", "International Standard Identifier for Libraries and Related Organizations", "International Standard Music Number", "International Standard Musical Work Code", "International Standard Name Identifier", "International Standard Recording Code", "International Standard Serial Number", "International Standard Text Code", "Isofix", "JBIG", "JPEG 2000", "JPEG XR", "Kappa number", "Knowledge Discovery Metamodel", "Kunrei-shiki romanization", "Language Of Temporal Ordering Specification", "Legal Entity Identifier", "Lexical Markup Framework", "Linux Standard Base", "List of IEC standards", "List of ISO romanizations", "List of International Organization for Standardization standards", "Longitudinal redundancy check", "MPEG-21", "MPEG-4", "MPEG-4 Part 11", "MPEG-4 Part 12", "MPEG-4 Part 14", "MPEG-4 Part 2", "MPEG-4 Part 3", "Magnetic ink character recognition", "Manufacturing Message Specification", "MaxiCode", "Meta-Object Facility", "Metadata", "Motion JPEG 2000", "Multibus", "O-ring", "OCR-A font", "OSI model", "Object Constraint Language", "Office Open XML", "On-board diagnostics", "OpenDocument", "Open Document Architecture", "Open Systems Interconnection", "Open Virtualization Format", "Organisation for Economic Co-operation and Development", "PDF/A", "PDF/E", "PDF/UA", "PDF/VT", "PDF/X", "PDF417", "PHIGS", "POSIX", "Pascal (programming language)", "Photographic Activity Test", "Pinyin", "Portable Document Format", "Power take-off", "Process Specification Language", "Prolog", "QR code", "RELAX NG", "RM-ODP", "Renard series", "Requirements engineering", "Resource Description Framework", "Romanization of Armenian", "Romanization of Georgian", "Ruby (programming language)", "SQL", "STEP-NC", "Salt spray test", "Shoe size", "Simple feature access", "Software maintenance", "Standard Generalized Markup Language", "Statistics", "Tag Image File Format / Electronic Photography", "Topic map", "Torx", "UN/CEFACT", "UN/EDIFACT", "Unified Modeling Language", "United Nations Statistics Division", "Universal Coded Character Set", "Vicat softening point", "W3C", "Water Resistant mark", "Web Content Accessibility Guidelines", "Web services", "Whirlpool (hash function)", "World Bank", "X.500", "X3D", "XML", "XML Metadata Interchange", "Z notation"], "references": ["http://ec.europa.eu/eurostat/", "http://ec.europa.eu/eurostat/web/sdmx-infospace/welcome", "http://www.ecb.int/stats/services/sdmx/html/index.en.html", "http://www.ecb.int/stats/services/sdmx/html/tutorial.en.html", "http://www.who.int/gho/indicatorregistry/", "http://www.iso.org/iso/catalogue_detail.htm?csnumber=52500", "http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=40555", "http://sdmx.org/", "http://sdmx.org/?page_id=2555/", "http://www.sdmx.org/", "http://www.sdmxsource.org", "http://www.w3.org/TR/vocab-data-cube/", "https://sdmx.org/", "https://sdmx.org/?page_id=2555/", "https://sdmx.org/?page_id=4345", "https://sdmx.org/?page_id=4500", "https://sdmx.org/?page_id=5008", "https://www.w3.org/blog/news/archives/3591"]}, "Calculus of predispositions": {"categories": ["All articles lacking reliable references", "Articles lacking reliable references from May 2008", "Probability assessment", "Probability interpretations"], "title": "Calculus of predispositions", "method": "Calculus of predispositions", "url": "https://en.wikipedia.org/wiki/Calculus_of_predispositions", "summary": "Calculus of predispositions is a basic part of predispositioning theory and belongs to the indeterministic procedures.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Aron Katsenelinboigen", "Frequency probability", "Indeterministic", "Karl Popper", "Predispositioning theory", "Probability"], "references": []}, "Longitudinal study": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2017", "CS1 maint: Multiple names: authors list", "Cohort study methods", "Design of experiments", "Epidemiological study projects", "Nursing research", "Research methods", "Statistical data types", "Wikipedia articles with GND identifiers"], "title": "Longitudinal study", "method": "Longitudinal study", "url": "https://en.wikipedia.org/wiki/Longitudinal_study", "summary": "A longitudinal study (or longitudinal survey, or panel study) is a research design that involves repeated observations of the same variables (e.g., people) over short or long periods of time (i.e., uses longitudinal data). It is often a type of observational study, although they can also be structured as longitudinal randomized experiments.Longitudinal studies are often used in social-personality and clinical psychology, to study rapid fluctuations in behaviors, thoughts, and emotions from moment to moment or day to day; in developmental psychology, to study developmental trends across the life span; and in sociology, to study life events throughout lifetimes or generations. The reason for this is that, unlike cross-sectional studies, in which different individuals with the same characteristics are compared, longitudinal studies track the same people, and so the differences observed in those people are less likely to be the result of cultural differences across generations. Longitudinal studies thus make observing changes more accurate and are applied in various other fields. In medicine, the design is used to uncover predictors of certain diseases. In advertising, the design is used to identify the changes that advertising has produced in the attitudes and behaviors of those within the target audience who have seen the advertising campaign. Longitudinal studies allow social scientists to distinguish short from long-term phenomena, such as poverty. If the poverty rate is 10% at a point in time, this may mean that 10% of the population are always poor or that the whole population experiences poverty for 10% of the time. It is impossible to conclude which of these possibilities is the case by using one-off cross-sectional studies.When longitudinal studies are observational, in the sense that they observe the state of the world without manipulating it, it has been argued that they may have less power to detect causal relationships than experiments. However, because of the repeated observation at the individual level, they have more power than cross-sectional observational studies, by virtue of being able to exclude time-invariant unobserved individual differences and also of observing the temporal order of events. Some of the disadvantages of longitudinal study are that they take a lot of time and are very expensive. Therefore, they are not very convenient.Longitudinal studies can be retrospective (looking back in time, thus using existing data such as medical records or claims database) or prospective (requiring the collection of new data).Cohort studies are one type of longitudinal study which sample a cohort (a group of people who share a defining characteristic, typically who experienced a common event in a selected period, such as birth or graduation) and perform cross-section observations at intervals through time. However, not all longitudinal studies are cohort studies, as longitudinal studies can instead include a group of people who do not share a common event.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20161201223606%21Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20120912121406%21Blue_pencil.svg"], "links": ["1970 British Cohort Study", "Academic clinical trials", "Adaptive clinical trial", "Alzheimer's Disease Neuroimaging Initiative", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Australian Longitudinal Study on Women's Health", "Avon Longitudinal Study of Parents and Children", "Blind experiment", "Born in Bradford", "British Doctors Study", "British Household Panel Survey", "Caerphilly Heart Disease Study", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Causality", "Children of Immigrants Longitudinal Study", "Clinical endpoint", "Clinical psychology", "Clinical research", "Clinical study design", "Clinical trial", "Cohort (statistics)", "Cohort study", "Congenital Heart Surgeons' Society", "Correlation does not imply causation", "Cross-sectional data", "Cross-sectional study", "Cumulative incidence", "Design of experiments", "Developmental psychology", "Digital object identifier", "Dunedin Multidisciplinary Health and Development Study", "Ecological study", "Epidemiological methods", "Evidence-based medicine", "Experiment", "First-in-man study", "Fragile Families and Child Wellbeing Study", "Framingham Heart Study", "Genetic Studies of Genius", "Glossary of clinical research", "Grant Study", "Hazard ratio", "Health and Retirement Study", "Household, Income and Labour Dynamics in Australia Survey", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Integrated Authority File", "Intention-to-treat analysis", "International Standard Book Number", "K. Warner Schaie", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal data", "Luxembourg Income Study (LIS)", "Manitoba Follow-Up Study (MFUS)", "Meta-analysis", "Millennium Cohort Study", "Millennium Cohort Study (United States)", "Minnesota Twin Family Study", "Morbidity", "Mortality rate", "Multicenter trial", "National Child Development Study", "National Health and Nutrition Examination Survey", "National Longitudinal Survey of Children and Youth", "National Longitudinal Surveys", "Nested case\u2013control study", "New Zealand Attitudes and Values Study", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "Pacific Islands Families Study", "Panel Study of Income Dynamics", "Period prevalence", "Point prevalence", "Population Impact Measures", "Poverty", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Prospective study", "Protocol (science)", "PubMed Identifier", "Randomized controlled trial", "Randomized experiment", "Relative risk reduction", "Repeated measures design", "Reproducibility", "Research design", "Retrospective cohort study", "Retrospective study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Rotterdam Study", "Scientific control", "Seattle 500 Study", "Seeding trial", "Selection bias", "Social scientists", "Socio-Economic Panel", "Sociology", "Specificity and sensitivity", "Study of Health in Pomerania", "Study of Mathematically Precocious Youth", "Study on Global Ageing and Adult Health", "Survey of Health, Ageing and Retirement in Europe", "Survivorship bias", "Systematic review", "The Irish Longitudinal Study on Ageing \u2013 TILDA", "Time series", "UK households: a longitudinal study", "Up Series", "Vaccine trial", "Virulence"], "references": ["http://www.growingupinaustralia.gov.au/index.html", "http://www.health.gov.au/internet/main/publishing.nsf/Content/Pharmaceutical+Benefits+Scheme+(PBS)-1", "http://www.mbsonline.gov.au/internet/mbsonline/publishing.nsf/Content/Home", "http://bpmri.org.au/research/key-projects-studies/busselton-health-study-2/busselton-health-study-past-projects.html", "http://www.psbh.be", "http://www.clsa-elcv.ca/", "http://www.mfus.ca/About.php", "http://psychology.about.com/od/lindex/g/longitudinal.htm", "http://academia.stackexchange.com/questions/54017/what-is-the-difference-between-a-panel-study-and-a-cohort-study", "http://childandfamilypolicy.duke.edu/project/child-development-project-developmental-pathways-to-adjustment-and-well-being-in-early-adulthood/", "http://www.ssc.wisc.edu/wlsresearch/", "http://www.fsd.uta.fi/en/data/background/jyls/", "http://www.ncbi.nlm.nih.gov/pubmed/10883707", "http://www.ncbi.nlm.nih.gov/pubmed/27551988", "http://doi.org/10.1097%2FPSY.0000000000000378", "http://www.lisdatacenter.org/wp-content/uploads/our-lis-documentation-by-be00-survey.pdf", "http://www.themegacitiesproject.org", "http://www.esds.ac.uk/longitudinal/access/introduction.asp", "http://www.cls.ioe.ac.uk", "http://sls.lscs.ac.uk/", "http://www.qub.ac.uk/research-centres/NILSResearchSupportUnit/", "http://www.ucl.ac.uk/celsius", "http://www.ons.gov.uk/ons/guide-method/user-guidance/longitudinal-study/index.html", "http://growingupinscotland.org.uk/about-gus/study-design-and-methodology/", "https://www.dss.gov.au/about-the-department/national-centre-for-longitudinal-studies/overview-of-footprints-in-time-the-longitudinal-study-of-indigenous-children-lsic", "https://www.dss.gov.au/about-the-department/national-centre-for-longitudinal-data", "https://www.dss.gov.au/our-responsibilities/families-and-children/programmes-services/building-a-new-life-in-australia-bnla-the-longitudinal-study-of-humanitarian-migrants", "https://www.saxinstitute.org.au/", "https://www.saxinstitute.org.au/our-work/45-up-study/", "https://encuestalongitudinal.uniandes.edu.co/", "https://encuestalongitudinal.uniandes.edu.co/images/stories/Archivos/Doc_CEDE-ELCA/dcede2014-42.pdf", "https://www.thestar.com/life/2012/04/24/landmark_study_on_aging_to_follow_50000_canadians_over_the_next_two_decades.html", "https://sharepoint.washington.edu/uwsom/sls/about/Pages/default.aspx", "https://d-nb.info/gnd/4034036-3", "https://dx.doi.org/10.1097/PSY.0000000000000378", "https://www.wikidata.org/wiki/Q1758614"]}, "Local independence": {"categories": ["All Wikipedia articles needing context", "All articles lacking in-text citations", "All pages needing cleanup", "Articles lacking in-text citations from June 2012", "Econometric modeling", "Independence (probability theory)", "Latent variable models", "Wikipedia articles needing context from December 2011", "Wikipedia introduction cleanup from December 2011"], "title": "Local independence", "method": "Local independence", "url": "https://en.wikipedia.org/wiki/Local_independence", "summary": "Local independence is the underlying assumption of latent variable models.\nThe observed items are conditionally independent of each other given an individual score on the latent variable(s). This means that the latent variable explains why the observed items are related to another. This can be explained by the following example.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Conditional independence", "Digital object identifier", "Latent variable", "Latent variable model"], "references": ["http://www.statisticalinnovations.com/articles/Locindep.pdf", "http://doi.org/10.1177%2F026553228900600108", "http://www.rasch.org/rmt/rmt53b.htm"]}, "Conditional probability": {"categories": ["Commons category link from Wikidata", "Conditional probability", "Invalid proofs", "Pages using web citations with no URL", "Statistical ratios"], "title": "Conditional probability", "method": "Conditional probability", "url": "https://en.wikipedia.org/wiki/Conditional_probability", "summary": "In probability theory, conditional probability is a measure of the probability of an event (some particular situation occurring) given that (by assumption, presumption, assertion or evidence) another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, \"the conditional probability of A given B\", or \"the probability of A under the condition B\", is usually written as P(A|B), or sometimes PB(A) or P(A/B). For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person has a cold, then they are much more likely to be coughing. The conditional probability of coughing given that you have a cold might be a much higher 75%.\nThe concept of conditional probability is one of the most fundamental and one of the most important concepts in probability theory. But conditional probabilities can be quite slippery and require careful interpretation. For example, there need not be a causal relationship between A and B, and they don\u2019t have to occur simultaneously.\nP(A|B) may or may not be equal to P(A) (the unconditional probability of A). If P(A|B) = P(A), then events A and B are said to be independent: in such a case, having knowledge about either event does not change our knowledge about the other event. Also, in general, P(A|B) (the conditional probability of A given B) is not equal to P(B|A). For example, if a person has dengue they might have a 90% chance of testing positive for dengue. In this case what is being measured is that if event B (\"having dengue\") has occurred, the probability of A (test is positive) given that B (having dengue) occurred is 90%: that is, P(A|B) = 90%. Alternatively, if a person tests positive for dengue they may have only a 15% chance of actually having dengue because most people do not have dengue and the false positive rate for the test may be high. In this case what is being measured is the probability of the event B (having dengue) given that the event A (test is positive) has occurred: P(B|A) = 15%. Falsely equating the two probabilities causes various errors of reasoning such as the base rate fallacy. Conditional probabilities can be correctly reversed using Bayes' theorem.\nConditional probabilities can be displayed in a conditional probability table.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/bf/Bayes_theorem_visualisation.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9b/Conditional_probability.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9c/Probability_tree_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/8/86/Venn_Pie_Chart_describing_Bayes%27_law.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Base rate fallacy", "Base rate neglect", "Bayes' theorem", "Bayesian probability", "Beg the question", "Boole's inequality", "Borel\u2013Kolmogorov paradox", "Bruno de Finetti", "Chain rule (probability)", "Class membership probabilities", "Common cold", "Complementary event", "Conditional expectation", "Conditional independence", "Conditional probability distribution", "Conditional probability table", "Conditioning (probability)", "Confusion of the inverse", "Conservatism (Bayesian)", "Continuous random variable", "Defined and undefined", "Dice", "Digital object identifier", "Elementary event", "Eric W. Weisstein", "Euler diagram", "Event (probability theory)", "Expected value", "F. Thomas Bruss", "False positive", "Goodman\u2013Nguyen\u2013van Fraassen algebra", "Independence (probability theory)", "Independent and identically distributed random variables", "International Standard Book Number", "Joint probability distribution", "Law of large numbers", "Law of total probability", "Marginal distribution", "Marginal probability", "MathWorld", "Measure (mathematics)", "Monty Hall problem", "Mutually exclusive events", "Partition of a set", "Posterior probability", "Probability", "Probability axioms", "Probability interpretations", "Probability measure", "Probability space", "Probability theory", "Quotient", "Radical probabilism", "Random variable", "Sample space", "Selection bias", "Sequelae", "Sigma-field", "Sigma algebra", "Statistical inference", "Statistics", "Subjective probability", "Tree diagram (probability theory)", "Venn diagram"], "references": ["http://lesswrong.com/r/discussion/lw/9om/the_conditional_fallacy_in_contemporary_philosophy/", "http://mathworld.wolfram.com/ConditionalProbability.html", "http://math.dartmouth.edu/~prob/prob/prob.pdf", "http://setosa.io/conditional/", "http://doi.org/10.13140%2FRG.2.2.10050.48323%2F3", "http://fpc.formcharts.org", "https://plato.stanford.edu/entries/epistemology-bayesian/"]}, "Stein's example": {"categories": ["Estimation theory", "Mathematical examples", "Statistical paradoxes"], "title": "Stein's example", "method": "Stein's example", "url": "https://en.wikipedia.org/wiki/Stein%27s_example", "summary": "Stein's example (or phenomenon or paradox), in decision theory and estimation theory, is the phenomenon that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters separately. It is named after Charles Stein of Stanford University, who discovered the phenomenon in 1955.An intuitive explanation is that optimizing for the mean-squared error of a combined estimator is not the same as optimizing for the errors of separate estimators of the individual parameters. In practical terms, if the combined error is in fact of interest, then a combined estimator should be used, even if the underlying parameters are independent; this occurs in channel estimation in telecommunications, for instance (different factors affect overall channel performance). On the other hand, if one is instead interested in estimating an individual parameter, then using a combined estimator does not help and is in fact worse.", "images": [], "links": ["Admissible decision rule", "Bradley Efron", "Channel estimation", "Charles Stein (statistician)", "Decision theory", "Digital object identifier", "Dominating decision rule", "Equivariant estimation", "Erich Leo Lehmann", "Estimation theory", "Estimator", "Gauss\u2013Markov theorem", "International Standard Book Number", "James\u2013Stein estimator", "Least squares", "Mathematical Reviews", "Maximum likelihood estimation", "Mean squared error", "Normal distribution", "Proof of Stein's example", "Random variable", "Risk function", "Scientific American", "Stanford University", "Statistical independence", "Strict"], "references": ["http://www-stat.stanford.edu/~ckirby/brad/other/Article1977.pdf", "http://www.ams.org/mathscinet-getitem?mr=0084922", "http://doi.org/10.1038%2Fscientificamerican0577-119", "http://projecteuclid.org/euclid.bsmsp/1200501656", "http://www.statslab.cam.ac.uk/~rjs57/SteinParadox.pdf"]}, "Convergence of random variables": {"categories": ["All articles to be merged", "All articles with unsourced statements", "Articles to be merged from October 2017", "Articles with unsourced statements from February 2013", "Articles with unsourced statements from May 2017", "Convergence (mathematics)", "Stochastic processes", "Wikipedia articles incorporating text from Citizendium"], "title": "Convergence of random variables", "method": "Convergence of random variables", "url": "https://en.wikipedia.org/wiki/Convergence_of_random_variables", "summary": "In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behaviour that is essentially unchanging when items far enough into the sequence are studied. The different possible notions of convergence relate to how such a behaviour can be characterised: two readily understood behaviours are that the sequence eventually takes a constant value, and that values in the sequence continue to change but can be described by an unchanging probability distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e3/Convergence_in_distribution_%28sum_of_uniform_rvs%29.gif", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg"], "links": ["Aad van der Vaart", "Almost surely", "Archery", "Asymptotic distribution", "Bernoulli distribution", "Big O in probability notation", "Binomial distribution", "Borel\u2013Cantelli lemma", "Bounded function", "Bullseye (target)", "Central limit theorem", "Characteristic function (probability theory)", "Citizendium", "Closed set", "Complete measure", "Consistent estimator", "Continuity set", "Continuous function", "Continuous mapping theorem", "Continuous stochastic process", "Convergence of measures", "Cumulative distribution function", "Degenerate distribution", "Digital object identifier", "Dominated convergence theorem", "Empirical process", "Existential quantification", "Expected value", "Fatou's lemma", "Independence (probability theory)", "Independent and identically distributed", "International Standard Book Number", "Ky Fan", "Law of large numbers", "Limit of a sequence", "Limit superior and limit inferior", "Lipschitz function", "Lower semi-continuous", "Lp space", "L\u00e9vy\u2013Prokhorov metric", "L\u00e9vy\u2019s continuity theorem", "Markov's inequality", "Mathematical Reviews", "Mathematics", "Mean", "Metric space", "Metrizable", "Michel Talagrand", "Moment (mathematics)", "Normal distribution", "Open set", "Pointwise convergence", "Portmanteau lemma", "Probability density function", "Probability distribution", "Probability space", "Probability theory", "Proofs of convergence of random variables", "Random element", "Random process", "Random variable", "Random variables", "Random vector", "Real analysis", "Sample space", "Separable metric space", "Sequence", "Skorokhod's representation theorem", "Slutsky's theorem", "Statistics", "Stochastic process", "Sufficiently large", "Systematic error", "Topology", "Tweedie distributions", "Uniform convergence in probability", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Uniformly integrable", "Upper semi-continuous", "Variance", "Weak convergence of measures", "Weak law of large numbers"], "references": ["http://www.ams.org/mathscinet-getitem?mr=1102015", "http://doi.org/10.1007%2F978-1-4899-2837-5", "https://www.ma.utexas.edu/users/gordanz/notes/weak.pdf"]}, "Stochastic calculus": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from August 2011", "Articles with unsourced statements from August 2011", "Integral calculus", "Mathematical finance", "Stochastic calculus"], "title": "Stochastic calculus", "method": "Stochastic calculus", "url": "https://en.wikipedia.org/wiki/Stochastic_calculus", "summary": "Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly.\nThe best-known stochastic process to which stochastic calculus is applied is the Wiener process (named in honor of Norbert Wiener), which is used for modeling Brownian motion as described by Louis Bachelier in 1900 and by Albert Einstein in 1905 and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the Wiener process has been widely applied in financial mathematics and economics to model the evolution in time of stock prices and bond interest rates.\nThe main flavours of stochastic calculus are the It\u00f4 calculus and its variational relative the Malliavin calculus. For technical reasons the It\u00f4 integral is the most useful for general classes of processes, but the related Stratonovich integral is frequently useful in problem formulation (particularly in engineering disciplines). The Stratonovich integral can readily be expressed in terms of the It\u00f4 integral. The main benefit of the Stratonovich integral is that it obeys the usual chain rule and therefore does not require It\u00f4's lemma. This enables problems to be expressed in a coordinate system invariant form, which is invaluable when developing stochastic calculus on manifolds other than Rn.\nThe dominated convergence theorem does not hold for the Stratonovich integral, consequently it is very difficult to prove results without re-expressing the integrals in It\u00f4 form.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Abel's test", "Albert Einstein", "Alternating series", "Alternating series test", "Antiderivative", "ArXiv", "Arithmetico-geometric sequence", "Binomial series", "Black\u2013Scholes model", "Brownian motion", "Calculus", "Calculus of variations", "Cauchy condensation test", "Chain rule", "Change of variables", "Continuous function", "Convergence tests", "Curl (mathematics)", "Derivative", "Differential (infinitesimal)", "Differential (mathematics)", "Differential calculus", "Differential of a function", "Differentiation rules", "Diffusion", "Digital object identifier", "Direct comparison test", "Directional derivative", "Dirichlet's test", "Disc integration", "Divergence", "Divergence theorem", "Dominated convergence theorem", "Economics", "Exterior derivative", "Fa\u00e0 di Bruno's formula", "Financial mathematics", "Fractional calculus", "Fundamental theorem of calculus", "General Leibniz rule", "Generalizations of the derivative", "Geometric Brownian motion", "Geometric calculus", "Geometric series", "Glossary of calculus", "Gradient", "Gradient theorem", "Green's theorem", "Harmonic series (mathematics)", "Hessian matrix", "Implicit function", "Improper integral", "Integral", "Integral test for convergence", "Integrals", "Integration by parts", "Integration by reduction formulae", "Integration by substitution", "International Standard Book Number", "Inverse functions and differentiation", "It\u00f4's lemma", "It\u00f4 calculus", "It\u00f4 integral", "Jacobian matrix and determinant", "Kelvin\u2013Stokes theorem", "Laplace operator", "Lebesgue integration", "Limit comparison test", "Limit of a function", "Line integral", "Lists of integrals", "Louis Bachelier", "Malliavin calculus", "Mathematics", "Matrix calculus", "Mean value theorem", "Methods of contour integration", "Multiple integral", "Multivariable calculus", "Norbert Wiener", "Notation for differentiation", "Order of integration (calculus)", "Partial derivative", "Partial fractions in integration", "Power rule", "Power series", "Product rule", "Quadratic variation", "Quantitative finance", "Quotient rule", "Ratio test", "Related rates", "Riemann integral", "Rolle's theorem", "Root test", "Second derivative", "Semimartingale", "Series (mathematics)", "Shell integration", "Stochastic differential equations", "Stochastic process", "Stokes' theorem", "Stratonovich integral", "Sum rule in differentiation", "Surface integral", "Taylor's theorem", "Taylor series", "Tensor calculus", "Term test", "Third derivative", "Total differential", "Trigonometric substitution", "Vector calculus", "Vector calculus identities", "Volume integral", "Wiener process"], "references": ["http://arxiv.org/abs/0712.3908", "http://doi.org/10.1007%2Fs10959-007-0140-8", "https://arxiv.org/PS_cache/arxiv/pdf/0712/0712.3908v2.pdf"]}, "Method of moments (statistics)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2018", "Articles with unsourced statements from September 2011", "Moment (mathematics)", "Probability distribution fitting", "Wikipedia articles needing clarification from March 2018"], "title": "Method of moments (statistics)", "method": "Method of moments (statistics)", "url": "https://en.wikipedia.org/wiki/Method_of_moments_(statistics)", "summary": "In statistics, the method of moments is a method of estimation of population parameters. One starts with deriving equations that relate the population moments (i.e., the expected values of powers of the random variable under consideration) to the parameters of interest. Then a sample is drawn and the population moments are estimated from the sample. The equations are then solved for the parameters of interest, using the sample moments in place of the (unknown) population moments. This results in estimates of those parameters. The method of moments was introduced by Pafnuty Chebyshev in 1887.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized method of moments", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Hankel matrix", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "K. O. Bowman", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (probability theory)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Newton\u2013Raphson method", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Pafnuty Chebyshev", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficiency (statistics)", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "Utility", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["https://doi.org/10.1371/journal.pone.0174573"]}, "Moffat distribution": {"categories": ["Continuous distributions"], "title": "Moffat distribution", "method": "Moffat distribution", "url": "https://en.wikipedia.org/wiki/Moffat_distribution", "summary": "The Moffat distribution, named after the physicist Anthony Moffat, is a continuous probability distribution based upon the Lorentzian distribution. Its particular importance in astrophysics is due to its ability to accurately reconstruct point spread functions, whose wings cannot be accurately portrayed by either a Gaussian or Lorentzian function.", "images": [], "links": ["ARGUS distribution", "Anthony Moffat", "Arcsine distribution", "Astronomical seeing", "Astrophysics", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate Student distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Physicist", "Point spread function", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://adsabs.harvard.edu/abs/1969A&A.....3..455M"]}, "Atkinson index": {"categories": ["Income inequality metrics"], "title": "Atkinson index", "method": "Atkinson index", "url": "https://en.wikipedia.org/wiki/Atkinson_index", "summary": "The Atkinson index (also known as the Atkinson measure or Atkinson inequality measure) is a measure of income inequality developed by British economist Anthony Barnes Atkinson. The measure is useful in determining which end of the distribution contributed most to the observed inequality.", "images": [], "links": ["Anthony Barnes Atkinson", "Coefficient", "Digital object identifier", "Generalized entropy index", "Generalized mean", "Geometric mean", "Gini index", "Income inequality", "Income inequality metrics", "Inter alia", "International Standard Book Number", "Lua programming language", "Mean", "Normative economics", "Python (programming language)", "Stata", "U.S. Census Bureau", "United States Census Bureau", "World Institute for Development Economics Research"], "references": ["http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=19968", "http://www.wider.unu.edu/research/Database/en_GB/database/", "http://www.r-project.org/", "http://ideas.repec.org/c/boc/bocode/s366007.html", "http://ideas.repec.org/c/boc/bocode/s366302.html", "http://ideas.repec.org/c/boc/bocode/s453601.html", "http://ideas.repec.org/p/iza/izadps/dp763.html", "http://www.poorcity.richcity.org/calculator.htm", "http://www.poorcity.richcity.org/oei/#Atkinson", "https://www.census.gov/hhes/www/income/incineq/p60204/p60204txt.html", "https://www.census.gov/prod/2011pubs/p60-239.pdf", "https://archive.is/20121204174230/http://www.wessa.net/co.wasp", "https://web.archive.org/web/20041012085224/http://luaforge.net/project/showfiles.php?group_id=49", "https://doi.org/10.1016%2F0022-0531(70)90039-6", "https://doi.org/10.2307%2F1913126"]}, "Quasi-experiment": {"categories": ["All articles with dead external links", "Articles with dead external links from July 2016", "Articles with permanently dead external links", "Design of experiments", "Observational study", "Social research", "Webarchive template wayback links"], "title": "Quasi-experiment", "method": "Quasi-experiment", "url": "https://en.wikipedia.org/wiki/Quasi-experiment", "summary": "A quasi-experiment is an empirical interventional study used to estimate the causal impact of an intervention on target population without random assignment. Quasi-experimental research shares similarities with the traditional experimental design or randomized controlled trial, but it specifically lacks the element of random assignment to treatment or control. Instead, quasi-experimental designs typically allow the researcher to control the assignment to the treatment condition, but using some criterion other than random assignment (e.g., an eligibility cutoff mark). In some cases, the researcher may have control over assignment to treatment.\nQuasi-experiments are subject to concerns regarding internal validity, because the treatment and control groups may not be comparable at baseline. With random assignment, study participants have the same chance of being assigned to the intervention group or the comparison group. As a result, differences between groups on both observed and unobserved characteristics would be due to chance, rather than to a systematic factor related to treatment (e.g., illness severity). Randomization itself does not guarantee that groups will be equivalent at baseline. Any change in characteristics post-intervention is likely attributable to the intervention. With quasi-experimental studies, it may not be possible to convincingly demonstrate a causal link between the treatment condition and observed outcomes. This is particularly true if there are confounding variables that cannot be controlled or accounted for.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Case-control study", "Categorical variable", "Causal", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort study", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Confounding variables", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Difference in differences", "Digital object identifier", "Divergence (statistics)", "Donald T. Campbell", "Durbin\u2013Watson statistic", "Ecological validity", "Econometrics", "Education", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental design", "Exponential family", "Exponential smoothing", "External validity", "Extraneous variables", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalization", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Grouping variable", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Instrumental variables", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interrupted time series design", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Longitudinal study", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural experiments", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Panel analysis", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Person-by-treatment", "Pie chart", "Pivotal quantity", "Placebo", "Plug-in principle", "Point estimation", "Poisson regression", "Policy analysis", "Population", "Population (statistics)", "Population statistics", "Posterior probability", "Posttraumatic stress disorder", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Propensity score matching", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Public health", "Quality control", "Quasi-independent variable", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression discontinuity design", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social sciences", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "True experiment", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://linguistics.byu.edu/faculty/henrichsenl/ResearchMethods/RM_2_09.html", "http://www.osulb.edu/~msaintg/ppa696/696quasi.htm", "http://www.otal.umd.edu/hci-rm/cntlexp.html", "http://www.ncbi.nlm.nih.gov/pubmed/22506721", "http://pareonline.net/getvn.asp?v=5&n=14", "http://socialresearchmethods.net/kb/quasiexp.php", "http://doi.org/10.1006%2Fjvbe.1998.1676", "http://doi.org/10.1037%2Fa0028244", "http://doi.org/10.1057%2F9780230226203.1162", "http://doi.org/10.1080%2F07350015.1995.10524589", "http://doi.org/10.1086%2F208920", "http://doi.org/10.1097%2F00004583-200006000-00020", "http://doi.org/10.2501%2Fs0021849909090230", "http://www.worldcat.org/issn/0021-8499", "http://ssmon.chb.kth.se/safebk/", "http://ssmon.chb.kth.se/safebk/Chp_4.pdf", "https://faculty.wharton.upenn.edu/wp-content/uploads/2012/04/JAR49_2-09023-Armstrong-PatnaikSPMay25.pdf", "https://web.archive.org/web/20120328052718/http://ssmon.chb.kth.se/safebk/", "https://web.archive.org/web/20120722015648/http://otal.umd.edu/hci-rm/cntlexp.html", "https://web.archive.org/web/20120916072343/http://ssmon.chb.kth.se/safebk/Chp_4.pdf", "https://web.archive.org/web/20130318182539/http://linguistics.byu.edu/faculty/henrichsenl/ResearchMethods/RM_2_09.html", "https://web.archive.org/web/20130502154016/http://pareonline.net/getvn.asp?v=5&n=14", "https://web.archive.org/web/20170817081006/https://faculty.wharton.upenn.edu/wp-content/uploads/2012/04/JAR49_2-09023-Armstrong-PatnaikSPMay25.pdf"]}, "Stochastic grammar": {"categories": ["All articles needing additional references", "All stub articles", "Articles needing additional references from March 2011", "Grammar frameworks", "Linguistics stubs", "Probabilistic models", "Statistical natural language processing"], "title": "Stochastic grammar", "method": "Stochastic grammar", "url": "https://en.wikipedia.org/wiki/Stochastic_grammar", "summary": "A stochastic grammar (statistical grammar) is a grammar framework with a probabilistic notion of grammaticality:\n\nStochastic context-free grammar\nStatistical parsing\nData-oriented parsing\nHidden Markov model\nEstimation theoryStatistical natural language processing uses stochastic, probabilistic and statistical methods, especially to resolve difficulties that arise because longer sentences are highly ambiguous when processed with realistic grammars, yielding thousands or millions of possible analyses. Methods for disambiguation often involve the use of corpora and Markov models. \"A probabilistic model consists of a non-probabilistic model plus some numerical quantities; it is not true that probabilistic models are inherently simpler or less structural than non-probabilistic models.\"The technology for statistical NLP comes mainly from machine learning and data mining, both of which are fields of artificial intelligence that involve learning from data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/dc/Linguistics_stub.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Artificial intelligence", "Colorless green ideas sleep furiously", "Computational linguistics", "Corpus linguistics", "Data-oriented parsing", "Data mining", "Estimation theory", "Grammar framework", "Grammaticality", "Hidden Markov model", "International Standard Book Number", "L-system", "Linguistics", "Machine learning", "Markov model", "Natural language processing", "Probabilistic", "Sequence alignment", "Statistical", "Statistical language acquisition", "Statistical parsing", "Stochastic", "Stochastic context-free grammar"], "references": ["http://ismir2009.ismir.net/proceedings/OS8-1.pdf", "https://www.researchgate.net/profile/John_Goldsmith/publication/255057469_Probabilistic_Models_of_Grammar_Phonology_as_Information_Minimization/links/543fb7070cf2be1758cf470d.pdf"]}, "Redescending M-estimator": {"categories": ["All articles lacking in-text citations", "All articles needing expert attention", "Articles lacking in-text citations from September 2010", "Articles needing expert attention from September 2010", "Articles needing expert attention with no reason or talk parameter", "M-estimators", "Robust statistics", "Statistics articles needing expert attention"], "title": "Redescending M-estimator", "method": "Redescending M-estimator", "url": "https://en.wikipedia.org/wiki/Redescending_M-estimator", "summary": "In statistics, Redescending M-estimators are \u03a8-type M-estimators which have \u03c8 functions that are non-decreasing near the origin, but decreasing toward 0 far from the origin. Their \u03c8 functions can be chosen to redescend smoothly to zero, so that they usually satisfy \u03c8(x) = 0 for all x with |x| > r, where r is referred to as the minimum rejection point.\nDue to these properties of the \u03c8 function, these kinds of estimators are very efficient, have a high breakdown point and, unlike other outlier rejection techniques, they do not suffer from a masking effect. They are efficient because they completely reject gross outliers, and do not completely ignore moderately large outliers (like median).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e3/Andrew.png", "https://upload.wikimedia.org/wikipedia/commons/e/ea/Hampel.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2d/Tukey.png"], "links": ["Cauchy distribution", "Huber loss function", "M-estimator", "Outlier rejection technique", "Robust statistics", "Statistics"], "references": []}, "Geometric standard deviation": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2016", "Scale statistics"], "title": "Geometric standard deviation", "method": "Geometric standard deviation", "url": "https://en.wikipedia.org/wiki/Geometric_standard_deviation", "summary": "In probability theory and statistics, the geometric standard deviation describes how spread out are a set of numbers whose preferred average is the geometric mean. For such data, it may be preferred to the more usual standard deviation. Note that unlike the usual arithmetic standard deviation, the geometric standard deviation is a multiplicative factor, and thus is dimensionless, rather than having the same dimension as the input values. Thus, the geometric standard deviation may be more appropriately called geometric SD factor . When using geometric SD factor in conjunction with geometric mean, it should be described as \"the range from (the geometric mean divided by the geometric SD factor) to (the geometric mean multiplied by the geometric SD factor), and one cannot add/subtract \"geometric SD factor\" to/from geometric mean .", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Arithmetic mean", "Confidence interval", "Dimensional analysis", "Dimensionless", "Geometric mean", "JSTOR", "Log-normal distribution", "Natural logarithm", "Probability theory", "Raw score", "Standard deviation", "Standard score", "Statistics"], "references": ["http://www.graphpad.com/guides/prism/7/statistics/stat_the_geometric_mean_and_geometr.htm?toc=0&printWindow", "http://www.jstor.org/stable/2530139", "https://doi.org/10.3109/03639049309038775"]}, "Indicators of spatial association": {"categories": ["Spatial data analysis"], "title": "Indicators of spatial association", "method": "Indicators of spatial association", "url": "https://en.wikipedia.org/wiki/Indicators_of_spatial_association", "summary": "Indicators of spatial association are statistics that evaluate the existence of clusters in the spatial arrangement of a given variable. For instance if we are studying cancer rates among census tracts in a given city local clusters in the rates mean that there are areas that have higher or lower rates than is to be expected by chance alone; that is, the values occurring are above or below those of a random distribution in space.", "images": [], "links": ["Cancer", "Census tract", "Cluster analysis", "Distance decay", "First law of geography", "GeoDA", "Luc Anselin", "Moran's I", "Space", "Spatial autocorrelation", "Statistics"], "references": ["http://geodacenter.asu.edu/system/files/geodaworkbook.pdf", "https://onlinelibrary.wiley.com/doi/epdf/10.1111/j.1538-4632.1995.tb00338.x"]}, "Sensitivity and specificity": {"categories": ["Accuracy and precision", "All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from June 2017", "Bioinformatics", "Biostatistics", "Cheminformatics", "Medical statistics", "Statistical classification", "Statistical ratios", "Wikipedia articles that are too technical from June 2017"], "title": "Sensitivity and specificity", "method": "Sensitivity and specificity", "url": "https://en.wikipedia.org/wiki/Sensitivity_and_specificity", "summary": "Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as a classification function:\n\nSensitivity (also called the true positive rate, the recall, or probability of detection in some fields) measures the proportion of actual positives that are correctly identified as such (e.g., the percentage of sick people who are correctly identified as having the condition).\nSpecificity (also called the true negative rate) measures the proportion of actual negatives that are correctly identified as such (e.g., the percentage of healthy people who are correctly identified as not having the condition).Equivalently, in medical tests sensitivity is the extent to which actual positives are not overlooked (so false negatives are few), and specificity is the extent to which actual negatives are classified as such (so false positives are few). Thus a highly sensitive test rarely overlooks an actual positive (for example, showing \"nothing bad\" despite something bad existing); a highly specific test rarely registers a positive classification for anything that is not the target of testing (for example, finding one bacterial species and mistaking it for another closely related one that is the true target); and a test that is highly sensitive and highly specific does both, so it \"rarely overlooks a thing that it is looking for\" and it \"rarely mistakes anything else for that thing.\" Because most medical tests do not have sensitivity and specificity values above 99%, \"rarely\" does not equate to certainty. But for practical reasons, tests with sensitivity and specificity values above 90% have high credibility, albeit usually no certainty, in differential diagnosis.\nSensitivity therefore quantifies the avoiding of false negatives and specificity does the same for false positives. For any test, there is usually a trade-off between the measures \u2013 for instance, in airport security, since testing of passengers is for potential threats to safety, scanners may be set to trigger alarms on low-risk items like belt buckles and keys (low specificity) in order to increase the probability of identifying dangerous objects and minimize the risk of missing objects that do pose a threat (high sensitivity). This trade-off can be represented graphically using a receiver operating characteristic curve. A perfect predictor would be described as 100% sensitive, meaning all sick individuals are correctly identified as sick, and 100% specific, meaning no healthy individuals are incorrectly identified as sick. In reality, however, any non-deterministic predictor will possess a minimum error bound known as the Bayes error rate.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e2/HighSensitivity_LowSpecificity_1401x1050.png", "https://upload.wikimedia.org/wikipedia/commons/2/2d/Issoria_lathonia.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a6/LowSensitivity_HighSpecificity_1400x1050.png", "https://upload.wikimedia.org/wikipedia/commons/8/8b/Nuvola_apps_kalzium.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e7/Sensitivity_and_specificity.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d6/WHO_Rod.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Academic clinical trials", "Accuracy", "Accuracy and precision", "Adaptive clinical trial", "Airport security", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Bayes error rate", "Binary classification", "Binomial proportion confidence interval", "Blind experiment", "Bowel cancer", "Brier score", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Certainty", "Classification rule", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Confidence intervals", "Confusion matrix", "Contingency table", "Correlation does not imply causation", "Cross-sectional study", "Cumulative accuracy profile", "Cumulative incidence", "Design of experiments", "Detection theory", "Diagnostic odds ratio", "Differential diagnosis", "Digital object identifier", "Dimensionless", "Discrimination", "Ecological study", "Endoscopy", "Epidemiological methods", "Evidence-based medicine", "Experiment", "F-score", "F1 score", "False alarm", "False discovery rate", "False negative", "False negative rate", "False omission rate", "False positive", "False positive paradox", "False positive rate", "False positives and false negatives", "Fecal occult blood", "First-in-man study", "Glossary of clinical research", "Harmonic mean", "Hazard ratio", "Hit rate", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Information retrieval", "Informedness", "Intention-to-treat analysis", "International Standard Book Number", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Matthews correlation coefficient", "Medical diagnosis", "Medical test", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "NCSS (statistical software)", "Negative likelihood ratio", "Negative predictive value", "Nested case\u2013control study", "Non-deterministic algorithm", "Normal distribution", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "OpenEpi", "Period prevalence", "Point prevalence", "Population Impact Measures", "Positive and negative predictive values", "Positive likelihood ratio", "Positive predictive value", "Pre- and post-test probability", "Precision (information retrieval)", "Precision and recall", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Recall (information retrieval)", "Receiver operating characteristic", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Scientific control", "Seeding trial", "Selection bias", "Sensitivity (test)", "Sensitivity (tests)", "Sensitivity index", "Specificity (tests)", "Specificity and sensitivity", "Statistic", "Statistical classification", "Statistical hypothesis testing", "Statistical population", "Statistical power", "Statistical significance", "Survivorship bias", "Systematic review", "True negative", "True negative rate", "True positive", "True positive rate", "Type II error", "Type I and type II errors", "Type I error", "Uncertainty coefficient", "Vaccine trial", "Virulence", "Youden's J statistic"], "references": ["http://www.flinders.edu.au/science_engineering/fms/School-CSEM/publications/tech_reps-research_artfcts/TRRA_2007.pdf", "http://www.mathworks.com/help/phased/examples/detector-performance-analysis-using-roc-curves.html", "http://www.med.emory.edu/EMAC/curriculum/diagnosis/sensand.htm", "http://omerad.msu.edu/ebm/Diagnosis/Diagnosis4.html", "http://araw.mede.uic.edu/cgi-bin/testcalc.pl", "http://open.umich.edu/education/med/m1/patientspop-decisionmaking/2010/materials", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC200804", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2540489", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2824341", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC487735", "http://www.ncbi.nlm.nih.gov/pubmed/14512479", "http://www.ncbi.nlm.nih.gov/pubmed/15271832", "http://www.ncbi.nlm.nih.gov/pubmed/20089911", "http://www.ncbi.nlm.nih.gov/pubmed/8019315", "http://www.ncbi.nlm.nih.gov/pubmed/8028462", "http://www.ncbi.nlm.nih.gov/pubmed/8028470", "http://people.inf.elte.hu/kiss/11dwhdm/roc.pdf", "http://www.cebm.net/sppin-and-snnout/", "http://vassarstats.net/clin1.html", "http://doi.org/10.1016%2Fj.patrec.2005.10.010", "http://doi.org/10.1136%2Fbmj.308.6943.1552", "http://doi.org/10.1136%2Fbmj.327.7417.716", "http://doi.org/10.1136%2Fbmj.329.7459.209", "http://doi.org/10.1177%2F0272989X9401400202", "http://doi.org/10.1177%2F0272989X9401400210", "http://doi.org/10.1523%2FJNEUROSCI.3585-09.2010", "http://www.medcalc.org/calc/diagnostic_test.php", "https://books.google.com/books?id=hDX65v9bReYC", "https://link.springer.com/referencework/10.1007%2F978-0-387-30164-8", "https://kennis-research.shinyapps.io/Bayes-App/", "https://web.archive.org/web/20130706035232/http://omerad.msu.edu/ebm/Diagnosis/Diagnosis4.html", "https://www.medcalc.org/calc/diagnostic_test.php"]}, "Sum of squares function": {"categories": ["Arithmetic functions", "Squares in number theory"], "title": "Sum of squares function", "method": "Sum of squares function", "url": "https://en.wikipedia.org/wiki/Sum_of_squares_function", "summary": "The sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n as the sum of k squares, where representations that differ only in the order of the summands or in the signs of the square roots are counted as different, and is denoted by rk(n).", "images": [], "links": ["Arithmetic function", "Cardinality", "Carl Gustav Jakob Jacobi", "Divisor function", "Eric W. Weisstein", "Generating series", "International Standard Book Number", "Jacobi's four-square theorem", "Jacobi theta function", "MathWorld", "Modular arithmetic", "Natural number", "Partition (number theory)", "Square root", "Summand"], "references": ["http://mathworld.wolfram.com/SumofSquaresFunction.html"]}, "Gambling and information theory": {"categories": ["Gambling mathematics", "Information theory", "Statistical inference", "Wagering"], "title": "Gambling and information theory", "method": "Gambling and information theory", "url": "https://en.wikipedia.org/wiki/Gambling_and_information_theory", "summary": "Statistical inference might be thought of as gambling theory applied to the world around us. The myriad applications for logarithmic information measures tell us precisely how to take the best guess in the face of partial information. In that sense, information theory might be considered a formal expression of the theory of gambling. It is no surprise, therefore, that information theory has applications to games of chance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/22/Sandebits.png"], "links": ["Advanced NFL Stats", "Bayesian inference", "Bit", "Entropy (information theory)", "Gambler's ruin", "Gambling", "Horse racing", "Information entropy", "Information theory", "International Standard Book Number", "Investing", "John Larry Kelly, Jr", "Kelly criterion", "Kullback\u2013Leibler divergence", "Mutual information", "Odds", "Posterior probability", "Principle of indifference", "Prior probability", "Quantities of information", "Random walk", "Self-information", "Statistical association football predictions", "Thomas M. Cover"], "references": ["http://betbubbles.com/sports-predictions/", "http://www.footballoutsiders.com/info/methods#DVOA", "http://pure.au.dk/portal/files/1627/000145742-145742.pdf", "http://bayes.wustl.edu/"]}, "Absorbing Markov chain": {"categories": ["Markov models", "Markov processes"], "title": "Absorbing Markov chain", "method": "Absorbing Markov chain", "url": "https://en.wikipedia.org/wiki/Absorbing_Markov_chain", "summary": "In the mathematical theory of probability, an absorbing Markov chain is a Markov chain in which every state can reach an absorbing state. An absorbing state is a state that, once entered, cannot be left.\nLike general Markov chains, there can be continuous-time absorbing Markov chains with an infinite state space. However, this article concentrates on the discrete-time discrete-state-space case.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/10/Drunkard%E2%80%99s_walk.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Hivmodelmarkov.png", "https://upload.wikimedia.org/wikipedia/commons/0/03/Probability_of_winning_Snakes_and_Ladders_by_turns.svg"], "links": ["Absorbing set (random dynamical systems)", "Diagonal matrix", "Digital object identifier", "Discrete phase-type distribution", "Empty string", "Fair coin", "Hadamard product (matrices)", "International Standard Book Number", "International Standard Serial Number", "J. Laurie Snell", "JSTOR", "John G. Kemeny", "Markov chain", "Probability", "PubMed Central", "PubMed Identifier", "Random walk", "Snakes and Ladders", "String generation"], "references": ["http://demonstrations.wolfram.com/AbsorbingMarkovChain/", "http://www.bewersdorff-online.de/amonopoly/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2869414", "http://www.ncbi.nlm.nih.gov/pubmed/20204538", "http://doi.org/10.1007%2Fs11606-010-1265-5", "http://doi.org/10.2307%2F3619261", "http://www.jstor.org/stable/3619261", "http://www.worldcat.org/issn/0884-8734", "https://www.amazon.com/Markov-Cambridge-Statistical-Probabilistic-Mathematics/dp/0521633966/ref=sr_1_1?s=books&ie=UTF8&qid=1532297444&sr=1-1&keywords=markov+chains", "https://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf"]}, "Inherent zero": {"categories": ["All stub articles", "Applied mathematics stubs", "Statistical data types"], "title": "Inherent zero", "method": "Inherent zero", "url": "https://en.wikipedia.org/wiki/Inherent_zero", "summary": "In statistics, an inherent zero is a reference point used to describe data sets which are indicative of magnitude of an absolute or relative nature. Inherent zeros are used in the \"ratio level\" of \"levels of measurement\" and imply \u201cnone.\u201d", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a3/Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a3/20120917204659%21Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a3/20100506100358%21Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a3/20070526080805%21Arithmetic_symbols.svg"], "links": ["Applied mathematics", "Level of measurement", "Ron Larson (mathematician)"], "references": []}, "Frequency (statistics)": {"categories": ["Frequency distribution"], "title": "Frequency (statistics)", "method": "Frequency (statistics)", "url": "https://en.wikipedia.org/wiki/Frequency_(statistics)", "summary": "In statistics the frequency (or absolute frequency) of an event \n \n \n \n i\n \n \n {\\displaystyle i}\n is the number \n \n \n \n \n n\n \n i\n \n \n \n \n {\\displaystyle n_{i}}\n of times the event occurred in an experiment or study. These frequencies are often graphically represented in histograms.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/35/Incarceration_Rates_Worldwide_ZP.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f7/Travel_time_histogram_total_n_Stata.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Aperiodic frequency", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Categorization", "Census", "Central limit theorem", "Central tendency", "Chart", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative frequency analysis", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical probability", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Event (probability theory)", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency (disambiguation)", "Frequency distribution", "Frequency domain", "Frequentist inference", "Frequentist probability", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval (mathematics)", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Wiley & Sons", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Length", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maurice Kendall", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiset", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normalization (statistics)", "Normalizing constant", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability density function", "Probability distribution", "Proportional hazards model", "Pseudocount", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Ranking", "Rao\u2013Blackwell theorem", "Rectangle", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Square", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical distribution", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical regularity", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Word frequency", "Z-test"], "references": ["http://www.leidenuniv.nl/fsw/verduin/stathist/1stword.htm", "http://doi.org/10.1093%2Fbiomet%2F36.1-2.101", "http://www.jstor.org/stable/2332534", "https://books.google.com/books/about/Mathematics_of_statistics.html?id=UdlLAAAAMAAJ"]}, "Stimulus-response model": {"categories": ["All articles with unsourced statements", "All stub articles", "Articles with unsourced statements from August 2009", "Behavioral concepts", "Specific models", "Statistics stubs"], "title": "Stimulus\u2013response model", "method": "Stimulus-response model", "url": "https://en.wikipedia.org/wiki/Stimulus%E2%80%93response_model", "summary": "The stimulus\u2013response model is a characterization of a statistical unit (such as a neuron) as a black box model, predicting a quantitative response to a quantitative stimulus, for example one administered by a researcher.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Black box", "Expected value", "International Standard Book Number", "Linear model", "Linear regression", "Neuron", "Neuropsychological test", "Neuroscience", "Risk assessment", "Statistical theory", "Statistical unit", "Statistics", "Stimulation"], "references": ["https://books.google.com/books?id=5V9nvsKeBgIC&pg=RA1-PA143&dq=stimulus-response-model++behavior#v=onepage&q=stimulus-response-model%20%20behavior&f=false", "https://books.google.com/books?id=B6nfz--ePEEC&pg=PA79&dq=stimulus-response++neuron#v=onepage&q=stimulus-response%20%20neuron&f=false", "https://books.google.com/books?id=FrNv8AwkoKgC&pg=PA172&dq=stimulus-response-model+statistical#v=onepage&q=stimulus-response-model%20statistical&f=false", "https://books.google.com/books?id=I9xIfeijGhMC&pg=PA167&dq=stimulus-response-model+statistical#v=onepage&q=stimulus-response-model%20statistical&f=false", "https://books.google.com/books?id=l7o31p-6dlAC&pg=PA12&dq=stimulus-response-model++neuron#v=onepage&q=stimulus-response-model%20%20neuron&f=false"]}, "Gallagher Index": {"categories": ["Electoral systems", "Psephology"], "title": "Gallagher index", "method": "Gallagher Index", "url": "https://en.wikipedia.org/wiki/Gallagher_index", "summary": "The Gallagher index \"measures an electoral system\u2019s relative disproportionality between votes received and seats allotted in a legislature.\" As such, it measures the difference between the percentage of votes each party gets and the percentage of seats each party gets in the resulting legislature, and it also measures this disproportionality from all parties collectively in any one given election. That collective disproportionality from the election is given a precise score, which can then be used in comparing various levels of proportionality among various elections from various electoral systems.Michael Gallagher, who created the index, referred to it as a \"least squares index\", inspired by the sum of squared residuals used in the method of least squares. The index is therefore commonly abbreviated as \"LSq\" even though the measured allocation is not necessarily a least squares fit. The Gallagher index is computed by taking the square root of half the sum of the squares of the difference between percent of votes (\n \n \n \n \n V\n \n i\n \n \n \n \n {\\displaystyle V_{i}}\n ) and percent of seats (\n \n \n \n \n S\n \n i\n \n \n \n \n {\\displaystyle S_{i}}\n ) for each of the political parties (\n \n \n \n i\n =\n 1...\n n\n \n \n {\\displaystyle i=1...n}\n ).\n\n \n \n \n \n L\n S\n q\n \n =\n \n \n \n \n 1\n 2\n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n (\n \n V\n \n i\n \n \n \u2212\n \n S\n \n i\n \n \n \n )\n \n 2\n \n \n \n \n \n \n {\\displaystyle \\mathrm {LSq} ={\\sqrt {{\\frac {1}{2}}\\sum _{i=1}^{n}(V_{i}-S_{i})^{2}}}}\n The index weighs the deviations by their own value, creating a responsive index, ranging from 0 to 100. The larger the differences between the percentage of the votes and the percentage of seats summed over all parties, the larger the Gallagher index. The larger the index value the larger the disproportionality and vice versa. Michael Gallagher included \"other\" parties as a whole category, and Arend Lijphart modified it, excluding those parties. Unlike the well-known Loosemore\u2013Hanby index, the Gallagher index is less sensitive to small discrepancies.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fb/2010_Election_Australia_Gallagher_Index.png", "https://upload.wikimedia.org/wikipedia/commons/2/21/2012_Election_Queensland_Gallagher_Index.png", "https://upload.wikimedia.org/wikipedia/commons/0/06/2015_Canadian_General_Election_Gallagher_Index.svg", "https://upload.wikimedia.org/wikipedia/commons/6/69/Swedish_general_election%2C_2018_%28Gallagher_Index%29.png", "https://upload.wikimedia.org/wikipedia/en/0/01/A_coloured_voting_box.svg"], "links": ["99 MP Party", "ACT New Zealand", "Alliance (New Zealand political party)", "Aotearoa Legalise Cannabis Party", "Arend Lijphart", "Australian Democrats", "Australian Greens", "Australian federal election, 2010", "Canadian House of Commons Special Committee on Electoral Reform", "Chief Electoral Office (New Zealand)", "Christian Heritage New Zealand", "Destiny New Zealand", "Digital object identifier", "Direct Democracy Party of New Zealand", "Elections in New Zealand", "Electoral systems", "Gallagher Index", "Green Party of Aotearoa New Zealand", "International Standard Book Number", "Least squares", "Liberal National Party of Queensland", "Libertarianz", "Loosemore\u2013Hanby index", "Michael Gallagher (academic)", "Mixed-member proportional representation", "M\u0101ori Party", "M\u0101ori electorates", "New Zealand Democratic Party", "New Zealand Family Rights Protection Party", "New Zealand First", "New Zealand House of Representatives", "New Zealand Labour Party", "New Zealand National Party", "New Zealand Progressive Party", "New Zealand general election, 2005", "One New Zealand Party", "Oxford", "Oxford University Press", "Parliament of Canada", "Pearson's chi-squared test", "Political parties", "Preferential voting", "Proportional representation", "Queensland state election, 2012", "Residual sum of squares", "Riksdag", "Sainte-Lagu\u00eb method", "Single-member district", "Square root", "Summation", "Swedish general election, 2018", "The Republic of New Zealand Party", "Trinity College, Dublin", "United Future New Zealand", "Webster/Sainte-Lagu\u00eb method"], "references": ["http://gallagherindex.blogspot.ca/", "http://gallagherindex.blogspot.ca/2016/12/its-important-and-easy-to-understand.html", "http://www.cbc.ca/news/politics/wherry-electoral-reform-committee-1.3866879", "http://www.parl.gc.ca/HousePublications/Publication.aspx?Language=e&Mode=1&Parl=42&Ses=1&DocId=8655791&File=177#50", "http://news.nationalpost.com/full-comment/colby-cosh-did-maryam-monsef-actually-read-the-whole-electoral-reform-report", "http://ottawacitizen.com/news/politics/read-the-full-electoral-reform-committee-report-plus-liberal-and-ndpgreen-opinions", "http://www.tcd.ie/Political_Science/staff/michael_gallagher/ElSystems/Docts/ElectionIndices.pdf", "http://www.electionresults.govt.nz/electionresults_2005/electoratestatus.html", "http://doi.org/10.1016%2F0261-3794(91)90004-c", "http://doi.org/10.1017%2Fs0007123400006499", "http://doi.org/10.1093%2Foxfordjournals.pan.a029822", "http://pan.oxfordjournals.org/content/8/4/381.short", "http://www.votingmatters.org.uk/ISSUE10/P6.HTM", "https://iscanadafair.ca/", "https://iscanadafair.ca/gallagher-index/", "https://docs.google.com/document/d/1j86Oylz9IRL_RLQ1CrVNmcxStbxzVXy0NvP10BjrVuI/edit#", "https://commons.wikimedia.org/wiki/Category:Gallagher_Index"]}, "Log-rank test": {"categories": ["Statistical tests", "Survival analysis"], "title": "Logrank test", "method": "Log-rank test", "url": "https://en.wikipedia.org/wiki/Logrank_test", "summary": "In statistics, the logrank test is a hypothesis test to compare the survival distributions of two samples. It is a nonparametric test and appropriate to use when the data are right skewed and censored (technically, the censoring must be non-informative). It is widely used in clinical trials to establish the efficacy of a new treatment in comparison with a control treatment when the measurement is the time to event (such as the time from initial treatment to a heart attack). The test is sometimes called the Mantel\u2013Cox test, named after Nathan Mantel and David Cox. The logrank test can also be viewed as a time-stratified Cochran\u2013Mantel\u2013Haenszel test.\nThe test was first proposed by Nathan Mantel and was named the logrank test by Richard and Julian Peto.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Censoring (statistics)", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Clinical trials", "Cluster analysis", "Cluster sampling", "Cochran\u2013Mantel\u2013Haenszel statistics", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data Monitoring Committee", "Data collection", "David Cox (statistician)", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hazard ratio", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypergeometric distribution", "Hypothesis test", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Julian Peto", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratio test", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Nathan Mantel", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peto logrank test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Proportional hazards models", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Richard Peto", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon rank sum test", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC403858", "http://www.ncbi.nlm.nih.gov/pubmed/15117797", "http://www.ncbi.nlm.nih.gov/pubmed/5910392", "http://doi.org/10.1002%2F0470011815.b2a11047", "http://doi.org/10.1093%2Fbiomet%2F68.1.316", "http://doi.org/10.1136%2Fbmj.328.7447.1073", "http://doi.org/10.2307%2F2344317", "http://www.jstor.org/stable/2335833", "http://www.jstor.org/stable/2344317"]}, "Algorithmic inference": {"categories": ["Algorithmic inference", "All articles lacking in-text citations", "Articles lacking in-text citations from July 2011", "Machine learning"], "title": "Algorithmic inference", "method": "Algorithmic inference", "url": "https://en.wikipedia.org/wiki/Algorithmic_inference", "summary": "Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst. Cornerstones in this field are computational learning theory, granular computing, bioinformatics, and, long ago, structural probability (Fraser 1966).\nThe main focus is on the algorithms which compute statistics rooting the study of a random phenomenon, along with the amount of data they must feed on to produce reliable results. This shifts the interest of mathematicians from the study of the distribution laws to the functional properties of the statistics, and the interest of computer scientists from the algorithms for processing data to the information they process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/Hazardconf.png", "https://upload.wikimedia.org/wikipedia/commons/5/57/Mucdf.png", "https://upload.wikimedia.org/wikipedia/commons/c/cd/Muconfint.png", "https://upload.wikimedia.org/wikipedia/commons/d/d1/Parecdf.png", "https://upload.wikimedia.org/wikipedia/commons/e/e2/Svmconf.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Algorithmic inference", "Bioinformatics", "Bootstrapping populations", "Central limit theorem", "Complexity", "Complexity index", "Computational learning theory", "Confidence interval", "Confidence intervals", "Confidence level", "Cumulative distribution function", "Degrees of freedom (statistics)", "Digital object identifier", "Epistemologic", "Fiducial distribution", "Granular computing", "Information", "Neuro-fuzzy", "Normal distribution", "Pareto distribution", "Posterior distribution", "Probability", "Probability distribution", "Random sample", "Random variables", "Regression analysis", "Standard normal distribution", "Statistical inference", "Statistics", "Student's t distribution", "Sufficient statistics", "Support vector machine", "Twisting properties", "Uniform distribution (continuous)", "VC dimension", "Well-behaved statistic"], "references": ["http://doi.org/10.1112/plms/s2-25.1.338", "http://doi.org/10.2307/2334048"]}, "Nested sampling algorithm": {"categories": ["All Wikipedia articles needing context", "All pages needing cleanup", "Bayesian statistics", "CS1 maint: Multiple names: authors list", "Model selection", "Randomized algorithms", "Wikipedia articles needing context from October 2009", "Wikipedia introduction cleanup from October 2009"], "title": "Nested sampling algorithm", "method": "Nested sampling algorithm", "url": "https://en.wikipedia.org/wiki/Nested_sampling_algorithm", "summary": "The nested sampling algorithm is a computational approach to the problem of comparing models in Bayesian statistics, developed in 2004 by physicist John Skilling.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["ArXiv", "Astronomy", "Bayes' theorem", "Bayes factor", "Bayesian model comparison", "Bayesian statistics", "Bibcode", "C++", "C (programming language)", "Computation", "Condensed matter physics", "Cosmology", "Curve fitting", "Digital object identifier", "Energy landscape", "Finite element", "Finite element updating", "Haskell (programming language)", "International Standard Book Number", "Lebesgue integration", "Markov chain Monte Carlo", "Model selection", "Phase transitions", "Physicist", "Programming language", "Python (programming language)", "R (programming language)", "Spectrum", "Statistical physics", "Structural dynamics"], "references": ["http://adsabs.harvard.edu/abs/2006ApJ...638L..51M", "http://adsabs.harvard.edu/abs/2008MNRAS.384..449F", "http://adsabs.harvard.edu/abs/2011MSSP...25.2399M", "http://adsabs.harvard.edu/abs/2012ASAJ..132.3251J", "http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704", "http://arxiv.org/abs/0704.3704", "http://arxiv.org/abs/astro-ph/0508461", "http://doi.org/10.1016%2Fj.ymssp.2011.04.001", "http://doi.org/10.1063%2F1.1835238", "http://doi.org/10.1086%2F501068", "http://doi.org/10.1111%2Fj.1365-2966.2007.12353.x", "http://doi.org/10.1121%2F1.4754550", "http://doi.org/10.1214%2F06-BA127", "http://hackage.haskell.org/package/NestedSampling", "http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html", "http://www.inference.phy.cam.ac.uk/bayesys/", "https://github.com/JorisDeRidder/DIAMONDS", "https://github.com/bnikolic/RNested", "https://github.com/js850/nested_sampling", "https://github.com/libAtoms/pymatnest", "https://books.google.com/books?id=R3GeFfshc7wC"]}, "Upside potential ratio": {"categories": ["Financial ratios", "Statistical ratios"], "title": "Upside potential ratio", "method": "Upside potential ratio", "url": "https://en.wikipedia.org/wiki/Upside_potential_ratio", "summary": "The upside-potential ratio is a measure of a return of an investment asset relative to the minimal acceptable return. The measurement allows a firm or individual to choose investments which have had relatively good upside performance, per unit of downside risk.\n\n \n \n \n U\n =\n \n \n \n \n \u2211\n \n min\n \n \n +\n \u221e\n \n \n \n (\n \n R\n \n r\n \n \n \u2212\n \n R\n \n min\n \n \n \n )\n \n P\n \n r\n \n \n \n \n \n \n \u2211\n \n \u2212\n \u221e\n \n \n min\n \n \n \n (\n \n R\n \n r\n \n \n \u2212\n \n R\n \n min\n \n \n \n \n )\n \n 2\n \n \n \n P\n \n r\n \n \n \n \n \n \n =\n \n \n \n \n E\n \n [\n (\n \n R\n \n r\n \n \n \u2212\n \n R\n \n min\n \n \n \n )\n \n +\n \n \n ]\n \n \n \n E\n \n [\n (\n \n R\n \n r\n \n \n \u2212\n \n R\n \n min\n \n \n \n )\n \n \u2212\n \n \n 2\n \n \n ]\n \n \n \n ,\n \n \n {\\displaystyle U={{\\sum _{\\min }^{+\\infty }{(R_{r}-R_{\\min }})P_{r}} \\over {\\sqrt {\\sum _{-\\infty }^{\\min }{(R_{r}-R_{\\min }})^{2}P_{r}}}}={\\frac {\\mathbb {E} [(R_{r}-R_{\\min })_{+}]}{\\sqrt {\\mathbb {E} [(R_{r}-R_{\\min })_{-}^{2}]}}},}\n where the returns \n \n \n \n \n R\n \n r\n \n \n \n \n {\\displaystyle R_{r}}\n have been put into increasing order. Here \n \n \n \n \n P\n \n r\n \n \n \n \n {\\displaystyle P_{r}}\n is the probability of the return \n \n \n \n \n R\n \n r\n \n \n \n \n {\\displaystyle R_{r}}\n and \n \n \n \n \n R\n \n min\n \n \n \n \n {\\displaystyle R_{\\min }}\n which occurs at \n \n \n \n r\n =\n min\n \n \n {\\displaystyle r=\\min }\n is the minimal acceptable return. In the secondary formula \n \n \n \n (\n X\n \n )\n \n +\n \n \n =\n \n \n {\n \n \n \n X\n \n \n \n if \n \n X\n \u2265\n 0\n \n \n \n \n 0\n \n \n \n else\n \n \n \n \n \n \n \n \n \n {\\displaystyle (X)_{+}={\\begin{cases}X&{\\text{if }}X\\geq 0\\\\0&{\\text{else}}\\end{cases}}}\n and \n \n \n \n (\n X\n \n )\n \n \u2212\n \n \n =\n (\n \u2212\n X\n \n )\n \n +\n \n \n \n \n {\\displaystyle (X)_{-}=(-X)_{+}}\n .The upside-potential ratio may also be expressed as a ratio of partial moments since \n \n \n \n \n E\n \n [\n (\n \n R\n \n r\n \n \n \u2212\n \n R\n \n min\n \n \n \n )\n \n +\n \n \n ]\n \n \n {\\displaystyle \\mathbb {E} [(R_{r}-R_{\\min })_{+}]}\n is the first upper moment and \n \n \n \n \n E\n \n [\n (\n \n R\n \n r\n \n \n \u2212\n \n R\n \n min\n \n \n \n )\n \n \u2212\n \n \n 2\n \n \n ]\n \n \n {\\displaystyle \\mathbb {E} [(R_{r}-R_{\\min })_{-}^{2}]}\n is the second lower partial moment.\nThe measure was developed by Frank A. Sortino.", "images": [], "links": ["Digital object identifier", "Downside risk", "Frank A. Sortino", "Minimal acceptable return", "Modern portfolio theory", "Modigliani risk-adjusted performance", "Moment (mathematics)", "Omega ratio", "Sharpe ratio", "Sortino ratio", "Standard deviation"], "references": ["http://doi.org/10.1080%2F14697680903081881"]}, "Stata": {"categories": ["1985 software", "All articles lacking reliable references", "All articles with a promotional tone", "Articles lacking reliable references from July 2016", "Articles with a promotional tone from July 2016", "Articles with multiple maintenance issues", "C software", "Econometrics software", "Proprietary commercial software for Linux", "Science software for Linux", "Statistical programming languages", "Statistical software", "Time series software"], "title": "Stata", "method": "Stata", "url": "https://en.wikipedia.org/wiki/Stata", "summary": "Stata is a general-purpose statistical software package created in 1985 by StataCorp. Most of its users work in research, especially in the fields of economics, sociology, political science, biomedicine and epidemiology.Stata's capabilities include data management, statistical analysis, graphics, simulations, regression, and custom programming. It also has a system to disseminate user-written programs that lets it grow continuously.\nThe name Stata is a syllabic abbreviation of the words statistics and data. The FAQ for the official forum of Stata insists that the correct English pronunciation of Stata \"must remain a mystery\"; any of \"Stay-ta\", \"Sta-ta\" or \"Stah-ta\" are considered acceptable.There are four major builds of each version of Stata:\nStata/MP for multiprocessor computers (including dual-core and multicore processors)\nStata/SE for large databases\nStata/IC, which is the standard version\nNumerics by Stata, supports any of the data sizes listed above in an embedded environmentSmall Stata, which was the smaller, student version for educational purchase only, is no longer available.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Features15-splash-wiki.png", "https://upload.wikimedia.org/wikipedia/commons/7/79/Stata_logo_med_blue.png", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikibooks-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/f/ff/Wikidata-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ADMB", "ASCII", "Analyse-it", "BMDP", "BV4.1 (software)", "Backward compatibility", "Biomedicine", "CSPro", "C (programming language)", "Comma-separated value", "Command line interface", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Data analysis", "Databank format", "Dataplot", "Dataset", "Dialog boxes", "EViews", "Econometrics", "Economics", "Epi Info", "Epidemiology", "FAQ", "File format", "Fizzbuzz", "Floating-point", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Graphical user interface", "Gretl", "H2O (software)", "Heteroscedasticity-consistent standard errors", "International Standard Book Number", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Linux", "List of statistical packages", "Logistic regression", "MATLAB", "MLwiN", "MacOS", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Menu (computing)", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Missing value", "NCSS (statistical software)", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Peer-reviewed", "Political science", "Proprietary software", "Public-domain software", "Qt Framework", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Random-access memory", "Ray Stata", "Research", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "Scatter plot", "Scripting language", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Sociology", "Software categories", "Software developer", "Software license", "Software release life cycle", "Software versioning", "Stada", "Stan (software)", "StatView", "StatXact", "Statistica", "Statistical analysis", "Statistics", "StatsDirect", "Syllabic abbreviation", "TSP (econometrics software)", "Technical support", "The Unscrambler", "UNISTAT", "Verification and Validation (software)", "Virtual memory", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.datascientistskills.com/2017/10/which-regression-model-to-use.html", "http://www.stata-journal.com/", "http://www.stata-journal.com/article.html?article=gn0018", "http://www.stata-press.com/", "http://www.stata.com/disciplines/", "http://www.statalist.org/forums/help", "https://books.google.com/books?id=-9ARswEACAAJ", "https://www.stata.com/", "https://www.stata.com/help.cgi?save", "https://www.stata.com/help.cgi?version", "https://www.stata.com/products/whichstata.html", "https://www.stata.com/support/faqs/res/history.html", "https://www.stata.com/support/faqs/res/statalist.html#pronounce", "https://www.stata.com/support/faqs/res/statalist.html#spell"]}, "Nested case-control study": {"categories": ["Cohort study methods", "Design of experiments", "Epidemiological study projects", "Nursing research"], "title": "Nested case\u2013control study", "method": "Nested case-control study", "url": "https://en.wikipedia.org/wiki/Nested_case%E2%80%93control_study", "summary": "A nested case\u2013control (NCC) study is a variation of a case\u2013control study in which cases and controls are drawn from the population in a fully enumerated cohort.Usually, the exposure of interest is only measured among the cases and the selected controls. Thus the nested case\u2013control study is less efficient than the full cohort design. The nested case\u2013control study can be analyzed using methods for missing covariates.The NCC design is often used when the exposure of interest is difficult or expensive to obtain and when the outcome is rare. By utilizing data previously collected from a large cohort study, the time and cost of beginning a new case\u2013control study is avoided. By only measuring the covariate in as many participants as necessary, the cost and effort of exposure assessment is reduced. This benefit is pronounced when the covariate of interest is biological, since assessments such as gene expression profiling are expensive, and because the quantity of blood available for such analysis is often limited, making it a valuable resource that should not be used unnecessarily.", "images": [], "links": ["Academic clinical trials", "Adaptive clinical trial", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Annals of Statistics", "ArXiv", "Attributable fraction among the exposed", "Attributable fraction for the population", "Blind experiment", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Conditional logistic regression", "Correlation does not imply causation", "Cross-sectional study", "Cumulative incidence", "David Cox (statistician)", "Design of experiments", "Digital object identifier", "Ecological study", "Epidemiological methods", "Evidence-based medicine", "Experiment", "First-in-man study", "Gene expression", "Gene expression profiling", "Glossary of clinical research", "Hazard ratio", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Intention-to-treat analysis", "International Standard Book Number", "Inverse probability weighting", "JSTOR", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "Null result", "Number needed to harm", "Number needed to treat", "Nurses' Health Study", "Observational study", "Odds ratio", "Open-label trial", "Period prevalence", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Scientific control", "Seeding trial", "Selection bias", "Specificity and sensitivity", "Survivorship bias", "Systematic review", "Tianxi Cai", "Vaccine trial", "Virulence"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3276269", "http://www.ncbi.nlm.nih.gov/pubmed/9051324", "http://arxiv.org/abs/0809.0445", "http://doi.org/10.1093%2Fbiostatistics%2Fkxr021", "http://doi.org/10.1214%2Faos%2F1176324322", "http://doi.org/10.3150%2F08-bej162", "http://www.jstor.org/stable/20680165", "http://www.jstor.org/stable/2242544", "https://books.google.com/books?id=GdXSAgAAQBAJ&pg=PA160", "https://www.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&tool=sumsearch.org/cite&retmode=ref&cmd=prlinks&id=9051324", "https://www.duo.uio.no/bitstream/10852/47861/1/1992-7.pdf"]}, "Coverage probability": {"categories": ["Estimation theory", "Use dmy dates from December 2013"], "title": "Coverage probability", "method": "Coverage probability", "url": "https://en.wikipedia.org/wiki/Coverage_probability", "summary": "In statistics, the coverage probability of a technique for calculating a confidence interval is the proportion of the time that the interval contains the true value of interest. For example, suppose our interest is in the mean number of months that people with a particular type of cancer remain in remission following successful treatment with chemotherapy. The confidence interval aims to contain the unknown mean remission duration with a given probability. This is the \"confidence level\" or \"confidence coefficient\" of the constructed interval which is effectively the \"nominal coverage probability\" of the procedure for constructing confidence intervals. The \"nominal coverage probability\" is often set at 0.95. The coverage probability is the actual probability that the interval contains the true mean remission duration in this example. \nIf all assumptions used in deriving a confidence interval are met, the nominal coverage probability will equal the coverage probability (termed \"true\" or \"actual\" coverage probability for emphasis). If any assumptions are not met, the actual coverage probability could either be less than or greater than the nominal coverage probability. When the actual coverage probability is greater than the nominal coverage probability, the interval is termed \"conservative\", if it is less than the nominal coverage probability, the interval is termed \"anti-conservative\", or \"permissive.\"\nA discrepancy between the coverage probability and the nominal coverage probability frequently occurs when approximating a discrete distribution with a continuous one. The construction of binomial confidence intervals is a classic example where coverage probabilities rarely equal nominal levels. For the binomial case, several techniques for constructing intervals have been created. The Wilson or Score confidence interval is one well known construction based on the normal distribution. Other constructions include the Wald, exact, Agresti-Coull, and likelihood intervals. While the Wilson interval may not be the most conservative estimate, it produces average coverage probabilities that are equal to nominal levels while still producing a comparatively narrow confidence interval. \nThe \"probability\" in coverage probability is interpreted with respect to a set of hypothetical repetitions of the entire data collection and analysis procedure. In these hypothetical repetitions, independent data sets following the same probability distribution as the actual data are considered, and a confidence interval is computed from each of these data sets; see Neyman construction. The coverage probability is the fraction of these computed confidence intervals that include the desired but unobservable parameter value.", "images": [], "links": ["Binomial proportion confidence interval", "Cancer", "Chemotherapy", "Confidence distribution", "Confidence interval", "Digital object identifier", "Expected value", "False coverage rate", "Independence (probability theory)", "International Standard Book Number", "Interval estimation", "JSTOR", "Neyman construction", "Probability distribution", "PubMed Identifier"], "references": ["http://www3.interscience.wiley.com/journal/3156/abstract", "http://www-stat.wharton.upenn.edu/~tcai/paper/Binomial-StatSci.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/9595616", "http://doi.org/10.1002%2F(SICI)1097-0258(19980430)17:8%3C857::AID-SIM777%3E3.0.CO;2-E", "http://doi.org/10.1214%2Fss%2F1009213286", "http://doi.org/10.2307%2F2685469", "http://www.jstor.org/stable/2685469"]}, "Kernel Fisher discriminant analysis": {"categories": ["CS1 maint: Multiple names: authors list", "Statistical classification"], "title": "Kernel Fisher discriminant analysis", "method": "Kernel Fisher discriminant analysis", "url": "https://en.wikipedia.org/wiki/Kernel_Fisher_discriminant_analysis", "summary": "In statistics, kernel Fisher discriminant analysis (KFD), also known as generalized discriminant analysis and kernel discriminant analysis, is a kernelized version of linear discriminant analysis (LDA). It is named after Ronald Fisher. Using the kernel trick, LDA is implicitly performed in a new feature space, which allows non-linear mappings to be learned.\n\n", "images": [], "links": ["Digital object identifier", "Dot product", "Face recognition", "Factor analysis", "Kernel principal component analysis", "Kernel trick", "Lagrange multiplier", "Linear discriminant analysis", "Ronald Fisher", "Statistics"], "references": ["http://crsouza.blogspot.com/2010/01/kernel-discriminant-analysis-in-c.html", "http://www.codeproject.com/KB/recipes/handwriting-kda.aspx", "http://homepage.tudelft.nl/19j49/Matlab_Toolbox_for_Dimensionality_Reduction.html", "http://doi.org/10.1016%2Fj.imavis.2003.08.010", "http://doi.org/10.1109%2FNNSP.1999.788121", "http://doi.org/10.1109%2Ftcsvt.2003.818352", "http://doi.org/10.1109%2Ftmi.2004.842457", "http://doi.org/10.1109%2Ftpami.2005.33", "http://doi.org/10.1162%2F089976600300014980"]}, "Probit": {"categories": ["All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from January 2013", "CS1 maint: Multiple names: authors list", "Normal distribution", "Single-equation methods (econometrics)", "Statistical analysis", "Wikipedia articles that are too technical from January 2013"], "title": "Probit", "method": "Probit", "url": "https://en.wikipedia.org/wiki/Probit", "summary": "In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution, which is commonly denoted as N(0,1). Mathematically, it is the inverse of the cumulative distribution function of the standard normal distribution, which is denoted as \n \n \n \n \u03a6\n (\n z\n )\n \n \n {\\displaystyle \\Phi (z)}\n , so the probit is denoted as \n \n \n \n \n \u03a6\n \n \u2212\n 1\n \n \n (\n p\n )\n \n \n {\\displaystyle \\Phi ^{-1}(p)}\n . It has applications in exploratory statistical graphics and specialized regression modeling of binary response variables.\nLargely because of the central limit theorem, the standard normal distribution plays a fundamental role in probability theory and statistics. If we consider the familiar fact that the standard normal distribution places 95% of probability between \u22121.96 and 1.96, and is symmetric around zero, it follows that\n\n \n \n \n \u03a6\n (\n \u2212\n 1.96\n )\n =\n 0.025\n =\n 1\n \u2212\n \u03a6\n (\n 1.96\n )\n .\n \n \n \n \n {\\displaystyle \\Phi (-1.96)=0.025=1-\\Phi (1.96).\\,\\!}\n The probit function gives the 'inverse' computation, generating a value of an N(0,1) random variable, associated with specified cumulative probability. Continuing the example,\n\n \n \n \n probit\n \u2061\n (\n 0.025\n )\n =\n \u2212\n 1.96\n =\n \u2212\n probit\n \u2061\n (\n 0.975\n )\n \n \n {\\displaystyle \\operatorname {probit} (0.025)=-1.96=-\\operatorname {probit} (0.975)}\n .In general,\n\n \n \n \n \u03a6\n (\n probit\n \u2061\n (\n p\n )\n )\n =\n p\n \n \n {\\displaystyle \\Phi (\\operatorname {probit} (p))=p}\n \nand\n\n \n \n \n probit\n \u2061\n (\n \u03a6\n (\n z\n )\n )\n =\n z\n .\n \n \n {\\displaystyle \\operatorname {probit} (\\Phi (z))=z.}", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/39/Logit-probit.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9b/Probit_plot.png", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Bimodal distribution", "Central limit theorem", "Chester Ittner Bliss", "Closed-form expression", "Continuous function", "Cumulative distribution function", "D. J. Finney", "Detection error tradeoff", "Digital object identifier", "Error function", "Generalized linear model", "International Standard Book Number", "JSTOR", "Kurtosis", "Logistic regression", "Logit", "Logit function", "Logit model", "Lognormal", "MATLAB", "Mathematica", "Microsoft Excel", "Monotonic function", "Multinomial probit", "Normal distribution", "OCLC", "Pesticide", "Probability theory", "Probit model", "PubMed Identifier", "Q-Q plot", "Quantile function", "R programming language", "Rankit", "Regression analysis", "Ridit scoring", "Sample (statistics)", "Science (journal)", "Sigmoid function", "Skewness", "Statistics"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/17813446", "http://doi.org/10.1017%2FS0956792508007341", "http://doi.org/10.1126%2Fscience.79.2037.38", "http://doi.org/10.2307%2F2347330", "http://www.jstor.org/stable/1659792", "http://www.jstor.org/stable/2347330", "http://www.worldcat.org/oclc/174198382", "https://stackedboxes.org/2017/05/01/acklams-normal-quantile-function/"]}, "E-statistics": {"categories": ["All articles lacking reliable references", "Articles lacking reliable references from January 2011", "CS1 maint: Multiple names: authors list", "Statistical distance", "Statistical hypothesis testing", "Theory of probability distributions"], "title": "Energy distance", "method": "E-statistics", "url": "https://en.wikipedia.org/wiki/Energy_distance", "summary": "Energy distance is a statistical distance between probability distributions. If X and Y are independent random vectors in Rd with cumulative distribution functions (cdf) F and G respectively, then the energy distance between the distributions F and G is defined to be the square root of\n\n \n \n \n \n D\n \n 2\n \n \n (\n F\n ,\n G\n )\n =\n 2\n E\n \u2061\n \u2016\n X\n \u2212\n Y\n \u2016\n \u2212\n E\n \u2061\n \u2016\n X\n \u2212\n \n X\n \u2032\n \n \u2016\n \u2212\n E\n \u2061\n \u2016\n Y\n \u2212\n \n Y\n \u2032\n \n \u2016\n \u2265\n 0\n ,\n \n \n {\\displaystyle D^{2}(F,G)=2\\operatorname {E} \\|X-Y\\|-\\operatorname {E} \\|X-X'\\|-\\operatorname {E} \\|Y-Y'\\|\\geq 0,}\n where (X, X', Y, Y') are independent, the cdf of X and X' is F, the cdf of Y and Y' is G, \n \n \n \n E\n \n \n {\\displaystyle \\operatorname {E} }\n is the expected value, and || . || denotes the length of a vector. Energy distance satisfies all axioms of a metric thus energy distance characterizes the equality of distributions: D(F,G) = 0 if and only if F = G.\nEnergy distance for statistical applications was introduced in 1985 by G\u00e1bor J. Sz\u00e9kely, who proved that for real-valued random variables \n \n \n \n \n D\n \n 2\n \n \n (\n F\n ,\n G\n )\n \n \n {\\displaystyle D^{2}(F,G)}\n is exactly twice Harald Cram\u00e9r's distance:\n\n \n \n \n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n (\n F\n (\n x\n )\n \u2212\n G\n (\n x\n )\n \n )\n \n 2\n \n \n \n d\n x\n .\n \n \n {\\displaystyle \\int _{-\\infty }^{\\infty }(F(x)-G(x))^{2}\\,dx.}\n For a simple proof of this equivalence, see Sz\u00e9kely (2002).In higher dimensions, however, the two distances are different because the energy distance is rotation invariant while Cram\u00e9r's distance is not. (Notice that Cram\u00e9r's distance is not the same as the distribution-free Cramer-von-Mises criterion.)", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ArXiv", "Borel sigma algebra", "Brownian covariance", "Change detection", "Convergence of random variables", "Cramer-von-Mises criterion", "Cumulative distribution function", "Digital object identifier", "Distance correlation", "Distances", "Distribution-free", "Euclidean norm", "Expected value", "G\u00e1bor J. Sz\u00e9kely", "Harald Cram\u00e9r", "Heavenly body", "Hierarchical clustering", "International Standard Book Number", "International Standard Serial Number", "Karolinum Press", "Kernel methods", "Machine learning", "Measurable space", "Metric (mathematics)", "Metric space", "Multivariate normal distribution", "Normal random variable", "Null hypothesis", "Potential energy", "Power law", "Probability distributions", "Probability measure", "PubMed Identifier", "R (programming language)", "Scoring rule", "Stable distribution", "Statistical distance", "Statistical sample", "Statistical test", "Taxicab geometry"], "references": ["http://www.sciencedirect.com/science/article/B6TGP-4WNXV3R-2/2/53ad7cb172888e652efe6fa9ab7213de", "http://www.sciencedirect.com/science/article/B6V18-4W4JDK7-7/2/67f1359392f5707961680dba01fd06cf", "http://www.sciencedirect.com/science/article/pii/S0378375813000633", "http://personal.bgsu.edu/~mrizzo/energy/MVN-GOF-2005.pdf", "http://personal.bgsu.edu/~mrizzo/energy/Szekely-E-statistics.pdf", "http://personal.bgsu.edu/~mrizzo/energy/reprint-ksamples.pdf", "http://www.eecs.harvard.edu/~syrah/nc/icdcs06.pdf", "http://faculty.washington.edu/dbp/PDFFILES/tr534.pdf", "http://www.stat.washington.edu/people/raftery/Research/PDF/Gneiting2007jasa.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/1154085", "http://www.ncbi.nlm.nih.gov/pubmed/19640752", "http://arxiv.org/abs/1106.5758", "http://arxiv.org/abs/1207.6076", "http://arxiv.org/abs/1806.05514", "http://doi.org/10.1016/j.jmgm.2009.06.006", "http://doi.org/10.1016/j.jmva.2003.12.002", "http://doi.org/10.1016/j.sigpro.2009.04.011", "http://doi.org/10.1109/ICDCS.2006.79", "http://doi.org/10.1198/016214506000001437", "http://doi.org/10.1214/12-aop803", "http://doi.org/10.1214/13-aos1140", "http://projecteuclid.org/euclid.aop/1378991840", "http://projecteuclid.org/euclid.aos/1383661264", "http://www.worldcat.org/issn/0165-1684", "http://eprints.whiterose.ac.uk/10328/1/Willett_10328.pdf", "https://arxiv.org/abs/1806.05514", "https://arxiv.org/pdf/0803.4101", "https://arxiv.org/pdf/1010.0297", "https://arxiv.org/pdf/1011.2288", "https://arxiv.org/pdf/1106.5758.pdf", "https://cran.r-project.org/package=energy"]}, "Bertrand's ballot theorem": {"categories": ["All articles lacking in-text citations", "Articles containing proofs", "Articles lacking in-text citations from June 2012", "Enumerative combinatorics", "Probability problems", "Probability theorems", "Theorems in combinatorics"], "title": "Bertrand's ballot theorem", "method": "Bertrand's ballot theorem", "url": "https://en.wikipedia.org/wiki/Bertrand%27s_ballot_theorem", "summary": "In combinatorics, Bertrand's ballot problem is the question: \"In an election where candidate A receives p votes and candidate B receives q votes with p > q, what is the probability that A will be strictly ahead of B throughout the count?\" The answer is\n\n \n \n \n \n \n \n p\n \u2212\n q\n \n \n p\n +\n q\n \n \n \n .\n \n \n {\\displaystyle {\\frac {p-q}{p+q}}.}\n The result was first published by W. A. Whitworth in 1878, but is named after Joseph Louis Fran\u00e7ois Bertrand who rediscovered it in 1887.In Bertrand's original paper, he sketches a proof based on a general formula for the number of favourable sequences using a recursion relation. He remarks that it seems probable that such a simple result could be proved by a more direct method. Such a proof was given by D\u00e9sir\u00e9 Andr\u00e9, based on the observation that the unfavourable sequences can be divided into two equally probable cases, one of which (the case where B receives the first vote) is easily computed; he proves the equality by an explicit bijection. A variation of his method is popularly known as Andr\u00e9's reflection method, although Andr\u00e9 did not use any reflections.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/AndreReflection.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Bijection", "Binomial coefficient", "Bruce Reed (mathematician)", "Catalan number", "Combinatorics", "D\u00e9sir\u00e9 Andr\u00e9", "Election", "Eric W. Weisstein", "Integer", "International Standard Book Number", "Joseph Louis Fran\u00e7ois Bertrand", "Lattice path", "L\u00e1szl\u00f3 Lov\u00e1sz", "MathWorld", "Mathematical induction", "Probability", "Random walk", "Recursion relation", "William Allen Whitworth", "William Feller"], "references": ["http://www.dms.umontreal.ca/~addario/papers/btsurvey.pdf", "http://mathworld.wolfram.com/BallotProblem.html", "http://webspace.ship.edu/msrenault/ballotproblem/", "http://webspace.ship.edu/msrenault/ballotproblem/monthly358-363-renault.pdf", "http://www.jehps.net/Decembre2006/Bru.pdf", "https://books.google.com/books?id=kIKW18ENfUMC"]}, "Bootstrap aggregating": {"categories": ["Computational statistics", "Ensemble learning", "Machine learning algorithms"], "title": "Bootstrap aggregating", "method": "Bootstrap aggregating", "url": "https://en.wikipedia.org/wiki/Bootstrap_aggregating", "summary": "Bootstrap aggregating, also called bagging, is a machine learning ensemble meta-algorithm designed to improve the stability and accuracy of machine learning algorithms used in statistical classification and regression. It also reduces variance and helps to avoid overfitting. Although it is usually applied to decision tree methods, it can be used with any type of method. Bagging is a special case of the model averaging approach.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/d/de/Ozone.png", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Boosting (machine learning)", "Boosting (meta-algorithm)", "Bootstrap (statistics)", "Bootstrapping (statistics)", "CURE data clustering algorithm", "Canonical correlation analysis", "CiteSeerX", "Classification and regression tree", "Cluster analysis", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "Cross-validation (statistics)", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Digital object identifier", "Dimensionality reduction", "E (mathematical constant)", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature engineering", "Feature learning", "Gated recurrent unit", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "Independent component analysis", "International Conference on Machine Learning", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Learning to rank", "Leo Breiman", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Local regression", "Logistic regression", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Mean-shift", "Meta-algorithm", "Multilayer perceptron", "Naive Bayes classifier", "Non-negative matrix factorization", "OPTICS algorithm", "Occam learning", "Online machine learning", "Outline of machine learning", "Overfitting", "Ozone", "Perceptron", "Peter Rousseeuw", "Prime (symbol)", "Principal component analysis", "Probability distribution", "Probably approximately correct learning", "Q-learning", "R (programming language)", "Random forest", "Random subspace method", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Resampled efficient frontier", "Restricted Boltzmann machine", "Sampling (statistics)", "Self-organizing map", "Semi-supervised learning", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Training set", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory", "Variance"], "references": ["http://people.csail.mit.edu/rivest/pubs/APR07.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.9399", "http://doi.org/10.1007%2FBF00058655", "https://arxiv.org/list/cs.LG/recent", "https://cran.r-project.org/package=adabag"]}, "Chi-squared distribution": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from September 2011", "Articles with unsourced statements from January 2016", "Infinitely divisible probability distributions", "Normal distribution", "Pages using deprecated image syntax"], "title": "Chi-squared distribution", "method": "Chi-squared distribution", "url": "https://en.wikipedia.org/wiki/Chi-squared_distribution", "summary": "In probability theory and statistics, the chi-squared distribution (also chi-square or \u03c72-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. The chi-square distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing or in construction of confidence intervals. When it is being distinguished from the more general noncentral chi-squared distribution, this distribution is sometimes called the central chi-squared distribution.\nThe chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also use this distribution, such as Friedman's analysis of variance by ranks.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2a/Chernoff-bound.svg", "https://upload.wikimedia.org/wikipedia/commons/0/01/Chi-square_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/3/35/Chi-square_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/en/9/96/Chi_on_SAS.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARGUS distribution", "Abramowitz and Stegun", "Analysis of variance", "Anders Hald", "Annals of Statistics", "Approximation", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Binomial test", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Characteristic function (probability theory)", "Chernoff bound", "Chi-squared test", "Chi2 (band)", "Chi (letter)", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Cochran's theorem", "Cochran\u2013Mantel\u2013Haenszel statistics", "Compound Poisson distribution", "Confidence interval", "Contingency tables", "Convergence of random variables", "Conway\u2013Maxwell\u2013Poisson distribution", "Covariance matrix", "Cumulant", "Cumulative distribution function", "Dagum distribution", "Data analysis", "Davis distribution", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Differential entropy", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Encyclopedia of Mathematics", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "F. R. Helmert", "Fisher's exact test", "Fisher's method", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Friedman test", "Friedrich Robert Helmert", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized chi-squared distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Goodness of fit", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Hypothesis testing", "I.i.d.", "Idempotent matrix", "Independence (probability theory)", "Independent and identically distributed random variables", "Inferential statistics", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irene Stegun", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Karl Pearson", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Library of Congress Control Number", "Likelihood-ratio test", "Linear regression", "List of probability distributions", "List of statistical packages", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Lower incomplete gamma function", "L\u00e9vy distribution", "Magnetic resonance imaging", "Marchenko\u2013Pastur distribution", "MathWorld", "Mathematical Reviews", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Michiel Hazewinkel", "Milton Abramowitz", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Neyman\u2013Pearson lemma", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral chi distribution", "Noncentral t-distribution", "Norm (mathematics)", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "P-value", "Parabolic fractal distribution", "Pareto distribution", "Particular values of the gamma function", "Pearson's chi-squared test", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability-generating function", "Probability density function", "Probability distribution", "Probability theory", "Proceedings of the National Academy of Sciences of the United States of America", "Proofs related to chi-squared distribution", "PubMed Central", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quadratic form", "Quantile function", "R. A. Fisher", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rank (linear algebra)", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Reduced chi-squared statistic", "Regularized gamma function", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Sampling distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Spreadsheet", "Stable distribution", "Standard deviation", "Standard normal", "Standard normal distribution", "Statistical independence", "Statistical significance", "Statistically independent", "Statistics", "Student's t-distribution", "Support (mathematics)", "Symmetric matrix", "T-statistic", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "William Palin Elderton", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.math.sfu.ca/~cbm/aands/page_940.htm", "http://www.planetmathematics.com/CentralChiDistr.pdf", "http://www.r-tutor.com/elementary-statistics/probability-distributions/chi-squared-distribution", "http://jeff560.tripod.com/c.html", "http://demonstrations.wolfram.com/StatisticsAssociatedWithNormalSamples/", "http://mathworld.wolfram.com/Chi-SquaredDistribution.html", "http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN599415665_0021&DMDID=DMDLOG_0018", "http://gdz.sub.uni-goettingen.de/dms/load/toc/?PPN=PPN599415665_0021", "http://adsabs.harvard.edu/abs/1931PNAS...17..684W", "http://www2.lv.psu.edu/jxm57/irp/chisquar.html", "http://cseweb.ucsd.edu/~dasgupta/papers/jl.pdf", "http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm", "http://lccn.loc.gov/64-60036", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076144", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm", "http://www.ams.org/mathscinet-getitem?mr=0167642", "http://arxiv.org/abs/1505.01957", "http://doi.org/10.1002%2Frsa.10073", "http://doi.org/10.1073%2Fpnas.17.12.684", "http://doi.org/10.1088%2F1751-8113%2F46%2F50%2F505202", "http://doi.org/10.1093%2Fbiomet%2F1.2.155", "http://doi.org/10.1109%2FTASLP.2017.2757601", "http://doi.org/10.1214%2F15-aos1407", "http://doi.org/10.2307%2F1164752", "http://ieeexplore.ieee.org/document/8052578/", "http://www.jstor.org/stable/2983618", "http://www.pnas.org/content/17/12/684.full.pdf+html", "https://lccn.loc.gov/65012253", "https://arxiv.org/pdf/1505.01957.pdf", "https://dx.doi.org/10.1016/j.ejmp.2014.05.002", "https://www.encyclopediaofmath.org/index.php?title=Chi-squared_distribution", "https://www.jstor.org/stable/1402731?seq=3", "https://www.jstor.org/stable/2348373"]}, "Bayesian inference in marketing": {"categories": ["All orphaned articles", "Applications of Bayesian inference", "Market research", "Orphaned articles from April 2014"], "title": "Bayesian inference in marketing", "method": "Bayesian inference in marketing", "url": "https://en.wikipedia.org/wiki/Bayesian_inference_in_marketing", "summary": "In marketing, Bayesian inference allows for decision making and market research evaluation under uncertainty and with limited data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/18/Bayes%27_Theorem_MMB_01.jpg", "https://upload.wikimedia.org/wikipedia/en/6/6c/Wiki_letter_w.svg"], "links": ["Advertising", "Bayes' theorem", "Bayesian decision theory", "Bayesian inference", "Bayesian probability", "Bayes\u2019 theorem", "Computer simulation", "Conditional probabilities", "Counter intuitive", "Data", "Decision theory", "Decision trees", "Experiment", "Falsifiability", "Frequentist probability", "Inferences", "Internet", "Iteration", "JSTOR", "Journal of the Royal Statistical Society, Series C", "LaplacesDemon", "Likelihood function", "Logic", "Logistics", "Market (economics)", "Market research", "Marketing", "Marketing mix", "Markov Chain Monte Carlo", "New product development", "Normal distribution", "Numerical data", "Objectivity (philosophy)", "Pierre Simon Laplace", "Posterior probability", "Pricing", "Prior probability", "Probability", "Probability distributions", "Promotion (marketing)", "Qualitative data", "R (programming language)", "Richard Price", "Risk perception", "Statistics", "Strategy", "Subjectivity", "Systematic error", "Thomas Bayes", "Weighted mean", "WinBUGS", "World wide web"], "references": ["http://edwardbetts.com/find_link?q=Bayesian_inference_in_marketing", "http://search.proquest.com/docview/274829688", "http://redwood.berkeley.edu/bruno/npb163/bayes.pdf", "https://support.sas.com/documentation/cdl/en/statug/63033/PDF/default/statug.pdf", "https://www.jstor.org/stable/2281640", "https://www.jstor.org/stable/2985299"]}, "Concomitant (statistics)": {"categories": ["Theory of probability distributions"], "title": "Concomitant (statistics)", "method": "Concomitant (statistics)", "url": "https://en.wikipedia.org/wiki/Concomitant_(statistics)", "summary": "In statistics, the concept of a concomitant, also called the induced order statistic, arises when one sorts the members of a random sample according to corresponding values of another random sample.\nLet (Xi, Yi), i = 1, . . ., n be a random sample from a bivariate distribution. If the sample is ordered by the Xi, then the Y-variate associated with Xr:n will be denoted by Y[r:n] and termed the concomitant of the rth order statistic.\nSuppose the parent bivariate distribution having the cumulative distribution function F(x,y) and its probability density function f(x,y), then the probability density function of rth concomitant \n \n \n \n \n Y\n \n [\n r\n :\n n\n ]\n \n \n \n \n {\\displaystyle Y_{[r:n]}}\n for \n \n \n \n 1\n \u2264\n r\n \u2264\n n\n \n \n {\\displaystyle 1\\leq r\\leq n}\n is\n\n \n \n \n \n f\n \n \n Y\n \n [\n r\n :\n n\n ]\n \n \n \n \n (\n y\n )\n =\n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n \n f\n \n Y\n \u2223\n X\n \n \n (\n y\n \n |\n \n x\n )\n \n f\n \n \n X\n \n r\n :\n n\n \n \n \n \n (\n x\n )\n \n \n d\n \n x\n \n \n {\\displaystyle f_{Y_{[r:n]}}(y)=\\int _{-\\infty }^{\\infty }f_{Y\\mid X}(y|x)f_{X_{r:n}}(x)\\,\\mathrm {d} x}\n \nIf all \n \n \n \n (\n \n X\n \n i\n \n \n ,\n \n Y\n \n i\n \n \n )\n \n \n {\\displaystyle (X_{i},Y_{i})}\n are assumed to be i.i.d., then for \n \n \n \n 1\n \u2264\n \n r\n \n 1\n \n \n <\n \u22ef\n <\n \n r\n \n k\n \n \n \u2264\n n\n \n \n {\\displaystyle 1\\leq r_{1}<\\cdots <r_{k}\\leq n}\n , the joint density for \n \n \n \n \n (\n \n \n Y\n \n [\n \n r\n \n 1\n \n \n :\n n\n ]\n \n \n ,\n \u22ef\n ,\n \n Y\n \n [\n \n r\n \n k\n \n \n :\n n\n ]\n \n \n \n )\n \n \n \n {\\displaystyle \\left(Y_{[r_{1}:n]},\\cdots ,Y_{[r_{k}:n]}\\right)}\n is given by\n\n \n \n \n \n f\n \n \n Y\n \n [\n \n r\n \n 1\n \n \n :\n n\n ]\n \n \n ,\n \u22ef\n ,\n \n Y\n \n [\n \n r\n \n k\n \n \n :\n n\n ]\n \n \n \n \n (\n \n y\n \n 1\n \n \n ,\n \u22ef\n ,\n \n y\n \n k\n \n \n )\n =\n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n \n \u222b\n \n \u2212\n \u221e\n \n \n \n x\n \n k\n \n \n \n \n \u22ef\n \n \u222b\n \n \u2212\n \u221e\n \n \n \n x\n \n 2\n \n \n \n \n \n \u220f\n \n i\n =\n 1\n \n \n k\n \n \n \n f\n \n Y\n \u2223\n X\n \n \n (\n \n y\n \n i\n \n \n \n |\n \n \n x\n \n i\n \n \n )\n \n f\n \n \n X\n \n \n r\n \n 1\n \n \n :\n n\n \n \n ,\n \u22ef\n ,\n \n X\n \n \n r\n \n k\n \n \n :\n n\n \n \n \n \n (\n \n x\n \n 1\n \n \n ,\n \u22ef\n ,\n \n x\n \n k\n \n \n )\n \n d\n \n \n x\n \n 1\n \n \n \u22ef\n \n d\n \n \n x\n \n k\n \n \n \n \n {\\displaystyle f_{Y_{[r_{1}:n]},\\cdots ,Y_{[r_{k}:n]}}(y_{1},\\cdots ,y_{k})=\\int _{-\\infty }^{\\infty }\\int _{-\\infty }^{x_{k}}\\cdots \\int _{-\\infty }^{x_{2}}\\prod _{i=1}^{k}f_{Y\\mid X}(y_{i}|x_{i})f_{X_{r_{1}:n},\\cdots ,X_{r_{k}:n}}(x_{1},\\cdots ,x_{k})\\mathrm {d} x_{1}\\cdots \\mathrm {d} x_{k}}\n \nThat is, in general, the joint concomitants of order statistics \n \n \n \n \n (\n \n \n Y\n \n [\n \n r\n \n 1\n \n \n :\n n\n ]\n \n \n ,\n \u22ef\n ,\n \n Y\n \n [\n \n r\n \n k\n \n \n :\n n\n ]\n \n \n \n )\n \n \n \n {\\displaystyle \\left(Y_{[r_{1}:n]},\\cdots ,Y_{[r_{k}:n]}\\right)}\n is dependent, but are conditionally independent given \n \n \n \n \n X\n \n \n r\n \n 1\n \n \n :\n n\n \n \n =\n \n x\n \n 1\n \n \n ,\n \u22ef\n ,\n \n X\n \n \n r\n \n k\n \n \n :\n n\n \n \n =\n \n x\n \n k\n \n \n \n \n {\\displaystyle X_{r_{1}:n}=x_{1},\\cdots ,X_{r_{k}:n}=x_{k}}\n for all k where \n \n \n \n \n x\n \n 1\n \n \n \u2264\n \u22ef\n \u2264\n \n x\n \n k\n \n \n \n \n {\\displaystyle x_{1}\\leq \\cdots \\leq x_{k}}\n . The conditional distribution of the joint concomitants can be derived from the above result by comparing the formula in marginal distribution and hence\n\n \n \n \n \n f\n \n \n Y\n \n [\n \n r\n \n 1\n \n \n :\n n\n ]\n \n \n ,\n \u22ef\n ,\n \n Y\n \n [\n \n r\n \n k\n \n \n :\n n\n ]\n \n \n \u2223\n \n X\n \n \n r\n \n 1\n \n \n :\n n\n \n \n \u22ef\n \n X\n \n \n r\n \n k\n \n \n :\n n\n \n \n \n \n (\n \n y\n \n 1\n \n \n ,\n \u22ef\n ,\n \n y\n \n k\n \n \n \n |\n \n \n x\n \n 1\n \n \n ,\n \u22ef\n ,\n \n x\n \n k\n \n \n )\n =\n \n \u220f\n \n i\n =\n 1\n \n \n k\n \n \n \n f\n \n Y\n \u2223\n X\n \n \n (\n \n y\n \n i\n \n \n \n |\n \n \n x\n \n i\n \n \n )\n \n \n {\\displaystyle f_{Y_{[r_{1}:n]},\\cdots ,Y_{[r_{k}:n]}\\mid X_{r_{1}:n}\\cdots X_{r_{k}:n}}(y_{1},\\cdots ,y_{k}|x_{1},\\cdots ,x_{k})=\\prod _{i=1}^{k}f_{Y\\mid X}(y_{i}|x_{i})}", "images": [], "links": ["Cumulative distribution function", "International Standard Book Number", "Marginal distribution", "Order statistic", "Probability density function", "Statistics", "Zentralblatt MATH"], "references": ["http://zbmath.org/?format=complete&q=an:1053.62060"]}, "Central limit theorem (illustration)": {"categories": ["Central limit theorem"], "title": "Illustration of the central limit theorem", "method": "Central limit theorem (illustration)", "url": "https://en.wikipedia.org/wiki/Illustration_of_the_central_limit_theorem", "summary": "This article gives two concrete illustrations of the central limit theorem. Both involve the sum of independent and identically-distributed random variables and show how the probability distribution of the sum approaches the normal distribution as the number of terms in the sum increases.\nThe first illustration involves a continuous probability distribution, for which the random variables have a probability density function.\nThe second illustration, for which most of the computation can be done by hand, involves a discrete probability distribution, which is characterized by a probability mass function.\nA free full-featured interactive simulation that allows the user to set up various distributions and adjust the sampling parameters is available through the External links section at the bottom of this page.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a6/Central_limit_thm_1.png", "https://upload.wikimedia.org/wikipedia/commons/f/f8/Central_limit_thm_2.png", "https://upload.wikimedia.org/wikipedia/commons/6/69/Central_limit_thm_3.png", "https://upload.wikimedia.org/wikipedia/commons/8/85/Central_limit_thm_4.png", "https://upload.wikimedia.org/wikipedia/commons/7/72/Central_theorem_2.svg"], "links": ["Bar graph", "Central limit theorem", "Continuity correction", "Continuous probability distribution", "Convolution", "Discrete Fourier transform", "Discrete probability distribution", "Discrete random variable", "Independent and identically-distributed random variables", "Independent identically distributed variables", "Monte Carlo method", "Normal distribution", "Piecewise", "Pointwise product", "Polynomial", "Probability density function", "Probability distribution", "Probability mass function", "Square root of 2"], "references": ["http://www.statisticalengineering.com/central_limit_theorem.html", "http://mathworld.wolfram.com/UniformSumDistribution.html", "http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem", "http://blog.vctr.me/posts/central-limit-theorem.html", "http://www.vias.org/simulations/simusoft_cenlimit.html"]}, "Dyadic distribution": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from July 2010", "Articles with unsourced statements from August 2010", "Data compression", "Discrete distributions", "Types of probability distributions"], "title": "Dyadic distribution", "method": "Dyadic distribution", "url": "https://en.wikipedia.org/wiki/Dyadic_distribution", "summary": "A dyadic (or 2-adic) distribution is a specific type of discrete or categorical probability distribution that is of some theoretical importance in data compression.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Data compression", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Entropy", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Integer", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Probability mass function", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": []}, "Graphical model": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from May 2017", "Bayesian statistics", "Graphical models"], "title": "Graphical model", "method": "Graphical model", "url": "https://en.wikipedia.org/wiki/Graphical_model", "summary": "A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics\u2014particularly Bayesian statistics\u2014and machine learning.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/39/Graph_model.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Ancestral graph", "Anderson\u2013Darling test", "Annals of Statistics", "Anomaly detection", "Arithmetic mean", "Artificial neural network", "Artificial neural networks", "Association rule 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"Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimensionality reduction", "Directed acyclic graph", "Discriminative model", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Edoardo Airoldi", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical risk minimization", "Engineering statistics", "Ensemble learning", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expectation\u2013maximization algorithm", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factor graph", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feature engineering", "Feature learning", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist 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Machine Learning Research", "Judea Pearl", "Junction tree algorithm", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Learning to rank", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local outlier factor", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Long short-term memory", "Loss function", "Low-density parity-check codes", "Lp space", "M-estimator", "Machine Learning (journal)", "Machine learning", "Mann\u2013Whitney U 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"Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recurrent neural network", "Regression analysis", "Regression model validation", "Reinforcement learning", "Relevance vector machine", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted Boltzmann machine", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Self-organizing map", "Semi-supervised learning", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Speech recognition", "Standard deviation", "Standard error", "State\u2013action\u2013reward\u2013state\u2013action", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation model", "Structural equation modeling", "Structured prediction", "Student's t-test", "Sufficient statistic", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Time domain", "Time series", "Tolerance interval", "Tree (graph theory)", "Trend estimation", "U-Net", "U-statistic", "Undirected graph", "Uniformly most powerful test", "Unsupervised learning", "V-statistic", "Vapnik\u2013Chervonenkis theory", "Variable-order Markov model", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "Zentralblatt MATH"], "references": ["http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html", "http://sandeep-aparajit.blogspot.com/2013/06/how-does-conditional-random-field-crf.html", "http://research.microsoft.com/en-us/um/people/heckerman/tutorial.pdf", "http://www.cedar.buffalo.edu/~srihari/CSE574", "http://www.cs.cmu.edu/~epxing/Class/10708/", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.4906", "http://pgm.stanford.edu/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2134967", "http://www.ncbi.nlm.nih.gov/pubmed/18069887", "http://www.ams.org/mathscinet-getitem?mr=0965765", "http://www.ams.org/mathscinet-getitem?mr=1096723", "http://www.ams.org/mathscinet-getitem?mr=1697175", "http://www.ams.org/mathscinet-getitem?mr=1926166", "http://www.ams.org/mathscinet-getitem?mr=2247587", "http://doi.org/10.1038%2Fnature14541", "http://doi.org/10.1214%2F088342304000000026", "http://doi.org/10.1214%2Faos%2F1031689015", "http://doi.org/10.1371%2Fjournal.pcbi.0030252", "http://www.jstor.org/stable/4616181", "http://zbmath.org/?format=complete&q=an:1033.60008", "https://www.microsoft.com/en-us/research/wp-content/uploads/2016/05/Bishop-PRML-sample.pdf", "https://www.nature.com/articles/nature14541", "https://www.springer.com/us/book/9780387310732", "https://arxiv.org/list/cs.LG/recent"]}, "Lincoln index": {"categories": ["Ecological techniques", "Environmental statistics", "Estimation methods"], "title": "Lincoln index", "method": "Lincoln index", "url": "https://en.wikipedia.org/wiki/Lincoln_index", "summary": "The Lincoln index is a statistical measure used in several fields to estimate the number of cases that have not yet been observed, based on two independent sets of observed cases. Described by Frederick Charles Lincoln in 1930, it is also sometimes known as the Lincoln-Petersen method after C.G. Johannes Petersen who was the first to use the related mark and recapture method.", "images": [], "links": ["C.G. Johannes Petersen", "Computational linguistics", "Digital object identifier", "Drake equation", "Estimator", "Frederick Charles Lincoln", "JSTOR", "Mark and recapture", "Sampling Theory", "Zipf's Law"], "references": ["http://www.sbs.utexas.edu/jcabbott/courses/bio208web/labs/populations/populations.htm", "http://doi.org/10.2307%2F2402438", "http://www.jstor.org/stable/3543331", "https://archive.org/details/calculatingwater118linc"]}, "Monte Carlo method for photon transport": {"categories": ["CS1 maint: Extra text: editors list", "Monte Carlo methods", "Photonics"], "title": "Monte Carlo method for photon transport", "method": "Monte Carlo method for photon transport", "url": "https://en.wikipedia.org/wiki/Monte_Carlo_method_for_photon_transport", "summary": "Modeling photon propagation with Monte Carlo methods is a flexible yet rigorous approach to simulate photon transport. In the method, local rules of photon transport are expressed as probability distributions which describe the step size of photon movement between sites of photon-tissue interaction and the angles of deflection in a photon's trajectory when a scattering event occurs. This is equivalent to modeling photon transport analytically by the radiative transfer equation (RTE), which describes the motion of photons using a differential equation. However, closed-form solutions of the RTE are often not possible; for some geometries, the diffusion approximation can be used to simplify the RTE, although this, in turn, introduces many inaccuracies, especially near sources and boundaries. In contrast, Monte Carlo simulations can be made arbitrarily accurate by increasing the number of photons traced. For example, see the movie, where a Monte Carlo simulation of a pencil beam incident on a semi-infinite medium models both the initial ballistic photon flow and the later diffuse propagation.\n\nThe Monte Carlo method is necessarily statistical and therefore requires significant computation time to achieve precision. In addition Monte Carlo simulations can keep track of multiple physical quantities simultaneously, with any desired spatial and temporal resolution. This flexibility makes Monte Carlo modeling a powerful tool. Thus, while computationally inefficient, Monte Carlo methods are often considered the standard for simulated measurements of photon transport for many biomedical applications. \n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/1/19/MonteCarlo.png", "https://upload.wikimedia.org/wikipedia/en/6/6c/MonteCarloSemiInf.gif"], "links": ["Absorption coefficient", "Beer\u2013Lambert law", "Bibcode", "Cartesian coordinate system", "Confocal microscopy", "Convolution", "Convolution for optical broad-beam responses in scattering media", "Diffuse optical imaging", "Digital object identifier", "Dirac delta function", "Green's functions", "Inverse transform sampling", "Monte Carlo method", "Monte Carlo methods for electron transport", "Optical coherence tomography", "Optical path length", "Pencil beam", "Photoacoustic imaging in biomedicine", "Photodynamic therapy", "Pseudorandom number generator", "Radiation therapy", "Radiative transfer equation and diffusion theory for photon transport in biological tissue", "Russian roulette", "Semi-infinite", "Two-photon excitation microscopy", "Unit vector"], "references": ["http://bmp.hust.edu.cn/GPU_Cluster/GPU_Cluster_MCML.HTM", "http://scratchapixel.com/old/lessons/3d-basic-lessons/lesson-17-monte-carlo-methods-in-practice/monte-carlo-simulation-2/", "http://adsabs.harvard.edu/abs/1994MedPh..21.1081W", "http://adsabs.harvard.edu/abs/2008JBO....13f0504A", "http://adsabs.harvard.edu/abs/2009OExpr..1720178F", "http://adsabs.harvard.edu/abs/2010OExpr..18.6811R", "http://omlc.ogi.edu/software/mc/", "http://labs.seas.wustl.edu/bme/Wang/epub/1994LWMPOpt.pdf", "http://labs.seas.wustl.edu/bme/Wang/epub/1995LWCMPBMcml.pdf", "http://labs.seas.wustl.edu/bme/Wang/epub/1997LWCMPBConv.pdf", "http://labs.seas.wustl.edu/bme/Wang/mc.html", "http://www.lighttransport.net/", "http://doi.org/10.1016%2F0169-2607(95)01640-F", "http://doi.org/10.1016%2FS0169-2607(97)00021-7", "http://doi.org/10.1117%2F1.3041496", "http://doi.org/10.1118%2F1.597351", "http://doi.org/10.1364%2Fboe.2.002461", "http://doi.org/10.1364%2Foe.17.020178", "http://doi.org/10.1364%2Foe.18.006811", "http://www.opticsinfobase.org/boe/abstract.cfm?uri=boe-2-9-2461", "http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-20178", "http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-6811", "http://www.atomic.physics.lu.se/fileadmin/atomfysik/Biophotonics/Publications/Alerstam2008_JBOLetters.pdf", "https://web.archive.org/web/20101031052710/http://www.atomic.physics.lu.se/biophotonics/our_research/monte_carlo_simulations/"]}, "Location-scale family": {"categories": ["Location-scale family probability distributions", "Parametric statistics", "Types of probability distributions"], "title": "Location\u2013scale family", "method": "Location-scale family", "url": "https://en.wikipedia.org/wiki/Location%E2%80%93scale_family", "summary": "In probability theory, especially in mathematical statistics, a location\u2013scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter. For any random variable \n \n \n \n X\n \n \n {\\displaystyle X}\n whose probability distribution function belongs to such a family, the distribution function of \n \n \n \n Y\n \n \n \n \n =\n \n \n d\n \n \n \n \n a\n +\n b\n X\n \n \n {\\displaystyle Y{\\stackrel {d}{=}}a+bX}\n also belongs to the family (where \n \n \n \n \n \n \n \n =\n \n \n d\n \n \n \n \n \n \n {\\displaystyle {\\stackrel {d}{=}}}\n means \"equal in distribution\"\u2014that is, \"has the same distribution as\"). Moreover, if \n \n \n \n X\n \n \n {\\displaystyle X}\n and \n \n \n \n Y\n \n \n {\\displaystyle Y}\n are two random variables whose distribution functions are members of the family, and assuming 1) existence of the first two moments and 2) \n \n \n \n X\n \n \n {\\displaystyle X}\n has zero mean and unit variance, then \n \n \n \n Y\n \n \n {\\displaystyle Y}\n can be written as \n \n \n \n Y\n \n \n \n \n =\n \n \n d\n \n \n \n \n \n \u03bc\n \n Y\n \n \n +\n \n \u03c3\n \n Y\n \n \n X\n \n \n {\\displaystyle Y{\\stackrel {d}{=}}\\mu _{Y}+\\sigma _{Y}X}\n , where \n \n \n \n \n \u03bc\n \n Y\n \n \n \n \n {\\displaystyle \\mu _{Y}}\n and \n \n \n \n \n \u03c3\n \n Y\n \n \n \n \n {\\displaystyle \\sigma _{Y}}\n are the mean and standard deviation of \n \n \n \n Y\n \n \n {\\displaystyle Y}\n .\nIn other words, a class \n \n \n \n \u03a9\n \n \n {\\displaystyle \\Omega }\n of probability distributions is a location\u2013scale family if for all cumulative distribution functions \n \n \n \n F\n \u2208\n \u03a9\n \n \n {\\displaystyle F\\in \\Omega }\n and any real numbers \n \n \n \n a\n \u2208\n \n R\n \n \n \n {\\displaystyle a\\in \\mathbb {R} }\n and \n \n \n \n b\n >\n 0\n \n \n {\\displaystyle b>0}\n , the distribution function \n \n \n \n G\n (\n x\n )\n =\n F\n (\n a\n +\n b\n x\n )\n \n \n {\\displaystyle G(x)=F(a+bx)}\n is also a member of \n \n \n \n \u03a9\n \n \n {\\displaystyle \\Omega }\n .\n\nIf \n \n \n \n X\n \n \n {\\displaystyle X}\n has a cumulative distribution function \n \n \n \n \n F\n \n X\n \n \n (\n x\n )\n =\n P\n (\n X\n \u2264\n x\n )\n \n \n {\\displaystyle F_{X}(x)=P(X\\leq x)}\n , then \n \n \n \n Y\n \n =\n \n a\n +\n b\n X\n \n \n {\\displaystyle Y{=}a+bX}\n has a cumulative distribution function \n \n \n \n \n F\n \n Y\n \n \n (\n y\n )\n =\n \n F\n \n X\n \n \n \n (\n \n \n \n y\n \u2212\n a\n \n b\n \n \n )\n \n \n \n {\\displaystyle F_{Y}(y)=F_{X}\\left({\\frac {y-a}{b}}\\right)}\n .\nIf \n \n \n \n X\n \n \n {\\displaystyle X}\n is a discrete random variable with probability mass function \n \n \n \n \n p\n \n X\n \n \n (\n x\n )\n =\n P\n (\n X\n =\n x\n )\n \n \n {\\displaystyle p_{X}(x)=P(X=x)}\n , then \n \n \n \n Y\n \n =\n \n a\n +\n b\n X\n \n \n {\\displaystyle Y{=}a+bX}\n is a discrete random variable with probability mass function \n \n \n \n \n p\n \n Y\n \n \n (\n y\n )\n =\n \n p\n \n X\n \n \n \n (\n \n \n \n y\n \u2212\n a\n \n b\n \n \n )\n \n \n \n {\\displaystyle p_{Y}(y)=p_{X}\\left({\\frac {y-a}{b}}\\right)}\n .\nIf \n \n \n \n X\n \n \n {\\displaystyle X}\n is a continuous random variable with probability density function \n \n \n \n \n f\n \n X\n \n \n (\n x\n )\n \n \n {\\displaystyle f_{X}(x)}\n , then \n \n \n \n Y\n \n =\n \n a\n +\n b\n X\n \n \n {\\displaystyle Y{=}a+bX}\n is a continuous random variable with probability density function \n \n \n \n \n f\n \n Y\n \n \n (\n y\n )\n =\n \n \n 1\n b\n \n \n \n f\n \n X\n \n \n \n (\n \n \n \n y\n \u2212\n a\n \n b\n \n \n )\n \n \n \n {\\displaystyle f_{Y}(y)={\\frac {1}{b}}f_{X}\\left({\\frac {y-a}{b}}\\right)}\n .In decision theory, if all alternative distributions available to a decision-maker are in the same location\u2013scale family, and the first two moments are finite, then a two-moment decision model can apply, and decision-making can be framed in terms of the means and the variances of the distributions.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARGUS distribution", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "American Economic Review", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous random variable", "Control chart", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Cumulative distribution functions", "Dagum distribution", "Data collection", "Davis distribution", "Decision theory", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete random variable", "Discrete uniform distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Ewens's sampling formula", "Expected value", "Experiment", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "Geostatistics", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hans-Werner Sinn", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabolic fractal distribution", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Proportional hazards model", "Psychometrics", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quantile function", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrix", "Random variable", "Random variate", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Review of Economic Studies", "Rice distribution", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable distribution", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Tracy\u2013Widom distribution", "Trend estimation", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Two-moment decision models", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Uniformly most powerful test", "Univariate distribution", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.jstor.org/stable/1804104", "http://www.jstor.org/stable/2297094", "http://www.randomservices.org/random/special/LocationScale.html"]}, "Lomax distribution": {"categories": ["Compound probability distributions", "Continuous distributions", "Pages using deprecated image syntax", "Probability distributions with non-finite variance"], "title": "Lomax distribution", "method": "Lomax distribution", "url": "https://en.wikipedia.org/wiki/Lomax_distribution", "summary": "The Lomax distribution, conditionally also called the Pareto Type II distribution, is a heavy-tail probability distribution used in business, economics, actuarial science, queueing theory and Internet traffic modeling. It is named after K. S. Lomax. It is essentially a Pareto distribution that has been shifted so that its support begins at zero.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c1/LomaxCDF.png", "https://upload.wikimedia.org/wikipedia/commons/6/6c/LomaxPDF.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Compound distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heavy tail", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "IEEE Communications Letters", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the American Statistical Association", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Power law", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.vosesoftware.com/content/ebook.pdf", "https://books.google.com/books?id=7wLGjyB128IC&pg=PA60", "https://www.jstor.org/stable/2281544"]}, "Standardised mortality rate": {"categories": ["Biostatistics", "Epidemiology", "Medical statistics", "Statistical ratios"], "title": "Standardized mortality ratio", "method": "Standardised mortality rate", "url": "https://en.wikipedia.org/wiki/Standardized_mortality_ratio", "summary": "In epidemiology, the standardized mortality ratio or SMR, is a quantity, expressed as either a ratio or percentage quantifying the increase or decrease in mortality of a study cohort with respect to the general population.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Age-specific mortality rate", "Analysis of variance", "Arsenic", "Asymptomatic carrier", "Auxology", "Bachelor of Science in Public Health", "Behavior change (public health)", "Behavioural change theories", "Biological hazard", "Biostatistics", "Bladder cancer", "Cancer", "Carl Rogers Darnall", "Case\u2013control study", "Centers for Disease Control and Prevention", "Chief Medical Officer", "Child mortality", "Cohort study", "Community health", "Confidence interval", "Council on Education for Public Health", "Crude death rate", "Cultural competence in health care", "Cumulative exposure", "Deviance (sociology)", "Diffusion of innovations", "Digital object identifier", "Disease surveillance", "Doctor of Public Health", "Drinking water", "Emergency sanitation", "Environmental health", "Epidemic", "Epidemiology", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Family planning", "Fecal\u2013oral route", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Genetically modified food", "Germ theory of disease", "Global health", "Globalization and disease", "Good agricultural practice", "Good manufacturing practice", "HACCP", "Hand washing", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Human factors and ergonomics", "Human nutrition", "Hygiene", "ISO 22000", "Infant mortality", "Infection control", "Injury prevention", "International Standard Book Number", "John Snow (physician)", "Joseph Lister", "Life insurance", "List of epidemics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "Margaret Sanger", "Mary Mallon", "Maternal health", "Medical anthropology", "Medical sociology", "Mental health", "Ministry of Health and Family Welfare", "Mortality rate", "Notifiable disease", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Open defecation", "Oral hygiene", "PRECEDE-PROCEED model", "P value", "Patient safety", "Patient safety organization", "Percentage", "Pharmaceutical policy", "Pharmacovigilance", "Population health", "Positive deviance", "Preventive healthcare", "Preventive nutrition", "Professional degrees of public health", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quarantine", "ROC curve", "Race and health", "Random variable", "Randomized controlled trial", "Ratio", "Regression analysis", "Relative risk", "Reproductive health", "Safe sex", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Sexually transmitted infection", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Sociology of health and illness", "Statistical hypothesis testing", "Statistical significance", "Student's t-test", "Theory of planned behavior", "Transtheoretical model", "Tropical disease", "Uncertainty", "United States Public Health Service", "Vaccination", "Vaccine trial", "Vector control", "Vulnerability index", "Waterborne diseases", "World Health Organization", "World Toilet Organization", "Z-test"], "references": ["http://www.dirk-taeger.de/pamcomp/index.html", "http://doi.org/10.1007%2F978-94-007-5989-3_22"]}, "Forecast error": {"categories": ["All articles needing additional references", "Articles needing additional references from June 2016", "Errors and residuals", "Forecasting", "Supply chain analytics"], "title": "Forecast error", "method": "Forecast error", "url": "https://en.wikipedia.org/wiki/Forecast_error", "summary": "In statistics, a forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest. Since the forecast error is derived from the same scale of data, comparisons between the forecast errors of different series can only be made when the series are on the same scale.In simple cases, a forecast is compared with an outcome at a single time-point and a summary of forecast errors is constructed over a collection of such time-points. Here the forecast may be assessed using the difference or using a proportional error. By convention, the error is defined using the value of the outcome minus the value of the forecast.\nIn other cases, a forecast may consist of predicted values over a number of lead-times; in this case an assessment of forecast error may need to consider more general ways of assessing the match between the time-profiles of the forecast and the outcome. If a main application of the forecast is to predict when certain thresholds will be crossed, one possible way of assessing the forecast is to use the timing-error\u2014the difference in time between when the outcome crosses the threshold and when the forecast does so. When there is interest in the maximum value being reached, assessment of forecasts can be done using any of:\n\nthe difference of times of the peaks;\nthe difference in the peak values in the forecast and outcome;\nthe difference between the peak value of the outcome and the value forecast for that time point.Forecast error can be a calendar forecast error or a cross-sectional forecast error, when we want to summarize the forecast error over a group of units. If we observe the average forecast error for a time-series of forecasts for the same product or phenomenon, then we call this a calendar forecast error or time-series forecast error. If we observe this for multiple products for the same period, then this is a cross-sectional performance error. Reference class forecasting has been developed to reduce forecast error. Combining forecasts has also been shown to reduce forecast error.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Calculating Demand Forecast Accuracy", "Errors and residuals in statistics", "Forecast bias", "Forecasting", "Forecasting accuracy", "Mean absolute percentage error", "Mean percentage error", "Mean squared error", "Mean squared prediction error", "Optimism bias", "Reference class forecasting", "Root mean squared error", "Statistics", "Time series", "Tracking signal"], "references": ["http://principlesofforecasting.com/paperpdf/Combining.pdf", "https://dl.dropbox.com/u/3662406/Articles/Graefe_et_al_Combining.pdf", "https://www.otexts.org/fpp/2/5"]}, "Belief propagation": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from April 2009", "Coding theory", "Graph algorithms", "Graphical models", "Use dmy dates from June 2013", "Webarchive template wayback links"], "title": "Belief propagation", "method": "Belief propagation", "url": "https://en.wikipedia.org/wiki/Belief_propagation", "summary": "Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each unobserved node, conditional on any observed nodes. Belief propagation is commonly used in artificial intelligence and information theory and has demonstrated empirical success in numerous applications including low-density parity-check codes, turbo codes, free energy approximation, and satisfiability.The algorithm was first proposed by Judea Pearl in 1982, who formulated it as an exact inference algorithm on trees, which was later extended to polytrees. While it is not exact on general graphs anymore, it has been shown to be a useful approximate algorithm.If X={Xi} is a set of discrete random variables with a joint mass function p, the marginal distribution of a single Xi is simply the summation of p over all other variables:\n\n \n \n \n \n p\n \n \n X\n \n i\n \n \n \n \n (\n \n x\n \n i\n \n \n )\n =\n \n \u2211\n \n \n \n x\n \n \u2032\n \n :\n \n x\n \n i\n \n \u2032\n \n \u2260\n \n x\n \n i\n \n \n \n \n p\n (\n \n \n x\n \n \u2032\n \n )\n .\n \n \n {\\displaystyle p_{X_{i}}(x_{i})=\\sum _{\\mathbf {x} ':x'_{i}\\neq x_{i}}p(\\mathbf {x} ').}\n However, this quickly becomes computationally prohibitive: if there are 100 binary variables, then one needs to sum over 299 \u2248 6.338 \u00d7 1029 possible values. By exploiting the polytree structure, belief propagation allows the marginals to be computed much more efficiently.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Algorithm", "Approximation error", "ArXiv", "Arg max", "Artificial intelligence", "Bayesian network", "Bayesian networks", "Bibcode", "Bipartite graph", "Cluster variation method", "Conjugate gradient method", "Cycle (graph theory)", "Diagonally dominant", "Diameter (graph theory)", "Digital object identifier", "Discrete probability distribution", "EXIT chart", "Factor graph", "Gauss\u2013Seidel method", "Generalized survey propagation", "Graph (discrete mathematics)", "Graph coloring", "Graphical model", "IEEE Signal Processing Magazine", "IEEE Trans. Signal Process.", "IEEE Transactions on Information Theory", "Inference", "Information theory", "Internal energy", "International Standard Book Number", "International Standard Serial Number", "Island algorithm", "Joint distribution", "Journal of Machine Learning Research", "Judea Pearl", "Junction tree algorithm", "Low-density parity-check codes", "Marginal distribution", "Markov random field", "Markov random fields", "Mathematical induction", "Maximum A Posteriori", "Monte Carlo method", "NP-complete", "NP-hard", "Neural Computation (journal)", "New Scientist", "Normal distribution", "Partition function (mathematics)", "Polytree", "Positive-definite matrix", "Probability mass function", "PubMed Identifier", "Random variable", "Ryoichi Kikuchi", "Satisfiability", "Sharp-P-complete", "Spectral radius", "Successive over-relaxation", "Survey propagation", "Thermodynamic free energy", "Thermodynamics", "Tree (graph theory)", "Turbo codes", "Variational Bayesian methods", "Viterbi algorithm", "Wayback Machine"], "references": ["http://www.merl.com/publications/TR2001-022/", "http://www.merl.com/publications/TR2004-040/", "http://research.microsoft.com/en-us/um/people/cmbishop/prml/pdf/Bishop-PRML-sample.pdf", "http://www.cs.cmu.edu/~bickson/gabp/index.html", "http://adsabs.harvard.edu/abs/1951PhRv...81..988K", "http://adsabs.harvard.edu/abs/1953JChPh..21..434K", "http://adsabs.harvard.edu/abs/1967JChPh..47..195K", "http://adsabs.harvard.edu/abs/2004ISPM...21...28L", "http://adsabs.harvard.edu/abs/2005JPhA...38R.309P", "http://adsabs.harvard.edu/abs/2015ITSP...63.1144S", "http://jmlr.csail.mit.edu/papers/v7/malioutov06a.html", "http://www.ncbi.nlm.nih.gov/pubmed/11570995", "http://www.cs.huji.ac.il/labs/danss/p2p/gabp/", "http://www.aaai.org/Library/AAAI/aaai82contents.php", "http://arxiv.org/abs/cond-mat/0508216", "http://arxiv.org/abs/cs/0212002", "http://arxiv.org/abs/cs/0504030", "http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=9780521873154", "http://computerrobotvision.org/2009/tutorial_day/crv09_belief_propagation_v2.pdf", "http://doi.org/10.1002%2Frsa.20057", "http://doi.org/10.1063%2F1.1698926", "http://doi.org/10.1063%2F1.1711845", "http://doi.org/10.1088%2F0305-4470%2F38%2F33%2FR01", "http://doi.org/10.1103%2FPhysRev.81.988", "http://doi.org/10.1109%2FTIT.2005.850085", "http://doi.org/10.1109%2FTIT.2007.909166", "http://doi.org/10.1109%2FTSP.2015.2389755", "http://doi.org/10.1109%2Fmsp.2004.1267047", "http://doi.org/10.1162%2F089976600300015880", "http://doi.org/10.1162%2F089976601750541769", "http://ieeexplore.ieee.org/document/1267047/", "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7004066", "http://www.ijcai.org/Proceedings/83-1/Papers/041.pdf", "http://www.ijcai.org/proceedings/1983-1", "http://stacks.iop.org/0305-4470/38/i=33/a=R01", "http://aip.scitation.org/doi/abs/10.1063/1.1698926", "http://aip.scitation.org/doi/abs/10.1063/1.1711845", "http://www.worldcat.org/issn/0305-4470", "https://www.newscientist.com/article/mg18725071-400-communication-speed-nears-terminal-velocity/", "https://www.aaai.org/Papers/AAAI/1982/AAAI82-032.pdf", "https://link.aps.org/doi/10.1103/PhysRev.81.988", "https://web.archive.org/web/20110614012544/http://www.cs.huji.ac.il/labs/danss/p2p/gabp/"]}, "Buzen's algorithm": {"categories": ["Queueing theory", "Statistical algorithms"], "title": "Buzen's algorithm", "method": "Buzen's algorithm", "url": "https://en.wikipedia.org/wiki/Buzen%27s_algorithm", "summary": "In queueing theory, a discipline within the mathematical theory of probability, Buzen's algorithm (or convolution algorithm) is an algorithm for calculating the normalization constant G(N) in the Gordon\u2013Newell theorem. This method was first proposed by Jeffrey P. Buzen in 1973. Computing G(N) is required to compute the stationary probability distribution of a closed queueing network.Performing a na\u00efve computation of the normalising constant requires enumeration of all states. For a system with N jobs and M states there are \n \n \n \n \n \n \n \n (\n \n \n \n N\n +\n M\n \u2212\n 1\n \n \n M\n \u2212\n 1\n \n \n \n )\n \n \n \n \n \n \n {\\displaystyle {\\tbinom {N+M-1}{M-1}}}\n states. Buzen's algorithm \"computes G(1), G(2), ..., G(N) using a total of NM multiplications and NM additions.\" This is a significant improvement and allows for computations to be performed with much larger networks.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Erlang (unit)", "Erlang distribution", "Expected value", "Exponentially distributed", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon F. Newell", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "JSTOR", "Jackson network", "Jeffrey P. Buzen", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Marginal distribution", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Normalization constant", "Operations Research (journal)", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability distribution", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations"], "references": ["http://cs.gmu.edu/~menasce/cs672/slides/CS672-convolution.pdf", "http://www-unix.ecs.umass.edu/~krishna/ece673/buzen.pdf", "http://www.cs.wustl.edu/~jain/cse567-08/ftp/k_35ca.pdf", "http://doi.org/10.1145%2F362342.362345", "http://doi.org/10.1287%2Fopre.15.2.254", "http://www.jstor.org/stable/168557"]}, "Moving average": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from February 2010", "Articles with unsourced statements from February 2018", "CS1 maint: Archived copy as title", "Chart overlays", "Commons category link is locally defined", "Statistical charts and diagrams", "Technical analysis", "Time series"], "title": "Moving average", "method": "Moving average", "url": "https://en.wikipedia.org/wiki/Moving_average", "summary": "In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating a series of averages of different subsets of the full data set. It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter. Variations include: simple, and cumulative, or weighted forms (described below).\nGiven a series of numbers and a fixed subset size, the first element of the moving average is obtained by taking the average of the initial fixed subset of the number series. Then the subset is modified by \"shifting forward\"; that is, excluding the first number of the series and including the next value in the subset.\nA moving average is commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles. The threshold between short-term and long-term depends on the application, and the parameters of the moving average will be set accordingly. For example, it is often used in technical analysis of financial data, like stock prices, returns or trading volumes. It is also used in economics to examine gross domestic product, employment or other macroeconomic time series. Mathematically, a moving average is a type of convolution and so it can be viewed as an example of a low-pass filter used in signal processing. When used with non-time series data, a moving average filters higher frequency components without any specific connection to time, although typically some kind of ordering is implied. Viewed simplistically it can be regarded as smoothing the data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/ba/Exponential_moving_average_weights_N%3D15.png", "https://upload.wikimedia.org/wikipedia/commons/d/d9/MovingAverage.GIF", "https://upload.wikimedia.org/wikipedia/commons/9/93/Moving_Average_Types_comparison_-_Simple_and_Exponential.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c7/Weighted_moving_average_weights_N%3D15.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Accumulation/distribution index", "Actuarial science", "Advance\u2013decline line", "Akaike information criterion", "Algorithms for calculating variance", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Average directional movement index", "Average true range", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bollinger Bands", "Bootstrapping (statistics)", "Bottom (technical analysis)", "Box plot", "Box\u2013Jenkins method", "Breadth of market", "Breakout (technical analysis)", "Breusch\u2013Godfrey test", "Broadening top", "Candlestick chart", "Candlestick pattern", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chart pattern", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Commodity channel index", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convergent series", "Convolution", "Coppock curve", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cup and handle", "Data", "Data collection", "Dead cat bounce", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Detrended price oscillator", "Dickey\u2013Fuller test", "Divergence (statistics)", "Doji", "Donchian channel", "Double top and double bottom", "Dow theory", "Durbin\u2013Watson statistic", "EWMA chart", "Ease of movement", "Econometric model", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliott wave principle", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential decay", "Exponential family", "Exponential function", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fibonacci retracement", "Finite impulse response", "First-hitting-time model", "Flag and pennant patterns", "Force index", "Forecasting", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gap (chart pattern)", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric progression", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Hammer (candlestick pattern)", "Hanging man (candlestick pattern)", "Harmonic mean", "Head and shoulders (chart pattern)", "Heteroscedasticity", "Hikkake pattern", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Ichimoku Kink\u014d Hy\u014d", "Index of dispersion", "Infinite impulse response", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverted hammer", "Island reversal", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kagi chart", "Kaplan\u2013Meier estimator", "Keltner channel", "Kendall rank correlation coefficient", "Kernel smoothing", "Know sure thing oscillator", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line chart", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Low-pass filter", "Lp space", "M-estimator", "MACD", "Mann\u2013Whitney U test", "Market trend", "Marubozu", "Mass index", "Maximum a posteriori estimation", "Maximum likelihood", "McClellan oscillator", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Median filter", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Momentum (finance)", "Money flow index", "Monotone likelihood ratio", "Morning star (candlestick pattern)", "Moving-average model", "Moving average (disambiguation)", "Moving average crossover", "Moving average model", "Moving least squares", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Negative volume index", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "On-balance volume", "One- and two-tailed tests", "Open-high-low-close chart", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabolic SAR", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivot point (stock market)", "Pivotal quantity", "Pixelisation", "Plug-in principle", "Point and figure chart", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Power series", "Prediction interval", "Price", "Price channels", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Put/call ratio", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative strength index", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Resistance (technical analysis)", "Return (finance)", "Rising moving average", "Robust regression", "Robust statistics", "Run chart", "Running total", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Savitzky\u2013Golay filter", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Series (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shooting star (candlestick pattern)", "Sign test", "Signal processing", "Simple linear regression", "Simultaneous equations model", "Skewness", "Skip list", "Smart money index", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spinning top (candlestick pattern)", "Standard deviation", "Standard error", "Standard score", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic oscillator", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Support (technical analysis)", "Support and resistance", "Survey methodology", "Survival analysis", "Survival function", "System identification", "TRIN (finance)", "Taylor Series", "Taylor series", "Technical analysis", "Technical indicator", "Three black crows", "Three white soldiers", "Time domain", "Time series", "Tolerance interval", "Top (technical analysis)", "Trend analysis", "Trend estimation", "Trend line (technical analysis)", "Triangle (chart pattern)", "Triangle number", "Triple top and triple bottom", "Trix (technical analysis)", "True strength index", "U-statistic", "Ulcer index", "Ultimate oscillator", "Uniformly most powerful test", "V-statistic", "VIX", "Variance", "Vector autoregression", "Volatility (finance)", "Volume (finance)", "Volume\u2013price trend", "Vortex indicator", "Wald test", "Wavelet", "Wedge pattern", "Whittle likelihood", "Wilcoxon signed-rank test", "Williams %R", "Window function", "Z-test", "Zero lag exponential moving average"], "references": ["http://code.activestate.com/recipes/576930/", "http://options-trading-notes.blogspot.com/2013/06/derivation-of-ea.html", "http://www.investopedia.com/articles/technical/060401.asp", "http://mathworld.wolfram.com/Spencers15-PointMovingAverage.html", "http://www.waterboards.ca.gov/waterrights/water_issues/programs/bay_delta/docs/cmnt091412/sldmwa/booth_et_al_2006.pdf", "http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc324.htm", "http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc431.htm", "http://people.ds.cam.ac.uk/fanf2/hermes/doc/antiforgery/stats.pdf", "http://lorien.ncl.ac.uk/ming/filter/filewma.htm", "https://web.archive.org/web/20100329135531/http://lorien.ncl.ac.uk/ming/filter/filewma.htm"]}, "Randomization test": {"categories": ["All articles to be merged", "All articles with incomplete citations", "Articles to be merged from August 2018", "Articles with incomplete citations from November 2012", "Monte Carlo methods", "Nonparametric statistics", "Resampling (statistics)", "Statistical inference", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from June 2016"], "title": "Resampling (statistics)", "method": "Randomization test", "url": "https://en.wikipedia.org/wiki/Resampling_(statistics)", "summary": "In statistics, resampling is any of a variety of methods for doing one of the following:\n\nEstimating the precision of sample statistics (medians, variances, percentiles) by using subsets of available data (jackknifing) or drawing randomly with replacement from a set of data points (bootstrapping)\nExchanging labels on data points when performing significance tests (permutation tests, also called exact tests, randomization tests, or re-randomization tests)\nValidating models by using random subsets (bootstrapping, cross validation)Common resampling techniques include bootstrapping, jackknifing and permutation tests.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute difference", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrew P. Holmes", "Annals of Mathematical Statistics", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balanced repeated replication", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behrens\u2013Fisher problem", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrap (statistics)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Bradley Efron", "Breusch\u2013Godfrey test", "C.F. Jeff Wu", "Canadian Journal of Forest Research", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chapman & Hall", "Chemometrics", "Chi-squared test", "Classical statistics", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational physics", "Confidence interval", "Confidence intervals", "Confounding", "Consistency (statistics)", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "E. J. G. Pitman", "Econometrica", "Econometrics", "Economics Letters", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical measure", "Engineering statistics", "Environmental Management", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Exact test", "Exchangeability", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's exact test", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Genetic algorithm", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Hafner Publishing", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human Brain Mapping (journal)", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife (statistics)", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Tukey", "John Wilder Tukey", "John Wiley & Sons", "Jonckheere's trend test", "Journal of Econometrics", "Journal of Mixed Methods Research", "Journal of Modern Applied Statistical Methods", "Journal of Statistical Computation and Simulation", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society", "Journal of the Royal Statistical Society, Series B", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marcel-Dekker", "Maurice Quenouille", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimator", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Meyer Dwass", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo methods", "Monte Carlo sampling", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Odds ratio", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Particle filter", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Persi Diaconis", "Phillip Good", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Poisson sampling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prasanta Chandra Mahalanobis", "Prediction interval", "Predictive modelling", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Proportionality (mathematics)", "Psychometrics", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R. A. Fisher", "Radar chart", "Random", "Random assignment", "Random permutation", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression coefficient", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (disambiguation)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "SAGE Publications", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific American", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shlomo Sawilowsky", "Sign test", "Significance test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Springer Science+Business Media", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Subsampling (statistics)", "Sufficient statistic", "Survey Methodology", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "Test statistic", "The Annals of Mathematical Statistics", "The Annals of Statistics", "The Design of Experiments", "Thomas E. Nichols", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.mansci.uwaterloo.ca/~msmucker/software.html", "http://statwww.epfl.ch/davison/BMA/library.html", "http://www.crcpress.com/product/isbn/9781466504059", "http://people.revoledu.com/kardi/tutorial/Bootstrap/index.html", "http://bcs.whfreeman.com/pbs/cat_140/chap18.pdf", "http://zanybooks.com/statist.htm", "http://adsabs.harvard.edu/abs/1989EnMan..13..783V", "http://tbf.coe.wayne.edu/jmasm/vol1_no2.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/11747097", "http://rosetta.ahmedmoustafa.io/bootstrap/", "http://rosetta.ahmedmoustafa.io/permutation/", "http://PAREonline.net/getvn.asp?v=8&n=19", "http://www.statistics101.net", "http://arxiv.org/abs/math/0612488", "http://www.bioconductor.org/packages/release/bioc/html/multtest.html", "http://doi.org/10.1002%2Fhbm.1058", "http://doi.org/10.1007%2Fbf01868317", "http://doi.org/10.1016%2Fj.jeconom.2004.08.004", "http://doi.org/10.1016%2Fs0165-1765(01)00494-3", "http://doi.org/10.1016%2Fs0304-4076(97)86569-4", "http://doi.org/10.1080%2F01621459.1983.10477989", "http://doi.org/10.1080%2F01621459.1988.10478691", "http://doi.org/10.1080%2F01621459.1990.10474929", "http://doi.org/10.1080%2F10629360500108053", "http://doi.org/10.1093%2Fbiomet%2F29.3-4.322", "http://doi.org/10.1093%2Fbiomet%2F43.3-4.353", "http://doi.org/10.1093%2Fbiomet%2F79.4.811", "http://doi.org/10.1093%2Fbiomet%2Fasm072", "http://doi.org/10.1111%2F1468-0262.00242", "http://doi.org/10.1111%2Fj.1467-9868.2005.00489.x", "http://doi.org/10.1111%2Fj.1467-9868.2006.00555.x", "http://doi.org/10.1139%2Fx86-222", "http://doi.org/10.1177%2F1558689812454457", "http://doi.org/10.1198%2Fjasa.2009.tm08368", "http://doi.org/10.1214%2Faoms%2F1177707045", "http://doi.org/10.1214%2Faos%2F1043351257", "http://doi.org/10.1214%2Faos%2F1176325770", "http://doi.org/10.1214%2Faos%2F1176344552", "http://doi.org/10.1214%2Faos%2F1176345580", "http://doi.org/10.1214%2Faos%2F1176350142", "http://doi.org/10.22237%2Fjmasm%2F1036110240", "http://doi.org/10.2307%2F2334363", "http://doi.org/10.2307%2F2335441", "http://www.ericdigests.org/1993/marriage.htm", "http://www.jstor.org/stable/2237031", "http://www.jstor.org/stable/2237363", "http://www.jstor.org/stable/2334363", "http://www.jstor.org/stable/2335441", "http://www.jstor.org/stable/2981330", "http://www.jstor.org/stable/2983696", "http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.aos/1176344552", "http://cran.at.r-project.org/web/packages/boot/index.html", "http://www.fil.ion.ucl.ac.uk/spm/doc/papers/NicholsHolmes.pdf", "https://github.com/searchivarius/PermTest", "https://www.springer.com/mathematics/probability/book/978-0-387-20268-6", "https://archive.is/20120712124533/http://lib.stat.cmu.edu/S/bootstrap.funs", "https://web.archive.org/web/20030505044125/http://tbf.coe.wayne.edu/jmasm/vol1_no2.pdf", "https://web.archive.org/web/20051223034539/http://www.resample.com/content/text/index.shtml", "https://web.archive.org/web/20060110182635/http://www.insightful.com/Hesterberg/bootstrap/", "https://web.archive.org/web/20060215221403/http://bcs.whfreeman.com/ips5e/content/cat_080/pdf/moore14.pdf", "https://www.jstor.org/stable/2983647", "https://www.jstor.org/stable/2984124", "https://cran.r-project.org/web/packages/permtest/index.html", "https://cran.r-project.org/web/packages/samplingVarEst"]}, "Opinion poll": {"categories": ["All articles to be expanded", "All articles with unsourced statements", "Anglophone-centric", "Articles to be expanded from March 2011", "Articles using small message boxes", "Articles with limited geographic scope from November 2016", "Articles with unsourced statements from May 2012", "Articles with unsourced statements from November 2012", "Commons category link is locally defined", "Polling", "Pollsters", "Psychometrics", "Public opinion", "Sampling (statistics)", "Survey methodology", "Types of polling", "Wikipedia articles needing clarification from July 2010", "Wikipedia articles with BNF identifiers", "Wikipedia articles with GND identifiers", "Wikipedia articles with NARA identifiers", "Wikipedia articles with NDL identifiers"], "title": "Opinion poll", "method": "Opinion poll", "url": "https://en.wikipedia.org/wiki/Opinion_poll", "summary": "An opinion poll, often simply referred to as a poll or a survey, is a human research survey of public opinion from a particular sample. Opinion polls are usually designed to represent the opinions of a population by conducting a series of questions and then extrapolating generalities in ratio or within confidence intervals.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/bd/Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/0/09/Dewey_Defeats_Truman.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/94/TallahaseePalmBeachBallotBox1.jpg", "https://upload.wikimedia.org/wikipedia/commons/6/67/USA_Gallup_abortion_opinion_poll_stacked_area.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fd/Voter_Turnout_by_Race-Ethnicity%2C_2008_US_Presidential_Election.png", "https://upload.wikimedia.org/wikipedia/commons/b/bf/Voter_poll.jpg", "https://upload.wikimedia.org/wikipedia/commons/6/69/WMF_Strategic_Plan_Survey.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Afrobarometer", "Akaike information criterion", "Alf Landon", "American Association for Public Opinion Research", "American National Election Studies", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrew Jackson", "Angus Reid Public Opinion", "Arithmetic mean", "Asymptotic theory (statistics)", "Attitude (psychology)", "Audience measurement", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bandwagon effect", "Bar chart", "Barack Obama", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Biblioth\u00e8que nationale de France", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Bradley effect", "Breusch\u2013Godfrey test", "Calvin Coolidge", "Canonical correlation", "Cartography", "Categorical data", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Chicago Tribune", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cognitive pretesting", "Cohen's kappa", "Cointegration", "Comparative Study of Electoral Systems", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Conservative Party (UK)", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Couple interview", "Coverage error", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data analysis", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Deliberative opinion poll", "Demographic statistics", "Demography", "Denazification", "Density estimation", "Descriptive statistics", "Design of experiments", "Dewey Defeats Truman", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Donald Trump", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Election Campaign Polls and Democracy in Canada: Examining the Evidence Behind Common Claims", "Elliptical distribution", "Elmo Roper", "Empirical distribution function", "Enfield Southgate (UK Parliament constituency)", "Engineering statistics", "English-speaking world", "Entrance poll", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Eurobarometer", "European Social Survey", "European Society for Opinion and Marketing Research", "European Values Study", "Everett Carll Ladd", "Exit poll", "Experiment", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Ferranti MRT", "First-hitting-time model", "Forest plot", "Fourier analysis", "Framing (social sciences)", "Franklin Roosevelt", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gallup (company)", "General Social Survey", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George Gallup", "Geostatistics", "Gerald Ford", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Harry S. Truman", "Herbert Hoover", "Heteroscedasticity", "Hillary Clinton", "Histogram", "Historical polling for U.S. Presidential elections", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Integrated Authority File", "Interaction (statistics)", "International Social Survey Programme", "International Standard Book Number", "International Statistical Institute", "Internet", "Interquartile range", "Interval estimation", "Interview (research)", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Quincy Adams", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Labour Party (UK)", "Latinobar\u00f3metro", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of household surveys in the United States", "List of polling organizations", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Louis Harris", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marcel D\u00e9at", "Margin of error", "Market research", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Metallic Metals Act", "Method of moments (statistics)", "Methods engineering", "Michael Portillo", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mobile telephone", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving average", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Nate Silver", "National Archives and Records Administration", "National Diet Library", "National Health and Nutrition Examination Survey", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New Deal", "New Zealand Attitudes and Values Study", "Non-response bias", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Open access poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Palm Beach County", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Hitchens", "Pew Research Center", "Pie chart", "Pierre Bourdieu", "Pivotal quantity", "Plug-in principle", "Plurality voting system", "Point estimation", "Poisson regression", "Political forecasting", "Poll average", "Population (statistics)", "Population statistics", "Postcard", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Professional association", "Proportional hazards model", "Psychometrics", "Public opinion", "Puck (magazine)", "Push poll", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Racism", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Referendum", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response bias", "Robust regression", "Robust statistics", "Roper Center for Public Opinion Research", "Run chart", "Safe seat", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling error", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Selection bias", "Self-fulfilling prophecy", "Semi-structured interview", "Semiparametric regression", "Sexism", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shy Tory Factor", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smithsonian Institution", "Social media", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spiral of silence", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen Twigg", "Stratified sampling", "Straw poll", "Structural break", "Structural equation modeling", "Structured interview", "Student's t-test", "Sufficient statistic", "Survey (human research)", "Survey data collection", "Survey methodology", "Survey research", "Survey sampling", "Survival analysis", "Survival function", "Swing (politics)", "System identification", "Tactical voting", "Telephone Consumer Protection Act of 1991", "The Broken Compass: How British Politics Lost its Way", "The Gallup Organization", "The Literary Digest", "Thomas Dewey", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Twitter", "U-statistic", "U.S. presidential election, 1948", "U.S. presidential election, 2016", "Underdog (competition)", "Uniformly most powerful test", "United Kingdom", "United Kingdom general election, 1945", "United Kingdom general election, 1970", "United Kingdom general election, 1992", "United Kingdom general election, 1997", "United Kingdom general election, 2015", "United Kingdom general election, 2017", "United Kingdom general election, February 1974", "United States", "United States Presidency", "United States Republican Party", "United States presidential election, 1824", "United States presidential election, 1936", "United States presidential election, 1976", "United States presidential election, 2008", "Unstructured interview", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Warren Harding", "Wavelet", "Western democratic nations", "Whittle likelihood", "Why Die for Danzig?", "Wilcoxon signed-rank test", "William Safire", "Winston Churchill", "Woodrow Wilson", "World Association for Public Opinion Research", "World Values Survey", "YouGov", "Z-test", "Zogby International"], "references": ["http://www2.parl.gc.ca/content/lop/researchpublications/bp371-e.htm", "http://www.cnn.com/ALLPOLITICS/1996/polls/cnn.usa.gallup/tracking/FAQ.html", "http://fivethirtyeight.com/features/final-election-update-theres-a-wide-range-of-outcomes-and-most-of-them-come-up-clinton/", "http://www.fivethirtyeight.com/2008/07/cellphone-problem-revisited.html", "http://www.fivethirtyeight.com/2008/11/cellphone-effect-continued.html", "http://abcnews.go.com/images/pdf/responserates.pdf", "http://www.pollster.com/blogs/more_cell_phone_data_from_gall.php", "http://www.pollster.com/blogs/more_pollsters_interviewing_by.php", "http://www.pollster.com/blogs/new_pew_data_on_cell_phones.php", "http://www.slate.com/articles/news_and_politics/politics/2012/05/survey_bias_how_can_we_trust_opinion_polls_when_so_few_people_respond_.single.html", "http://slatestarcodex.com/2013/04/12/noisy-poll-results-and-reptilian-muslim-climatologists-from-mars/", "http://climatecommunication.yale.edu/publications/whats-in-a-name-global-warming-vs-climate-change/", "http://data.bnf.fr/ark:/12148/cb119412772", "http://transition.fcc.gov/cgb/policy/TCPA-Rules.pdf", "http://www.aapor.org/Education-Resources/Election-Polling-Resources/Margin-of-Sampling-Error-Credibility-Interval.aspx", "http://www.aapor.org/Education-Resources/For-Researchers/Poll-Survey-FAQ/Response-Rates-An-Overview.aspx", "http://doi.org/10.1080%2F00344890208523210", "http://doi.org/10.1162%2Fglep_a_00215", "http://doi.org/10.1257%2Fjep.31.2.211", "http://www.journalism.org/2016/05/26/news-use-across-social-media-platforms-2016/", "http://www.ncpp.org/?q=home", "http://www.ncpp.org/?q=node/4", "http://www.people-press.org/2013/07/26/government-surveillance-a-question-wording-experiment/", "http://pewresearch.org/pubs/515/polling-cell-only-problem", "http://www.pewresearch.org", "http://www.pewresearch.org/2010/11/22/the-growing-gap-between-landline-and-dual-frame-election-polls/", "http://www.publicagenda.org/pages/seven-stages-public-opinion", "https://books.google.com/books?id=RgoXBQAAQBAJ&pg=PA235", "https://www.questia.com/PM.qst?a=o&d=100501261", "https://www.questia.com/PM.qst?a=o&d=104829752", "https://www.questia.com/PM.qst?a=o&d=28537852", "https://www.questia.com/PM.qst?a=o&d=28621255", "https://www.questia.com/PM.qst?a=o&d=59669912", "https://www.questia.com/PM.qst?a=o&d=71288534", "https://www.questia.com/PM.qst?a=o&d=8540600", "https://www.questia.com/PM.qst?a=o&d=89021667", "https://www.questia.com/PM.qst?a=o&d=8971691", "https://www.questia.com/PM.qst?a=o&d=98754501", "https://www.questia.com/read/98754561?title=Public%20Opinion,%201935-1946", "https://www.washingtonpost.com/wp-dyn/content/article/2011/03/09/AR2011030902885.html", "https://web.stanford.edu/~gentzkow/research/fakenews.pdf", "https://catalogue.bnf.fr/ark:/12148/cb119412772", "https://catalog.archives.gov/id/10644551", "https://www.cdc.gov/nchs/data/nhis/earlyrelease/wireless200705.pdf", "https://d-nb.info/gnd/4011425-9", "https://archive.is/20130131181005/http://www.pollster.com/blogs/more_cell_phone_data_from_gall.php", "https://id.ndl.go.jp/auth/ndlna/00574312", "https://www.researchgate.net/publication/236142275_A_user-centric_model_of_voting_intention_from_Social_Media", "https://web.archive.org/web/20051025015346/http://ucblibraries.colorado.edu/govpubs/us/polls.htm", "https://web.archive.org/web/20080926154657/http://www.daytodaypolitics.com/polls/presidential_election_Obama_vs_McCain_2008.htm", "https://web.archive.org/web/20081011164858/http://www.pollster.com/blogs/new_pew_data_on_cell_phones.php", "https://web.archive.org/web/20081030215501/http://pewresearch.org/pubs/515/polling-cell-only-problem", "https://web.archive.org/web/20081121023257/http://www.pollster.com/blogs/more_pollsters_interviewing_by.php", "https://web.archive.org/web/20151010133249/http://www.aapor.org/AAPORKentico/AAPOR_Main/media/MainSiteFiles/AAPOR_Social_Media_Report_FNL.pdf", "https://www.npr.org/templates/transcript/transcript.php?storyId=487654380", "https://www.wikidata.org/wiki/Q49958"]}, "Maximum entropy probability distribution": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from December 2013", "Articles needing additional references from August 2009", "Articles with multiple maintenance issues", "Continuous distributions", "Discrete distributions", "Entropy and information", "Particle statistics", "Types of probability distributions", "Wikipedia articles needing clarification from July 2015"], "title": "Maximum entropy probability distribution", "method": "Maximum entropy probability distribution", "url": "https://en.wikipedia.org/wiki/Maximum_entropy_probability_distribution", "summary": "In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class (usually defined in terms of specified properties or measures), then the distribution with the largest entropy should be chosen as the least-informative default. The motivation is twofold: first, maximizing entropy minimizes the amount of prior information built into the distribution; second, many physical systems tend to move towards maximal entropy configurations over time.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Average absolute deviation", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bit", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Calculus of variations", "Cambridge University Press", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular mean", "Circular uniform distribution", "Circular variance", "Closed set", "Compound Poisson distribution", "Continuous random variable", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Deviation risk measure", "Differential entropy", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete random variable", "Discrete uniform distribution", "Edward Arnold (publisher)", "Elliptical distribution", "Entropy (information theory)", "Erlang distribution", "Euler-Mascheroni constant", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Functional (mathematics)", "Functional derivative", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gibbs measure", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "IEEE Transactions on Information Theory", "Information entropy", "Information theory", "International Standard Book Number", "International Standard Serial Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Karush\u2013Kuhn\u2013Tucker conditions", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Lagrange multiplier", "Lagrange multipliers", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithm", "Logarithmic distribution", "Logarithmically concave function", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Ludwig Boltzmann", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximal Entropy Random Walk", "Maximal entropy configuration", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Measurable function", "Mittag-Leffler distribution", "Mixture distribution", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Nat (unit)", "Natural exponential family", "Natural logarithm", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Partition function (mathematics)", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Principle of indifference", "Principle of maximum entropy", "Prior information", "Probability axioms", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard deviation", "Statistics", "Student's t-distribution", "Thomas M. Cover", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.mtm.ufsc.br/~taneja/book/book.html", "http://www.mtm.ufsc.br/~taneja/book/node14.html", "http://www.wise.xmu.edu.cn/Master/Download/..%5C..%5CUploadFiles%5Cpaper-masterdownload%5C2009519932327055475115776.pdf", "http://doi.org/10.1007%2Fs11009-007-9057-z", "http://doi.org/10.1007%2Fs11009-009-9133-7", "http://doi.org/10.1109%2F18.930936", "http://doi.org/10.1109%2Ftit.1973.1055060", "http://doi.org/10.1111%2Fj.1467-9574.1972.tb00152.x", "http://ieeexplore.ieee.org/document/1055060/", "http://www.worldcat.org/issn/0018-9448", "http://coltech.vnu.edu.vn/~thainp/books/Wiley_-_2006_-_Elements_of_Information_Theory_2nd_Ed.pdf", "https://books.google.com/books?id=sKqWMGqQXQkC&printsec=frontcover&dq=Jammalamadaka+Topics+in+circular&hl=en&ei=iJ3QTe77NKL00gGdyqHoDQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDcQ6AEwAA#v=onepage&q&f=false", "https://link.springer.com/article/10.1007/s11009-007-9057-z", "https://link.springer.com/article/10.1007/s11009-009-9133-7", "https://www.researchgate.net/publication/220442393_Maximum_Entropy_Principle_with_General_Deviation_Measures"]}, "Multistage testing": {"categories": ["All articles with dead external links", "Articles with dead external links from February 2018", "Articles with permanently dead external links", "Psychometrics"], "title": "Multistage testing", "method": "Multistage testing", "url": "https://en.wikipedia.org/wiki/Multistage_testing", "summary": "Multistage testing is an algorithm-based approach to administering tests. It is very similar to computer-adaptive testing in that items are interactively selected for each examinee by the algorithm, but rather than selecting individual items, groups of items are selected, building the test in stages. These groups are called testlets or panels.While multistage tests could theoretically be administered by a human, the extensive computations required (often using item response theory) mean that multistage tests are administered by computer.\nThe number of stages or testlets can vary. If the testlets are relatively small, such as five items, ten or more could easily be used in a test. Some multistage tests are designed with the minimum of two stages (one stage would be a conventional fixed-form test).In response to the increasing use of multistage testing, the scholarly journal Applied Measurement in Education published a special edition on the topic in 2006.", "images": [], "links": ["Algorithm", "Computer-adaptive testing", "Howard Wainer", "Item response theory", "Mauve (test suite)", "Test (student assessment)", "Testlet"], "references": ["http://www.leaonline.com/toc/ame/19/3", "http://dwb.unl.edu/Diss/RCastle/ReedCastleDiss.html"]}, "Spatial descriptive statistics": {"categories": ["All articles needing additional references", "Articles needing additional references from October 2009", "Spatial data analysis"], "title": "Spatial descriptive statistics", "method": "Spatial descriptive statistics", "url": "https://en.wikipedia.org/wiki/Spatial_descriptive_statistics", "summary": "Spatial descriptive statistics are used for a variety of purposes in geography, particularly in quantitative data analyses involving Geographic Information Systems (GIS).", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Central tendency", "Centroid", "Correlogram", "Covariance matrix", "Cuzick\u2013Edwards test", "Descriptive statistics", "Determinant", "Digital object identifier", "Eigenvalue", "GIS", "Geostatistics", "Indicator function", "International Standard Book Number", "JSTOR", "Kriging", "Poisson process", "PubMed Central", "Spatial analysis", "Statistical dispersion", "Trace (linear algebra)", "Variogram"], "references": ["http://onlinelibrary.wiley.com/doi/10.1111/jbi.12534/abstract", "http://www.public.iastate.edu/~pcaragea/S40608/Notes/Dixon_Ripley_K.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4737218", "http://doi.org/10.1111%2Fjbi.12534", "http://doi.org/10.2307%2F1931034", "http://doi.org/10.2307%2F3212829", "http://www.jstor.org/stable/1931034"]}, "Pearson correlation coefficient": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2012", "Articles with unsourced statements from February 2015", "Articles with unsourced statements from January 2011", "Articles with unsourced statements from November 2009", "Covariance and correlation", "Parametric statistics", "Statistical ratios", "Use dmy dates from September 2010", "Wikipedia articles needing clarification from February 2015", "Wikipedia articles needing page number citations from September 2010"], "title": "Pearson correlation coefficient", "method": "Pearson correlation coefficient", "url": "https://en.wikipedia.org/wiki/Pearson_correlation_coefficient", "summary": "In statistics, the Pearson correlation coefficient (PCC, pronounced ), also referred to as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC) or the bivariate correlation, is a measure of the linear correlation between two variables X and Y. Owing to the Cauchy\u2013Schwarz inequality it has a value between +1 and \u22121, where 1 is total positive linear correlation, 0 is no linear correlation, and \u22121 is total negative linear correlation. It is widely used in the sciences. It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/34/Correlation_coefficient.png", "https://upload.wikimedia.org/wikipedia/commons/d/d4/Correlation_examples2.svg", "https://upload.wikimedia.org/wikipedia/commons/2/24/Critical_correlation_vs._sample_size.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a7/Pearson_correlation_and_prediction_intervals.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d1/Regression_lines.png", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute value", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Angle", "Anscombe's quartet", "Anti-correlation", "Arithmetic mean", "Association (statistics)", "Asymptotic distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Beta function", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Bivariate normal distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Cauchy distribution", "Cauchy\u2013Schwarz inequality", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlation matrix", "Correlogram", "Cosine", "Cosine similarity", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Decorrelation", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Directional statistics", "Disattenuation", "Distance correlation", "Divergence (statistics)", "Dot product", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Exchangeable random variables", "Expected Value", "Experiment", "Explained sum of squares", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher transformation", "Forest plot", "Fourier analysis", "Francis Galton", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gamma function", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "H. E. Soper", "Harmonic mean", "Heavy-tailed distribution", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypergeometric function", "Hypothesis test", "Independent and identically distributed", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Invariant estimator", "Inverse hyperbolic function", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line (mathematics)", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marginal distribution", "Matrix inverse", "Matrix square root", "Maximal information coefficient", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimate", "McNemar's test", "Mean", "Mean of circular quantities", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiple correlation", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normally distributed and uncorrelated does not imply independent", "Nova Science Publishers, Inc.", "Null hypothesis", "Numerical stability", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "P-value", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polychoric correlation", "Population (statistics)", "Population statistics", "Population variance", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal components analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quadrant count ratio", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "RV coefficient", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled correlation", "Scatter plot", "Scatterplot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Sine", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard deviations", "Standard error", "Standard score", "Stationary process", "Statistic", "Statistical classification", "Statistical dependence", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Total sum of squares", "Trend estimation", "Trigonometric functions", "Two-tailed test", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector (geometry)", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.danko-nikolic.com/wp-content/uploads/2012/03/Scaled-correlation-analysis.pdf", "http://guessthecorrelation.com", "http://www.mathworks.com/matlabcentral/fileexchange/20846-weighted-correlation-matrix", "http://www.real-statistics.com/correlation/basic-concepts-correlation/", "http://www.sciencedirect.com/science/article/pii/S0167715298000352", "http://mathworld.wolfram.com/CorrelationCoefficientBivariateNormalDistribution.html", "http://www.hawaii.edu/powerkills/UC.HTM", "http://libguides.library.kent.edu/SPSS/PearsonCorr", "http://frank.mtsu.edu/~dkfuller/tables/correlationtable.pdf", "http://nagysandor.eu/AsimovTeka/correlation_en/index.html", "http://www.hackmath.net/en/calculator/linear-regression", "http://sci.tech-archive.net/Archive/sci.stat.math/2006-02/msg00171.html", "http://comparingcorrelations.org", "http://doi.org/10.1016%2FS0167-7152(98)00035-2", "http://doi.org/10.1093%2Fbiomet%2F11.4.328", "http://doi.org/10.1093%2Fbiomet%2F62.3.531", "http://doi.org/10.1109%2Ftit.2014.2342744", "http://doi.org/10.1111%2Fj.1460-9568.2011.07987.x", "http://doi.org/10.1214%2Faoms%2F1177706717", "http://doi.org/10.1214%2Fss%2F1177012580", "http://doi.org/10.2307%2F2685263", "http://www.jstor.org/stable/2237306", "http://www.jstor.org/stable/2245329", "http://www.jstor.org/stable/2335508", "http://www.jstor.org/stable/27528906", "http://www.jstor.org/stable/2983768", "https://books.google.com/books?id=60aL0zlT-90C&pg=PA240#v=onepage&q&f=false", "https://books.google.com/books?id=JPcRAAAAYAAJ&pg=PA246#v=onepage&q&f=false", "https://books.google.com/books?id=eskKAAAAYAAJ&pg=PA512#v=onepage&q&f=false", "https://books.google.com/books?id=lN3RjXLUuWsC&pg=PA499#v=onepage&q&f=false", "https://books.google.com/books?id=sKqWMGqQXQkC&printsec=frontcover&dq=Jammalamadaka+Topics+in+circular&hl=en&ei=iJ3QTe77NKL00gGdyqHoDQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDcQ6AEwAA#v=onepage&q&f=false", "https://www.stat.berkeley.edu/~rabbee/correlation.pdf", "https://www.researchgate.net/publication/265604603_Minimum_Pearson_Distance_Detection_for_Multilevel_Channels_With_Gain_andor_Offset_Mismatch", "https://doi.org/10.2277%2F052154985X"]}, "Cepstrum": {"categories": ["CS1 German-language sources (de)", "Frequency-domain analysis", "Signal processing", "Use mdy dates from November 2011"], "title": "Cepstrum", "method": "Cepstrum", "url": "https://en.wikipedia.org/wiki/Cepstrum", "summary": "A cepstrum () is the result of taking the inverse Fourier transform (IFT) of the logarithm of the estimated spectrum of a signal. It may be pronounced in the two ways given, the second having the advantage of avoiding confusion with \"kepstrum\", which also exists (see below). There is a complex cepstrum, a real cepstrum, a power cepstrum, and a phase cepstrum.\nThe power cepstrum in particular finds applications in the analysis of human speech.\nThe name \"cepstrum\" was derived by reversing the first four letters of \"spectrum\". Operations on cepstra are labelled quefrency analysis (aka quefrency alanysis), liftering, or cepstral analysis.", "images": ["https://upload.wikimedia.org/wikipedia/en/1/15/Cepstrum_signal_analysis.png"], "links": ["Autocorrelation", "Bomb", "Cepstral", "Cepstral (company)", "Complex logarithm", "Complex number", "Convolution", "Dependent and independent variables", "Earthquake", "Echo (phenomenon)", "Formant", "Frequency domain", "Function (mathematics)", "Homomorphic filtering", "Human speech", "Imaginary part", "Instantaneous phase", "International Standard Book Number", "Inverse Fourier transform", "J. W. Tukey", "Karl W. Steinbuch", "Library of Congress Control Number", "Logarithm", "Manfred R. Schroeder", "Mel-frequency cepstrum", "Mel scale", "Phase unwrapping", "Pitch detection algorithm", "Power spectrum", "Radar", "Real number", "Springer Verlag", "Time domain", "Vocal cord", "Vocal tract"], "references": ["http://www.advsolned.com/example_speech_coding.html", "http://www.practicalcryptography.com/miscellaneous/machine-learning/tutorial-cepstrum-and-lpccs/", "http://lccn.loc.gov/73-80607", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1455016", "http://www.phon.ucl.ac.uk/courses/spsci/matlab/lect10.html", "https://books.google.com/books?id=H_5SAAAAMAAJ", "https://books.google.com/books?id=jDeRCSqtev4C", "https://books.google.com/books?id=nZ-TetwzVcIC"]}, "Kendall rank correlation coefficient": {"categories": ["Covariance and correlation", "Independence (probability theory)", "Nonparametric statistics", "Statistical tests"], "title": "Kendall rank correlation coefficient", "method": "Kendall rank correlation coefficient", "url": "https://en.wikipedia.org/wiki/Kendall_rank_correlation_coefficient", "summary": "In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's tau coefficient (after the Greek letter \u03c4), is a statistic used to measure the ordinal association between two measured quantities. A tau test is a non-parametric hypothesis test for statistical dependence based on the tau coefficient.\nIt is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities. It is named after Maurice Kendall, who developed it in 1938, though Gustav Fechner had proposed a similar measure in the context of time series in 1897.Intuitively, the Kendall correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations have a dissimilar (or fully different for a correlation of -1) rank between the two variables. \nBoth Kendall's \n \n \n \n \u03c4\n \n \n {\\displaystyle \\tau }\n and Spearman's \n \n \n \n \u03c1\n \n \n {\\displaystyle \\rho }\n can be formulated as special cases of a more general correlation coefficient.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Bubble Sort", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Contingency tables", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cross tabulation", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Denominator", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General correlation coefficient", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodman and Kruskal's gamma", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gustav Fechner", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis test", "Independence (probability theory)", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jean D. Gibbons", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall's W", "Kendall tau distance", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maurice Kendall", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Merge Sort", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal association", "Ordinal level", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Psychometrika", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Ranked", "Ranking", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Strength of association", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Tau coefficient", "Tau distribution", "Test statistic", "Theil\u2013Sen estimator", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Kruskal", "Z-test", "\u03a4"], "references": ["http://www-01.ibm.com/support/docview.wss?uid=swg27047033#en", "http://www.statsdirect.com/help/nonparametric_methods/kend.htm", "http://technology.msb.edu/old/training/statistics/sas/books/pguide/zompmeth.htm", "http://www.utdallas.edu/~herve/Abdi-KendallCorrelation2007-pretty.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/19897822", "http://law.di.unimi.it/software/law-docs/it/unimi/dsi/law/stat/KendallTau.html", "http://www.wessa.net/rwasp_kendall.wasp", "http://www.ams.org/mathscinet-getitem?mr=0100941", "http://doi.org/10.1007%2FBF02294183", "http://doi.org/10.1093%2Fbiomet%2F30.1-2.81", "http://doi.org/10.2307%2F2281954", "http://doi.org/10.2307%2F2282833", "http://doi.org/10.2307%2F2333101", "http://doi.org/10.3758%2Fbrm.41.4.1144", "http://www.jstor.org/stable/2281954", "http://www.jstor.org/stable/2282833", "http://www.jstor.org/stable/2332226", "http://www.jstor.org/stable/2333101", "https://books.google.com/books?id=0hPvAAAAMAAJ&pg=PA365", "https://www.encyclopediaofmath.org/index.php?title=K/k055200", "https://www.encyclopediaofmath.org/index.php?title=K/k130020"]}, "Phi coefficient": {"categories": ["Statistical ratios", "Summary statistics for contingency tables"], "title": "Phi coefficient", "method": "Phi coefficient", "url": "https://en.wikipedia.org/wiki/Phi_coefficient", "summary": "In statistics, the phi coefficient (or mean square contingency coefficient and denoted by \u03c6 or r\u03c6) is a measure of association for two binary variables. Introduced by Karl Pearson, this measure is similar to the Pearson correlation coefficient in its interpretation. In fact, a Pearson correlation coefficient estimated for two binary variables will return the phi coefficient. The square of the phi coefficient is related to the chi-squared statistic for a 2\u00d72 contingency table (see Pearson's chi-squared test)\n\n \n \n \n \n \u03d5\n \n 2\n \n \n =\n \n \n \n \u03c7\n \n 2\n \n \n n\n \n \n \n \n {\\displaystyle \\phi ^{2}={\\frac {\\chi ^{2}}{n}}}\n where n is the total number of observations. Two binary variables are considered positively associated if most of the data falls along the diagonal cells. In contrast, two binary variables are considered negatively associated if most of the data falls off the diagonal. If we have a 2\u00d72 table for two random variables x and y\n\nwhere n11, n10, n01, n00, are non-negative counts of numbers of observations that sum to n, the total number of observations. The phi coefficient that describes the association of x and y is\n\n \n \n \n \u03d5\n =\n \n \n \n \n n\n \n 11\n \n \n \n n\n \n 00\n \n \n \u2212\n \n n\n \n 10\n \n \n \n n\n \n 01\n \n \n \n \n \n n\n \n 1\n \u2219\n \n \n \n n\n \n 0\n \u2219\n \n \n \n n\n \n \u2219\n 0\n \n \n \n n\n \n \u2219\n 1\n \n \n \n \n \n .\n \n \n {\\displaystyle \\phi ={\\frac {n_{11}n_{00}-n_{10}n_{01}}{\\sqrt {n_{1\\bullet }n_{0\\bullet }n_{\\bullet 0}n_{\\bullet 1}}}}.}\n Phi is related to the point-biserial correlation coefficient and Cohen's d and estimates the extent of the relationship between two variables (2\u00d72).The phi coefficient can also be expressed using only \n \n \n \n n\n \n \n {\\displaystyle n}\n , \n \n \n \n \n n\n \n 11\n \n \n \n \n {\\displaystyle n_{11}}\n , \n \n \n \n \n n\n \n 1\n \u2219\n \n \n \n \n {\\displaystyle n_{1\\bullet }}\n , and \n \n \n \n \n n\n \n \u2219\n 1\n \n \n \n \n {\\displaystyle n_{\\bullet 1}}\n , as\n\n \n \n \n \u03d5\n =\n \n \n \n n\n \n n\n \n 11\n \n \n \u2212\n \n n\n \n 1\n \u2219\n \n \n \n n\n \n \u2219\n 1\n \n \n \n \n \n n\n \n 1\n \u2219\n \n \n \n n\n \n \u2219\n 1\n \n \n (\n n\n \u2212\n \n n\n \n 1\n \u2219\n \n \n )\n (\n n\n \u2212\n \n n\n \n \u2219\n 1\n \n \n )\n \n \n \n .\n \n \n {\\displaystyle \\phi ={\\frac {nn_{11}-n_{1\\bullet }n_{\\bullet 1}}{\\sqrt {n_{1\\bullet }n_{\\bullet 1}(n-n_{1\\bullet })(n-n_{\\bullet 1})}}}.}\n \n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared statistic", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Cram\u00e9r's V (statistics)", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Matthews correlation coefficient", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point-biserial correlation coefficient", "Point estimation", "Poisson regression", "Polychoric correlation", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.eric.ed.gov/ERICWebPortal/custom/portlets/recordDetails/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=ED433353&ERICExtSearch_SearchType_0=no&accno=ED433353"]}, "Whipple's index": {"categories": ["Population", "Sampling (statistics)"], "title": "Whipple's index", "method": "Whipple's index", "url": "https://en.wikipedia.org/wiki/Whipple%27s_index", "summary": "Whipple's index (or index of concentration), invented by American demographer George Chandler Whipple (1866\u20131924), is a method to measure the tendency for individuals to inaccurately report their actual age or date of birth. Respondents to a census or other survey sometimes report their age or date of birth as a round number (typically ending in 0 and 5), or to be more culturally favorable, for example, so that they appear younger or to have been born on a date considered luckier than their actual date of birth.", "images": [], "links": ["Census", "Chinese calendar", "Dragon (zodiac)", "GeoJournal", "George Chandler Whipple", "Han Chinese", "Kazakhs", "Rounding", "Statistical survey", "Turkic peoples", "United Nations", "Uyghur people", "Xinjiang"], "references": ["http://www.demogr.mpg.de/books/odense/6/12a.htm", "https://www.washingtonpost.com/wp-dyn/content/article/2007/02/28/AR2007022802104.html"]}, "Theil\u2013Sen estimator": {"categories": ["Computational geometry", "Good articles", "Robust regression"], "title": "Theil\u2013Sen estimator", "method": "Theil\u2013Sen estimator", "url": "https://en.wikipedia.org/wiki/Theil%E2%80%93Sen_estimator", "summary": "In non-parametric statistics, the Theil\u2013Sen estimator is a method for robustly fitting a line to sample points in the plane (simple linear regression) by choosing the median of the slopes of all lines through pairs of points. It has also been called Sen's slope estimator, slope selection, the single median method, the Kendall robust line-fit method, and the Kendall\u2013Theil robust line. It is named after Henri Theil and Pranab K. Sen, who published papers on this method in 1950 and 1968 respectively, and after Maurice Kendall because of its relation to the Kendall tau rank correlation coefficient.This estimator can be computed efficiently, and is insensitive to outliers. It can be significantly more accurate than non-robust simple linear regression for skewed and heteroskedastic data, and competes well against non-robust least squares even for normally distributed data in terms of statistical power. It has been called \"the most popular nonparametric technique for estimating a linear trend\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e9/Thiel-Sen_estimator.svg", "https://upload.wikimedia.org/wikipedia/en/9/94/Symbol_support_vote.svg"], "links": ["Affine transformation", "Algorithmica", "ArXiv", "Arrangement of lines", "Astronomy", "Bernard Chazelle", "Bibcode", "Biophysics", "Bitwise operation", "Breakdown point", "Censored regression model", "Climatology", "Computational Geometry (journal)", "Computational geometry", "Computer science", "Confidence interval", "David Eppstein", "David Mount", "Digital object identifier", "Efficiency (statistics)", "Endre Szemer\u00e9di", "Equivariant", "Errors and residuals", "Fitting a line", "Henri Theil", "Heteroskedastic", "Information Processing Letters", "International Standard Book Number", "JSTOR", "Ji\u0159\u00ed Matou\u0161ek (mathematician)", "Journal of the American Statistical Association", "Kendall tau rank correlation coefficient", "Least squares", "Linear equation", "Linear transformation", "Mathematical Reviews", "Maurice Kendall", "Median", "Meteorology", "Micha Sharir", "Michael T. Goodrich", "Mihai P\u0103tra\u015fcu", "Nathan Netanyahu", "Non-parametric statistics", "Normal distribution", "Ordinary least squares", "Outlier", "Peter Rousseeuw", "Pranab K. Sen", "Projective duality", "Python (programming language)", "R (programming language)", "Randomized algorithm", "Regression dilution", "Repeated median regression", "Robert M. Hirsch", "Robert R. Sokal", "Robust estimator", "Robust regression", "Robust statistics", "SIAM Journal on Computing", "Sampling (statistics)", "SciPy", "Scikit-learn", "Selection algorithm", "Simple linear regression", "Skewness", "Slope", "Software aging", "Statistical power", "Streaming algorithm", "Susan Murphy", "Timothy M. Chan", "US Geological Survey", "Unbiased estimator", "Visual Basic", "Water quality", "Weighted median", "Y-intercept", "\u0395-net (computational geometry)"], "references": ["http://adsabs.harvard.edu/abs/1982WRR....18..107H", "http://adsabs.harvard.edu/abs/2005RSEnv..95..303F", "http://adsabs.harvard.edu/abs/2015IJCli..35..288R", "http://www.ams.org/mathscinet-getitem?mr=0036489", "http://www.ams.org/mathscinet-getitem?mr=0258201", "http://www.ams.org/mathscinet-getitem?mr=0348930", "http://www.ams.org/mathscinet-getitem?mr=0468054", "http://www.ams.org/mathscinet-getitem?mr=1004799", "http://www.ams.org/mathscinet-getitem?mr=1130747", "http://www.ams.org/mathscinet-getitem?mr=1159839", "http://www.ams.org/mathscinet-getitem?mr=1237287", "http://www.ams.org/mathscinet-getitem?mr=1325124", "http://www.ams.org/mathscinet-getitem?mr=1484533", "http://www.ams.org/mathscinet-getitem?mr=1614381", "http://www.ams.org/mathscinet-getitem?mr=2165096", "http://www.ams.org/mathscinet-getitem?mr=2263136", "http://www.ams.org/mathscinet-getitem?mr=2335299", "http://arxiv.org/abs/cs/0307027", "http://doi.org/10.1002%2F(SICI)1521-4036(199807)40:3%3C261::AID-BIMJ261%3E3.0.CO;2-V", "http://doi.org/10.1002%2Fjoc.3981", "http://doi.org/10.1007%2F11758471_6", "http://doi.org/10.1007%2FPL00009190", "http://doi.org/10.1016%2F0020-0190(91)90177-J", "http://doi.org/10.1016%2F0020-0190(93)90234-Z", "http://doi.org/10.1016%2FS0925-7721(97)00025-4", "http://doi.org/10.1016%2Fj.rse.2005.01.005", "http://doi.org/10.1029%2FWR018i001p00107", "http://doi.org/10.1080%2F01621459.1978.10480067", "http://doi.org/10.1080%2F01621459.1995.10476499", "http://doi.org/10.1080%2F10485250500039452", "http://doi.org/10.1093%2Fbiomet%2F69.1.242", "http://doi.org/10.1109%2FTDSC.2005.15", "http://doi.org/10.1137%2F0218055", "http://doi.org/10.1142%2FS0218195992000020", "http://doi.org/10.1145%2F1240233.1240239", "http://doi.org/10.1214%2Faoms%2F1177692377", "http://doi.org/10.1214%2Faos%2F1176344204", "http://doi.org/10.2307%2F2285891", "http://www.jstor.org/stable/2285891", "http://www.jstor.org/stable/2286613", "http://www.jstor.org/stable/2291140", "http://www.jstor.org/stable/2958563", "http://siam.org/proceedings/soda/2010/SODA10_015_chant.pdf", "https://books.google.com/books?id=Bm4KQsT9kBUC&pg=PA19", "https://books.google.com/books?id=Lj5PU_psLCMC&pg=PA577", "https://books.google.com/books?id=N6KCNw5NHNkC&pg=PA539", "https://books.google.com/books?id=YSFb4QX2UIoC&pg=PA207", "https://books.google.com/books?id=ZvOljlNiWGkC&pg=PT229", "https://books.google.com/books?id=ZvOljlNiWGkC&pg=PT237", "https://books.google.com/books?id=ZvulFAhLIHYC&pg=PA230", "https://books.google.com/books?id=_vtvDQAAQBAJ&pg=PA177", "https://books.google.com/books?id=cfYS323GJAwC&pg=PA55", "https://books.google.com/books?id=jF0QhuxXeIwC&pg=PA355", "https://books.google.com/books?id=kF4L6eblK6wC&pg=PA113", "https://books.google.com/books?id=lEo1rvDGUEkC&pg=PA217", "https://books.google.com/books?id=lK9gHXwYnqgC&pg=PA67", "https://pubs.usgs.gov/tm/2006/tm4a7/", "https://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.stats.mstats.theilslopes.html", "https://books.google.co.uk/books?id=M5_FCgCuwFgC&pg=PA273#v=onepage&q&f=false"]}, "Linear least squares (mathematics)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2010", "Broad-concept articles", "Computational statistics", "Least squares", "Wikipedia articles needing page number citations from December 2010"], "title": "Linear least squares", "method": "Linear least squares (mathematics)", "url": "https://en.wikipedia.org/wiki/Linear_least_squares", "summary": "Linear least squares is the least squares approximation of linear functions to data.\nIt is a set of formulations for solving statistical problems involved in linear regression, including variants for \nordinary (unweighted),\nweighted, and \ngeneralized (correlated) residuals.\nNumerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e3/Linear_least_squares2.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b0/Linear_least_squares_example2.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Analysis of covariance", "Analysis of variance", "Approximation theory", "Arithmetic mean", "B-spline", "Bayesian experimental design", "Bayesian linear regression", "Bayesian multivariate linear regression", "Beer-Lambert law", "Bias of an estimator", "Bibcode", "Binomial regression", "Calibration curve", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared distribution", "Closed-form expression", "Computational statistics", "Confounding", "Consistent estimator", "Constrained least squares", "Convex function", "Correlation and dependence", "Cumulative distribution function", "Curve fitting", "Data", "Data fitting", "Degrees of freedom (statistics)", "Dependent variable", "Descriptive statistics", "Design of experiments", "Digital object identifier", "Discrete choice", "Dominating decision rule", "Efficiency (statistics)", "Errors-in-variables models", "Errors and residuals in statistics", "Expected value", "Experiment", "Fixed effects model", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Gran plot", "Growth curve (statistics)", "Heteroscedasticity", "Homoscedasticity", "Ill-conditioned", "Independent variable", "Instrumental variables", "International Standard Book Number", "Isotonic regression", "Iterative method", "Iteratively reweighted least squares", "JSTOR", "James\u2013Stein estimator", "Kendall tau rank correlation coefficient", "Least-angle regression", "Least absolute deviations", "Least squares", "Least squares approximation", "Line-line intersection", "Line fitting", "Linear functions", "Linear least squares (mathematics)", "Linear regression", "List of statistics articles", "Local regression", "Logistic regression", "Mallows's Cp", "Mathematical model", "Mathematical optimization", "Mathematics", "Maxima and minima", "Maximum likelihood", "Mean and predicted response", "Mean squared error", "Minimum mean-square error", "Minimum mean square error", "Mixed logit", "Mixed model", "Model selection", "Moving least squares", "Multicollinearity", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate analysis of variance", "Non-linear least squares", "Non-negative least squares", "Nonlinear least squares", "Nonlinear regression", "Nonparametric regression", "Normal distribution", "Numerical analysis", "Numerical integration", "Numerical methods for linear least squares", "Numerical smoothing and differentiation", "Objective function", "Observational study", "Optimal design", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Outline of regression analysis", "Outline of statistics", "Overdetermined system", "Parameter", "Partial correlation", "Partial derivative", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson product-moment correlation coefficient", "Poisson regression", "Polynomial", "Polynomial regression", "Prediction", "Principal component regression", "Prior probability", "Probit model", "Proceedings of the National Academy of Sciences", "PubMed Central", "Quantile regression", "Random effects model", "Rank correlation", "Regression analysis", "Regression model validation", "Regularization (mathematics)", "Regularized least squares", "Residual (statistics)", "Residuals (statistics)", "Response surface methodology", "Ridge regression", "Robust regression", "Segmented regression", "Semiparametric regression", "Shrinkage estimator", "Simple linear regression", "Social Science Research Network", "Spearman's rank correlation coefficient", "Standard addition", "Statistical inference", "Statistical model", "Statistics", "Stein's phenomenon", "Stepwise regression", "Studentized residual", "System identification", "Tikhonov regularization", "Total least squares", "Vandermonde matrix", "Weighted least squares"], "references": ["http://ssrn.com/abstract=1406472", "http://mathworld.wolfram.com/LeastSquaresFitting.html", "http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html", "http://adsabs.harvard.edu/abs/1978PNAS...75.3034L", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC392707", "http://doi.org/10.1073%2Fpnas.75.7.3034", "http://doi.org/10.1137%2F1036055", "http://doi.org/10.1214%2Faos%2F1176345987", "http://doi.org/10.1214%2Fss%2F1177012408", "http://doi.org/10.2139%2Fssrn.1406472", "http://www.jstor.org/stable/2132463", "http://www.jstor.org/stable/2240725", "http://www.jstor.org/stable/2245853", "http://www.jstor.org/stable/2986237", "http://www.jstor.org/stable/68164"]}, "Conservatism (belief revision)": {"categories": ["All articles lacking reliable references", "All articles needing expert attention", "All articles that are too technical", "Articles lacking reliable references from May 2012", "Articles needing expert attention from August 2016", "Articles with multiple maintenance issues", "Bayesian inference", "Belief revision", "Cognitive inertia", "Error", "Ignorance", "Wikipedia articles that are too technical from August 2016"], "title": "Conservatism (belief revision)", "method": "Conservatism (belief revision)", "url": "https://en.wikipedia.org/wiki/Conservatism_(belief_revision)", "summary": "In cognitive psychology and decision science, conservatism or conservatism bias is a bias in human information processing, which refers to the tendency to revise one's belief insufficiently when presented with new evidence. This bias describes human belief revision in which persons over-weigh the prior distribution (base rate) and under-weigh new sample evidence when compared to Bayesian belief-revision.\nAccording to the theory, \"opinion change is very orderly, and usually proportional to the numbers of Bayes' theorem \u2013 but it is insufficient in amount\". In other words, persons update their prior beliefs as new evidence becomes available, but they do so more slowly than they would if they used Bayes' theorem.\nThis bias was discussed by Ward Edwards in 1968, who reported on experiments like the following one:\n\nThere are two bookbags, one containing 700 red and 300 blue chips, the other containing 300 red and 700 blue. Take one of the bags. Now, you sample, randomly, with replacement after each chip. In 12 samples, you get 8 reds and 4 blues. what is the probability that this is the predominantly red bag?\nMost subjects chose an answer around .7. The correct answer according to Bayes' theorem is closer to .97. Edwards suggested that people updated beliefs conservatively, in accordance with Bayes' theorem more slowly. They updated from .5 incorrectly according to an observed bias in several experiments.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Anchoring bias", "Base rate", "Base rate fallacy", "Bayes' theorem", "Belief perseverance", "Belief revision", "Cognitive bias", "Cognitive psychology", "Decision science", "Digital object identifier", "Dividend", "Information-theoretic", "International Standard Book Number", "JSTOR", "Prior distribution", "Psychological Bulletin", "Statistical sample", "Stock split", "Ward Edwards"], "references": ["http://www.sciencedirect.com/science/article/pii/S0167268109001103", "http://www.martinhilbert.net/HilbertPsychBull.pdf", "http://psycnet.apa.org/psycinfo/2011-27261-001", "http://doi.org/10.1016%2Fj.jebo.2009.04.018", "http://doi.org/10.1086%2F381273", "http://www.jstor.org/stable/10.1086/381273", "https://doi.org/10.2139%2Fssrn.249979"]}, "Lotka's law": {"categories": ["Bibliometrics", "Statistical laws"], "title": "Lotka's law", "method": "Lotka's law", "url": "https://en.wikipedia.org/wiki/Lotka%27s_law", "summary": "Lotka's law, named after Alfred J. Lotka, is one of a variety of special applications of Zipf's law. It describes the frequency of publication by authors in any given field. It states that the number of authors making \n \n \n \n x\n \n \n {\\displaystyle x}\n contributions in a given period is a fraction of the number making a single contribution, following the formula \n \n \n \n 1\n \n /\n \n \n x\n \n a\n \n \n \n \n {\\displaystyle 1/x^{a}}\n where a nearly always equals two, i.e., an approximate inverse-square law, where the number of authors publishing a certain number of articles is a fixed ratio to the number of authors publishing a single article. As the number of articles published increases, authors producing that many publications become less frequent. There are 1/4 as many authors publishing two articles within a specified time period as there are single-publication authors, 1/9 as many publishing three articles, 1/16 as many publishing four articles, etc. Though the law itself covers many disciplines, the actual ratios involved (as a function of 'a') are discipline-specific.\n\nThe general formula says:\n\n \n \n \n \n X\n \n n\n \n \n Y\n =\n C\n \n \n {\\displaystyle X^{n}Y=C}\n or\n\n \n \n \n Y\n =\n C\n \n /\n \n \n X\n \n n\n \n \n ,\n \n \n \n {\\displaystyle Y=C/X^{n},\\,}\n where X is the number of publications, Y the relative frequency of authors with X publications, and n and \n \n \n \n C\n \n \n {\\displaystyle C}\n are constants depending on the specific field (\n \n \n \n n\n \u2248\n 2\n \n \n {\\displaystyle n\\approx 2}\n ).", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1e/Lotka_plot.png"], "links": ["Alfred J. Lotka", "Digital object identifier", "International Standard Serial Number", "Inverse-square law", "JSTOR", "Lotka's principle", "Price's law", "The rich get richer and the poor get poorer", "Zipf's law"], "references": ["http://doi.org/10.1002%2Fasi.20157", "http://doi.org/10.2307%2F2328824", "http://www.jstor.org/stable/2328824", "http://www.worldcat.org/issn/1137-5019", "http://www.revistadestatistica.ro/index.php/the-power-of-lotkas-law-through-the-eyes-of-r/", "https://archive.org/details/journalofwashin161926wash", "https://web.archive.org/web/20100204183250/http://www.cindoc.csic.es/cybermetrics/articles/v4i1p4.html", "https://www.worldcat.org/search?fq=x0:jrnl&q=n2:1018-046X"]}, "Inverse-chi-squared distribution": {"categories": ["Continuous distributions", "Exponential family distributions", "Pages using deprecated image syntax", "Probability distributions with non-finite variance"], "title": "Inverse-chi-squared distribution", "method": "Inverse-chi-squared distribution", "url": "https://en.wikipedia.org/wiki/Inverse-chi-squared_distribution", "summary": "In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued random variable. It is closely related to the chi-squared distribution and its specific importance is that it arises in the application of Bayesian inference to the normal distribution, where it can be used as the prior and posterior distribution for an unknown variance.", "images": ["https://upload.wikimedia.org/wikipedia/en/5/5a/Inverse_chi_squared_density.png", "https://upload.wikimedia.org/wikipedia/en/f/f0/Inverse_chi_squared_distribution.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian inference", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multiplicative inverse", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Posterior distribution", "Prior distribution", "Probability and statistics", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled-inverse-chi-squared distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["https://web.archive.org/web/20091031132559/http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/geoR/html/InvChisquare.html"]}, "Correlation inequality": {"categories": ["All stub articles", "Inequalities", "Probabilistic inequalities", "Quantum physics stubs", "Statistical mechanics"], "title": "Correlation inequality", "method": "Correlation inequality", "url": "https://en.wikipedia.org/wiki/Correlation_inequality", "summary": "A correlation inequality is any of a number of inequalities satisfied by the correlation functions of a model. Such inequalities are of particular use in statistical mechanics and in percolation theory.Examples include:\n\nBell's inequality\nFKG inequality\nGriffiths inequality, and its generalisation, the Ginibre inequality", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/ad/Hydrogen300.png"], "links": ["Bell's inequality", "Correlation function", "Encyclopedia of Mathematics", "FKG inequality", "Ginibre inequality", "Griffiths inequality", "International Standard Book Number", "Mathematical Reviews", "Michiel Hazewinkel", "Percolation theory", "Quantum mechanics", "Statistical mechanics"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0421547", "https://www.encyclopediaofmath.org/index.php?title=c/c110420"]}, "Neyman\u2013Pearson lemma": {"categories": ["All articles lacking in-text citations", "Articles containing proofs", "Articles lacking in-text citations from May 2018", "Lemmas", "Statistical tests", "Statistical theorems"], "title": "Neyman\u2013Pearson lemma", "method": "Neyman\u2013Pearson lemma", "url": "https://en.wikipedia.org/wiki/Neyman%E2%80%93Pearson_lemma", "summary": "In statistics, the Neyman\u2013Pearson lemma was introduced by Jerzy Neyman and Egon Pearson in a paper in 1933.Suppose one is performing a hypothesis test between two simple hypotheses H0: \u03b8 = \u03b80 and H1: \u03b8 = \u03b81 using the likelihood-ratio test with threshold \n \n \n \n \u03b7\n \n \n {\\displaystyle \\eta }\n , which rejects H0 in favour of H1 at a significance level of \n\n \n \n \n \u03b1\n =\n P\n (\n \u039b\n (\n X\n )\n \u2264\n \u03b7\n \u2223\n \n H\n \n 0\n \n \n )\n ,\n \n \n {\\displaystyle \\alpha =P(\\Lambda (X)\\leq \\eta \\mid H_{0}),}\n where\n\n \n \n \n \u039b\n (\n x\n )\n :=\n \n \n \n \n \n L\n \n \n (\n \n \u03b8\n \n 0\n \n \n \u2223\n x\n )\n \n \n \n \n L\n \n \n (\n \n \u03b8\n \n 1\n \n \n \u2223\n x\n )\n \n \n \n \n \n {\\displaystyle \\Lambda (x):={\\frac {{\\mathcal {L}}(\\theta _{0}\\mid x)}{{\\mathcal {L}}(\\theta _{1}\\mid x)}}}\n and \n \n \n \n \n \n L\n \n \n (\n \u03b8\n \u2223\n x\n )\n \n \n {\\displaystyle {\\mathcal {L}}(\\theta \\mid x)}\n is the likelihood function.\nThen, the lemma states that \n \n \n \n \u039b\n (\n x\n )\n \n \n {\\displaystyle \\Lambda (x)}\n is the most powerful test at significance level \u03b1.\nIf the test is most powerful for all \n \n \n \n \n \u03b8\n \n 1\n \n \n \u2208\n \n \u0398\n \n 1\n \n \n \n \n {\\displaystyle \\theta _{1}\\in \\Theta _{1}}\n , it is said to be uniformly most powerful (UMP) for alternatives in the set \n \n \n \n \n \u0398\n \n 1\n \n \n \n \n {\\displaystyle \\Theta _{1}}\n .\nIn practice, the likelihood ratio is often used directly to construct tests \u2014 see likelihood-ratio test. However it can also be used to suggest particular test-statistics that might be of interest or to suggest simplified tests \u2014 for this, one considers algebraic manipulation of the ratio to see if there are key statistics in it related to the size of the ratio (i.e. whether a large statistic corresponds to a small ratio or to a large one).", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Consumer theory", "Data transmission", "Decreasing function", "Demand function", "Digital object identifier", "Egon Pearson", "Electronics engineering", "F-distribution", "False positives and false negatives", "Inequality (mathematics)", "International Standard Serial Number", "Jerzy Neyman", "Large Hadron Collider", "Lemma (mathematics)", "Likelihood-ratio test", "Likelihood function", "New physics", "Normally distributed", "Radar", "Signal processing", "Standard Model", "Statistical hypothesis testing", "Statistical power", "Statistics", "Type I and type II errors", "Uniformly most powerful"], "references": ["http://bactra.org/weblog/630.html", "http://cnx.org/content/m11548/latest/", "http://doi.org/10.1016%2F0022-0531(84)90091-7", "http://doi.org/10.1098%2Frsta.1933.0009", "http://rsta.royalsocietypublishing.org/content/231/694-706/289", "http://www.worldcat.org/issn/0264-3952"]}, "Multivariate Pareto distribution": {"categories": ["Multivariate continuous distributions"], "title": "Multivariate Pareto distribution", "method": "Multivariate Pareto distribution", "url": "https://en.wikipedia.org/wiki/Multivariate_Pareto_distribution", "summary": "In statistics, a multivariate Pareto distribution is a multivariate extension of a univariate Pareto distribution.There are several different types of univariate Pareto distributions including Pareto Types I\u2212IV and Feller\u2212Pareto. Multivariate Pareto distributions have been defined for many of these types.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://doi.org/10.1214%2Faoms%2F1177704468"]}, "XLispStat": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from January 2016", "Lisp programming language family", "Pages using Infobox software with unknown parameters", "Statistical programming languages", "Statistical software"], "title": "XLispStat", "method": "XLispStat", "url": "https://en.wikipedia.org/wiki/XLispStat", "summary": "XLispStat is a statistical scientific package based on the XLISP language.\nAs from xlispstat startup:\n\n XLISP-PLUS version 3.04\n Portions Copyright (c) 1988, by David Betz.\n Modified by Thomas Almy and others.\n XLISP-STAT Release 3.52.20 (Beta).\n Copyright (c) 1989-1999, by Luke Tierney.\n\nMany free statistical software like ARC (nonlinear curve fitting problems) and ViSta are based on this package.It includes a variety of statistical functions and methods, including routines for nonlinear curve fit. Many add-on packages have been developed to extend XLispStat, including contingency tables and regression analysisXLispStat has seen usage in many fields, including astronomy, GIS, speech acoustics, econometrics, and epidemiology.XLispStat was historically influential in the field of statistical visualization.Its author, Luke Tierney, wrote a 1990 book on it.XLispStat dates to the late 1980s/early 1990s and probably saw its greatest popularity in the early-to-mid 1990s with greatly declining usage since. In the 1990s it was in very widespread use in statistical education, but has since been mostly replaced by R. There is a paper explaining why UCLA's Department of Statistics abandoned it in 1998, and their reasons for doing so likely hold true for many other of its former users.\nSource code to XLispStat is available under a permissive license (similar terms to BSD)", "images": [], "links": ["ADMB", "AmigaOS", "Analyse-it", "BMDP", "BSD licenses", "BV4.1 (software)", "CSPro", "Classic MacOS", "Commercial software", "Comparison of statistical packages", "Contingency table", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "Digital object identifier", "EViews", "Epi Info", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "International Standard Book Number", "International Standard Serial Number", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "MS-DOS", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "UNIX", "ViSta, The Visual Statistics system", "Win16", "Win32", "WinBUGS", "World Programming System", "X-12-ARIMA", "X11", "XLISP", "XLfit (software)", "XploRe"], "references": ["http:ftp://ftp.stat.umn.edu/pub/xlispstat/current/xlispstat-3-52-20.tar.gz", "http://lib.stat.cmu.edu/xlispstat/", "http://homepage.divms.uiowa.edu/~luke/xls/xlispstat/old/amiga/", "http://homepage.divms.uiowa.edu/~luke/xls/xlispstat/old/readme.dos", "http://homepage.divms.uiowa.edu/~luke/xls/xlsinfo/", "http://www.stat.uiowa.edu/~luke/xls/xlsinfo/xlsinfo.html", "http://www.stat.umn.edu/arc/", "http://doi.org/10.1007%2F978-3-662-26811-7_33", "http://www.worldcat.org/issn/1548-7660", "https://books.google.com/books?id=8qIMMbsO784C&pg=PA855", "https://books.google.com/books?id=ChpGSsqXIdoC&pg=PA25", "https://books.google.com/books?id=WESwss9Mjc0C&pg=PA186", "https://books.google.com/books?id=fjn0BwAAQBAJ&pg=PA193", "https://books.google.com/books?id=ie_KKAamFM4C&pg=PR3", "https://books.google.com/books?id=k1esnwVBVSwC&pg=PP1", "https://books.google.com/books?id=yej1K0wMTagC&pg=PA5", "https://books.google.com/books?id=zGkyBwAAQBAJ&pg=PP10", "https://www.jstatsoft.org/article/view/v013i07/v13i07.pdf"]}, "Sample mean and covariance": {"categories": ["All articles needing additional references", "All articles needing expert attention", "All articles that are too technical", "Articles needing additional references from February 2008", "Articles needing expert attention from June 2014", "Articles with multiple maintenance issues", "Covariance and correlation", "Estimation methods", "Matrices", "Summary statistics", "U-statistics", "Wikipedia articles that are too technical from June 2014"], "title": "Sample mean and covariance", "method": "Sample mean and covariance", "url": "https://en.wikipedia.org/wiki/Sample_mean_and_covariance", "summary": "The sample mean or empirical mean and the sample covariance are statistics computed from a collection (the sample) of data on one or more random variables.\nThe sample mean and sample covariance are estimators of the population mean and population covariance, where the term population refers to the set from which the sample was taken.\nThe sample mean is a vector each of whose elements is the sample mean of one of the random variables \u2013 that is, each of whose elements is the arithmetic average of the observed values of one of the variables. The sample covariance matrix is a square matrix whose i, j element is the sample covariance (an estimate of the population covariance) between the sets of observed values of two of the variables and whose i, i element is the sample variance of the observed values of one of the variables. If only one variable has had values observed, then the sample mean is a single number (the arithmetic average of the observed values of that variable) and the sample covariance matrix is also simply a single value (a 1x1 matrix containing a single number, the sample variance of the observed values of that variable).\nDue to their ease of calculation and other desirable characteristics, the sample mean and sample covariance are widely used in statistics and applications to numerically represent the location and dispersion, respectively, of a distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Arithmetic average", "Arithmetic mean", "Bart Kosko", "Bessel's correction", "Bias of an estimator", "Covariance", "Covariance matrix", "Estimation of covariance matrices", "Estimator", "Estimators", "Gaussian distribution", "International Standard Book Number", "Interquartile range", "Location parameter", "Matrix (mathematics)", "Maximum likelihood", "Mean", "Multivariate random variable", "Normalizing constant", "Outliers", "Positive semi-definite matrix", "Probability distribution", "Quantile", "Random variable", "Random variables", "Random vector", "Realization (probability)", "Robust statistics", "Sample (statistics)", "Sample median", "Sample variance", "Scatter matrix", "Standard error of the mean", "Statistic", "Statistical dispersion", "Statistical population", "Trimmed estimator", "Trimmed mean", "Unbiased estimation of standard deviation", "Vector (mathematics)", "Weighted mean", "Winsorising", "Winsorized mean"], "references": ["http://www.edge.org/q2008/q08_16.html#kosko", "https://books.google.com/books?id=gFWcQgAACAAJ", "https://www.gnu.org/software/gsl/manual", "https://www.gnu.org/software/gsl/manual/html_node/Weighted-Samples.html"]}, "Brownian excursion": {"categories": ["Wiener process"], "title": "Brownian excursion", "method": "Brownian excursion", "url": "https://en.wikipedia.org/wiki/Brownian_excursion", "summary": "In probability theory a Brownian excursion process is a stochastic process that is closely related to a Wiener process (or Brownian motion). Realisations of Brownian excursion processes are essentially just realizations of a Wiener process selected to satisfy certain conditions. In particular, a Brownian excursion process is a Wiener process conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. BEPs are important because, among other reasons, they naturally arise as the limit process of a number of conditional functional central limit theorems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5f/BrownExcursion1D.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "ArXiv", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Bibcode", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Conditional probability", "Confluent hypergeometric function", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Henry McKean", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "JSTOR", "Jump diffusion", "Jump process", "Kai Lai Chung", "Kiyoshi It\u014d", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Laplace transform", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical Reviews", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Paul L\u00e9vy (mathematician)", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "Svante Janson", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://www.emis.de/journals/EJP-ECP/article/view/471.html", "http://adsabs.harvard.edu/abs/1976ArM....14..155C", "http://www.ams.org/mathscinet-getitem?mr=0029120", "http://www.ams.org/mathscinet-getitem?mr=0345224", "http://www.ams.org/mathscinet-getitem?mr=0373035", "http://www.ams.org/mathscinet-getitem?mr=0402955", "http://www.ams.org/mathscinet-getitem?mr=0436354", "http://www.ams.org/mathscinet-getitem?mr=0467948", "http://www.ams.org/mathscinet-getitem?mr=0515820", "http://www.ams.org/mathscinet-getitem?mr=0714964", "http://www.ams.org/mathscinet-getitem?mr=0733673", "http://www.ams.org/mathscinet-getitem?mr=0752014", "http://www.ams.org/mathscinet-getitem?mr=0981568", "http://www.ams.org/mathscinet-getitem?mr=1725357", "http://www.ams.org/mathscinet-getitem?mr=2318402", "http://www.ams.org/mathscinet-getitem?mr=2365879", "http://arxiv.org/abs/0704.2289", "http://arxiv.org/abs/math/0306185", "http://doi.org/10.1002%2F(sici)1097-0312(199703)50:3%3C291::aid-cpa4%3E3.0.co;2-6", "http://doi.org/10.1006%2Fjctb.1994.1041", "http://doi.org/10.1007%2FBF00343738", "http://doi.org/10.1007%2Fbf02385832", "http://doi.org/10.1007%2Fs00453-001-0056-0", "http://doi.org/10.1007%2Fs10468-005-8762-y", "http://doi.org/10.1017%2Fs0001867800023739", "http://doi.org/10.1090%2Fs0002-9904-1975-13852-3", "http://doi.org/10.1214%2F07-ps104", "http://doi.org/10.1214%2Faop%2F1176993450", "http://doi.org/10.1214%2Faop%2F1176995155", "http://doi.org/10.1214%2Faop%2F1176995896", "http://doi.org/10.1214%2Faop%2F1176996607", "http://doi.org/10.1214%2Fejp.v12-471", "http://www.jstor.org/stable/2242808", "http://www.jstor.org/stable/2242845", "http://www.jstor.org/stable/2243513", "http://www.jstor.org/stable/3212843", "http://www.jstor.org/stable/3213611", "http://projecteuclid.org/euclid.aop/1176993450", "http://projecteuclid.org/euclid.aop/1176995155", "http://projecteuclid.org/euclid.aop/1176995896", "http://projecteuclid.org/euclid.bams/1183537153", "https://link.springer.com/article/10.1007%2FBF00343738", "https://link.springer.com/article/10.1007%2FBF02385832"]}, "Chernoff's distribution": {"categories": ["All stub articles", "Continuous distributions", "Probability stubs", "Statistics stubs", "Stochastic processes"], "title": "Chernoff's distribution", "method": "Chernoff's distribution", "url": "https://en.wikipedia.org/wiki/Chernoff%27s_distribution", "summary": "In probability theory, Chernoff's distribution, named after Herman Chernoff, is the probability distribution of the random variable\n\n \n \n \n Z\n =\n \n \n argmax\n \n s\n \u2208\n \n R\n \n \n \n \n \n (\n W\n (\n s\n )\n \u2212\n \n s\n \n 2\n \n \n )\n ,\n \n \n {\\displaystyle Z={\\underset {s\\in \\mathbf {R} }{\\operatorname {argmax} }}\\ (W(s)-s^{2}),}\n where W is a \"two-sided\" Wiener process (or two-sided \"Brownian motion\") satisfying W(0) = 0. \nIf\n\n \n \n \n V\n (\n a\n ,\n c\n )\n =\n \n \n argmax\n \n s\n \u2208\n \n R\n \n \n \n \n \n (\n W\n (\n s\n )\n \u2212\n c\n (\n s\n \u2212\n a\n \n )\n \n 2\n \n \n )\n ,\n \n \n {\\displaystyle V(a,c)={\\underset {s\\in \\mathbf {R} }{\\operatorname {argmax} }}\\ (W(s)-c(s-a)^{2}),}\n then V(0, c) has density\n\n \n \n \n \n f\n \n c\n \n \n (\n t\n )\n =\n \n \n 1\n 2\n \n \n \n g\n \n c\n \n \n (\n t\n )\n \n g\n \n c\n \n \n (\n \u2212\n t\n )\n \n \n {\\displaystyle f_{c}(t)={\\frac {1}{2}}g_{c}(t)g_{c}(-t)}\n where gc has Fourier transform given by\n\n \n \n \n \n \n \n \n g\n ^\n \n \n \n \n c\n \n \n (\n s\n )\n =\n \n \n \n (\n 2\n \n /\n \n c\n \n )\n \n 1\n \n /\n \n 3\n \n \n \n \n Ai\n \u2061\n (\n i\n (\n 2\n \n c\n \n 2\n \n \n \n )\n \n \u2212\n 1\n \n /\n \n 3\n \n \n s\n )\n \n \n \n ,\n \n \n \n s\n \u2208\n \n R\n \n \n \n {\\displaystyle {\\hat {g}}_{c}(s)={\\frac {(2/c)^{1/3}}{\\operatorname {Ai} (i(2c^{2})^{-1/3}s)}},\\ \\ \\ s\\in \\mathbf {R} }\n and where Ai is the Airy function. Thus fc is symmetric about 0 and the density \u0192Z = \u01921. Groeneboom (1989) shows that\n\n \n \n \n \n f\n \n Z\n \n \n (\n z\n )\n \u223c\n \n \n 1\n 2\n \n \n \n \n \n \n 4\n \n 4\n \n /\n \n 3\n \n \n \n |\n \n z\n \n |\n \n \n \n \n Ai\n \u2032\n \n \u2061\n (\n \n \n \n \n a\n ~\n \n \n \n \n 1\n \n \n )\n \n \n \n exp\n \u2061\n \n (\n \n \u2212\n \n \n 2\n 3\n \n \n \n |\n \n z\n \n \n |\n \n \n 3\n \n \n +\n \n 2\n \n 1\n \n /\n \n 3\n \n \n \n \n \n \n a\n ~\n \n \n \n \n 1\n \n \n \n |\n \n z\n \n |\n \n \n )\n \n \n as \n \n z\n \u2192\n \u221e\n \n \n {\\displaystyle f_{Z}(z)\\sim {\\frac {1}{2}}{\\frac {4^{4/3}|z|}{\\operatorname {Ai} '({\\tilde {a}}_{1})}}\\exp \\left(-{\\frac {2}{3}}|z|^{3}+2^{1/3}{\\tilde {a}}_{1}|z|\\right){\\text{ as }}z\\rightarrow \\infty }\n where \n \n \n \n \n \n \n \n a\n ~\n \n \n \n \n 1\n \n \n \u2248\n \u2212\n 2.3381\n \n \n {\\displaystyle {\\tilde {a}}_{1}\\approx -2.3381}\n is the largest zero of the Airy function Ai and where \n \n \n \n \n Ai\n \u2032\n \n \u2061\n (\n \n \n \n \n a\n ~\n \n \n \n \n 1\n \n \n )\n \u2248\n 0.7022\n \n \n {\\displaystyle \\operatorname {Ai} '({\\tilde {a}}_{1})\\approx 0.7022}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg"], "links": ["ARGUS distribution", "Airy function", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Brownian motion", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fourier transform", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Herman Chernoff", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mathematical Reviews", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wiener process", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0981568", "http://www.ams.org/mathscinet-getitem?mr=1939706", "http://doi.org/10.1007%2FBF00343738", "http://doi.org/10.1198%2F10618600152627997"]}, "Bootstrap error-adjusted single-sample technique": {"categories": ["All articles needing additional references", "All articles needing expert attention", "All articles that are too technical", "All articles with incomplete citations", "All orphaned articles", "Articles created via the Article Wizard", "Articles needing additional references from February 2011", "Articles needing expert attention from March 2011", "Articles with incomplete citations from November 2012", "Articles with multiple maintenance issues", "Computational statistics", "Orphaned articles from February 2011", "Resampling (statistics)", "Wikipedia articles needing clarification from February 2011", "Wikipedia articles needing clarification from March 2011", "Wikipedia articles that are too technical from March 2011"], "title": "Bootstrap error-adjusted single-sample technique", "method": "Bootstrap error-adjusted single-sample technique", "url": "https://en.wikipedia.org/wiki/Bootstrap_error-adjusted_single-sample_technique", "summary": "In statistics, the bootstrap error-adjusted single-sample technique (BEST or the BEAST) is a non-parametric method that is intended to allow an assessment to be made of the validity of a single sample. It is based on estimating a probability distribution representing what can be expected from valid samples. This is done use a statistical method called bootstrapping, applied to previous samples that are known to be valid.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/6/6c/Wiki_letter_w.svg"], "links": ["Analytical Chemistry (journal)", "Bootstrapping (statistics)", "Cluster analysis", "Covariance", "Digital object identifier", "ICP-AES", "Mahalanobis distance", "Monte Carlo method", "Non-parametric statistics", "Nondestructive testing", "Normal distribution", "Probability distribution", "Standard deviation", "Statistics", "The American Statistician"], "references": ["http://edwardbetts.com/find_link?q=Bootstrap_error-adjusted_single-sample_technique", "http://doi.org/10.1021/ac00142a008", "http://doi.org/10.1366/0003702884429652", "http://doi.org/10.2307/2685844", "http://www.opticsinfobase.org/abstract.cfm?URI=as-42-8-1351"]}, "Quadratic variation": {"categories": ["Stochastic processes"], "title": "Quadratic variation", "method": "Quadratic variation", "url": "https://en.wikipedia.org/wiki/Quadratic_variation", "summary": "In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and other martingales. Quadratic variation is just one kind of variation of a process.", "images": [], "links": ["Bounded variation", "Brownian Motion", "Convergence of random variables", "C\u00e0dl\u00e0g", "Doob\u2013Meyer decomposition theorem", "International Standard Book Number", "It\u00f4's lemma", "It\u00f4 integral", "It\u00f4 isometry", "It\u00f4 process", "Local martingale", "Martingale (probability theory)", "Mathematics", "Mesh (mathematics)", "P-variation", "Partition of an interval", "Polarization identity", "Predictable process", "Probability space", "Proceedings - Mathematical Sciences", "Semimartingale", "Square integrable", "Stochastic process", "Total variation", "Wiener process"], "references": ["http://www.ias.ac.in/article/fulltext/pmsc/124/03/0457-0469"]}, "Stationary distribution": {"categories": ["All set index articles", "Set indices on mathematics", "Time series"], "title": "Stationary distribution", "method": "Stationary distribution", "url": "https://en.wikipedia.org/wiki/Stationary_distribution", "summary": "Stationary distribution may refer to:\n\nA special distribution for a Markov chain such that if the chain starts with its stationary distribution, the marginal distribution of all states at any time will always be the stationary distribution. Assuming irreducibility, the stationary distribution is always unique if it exists, and its existence can be implied by positive recurrence of all states. The stationary distribution has the interpretation of the limiting distribution when the chain is ergodic.\nThe marginal distribution of a stationary process or stationary time series\nThe set of joint probability distributions of a stationary process or stationary time seriesIn some fields of application, the term stable distribution is used for the equivalent of a stationary (marginal) distribution, although in probability and statistics the term has a rather different meaning: see stable distribution.\nCrudely stated, all of the above are specific cases of a common general concept. A stationary distribution is a specific entity which is unchanged by the effect of some matrix or operator: it need not be unique. Thus stationary distributions are related to eigenvectors for which the eigenvalue is unity.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8c/DAB_list_gray.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/8c/20090407201847%21DAB_list_gray.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/8c/20090407180053%21DAB_list_gray.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/8c/20090407175200%21DAB_list_gray.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/8c/20090407145503%21DAB_list_gray.svg"], "links": ["Asymptotic distribution", "Eigenvalue", "Eigenvector", "Ground state", "Joint probability distribution", "Marginal distribution", "Markov chain", "Perron\u2013Frobenius theorem", "Probability", "Stable distribution", "Stationary ergodic process", "Stationary process", "Stationary state", "Statistics", "Time series"], "references": []}, "Lukacs's proportion-sum independence theorem": {"categories": ["Characterization of probability distributions", "Probability theorems"], "title": "Lukacs's proportion-sum independence theorem", "method": "Lukacs's proportion-sum independence theorem", "url": "https://en.wikipedia.org/wiki/Lukacs%27s_proportion-sum_independence_theorem", "summary": "In statistics, Lukacs's proportion-sum independence theorem is a result that is used when studying proportions, in particular the Dirichlet distribution. It is named for Eugene Lukacs.", "images": [], "links": ["Digital object identifier", "Dirichlet distribution", "Eugene Lukacs", "Gamma distribution", "If and only if", "International Standard Book Number", "JSTOR", "Random variable", "Statistical independence", "Statistics"], "references": ["http://doi.org/10.1093%2Fbiomet%2F49.1-2.65", "http://doi.org/10.1214%2Faoms%2F1177728549", "http://www.jstor.org/stable/2333468", "https://books.google.com/books?id=k8GS868oyo4C&pg=PT81&dq#v=onepage&q&f=false"]}, "Median-unbiased estimator": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2012", "Articles with unsourced statements from May 2012", "Articles with unsourced statements from October 2015", "Means", "Robust statistics", "Webarchive template wayback links", "Wikipedia articles incorporating text from PlanetMath"], "title": "Median", "method": "Median-unbiased estimator", "url": "https://en.wikipedia.org/wiki/Median", "summary": "The median is the value separating the higher half from the lower half of a data sample (a population or a probability distribution). For a data set, it may be thought of as the \"middle\" value. For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6, the fourth largest, and also the fourth smallest, number in the sample. For a continuous probability distribution, the median is the value such that a number is equally likely to fall above or below it.\nThe median is a commonly used measure of the properties of a data set in statistics and probability theory. The basic advantage of the median in describing data compared to the mean (often simply described as the \"average\") is that it is not skewed so much by extremely large or small values, and so it may give a better idea of a \"typical\" value. For example, in understanding statistics like household income or assets which vary greatly, a mean may be skewed by a small number of extremely high or low values. Median income, for example, may be a better way to suggest what a \"typical\" income is.\nBecause of this, the median is of central importance in robust statistics, as it is the most resistant statistic, having a breakdown point of 50%: so long as no more than half the data are contaminated, the median will not give an arbitrarily large or small result.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/de/Comparison_mean_median_mode.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cf/Finding_the_median.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/3/33/Visualisation_mode_median_mean.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["A Treatise on Probability", "Abraham Wald", "Absolute continuity", "Absolute deviation", "Accelerated failure time model", "Actuarial science", "Adrien-Marie Legendre", "Akaike information criterion", "Allan Birnbaum", "An inequality on location and scale parameters", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Mathematical Statistics", "Annals of Statistics", "Antoine Augustin Cournot", "Arithmetic mean", "Array (data structure)", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Banach space", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Big O notation", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breakdown point", "Breusch\u2013Godfrey test", "Canonical correlation", "Cantelli's inequality", "Carl Friedrich Gauss", "Cartography", "Categorical variable", "Cauchy distribution", "Census", "Centerpoint (geometry)", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Compass", "Completeness (statistics)", "Computational complexity theory", "Concentration of measure", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decile", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension (linear algebra)", "Distance metric", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Edward Wright (mathematician)", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empty set", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Euclidean norm", "Expected loss", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Francis Galton", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gauss", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric median", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gustav Theodor Fechner", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Image processing", "Income inequality metrics", "Index of dispersion", "Injective function", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval (mathematics)", "Interval estimation", "Iowa", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen's inequality", "Johansen test", "John Tukey", "Jonckheere's trend test", "Journal of the American Statistical Association", "K-means clustering", "K-medians clustering", "K-medoids", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "L1-norm", "L1 norm", "Laplace", "Least squares", "Lebesgue\u2013Stieltjes integral", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Lipschitz functions", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location theory", "Location\u2013scale family", "Log-normal distribution", "Log-rank test", "Logistic regression", "Loss function", "Loss functions", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "MathWorld", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean absolute deviation", "Median-unbiased estimator", "Median (disambiguation)", "Median (geometry)", "Median absolute deviation", "Median filter", "Median graph", "Median search", "Median slope", "Median voter theory", "Medical statistics", "Medoid", "Method of moments (statistics)", "Methods engineering", "Metric (mathematics)", "Michiel Hazewinkel", "Mid-range", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monochrome", "Monotone likelihood ratio", "Multiple comparisons", "Multiset", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate median", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New York (state)", "Noise reduction", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normed space", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Pareto distribution", "Pareto interpolation", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Rousseeuw", "Pie chart", "Pierre-Simon Laplace", "Pivotal quantity", "PlanetMath", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Power law", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability theory", "Proceedings of the National Academy of Sciences of the United States of America", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quartile", "Quasi-experiment", "Questionnaire", "Quicksort", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raster image", "Rate parameter", "Real number", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Resistant 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"Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen Stigler", "Stratified sampling", "Strictly convex function", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Summary statistic", "Survey methodology", "Survival analysis", "Survival function", "Symmetric distribution", "System identification", "Talmud", "Theil\u2013Sen estimator", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Trimmed estimator", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "Unimodal distribution", "V-statistic", "Variance", "Vector autoregression", "Vector space", "Wald test", "Wavelet", "Wayback Machine", "Weak ordering", "Weibull distribution", "Weighted median", "Whittle likelihood", "Wilcoxon signed-rank test", "Yisrael Aumann", "Z-test", "Zentralblatt MATH"], "references": ["http://www.montefiore.ulg.ac.be/~kvansteen/MATH0008-2/ac20112012/Class3/Chapter2_ac1112_vfinalPartII.pdf", "http://wis.kuleuven.be/stat/robust/papers/publications-1990/rousseeuwbassett-remedian-jasa-1990.pdf", "http://www.statcan.gc.ca/edu/power-pouvoir/ch11/median-mediane/5214872-eng.htm", "http://www.accessecon.com/pubs/EB/2004/Volume3/EB-04C10011A.pdf", "http://www.celiagreen.com/charlesmccreery/statistics/meanmedianmode.pdf", "http://danadler.com/blog/2014/12/31/talmud-and-modern-economics/", "http://apstatsreview.tumblr.com/post/50058615236/density-curves-and-the-normal-distributions?action=purge", "http://mathworld.wolfram.com/StatisticalMedian.html", "http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.8162", "http://www.personal.psu.edu/users/e/c/ecb5/Courses/M475W/WeeklyReadings/Week%2013/DevelopmentOfModernStatistics.pdf", "http://www.stat.psu.edu/old_resources/ClassNotes/ljs_07/sld008.htm", "http://www.iowa.gov/tax/locgov/Statistical_Calculation_Definitions.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC26449", "http://www.ncbi.nlm.nih.gov/pubmed/10677477", "http://www.tax.ny.gov/research/property/reports/cod/2010mvs/reporttext.htm", "http://www.wisdom.weizmann.ac.il/math/AABeyond12/presentations/Aumann.pdf", "http://mathschallenge.net/index.php?section=problems&show=true&titleid=average_problem", "http://repository.tudelft.nl/islandora/object/uuid:8e67fb99-7cb7-4b11-8e6a-02039c7ed1bb/datastream/OBJ/view", "http://www.ams.org/mathscinet-getitem?mr=0125674", "http://www.ams.org/mathscinet-getitem?mr=0326872", "http://www.ams.org/mathscinet-getitem?mr=0902264", "http://www.ams.org/mathscinet-getitem?mr=0949228", "http://www.ams.org/mathscinet-getitem?mr=1291393", "http://www.ams.org/mathscinet-getitem?mr=1604954", "http://www.ams.org/mathscinet-getitem?mr=2598854", "http://www.amstat.org/publications/jse/v13n2/vonhippel.html", "http://doi.org/10.1002%2Fbimj.200410148", "http://doi.org/10.1002%2Fspe.4380231105", "http://doi.org/10.1007%2F978-1-4419-0468-3", "http://doi.org/10.1007%2FBF00356105", "http://doi.org/10.1016%2Fj.spl.2004.11.010", "http://doi.org/10.1073%2Fpnas.97.4.1423", "http://doi.org/10.1080%2F00031305.1991.10475815", "http://doi.org/10.1080%2F01621459.1960.10482056", "http://doi.org/10.1080%2F01621459.1990.10475311", "http://doi.org/10.1093%2Fbiomet%2F60.3.439", "http://doi.org/10.1117%2F12.946562", "http://doi.org/10.1137%2FS0040585X97975447", "http://doi.org/10.1214%2Faoms%2F1177705051", "http://doi.org/10.1214%2Faoms%2F1177705145", "http://doi.org/10.1214%2Faoms%2F1177729549", "http://doi.org/10.1214%2Faoms%2F1177730349", "http://doi.org/10.1214%2Faoms%2F1177731868", "http://doi.org/10.1214%2Faos%2F1176344552", "http://doi.org/10.1214%2Faos%2F1176347263", "http://doi.org/10.1214%2Faos%2F1176347978", "http://doi.org/10.1214%2Faos%2F1176350511", "http://www.jstor.org/stable/2235677", "http://www.jstor.org/stable/2236236", "http://www.jstor.org/stable/2236928", "http://www.jstor.org/stable/2237612", "http://www.jstor.org/stable/2237754", "http://www.jstor.org/stable/2241717", "http://www.jstor.org/stable/2241852", "http://www.jstor.org/stable/2334992", "http://www.jstor.org/stable/25047749", "http://www.jstor.org/stable/2958830", "http://projecteuclid.org/euclid.aos/1176343543", "http://www.poorcity.richcity.org/cgi-bin/inequality.cgi", "http://www.poorcity.richcity.org/oei/#GiniHooverTheil", "http://zbmath.org/?format=complete&q=an:0045.08606", "http://www3.stat.sinica.edu.tw/statistica/password.asp?vol=14&num=4&art=11", "http://www.state.sd.us/drr2/publications/assess1199.pdf", "https://books.google.com/books?id=YSFb4QX2UIoC&pg=PA207", "https://books.google.com/books?id=bmwhcJqq01cC&pg=PA7", "https://books.google.com/books?id=cTwwtyBX7PAC&pg=PA26", "https://web.archive.org/web/20090510034115/http://www.state.sd.us/drr2/publications/assess1199.pdf", "https://web.archive.org/web/20100730032416/http://www.stat.psu.edu/old_resources/ClassNotes/ljs_07/sld008.htm", "https://web.archive.org/web/20101111214903/http://iowa.gov/tax/locgov/Statistical_Calculation_Definitions.pdf", "https://web.archive.org/web/20110310043642/http://www.universityofcalifornia.edu/senate/inmemoriam/georgewbrown.htm", "https://web.archive.org/web/20121106015231/http://www.tax.ny.gov/research/property/reports/cod/2010mvs/reporttext.htm", "https://arxiv.org/abs/0806.3301", "https://arxiv.org/pdf/cond-mat/0412004.pdf", "https://www.biodiversitylibrary.org/item/94448", "https://doi.org/10.1214%2Faos%2F1176343543", "https://doi.org/10.2307%2F1403809", "https://www.encyclopediaofmath.org/index.php/Galton,_Francis", "https://www.encyclopediaofmath.org/index.php?title=p/m063310", "https://www.jstor.org/stable/1403809"]}, "Bates distribution": {"categories": ["All articles lacking in-text citations", "All stub articles", "Articles lacking in-text citations from June 2011", "Continuous distributions", "Pages using deprecated image syntax", "Probability stubs"], "title": "Bates distribution", "method": "Bates distribution", "url": "https://en.wikipedia.org/wiki/Bates_distribution", "summary": "In probability and statistics, the Bates distribution, named after Grace Bates, is a probability distribution of the mean of a number of statistically independent uniformly distributed random variables on the unit interval. This distribution is sometimes confused with the Irwin\u2013Hall distribution, which is the distribution of the sum (not the mean) of n independent random variables uniformly distributed from 0 to 1.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/BatesCDF.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1d/BatesPDF.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg"], "links": ["ARGUS distribution", "Annals of Mathematical Statistics", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous uniform distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Grace Bates", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independence (probability theory)", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign function", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistically independent", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unit interval", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["https://github.com/d3/d3/issues/1647"]}, "Fisher's z-distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax"], "title": "Fisher's z-distribution", "method": "Fisher's z-distribution", "url": "https://en.wikipedia.org/wiki/Fisher%27s_z-distribution", "summary": "Fisher's z-distribution is the statistical distribution of half the logarithm of an F-distribution variate:\n\n \n \n \n z\n =\n \n \n 1\n 2\n \n \n log\n \u2061\n F\n \n \n {\\displaystyle z={\\frac {1}{2}}\\log F}\n It was first described by Ronald Fisher in a paper delivered at the International Mathematical Congress of 1924 in Toronto. Nowadays one usually uses the F-distribution instead.\nThe probability density function and cumulative distribution function can be found by using the F-distribution at the value of \n \n \n \n \n x\n \u2032\n \n =\n \n e\n \n 2\n x\n \n \n \n \n \n {\\displaystyle x'=e^{2x}\\,}\n . However, the mean and variance do not follow the same transformation.\nThe probability density function is\n\n \n \n \n f\n (\n x\n ;\n \n d\n \n 1\n \n \n ,\n \n d\n \n 2\n \n \n )\n =\n \n \n \n 2\n \n d\n \n 1\n \n \n \n d\n \n 1\n \n \n \n /\n \n 2\n \n \n \n d\n \n 2\n \n \n \n d\n \n 2\n \n \n \n /\n \n 2\n \n \n \n \n B\n (\n \n d\n \n 1\n \n \n \n /\n \n 2\n ,\n \n d\n \n 2\n \n \n \n /\n \n 2\n )\n \n \n \n \n \n \n e\n \n \n d\n \n 1\n \n \n x\n \n \n \n \n (\n \n \n d\n \n 1\n \n \n \n e\n \n 2\n x\n \n \n +\n \n d\n \n 2\n \n \n \n )\n \n \n (\n \n d\n \n 1\n \n \n +\n \n d\n \n 2\n \n \n )\n \n /\n \n 2\n \n \n \n \n ,\n \n \n {\\displaystyle f(x;d_{1},d_{2})={\\frac {2d_{1}^{d_{1}/2}d_{2}^{d_{2}/2}}{B(d_{1}/2,d_{2}/2)}}{\\frac {e^{d_{1}x}}{\\left(d_{1}e^{2x}+d_{2}\\right)^{(d_{1}+d_{2})/2}}},}\n where B is the beta function.\nWhen the degrees of freedom becomes large (\n \n \n \n \n d\n \n 1\n \n \n ,\n \n d\n \n 2\n \n \n \u2192\n \u221e\n \n \n {\\displaystyle d_{1},d_{2}\\rightarrow \\infty }\n ) the distribution approach normality with mean\n\n \n \n \n \n \n \n x\n \u00af\n \n \n \n =\n \n \n 1\n 2\n \n \n \n (\n \n \n \n 1\n \n d\n \n 2\n \n \n \n \n \u2212\n \n \n 1\n \n d\n \n 1\n \n \n \n \n \n )\n \n \n \n {\\displaystyle {\\bar {x}}={\\frac {1}{2}}\\left({\\frac {1}{d_{2}}}-{\\frac {1}{d_{1}}}\\right)}\n and variance\n\n \n \n \n \n \u03c3\n \n x\n \n \n 2\n \n \n =\n \n \n 1\n 2\n \n \n \n (\n \n \n \n 1\n \n d\n \n 1\n \n \n \n \n +\n \n \n 1\n \n d\n \n 2\n \n \n \n \n \n )\n \n .\n \n \n {\\displaystyle \\sigma _{x}^{2}={\\frac {1}{2}}\\left({\\frac {1}{d_{1}}}+{\\frac {1}{d_{2}}}\\right).}", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b3/FisherZDistriPDF.svg", "https://upload.wikimedia.org/wikipedia/commons/a/aa/Youngronaldfisher2.JPG"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Charles Ernest Weatherburn", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher z-transformation", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Mathematical Congress", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Leo A. Aroian", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Ronald Fisher", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Statistical distribution", "Student's t-distribution", "Support (mathematics)", "Toronto", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Variate", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://digital.library.adelaide.edu.au/coll/special/fisher/36.pdf", "http://mathworld.wolfram.com/Fishersz-Distribution.html", "http://doi.org/10.1214%2Faoms%2F1177731681", "http://www.jstor.org/stable/2235955", "https://web.archive.org/web/20110412083610/http://digital.library.adelaide.edu.au/coll/special//fisher/36.pdf"]}, "Q-exponential distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax", "Probability distributions with non-finite variance", "Statistical mechanics"], "title": "Q-exponential distribution", "method": "Q-exponential distribution", "url": "https://en.wikipedia.org/wiki/Q-exponential_distribution", "summary": "The q-exponential distribution is a probability distribution arising from the maximization of the Tsallis entropy under appropriate constraints, including constraining the domain to be positive. It is one example of a Tsallis distribution. The q-exponential is a generalization of the exponential distribution in the same way that Tsallis entropy is a generalization of standard Boltzmann\u2013Gibbs entropy or Shannon entropy. The exponential distribution is recovered as \n \n \n \n q\n \u2192\n 1.\n \n \n {\\displaystyle q\\rightarrow 1.}\n \nOriginally proposed by the statisticians George Box and David Cox in 1964, and known as the reverse Box\u2013Cox transformation for \n \n \n \n q\n =\n 1\n \u2212\n \u03bb\n ,\n \n \n {\\displaystyle q=1-\\lambda ,}\n a particular case of power transform in statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d9/The_Probability_Density_Function_of_q-exponential_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/d9/20140814232149%21The_Probability_Density_Function_of_q-exponential_distribution.svg"], "links": ["ARGUS distribution", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Box\u2013Cox transformation", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Constantino Tsallis", "Conway\u2013Maxwell\u2013Poisson distribution", "Copula (probability theory)", "Cumulative distribution function", "Dagum distribution", "David Cox (statistician)", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Entropy (information theory)", "Entropy (statistical thermodynamics)", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "George Box", "George E. P. Box", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverse transform sampling", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the Royal Statistical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mathematical Reviews", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Phys. Rev. A", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Power transform", "Probability density function", "Probability distribution", "Q-Gaussian", "Q-Gaussian distribution", "Q-Weibull distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rate parameter", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tsallis distribution", "Tsallis entropy", "Tsallis statistics", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://e1.newcastle.edu.au/coffee/pubs/wp/2007/07-10.pdf", "http://adsabs.harvard.edu/abs/2016PhRvA..94c3808S", "http://www.cscs.umich.edu/~crshalizi/notebooks/tsallis.html", "http://www.ams.org/mathscinet-getitem?mr=0192611", "http://arxiv.org/abs/1606.08430", "http://doi.org/10.1103%2FPhysRevA.94.033808", "http://www.jstor.org/stable/2984418"]}, "Long-tail traffic": {"categories": ["Autocorrelation", "CS1 maint: Multiple names: authors list", "Stochastic processes", "Tails of probability distributions", "Teletraffic", "Webarchive template wayback links"], "title": "Long-tail traffic", "method": "Long-tail traffic", "url": "https://en.wikipedia.org/wiki/Long-tail_traffic", "summary": "A long-tailed or heavy-tailed probability distribution is one that assigns relatively high probabilities to regions far from the mean or median. A more formal mathematical definition is given below. In the context of teletraffic engineering a number of quantities of interest have been shown to have a long-tailed distribution. For example, if we consider the sizes of files transferred from a web-server, then, to a good degree of accuracy, the distribution is heavy-tailed, that is, there are a large number of small files transferred but, crucially, the number of very large files transferred remains a major component of the volume downloaded.\nMany processes are technically long-range dependent but not self-similar. The differences between these two phenomena are subtle. Heavy-tailed refers to a probability distribution, and long-range dependent refers to a property of a time series and so these should be used with care and a distinction should be made. The terms are distinct although superpositions of samples from heavy-tailed distributions aggregate to form long-range dependent time series.\nAdditionally there is Brownian motion which is self-similar but not long-range dependent.", "images": [], "links": ["ARIMA", "Agner Krarup Erlang", "ArXiv", "Asynchronous transfer mode", "Autocorrelation", "Autocovariance", "Availability", "Bandwidth (computing)", "Beno\u00eet Mandelbrot", "Bibcode", "Brownian motion", "Buffer (computer science)", "Burstiness", "Central limit theorem", "Client/server", "Cumulative distribution function", "Digital object identifier", "Elephant Flow", "Ethernet", "Exponential distribution", "File Transfer Protocol", "Fractal", "Gaussian process", "HTTP", "Heavy-tailed", "Hurst parameter", "International Standard Book Number", "Internet", "Internet protocol", "JSTOR", "Jitter", "Latency (engineering)", "Long-tail traffic", "Long-tailed distribution", "Markov chain", "Multimedia", "Multiplexing", "Network congestion", "Network performance", "Network topology", "Nonlinearity", "Normal distribution", "Open-loop controller", "Packet loss", "Pareto distribution", "Poisson distribution", "Probability distribution", "Probability mass function", "Protocol (computing)", "Provisioning", "PubMed Central", "PubMed Identifier", "Quality of service", "Random variable", "Self-similar", "Self-similarity", "Service level agreement", "Signalling System No. 7", "Stateless server", "Statistical independence", "TELNET", "Telephony", "Teletraffic engineering", "Throughput", "Time-series", "Time series", "Traffic generation model", "Transmission control protocol", "Transport layer", "Tweedie distributions", "Variable bitrate", "Variance", "Wayback Machine", "World wide web"], "references": ["http://www.ee.mu.oz.au/pgrad/tneame/presentations/Cubin_April_2002", "http://www.ibm.com/developerworks/websphere/library/techarticles/hipods/capacity.html", "http://www2.rad.com/networks/1994/gbiran/atm_swi.htm#why", "http://www.cs.bu.edu/brite/user_manual/node42.html", "http://www.cs.bu.edu/faculty/crovella/paper-archive/icnp96.pdf", "http://www.cs.bu.edu/pub/barford/ss_lrd.html", "http://ite.gmu.edu/graduateresearch/heavy_tails.htm", "http://adsabs.harvard.edu/abs/2002PNAS...99.2573W", "http://citeseer.ist.psu.edu/update/438672", "http://www.cs.purdue.edu/nsl/nsf-ani-9714707.html", "http://www-ece.rice.edu/INCITE/modeling_synopsis.html", "http://www.utdallas.edu/~sanna/research.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC128578", "http://www.ncbi.nlm.nih.gov/pubmed/11875212", "http://www.ee.cityu.edu.hk/~zukerman/traffmod.ppt", "http://www.rl.af.mil/tech/programs/aior/HTDist.html?return=BACK", "http://arxiv.org/abs/0807.3374", "http://doi.org/10.1073%2Fpnas.012583099", "http://doi.org/10.1109%2F90.803379", "http://doi.org/10.1109%2FICNP.1996.564935", "http://doi.org/10.1142%2FS0219525911003451", "http://www.jstor.org/stable/3057595", "http://www.cs.kent.ac.uk/people/staff/pfl/presentations/longrange", "https://web.archive.org/web/20041204211954/http://www2.rad.com/networks/1994/gbiran/atm_swi.htm#why", "https://web.archive.org/web/20050216173935/http://utdallas.edu/~sanna/research.html", "https://web.archive.org/web/20050315175119/http://ite.gmu.edu/graduateresearch/heavy_tails.htm", "https://web.archive.org/web/20051215045809/http://www.rl.af.mil/tech/programs/aior/HTDist.html?return=BACK", "https://web.archive.org/web/20110526141249/http://www.ee.mu.oz.au/pgrad/tneame/presentations/Cubin_April_2002", "https://web.archive.org/web/20121023070218/http://www.ibm.com/developerworks/websphere/library/techarticles/hipods/capacity.html"]}, "Kendall's notation": {"categories": ["Mathematical notation", "Single queueing nodes"], "title": "Kendall's notation", "method": "Kendall's notation", "url": "https://en.wikipedia.org/wiki/Kendall%27s_notation", "summary": "In queueing theory, a discipline within the mathematical theory of probability, Kendall's notation (or sometimes Kendall notation) is the standard system used to describe and classify a queueing node. D. G. Kendall proposed describing queueing models using three factors written A/S/c in 1953 where A denotes the time between arrivals to the queue, S the service time distribution and c the number of servers at the node. It has since been extended to A/S/c/K/N/D where K is the capacity of the queue, N is the size of the population of jobs to be served, and D is the queueing discipline.When the final three parameters are not specified (e.g. M/M/1 queue), it is assumed K = \u221e, N = \u221e and D = FIFO.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Mm1_queue.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival rate", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "David George Kendall", "Decomposition method (queueing theory)", "Degenerate distribution", "Digital object identifier", "Effective arrival rate", "Erlang (unit)", "Erlang distribution", "Exponential distribution", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Independent and identically distributed random variables", "Information system", "International Standard Book Number", "JSTOR", "Jackson network", "Kelly network", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "MX/MY/1 queue", "Markov process", "Markovian arrival process", "Markovian arrival processes", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Phase-type distribution", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing discipline", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shape parameter", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations"], "references": ["http://fic.wharton.upenn.edu/fic/papers/99/p9940.html", "http://doi.org/10.1007%2F978-1-4614-1734-7_9", "http://doi.org/10.1201%2F9781420009712.ch9", "http://doi.org/10.1214%2Faoms%2F1177728975", "http://www.jstor.org/stable/2236285", "http://projecteuclid.org/euclid.aoms/1177728975"]}, "Stochastic matrix": {"categories": ["Markov models", "Matrices"], "title": "Stochastic matrix", "method": "Stochastic matrix", "url": "https://en.wikipedia.org/wiki/Stochastic_matrix", "summary": "In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix.The stochastic matrix was first developed by Andrey Markov at the beginning of the 20th century, and has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics.There are several different definitions and types of stochastic matrices:\nA right stochastic matrix is a real square matrix, with each row summing to 1.\nA left stochastic matrix is a real square matrix, with each column summing to 1.\nA doubly stochastic matrix is a square matrix of nonnegative real numbers with each row and column summing to 1.In the same vein, one may define a stochastic vector (also called probability vector) as a vector whose elements are nonnegative real numbers which sum to 1. Thus, each row of a right stochastic matrix (or column of a left stochastic matrix) is a stochastic vector.A common convention in English language mathematics literature is to use row vectors of probabilities and right stochastic matrices rather than column vectors of probabilities and left stochastic matrices; this article follows that convention.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/66/Andrej_Markov.jpg", "https://upload.wikimedia.org/wikipedia/commons/6/67/Mousesurvival.jpg"], "links": ["20th century", "Andrey Kolmogorov", "Andrey Markov", "Behavioural sciences", "Brouwer Fixed Point Theorem", "Cardinality", "Column vector", "Computer science", "Density matrix", "Digital object identifier", "Discrete phase-type distribution", "Dissipative dynamical system", "Doubly stochastic matrix", "Econometrics", "Eigenvalue", "Eigenvector", "Ergodic theorem", "Euclidean vector", "Finite set", "Geology", "Gershgorin circle theorem", "Human resource management", "Identity matrix", "International Standard Book Number", "International Standard Serial Number", "Irreducibility (mathematics)", "JSTOR", "Land change modeling", "Linear algebra", "List of Russian mathematicians", "Markov chain", "Markov kernel", "Mathematical finance", "Mathematics", "Matrix polynomial", "Medical diagnosis", "Models of DNA evolution", "Muirhead's inequality", "Network analysis (electrical circuits)", "Nonnegative", "Parity (mathematics)", "Perron\u2013Frobenius theorem", "Population genetics", "Probabilistic automaton", "Probability", "Probability space", "Probability theory", "Probability vector", "Random matrix", "Random variable", "Real number", "Residential area", "Row vector", "Saint Petersburg State University", "Shuffling", "Spectral radius", "Square matrix", "Stationary state", "Statistics", "Structural engineering", "Transition probabilities"], "references": ["http://archives.datapages.com/data/doi/10.1306/74D71C4E-2B21-11D7-8648000102C1865D", "http://www.sciencedirect.com/science/article/pii/0167473089900258", "http://www.sciencedirect.com/science/article/pii/S0143622808000702", "http://onlinelibrary.wiley.com/doi/10.1002/bs.3830120407/abstract", "http://doi.org/10.1002%2Fbs.3830120407", "http://doi.org/10.1007%2F0-387-21525-5_1", "http://doi.org/10.1007%2FBF02047072", "http://doi.org/10.1016%2F0167-4730(89)90025-8", "http://doi.org/10.1016%2Fj.apgeog.2008.10.002", "http://doi.org/10.1080%2F01944366708977915", "http://doi.org/10.1109%2FTCT.1956.1086324", "http://doi.org/10.1112%2Fblms%2F22.1.31", "http://doi.org/10.1177%2F0272989X8300300403", "http://doi.org/10.1287%2Fmnsc.29.3.335", "http://doi.org/10.1306%2F74d71c4e-2b21-11d7-8648000102c1865d", "http://doi.org/10.2307%2F1907805", "http://ieeexplore.ieee.org/abstract/document/1086324/", "http://pubsonline.informs.org/doi/abs/10.1287/mnsc.29.3.335", "http://www.jstor.org/stable/1907805", "http://www.worldcat.org/issn/0002-8991", "http://www.worldcat.org/issn/0020-5958", "http://www.worldcat.org/issn/0025-1909", "http://www.worldcat.org/issn/0096-2007", "http://www.worldcat.org/issn/0272-989X", "http://www.worldcat.org/issn/1099-1743", "http://www.worldcat.org/issn/1527-1404", "https://link.springer.com/article/10.1007/BF02047072", "https://dx.doi.org/10.1080/01944366708977915", "https://dx.doi.org/10.1177/0272989X8300300403"]}, "Correlation_sum": {"categories": ["All Wikipedia articles needing context", "All articles needing additional references", "All pages needing cleanup", "Articles needing additional references from November 2007", "Articles with multiple maintenance issues", "Chaos theory", "Dimension theory", "Dynamical systems", "Wikipedia articles needing context from October 2009", "Wikipedia introduction cleanup from October 2009"], "title": "Correlation sum", "method": "Correlation_sum", "url": "https://en.wikipedia.org/wiki/Correlation_sum", "summary": "In chaos theory, the correlation sum is the estimator of the correlation integral, which reflects the mean probability that the states at two different times are close:\n\n \n \n \n C\n (\n \u03b5\n )\n =\n \n \n 1\n \n N\n \n 2\n \n \n \n \n \n \u2211\n \n \n \n \n i\n \u2260\n j\n \n \n i\n ,\n j\n =\n 1\n \n \n \n \n \n N\n \n \n \u0398\n (\n \u03b5\n \u2212\n \n |\n \n \n |\n \n \n \n \n x\n \u2192\n \n \n \n (\n i\n )\n \u2212\n \n \n \n x\n \u2192\n \n \n \n (\n j\n )\n \n |\n \n \n |\n \n )\n ,\n \n \n \n \n x\n \u2192\n \n \n \n (\n i\n )\n \u2208\n \n \n \n R\n \n \n \n m\n \n \n ,\n \n \n {\\displaystyle C(\\varepsilon )={\\frac {1}{N^{2}}}\\sum _{\\stackrel {i,j=1}{i\\neq j}}^{N}\\Theta (\\varepsilon -||{\\vec {x}}(i)-{\\vec {x}}(j)||),\\quad {\\vec {x}}(i)\\in {\\mathbb {R} }^{m},}\n where \n \n \n \n N\n \n \n {\\displaystyle N}\n is the number of considered states \n \n \n \n \n \n \n x\n \u2192\n \n \n \n (\n i\n )\n \n \n {\\displaystyle {\\vec {x}}(i)}\n , \n \n \n \n \u03b5\n \n \n {\\displaystyle \\varepsilon }\n is a threshold distance, \n \n \n \n \n |\n \n \n |\n \n \u22c5\n \n |\n \n \n |\n \n \n \n {\\displaystyle ||\\cdot ||}\n a norm (e.g. Euclidean norm) and \n \n \n \n \u0398\n (\n \u22c5\n )\n \n \n {\\displaystyle \\Theta (\\cdot )}\n the Heaviside step function. If only a time series is available, the phase space can be reconstructed by using a time delay embedding (see Takens' theorem):\n\n \n \n \n \n \n \n x\n \u2192\n \n \n \n (\n i\n )\n =\n (\n u\n (\n i\n )\n ,\n u\n (\n i\n +\n \u03c4\n )\n ,\n \u2026\n ,\n u\n (\n i\n +\n \u03c4\n (\n m\n \u2212\n 1\n )\n )\n ,\n \n \n {\\displaystyle {\\vec {x}}(i)=(u(i),u(i+\\tau ),\\ldots ,u(i+\\tau (m-1)),}\n where \n \n \n \n u\n (\n i\n )\n \n \n {\\displaystyle u(i)}\n is the time series, \n \n \n \n m\n \n \n {\\displaystyle m}\n the embedding dimension and \n \n \n \n \u03c4\n \n \n {\\displaystyle \\tau }\n the time delay.\nThe correlation sum is used to estimate the correlation dimension.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bibcode", "Chaos theory", "Correlation dimension", "Correlation integral", "Digital object identifier", "Euclidean norm", "Heaviside step function", "Recurrence quantification analysis", "Takens' theorem", "Time series"], "references": ["http://adsabs.harvard.edu/abs/1983PhyD....9..189G", "http://doi.org/10.1016%2F0167-2789(83)90298-1"]}, "Population pyramid": {"categories": ["Ageing", "All articles needing additional references", "Articles needing additional references from September 2018", "CS1 German-language sources (de)", "CS1 maint: Multiple names: authors list", "Commons category link is on Wikidata", "Demographic economics", "Demographics", "Demography", "Population", "Statistical charts and diagrams", "Webarchive template wayback links"], "title": "Population pyramid", "method": "Population pyramid", "url": "https://en.wikipedia.org/wiki/Population_pyramid", "summary": "A population pyramid, also called an \"age-sex pyramid\", is a graphical illustration that shows the distribution of various age groups in a population (typically that of a country or region of the world), which forms the shape of a pyramid when the population is growing. Males are conventionally shown on the left and females on the right, and they may be measured by raw number or as a percentage of the total population. This tool can be used to visualize and age of a particular population. It is also used in ecology to determine the overall age distribution of a population; an indication of the reproductive capabilities and likelihood of the continuation of a species.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b7/2017_world_map%2C_median_age_by_country.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9a/Egypt_population_pyramid_2005.svg", "https://upload.wikimedia.org/wikipedia/commons/7/78/Fertility_rate_world_map_2.png", "https://upload.wikimedia.org/wikipedia/commons/2/26/LibyaPopulation2011.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/6a/Population_pyramid_example.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["7 Billion Actions", "A Modest Proposal", "Age class structure", "Age stratification", "An Essay on the Principle of Population", "Arab Spring", "Baby boom", "Biocapacity", "CIA World Factbook", "Carrying capacity", "Classic Maya collapse", "Cold War", "Communism", "Darfur conflict", "Deep ecology", "Deforestation", "Demographic analysis", "Demographic gift", "Demographic transition", "Demographic trap", "Demographics of Africa", "Dependency ratio", "Desalination", "Desertification", "Digital object identifier", "Doubling time", "Earth's energy budget", "Economic recession", "Egypt", "Environmental impact of agriculture", "Environmental impact of aviation", "Environmental impact of biodiesel", "Environmental impact of concrete", "Environmental impact of electricity generation", "Environmental impact of fishing", "Environmental impact of irrigation", "Environmental impact of mining", "Environmental impact of paper", "Environmental impact of reservoirs", "Environmental impact of shipping", "Environmental impact of the energy industry", "Environmental impact of the oil shale industry", "Environmental impact of the petroleum industry", "Environmental impact of war", "Family planning", "Fascism", "Fertility and intelligence", "Fertility rate", "First European colonization wave (15th century\u201319th century)", "Food security", "Genocide", "Great Depression", "Green Revolution", "Green belt", "Gunnar Heinsohn", "Habitat destruction", "Holocene extinction", "How Much Land Does a Man Need?", "Human impact on the environment", "Human migration", "Human overpopulation", "Human population planning", "Human sex ratio", "I = PAT", "Industrialisation", "International Conference on Population and Development", "International Standard Book Number", "International Standard Serial Number", "Korotayev", "Land degradation", "Land reclamation", "Late 2000s recession", "Libya", "Life expectancy", "List of countries by median age", "List of metropolitan areas by population", "Malthusian catastrophe", "Malthusian growth model", "Median", "Middle East", "Middle East Youth Initiative", "North Africa", "Observations Concerning the Increase of Mankind, Peopling of Countries, etc.", "Off-roading", "One-child policy", "Operating Manual for Spaceship Earth", "Optimum population", "Orell F\u00fcssli", "Overconsumption", "Overdrafting", "Overshoot (population)", "Percent", "Physiological density", "Political demography", "Pollution", "Population", "Population Action International", "Population Connection", "Population Control: Real Costs, Illusory Benefits", "Population Matters", "Population Research Institute", "Population and Development Review", "Population and Environment", "Population and housing censuses by country", "Population biology", "Population decline", "Population density", "Population dynamics", "Population ecology", "Population ethics", "Population growth", "Population model", "Population momentum", "Projections of population growth", "Pyramid", "Quarry", "Reproductive rights", "Sine qua non", "Social and environmental impact of palm oil", "Sub-replacement fertility", "Sustainable development", "Terrorism", "The Limits to Growth", "The Population Bomb", "The Skeptical Environmentalist", "The Ultimate Resource", "Two-child policy", "United Nations Population Fund", "Urban sprawl", "Urbanization", "Urdal, Henrik", "Voluntary Human Extinction Movement", "Waithood", "War", "Waste", "Water scarcity", "Wayback Machine", "World3", "World Population Day", "World Population Foundation", "World energy consumption", "World energy resources", "World population", "World population milestones", "Zero population growth"], "references": ["http://www.abs.gov.au/websitedbs/d3310114.nsf/home/population%20pyramid%20preview", "http://www.china-profile.com/data/ani_ceu_pop.htm#", "http://www.paradigmpublishers.com/books/BookDetail.aspx?productID=280257", "http://cmp.sagepub.com/content/33/1/25", "http://www.visualinfoglobal.com/En/Poblacio/Piramides/", "http://www.washingtonexaminer.com/article/2615183", "http://www.websitetoolbox.com/tool/post/sfew/vpost?id=1579036", "http://www.fsl.orst.edu/pnwerc/wrb/Atlas_web_compressed/5.Human_Populations/5h.pyramids_web.pdf", "http://www.insee.fr/fr/ppp/bases-de-donnees/irweb/projpop0760/dd/pyramide/pyramide.htm", "http://www.census.gov/data-tools/demo/idb/informationGateway.php", "http://www.childmigration.net/files/433720SR0WHITE11PUBLIC10YPN1English.pdf", "http://populationpyramid.net", "http://populationpyramid.net/", "http://www.cfr.org/society-and-culture/effects-youth-bulge-civil-conflicts/p13093", "http://www.cfr.org/world/effects-youth-bulge-civil-conflicts/p13093", "http://doi.org/10.1177%2F0738894214544613", "http://www.pnas.org/content/early/2018/01/03/1701535115", "http://www.prb.org/Publications/Articles/2013/population-pyramids.aspx", "http://www.prb.org/data/", "http://shababinclusion.org/content/document/detail/623/1", "http://www.shababinclusion.org/content/blog/detail/986/", "http://www.shababinclusion.org/section/about/why_shabab", "http://www.shababinclusion.org/section/topics/employment", "http://esa.un.org/unpd/wpp/Demographic-Profiles/index.shtm", "http://www.un.org/en/databases/index.html", "http://www.worldcat.org/issn/0738-8942", "http://cliodynamics.ru/index.php?option=com_content&task=view&id=309&Itemid=1", "http://www.health.state.pa.us/hpa/stats/techassist/pyramids.htm", "https://www.britannica.com/topic/population-pyramid", "https://repository.library.georgetown.edu/bitstream/handle/10822/1042998/TheMuslimWorld_CIRS_Special_Issue_Intro_January2017.pdf?sequence=1", "https://web.archive.org/web/20061127014106/http://www.populationaction.org/resources/publications/securitydemographic/", "https://web.archive.org/web/20070311022800/http://www.zmag.org/Sustainers/Content/2003-03/14hendrixson.cfm", "https://web.archive.org/web/20070520191543/http://www.populationaction.org/Publications/Reports/The_Shape_of_Things_to_Come/Summary.shtml", "https://web.archive.org/web/20080830074502/http://www.brookings.edu/~/media/Files/events/2008/0107_youth/20080107_youth.pdf", "https://web.archive.org/web/20080830094355/http://www.brookings.edu/speeches/2008/0522_middle_east_youth_dhillon.aspx", "https://web.archive.org/web/20080911041519/http://www.brookings.edu/~/media/Files/rc/papers/2003/06middleeast_fuller/fuller20030601.pdf", "https://web.archive.org/web/20090830154203/http://www.health.state.pa.us/hpa/stats/techassist/pyramids.htm", "https://web.archive.org/web/20130522034538/http://www.ispu.org/files/PDFs/graham%20fuller%20paper.pdf", "https://web.archive.org/web/20170208114205/http://www.census.gov/population/international/data/idb/informationGateway.php", "https://web.archive.org/web/20170707170519/https://www.census.gov/population/international/links/stat_int.html", "https://doi.org/10.1111%2Fj.1468-2478.2006.00416.x", "https://www.populationeducation.org/content/what-are-different-types-population-pyramids"]}, "Relative risk": {"categories": ["Biostatistics", "Commons category link is on Wikidata", "Epidemiology", "Medical statistics", "Statistical ratios"], "title": "Risk ratio", "method": "Relative risk", "url": "https://en.wikipedia.org/wiki/Risk_ratio", "summary": "In epidemiology, risk ratio (RR) or relative risk is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. It is computed as \n \n \n \n \n I\n \n e\n \n \n \n /\n \n \n I\n \n u\n \n \n \n \n {\\displaystyle I_{e}/I_{u}}\n , where \n \n \n \n \n I\n \n e\n \n \n \n \n {\\displaystyle I_{e}}\n is the incidence in the exposed group, and \n \n \n \n \n I\n \n u\n \n \n \n \n {\\displaystyle I_{u}}\n is the incidence in the unexposed group. Together with risk difference and odds ratio, risk ratio measures the association between the exposure and the outcome.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5d/Illustration_of_risk_reduction.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Abbreviation", "Absolute risk", "Absolute risk reduction", "Academic clinical trials", "Adaptive clinical trial", "Analysis of clinical trials", "Analysis of variance", "Animal testing", "Animal testing on non-human primates", "Asymptomatic carrier", "Attributable fraction among the exposed", "Attributable fraction for the population", "Auxology", "Bachelor of Science in Public Health", "Behavior change (public health)", "Behavioural change theories", "Biological hazard", "Biostatistics", "Blind experiment", "Carl Rogers Darnall", "Case-control study", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Centers for Disease Control and Prevention", "Chief Medical Officer", "Child mortality", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Community health", "Contingency table", "Control event rate", "Correlation does not imply causation", "Council on Education for Public Health", "Cross-sectional study", "Cultural competence in health care", "Cumulative incidence", "Design of experiments", "Deviance (sociology)", "Diffusion of innovations", "Digital object identifier", "Disease surveillance", "Doctor of Public Health", "Dummy variable (statistics)", "Ecological study", "Emergency sanitation", "Environmental health", "Epidemic", "Epidemiological methods", "Epidemiology", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Evidence-based medicine", "Experiment", "Experimental event rate", "Exponentiation", "Family planning", "Fecal\u2013oral route", "First-in-man study", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Genetically modified food", "Germ theory of disease", "Global health", "Globalization and disease", "Glossary of clinical research", "Good agricultural practice", "Good manufacturing practice", "HACCP", "Hand washing", "Hazard ratio", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Human factors and ergonomics", "Human nutrition", "Hygiene", "ISO 22000", "In vitro", "In vivo", "Incidence (epidemiology)", "Infant mortality", "Infection control", "Infectivity", "Injury prevention", "Intention-to-treat analysis", "International Standard Book Number", "John Snow (physician)", "Joseph Lister", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "List of epidemics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "Logistic regression", "Longitudinal study", "Margaret Sanger", "Mary Mallon", "Maternal health", "Mean", "Medical anthropology", "Medical sociology", "Mental health", "Meta-analysis", "Ministry of Health and Family Welfare", "Morbidity", "Mortality rate", "Multicenter trial", "Nested case\u2013control study", "Notifiable disease", "Null result", "Number needed to harm", "Number needed to treat", "OCLC", "Observational study", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Odds ratio", "Open-label trial", "OpenEpi", "Open defecation", "Oral hygiene", "PRECEDE-PROCEED model", "Patient safety", "Patient safety organization", "Period prevalence", "Pharmaceutical policy", "Pharmacovigilance", "Point prevalence", "Poisson regression", "Population Impact Measures", "Population health", "Positive deviance", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Preventive healthcare", "Preventive nutrition", "Probability", "Professional degrees of public health", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quarantine", "ROC curve", "Race and health", "Randomized controlled trial", "Rate ratio", "Regression analysis", "Relative risk", "Relative risk reduction", "Reproducibility", "Reproductive health", "Retrospective cohort study", "Risk difference", "Risk\u2013benefit ratio", "Safe sex", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scientific control", "Seeding trial", "Selection bias", "Sexually transmitted infection", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Sociology of health and illness", "Specificity and sensitivity", "Standard score", "Statistical hypothesis testing", "Statistical significance", "Student's t-test", "Survivorship bias", "Systematic review", "The rare disease assumption", "Theory of planned behavior", "Transtheoretical model", "Tropical disease", "United States Public Health Service", "Vaccination", "Vaccine trial", "Vector control", "Virulence", "Waterborne diseases", "World Health Organization", "World Toilet Organization", "Z-test"], "references": ["http://www.oxfordreference.com/view/10.1093/acref/9780199976720.001.0001/acref-9780199976720", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2844943", "http://www.ncbi.nlm.nih.gov/pubmed/14695382", "http://www.ncbi.nlm.nih.gov/pubmed/20332511", "http://www.ncbi.nlm.nih.gov/pubmed/28339913", "http://www.ncbi.nlm.nih.gov/pubmed/9643696", "http://doi.org/10.1002%2F9780470773666", "http://doi.org/10.1016%2Fs0140-6736(05)79123-6", "http://doi.org/10.1093%2Facref%2F9780199976720.001.0001", "http://doi.org/10.1093%2Fndt%2Fgfw465", "http://doi.org/10.1136%2Fbmj.c869", "http://doi.org/10.1148%2Fradiol.2301031028", "http://doi.org/10.2307%2F2530610", "http://www.jstor.org/stable/2530610", "http://www.medcalc.org/calc/relative_risk.php", "http://www.worldcat.org/oclc/1019839414", "http://www.worldcat.org/oclc/56415070", "https://www.stata.com/support/faqs/stat/2deltameth.html", "https://www.worldcat.org/oclc/1019839414"]}, "Critical region": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2012", "Articles with unsourced statements from December 2015", "CS1 maint: Multiple names: authors list", "CS1 maint: Unfit url", "Commons category link is on Wikidata", "Design of experiments", "Logic and statistics", "Mathematical and quantitative methods (economics)", "Psychometrics", "Statistical hypothesis testing", "Use mdy dates from November 2016", "Webarchive template archiveis links", "Webarchive template wayback links"], "title": "Statistical hypothesis testing", "method": "Critical region", "url": "https://en.wikipedia.org/wiki/Statistical_hypothesis_testing", "summary": "A statistical hypothesis, sometimes called confirmatory data analysis, is an hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables. A statistical hypothesis test is a method of statistical inference. Commonly, two statistical data sets are compared, or a data set obtained by sampling is compared against a synthetic data set from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis that proposes no relationship between two data sets. The comparison is deemed statistically significant if the relationship between the data sets would be an unlikely realization of the null hypothesis according to a threshold probability\u2014the significance level. Hypothesis tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance. The process of distinguishing between the null hypothesis and the alternative hypothesis is aided by identifying two conceptual types of errors, type 1 and type 2, and by specifying parametric limits on e.g. how much type 1 error will be permitted.\nAn alternative framework for statistical hypothesis testing is to specify a set of statistical models, one for each candidate hypothesis, and then use model selection techniques to choose the most appropriate model. The most common selection techniques are based on either Akaike information criterion or Bayes factor.\nConfirmatory data analysis can be contrasted with exploratory data analysis, which may not have pre-specified hypotheses.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Almost sure hypothesis testing", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Archive.is", "Argument from ignorance", "Arithmetic mean", 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"Statistical process control", "Statistical significance", "Statistical theory", "Statistically significant", "Statistics", "Statistics education", "Stem-and-leaf display", "Stratified sampling", "Strawman", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Student's t distribution", "Subjectivity", "Sufficient statistic", "Suit (cards)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Theory of planned behavior", "Time domain", "Time series", "Tolerance interval", "Transtheoretical model", "Trend estimation", "Trial (law)", "Tropical disease", "Type I and type II errors", "U-statistic", "Uniformly most powerful test", "United States Public Health Service", "V-statistic", "Vaccination", "Vaccine trial", "Variance", "Vector autoregression", "Vector control", "Wald test", "Walter Frank Raphael Weldon", "Waterborne diseases", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "William Sealy Gosset", "World Health Organization", "World Toilet Organization", "Z-test"], "references": ["http://www.schramm.cc/link/Statistics-calculator.php", "http://www.epidemiology.ch/history/PDF%20bg/Cornfield%20J%201976%20recent%20methodological%20contributions.pdf", "http://www.collegeboard.com/student/testing/ap/sub_stats.html", "http://www.jasnh.com/", "http://library.mpib-berlin.mpg.de/ft/gg/GG_Null_2004.pdf", "http://ba.stat.cmu.edu/journal/2008/vol03/issue01/aldrich.pdf", "http://escholarshare.drake.edu/bitstream/handle/2092/413/WhyWeDon't.pdf", "http://ftp.isds.duke.edu/WorkingPapers/03-26.pdf", "http://core.ecu.edu/psyc/wuenschk/StatHelp/NHST-SHIT.htm", "http://mres.gmu.edu/pmwiki/uploads/Main/Meehl1967.pdf", "http://www.indiana.edu/~kruschke/articles/Kruschke2012JEPG.pdf", "http://www.nap.edu/openbook.php?record_id=13163&page=211", "http://rhowell.ba.ttu.edu/meehl1.pdf", "http://www.tufts.edu/~gdallal/LHSP.HTM", "http://www.cs.ucsd.edu/users/goguen/courses/275f00/stat.html", "http://repository.upenn.edu/cgi/viewcontent.cgi?article=1104&context=marketing_papers", "http://www-stat.wharton.upenn.edu/~steele/Publications/PDF/TN148.pdf", "http://www.webapps.cee.vt.edu/ewr/environmental/teach/smprimer/hypotest/ht.html", "http://www.phil.vt.edu/dmayo/PhilStatistics/Triad/Fisher%201955.pdf", "http://www.stat.washington.edu/research/reports/1993/tr254.pdf", "http://cerebro.xu.edu/math/Sources/Laplace/memoir_probabilities.pdf", "http://gallica.bnf.fr/ark:/12148/bpt6k77597p/f386", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC389491", "http://www.ncbi.nlm.nih.gov/pubmed/10383371", "http://www.ncbi.nlm.nih.gov/pubmed/10937333", "http://www.ncbi.nlm.nih.gov/pubmed/17286092", "http://www.mbastats.net", "http://www.stat.auckland.ac.nz/~iase/publications/isr/97.Moore.pdf", "http://annals.org/article.aspx?articleid=712762", "http://www.corestandards.org/the-standards/mathematics/hs-statistics-and-probability/introduction/", "http://doi.org/10.1016%2Fj.edurev.2007.04.001", "http://doi.org/10.1016%2Fj.ijforecast.2007.03.004", "http://doi.org/10.1016%2Fj.socec.2004.09.033", "http://doi.org/10.1037%2F0003-066X.49.12.997", "http://doi.org/10.1037%2F0003-066X.54.8.594", "http://doi.org/10.1037%2F029395", "http://doi.org/10.1037%2F1082-989X.5.2.241", "http://doi.org/10.1037%2Fa0029146", "http://doi.org/10.1037%2Fh0020412", "http://doi.org/10.1037%2Fh0042040", "http://doi.org/10.1073%2Fpnas.68.11.2643", "http://doi.org/10.1080%2F00401706.1960.10489909", "http://doi.org/10.1080%2F01621459.1951.10500764", "http://doi.org/10.1080%2F01621459.1993.10476404", "http://doi.org/10.1080%2F14786440009463897", "http://doi.org/10.1086%2F288135", "http://doi.org/10.1093%2Fbjps%2Faxi152", "http://doi.org/10.1093%2Fbjps%2Faxl003", "http://doi.org/10.1098%2Frsta.1933.0009", "http://doi.org/10.1098%2Frstl.1710.0011", "http://doi.org/10.1126%2Fscience.156.3781.1456", "http://doi.org/10.1177%2F001316446002000401", "http://doi.org/10.1177%2F0273475306288399", "http://doi.org/10.1177%2F0959354314525282", "http://doi.org/10.1177%2F0959354397074006", "http://doi.org/10.1207%2Fs15327965pli0102_1", "http://doi.org/10.1214%2F06-ba115", "http://doi.org/10.1214%2F08-BA306", "http://doi.org/10.1214%2Fss%2F1029963261", "http://doi.org/10.1214%2Fss%2F1032280216", "http://doi.org/10.1214%2Fss%2F1056397485", "http://doi.org/10.1214%2Fss%2F1177012488", "http://doi.org/10.2307%2F1403333", "http://doi.org/10.2307%2F20445367", "http://doi.org/10.4135%2F9781412986311", "http://doi.org/10.7326%2F0003-4819-130-12-199906150-00008", "http://www.icmje.org/publishing_1negative.html", "http://www.jstor.org/stable/20445367", "http://www.jstor.org/stable/2245634", "http://www.jstor.org/stable/2246117", "http://www.randomservices.org/random/hypothesis/Introduction.html", "http://en.wikisource.org/w/index.php?oldid=3592335", "http://www.economics.soton.ac.uk/staff/aldrich/1900.pdf", "http://www.york.ac.uk/depts/maths/histstat/arbuthnot.pdf", "http://www.york.ac.uk/depts/maths/histstat/fisher272.pdf", "http://stats.org.uk/statistical-inference/Rozeboom1960.pdf", "https://lirias.kuleuven.be/bitstream/123456789/136347/1/CastroSotos.pdf", "https://books.google.com/?id=oKZwtLQTmNAC&pg=PA1512&dq=%22mathematics+of+a+lady+tasting+tea%22", "https://books.google.com/books?id=M7yvkERHIIMC&lpg=PA225&ots=Glm4Zj_E6p&pg=PA225#v=onepage", "https://www.ics.uci.edu/~sternh/courses/210/loftus91_tyranny.pdf", "https://archive.is/20120728122912/http://www.corestandards.org/the-standards/mathematics/hs-statistics-and-probability/introduction/", "https://archive.org/details/cu31924003064833", "https://web.archive.org/web/20051124221846/http://www.npwrc.usgs.gov/resource/methods/statsig/stathyp.htm", "https://web.archive.org/web/20060518054857/http://hops.wharton.upenn.edu/ideas/pdf/Armstrong/StatisticalSignificance.pdf", "https://web.archive.org/web/20091029162244/http://www.wiwi.uni-muenster.de/ioeb/en/organisation/pfaff/stat_overview_table.html", "https://web.archive.org/web/20120716211637/http://www.icmje.org/publishing_1negative.html", "https://web.archive.org/web/20130904000350/http://ftp.isds.duke.edu/WorkingPapers/03-26.pdf", "https://web.archive.org/web/20131203010657/http://mres.gmu.edu/pmwiki/uploads/Main/Meehl1967.pdf", "https://web.archive.org/web/20140906190025/http://ba.stat.cmu.edu/journal/2008/vol03/issue01/aldrich.pdf", "https://www.encyclopediaofmath.org/index.php?title=p/s087400"]}, "Deviance information criterion": {"categories": ["Bayesian statistics", "Model selection", "Regression variable selection"], "title": "Deviance information criterion", "method": "Deviance information criterion", "url": "https://en.wikipedia.org/wiki/Deviance_information_criterion", "summary": "The deviance information criterion (DIC) is a hierarchical modeling generalization of the Akaike information criterion (AIC). It is particularly useful in Bayesian model selection problems where the posterior distributions of the models have been obtained by Markov chain Monte Carlo (MCMC) simulation. DIC is an asymptotic approximation as the sample size becomes large, like AIC. It is only valid when the posterior distribution is approximately multivariate normal.\n\n", "images": [], "links": ["Akaike information criterion", "American Journal of Mathematical and Management Sciences", "Andrew Gelman", "Asymptotic approximation", "Asymptotic distribution", "Bayesian inference", "Bayesian information criterion", "Biometrika", "CRC Press", "David Spiegelhalter", "Deviance (statistics)", "Digital object identifier", "Donald Rubin", "Focused information criterion", "Gerda Claeskens", "Hannan-Quinn information criterion", "Hierarchical linear model", "International Standard Book Number", "JSTOR", "Jensen\u2013Shannon divergence", "Journal of the Royal Statistical Society, Series B", "Kullback\u2013Leibler divergence", "Library of Congress Control Number", "Likelihood function", "Markov chain Monte Carlo", "Mathematical Reviews", "Model selection", "Multivariate normal distribution", "Nils Lid Hjort", "Over-fitting", "Posterior distribution", "Statistical model", "Watanabe\u2013Akaike information criterion", "YouTube"], "references": ["http://lccn.loc.gov/2003051474", "http://www.ams.org/mathscinet-getitem?mr=1979380", "http://www.ams.org/mathscinet-getitem?mr=2027492", "http://doi.org/10.1080%2F01966324.2011.10737798", "http://doi.org/10.1093%2Fbiomet%2Fasm017", "http://doi.org/10.1111%2F1467-9868.00353", "http://www.jstor.org/stable/3088806", "https://www.youtube.com/watch?v=vSjL2Zc-gEQ&list=PLDcUM9US4XdMdZOhJWJJD4mDBMnbTWw_z&index=8#t=31m25s", "https://dx.doi.org/10.1111/j.1467-9574.2005.00278.x"]}, "Fisher transformation": {"categories": ["Covariance and correlation", "Transforms", "Wikipedia articles needing clarification from March 2017"], "title": "Fisher transformation", "method": "Fisher transformation", "url": "https://en.wikipedia.org/wiki/Fisher_transformation", "summary": "In statistics, hypotheses about the value of the population correlation coefficient \u03c1 between variables X and Y can be tested using the Fisher transformation (aka Fisher z-transformation) applied to the sample correlation coefficient.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6a/Fisher_Transformation.png", "https://upload.wikimedia.org/wikipedia/commons/e/e3/Fisher_transformation.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian 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"Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", 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It is the conjugate prior of a normal distribution with unknown mean and precision.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayes' theorem", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conditional distribution", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum 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inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", 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"title": "Anomaly detection", "method": "Anomaly detection", "url": "https://en.wikipedia.org/wiki/Anomaly_detection", "summary": "In data mining, anomaly detection (also outlier detection) is the identification of rare items, events or observations which raise suspicions by differing significantly from the majority of the data. Typically the anomalous items will translate to some kind of problem such as bank fraud, a structural defect, medical problems or errors in a text. Anomalies are also referred to as outliers, novelties, noise, deviations and exceptions.In particular, in the context of abuse and network intrusion detection, the interesting objects are often not rare objects, but unexpected bursts in activity. This pattern does not adhere to the common statistical definition of an outlier as a rare object, and many outlier detection methods (in particular unsupervised methods) will fail on such data, unless it has been aggregated appropriately. Instead, a cluster analysis algorithm may be able to detect the micro clusters formed by these patterns.Three broad categories of anomaly detection techniques exist. Unsupervised anomaly detection techniques detect anomalies in an unlabeled test data set under the assumption that the majority of the instances in the data set are normal by looking for instances that seem to fit least to the remainder of the data set. Supervised anomaly detection techniques require a data set that has been labeled as \"normal\" and \"abnormal\" and involves training a classifier (the key difference to many other statistical classification problems is the inherent unbalanced nature of outlier detection). Semi-supervised anomaly detection techniques construct a model representing normal behavior from a given normal training data set, and then test the likelihood of a test instance to be generated by the learnt model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ACM Computing Surveys", "Arthur Zimek", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bank fraud", "Bayesian Network", "Bayesian network", "Bias-variance dilemma", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Change detection", "CiteSeerX", "Cluster analysis", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Digital object identifier", "Dimensionality reduction", "Dorothy E. 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"http://doi.org/10.1109%2FICDM.2012.21", "http://doi.org/10.1109%2FIJCNN.2011.6033571", "http://doi.org/10.1109%2FRISP.1990.63857", "http://doi.org/10.1109%2FTSE.1987.232894", "http://doi.org/10.1109%2FTSMC.1976.4309523", "http://doi.org/10.1137%2F1.9781611972818.2", "http://doi.org/10.1137%2F1.9781611972825.90", "http://doi.org/10.1145%2F1081870.1081891", "http://doi.org/10.1145%2F1541880.1541882", "http://doi.org/10.1145%2F2594473.2594476", "http://doi.org/10.1145%2F2618243.2618257", "http://doi.org/10.1145%2F2733381", "http://doi.org/10.1145%2F335191.335388", "http://doi.org/10.1145%2F342009.335437", "http://doi.org/10.1162%2F089976601750264965", "http://epubs.siam.org/doi/pdf/10.1137/1.9781611972818.2", "http://epubs.siam.org/doi/pdf/10.1137/1.9781611972825.90", "http://www.worldcat.org/issn/1384-5810", "http://www.worldcat.org/issn/1942-4787", "http://eprints.whiterose.ac.uk/767/1/hodgevj4.pdf", "https://arxiv.org/list/cs.LG/recent", "https://www.computer.org/csdl/proceedings/icdm/2008/3502/00/3502a413-abs.html"]}, "Bernoulli process": {"categories": ["All articles lacking in-text citations", "All articles lacking reliable references", "All pages needing factual verification", "Articles lacking in-text citations from September 2011", "Articles lacking reliable references from January 2014", "Stochastic processes", "Wikipedia articles needing factual verification from March 2010"], "title": "Bernoulli process", "method": "Bernoulli process", "url": "https://en.wikipedia.org/wiki/Bernoulli_process", "summary": "In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1. The component Bernoulli variables Xi are identically distributed and independent. Prosaically, a Bernoulli process is a repeated coin flipping, possibly with an unfair coin (but with consistent unfairness). Every variable Xi in the sequence is associated with a Bernoulli trial or experiment. They all have the same Bernoulli distribution. Much of what can be said about the Bernoulli process can also be generalized to more than two outcomes (such as the process for a six-sided dice); this generalization is known as the Bernoulli scheme.\nThe problem of determining the process, given only a limited sample of the Bernoulli trials, may be called the problem of checking whether a coin is fair.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost all", "Asymptotic equipartition property", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli distribution", "Bernoulli entropy", "Bernoulli measure", "Bernoulli polynomial", "Bernoulli scheme", "Bernoulli trial", "Bessel process", "Biased random walk on a graph", "Binomial coefficient", "Binomial distribution", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Borel algebra", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Checking whether a coin is fair", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Coin flipping", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Countably infinite", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Cylinder set", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Direct product", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynamical system", "Dynkin's formula", "Econometrics", "Eigenfunction", "Empirical process", "Ergodic sequence", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Expectation value", "Expected value", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Geometric distribution", "Gibbs measure", "Girsanov theorem", "Haar measure", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Independent identically distributed", "Infinitesimal generator (stochastic processes)", "Information entropy", "Interacting particle system", "International Standard Book Number", "Ising model", "Isomorphic", "Isomorphism of dynamical systems", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Iverson bracket", "Jacob Bernoulli", "John von Neumann", "Jump diffusion", "Jump process", "Kolmogorov 0-1 law", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Measure-preserving dynamical system", "Measure (mathematics)", "Measure zero", "Mixing (mathematics)", "Moran process", "Moving-average model", "Negative binomial distribution", "Non-homogeneous Poisson process", "Normal distribution", "Optional stopping theorem", "Ornstein isomorphism theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability", "Probability space", "Probability theory", "Product topology", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Randomness extractor", "Realization (probability)", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sequence", "Shift operator", "Sigma-martingale", "Sigma algebra", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistical independence", "Statistics", "Stirling's approximation", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "String (computer science)", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Timing attack", "Topology", "Transfer operator", "Uncorrelated", "Uniform integrability", "Universal property", "Usual hypotheses", "Variance gamma process", "Vasicek model", "Von Neumann extractor", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://www.r-statistics.com/2011/11/diagram-for-a-bernoulli-process-using-r/", "http://www.stat.berkeley.edu/~peres/mine/vn.pdf", "http://www.eecs.harvard.edu/~michaelm/coinflipext.pdf", "http://doi.org/10.1109%2FHST.2016.7495553", "http://doi.org/10.1214%2Faos%2F1176348543", "http://ieeexplore.ieee.org/document/7495553/"]}, "Pseudolikelihood": {"categories": ["Accuracy disputes from October 2016", "All accuracy disputes", "All articles with incomplete citations", "Articles with incomplete citations from March 2017", "Statistical inference"], "title": "Pseudolikelihood", "method": "Pseudolikelihood", "url": "https://en.wikipedia.org/wiki/Pseudolikelihood", "summary": "In statistical theory, a pseudolikelihood is an approximation to the joint probability distribution of a collection of random variables. The practical use of this is that it can provide an approximation to the likelihood function of a set of observed data which may either provide a computationally simpler problem for estimation, or may provide a way of obtaining explicit estimates of model parameters.\nThe pseudolikelihood approach was introduced by Julian Besag in the context of analysing data having spatial dependence.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/17/System-search.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/17/20150413103857%21System-search.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/17/20120911200436%21System-search.svg"], "links": ["Approximation", "Bayesian network", "Conditional independence", "Estimation theory", "International Standard Book Number", "JSTOR", "Joint probability distribution", "Julian Besag", "Likelihood function", "Markov random field", "Maximum likelihood", "Random variable", "Spatial dependence", "Statistical significance", "Statistical theory"], "references": ["http://www.jstor.org/stable/2987782"]}, "Length time bias": {"categories": ["Bias", "Clinical trials", "Epidemiology", "Medical statistics", "Oncology"], "title": "Length time bias", "method": "Length time bias", "url": "https://en.wikipedia.org/wiki/Length_time_bias", "summary": "Length time bias is a form of selection bias, a statistical distortion of results that can lead to incorrect conclusions about the data. Length time bias can occur when the lengths of intervals are analysed by selecting intervals that occupy randomly chosen points in time or space. That process favors longer intervals and so skews the data.\nLength time bias is often discussed in the context of the benefits of cancer screening, and it can lead to the perception that screening leads to better outcomes when in reality it has no effect. Fast-growing tumors generally have a shorter asymptomatic phase than slower-growing tumors. Thus, there is a shorter period of time during which the cancer is present in the body (and so might be detected by screening) but not yet large enough to cause symptoms, that would cause the patient to seek medical care and be diagnosed without screening.\nAs a result, if the same number of slow-growing and fast-growing tumors appear in a year, the screening test detects more slow-growers than fast-growers. If the slow growing tumors are less likely to be fatal than the fast growers, the people whose cancer is detected by screening do better, on average, than the people whose tumors are detected from symptoms (or at autopsy) even if there is no real benefit to catching the cancer earlier. That can give the impression that detecting cancers by screening causes cancers to be less dangerous even if less dangerous cancers are simply more likely to be detected by screening.[1]", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a1/Length_time_bias.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8b/Nuvola_apps_kalzium.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d8/Nuvola_apps_package_favorite.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d6/WHO_Rod.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Academic bias", "Acquiescence bias", "Anchoring", "Asymptomatic", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "Belief bias", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Cancer", "Choice-supportive bias", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Confirmation bias", "Congruence bias", "Cultural bias", "Debiasing", "Distinction bias", "Dunning\u2013Kruger effect", "Egocentric bias", "Emotional bias", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Forecast bias", "Fundamental attribution error", "Funding bias", "Halo effect", "Healthy user bias", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "Impact bias", "In-group favoritism", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "Lead time bias", "List of cognitive biases", "List of memory biases", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Negativity bias", "Net bias", "Normalcy bias", "Omission bias", "Omitted-variable bias", "Optimism bias", "Outcome bias", "Overton window", "Participation bias", "Precision bias", "Pro-innovation bias", "Publication bias", "Recall bias", "Reporting bias", "Response bias", "Restraint bias", "Sampling bias", "Selection bias", "Self-selection bias", "Self-serving bias", "Social comparison bias", "Social desirability bias", "Spectrum bias", "Status quo bias", "Survivorship bias", "Systematic error", "Systemic bias", "Time-saving bias", "Trait ascription bias", "Tumors", "United States news media and the Vietnam War", "Verification bias", "Von Restorff effect", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://www.fpnotebook.com/Prevent/Epi/LngthBs.htm"]}, "Frequency distribution": {"categories": ["Frequency distribution"], "title": "Frequency distribution", "method": "Frequency distribution", "url": "https://en.wikipedia.org/wiki/Frequency_distribution", "summary": "In statistics, a frequency distribution is a list, table or graph that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Cipher", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Contingency tables", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cross tabulation", "Cumulative frequency analysis", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency (statistics)", "Frequency analysis (cryptanalysis)", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Letter frequency", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line chart", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marginal distribution", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measures of central tendency", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Ranking", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical distribution", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Symmetric distribution", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variable (mathematics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-+frequency+distribution", "http://www.exceldemy.com/frequency-distribution-excel-make-table-and-graph/", "http://stattrek.com/statistics/dictionary.aspx?definition=Joint_frequency", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3117575", "http://www.ncbi.nlm.nih.gov/pubmed/21701652", "http://doi.org/10.4103%2F0976-500X.77120", "http://www.worldcat.org/issn/0976-500X"]}, "Artificial neural network": {"categories": ["All Wikipedia articles needing clarification", "All articles containing potentially dated statements", "All articles with unsourced statements", "Articles containing potentially dated statements from 2011", "Articles with excessive see also sections from March 2018", "Articles with unsourced statements from August 2017", "Articles with unsourced statements from February 2017", "Articles with unsourced statements from June 2017", "Articles with unsourced statements from June 2018", "Articles with unsourced statements from November 2014", "Artificial neural networks", "CS1 German-language sources (de)", "CS1 maint: Explicit use of et al.", "CS1 maint: Uses editors parameter", "Classification algorithms", "Computational neuroscience", "Computational statistics", "Market research", "Market segmentation", "Mathematical and quantitative methods (economics)", "Mathematical psychology", "Pages using citations with accessdate and no URL", "Use dmy dates from June 2013", "Wikipedia articles needing clarification from April 2017", "Wikipedia articles needing clarification from January 2018", "Wikipedia articles needing clarification from June 2017"], "title": "Artificial neural network", "method": "Artificial neural network", "url": "https://en.wikipedia.org/wiki/Artificial_neural_network", "summary": "Artificial neural networks (ANN) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains. The neural network itself is not an algorithm, but rather a framework for many different machine learning algorithms to work together and process complex data inputs. Such systems \"learn\" to perform tasks by considering examples, generally without being programmed with any task-specific rules. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as \"cat\" or \"no cat\" and using the results to identify cats in other images. They do this without any prior knowledge about cats, for example, that they have fur, tails, whiskers and cat-like faces. Instead, they automatically generate identifying characteristics from the learning material that they process.\nAn ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal from one artificial neuron to another. An artificial neuron that receives a signal can process it and then signal additional artificial neurons connected to it.\nIn common ANN implementations, the signal at a connection between artificial neurons is a real number, and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs. The connections between artificial neurons are called 'edges'. Artificial neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Artificial neurons may have a threshold such that the signal is only sent if the aggregate signal crosses that threshold. Typically, artificial neurons are aggregated into layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first layer (the input layer), to the last layer (the output layer), possibly after traversing the layers multiple times.\nThe original goal of the ANN approach was to solve problems in the same way that a human brain would. However, over time, attention moved to performing specific tasks, leading to deviations from biology. Artificial neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/dd/Ann_dependency_%28graph%29.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e4/Artificial_neural_network.svg", "https://upload.wikimedia.org/wikipedia/commons/6/6d/Cmac.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/46/Colored_neural_network.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/4/44/Neuron3.png", "https://upload.wikimedia.org/wikipedia/commons/7/79/Recurrent_ann_dependency_graph.png", "https://upload.wikimedia.org/wikipedia/commons/e/e8/Restricted_Boltzmann_machine.svg", "https://upload.wikimedia.org/wikipedia/commons/3/32/Single-layer_feedforward_artificial_neural_network.png", "https://upload.wikimedia.org/wikipedia/commons/b/be/Single_layer_ann.svg", "https://upload.wikimedia.org/wikipedia/commons/5/58/Two-layer_feedforward_artificial_neural_network.png", "https://upload.wikimedia.org/wikipedia/commons/7/7f/Two_layer_ann.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/2/22/Synapse_deployment.jpg"], "links": ["1-bit architecture", "128-bit", "16-bit", "2-bit architecture", "20Q", "256-bit", "32-bit", "4-bit", "48-bit", "512-bit", "64-bit computing", "8-bit", "ADALINE", "AI accelerator", "ARM architecture", "A priori and a posteriori", "Action potential", "Activation function", "Ad hoc", "Adaptive resonance theory", "Adder (electronics)", "Address decoder", "Address generation unit", "Addressing mode", "Advanced Configuration and Power Interface", "Advanced Power Management", "Affine transformation", "Alex Graves (computer scientist)", "Alexander Dewdney", "Alexey Grigorevich Ivakhnenko", "Algorithm", "Algorithmic trading", "Algorithms", "Analog circuit", "Analog signal", "Andrew Ng", "Andrey Kolmogorov", "Anomaly detection", "Application-specific instruction set processor", "Application-specific integrated circuit", "Approximation", "ArXiv", "Arithmetic logic unit", "Arthur E. Bryson", "Artificial intelligence", "Artificial life", "Artificial neural networks", "Artificial neuron", "Artificial neurons", "Association rule learning", "Associative Memory Base", "Auditory cortex", "Auto encoder", "Autoencoder", "Automated machine learning", "Automatic differentiation", "BEAM robotics", "BIRCH", "Back-propagation", "Backgammon", "Backpropagation", "Baidu", "Barrel processor", "Barrel shifter", "Baseband processor", "Bayesian network", "Bayesian probability", "Bayesian spam filtering", "Belt machine", "Bias-variance dilemma", "Bibcode", "Bilinear map", "Binary decoder", "Binary multiplier", "Binary variable", "Biological cybernetics", "Biological neural network", "Biological neuron model", "Biological neuron models", "Biologically inspired computing", "Biology", "Bipartite graph", "Bit-level parallelism", "Bit-serial architecture", "Blind source separation", "Blue Brain Project", "Boolean circuit", "Boosting (machine learning)", "Bootstrap aggregating", "Brain", "Branch predictor", "Brian D. Ripley", "Broyden\u2013Fletcher\u2013Goldfarb\u2013Shanno algorithm", "Bus (computing)", "CMOS", "CPU", "CPU cache", "CPU multiplier", "CURE data clustering algorithm", "Cache (computing)", "Cache coherence", "Cache hierarchy", "Cache performance measurement and metric", "Cache replacement policies", "Cambridge University Press", "Canonical correlation analysis", "Capsule neural network", "Catastrophic interference", "Cellular architecture", "Central processing unit", "Cerebellar Model Articulation Controller", "Cerebellar model articulation controller", "Chain rule", "Chess", "CiteSeerX", "Classic RISC pipeline", "Clock gating", "Clock rate", "Closed-form expression", "Cluster analysis", "Coastal engineering", "Cochlea", "Cognitive architecture", "Cognitive computing", "Cognitive model", "Cognitive science", "Colorectal cancer", "Combinational logic", "Comparison of instruction set architectures", "Complex cell", "Complex instruction set computer", "Complex programmable logic device", "Computational complexity theory", "Computational learning theory", "Computer architecture", "Computer data storage", "Computer numerical control", "Computer performance", "Computer performance by orders of magnitude", "Computer vision", "Conditional probability distribution", "Conditional random field", "Conference on Neural Information Processing Systems", "Confidence interval", "Conjugate gradient method", "Connectionism", "Connectionist expert system", "Connectomics", "Content-addressable memory", "Context-sensitive languages", "Control engineering", "Control hazard", "Control theory", "Control unit", "Convex function", "Convex optimization", "Convex optimization problem", "Convolution", "Convolutional neural network", "Cooperative multithreading", "Coprocessor", "Counter (digital)", "Counter machine", "Covariance", "Cross-entropy", "Cross-validation (statistics)", "Cross entropy", "Cultured neuronal networks", "Cycle (graph theory)", "Cycles per instruction", "DBSCAN", "Data buffer", "Data clustering", "Data compression", "Data dependency", "Data mining", "Data parallelism", "Data processing", "Database", "Dataflow architecture", "Datapath", "David E. 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and specificity is the extent to which actual negatives are classified as such (so false positives are few). Thus a highly sensitive test rarely overlooks an actual positive (for example, showing \"nothing bad\" despite something bad existing); a highly specific test rarely registers a positive classification for anything that is not the target of testing (for example, finding one bacterial species and mistaking it for another closely related one that is the true target); and a test that is highly sensitive and highly specific does both, so it \"rarely overlooks a thing that it is looking for\" and it \"rarely mistakes anything else for that thing.\" Because most medical tests do not have sensitivity and specificity values above 99%, \"rarely\" does not equate to certainty. But for practical reasons, tests with sensitivity and specificity values above 90% have high credibility, albeit usually no certainty, in differential diagnosis.\nSensitivity therefore quantifies the avoiding of false negatives and specificity does the same for false positives. For any test, there is usually a trade-off between the measures \u2013 for instance, in airport security, since testing of passengers is for potential threats to safety, scanners may be set to trigger alarms on low-risk items like belt buckles and keys (low specificity) in order to increase the probability of identifying dangerous objects and minimize the risk of missing objects that do pose a threat (high sensitivity). This trade-off can be represented graphically using a receiver operating characteristic curve. A perfect predictor would be described as 100% sensitive, meaning all sick individuals are correctly identified as sick, and 100% specific, meaning no healthy individuals are incorrectly identified as sick. 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"False positive rate", "False positives and false negatives", "Fecal occult blood", "First-in-man study", "Glossary of clinical research", "Harmonic mean", "Hazard ratio", "Hit rate", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Information retrieval", "Informedness", "Intention-to-treat analysis", "International Standard Book Number", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Matthews correlation coefficient", "Medical diagnosis", "Medical test", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "NCSS (statistical software)", "Negative likelihood ratio", "Negative predictive value", "Nested case\u2013control study", "Non-deterministic algorithm", "Normal distribution", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "OpenEpi", "Period prevalence", "Point prevalence", "Population Impact Measures", "Positive and negative predictive values", "Positive likelihood ratio", "Positive predictive value", "Pre- and post-test probability", "Precision (information retrieval)", "Precision and recall", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Recall (information retrieval)", "Receiver operating characteristic", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Scientific control", "Seeding trial", "Selection bias", "Sensitivity (test)", "Sensitivity (tests)", "Sensitivity index", "Specificity (tests)", "Specificity and sensitivity", "Statistic", "Statistical classification", "Statistical hypothesis testing", "Statistical population", "Statistical power", "Statistical significance", "Survivorship bias", "Systematic review", "True negative", "True negative rate", "True positive", "True positive rate", "Type II error", "Type I and type II errors", "Type I error", "Uncertainty coefficient", "Vaccine trial", "Virulence", "Youden's J statistic"], "references": ["http://www.flinders.edu.au/science_engineering/fms/School-CSEM/publications/tech_reps-research_artfcts/TRRA_2007.pdf", "http://www.mathworks.com/help/phased/examples/detector-performance-analysis-using-roc-curves.html", "http://www.med.emory.edu/EMAC/curriculum/diagnosis/sensand.htm", "http://omerad.msu.edu/ebm/Diagnosis/Diagnosis4.html", "http://araw.mede.uic.edu/cgi-bin/testcalc.pl", "http://open.umich.edu/education/med/m1/patientspop-decisionmaking/2010/materials", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC200804", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2540489", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2824341", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC487735", "http://www.ncbi.nlm.nih.gov/pubmed/14512479", "http://www.ncbi.nlm.nih.gov/pubmed/15271832", "http://www.ncbi.nlm.nih.gov/pubmed/20089911", "http://www.ncbi.nlm.nih.gov/pubmed/8019315", "http://www.ncbi.nlm.nih.gov/pubmed/8028462", "http://www.ncbi.nlm.nih.gov/pubmed/8028470", "http://people.inf.elte.hu/kiss/11dwhdm/roc.pdf", "http://www.cebm.net/sppin-and-snnout/", "http://vassarstats.net/clin1.html", "http://doi.org/10.1016%2Fj.patrec.2005.10.010", "http://doi.org/10.1136%2Fbmj.308.6943.1552", "http://doi.org/10.1136%2Fbmj.327.7417.716", "http://doi.org/10.1136%2Fbmj.329.7459.209", "http://doi.org/10.1177%2F0272989X9401400202", "http://doi.org/10.1177%2F0272989X9401400210", "http://doi.org/10.1523%2FJNEUROSCI.3585-09.2010", "http://www.medcalc.org/calc/diagnostic_test.php", "https://books.google.com/books?id=hDX65v9bReYC", "https://link.springer.com/referencework/10.1007%2F978-0-387-30164-8", "https://kennis-research.shinyapps.io/Bayes-App/", "https://web.archive.org/web/20130706035232/http://omerad.msu.edu/ebm/Diagnosis/Diagnosis4.html", "https://www.medcalc.org/calc/diagnostic_test.php"]}, "MANCOVA": {"categories": ["Analysis of variance"], "title": "Multivariate analysis of covariance", "method": "MANCOVA", "url": "https://en.wikipedia.org/wiki/Multivariate_analysis_of_covariance", "summary": "Multivariate analysis of covariance (MANCOVA) is an extension of analysis of covariance (ANCOVA) methods to cover cases where there is more than one dependent variable and where the control of concomitant continuous independent variables \u2013 covariates \u2013 is required. The most prominent benefit of the MANCOVA design over the simple MANOVA is the 'factoring out' of noise or error that has been introduced by the covariant. A commonly used multivariate version of the ANOVA F-statistic is Wilks' Lambda (\u039b), which represents the ratio between the error variance (or covariance) and the effect variance (or covariance).", "images": [], "links": ["ANCOVA", "ANOVA", "Analysis of covariance", "Covariate", "Dependent variable", "Dimension", "Discriminant function analysis", "Eigenvalues", "F-distribution", "Harold Hotelling", "Heteroscedasticity", "International Standard Book Number", "Levene's test", "M. S. Bartlett", "MANOVA", "Magnitude (mathematics)", "Normal distribution", "Random sample", "Roy's greatest root", "Samuel Stanley Wilks", "Singular value decomposition", "Statistical noise", "Statistical power", "Trace of a matrix", "Type I error", "Wilks' lambda distribution"], "references": ["http://www.utsc.utoronto.ca/~bors/HomoVariance.ppt", "http://www.statsoft.com/textbook/anova-manova/#multivariate", "http://ibgwww.colorado.edu/~carey/p7291dir/handouts/manova1.pdf", "http://faculty.chass.ncsu.edu/garson/PA765/manova.htm", "http://userwww.sfsu.edu/~efc/classes/biol710/manova/MANOVAnewest.pdf", "http://schatz.sju.edu//multivar/guide/Mancova.pdf", "http://www.ats.ucla.edu/stat/stata/output/Stata_MANOVA.htm", "http://www-bcf.usc.edu/~mmclaugh/550x/PPTslides/WeekElevenSlides/MANOVA.ppt"]}, "Law of the unconscious statistician": {"categories": ["Statistical laws", "Theory of probability distributions"], "title": "Law of the unconscious statistician", "method": "Law of the unconscious statistician", "url": "https://en.wikipedia.org/wiki/Law_of_the_unconscious_statistician", "summary": "In probability theory and statistics, the law of the unconscious statistician (also called LOTUS) is a theorem used to calculate the expected value of a function g(X) of a random variable X when one knows the probability distribution of X but one does not know the distribution of g(X). The form of the law can depend on the form in which one states the probability distribution of the random variable X. If it is a discrete distribution and one knows its probability mass function \u0192X (but not \u0192g(X)), then the expected value of g(X) is\n\n \n \n \n E\n \u2061\n [\n g\n (\n X\n )\n ]\n =\n \n \u2211\n \n x\n \n \n g\n (\n x\n )\n \n f\n \n X\n \n \n (\n x\n )\n ,\n \n \n \n {\\displaystyle \\operatorname {E} [g(X)]=\\sum _{x}g(x)f_{X}(x),\\,}\n where the sum is over all possible values x of X. If it is a continuous distribution and one knows its probability density function \u0192X (but not \u0192g(X)), then the expected value of g(X) is\n\n \n \n \n E\n \u2061\n [\n g\n (\n X\n )\n ]\n =\n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n g\n (\n x\n )\n \n f\n \n X\n \n \n (\n x\n )\n \n \n d\n \n x\n \n \n {\\displaystyle \\operatorname {E} [g(X)]=\\int _{-\\infty }^{\\infty }g(x)f_{X}(x)\\,\\mathrm {d} x}\n If one knows the cumulative probability distribution function FX (but not Fg(X)), then the expected value of g(X) is given by a Riemann\u2013Stieltjes integral\n\n \n \n \n E\n \u2061\n [\n g\n (\n X\n )\n ]\n =\n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n g\n (\n x\n )\n \n \n d\n \n \n F\n \n X\n \n \n (\n x\n )\n \n \n {\\displaystyle \\operatorname {E} [g(X)]=\\int _{-\\infty }^{\\infty }g(x)\\,\\mathrm {d} F_{X}(x)}\n (again assuming X is real-valued).", "images": [], "links": ["Chain rule", "Continuous probability distribution", "Cumulative probability distribution function", "Discrete probability distribution", "Expected value", "Function (mathematics)", "Integration by substitution", "Inverse functions and differentiation", "Joint distribution", "Measure theory", "Probability density function", "Probability distribution", "Probability mass function", "Probability space", "Probability theory", "Pushforward measure", "Radon-Nikodym derivative", "Random variable", "Riemann\u2013Stieltjes integral", "Statistics"], "references": ["http://pages.pomona.edu/~ajr04747/Spring2008/Math151/Math151NotesSpring08.pdf", "http://www.math.uah.edu/stat/index.html", "http://www.uwm.edu/~ericskey/361material/361F98/L06/index.html", "http://www.maths.lth.se/matstat/staff/bengtr/mathprob/unconscious.pdf"]}, "Point process": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2007", "Articles with unsourced statements from November 2017", "CS1 maint: Multiple names: authors list", "Point processes", "Spatial processes", "Statistical data types", "Wikipedia articles needing clarification from October 2011", "Wikipedia articles needing page number citations from June 2011", "Wikipedia articles needing page number citations from October 2011"], "title": "Point process", "method": "Point process", "url": "https://en.wikipedia.org/wiki/Point_process", "summary": "In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on some underlying mathematical space such as the real line, the Cartesian plane, or more abstract spaces. Point processes can be used as mathematical models of phenomena or objects representable as points in some type of space.\nThere are different mathematical interpretations of a point process, such as a random counting measure or a random set. Some authors regard a point process and stochastic process as two different objects such that a point process is a random object that arises from or is associated with a stochastic process, though it has been remarked that the difference between point processes and stochastic processes is not clear. Others consider a point process as a stochastic process, where the process is indexed by sets of the underlying space on which it is defined, such as the real line or \n \n \n \n n\n \n \n {\\displaystyle n}\n -dimensional Euclidean space. Other stochastic processes such as renewal and counting processes are studied in the theory of point processes. Sometimes the term \"point process\" is not preferred, as historically the word \"process\" denoted an evolution of some system in time, so point process is also called a random point field.Point processes are well studied objects in probability theory and the subject of powerful tools in statistics for modeling and analyzing spatial data, which is of interest in such diverse disciplines as forestry, plant ecology, epidemiology, geography, seismology, materials science, astronomy, telecommunications, computational neuroscience, economics and others.\nPoint processes on the real line form an important special case that is particularly amenable to study, because the points are ordered in a natural way, and the whole point process can be described completely by the (random) intervals between the points. These point processes are frequently used as models for random events in time, such as the arrival of customers in a queue (queueing theory), of impulses in a neuron (computational neuroscience), particles in a Geiger counter, location of radio stations in a telecommunication network or of searches on the world-wide web.", "images": [], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost surely", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Borel sigma-algebra", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Characteristic function (probability theory)", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Combinatorics", "Complete spatial randomness", "Compound Poisson process", "Computational neuroscience", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Countable set", "Counting measure", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "David Cox (statistician)", "Determinantal point process", "Diffusion process", "Digital object identifier", "Dirac measure", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Edgar N. Gilbert", "Empirical measure", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geiger counter", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Hausdorff space", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Inhomogeneous Poisson process", "Intensity measure", "Interacting particle system", "International Standard Book Number", "Invariant measure", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Koopman operator", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Lebesgue measure", "Limit point", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Locally compact space", "Locally finite measure", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical Reviews", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Measurable space", "Mixing (mathematics)", "Moment (mathematics)", "Moment measure", "Monotone class theorem", "Moran process", "Moving-average model", "Multivariate statistics", "Non-homogeneous Poisson process", "Olav Kallenberg", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Physics", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Point process notation", "Point process operation", "Poisson distribution", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability space", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Radon\u2013Nikodym theorem", "Random dynamical system", "Random element", "Random field", "Random graph", "Random matrix theory", "Random measure", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Relatively compact subset", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Second-countable space", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Set (mathematics)", "Shift operator", "Sigma-algebra", "Sigma-martingale", "Simple point process", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Spatial data analysis", "Spatial statistics", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic geometry", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telecommunication network", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Transfer operator", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "World-wide web"], "references": ["http://doi.org/10.1038%2Fnn1228", "http://doi.org/10.1093%2Fjjfinec%2Fnbg011", "http://doi.org/10.1109%2Ftit.1972.1054897", "http://doi.org/10.1111%2F1467-9469.00115", "https://books.google.com/books?id=6Sv4BwAAQBAJ", "https://books.google.com/books?id=825NfM6Nc-EC", "https://books.google.com/books?id=CLtDhblwWEgC", "https://books.google.com/books?id=KWF2xY6s3PoC", "https://books.google.com/books?id=VEiM-OtwDHkC", "https://books.google.com/books?id=brsUBQAAQBAJ&pg=PR5", "https://books.google.com/books?id=dBNOHvElXZ4C", "https://books.google.com/books?id=dSDxjX9nmmMC", "https://mathscinet.ams.org/mathscinet-getitem?mr=11402", "https://mathscinet.ams.org/mathscinet-getitem?mr=1353912", "https://mathscinet.ams.org/mathscinet-getitem?mr=854102", "https://mathscinet.ams.org/mathscinet-getitem?mr=950166", "https://doi.org/10.1145%2F1553374.1553376"]}, "Matrix gamma distribution": {"categories": ["Continuous distributions", "Multivariate continuous distributions", "Random matrices"], "title": "Matrix gamma distribution", "method": "Matrix gamma distribution", "url": "https://en.wikipedia.org/wiki/Matrix_gamma_distribution", "summary": "In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices. It is a more general version of the Wishart distribution, and is used similarly, e.g. as the conjugate prior of the precision matrix of a multivariate normal distribution and matrix normal distribution. The compound distribution resulting from compounding a matrix normal with a matrix gamma prior over the precision matrix is a generalized matrix t-distribution.This reduces to the Wishart distribution with \n \n \n \n \u03b2\n =\n 2\n ,\n \u03b1\n =\n \n \n n\n 2\n \n \n .\n \n \n {\\displaystyle \\beta =2,\\alpha ={\\frac {n}{2}}.}", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Compound distribution", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized matrix t-distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix (mathematics)", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate gamma function", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Positive-definite matrix", "Precision matrix", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale matrix", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.ijmsi.ir/browse.php?a_code=A-10-1-83&slc_lang=en&sid=1"]}, "Mallows's Cp": {"categories": ["Regression diagnostics", "Regression variable selection"], "title": "Mallows's Cp", "method": "Mallows's Cp", "url": "https://en.wikipedia.org/wiki/Mallows%27s_Cp", "summary": "In statistics, Mallows\u2019s Cp, named for Colin Lingwood Mallows, is used to assess the fit of a regression model that has been estimated using ordinary least squares. It is applied in the context of model selection, where a number of predictor variables are available for predicting some outcome, and the goal is to find the best model involving a subset of these predictors. A small value of Cp means that the model is relatively precise.\nMallows\u2019s Cp has been shown to be equivalent to Akaike information criterion in the special case of Gaussian linear regression.", "images": [], "links": ["Akaike information criterion", "ArXiv", "Biometrics (journal)", "Colin Lingwood Mallows", "Collinearity", "Dependent and independent variables", "Digital object identifier", "Effect size", "Feature selection", "Goodness of fit", "Gregory Chow", "International Standard Book Number", "JSTOR", "Linear regression", "Mean square error", "Mean squared prediction error", "Model selection", "Ordinary least squares", "Overfitting", "Predict", "Regression analysis", "Regressor", "Residual sum of squares", "Sample (statistics)", "Sample size", "Statistical population", "Statistics", "Stepwise regression"], "references": ["http://www-bcf.usc.edu/~gareth/ISL/ISLR%20Sixth%20Printing.pdf", "http://arxiv.org/abs/1308.2766", "http://doi.org/10.2307%2F1267380", "http://doi.org/10.2307%2F2529336", "http://www.jstor.org/stable/1267380", "http://www.jstor.org/stable/2348411", "http://www.jstor.org/stable/2529336"]}, "Confounding factor": {"categories": ["All articles with unsourced statements", "Analysis of variance", "Articles with short description", "Articles with unsourced statements from April 2012", "Causal inference", "Design of experiments"], "title": "Confounding", "method": "Confounding factor", "url": "https://en.wikipedia.org/wiki/Confounding", "summary": "In statistics, a confounder (also confounding variable, confounding factor or lurking variable) is a variable that influences both the dependent variable and independent variable causing a spurious association. Confounding is a causal concept, and as such, cannot be described in terms of correlations or associations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/Confounding.PNG", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b8/Simple_Confounding_Case.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alaska", "American Journal of Epidemiology", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anecdotal evidence", "Antidepressant", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Berkson's paradox", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Case-control study", "Categorical variable", "Causal inference", "Causality", "Cause", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort study", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding Factor (games company)", "Confounding factor", "Confusion", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Donald Rubin", "Double blinding", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiological method", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Health", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Judea Pearl", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Leslie Kish", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Lippincott Williams & Wilkins", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Medieval Latin", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New England Journal of Medicine", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational studies", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Peer review", "Percentile", "Permutation test", "Pesticide", "Pie chart", "Pivotal quantity", "Placebo effect", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Risk assessment", "Risk ratio", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "SSRI", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific Reports", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sherry L Mayrent", "Sign test", "Simple linear regression", "Simpson's Paradox", "Simpson's paradox", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratification (statistics)", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tricyclic antidepressant", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.une.edu.au/WebStat/unit_materials/c1_behavioural_science_research/confounds.html", "http://adsabs.harvard.edu/abs/2014NatSR...4E6085L", "http://ftp.cs.ucla.edu/pub/stat_ser/R256.pdf", "http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1009818", "http://www.ncbi.nlm.nih.gov/pubmed/11565527", "http://arxiv.org/abs/1304.0564", "http://doi.org/10.1037%2Fh0037350", "http://doi.org/10.1038%2Fsrep06085", "http://doi.org/10.1056%2Fnejm200109203451211", "http://doi.org/10.1093%2Faje%2F154.3.276", "http://doi.org/10.1093%2Fije%2F15.3.413", "http://doi.org/10.1136%2Fjech.2010.112565", "http://doi.org/10.1136%2Foem.46.8.505", "http://doi.org/10.1214%2F12-aos1058", "http://doi.org/10.1214%2Fss%2F1009211805"]}, "List of stochastic processes topics": {"categories": ["Mathematics-related lists", "Statistics-related lists", "Stochastic processes"], "title": "List of stochastic processes topics", "method": "List of stochastic processes topics", "url": "https://en.wikipedia.org/wiki/List_of_stochastic_processes_topics", "summary": "In the mathematics of probability, a stochastic process is a random function. In practical applications, the domain over which the function is defined is a time interval (time series) or a region of space (random field).\nFamiliar examples of time series include stock market and exchange rate fluctuations, signals such as speech, audio and video; medical data such as a patient's EKG, EEG, blood pressure or temperature; and random movement such as Brownian motion or random walks.\nExamples of random fields include static images, random topographies (landscapes), or composition variations of an inhomogeneous material.", "images": [], "links": ["Basic affine jump diffusion", "Bernoulli process", "Bernoulli scheme", "Birth\u2013death process", "Branching process", "Branching random walk", "Brownian bridge", "Brownian motion", "CIR process", "Chinese restaurant process", "Compound Poisson process", "Continuous-time Markov process", "Continuous stochastic process", "Cox process", "Dirichlet process", "Discrete-time stochastic process", "EKG", "Electroencephalography", "Finite-dimensional distribution", "First Passage Time", "Function (mathematics)", "Galton\u2013Watson process", "Gamma process", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Girsanov's theorem", "Homogeneous process", "It\u014d calculus", "Karhunen\u2013Lo\u00e8ve theorem", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "Malliavin calculus", "Markov chain", "Markov process", "Markov random field", "Martingale (probability theory)", "Mathematics", "Normal distribution", "Onsager\u2013Machlup function", "Ornstein\u2013Uhlenbeck process", "Point process", "Poisson process", "Population process", "Probability", "Queue (data structure)", "Queueing theory", "Random field", "Random walk", "Sample-continuous process", "Semi-Markov process", "Semimartingale", "Stationary process", "Stochastic calculus", "Stochastic cellular automaton", "Stochastic control", "Stochastic differential equation", "Stochastic process", "Stock market", "Stratonovich integral", "Symmetry", "Telegraph process", "Time series", "Wald's martingale", "Wiener process"], "references": []}, "Hyperbolic secant distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax"], "title": "Hyperbolic secant distribution", "method": "Hyperbolic secant distribution", "url": "https://en.wikipedia.org/wiki/Hyperbolic_secant_distribution", "summary": "In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function. The hyperbolic secant function is equivalent to the reciprocal hyperbolic cosine, and thus this distribution is also called the inverse-cosh distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/43/Hyper_secant_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e6/Hyper_secant_pdf.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biometrika", "Bivariate von Mises distribution", "Borel distribution", "Bulletin of the American Mathematical Society", "Burr distribution", "Cantor distribution", "Catalan's constant", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic function", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse hyperbolic function", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Trigonometric function", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://cgm.cs.mcgill.ca/~luc/rnbookindex.html", "http://doi.org/10.1002%2Fsia.740141207", "http://doi.org/10.1090%2FS0002-9904-1934-05852-X", "http://doi.org/10.1093%2Fbiomet%2F81.2.396", "http://www.statsci.org/smyth/pubs/sech.pdf"]}, "Additive Markov chain": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2010", "Markov processes"], "title": "Additive Markov chain", "method": "Additive Markov chain", "url": "https://en.wikipedia.org/wiki/Additive_Markov_chain", "summary": "In probability theory, an additive Markov chain is a Markov chain with an additive conditional probability function. Here the process is a discrete-time Markov chain of order m and the transition probability to a state at the next time is a sum of functions, each depending on the next state and one of the m previous states.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Additive map", "ArXiv", "Bibcode", "Conditional probability", "Correlation", "Correlation function", "Digital object identifier", "Discrete-time stochastic process", "Examples of Markov chains", "JSTOR", "Markov chain", "Probability theory", "Random variable", "State space"], "references": ["http://adsabs.harvard.edu/abs/2004PhRvE..70a5104H", "http://adsabs.harvard.edu/abs/2005EL.....69...22N", "http://arxiv.org/abs/cond-mat/0311483", "http://arxiv.org/abs/cond-mat/0409042", "http://doi.org/10.1103%2FPhysRevE.70.015104", "http://doi.org/10.1209%2Fepl%2Fi2004-10307-2", "https://doi.org/10.1016%2Fj.physa.2005.06.083", "https://www.jstor.org/stable/1998493"]}, "Berkson error model": {"categories": ["Accuracy and precision", "All stub articles", "Errors and residuals", "Statistical deviation and dispersion", "Statistics stubs"], "title": "Berkson error model", "method": "Berkson error model", "url": "https://en.wikipedia.org/wiki/Berkson_error_model", "summary": "The Berkson error model is a description of random error (or misclassification) in measurement. Unlike classical error, Berkson error causes little or no bias in the measurement. It was proposed by Joseph Berkson in an article entitled \u201cAre there two regressions?,\u201d published in 1950.\nAn example of Berkson error arises in exposure assessment in epidemiological studies. Berkson error may predominate over classical error in cases where exposure data are highly aggregated. While this kind of error reduces the power of a study, risk estimates themselves are not themselves attenuated (as would be the case where random error predominates).", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Classical error", "Digital object identifier", "Exposure assessment", "International Standard Book Number", "JSTOR", "Joseph Berkson", "Journal of the American Statistical Association", "Measurement", "Random error", "Statistical power", "Statistics"], "references": ["http://doi.org/10.1080/01621459.1950.10483349", "http://www.jstor.org/stable/2280676", "https://books.google.com/books?id=9kBx5CPZCqkC&pg=PA26", "https://books.google.com/books?id=QVtVmaCqLHMC&pg=PA76"]}, "Loess curve": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from June 2011", "Articles with unsourced statements from July 2011", "Nonparametric regression", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Local regression", "method": "Loess curve", "url": "https://en.wikipedia.org/wiki/Local_regression", "summary": "Local regression or local polynomial regression, also known as moving regression, is a generalization of moving average and polynomial regression.\nIts most common methods, initially developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced . They are two strongly related non-parametric regression methods that combine multiple regression models in a k-nearest-neighbor-based meta-model.\nLOESS and LOWESS thus build on \"classical\" methods, such as linear and nonlinear least squares regression. They address situations in which the classical procedures do not perform well or cannot be effectively applied without undue labor. LOESS combines much of the simplicity of linear least squares regression with the flexibility of nonlinear regression. It does this by fitting simple models to localized subsets of the data to build up a function that describes the deterministic part of the variation in the data, point by point. In fact, one of the chief attractions of this method is that the data analyst is not required to specify a global function of any form to fit a model to the data, only to fit segments of the data.\nThe trade-off for these features is increased computation. Because it is so computationally intensive, LOESS would have been practically impossible to use in the era when least squares regression was being developed. Most other modern methods for process modeling are similar to LOESS in this respect. These methods have been consciously designed to use our current computational ability to the fullest possible advantage to achieve goals not easily achieved by traditional approaches.\nA smooth curve through a set of data points obtained with this statistical technique is called a Loess Curve, particularly when each smoothed value is given by a weighted quadratic least squares regression over the span of values of the y-axis scattergram criterion variable. When each smoothed value is given by a weighted linear least squares regression over the span, this is known as a Lowess curve; however, some authorities treat Lowess and Loess as synonyms.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d2/Loess_curve.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Classical statistics", "Copyright status of work by the U.S. government", "Data set", "Digital object identifier", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "Explanatory variable", "Finite impulse response", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Journal of the American Statistical Association", "K-nearest neighbor algorithm", "Kernel (statistics)", "Kernel regression", "Least-angle regression", "Least absolute deviations", "Least squares", "Least squares regression", "Linear least squares", "Linear regression", "Logistic regression", "Mathematical Reviews", "Mean and predicted response", "Mixed logit", "Mixed model", "Moving average", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate adaptive regression splines", "National Institute of Standards and Technology", "Non-linear least squares", "Non-linear regression", "Non-negative least squares", "Non-parametric regression", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Outliers", "Parameter", "Partial least squares regression", "Poisson regression", "Polynomial", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "R (programming language)", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Response variable", "Robust regression", "Robust statistics", "Scattergram", "Scatterplot smoothing", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Sine wave", "Statistical estimation", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Weighted least squares", "William S. Cleveland"], "references": ["http://stat.ethz.ch/R-manual/R-patched/library/stats/html/lowess.html", "http://fivethirtyeight.blogs.nytimes.com/2013/03/26/how-opinion-on-same-sex-marriage-is-changing-and-what-it-means/?hp", "http://peltiertech.com/WordPress/loess-smoothing-in-excel/", "http://www.r-statistics.com/2010/04/quantile-loess-combining-a-moving-quantile-window-with-loess-r-function/", "http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-3477.pdf", "http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd144.htm", "http://www.nist.gov", "http://voteforamerica.net/editorials/Comments.aspx?ArticleId=28&ArticleName=Electoral+Projections+Using+LOESS", "http://www.ams.org/mathscinet-getitem?mr=0556476", "http://doi.org/10.2307%2F2286407", "http://doi.org/10.2307%2F2289282", "http://doi.org/10.2307%2F2683591", "http://www.jstor.org/stable/2286407", "http://www.jstor.org/stable/2289282", "http://www.jstor.org/stable/2683591", "http://www.netlib.org/go/lowess.f", "http://svn.r-project.org/R/trunk/src/library/stats/src/lowess.c", "http://slendermeans.org/lowess-speed.html", "https://socialsciences.mcmaster.ca/jfox/Books/Companion/appendices/Appendix-Nonparametric-Regression.pdf", "https://stat.ethz.ch/R-manual/R-devel/library/stats/html/loess.html", "https://stat.ethz.ch/R-manual/R-devel/library/stats/html/lowess.html", "https://stat.ethz.ch/R-manual/R-devel/library/stats/html/supsmu.html", "https://books.google.cl/books?id=94RgCgAAQBAJ&lpg=PA29&dq=moving%20regression&pg=PA29#v=onepage&q=moving%20regression&f=false", "https://github.com/dcjones/Loess.jl", "https://github.com/livingsocial/cylowess", "https://github.com/statsmodels/statsmodels/blob/master/statsmodels/nonparametric/smoothers_lowess.py", "https://www.npmjs.com/package/loess", "https://www.osti.gov/biblio/1367799-simple-introduction-moving-least-squares-local-regression-estimation", "https://web.archive.org/web/20050912090738/http://www.stat.purdue.edu/~wsc/localfitsoft.html", "https://web.archive.org/web/20060831004244/http://www.stat.purdue.edu/~wsc/papers/localregression.principles.ps"]}, "ARGUS distribution": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2011", "Continuous distributions", "Pages using deprecated image syntax", "Particle physics", "Wikipedia articles needing clarification from March 2011"], "title": "ARGUS distribution", "method": "ARGUS distribution", "url": "https://en.wikipedia.org/wiki/ARGUS_distribution", "summary": "In physics, the ARGUS distribution, named after the particle physics experiment ARGUS, is the probability distribution of the reconstructed invariant mass of a decayed particle candidate in continuum background.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2d/ArgusCDF.svg", "https://upload.wikimedia.org/wikipedia/commons/1/13/ArgusPDF.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARGUS (experiment)", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Asymptotic normality", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bessel function", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Consistent estimator", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Invariant mass", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Particle physics", "Pearson distribution", "Phase-type distribution", "Physics", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "PubMed Identifier", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Standard normal", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Upper incomplete gamma function", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://adsabs.harvard.edu/abs/1990PhLB..241..278A", "http://adsabs.harvard.edu/abs/1994PhLB..340..217A", "http://adsabs.harvard.edu/abs/2010PhRvL.104o1802L", "http://adsabs.harvard.edu/abs/2011PhRvL.107d1803P", "http://www.ncbi.nlm.nih.gov/pubmed/20481982", "http://www.ncbi.nlm.nih.gov/pubmed/21866994", "http://arxiv.org/abs/1001.1883", "http://arxiv.org/abs/1104.2025", "http://doi.org/10.1016%2F0370-2693(90)91293-K", "http://doi.org/10.1016%2F0370-2693(94)01302-0", "http://doi.org/10.1103%2FPhysRevLett.104.151802", "http://doi.org/10.1103%2FPhysRevLett.107.041803"]}, "Bernoulli trial": {"categories": ["Coin flipping", "Commons category link from Wikidata", "Discrete distributions", "Experiment (probability theory)"], "title": "Bernoulli trial", "method": "Bernoulli trial", "url": "https://en.wikipedia.org/wiki/Bernoulli_trial", "summary": "In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, \"success\" and \"failure\", in which the probability of success is the same every time the experiment is conducted. It is named after Jacob Bernoulli, a 17th-century Swiss mathematician, who analyzed them in his Ars Conjectandi (1713).The mathematical formalisation of the Bernoulli trial is known as the Bernoulli process. This article offers an elementary introduction to the concept, whereas the article on the Bernoulli process offers a more advanced treatment.\nSince a Bernoulli trial has only two possible outcomes, it can be framed as some \"yes or no\" question. For example:\n\nIs the top card of a shuffled deck an ace?\nWas the newborn child a girl? (See human sex ratio.)Therefore, success and failure are merely labels for the two outcomes, and should not be construed literally. The term \"success\" in this sense consists in the result meeting specified conditions, not in any moral judgement. More generally, given any probability space, for any event (set of outcomes), one can define a Bernoulli trial, corresponding to whether the event occurred or not (event or complementary event). Examples of Bernoulli trials include:\n\nFlipping a coin. In this context, obverse (\"heads\") conventionally denotes success and reverse (\"tails\") denotes failure. A fair coin has the probability of success 0.5 by definition. In this case there are exactly two possible outcomes.\nRolling a die, where a six is \"success\" and everything else a \"failure\". In this case there are six possible outcomes, and the event is a six; the complementary event \"not a six\" corresponds to the other five possible outcomes.\nIn conducting a political opinion poll, choosing a voter at random to ascertain whether that voter will vote \"yes\" in an upcoming referendum.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Bernoulli_trial_progression.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Ars Conjectandi", "Bernoulli distribution", "Bernoulli process", "Bernoulli sampling", "Bernoulli scheme", "Binomial coefficient", "Binomial distribution", "Binomial proportion confidence interval", "Coin flipping", "Collectively exhaustive events", "Complementary event", "Dice", "Encyclopedia of Mathematics", "Equally likely outcomes", "Event (probability theory)", "Experiment (probability theory)", "Fair coin", "Fisher's exact test", "Human sex ratio", "International Standard Book Number", "Jacob Bernoulli", "McGraw-Hill", "Michiel Hazewinkel", "Multiplicative inverse", "Mutually exclusive", "Negative binomial distribution", "Odds (statistics)", "Opinion poll", "Outcome (probability)", "Poisson sampling", "Poisson trial", "Probability", "Probability space", "Rajeev Motwani", "Random variable", "Sampling design", "Statistically independent", "Statistics", "Unity (mathematics)", "Yahtzee"], "references": ["http://www.math.uah.edu/stat/applets/BinomialTimelineExperiment.html", "https://www.encyclopediaofmath.org/index.php?title=p/b015690"]}, "Null result": {"categories": ["Design of experiments", "Logic and statistics"], "title": "Null result", "method": "Null result", "url": "https://en.wikipedia.org/wiki/Null_result", "summary": "In science, a null result is a result without the expected content: that is, the proposed result is absent. It is an experimental outcome which does not show an otherwise expected effect. This does not imply a result of zero or nothing, simply a result that does not support the hypothesis. The term is a translation of the scientific Latin nullus resultarum, meaning \"no consequence\".\nIn statistical hypothesis testing, a null result occurs when an experimental result is not significantly different from what is to be expected under the null hypothesis; its probability (under the null hypothesis) does not exceed the significance level, i.e., the threshold set prior to testing for rejection of the null hypothesis. The significance level varies, but is often set at p-value 0.05 (5%).\nAs an example in physics, the results of the Michelson\u2013Morley experiment were of this type, as it did not detect the expected velocity relative to the postulated luminiferous aether. This experiment's famous failed detection, commonly referred to as the null result, contributed to the development of special relativity. The experiment did appear to measure a non-zero \"drift\", but the value was far too small to account for the theoretically expected results; it is generally thought to be inside the noise level of the experiment.", "images": [], "links": ["Academic clinical trials", "Adaptive clinical trial", "Aether theories", "All Results Journals", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Blind experiment", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Correlation does not imply causation", "Cross-sectional study", "Cumulative incidence", "Data - the journal for Negative, Null and Inconclusive results (NNI results)", "Design of experiments", "Digital object identifier", "Ecological study", "Epidemiological methods", "European Journal of Negative Results in Biomedicine", "Evidence-based medicine", "Experiment", "First-in-man study", "Glossary of clinical research", "Hazard ratio", "Hypothesis", "Imponderable fluid", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Intention-to-treat analysis", "Journal of Articles in Support of the Null Hypothesis", "Journal of Negative Results", "Journal of Negative Results in Biomedicine", "Journal of Pharmaceutical Negative Results", "Latin", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Luminiferous aether", "Meta-analysis", "Michelson\u2013Morley experiment", "Morbidity", "Mortality rate", "Multicenter trial", "NNI results", "Nested case\u2013control study", "Noise level", "Null hypothesis", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "P-value", "Period prevalence", "Physical Review", "Physics", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "Publication bias", "Randomized controlled trial", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Science", "Scientific control", "Seeding trial", "Selection bias", "Significance level", "Special relativity", "Specificity and sensitivity", "Statistical hypothesis testing", "Survivorship bias", "Systematic review", "Vaccine trial", "Virulence"], "references": ["http://hsc.csu.edu.au/physics/core/space/9_2_4/924net.html#net4", "http://doi.org/10.1103/PhysRevD.59.053001"]}, "DAP (software)": {"categories": ["All articles needing additional references", "All stub articles", "Articles needing additional references from June 2018", "Free software programmed in C", "Free statistical software", "GNU Project software", "Official website different in Wikidata and Wikipedia", "Science software stubs"], "title": "DAP (software)", "method": "DAP (software)", "url": "https://en.wikipedia.org/wiki/DAP_(software)", "summary": "Dap is a statistics and graphics program based on the C programming language that performs data management, analysis, and C-style graphical visualization tasks without requiring complex syntax.\nDap was written to be a free replacement for SAS, but users are assumed to have a basic familiarity with the C programming language in order to permit greater flexibility.\nIt has been designed to be used on large data sets and is primarily used in statistical consulting practices.\nHowever, even with its clear benefits, Dap hasn't been updated since 2014 and hasn't seen widespread use when compared to other statistical analysis programs.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/31/Free_and_open-source_software_logo_%282009%29.svg", "https://upload.wikimedia.org/wikipedia/commons/7/75/Science-symbol-2.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ADMB", "ANOVA\u2013simultaneous component analysis", "Alexandre Oliva", "Analyse-it", "BMDP", "BV4.1 (software)", "Bash (Unix shell)", "Benjamin Mako Hill", "Bradley M. Kuhn", "CSPro", "C (programming language)", "C programming language", "Commercial software", "Comparison of statistical packages", "Computer data storage", "Correlation", "Cross-platform", "CumFreq", "Data Desk", "Dataplot", "Defective by Design", "EViews", "Eben Moglen", "Electric (software)", "Epi Info", "Federico Heinz", "Free Software Foundation", "Free Software Foundation Europe", "Free Software Foundation Latin America", "Free Software Foundation anti-Windows campaigns", "Free Software Foundation of India", "Freeware", "GAUSS (software)", "GIMP", "GNOME", "GNU", "GNU/Linux naming controversy", "GNU Affero General Public License", "GNU Archimedes", "GNU Binutils", "GNU Build System", "GNU C Library", "GNU Chess", "GNU Compiler Collection", "GNU Core Utilities", "GNU Debugger", "GNU Emacs", "GNU Find Utilities", "GNU Free Documentation License", "GNU GRUB", "GNU General Public License", "GNU Go", "GNU Guix", "GNU Health", "GNU Hurd", "GNU IceCat", "GNU Lesser General Public License", "GNU Manifesto", "GNU Multiple Precision Arithmetic Library", "GNU Octave", "GNU Privacy Guard", "GNU Project", "GNU Scientific Library", "GNU TeXmacs", "GNU variants", "GNUmed", "GNUnet", "GNUstep", "GPL linking exception", "GenStat", "Georg C. F. Greve", "Gnash (software)", "Gnuzilla", "GraphPad InStat", "GraphPad Prism", "Graphics", "Gretl", "Guix System Distribution", "H2O (software)", "Histograms", "History of free and open-source software", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Latin square", "LilyPond", "Line graph", "Linear model", "Linear regression", "Linux-libre", "List of GNU packages", "List of statistical packages", "Log-linear model", "Logistic regression", "Lo\u00efc Dachary", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "Matt Lee (artist)", "Mean", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Nagarjuna G.", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Percentiles", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "Revolution OS", "Ricardo Galli", "Richard Stallman", "Ring (software)", "Robert J. Chassell", "S-PLUS", "SAS (software)", "SAS System", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "Scatterplot", "Scientific software", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Split plot", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistical Analysis", "Statistics", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "William John Sullivan", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.gnu.org/software/dap/", "https://savannah.gnu.org/projects/dap/", "https://www.gnu.org/software/dap"]}, "Spatial analysis": {"categories": ["All articles with specifically marked weasel-worded phrases", "All articles with unsourced statements", "Articles with short description", "Articles with specifically marked weasel-worded phrases from February 2018", "Articles with unsourced statements from August 2014", "Articles with unsourced statements from December 2010", "Articles with unsourced statements from February 2013", "Cartography", "Commons category link is on Wikidata", "Geographic data and information", "Geography", "Geostatistics", "Mathematical and quantitative methods (economics)", "Spatial data analysis", "Statistical data types", "Webarchive template wayback links", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from June 2014"], "title": "Spatial analysis", "method": "Spatial analysis", "url": "https://en.wikipedia.org/wiki/Spatial_analysis", "summary": "Spatial analysis or spatial statistics includes any of the formal techniques which study entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of \"place and route\" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic data.\nComplex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research. The most fundamental of these is the problem of defining the spatial location of the entities being studied.\nClassification of the techniques of spatial analysis is difficult because of the large number of different fields of research involved, the different fundamental approaches which can be chosen, and the many forms the data can take.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c8/Britain-fractal-coastline-100km.png", "https://upload.wikimedia.org/wikipedia/commons/7/78/Britain-fractal-coastline-200km.png", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Britain-fractal-coastline-50km.png", "https://upload.wikimedia.org/wikipedia/commons/1/15/Bubonic_plague-en.svg", "https://upload.wikimedia.org/wikipedia/commons/8/83/Jubilee_Campus_MMB_%C2%AB24_Nottingham_Geospatial_Building.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/08/Manhattan_distance.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d1/Q-fig2.jpg", "https://upload.wikimedia.org/wikipedia/commons/c/c7/Snow-cholera-map.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/commons/2/29/Minard.png"], "links": ["1854 Broad Street cholera outbreak", "Ade Olufeko", "Adolphe Quetelet", "Agent-based model", "Alan MacEachren", "Algorithm", "Analysis", "ArXiv", "Arthur H. Robinson", "Artificial neural networks", "Aspect (geography)", "Astronomy", "August Kekul\u00e9", "Autocorrelation", "Bang Wong", "Bayesian hierarchical modeling", "Ben Shneiderman", "Benoit Mandelbrot", "Bibcode", "Biogeography", "Biological data visualization", "Biology", "Botany", "Boundary problem (in spatial analysis)", "Bruce H. McCormick", "Cartography", "Cellular automata", "Charles Joseph Minard", "Chart", "Chartjunk", "Chemical imaging", "Christopher R. Johnson", "CiteSeerX", "Clifford A. Pickover", "Cluster (epidemiology)", "Complete spatial randomness", "Complex adaptive systems", "Computational geometry", "Computer graphics", "Computer graphics (computer science)", "Computer science", "Cosmos", "Crime mapping", "DE-9IM", "Data mining", "Data visualization", "Database", "Diagram", "Digital cartography", "Digital object identifier", "Ecological fallacy", "Ecology", "Economics", "Edward Tufte", "Eigenvalues and eigenvectors", "Engineering drawing", "Epidemiology", "Ethology", "Euclidean distance", "Exploratory data analysis", "Extrapolation domain analysis", "Factor analysis", "Fernanda Vi\u00e9gas", "Florence Nightingale", "Flow visualization", "Fractal", "Fractals", "Fraser Stoddart", "Fuzzy architectural spatial analysis", "GIS", "Gaspard Monge", "Gaussian processes", "Geary's C", "GeoComputation", "Geodemographic segmentation", "Geographic", "Geographic data", "Geographic information science", "Geographic information system", "Geographic information systems", "Geoinformatics", "Geology", "Geomatics", "Geometric", "George Furnas", "George G. Robertson", "Geospatial intelligence", "Geospatial predictive modeling", "Geospatial topology", "Geovisualization", "Getis's G", "Gradient", "Graph drawing", "Graph of a function", "Graphic design", "Graphic organizer", "Gravity model", "Hanspeter Pfister", "Heterogeneity", "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", "Howard Wainer", "Hydrology", "Ideogram", "Imaging science", "Infographic", "Information science", "Information visualization", "International Standard Book Number", "International Standard Serial Number", "Inverse distance weighting", "Jacques Bertin", "Jock D. Mackinlay", "John Snow (physician)", "Jubilee Campus", "Karl Wilhelm Pohlke", "Kriging", "Landscape ecology", "Lawrence J. Rosenblum", "List of spatial analysis software", "Local regression", "London", "Manuel Lima", "Map", "Marco A. Janssen", "Markov Chain Monte Carlo", "Martin M. Wattenberg", "Mathematical diagram", "Mathematical statistics", "Mathematics", "Measurement", "Medical imaging", "Mental image", "Michael Friendly", "Michael Maltz", "Miriah Meyer", "Misleading graph", "Modifiable areal unit problem", "Molecular graphics", "Moran's I", "Neuroimaging", "Nigel Holmes", "OCLC", "Open Geospatial Consortium", "Operations research", "Otto Neurath", "Pat Hanrahan", "Patent drawing", "Photograph", "Pictogram", "Pixel", "Plot (graphics)", "PubMed Central", "PubMed Identifier", "Public Safety", "Regression-Kriging", "Regression analysis", "Remote sensing", "Rudolf Modley", "Sampling (statistics)", "Scale invariance", "Scale invariant", "Schematic", "Scientific modelling", "Scientific technique", "Scientific visualization", "Skeletal formula", "Software visualization", "Spatial association", "Spatial autocorrelation", "Spatial database", "Spatial decision support system", "Spatial econometrics", "Spatial epidemiology", "Spatial interpolation", "Spatial relation", "Standard deviational ellipse", "Statistical analysis", "Statistical graphics", "Statistics", "Stuart Card", "Suitability analysis", "Surveying", "Table (information)", "Tamara Munzner", "Taxicab geometry", "Technical drawing", "Technical illustration", "Thomas A. DeFanti", "Tobler's first law of geography", "Topological", "University of Nottingham", "User interface", "User interface design", "Visibility", "Visibility analysis", "Visual analytics", "Visual culture", "Visual perception", "Visualization (computer graphics)", "Visualization (graphics)", "Volume cartography", "Volume rendering", "Wayback Machine", "William Playfair"], "references": ["http://www.ryerson.ca/graduate/programs/spatial/index.html", "http://www.artechhouse.com/International/Books/Geospatial-Computing-in-Mobile-Devices-2159.aspx", "http://www.collinsdictionary.com/dictionary/english/geospatial", "http://dictionary.reference.com/browse/geospatial", "http://www.spatialanalysisonline.com/", "http://www.receiver.vodafone.com/the-geospatial-web", "http://adsabs.harvard.edu/abs/2015PhRvE..91c2401T", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.1825", "http://www.ncgia.ucsb.edu/", "http://www.icpsr.umich.edu/CrimeStat", "http://www-ohp.univ-paris1.fr", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2741335", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4936159", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5927603", "http://www.ncbi.nlm.nih.gov/pubmed/19750209", "http://www.ncbi.nlm.nih.gov/pubmed/20503184", "http://www.ncbi.nlm.nih.gov/pubmed/25871117", "http://www.ncbi.nlm.nih.gov/pubmed/27387921", "http://www.ncbi.nlm.nih.gov/pubmed/29720777", "http://eprints.maynoothuniversity.ie/6102/1/MC_gwr%201998.pdf", "http://rgdoi.net/10.13140/2.1.1560.2247", "http://www.ai-geostats.org/", "http://arxiv.org/abs/1406.7343", "http://www.bioversityinternational.org/index.php?id=244&tx_news_pi1%5Bnews%5D=1256&cHash=110ef499ad0d2d17abb48849909f1356", "http://doi.org/10.1007%2Fs10596-012-9287-1", "http://doi.org/10.1007%2Fs11004-010-9276-7", "http://doi.org/10.1007%2Fs11242-015-0471-3", "http://doi.org/10.1016%2FS0198-9715(01)00014-X", "http://doi.org/10.1016%2FS1470-160X(02)00052-3", "http://doi.org/10.1016%2Fj.compenvurbsys.2017.06.003", "http://doi.org/10.1016%2Fj.ecolind.2016.02.052", "http://doi.org/10.1016%2Fj.eiar.2012.06.007", "http://doi.org/10.1016%2Fs0198-9715(01)00047-3", "http://doi.org/10.1068%2Fa301905", "http://doi.org/10.1068%2Fb240235", "http://doi.org/10.1080%2F01621459.2015.1044091", "http://doi.org/10.1080%2F02693798708927820", "http://doi.org/10.1080%2F02693799308901936", "http://doi.org/10.1080%2F02723638.2015.1096118", "http://doi.org/10.1080%2F0965431042000312424", "http://doi.org/10.1103%2FPhysRevE.91.032401", "http://doi.org/10.1111%2F1467-8306.9302004", "http://doi.org/10.1111%2F1467-9671.00017", "http://doi.org/10.1111%2Fj.1461-0248.2004.00568.x", "http://doi.org/10.1111%2Fj.1467-8306.2004.09402005.x", "http://doi.org/10.1111%2Fj.1467-9671.1997.tb00010.x", "http://doi.org/10.1111%2Fj.1467-9868.2008.00663.x", "http://doi.org/10.1111%2Fj.1745-7939.1971.tb00636.x", "http://doi.org/10.1177%2F0042098016686493", "http://doi.org/10.1186%2Fs12936-016-1395-2", "http://doi.org/10.13140%2F2.1.1560.2247", "http://doi.org/10.1890%2F09-1359.1", "http://doi.org/10.4081%2Fgh.2010.196", "http://www.icaci.org", "http://www.worldcat.org/issn/1461-0248", "http://www.worldcat.org/oclc/973767077", "http://sasi.group.shef.ac.uk/", "https://sites.google.com/site/commissionofica/", "https://www.e-education.psu.edu/sgam/node/214", "https://web.archive.org/web/20110919052807/http://www.drs.wisc.edu/documents/articles/curtis/cesoc977/Anselin1995.pdf", "https://web.archive.org/web/20111002151826/http://www.receiver.vodafone.com/the-geospatial-web"]}, "Checking whether a coin is fair": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from January 2010", "Bayesian inference", "Coin flipping", "Experiments", "Statistical tests"], "title": "Checking whether a coin is fair", "method": "Checking whether a coin is fair", "url": "https://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair", "summary": "In statistics, the question of checking whether a coin is fair is one whose importance lies, firstly, in providing a simple problem on which to illustrate basic ideas of statistical inference and, secondly, in providing a simple problem that can be used to compare various competing methods of statistical inference, including decision theory. The practical problem of checking whether a coin is fair might be considered as easily solved by performing a sufficiently large number of trials, but statistics and probability theory can provide guidance on two types of question; specifically those of how many trials to undertake and of the accuracy an estimate of the probability of turning up heads, derived from a given sample of trials.\nA fair coin is an idealized randomizing device with two states (usually named \"heads\" and \"tails\") which are equally likely to occur. It is based on the coin flip used widely in sports and other situations where it is required to give two parties the same chance of winning. Either a specially designed chip or more usually a simple currency coin is used, although the latter might be slightly \"unfair\" due to an asymmetrical weight distribution, which might cause one state to occur more frequently than the other, giving one party an unfair advantage. So it might be necessary to test experimentally whether the coin is in fact \"fair\" \u2013 that is, whether the probability of the coin falling on either side when it is tossed is exactly 50%. It is of course impossible to rule out arbitrarily small deviations from fairness such as might be expected to affect only one flip in a lifetime of flipping; also it is always possible for an unfair (or \"biased\") coin to happen to turn up exactly 10 heads in 20 flips. Therefore, any fairness test must only establish a certain degree of confidence in a certain degree of fairness (a certain maximum bias). In more rigorous terminology, the problem is of determining the parameters of a Bernoulli process, given only a limited sample of Bernoulli trials.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4f/Plot_of_1320p7q3at500by420.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Abstain", "Andrew Gelman", "Bayes' theorem", "Bayesian inference", "Bayesian probability", "Bayesian probability theory", "Bernoulli process", "Bernoulli trial", "Beta distribution", "Beta function", "Binomial distribution", "Binomial test", "Casino token", "Coin", "Coin flip", "Coin flipping", "Confidence interval", "Conjugate prior", "Credibility theory", "Decision theory", "Dice", "Digital object identifier", "Estimation theory", "Expected value", "Factorial", "Fair coin", "Frequency probability", "Inferential statistics", "International Standard Book Number", "Likelihood function", "Loss function", "Margin of error", "Maximum a posteriori estimation", "Normal distribution", "Point estimation", "Posterior distribution", "Prior distribution", "Probability density function", "Probability theory", "Standard score", "Statistical inference", "Statistical randomness", "Statistics", "Systematic bias", "Uniform distribution (continuous)", "Utility function"], "references": ["http://doi.org/10.1198%2F000313002605"]}, "Mode (statistics)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from November 2010", "Means", "Summary statistics"], "title": "Mode (statistics)", "method": "Mode (statistics)", "url": "https://en.wikipedia.org/wiki/Mode_(statistics)", "summary": "The mode of a set of data values is the value that appears most often. It is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.\nLike the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions.\nThe mode is not necessarily unique to a given discrete distribution, since the probability mass function may take the same maximum value at several points x1, x2, etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently.\nWhen the probability density function of a continuous distribution has multiple local maxima it is common to refer to all of the local maxima as modes of the distribution. Such a continuous distribution is called multimodal (as opposed to unimodal). A mode of a continuous probability distribution is often considered to be any value x at which its probability density function has a locally maximum value, so any peak is a mode.In symmetric unimodal distributions, such as the normal distribution, the mean (if defined), median and mode all coincide. For samples, if it is known that they are drawn from a symmetric unimodal distribution, the sample mean can be used as an estimate of the population mode.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/de/Comparison_mean_median_mode.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/3/33/Visualisation_mode_median_mean.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Affine transformation", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arg max", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bimodal", "Bimodal distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical variable", "Census", "Centerpoint (geometry)", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous distribution", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Damodar N. Gujarati", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension", "Discrete distribution", "Distribution of wealth", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "GNU Octave", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric median", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Integer", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval (mathematics)", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kernel density estimation", "Kim (Korean name)", "Kolmogorov\u2013Smirnov test", "Korean name", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear order", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local maximum", "Location parameter", "Location\u2013scale family", "Log-normal distribution", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MATLAB", "Mann\u2013Whitney U test", "MathWorld", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (disambiguation)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multimodal distribution", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nominal data", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Number", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outliers", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pathological (mathematics)", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plane (mathematics)", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability mass function", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real number", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewed distribution", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Summary statistics", "Survey methodology", "Survival analysis", "Survival function", "Symmetric distribution", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniform distribution (discrete)", "Uniformly most powerful test", "Unimodal distribution", "Unimodal function", "V-statistic", "Variance", "Vector autoregression", "Vector space", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://apstatsreview.tumblr.com/post/50058615236/density-curves-and-the-normal-distributions?action=purge", "http://mathworld.wolfram.com/Mode.html", "http://www.se16.info/hgb/median.htm", "http://www.se16.info/hgb/mode.pdf", "http://www.amstat.org/publications/jse/v13n2/vonhippel.html", "http://doi.org/10.1080%2F10691898.2005.11910556", "http://doi.org/10.1098%2Frsta.1895.0010", "http://doi.org/10.1111%2Fj.1467-9574.1979.tb00657.x", "http://doi.org/10.1256%2Fqj.02.16", "http://www.khanacademy.org/math/statistics/v/mean-median-and-mode", "http://epubs.siam.org/doi/pdf/10.1137/S0040585X97975447", "https://web.archive.org/web/20071030070638/http://www.stats4students.com/Essentials/Measures-Central-Tendency/Overview_2.php", "https://www.encyclopediaofmath.org/index.php?title=p/m064340"]}, "Probability plot correlation coefficient": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2015", "Commons category link is on Wikidata", "Statistical charts and diagrams", "Use dmy dates from August 2012", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Q\u2013Q plot", "method": "Probability plot correlation coefficient", "url": "https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot", "summary": "In statistics, a Q\u2013Q (quantile-quantile) plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other. First, the set of intervals for the quantiles is chosen. A point (x, y) on the plot corresponds to one of the quantiles of the second distribution (y-coordinate) plotted against the same quantile of the first distribution (x-coordinate). Thus the line is a parametric curve with the parameter which is the number of the interval for the quantile.\nIf the two distributions being compared are similar, the points in the Q\u2013Q plot will approximately lie on the line y = x. If the distributions are linearly related, the points in the Q\u2013Q plot will approximately lie on a line, but not necessarily on the line y = x. Q\u2013Q plots can also be used as a graphical means of estimating parameters in a location-scale family of distributions.\nA Q\u2013Q plot is used to compare the shapes of distributions, providing a graphical view of how properties such as location, scale, and skewness are similar or different in the two distributions. Q\u2013Q plots can be used to compare collections of data, or theoretical distributions. The use of Q\u2013Q plots to compare two samples of data can be viewed as a non-parametric approach to comparing their underlying distributions. A Q\u2013Q plot is generally a more powerful approach to do this than the common technique of comparing histograms of the two samples, but requires more skill to interpret. Q\u2013Q plots are commonly used to compare a data set to a theoretical model. This can provide an assessment of \"goodness of fit\" that is graphical, rather than reducing to a numerical summary. Q\u2013Q plots are also used to compare two theoretical distributions to each other. Since Q\u2013Q plots compare distributions, there is no need for the values to be observed as pairs, as in a scatter plot, or even for the numbers of values in the two groups being compared to be equal.\nThe term \"probability plot\" sometimes refers specifically to a Q\u2013Q plot, sometimes to a more general class of plots, and sometimes to the less commonly used P\u2013P plot. The probability plot correlation coefficient plot (PPCC plot) is a quantity derived from the idea of Q\u2013Q plots, which measures the agreement of a fitted distribution with observed data and which is sometimes used as a means of fitting a distribution to data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/11/Normal_exponential_qq.svg", "https://upload.wikimedia.org/wikipedia/commons/0/08/Normal_normal_qq.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2e/Ohio_temps_qq.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ea/State_Route_20.png", "https://upload.wikimedia.org/wikipedia/commons/c/ca/Weibull_qq.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Affine transformation", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "BMDP", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chester Ittner Bliss", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "German tank problem", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interpolation", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jean D. Gibbons", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of graphical methods", "List of statistics articles", "Ljung\u2013Box test", "Location-scale family", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MINITAB", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum spacing estimation", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Normal probability plot", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Order statistics", "Ordinary least squares", "Outline of statistics", "Parametric equation", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Pearson product moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability plot", "Probability plot correlation coefficient", "Probability plot correlation coefficient plot", "Probit", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "P\u2013P plot", "Quality control", "Quantile", "Quantile function", "Quasi-experiment", "Questionnaire", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rankit", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Slope", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard score", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Symmetrical", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Washington State Route 20", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wilcoxon signed-rank test", "Y-intercept", "Z-test"], "references": ["http://engineering.tufts.edu/cee/people/vogel/publications/probability1986.pdf", "http://cat.inist.fr/?aModele=afficheN&cpsidt=14151257", "http://www.ncbi.nlm.nih.gov/pubmed/5661047", "http://www.itl.nist.gov/div898/handbook/eda/section3/normprpl.htm", "http://www.itl.nist.gov/div898/handbook/eda/section3/probplot.htm", "http://www.nist.gov", "http://www.wsdot.wa.gov/Traffic/Passes/NorthCascades/closurehistory.htm", "http://doi.org/10.1093%2Fbiomet%2F55.1.1", "http://doi.org/10.2307%2F1268008", "http://www.jstor.org/stable/1268008", "http://www.jstor.org/stable/2334448", "http://www.stats.gla.ac.uk/steps/glossary/probability_distributions.html#qqplot", "https://books.google.com/?id=gbegXB4SdosC", "https://books.google.com/?id=kJbVO2G6VicC", "https://books.google.com/books?id=gbegXB4SdosC", "https://books.google.com/books?id=gbegXB4SdosC&pg=PA21#PPA21,M1", "https://books.google.com/books?id=gbegXB4SdosC&pg=PA31", "https://books.google.com/books?id=kJbVO2G6VicC&pg=PA144#PPA144,M1", "https://doi.org/10.1111%2Fj.1467-9574.1953.tb00821.x"]}, "Random naive Bayes": {"categories": ["All articles with dead external links", "Articles with dead external links from May 2017", "Articles with permanently dead external links", "Articles with short description", "CS1 maint: Uses authors parameter", "Classification algorithms", "Computational statistics", "Decision theory", "Decision trees", "Ensemble learning", "Machine learning"], "title": "Random forest", "method": "Random naive Bayes", "url": "https://en.wikipedia.org/wiki/Random_forest", "summary": "Random forests or random decision forests are an ensemble learning method for classification, regression and other tasks, that operate by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees. Random decision forests correct for decision trees' habit of overfitting to their training set.The first algorithm for random decision forests was created by Tin Kam Ho using the random subspace method, which, in Ho's formulation, is a way to implement the \"stochastic discrimination\" approach to classification proposed by Eugene Kleinberg.An extension of the algorithm was developed by Leo Breiman and Adele Cutler, and \"Random Forests\" is their trademark. The extension combines Breiman's \"bagging\" idea and random selection of features, introduced first by Ho and later independently by Amit and Geman in order to construct a collection of decision trees with controlled variance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Annals of Mathematics and Artificial Intelligence", "Annals of Statistics", "Anomaly detection", "ArXiv", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Bias\u2013variance dilemma", "Bias\u2013variance tradeoff", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "CiteSeerX", "Classification and regression tree", "Cluster analysis", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "Correlation", "Cross-validation (statistics)", "DBSCAN", "Data mining", "Decision tree", "Decision tree learning", "DeepDream", "Deep learning", "Digital object identifier", "Dimensionality reduction", "Donald Geman", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature (machine learning)", "Feature engineering", "Feature learning", "Gated recurrent unit", "Generalization error", "Gini impurity", "Glossary of artificial intelligence", "Gradient boosting", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "I.i.d.", "Independent component analysis", "Information gain", "International Conference on Machine Learning", "International Standard Book Number", "JSTOR", "Jerome H. Friedman", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbor algorithm", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kernel method", "Kernel methods", "Kernel random forest", "Learning to rank", "Lecture Notes in Computer Science", "Leo Breiman", "Linear discriminant analysis", "Linear regression", "Linear subspace", "Lipschitz", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Mathematical Reviews", "Mean-shift", "Mode (statistics)", "Multilayer perceptron", "Multinomial logistic regression", "Naive Bayes classifier", "Neural Computation (journal)", "Non-negative matrix factorization", "Non-parametric statistics", "OPTICS algorithm", "Occam learning", "Online machine learning", "Orange (software)", "Out-of-bag error", "Outline of machine learning", "Overfitting", "Partial permutation", "Perceptron", "Principal component analysis", "Probably approximately correct learning", "PubMed Central", "PubMed Identifier", "Q-learning", "R (programming language)", "R programming language", "Random forests", "Random subspace method", "Random tree", "Randomized algorithm", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Robert Tibshirani", "Sampling (statistics)", "Scikit-learn", "Self-organizing map", "Semi-supervised learning", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Test set", "Tin Kam Ho", "Trademark", "Trevor Hastie", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory", "Wikipedia"], "references": ["http://orbi.ulg.ac.be/bitstream/2268/9357/1/geurts-mlj-advance.pdf", "http://ect.bell-labs.com/who/tkh/publications/papers/compare.pdf", "http://ect.bell-labs.com/who/tkh/publications/papers/df.pdf", "http://ect.bell-labs.com/who/tkh/publications/papers/odt.pdf", "http://code.google.com/p/randomforest-matlab", "http://www.nature.com/modpathol/journal/v18/n4/full/3800322a.html", "http://oz.berkeley.edu/~breiman/some_theory2000.pdf", "http://www.stat.berkeley.edu/~breiman/RandomForests/cc_software.htm", "http://www.cis.jhu.edu/publications/papers_in_database/GEMAN/shape.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.9168", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.9168", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.6750", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.6069", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.698.2365", "http://www-stat.stanford.edu/~tibs/ElemStatLearn/", "http://sqp.upf.edu", "http://www-bcf.usc.edu/~gareth/ISL/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4760114", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5828645", "http://www.ncbi.nlm.nih.gov/pubmed/15529185", "http://www.ncbi.nlm.nih.gov/pubmed/20385727", "http://www.ncbi.nlm.nih.gov/pubmed/21576180", "http://www.ncbi.nlm.nih.gov/pubmed/26903687", "http://www.ncbi.nlm.nih.gov/pubmed/28114007", "http://www.ncbi.nlm.nih.gov/pubmed/29440440", "http://www.alglib.net/dataanalysis/decisionforest.php", "http://weka.sourceforge.net/doc.dev/weka/classifiers/trees/RandomForest.html", "http://www.ams.org/mathscinet-getitem?mr=1425956", "http://arxiv.org/abs/1402.4293", "http://arxiv.org/abs/1407.3939", "http://arxiv.org/abs/1502.03836", "http://arxiv.org/abs/1512.03444", "http://arxiv.org/archive/math.ST", "http://arxiv.org/archive/stat.ML", "http://doi.org/10.1007%2F978-3-319-26762-3_27", "http://doi.org/10.1007%2F978-3-319-46254-7_50", "http://doi.org/10.1007%2F978-3-540-74469-6_35", "http://doi.org/10.1007%2FBF01531079", "http://doi.org/10.1007%2Fs10994-006-6226-1", "http://doi.org/10.1016%2Fj.eswa.2007.01.029", "http://doi.org/10.1023%2FA:1010933404324", "http://doi.org/10.1038%2Fmodpathol.3800322", "http://doi.org/10.1073%2Fpnas.1800256115", "http://doi.org/10.1080%2F01621459.2015.1036994", "http://doi.org/10.1093%2Fbioinformatics%2Fbtq134", "http://doi.org/10.1093%2Fbioinformatics%2Fbtr300", "http://doi.org/10.1109%2F34.709601", "http://doi.org/10.1109%2Ftpami.2016.2636831", "http://doi.org/10.1145%2F2491055.2491063", "http://doi.org/10.1162%2Fneco.1997.9.7.1545", "http://doi.org/10.1198%2F016214505000001230", "http://doi.org/10.1198%2F106186006X94072", "http://doi.org/10.1214%2Faos%2F1032181157", "http://www.jstor.org/stable/27594168", "http://bioinformatics.oxfordjournals.org/content/27/14/1986.abstract", "http://bioinformatics.oxfordjournals.org/content/early/2010/04/12/bioinformatics.btq134.abstract", "http://cran.r-project.org/web/packages/party/index.html", "http://cran.r-project.org/web/packages/randomForest/index.html", "http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html", "https://github.com/imbs-hl/ranger", "https://epub.ub.uni-muenchen.de/1833/1/paper_464.pdf", "https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm", "https://www.researchgate.net/profile/Dirk_Van_den_Poel/publication/225175169_Random_Multiclass_Classification_Generalizing_Random_Forests_to_Random_MNL_and_Random_NB/links/02e7e5278a0a7b8e7f000000.pdf", "https://www.researchgate.net/profile/Houtao_Deng/publication/221079908_Bias_of_Importance_Measures_for_Multi-valued_Attributes_and_Solutions/links/0046351909faa8f0eb000000/Bias-of-Importance-Measures-for-Multi-valued-Attributes-and-Solutions.pdf", "https://dl.acm.org/citation.cfm?id=2491063", "https://web.archive.org/web/20160417030218/http://ect.bell-labs.com/who/tkh/publications/papers/odt.pdf", "https://arxiv.org/list/cs.LG/recent", "https://cran.r-project.org/doc/Rnews/Rnews_2002-3.pdf", "https://cran.r-project.org/web/packages/randomForest/randomForest.pdf", "https://pdfs.semanticscholar.org/8956/845b0701ec57094c7a8b4ab1f41386899aea.pdf", "https://pdfs.semanticscholar.org/faa4/c502a824a9d64bf3dc26eb90a2c32367921f.pdf"]}, "Crime statistics": {"categories": ["All articles lacking in-text citations", "All articles with dead external links", "Articles lacking in-text citations from September 2010", "Articles with dead external links from February 2014", "Articles with dead external links from November 2016", "Articles with permanently dead external links", "CS1 maint: Multiple names: authors list", "Commons category link is on Wikidata", "Crime statistics", "Law enforcement", "Webarchive template wayback links", "Wikipedia articles with GND identifiers"], "title": "Crime statistics", "method": "Crime statistics", "url": "https://en.wikipedia.org/wiki/Crime_statistics", "summary": "There are several methods for measuring the prevalence of crime. Public surveys are sometimes conducted to estimate the amount of crime not reported to police. Such surveys are usually more reliable for assessing trends. However, they also have their limitations and generally don't procure statistics useful for local crime prevention, often ignore offenses against children and do not count offenders brought before the criminal justice system.\nLaw enforcement agencies in some countries offer compilations of statistics for various types of crime.\nTwo major methods for collecting crime data are law enforcement reports, which only reflect crimes that are reported, recorded, and not subsequently canceled; and victim study (victimization statistical surveys), which rely on individual memory and honesty. For less frequent crimes such as intentional homicide and armed robbery, reported incidences are generally more reliable, but suffer from under-recording; for example, no criming in the United Kingdom sees over one third of reported violent crimes being not recorded by the police. Because laws and practices vary between jurisdictions, comparing crime statistics between and even within countries can be difficult: typically only violent deaths (homicide or manslaughter) can reliably be compared, due to consistent and high reporting and relative clear definition.\nThe U.S. has two major data collection programs, the Uniform Crime Reports from the FBI and the National Crime Victimization Survey from the Bureau of Justice Statistics. However, the U.S. has no comprehensive infrastructure to monitor crime trends and report the information to related parties such as law enforcement.Research using a series of victim surveys in 18 countries of the European Union, funded by the European Commission, has reported (2005) that the level of crime in Europe has fallen back to the levels of 1990, and notes that levels of common crime have shown declining trends in the U.S., Canada, Australia and other industrialized countries as well. The European researchers say a general consensus identifies demographic change as the leading cause for this international trend. Although homicide and robbery rates rose in the U.S. in the 1980s, by the end of the century they had declined by 40%.However, the European research suggests that \"increased use of crime prevention measures may indeed be the common factor behind the near universal decrease in overall levels of crime in the Western world\", since decreases have been most pronounced in property crime and less so, if at all, in contact crimes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Crime prevention", "Crime science", "Dark figure of crime", "European Commission", "European Union", "FBI", "Homicide", "Integrated Authority File", "International Standard Book Number", "List of countries by execution rate", "List of countries by incarceration rate", "List of countries by intentional homicide rate", "Moral statistics", "Murder", "National Crime Victimization Survey", "No criming", "Prima facie", "Questionnaire", "Self report study", "Statistical survey", "The International Crime Victims Survey", "The Weekly Standard", "U.S. National Research Council", "Uniform Crime Reports", "United States cities by crime rate", "Victim study", "Victimology", "Wayback Machine"], "references": ["http://www.nap.edu/catalog.php?record_id=12472#toc", "http://www.unicri.it/services/library_documentation/publications/icvs/data/participating_20countries.pdf", "http://www.unicri.it/services/library_documentation/publications/icvs/data/overview2000cati.PDF", "http://www.unicri.it/services/library_documentation/publications/icvs/", "http://www.brain-gain.net/index.php?option=com_content&view=article&id=59:experience-and-communication-as-factors-explaining-criminal-risk-perception&catid=56:cat-crime-perception&Itemid=92&lang=de", "http://www.tilburguniversity.nl/intervict/burdenofcrimefinal.pdf", "http://rechten.uvt.nl/icvs", "http://rechten.uvt.nl/icvs/pdffiles/ICVS2004_05.pdf", "http://english.wodc.nl/images/ob257_full%20text_tcm45-103353.pdf", "http://www.wodc.nl/Onderzoeken/Onderzoek_W00187.asp", "http://www.europeansourcebook.org/ob285_full.pdf", "http://www.justiceinspectorates.gov.uk/hmic/news/news-feed/victims-let-down-by-poor-crime-recording/", "https://d-nb.info/gnd/4134292-6", "https://archive.is/20130105191708/http://www.weeklystandard.com/Content/Public/Articles/000/000/006/344eyaxi.asp?pg=1", "https://web.archive.org/web/20070221124606/http://www.tilburguniversity.nl/intervict/burdenofcrimefinal.pdf", "https://web.archive.org/web/20080625184952/http://rechten.uvt.nl/icvs/pdffiles/ICVS2004_05.pdf", "https://web.archive.org/web/20090219193853/http://nap.edu/catalog.php?record_id=12472#toc", "https://web.archive.org/web/20130120065651/http://english.wodc.nl/images/ob257_full%20text_tcm45-103353.pdf", "https://web.archive.org/web/20130201125851/http://rechten.uvt.nl/icvs/", "https://web.archive.org/web/20160303215512/http://www.europeansourcebook.org/ob285_full.pdf", "https://web.archive.org/web/20160304034747/http://www.unicri.it/services/library_documentation/publications/icvs/data/overview2000cati.PDF", "https://web.archive.org/web/20160304145307/http://www.justiceinspectorates.gov.uk/hmic/news/news-feed/victims-let-down-by-poor-crime-recording/", "https://web.archive.org/web/20160305143934/https://www.fbi.gov/news/stories/2012/october/annual-crime-in-the-u.s.-report-released/annual-crime-in-the-u.s.-report-released", "https://web.archive.org/web/20160314205131/http://www.unicri.it/services/library_documentation/publications/icvs/", "https://web.archive.org/web/20160418111902/http://www.unicri.it/services/library_documentation/publications/icvs/data/participating_20countries.pdf", "https://web.archive.org/web/20160428023232/http://www.disastercenter.com/crime/", "https://web.archive.org/web/20160602124958/https://www.fbi.gov/news/stories/2014/november/crime-statistics-for-2013-released", "https://web.archive.org/web/20161024175651/http://www.crime-statistics.co.uk/", "https://www.wikidata.org/wiki/Q330344"]}, "Multilevel model": {"categories": ["All accuracy disputes", "Analysis of variance", "Articles with disputed statements from August 2016", "Regression models"], "title": "Multilevel model", "method": "Multilevel model", "url": "https://en.wikipedia.org/wiki/Multilevel_model", "summary": "Multilevel models (also known as hierarchical linear models, nested data models, mixed models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parameters that vary at more than one level. An example could be a model of student performance that contains measures for individual students as well as measures for classrooms within which the students are grouped. These models can be seen as generalizations of linear models (in particular, linear regression), although they can also extend to non-linear models. These models became much more popular after sufficient computing power and software became available.Multilevel models are particularly appropriate for research designs where data for participants are organized at more than one level (i.e., nested data). The units of analysis are usually individuals (at a lower level) who are nested within contextual/aggregate units (at a higher level). While the lowest level of data in multilevel models is usually an individual, repeated measurements of individuals may also be examined. As such, multilevel models provide an alternative type of analysis for univariate or multivariate analysis of repeated measures. Individual differences in growth curves may be examined. Furthermore, multilevel models can be used as an alternative to ANCOVA, where scores on the dependent variable are adjusted for covariates (e.g. individual differences) before testing treatment differences. Multilevel models are able to analyze these experiments without the assumptions of homogeneity-of-regression slopes that is required by ANCOVA.Multilevel models can be used on data with many levels, although 2-level models are the most common and the rest of this article deals only with these. The dependent variable must be examined at the lowest level of analysis.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["ANCOVA", "ANOVA", "Akaike information criterion", "Andrew Gelman", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Categorical variable", "Digital object identifier", "Discrete choice", "Ecological fallacy", "Educational research", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Growth curve (statistics)", "Hierarchical Bayesian model", "Homoscedasticity", "Hyperparameter", "Independent variable", "Industrial and organizational psychology", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Joop Hox", "Latent class model", "Least-angle regression", "Least absolute deviations", "Least squares", "Likelihood-ratio test", "Linear least squares", "Linear model", "Linear regression", "Linear regression model", "Local regression", "Logistic regression", "Mean and predicted response", "Mixed-design analysis of variance", "Mixed logit", "Mixed model", "Mobile, Alabama", "Model selection", "Multilevel Modeling for Repeated Measures", "Multinomial logit", "Multinomial probit", "Multivariate analysis", "Nested data", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Parameter", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Random variable", "Regression analysis", "Regression model validation", "Regularized least squares", "Repeated measures", "Restricted randomization", "Robust regression", "SAS (software)", "Seattle", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistical model", "Statistics", "Structural equation modeling", "Studentized residual", "T-test", "Tikhonov regularization", "Total least squares", "Variable (mathematics)", "Weighted least squares", "Z-test"], "references": ["http://www.ats.ucla.edu/stat/hlm/seminars/hlm6/outline_hlm_seminar.pdf", "http://doi.org/10.1037%2F0033-2909.104.3.396", "http://doi.org/10.1093%2Fbiomet%2F78.1.45", "http://www.jstor.org/stable/2336894", "http://www.cmm.bristol.ac.uk", "https://books.google.com/books?id=jLPHBQAAQBAJ", "https://books.google.com/books?id=lV3DIdV0F9AC&pg=PA235", "https://books.google.com/books?id=mdwt7ibSGUYC"]}, "Forest plot": {"categories": ["Commons category without a link on Wikidata", "Meta-analysis", "Statistical charts and diagrams", "Systematic review"], "title": "Forest plot", "method": "Forest plot", "url": "https://en.wikipedia.org/wiki/Forest_plot", "summary": "A forest plot, also known as a blobbogram, is a graphical display of estimated results from a number of scientific studies addressing the same question, along with the overall results. It was developed for use in medical research as a means of graphically representing a meta-analysis of the results of randomized controlled trials. In the last twenty years, similar meta-analytical techniques have been applied in observational studies (e.g. environmental epidemiology) and forest plots are often used in presenting the results of such studies also.\nAlthough forest plots can take several forms, they are commonly presented with two columns. The left-hand column lists the names of the studies (frequently randomized controlled trials or epidemiological studies), commonly in chronological order from the top downwards. The right-hand column is a plot of the measure of effect (e.g. an odds ratio) for each of these studies (often represented by a square) incorporating confidence intervals represented by horizontal lines. The graph may be plotted on a natural logarithmic scale when using odds ratios or other ratio-based effect measures, so that the confidence intervals are symmetrical about the means from each study and to ensure undue emphasis is not given to odds ratios greater than 1 when compared to those less than 1. The area of each square is proportional to the study's weight in the meta-analysis. The overall meta-analysed measure of effect is often represented on the plot as a dashed vertical line. This meta-analysed measure of effect is commonly plotted as a diamond, the lateral points of which indicate confidence intervals for this estimate.\nA vertical line representing no effect is also plotted. If the confidence intervals for individual studies overlap with this line, it demonstrates that at the given level of confidence their effect sizes do not differ from no effect for the individual study. The same applies for the meta-analysed measure of effect: if the points of the diamond overlap the line of no effect the overall meta-analysed result cannot be said to differ from no effect at the given level of confidence.\nForest plots date back to at least the 1970s. One plot is shown in a 1985 book about meta-analysis.\nThe first use in print of the expression \"forest plot\" may be in an abstract for a poster at the Pittsburgh (US) meeting of the Society for Clinical Trials in May 1996. An informative investigation on the origin of the notion \"forest plot\" was published in 2001. \nThe name refers to the forest of lines produced. In September 1990, Richard Peto joked that the plot was named after a breast cancer researcher called Pat Forrest and as a result the name has sometimes been spelled \"forrest plot\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f0/Generic_forest_plot.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5d/Pre-term_corticosteroid_data.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Academic Press", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "BMJ", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blobbogram", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Chronological order", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochrane (organisation)", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental epidemiology", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Funnel plot", "Further research is needed", "G-test", "Galbraith plot", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homogeneity (statistics)", "Homoscedasticity", "Index of dispersion", "Infant respiratory distress syndrome", "Ingram Olkin", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Larry V. Hedges", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Meta-analysis", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural logarithm", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Odds ratio", "Odds ratios", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Premature birth", "Preterm birth", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized controlled trials", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Richard Peto", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Society for Clinical Trials", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Steff Lewis", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Systematic review", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighting", "Whittle likelihood", "Wilcoxon signed-rank test", "Woodlot", "Y-axis", "Z-test"], "references": ["http://www.bmj.com/cgi/content/full/322/7300/1479", "http://www.epigear.com", "http://www.meta-analysis-made-easy.com", "http://onlinelibrary.wiley.com/doi/10.1002/14651858.CD004454.pub3/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1120528", "http://www.ncbi.nlm.nih.gov/pubmed/11408310", "http://www.evidentlycochrane.net/cochrane-logo-health-warning/", "http://doi.org/10.1136%2Fbmj.322.7300.1479", "http://ceaccp.oxfordjournals.org/cgi/reprint/8/4/143.pdf"]}, "Spectrum bias": {"categories": ["Bias", "Biostatistics", "Design of experiments", "Medical statistics"], "title": "Spectrum bias", "method": "Spectrum bias", "url": "https://en.wikipedia.org/wiki/Spectrum_bias", "summary": "In biostatistics, spectrum bias refers to the phenomenon that the performance of a diagnostic test may vary in different clinical settings because each setting has a different mix of patients. Because the performance may be dependent on the mix of patients, performance at one clinic may not be predictive of performance at another clinic. These differences are interpreted as a kind of bias. Mathematically, the spectrum bias is a sampling bias and not a traditional statistical bias; this has led some authors to refer to the phenomenon as spectrum effects, whilst others maintain it is a bias if the true performance of the test differs from that which is 'expected'. Usually the performance of a diagnostic test is measured in terms of its sensitivity and specificity and it is changes in these that are considered when referring to spectrum bias. However, other performance measures such as the likelihood ratios may also be affected by spectrum bias.Generally spectrum bias is considered to have three causes. The first is due to a change in the case-mix of those patients with the target disorder (disease) and this affects the sensitivity. The second is due to a change in the case-mix of those without the target disorder (disease-free) and this affects the specificity. The third is due to a change in the prevalence, and this affects both the sensitivity and specificity. This final cause is not widely appreciated, but there is mounting empirical evidence as well as theoretical arguments which suggest that it does indeed affect a test's performance.\nExamples where the sensitivity and specificity change between different sub-groups of patients may be found with the carcinoembryonic antigen test and urinary dipstick tests.Diagnostic test performances reported by some studies may be artificially overestimated if it is a case-control design where a healthy population ('fittest of the fit') is compared with a population with advanced disease ('sickest of the sick'); that is two extreme populations are compared, rather than typical healthy and diseased populations.If properly analyzed, recognition of heterogeneity of subgroups can lead to insights about the test's performance in varying populations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/77/Open_Access_logo_PLoS_transparent.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/77/20130415131803%21Open_Access_logo_PLoS_transparent.svg"], "links": ["Academic bias", "Acquiescence bias", "Anchoring", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "BMJ Open", "Belief bias", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Biased sample", "Biostatistics", "Carcinoembryonic antigen", "Choice-supportive bias", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Confirmation bias", "Congruence bias", "Cultural bias", "Debiasing", "Diagnostic test", "Digital object identifier", "Distinction bias", "Dunning\u2013Kruger effect", "Egocentric bias", "Emotional bias", "Empirical evidence", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Forecast bias", "Fundamental attribution error", "Funding bias", "Halo effect", "Healthy user bias", "Heuristics in judgment and decision-making", "Hindsight bias", "Homogeneity (statistics)", "Horn effect", "Hostile attribution bias", "Impact bias", "In-group favoritism", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "Lead time bias", "Length time bias", "Likelihood ratios in diagnostic testing", "List of cognitive biases", "List of memory biases", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Negativity bias", "Net bias", "Normalcy bias", "Omission bias", "Omitted-variable bias", "Open access", "Optimism bias", "Outcome bias", "Overton window", "Participation bias", "Precision bias", "Pro-innovation bias", "PubMed Central", "PubMed Identifier", "Publication bias", "Recall bias", "Reporting bias", "Response bias", "Restraint bias", "Sampling bias", "Selection bias", "Self-selection bias", "Self-serving bias", "Sensitivity (tests)", "Social comparison bias", "Social desirability bias", "Specificity (tests)", "Status quo bias", "Survivorship bias", "Systematic error", "Systemic bias", "Time-saving bias", "Trait ascription bias", "United States news media and the Vietnam War", "Urine test strip", "Verification bias", "Von Restorff effect", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://bmjopen.bmj.com/content/2/1/e000746.full.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1785941", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3274715", "http://www.ncbi.nlm.nih.gov/pubmed/12353947", "http://www.ncbi.nlm.nih.gov/pubmed/14695644", "http://www.ncbi.nlm.nih.gov/pubmed/1605428", "http://www.ncbi.nlm.nih.gov/pubmed/18765409", "http://www.ncbi.nlm.nih.gov/pubmed/22307105", "http://www.ncbi.nlm.nih.gov/pubmed/3510056", "http://www.ncbi.nlm.nih.gov/pubmed/692598", "http://www.annals.org/content/137/7/598.full.pdf", "http://doi.org/10.1002%2Fsim.1591", "http://doi.org/10.1056%2FNEJM197810262991705", "http://doi.org/10.1093%2Ffampra%2Fcmn051", "http://doi.org/10.1136%2Fbmjopen-2011-000746", "http://doi.org/10.7326%2F0003-4819-104-1-66", "http://doi.org/10.7326%2F0003-4819-117-2-135", "http://doi.org/10.7326%2F0003-4819-137-7-200210010-00011", "http://fampra.oxfordjournals.org/cgi/content/full/25/5/390"]}, "Survival rate": {"categories": ["Accuracy disputes from May 2014", "All accuracy disputes", "All articles needing additional references", "All articles needing expert attention", "All articles with unsourced statements", "Articles needing additional references from May 2014", "Articles needing expert attention from May 2014", "Articles with multiple maintenance issues", "Articles with unsourced statements from April 2016", "Demography", "Epidemiology", "Medicine articles needing expert attention", "Statistical ratios"], "title": "Survival rate", "method": "Survival rate", "url": "https://en.wikipedia.org/wiki/Survival_rate", "summary": "Survival rate is a part of survival analysis. It is the percentage of people in a study or treatment group still alive for a given period of time after diagnosis.It is a method of describing prognosis in certain disease conditions.\nSurvival rate can be used as yardstick for the assessment of standards of therapy. The survival period is usually reckoned from date of diagnosis or start of treatment. Survival rates are important for prognosis, but because the rate is based on the population as a whole, an individual prognosis may be different depending on newer treatments since the last statistical analysis as well as the overall general health of the patient. There are various types of survival rates (discussed below). They often serve as endpoints of clinical trials and should not be confused with mortality rates, a population metric.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/1/17/System-search.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Arithmetical mean", "Cancer", "Cancer research", "Cancer staging", "Car accident", "Cause of death", "Clinical endpoint", "Clinical trial", "Colorectal cancer", "Disease", "End point of clinical trials", "Five-year survival rate", "International Standard Serial Number", "Median", "Metastasis", "Mortality rates", "Pancreatic cancer", "Patient", "Prognosis", "Progression-free survival", "Prostate cancer", "Relative survival", "Response Evaluation Criteria in Solid Tumors", "Surveillance, Epidemiology, and End Results database", "Survival analysis"], "references": ["http://www.cancer.gov/dictionary?cdrid=655248", "http://www.cancer.gov/publications/dictionaries/cancer-terms?cdrid=44311", "http://www.cancer.gov/publications/dictionaries/cancer-terms?cdrid=44301", "http://www.worldcat.org/issn/2067-7855", "https://www.ncbi.nlm.nih.gov/pubmed/26705497", "https://ami.info.umfcluj.ro/index.php/AMI/article/view/572"]}, "GraphPad InStat": {"categories": ["Companies based in San Diego", "Software companies based in California", "Wikipedia articles with possible conflicts of interest from March 2018"], "title": "GraphPad Software", "method": "GraphPad InStat", "url": "https://en.wikipedia.org/wiki/GraphPad_Software", "summary": "GraphPad Software Inc. is a privately held California corporation. They publish scientific software, including:\n\nGraphPad Prism combines 2D scientific graphing, biostatistics with explanations, and curve fitting via nonlinear regression (Windows and Mac).\nGraphPad InStat guides students and scientists through basic biostatistics (Windows).\nGraphPad StatMate performs power and sample size calculations (Windows).\nGraphPad QuickCalcs are a set of statistical calculators (Free, web-based).", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Unbalanced_scales.svg"], "links": ["2D geometric model", "Biostatistics", "Commercial software", "Error bars", "Free content", "GraphPad InStat", "GraphPad Prism", "MacOS", "Mac OS", "Microsoft Windows", "Nonlinear regression", "Operating system", "Proprietary software", "R (programming language)", "SciDAVis", "Software categories", "Software developer", "Software license", "Software release life cycle", "Statistics software", "Windows"], "references": ["http://graphpad.com/prism", "http://www.graphpad.com", "http://www.graphpad.com/instat", "http://www.sciencemag.org/products/bt-statsw.dtl", "https://www.ncbi.nlm.nih.gov/sites/entrez?db=pubmed&cmd=DetailsSearch&term=graphpad&log$=activity", "https://www.google.it/search?q=%22r+software%22+OR+%22r+project%22+OR+%22r+language%22+site:www.ncbi.nlm.nih.gov/pubmed/"]}, "Cox\u2013Ingersoll\u2013Ross model": {"categories": ["CS1 maint: Multiple names: authors list", "Financial models", "Fixed income analysis", "Interest rates", "Short-rate models", "Stochastic models"], "title": "Cox\u2013Ingersoll\u2013Ross model", "method": "Cox\u2013Ingersoll\u2013Ross model", "url": "https://en.wikipedia.org/wiki/Cox%E2%80%93Ingersoll%E2%80%93Ross_model", "summary": "In mathematical finance, the Cox\u2013Ingersoll\u2013Ross model (or CIR model) describes the evolution of interest rates. It is a type of \"one factor model\" (short rate model) as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives. It was introduced in 1985 by John C. Cox, Jonathan E. Ingersoll and Stephen A. Ross as an extension of the Vasicek model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5d/CIR_Process.png", "https://upload.wikimedia.org/wikipedia/commons/f/f4/SQRTDiffusion.png"], "links": ["Abstract Wiener space", "Accrual bond", "Actuarial mathematics", "Agency debt", "Asset-backed security", "Auction rate security", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Basic affine jump diffusion", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Bond (finance)", "Bond convexity", "Bond duration", "Bond market", "Bond option", "Bond valuation", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Callable bond", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Clean price", "Closed-form expression", "Collateralized debt obligation", "Collateralized mortgage obligation", "Commercial Mortgage Securities Association", "Commercial mortgage-backed security", "Commercial paper", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Contingent convertible bond", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Convertible bond", "Corporate bond", "Coupon (bond)", "Cox process", "Cram\u00e9r\u2013Lundberg model", "Credit spread (bond)", "Current yield", "C\u00e0dl\u00e0g", "Debenture", "Diffusion process", "Digital object identifier", "Dirichlet process", "Dirty price", "Discrete-time stochastic process", "Discretization", "Distressed securities", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrica", "Econometrics", "Embedded option", "Emerging market debt", "Empirical process", "Ergodic", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable bond", "Exchangeable random variables", "Extendible bond", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fixed income", "Fixed rate bond", "Fleming\u2013Viot process", "Floating rate note", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Government bond", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "High-yield debt", "Hopfield model", "Ho\u2013Lee model", "Hull-White model", "Hull\u2013White model", "Hunt process", "I-spread", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Inflation-indexed bond", "Interacting particle system", "Interest rate", "Interest rate derivative", "International Capital Market Association", "International Standard Book Number", "Inverse floating rate note", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "John C. Cox", "Jonathan E. Ingersoll", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Market risk", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "Maximum likelihood", "McKean\u2013Vlasov process", "Mean reversion (finance)", "Mixing (mathematics)", "Moran process", "Mortgage-backed security", "Mortgage yield", "Moving-average model", "Municipal bond", "Nominal yield", "Non-homogeneous Poisson process", "Noncentral chi-squared distribution", "Option-adjusted spread", "Optional stopping theorem", "Ordinary least squares", "Ornstein\u2013Uhlenbeck process", "Parameter", "Percolation theory", "Perpetual bond", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Prentice Hall", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Puttable bond", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Reverse convertible securities", "Risk-free bond", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Securities Industry and Financial Markets Association", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Senior debt", "Short rate model", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Standard deviation", "Stationary process", "Statistics", "Steady state", "Stephen Ross (economist)", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stochastic simulation", "Stopping time", "Stratonovich integral", "Submartingale", "Subordinated debt", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "Weighted-average life", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "Yield curve", "Yield spread", "Yield to maturity", "Z-spread", "Zero-coupon bond"], "references": ["http://doi.org/10.2307%2F1911242", "http://ideas.repec.org/a/spr/finsto/v5y2001i3p369-387.html", "https://github.com/AlexandreMoulti/bachelier"]}, "Demand forecasting": {"categories": ["Demand", "Statistical forecasting", "Supply chain management", "Wikipedia articles with NDL identifiers"], "title": "Demand forecasting", "method": "Demand forecasting", "url": "https://en.wikipedia.org/wiki/Demand_forecasting", "summary": "Demand forecasting is a field of predictive analytics which tries to understand and predict customer demand to optimize supply decisions by corporate supply chain and business management. Demand forecasting involves quantitative methods such as the use of data, and especially historical sales data, as well as statistical techniques from test markets. Demand forecasting may be used in production planning, inventory management, and at times in assessing future capacity requirements, or in making decisions on whether to enter a new market.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20161201223606%21Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20120912121406%21Blue_pencil.svg"], "links": ["Causal model", "Conjoint analysis (in marketing)", "Consensus forecasts", "Data", "Data mining", "Delphi method", "Demand Modeling", "Demand chain", "Discrete event simulation", "Extrapolation", "Forecast bias", "Game theory", "Group method of data handling", "Inventory", "Market entry", "Mean absolute percentage error", "Mean percentage error", "National Diet Library", "Neural network", "Optimism bias", "Prediction market", "Predictive analytics", "Reference class forecasting", "Root mean squared error", "Supply and demand", "Symmetric mean absolute percentage error", "Test market", "Tracking signal"], "references": ["http://www.robjhyndman.com/papers/mase.pdf", "http://www.statsoft.com/Textbook/Demand-Forecasting", "http://datascienceassn.org/sites/default/files/Another%20Look%20at%20Measures%20of%20Forecast%20Accuracy.pdf", "http://forecasters.org/pdfs/foresight/Foresight_ForecastAccReprint.pdf", "https://id.ndl.go.jp/auth/ndlna/00575164", "https://www.wikidata.org/wiki/Q3409300"]}, "Morris method": {"categories": ["CS1 maint: Multiple names: authors list", "Computational physics", "Randomized algorithms", "Statistical approximations", "Statistical mechanics"], "title": "Morris method", "method": "Morris method", "url": "https://en.wikipedia.org/wiki/Morris_method", "summary": "In applied statistics, the Morris method for global sensitivity analysis is a so-called one-step-at-a-time method (OAT), meaning that in each run only one input parameter is given a new value. It facilitates a global sensitivity analysis by making a number r of local changes at different points x(1 \u2192 r) of the possible range of input values.", "images": [], "links": ["Applied statistics", "Bibcode", "Digital object identifier", "Global sensitivity analysis", "Monte Carlo method", "One-step-at-a-time method", "Sensitivity analysis"], "references": ["http://www.sciencedirect.com/science/article/pii/S0010465598001659", "http://adsabs.harvard.edu/abs/1999CoPhC.117...75C", "http://www.abe.ufl.edu/Faculty/jjones/ABE_5646/2010/Morris.1991%20SA%20paper.pdf", "http://library.lanl.gov/cgi-bin/getdoc?event=SAMO2004&document=samo04-52.pdf", "http://doi.org/10.1016%2FS0010-4655(98)00165-9", "http://doi.org/10.2307%2F1269043"]}, "Statistical parametric mapping": {"categories": ["All articles lacking sources", "Articles lacking sources from November 2010", "Biostatistics", "Neuroimaging", "Neuroimaging software"], "title": "Statistical parametric mapping", "method": "Statistical parametric mapping", "url": "https://en.wikipedia.org/wiki/Statistical_parametric_mapping", "summary": "Statistical parametric mapping or SPM is a statistical technique created by Karl Friston for examining differences in brain activity recorded during functional neuroimaging experiments using neuroimaging technologies such as fMRI or PET. It may also refer to a specific piece of software created by the Wellcome Department of Imaging Neuroscience (part of University College London) to carry out such analyses.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/87/Functional_magnetic_resonance_imaging.jpg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Analysis of Functional NeuroImages", "Brain", "Cerebral cortex", "Cognitive neuroscience", "Convolution", "Corpus callosum", "Dynamic causal modelling", "FMRI", "FMRIB Software Library", "FreeSurfer", "Free software", "Functional Magnetic Resonance Imaging", "Functional magnetic resonance imaging", "Functional neuroimaging", "Gaussian", "General linear model", "Gyri", "Image realignment", "Karl Friston", "MATLAB", "Montr\u00e9al Neurological Institute", "Multiple comparisons", "Neuroimaging", "Parametric statistics", "Positron Emission Tomography", "Random field", "Resel", "SPM (disambiguation)", "Spatial normalization", "Statistical", "Sulcus (neuroanatomy)", "Talairach coordinates", "Time series", "Type I error", "University College London", "Voxel", "Wavelet"], "references": ["http://www.imagilys.com/autospm.html", "http://www.mccauslandcenter.sc.edu/CRNL/", "http://spect.yale.edu", "http://cogprints.org/6193/", "http://www.mrc-cbu.cam.ac.uk/Imaging/Common/", "http://www.fil.ion.ucl.ac.uk/spm/", "http://www.fil.ion.ucl.ac.uk/~mgray/Presentations/Buttons%20in%20SPM5.ppt"]}, "Parametric model": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from May 2012", "Articles with unsourced statements from October 2010", "Statistical models"], "title": "Parametric model", "method": "Parametric model", "url": "https://en.wikipedia.org/wiki/Parametric_model", "summary": "In statistics, a parametric model or parametric family or finite-dimensional model is a family of distributions that can be described using a finite number of parameters. These parameters are usually collected together to form a single k-dimensional parameter vector \u03b8 = (\u03b81, \u03b82, \u2026, \u03b8k).\nParametric models are contrasted with the semi-parametric, semi-nonparametric, and non-parametric models, all of which consist of an infinite set of \"parameters\" for description. The distinction between these four classes is as follows:\nin a \"parametric\" model all the parameters are in finite-dimensional parameter spaces;\na model is \"non-parametric\" if all the parameters are in infinite-dimensional parameter spaces;\na \"semi-parametric\" model contains finite-dimensional parameters of interest and infinite-dimensional nuisance parameters;\na \"semi-nonparametric\" model has both finite-dimensional and infinite-dimensional unknown parameters of interest.Some statisticians believe that the concepts \"parametric\", \"non-parametric\", and \"semi-parametric\" are ambiguous. It can also be noted that the set of all probability measures has cardinality of continuum, and therefore it is possible to parametrize any model at all by a single number in (0,1) interval. This difficulty can be avoided by considering only \"smooth\" parametric models.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Cambridge University Press", "Cardinality", "Continuous function", "Continuum (set theory)", "Coordinate system", "David Freedman (statistician)", "Erich Leo Lehmann", "Exponential family", "Fisher information matrix", "Fr\u00e9chet derivative", "George Casella", "Grace Yang", "Identifiable", "International Standard Book Number", "Invertible matrix", "L2 space", "Local asymptotic normality", "Location-scale family", "Lucien Le Cam", "Mathematical Reviews", "Measurable space", "Measure domination", "Non-parametric model", "Normal distribution", "Nuisance parameter", "Occam's razor", "Open set", "Parameter", "Parametric family", "Parametrization", "Poisson distribution", "Prentice-Hall", "Probability density function", "Probability distribution", "Probability mass function", "Score (statistics)", "Semi-nonparametric model", "Semiparametric model", "Solid modeling", "Statistical model", "Statistics", "Transpose", "Walter de Gruyter", "Weibull distribution", "\u03a3-finite measure"], "references": ["http://www.ams.org/mathscinet-getitem?mr=1291393", "http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521671057"]}, "classical Wiener space": {"categories": ["Metric geometry", "Stochastic processes"], "title": "Classical Wiener space", "method": "classical Wiener space", "url": "https://en.wikipedia.org/wiki/Classical_Wiener_space", "summary": "In mathematics, classical Wiener space is the collection of all continuous functions on a given domain (usually a sub-interval of the real line), taking values in a metric space (usually n-dimensional Euclidean space). Classical Wiener space is useful in the study of stochastic processes whose sample paths are continuous functions. It is named after the American mathematician Norbert Wiener.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4d/Norbert_wiener.jpg"], "links": ["Abstract Wiener space", "Almost surely", "Arzel\u00e0-Ascoli theorem", "Banach space", "Brownian motion", "Complete space", "Continuous function", "Cylinder set measure", "C\u00e0dl\u00e0g", "Domain of a function", "Euclidean space", "Gaussian measure", "Hilbert space", "If and only if", "Independent increments", "Interval (mathematics)", "Law (stochastic processes)", "Linear subspace", "Markov property", "Mathematician", "Mathematics", "Metric (mathematics)", "Metric space", "Modulus of continuity", "Norbert Wiener", "Normed vector space", "Open set", "Polish space", "Probability measure", "Product measure", "Radonifying function", "Real line", "Separable space", "Stochastic process", "Stochastic processes", "Stone-Weierstrass theorem", "Strictly positive measure", "Tightness of measures", "Topology", "Uniform convergence", "Uniform norm", "Uniform topology (disambiguation)", "United States", "Vector space", "Wiener process"], "references": []}, "Triangular distribution": {"categories": ["CS1 maint: Archived copy as title", "Continuous distributions", "Pages using deprecated image syntax"], "title": "Triangular distribution", "method": "Triangular distribution", "url": "https://en.wikipedia.org/wiki/Triangular_distribution", "summary": "In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit a, upper limit b and mode c, where a < b and a \u2264 c \u2264 b.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e5/Triangular_distribution_CMF.png", "https://upload.wikimedia.org/wikipedia/commons/4/45/Triangular_distribution_PMF.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Corporate finance", "Critical path method", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Decision making", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Dither", "Elliptical distribution", "Eric W. Weisstein", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Five-number summary", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "MathWorld", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "PERT", "PERT distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Project management", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Seven-number summary", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Simulation", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Thomas Simpson", "Three-point estimation", "Tracy\u2013Widom distribution", "Trapezoidal distribution", "Triangular function", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://mathworld.wolfram.com/TriangularDistribution.html", "http://www.decisionsciences.org/DecisionLine/Vol31/31_3/31_3clas.pdf", "https://books.google.de/books?id=JO7ICgAAQBAJ&lpg=PA1&dq=chapter%201%20dig%20out%20suitable%20substitutes%20of%20the%20beta%20distribution%20one%20of%20our%20goals&pg=PA3#v=onepage&q&f=false", "https://web.archive.org/web/20060923225843/http://www.decisionsciences.org/DecisionLine/Vol31/31_3/31_3clas.pdf", "https://web.archive.org/web/20130318003944/http://www.brighton-webs.co.uk/distributions/triangular.htm", "https://web.archive.org/web/20140407075018/http://www.asianscientist.com/books/wp-content/uploads/2013/06/5720_chap1.pdf"]}, "Hyper-exponential distribution": {"categories": ["Continuous distributions"], "title": "Hyperexponential distribution", "method": "Hyper-exponential distribution", "url": "https://en.wikipedia.org/wiki/Hyperexponential_distribution", "summary": "In probability theory, a hyperexponential distribution is a continuous probability distribution whose probability density function of the random variable X is given by\n\n \n \n \n \n f\n \n X\n \n \n (\n x\n )\n =\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n f\n \n \n Y\n \n i\n \n \n \n \n (\n x\n )\n \n \n p\n \n i\n \n \n ,\n \n \n {\\displaystyle f_{X}(x)=\\sum _{i=1}^{n}f_{Y_{i}}(x)\\;p_{i},}\n where each Yi is an exponentially distributed random variable with rate parameter \u03bbi, and pi is the probability that X will take on the form of the exponential distribution with rate \u03bbi. It is named the hyperexponential distribution since its coefficient of variation is greater than that of the exponential distribution, whose coefficient of variation is 1, and the hypoexponential distribution, which has a coefficient of variation smaller than one. While the exponential distribution is the continuous analogue of the geometric distribution, the hyperexponential distribution is not analogous to the hypergeometric distribution. The hyperexponential distribution is an example of a mixture density.\nAn example of a hyperexponential random variable can be seen in the context of telephony, where, if someone has a modem and a phone, their phone line usage could be modeled as a hyperexponential distribution where there is probability p of them talking on the phone with rate \u03bb1 and probability q of them using their internet connection with rate \u03bb2.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e9/Hyperexponential.svg"], "links": ["ARGUS distribution", "Anja Feldmann", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Coefficient of variation", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heavy-tailed distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture density", "Mixture distribution", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Prony's method", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Student's t-distribution", "Telephony", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Ward Whitt", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.columbia.edu/~ww2040/FittingMixturesPerfEval98.pdf", "http://doi.org/10.1016%2FS0166-5316(97)00003-5", "http://doi.org/10.1080%2F15501320701259925", "https://books.google.com/books?id=9pf5MCf9VDYC&pg=PA35"]}, "Falconer's formula": {"categories": ["All stub articles", "Genetics", "Genetics stubs", "Statistical genetics", "Statistics stubs"], "title": "Falconer's formula", "method": "Falconer's formula", "url": "https://en.wikipedia.org/wiki/Falconer%27s_formula", "summary": "Falconer's formula is a mathematical formula that is used used in twin studies to estimate the relative contribution of genetics vs. environment to variation in a particular trait (that is, the heritability of the trait) based on the difference between twin correlations. It was first proposed by the Scottish geneticist Douglas Falconer.The formula is\n\nHb2 = 2(rmz - rdz)where Hb2 is the broad sense heritability, rmz is the (monozygotic, MZ) identical twin correlation, and rdz is the (dizygotic, DZ) fraternal twin correlation. The correlation of same sex MZ twins is always higher than the DZ twin correlation with various sexes and thus all gender differences are evaluated as heritable. To avoid this error, only genetic studies comparing MZ twins with the same sex DZ twins are valid. Correlations between A = hb2 (additive genetics) and C (common environment) must be included in the derivation shown below.\n\nrmz = A + C + 2 Corr(A,C)rdz = \u00bdA + C + 2 Corr(\u00bdA,C)Falconer's formula is based on assumptions that have been widely criticized as flawed. For example, it only calculates narrow-sense heritability, meaning it assumes that all genetic effects are additive; this assumption does not comport with the functioning of genes in real biological systems. The formula also overestimates broad-sense heritability due to an overestimation of dominance variance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cf/Plain_DNA_icon.svg"], "links": ["Correlation", "Digital object identifier", "Douglas Scott Falconer", "Formula", "Fraternal twin", "Gender differences", "Genetics", "Heritability", "International Standard Book Number", "PubMed Central", "PubMed Identifier", "Quantitative genetics", "Statistics", "Trait (biology)", "Twin", "Twin studies"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4450891", "http://www.ncbi.nlm.nih.gov/pubmed/25895112", "http://doi.org/10.1097/mib.0000000000000393", "https://books.google.com/books?id=xvK8BKbeNWAC", "https://books.google.com/books?id=xvK8BKbeNWAC&pg=PA107"]}, "Pseudo-random number sampling": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2011", "Non-uniform random numbers", "Pseudorandom number generators", "Wikipedia articles needing page number citations from June 2011"], "title": "Pseudo-random number sampling", "method": "Pseudo-random number sampling", "url": "https://en.wikipedia.org/wiki/Pseudo-random_number_sampling", "summary": "Pseudo-random number sampling or non-uniform pseudo-random variate generation is the numerical practice of generating pseudo-random numbers that are distributed according to a given probability distribution.\nMethods of sampling a non-uniform distribution are typically based on the availability of a pseudo-random number generator producing numbers X that are uniformly distributed. Computational algorithms are then used to manipulate a single random variate, X, or often several such variates, into a new random variate Y such that these values have the required distribution.\nHistorically, basic methods of pseudo-random number sampling were developed for Monte-Carlo simulations in the Manhattan project; they were first published by John von Neumann in the early 1950s.", "images": [], "links": ["Alias method", "Binary search", "Box\u2013Muller transform", "Convolution random number generator", "Correlated", "Discrete probability distribution", "Donald Knuth", "GNU Scientific Library", "Gibbs sampling", "Indexed search", "Inverse transform sampling", "John von Neumann", "Journal of Research of the National Institute of Standards and Technology", "Linear search", "Manhattan project", "Markov chain", "Markov chain Monte Carlo", "Marsaglia polar method", "Metropolis\u2013Hastings algorithm", "Mixture model", "Monte-Carlo method", "Normal distribution", "Numerical analysis", "Particle filter", "Poisson distribution", "Probability distribution", "Probability mass function", "Pseudo-random number", "Pseudo-random number generator", "Random variate", "Rejection sampling", "Reversible-jump Markov chain Monte Carlo", "Slice sampling", "Statistical independence", "The Art of Computer Programming", "Uniform distribution (continuous)", "Ziggurat algorithm"], "references": ["http://search.proquest.com/openview/84d724fc612fbfb1b7c6b7976198e5ff/1?pq-origsite=gscholar&cbl=30748", "https://books.google.com/books?id=dogHCAAAQBAJ&printsec=frontcover#v=onepage&q&f=false", "https://books.google.com/books?id=tiTyCAAAQBAJ&printsec=frontcover#v=onepage&q&f=false", "https://dornsifecms.usc.edu/assets/sites/520/docs/VonNeumann-ams12p36-38.pdf", "https://mcnp.lanl.gov/pdf_files/nbs_vonneumann.pdf"]}, "Cross-covariance": {"categories": ["All articles needing additional references", "Articles needing additional references from December 2016", "Covariance and correlation", "Signal processing", "Time domain analysis"], "title": "Cross-covariance", "method": "Cross-covariance", "url": "https://en.wikipedia.org/wiki/Cross-covariance", "summary": "In probability and statistics, given two stochastic processes \n \n \n \n X\n =\n (\n \n X\n \n t\n \n \n )\n \n \n {\\displaystyle X=(X_{t})}\n and \n \n \n \n Y\n =\n (\n \n Y\n \n t\n \n \n )\n \n \n {\\displaystyle Y=(Y_{t})}\n , the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. With the usual notation \n \n \n \n E\n \n \n {\\displaystyle \\operatorname {E} }\n ; for the expectation operator, if the processes have the mean functions \n \n \n \n \n \u03bc\n \n X\n \n \n (\n t\n )\n =\n \n E\n \n \u2061\n [\n \n X\n \n t\n \n \n ]\n \n \n {\\displaystyle \\mu _{X}(t)=\\operatorname {\\operatorname {E} } [X_{t}]}\n and \n \n \n \n \n \u03bc\n \n Y\n \n \n (\n t\n )\n =\n E\n \u2061\n [\n \n Y\n \n t\n \n \n ]\n \n \n {\\displaystyle \\mu _{Y}(t)=\\operatorname {E} [Y_{t}]}\n , then the cross-covariance is given by\n\n \n \n \n \n C\n \n X\n Y\n \n \n (\n t\n ,\n s\n )\n =\n cov\n \u2061\n (\n \n X\n \n t\n \n \n ,\n \n Y\n \n s\n \n \n )\n =\n E\n \u2061\n [\n (\n \n X\n \n t\n \n \n \u2212\n \n \u03bc\n \n X\n \n \n (\n t\n )\n )\n (\n \n Y\n \n s\n \n \n \u2212\n \n \u03bc\n \n Y\n \n \n (\n s\n )\n )\n ]\n =\n E\n \u2061\n [\n \n X\n \n t\n \n \n \n Y\n \n s\n \n \n ]\n \u2212\n \n \u03bc\n \n X\n \n \n (\n t\n )\n \n \u03bc\n \n Y\n \n \n (\n s\n )\n .\n \n \n \n {\\displaystyle C_{XY}(t,s)=\\operatorname {cov} (X_{t},Y_{s})=\\operatorname {E} [(X_{t}-\\mu _{X}(t))(Y_{s}-\\mu _{Y}(s))]=\\operatorname {E} [X_{t}Y_{s}]-\\mu _{X}(t)\\mu _{Y}(s).\\,}\n Cross-covariance is related to the more commonly used cross-correlation of the processes in question.\nIn the case of two random vectors \n \n \n \n \n X\n \n =\n (\n \n X\n \n 1\n \n \n ,\n \n X\n \n 2\n \n \n ,\n \u2026\n ,\n \n X\n \n p\n \n \n \n )\n \n \n T\n \n \n \n \n \n {\\displaystyle \\mathbf {X} =(X_{1},X_{2},\\ldots ,X_{p})^{\\rm {T}}}\n and \n \n \n \n \n Y\n \n =\n (\n \n Y\n \n 1\n \n \n ,\n \n Y\n \n 2\n \n \n ,\n \u2026\n ,\n \n Y\n \n q\n \n \n \n )\n \n \n T\n \n \n \n \n \n {\\displaystyle \\mathbf {Y} =(Y_{1},Y_{2},\\ldots ,Y_{q})^{\\rm {T}}}\n , the cross-covariance would be a \n \n \n \n p\n \u00d7\n q\n \n \n {\\displaystyle p\\times q}\n matrix \n \n \n \n \n C\n \n X\n Y\n \n \n \n \n {\\displaystyle C_{XY}}\n (often denoted \n \n \n \n cov\n \u2061\n (\n X\n ,\n Y\n )\n \n \n {\\displaystyle \\operatorname {cov} (X,Y)}\n ) with entries \n \n \n \n \n C\n \n X\n Y\n \n \n (\n j\n ,\n k\n )\n =\n cov\n \u2061\n (\n \n X\n \n j\n \n \n ,\n \n Y\n \n k\n \n \n )\n .\n \n \n \n {\\displaystyle C_{XY}(j,k)=\\operatorname {cov} (X_{j},Y_{k}).\\,}\n Thus the term cross-covariance is used in order to distinguish this concept from the covariance of a random vector \n \n \n \n \n X\n \n \n \n {\\displaystyle \\mathbf {X} }\n , which is understood to be the matrix of covariances between the scalar components of \n \n \n \n \n X\n \n \n \n {\\displaystyle \\mathbf {X} }\n itself.\nIn signal processing, the cross-covariance is often called cross-correlation and is a measure of similarity of two signals, commonly used to find features in an unknown signal by comparing it to a known one. It is a function of the relative time between the signals, is sometimes called the sliding dot product, and has applications in pattern recognition and cryptanalysis.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Autocorrelation", "Autocovariance", "Complex-valued", "Complex conjugate", "Convolution", "Correlation", "Covariance", "Covariance matrix", "Cross-correlation", "Cryptanalysis", "Dot product", "Expected value", "Mean", "Pattern recognition", "Probability", "Random element", "Random processes", "Random vector", "Sampling (statistics)", "Signal (information theory)", "Signal processing", "Similarity measure", "Statistics", "Stochastic process", "Stochastic processes", "Time", "Variance", "Wide-sense stationary"], "references": ["http://www.statlect.com/varian2.htm", "http://mathworld.wolfram.com/Cross-Correlation.html", "http://www.phys.ufl.edu/LIGO/stochastic/sign05.pdf", "http://scribblethink.org/Work/nvisionInterface/nip.html", "http://www.staff.ncl.ac.uk/oliver.hinton/eee305/Chapter6.pdf"]}, "Three-stage least squares": {"categories": ["Mathematical and quantitative methods (economics)", "Regression models", "Simultaneous equation methods (econometrics)"], "title": "Simultaneous equations model", "method": "Three-stage least squares", "url": "https://en.wikipedia.org/wiki/Simultaneous_equations_model", "summary": "Simultaneous equation models are a type of statistical model in the form of a set of linear simultaneous equations. They are often used in econometrics. One can estimate these models equation by equation; however, estimation methods that exploit the system of equations, such as generalized method of moments (GMM) and instrumental variables estimation (IV) tend to be more efficient.", "images": [], "links": ["2SLS", "Annals of Mathematical Statistics", "Arnold Zellner", "Coefficient", "Demography", "Digital object identifier", "Econometrica", "Econometrics", "Economics", "Efficiency (statistics)", "Endogenous", "G. S. Maddala", "General linear model", "Generalized eigenvalue problem", "Generalized method of moments", "Gregory R. Hancock", "Henri Theil", "Identification condition", "Independent and identically distributed", "Instrumental variable", "Instrumental variables estimation", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Linear simultaneous equations", "Mark Thoma", "Ordinary least squares", "Parameter identification problem", "Political science", "Reduced form", "Robert Basmann", "Seemingly unrelated regressions", "Sociology", "Statistical model", "Two-stage least squares", "Wayne Fuller", "YouTube"], "references": ["http://economics.about.com/library/glossary/bldef-ils.htm", "http://orm.sagepub.com/content/2/1/69", "http://onlinelibrary.wiley.com/doi/10.1111/psj.12171/abstract", "http://doi.org/10.1016%2F0005-1098(87)90027-6", "http://doi.org/10.1093%2Fjeg%2Flbp031", "http://doi.org/10.1111%2Fpsj.12171", "http://doi.org/10.1177%2F109442819921005", "http://doi.org/10.1214%2Faoms%2F1177730090", "http://doi.org/10.2307%2F1907743", "http://doi.org/10.2307%2F1911287", "http://doi.org/10.2307%2F1912683", "http://doi.org/10.2307%2F1953990", "http://doi.org/10.2307%2F2095464", "http://doi.org/10.2307%2F2111666", "http://www.jstor.org/stable/1907743", "http://www.jstor.org/stable/1911287", "http://www.jstor.org/stable/2095464", "http://www.jstor.org/stable/2111666", "http://www.jstor.org/stable/2236803", "http://www.worldcat.org/issn/0003-0554", "http://www.worldcat.org/issn/1094-4281", "http://www.worldcat.org/issn/1468-2702", "http://www.worldcat.org/issn/1541-0072", "https://books.google.com/books?id=Bxq7AAAAIAAJ&pg=PA695", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA276", "https://academic.oup.com/joeg/article-lookup/doi/10.1093/jeg/lbp031", "https://www.youtube.com/watch?v=D5lt9bhOshc&list=PLD15D38DC7AA3B737&index=15", "https://www.cambridge.org/core/journals/american-political-science-review/article/reciprocal-effects-of-policy-preferences-party-loyalties-and-the-vote/D837D22D662FBFEB7779001CF52DB361", "https://www.jstor.org/stable/3314964"]}, "Validity (statistics)": {"categories": ["All articles needing expert attention", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Educational psychology", "Philosophy of science", "Psychometrics", "Statistics articles needing expert attention", "Validity (statistics)", "Wikipedia articles with GND identifiers"], "title": "Validity (statistics)", "method": "Validity (statistics)", "url": "https://en.wikipedia.org/wiki/Validity_(statistics)", "summary": "Validity is the extent to which a concept, conclusion or measurement is well-founded and likely corresponds accurately to the real world based on probability. The word \"valid\" is derived from the Latin validus, meaning strong. This should not be confused with notions of certainty nor necessity. The validity of a measurement tool (for example, a test in education) is considered to be the degree of probability to which the tool measures what it claims to measure; in this case, the validity is an equivalent to a percent of how accurately the claim corresponds to reality. \nIn psychometrics, validity has a particular application known as test validity: \"the degree to which evidence and theory support the interpretations of test scores\" (\"as entailed by proposed uses of tests\").It is generally accepted that the concept of scientific validity addresses the nature of reality in terms of statistical probability and as such is an epistemological and philosophical issue as well as a question of measurement of the possibility that a scientific claim is true. The use of the term in logic is narrower, relating to the truth of inferences made from premises. In logic, and therefore as the term is applied to any epistemological claim, validity refers to the consistency of an argument flowing from the premises to the conclusion; as such, the truth of the claim in logic is not only reliant on validity. Rather, an argumentative claim is true if and only if it is both valid and sound. This means the argument flows without contradiction from the premises or the conclusion, and all of the premises and the conclusion correspond to known facts. As such, \"scientific or statistical validity\" is not a deductive claim that is necessarily truth preserving, but is an inductive claim that remains true or false in an undecided manner. This is why \"scientific or statistical validity\" is a claim that is qualified as being either strong or weak in its nature, it is never necessary nor certainly true. This has the effect of making claims of \"scientific or statistical validity\" open to interpretation as to what, in fact, the facts of the matter mean. \nValidity is important because it can help determine what types of tests to use, and help to make sure researchers are using methods that are not only ethical, and cost-effective, but also a method that truly measures the idea or constructs in question.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg"], "links": ["Anne Lewellyn Barstow", "Brian Levack", "Classification of mental disorders", "Cognitive neuroscience", "Concept", "Concurrent validity", "Confounding", "Construct validity", "Content validity", "Convergent validity", "Criterion validity", "Cross-validation (statistics)", "Daubert v. Merrell Dow Pharmaceuticals", "Dependent variable", "Digital object identifier", "Discriminant validity", "Ecological validity", "Empiricism", "Epistemological", "Essentialist", "External validity", "Face validity", "Falsifiability", "Feighner Criteria", "Gene", "Hereditary", "Independent variable", "Inductive reasoning", "Integrated Authority File", "Internal validity", "International Standard Serial Number", "Malleus Malificarum", "Measurement", "Molecular biology", "Molecular genetics", "Nancy Coover Andreasen", "Neural substrate", "Neuroanatomy", "Neurochemistry", "Neurophysiology", "Philosophical", "Precision and accuracy", "Predictive validity", "Psychiatry", "Psychometrics", "PubMed Identifier", "Regression model validation", "Reliability (psychometrics)", "Research Diagnostic Criteria", "Research ethics", "Scientific method", "Standards for Educational and Psychological Testing", "Statistical conclusion validity", "Test validity", "Utility", "Validation (disambiguation)", "Validity (disambiguation)", "Validity (logic)", "Validity scale", "Variable (research)"], "references": ["http://psychclassics.yorku.ca/Cronbach/construct.htm", "http://www.all-about-forensic-psychology.com/support-files/the-precarious-use-of-forensic-psychology-as-evidence.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/12505793", "http://www.ncbi.nlm.nih.gov/pubmed/13245896", "http://www.ncbi.nlm.nih.gov/pubmed/16816216", "http://www.slideshare.net/JonathanJavid/measurement-validity-and-reliability", "http://doi.org/10.1037%2Fh0040957", "http://doi.org/10.1176%2Fappi.ajp.160.1.4", "http://doi.org/10.1176%2Fappi.ajp.163.7.1138", "http://www.ncme.org/ncme/NCME/Resource_Center/Glossary/NCME/Resource_Center/Glossary1.aspx?hkey=4bb87415-44dc-4088-9ed9-e8515326a061#anchorV", "http://ajp.psychiatryonline.org/cgi/content/full/160/1/4", "http://ajp.psychiatryonline.org/cgi/content/full/163/7/1138", "http://www.worldcat.org/issn/0033-2909", "http://www.hsrc.ac.za/research/output/outputDocuments/1716_Foxcroft_Psychologicalassessmentin%20SA.pdf", "https://d-nb.info/gnd/4062305-1", "https://www.wikidata.org/wiki/Q18757"]}, "List of probability distributions": {"categories": ["Statistics-related lists"], "title": "List of probability distributions", "method": "List of probability distributions", "url": "https://en.wikipedia.org/wiki/List_of_probability_distributions", "summary": "Many probability distributions that are important in theory or applications have been given specific names.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9a/Beta_distribution_pdf.png", "https://upload.wikimedia.org/wikipedia/commons/7/75/Binomial_distribution_pmf.svg", "https://upload.wikimedia.org/wikipedia/commons/1/15/CMP_PMF.png", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Cauchy_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/2/21/Chi-square_distributionPDF.png", "https://upload.wikimedia.org/wikipedia/commons/9/9e/Degenerate_distribution_PMF.png", "https://upload.wikimedia.org/wikipedia/commons/e/e6/Gamma_distribution_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/1/10/JohnsonSU.png", "https://upload.wikimedia.org/wikipedia/commons/8/8c/KumaraswamyPDF.png", "https://upload.wikimedia.org/wikipedia/commons/8/89/Laplace_distribution_pdf.png", "https://upload.wikimedia.org/wikipedia/commons/5/58/LevyDistribution.png", "https://upload.wikimedia.org/wikipedia/commons/f/f6/PDF_of_Pareto_Distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/1/16/Poisson_pmf.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a9/Skellam_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c2/Uniform_distribution.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARGUS distribution", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behrens\u2013Fisher distribution", "Behrens\u2013Fisher problem", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Birnbaum\u2013Saunders distribution", "Bivariate von Mises distribution", "Blocking (statistics)", "Boltzmann distribution", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Champernowne distribution", "Chemometrics", "Chen distribution", "Chernoff's distribution", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Conway\u2013Maxwell\u2013Poisson distribution", "Copula (statistics)", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crusher", "Cumulative distribution function", "Dagum distribution", "Data collection", "Davis distribution", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Dirac comb", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Displaced Poisson distribution", "Divergence (statistics)", "Doppler broadening", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Ewens's sampling formula", "Expected value", "Experiment", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Exponentially modified Gaussian distribution", "Extended hypergeometric distribution", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's noncentral hypergeometric distribution", "Fisher's z-distribution", "Fisher\u2013Tippett distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian minus exponential distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized gamma distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized logistic distribution", "Generalized multivariate log-gamma distribution", "Generalized normal distribution", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "Geostatistics", "Gibbs distribution", "Gompertz distribution", "Goodness-of-fit", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harmonic mean", "Henyey-Greenstein phase function", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Index of dispersion", "Integer partition", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Johnson SU distribution", "Joint distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Linnik distribution", "List of fields of application of statistics", "List of statistical topics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logarithmic distribution (continuous)", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lomax distribution", "Lorentzian function", "Loss function", "Lp space", "L\u00e9vy distribution", "L\u00e9vy skew alpha-stable distribution", "M-estimator", "Mann\u2013Whitney U test", "Map-Airy distribution", "Marchenko\u2013Pastur distribution", "Marshall\u2013Olkin exponential distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Mie phase function", "Mill (grinding)", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Noncentral F-distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral chi distribution", "Noncentral t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-exponential-gamma distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "PERT distribution", "Parabolic fractal distribution", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Particle size distribution", "Partition of sums of squares", "Pearson Type IV distribution", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pharmacokinetics", "Phase-type distribution", "Phased bi-Weibull distribution", "Phased bi-exponential distribution", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Polya\u2013Eggenberger distribution", "Population (statistics)", "Population genetics", "Population statistics", "Posterior probability", "Power (statistics)", "Power law", "Prediction interval", "Principal component analysis", "Prior probability", "ProbOnto", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quasi-experiment", "Questionnaire", "Queueing theory", "Queuing systems", "Q\u2013Q plot", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrices", "Random matrix", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Rayleigh mixture distribution", "Reciprocal distribution", "Rectangular distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relationships among probability distributions", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Resonance", "Rice distribution", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set theory", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Skellam distribution", "Skew elliptical distribution", "Skew normal distribution", "Skew t distribution", "Skewed generalized t distribution", "Skewness", "Slash distribution", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spectral line", "Stable distribution", "Standard deviation", "Standard error", "Stark effect", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical physics", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Thermal equilibrium", "Time domain", "Time series", "Tolerance interval", "Tracy\u2013Widom distribution", "Trapezoidal distribution", "Trend estimation", "Triangular distribution", "Truncated distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wakeby distribution", "Wald test", "Wallenius' noncentral hypergeometric distribution", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped Laplace distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zero-truncated Poisson distribution", "Zeta distribution", "Zipf's law", "Zipf distribution", "Zipf\u2013Mandelbrot law"], "references": ["http://probonto.org"]}, "Coefficient of coherence": {"categories": ["All articles covered by WikiProject Wikify", "All pages needing cleanup", "Articles covered by WikiProject Wikify from June 2017", "Bayesian statistics", "Frequency-domain analysis", "Probability assessment", "Statistical principles", "Wikipedia introduction cleanup from June 2017"], "title": "Coherence (statistics)", "method": "Coefficient of coherence", "url": "https://en.wikipedia.org/wiki/Coherence_(statistics)", "summary": "In probability theory and statistics, coherence can have several different meanings.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Bayesian decision theory", "Coherence (philosophical gambling strategy)", "Coherence (signal processing)", "Frequency spectrum", "International Standard Book Number", "Probability theory", "Statistics", "Time series analysis"], "references": []}, "Correlation function (statistical mechanics)": {"categories": ["Covariance and correlation", "Specific models", "Statistical mechanics"], "title": "Correlation function (statistical mechanics)", "method": "Correlation function (statistical mechanics)", "url": "https://en.wikipedia.org/wiki/Correlation_function_(statistical_mechanics)", "summary": "In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe how microscopic variables, such as spin and density, at different positions are related. More specifically, correlation functions quantify how microscopic variables co-vary with one another on average across space and time. A classic example of such spatial correlations is in ferro- and antiferromagnetic materials, where the spins prefer to align parallel and antiparallel with their nearest neighbors, respectively. The spatial correlation between spins in such materials is shown in the figure to the right.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a8/Ferro_antiferro_spatial_corrs_png.png", "https://upload.wikimedia.org/wikipedia/commons/5/51/Ferromagnetic_correlation_functions_around_Tc.svg"], "links": ["ArXiv", "Arxiv.org", "Autocorrelation function", "Bethe ansatz", "Bibcode", "Canonical ensemble", "Correlation function", "Correlation function (disambiguation)", "Critical exponent", "Cross-correlation", "Cyril Domb", "Digital object identifier", "International Standard Book Number", "Joel Lebowitz", "Lars Onsager", "Melville S. Green", "Michael E. Fisher", "Neutron scattering", "Onsager Regression Hypothesis", "Phase Transitions and Critical Phenomena", "Power law", "PubMed Central", "PubMed Identifier", "Quantum inverse scattering method", "Radial distribution function", "Scaling invariance", "Spin (physics)", "Statistical mechanics", "Universality (dynamical systems)"], "references": ["http://pages.physics.cornell.edu/~sethna/StatMech/", "http://adsabs.harvard.edu/abs/1931PhRv...37..405O", "http://adsabs.harvard.edu/abs/1974RvMP...46..597F", "http://adsabs.harvard.edu/abs/2009PNAS..10611511W", "http://adsabs.harvard.edu/abs/2010PhRvB..82j4207A", "http://xbeams.chem.yale.edu/~batista/vaa/node56.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2703671", "http://www.ncbi.nlm.nih.gov/pubmed/20716512", "http://arxiv.org/abs/1006.5382", "http://arxiv.org/abs/1402.1432", "http://doi.org/10.1073%2Fpnas.0905337106", "http://doi.org/10.1103%2FPhysRev.37.405", "http://doi.org/10.1103%2FPhysRevB.82.104207", "http://doi.org/10.1103%2FRevModPhys.46.597", "http://doi.org/10.1107%2FS1600576714012424", "https://arxiv.org/pdf/0909.4751", "https://dx.doi.org/10.1103/PhysRev.37.405"]}, "Financial models with long-tailed distributions and volatility clustering": {"categories": ["Actuarial science", "Financial models"], "title": "Financial models with long-tailed distributions and volatility clustering", "method": "Financial models with long-tailed distributions and volatility clustering", "url": "https://en.wikipedia.org/wiki/Financial_models_with_long-tailed_distributions_and_volatility_clustering", "summary": "Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of classical financial models. These classical models of financial time series typically assume homoskedasticity and normality cannot explain stylized phenomena such as skewness, heavy tails, and volatility clustering of the empirical asset returns in finance. In 1963, Benoit Mandelbrot first used the stable (or \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n -stable) distribution to model the empirical distributions which have the skewness and heavy-tail property. Since \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n -stable distributions have infinite \n \n \n \n p\n \n \n {\\displaystyle p}\n -th moments for all \n \n \n \n p\n >\n \u03b1\n \n \n {\\displaystyle p>\\alpha }\n , the tempered stable processes have been proposed for overcoming this limitation of the stable distribution.\nOn the other hand, GARCH models have been developed to explain the volatility clustering. In the GARCH model, the innovation (or residual) distributions are assumed to be a standard normal distribution, despite the fact that this assumption is often rejected empirically. For this reason, GARCH models with non-normal innovation distribution have been developed.\nMany financial models with stable and tempered stable distributions together with volatility clustering have been developed and applied to risk management, option pricing, and portfolio selection.", "images": [], "links": ["Beno\u00eet Mandelbrot", "Borel measure", "Characteristic function (probability theory)", "Digital object identifier", "Frank J. Fabozzi", "GARCH", "Heavy tails", "Homoskedasticity", "Independent and identically-distributed random variables", "Infinite divisibility (probability)", "International Journal of Theoretical and Applied Finance", "Levy measure", "Normal distribution", "Skewness", "Stable distribution", "Stefan Mittnik", "Time series", "Volatility clustering"], "references": ["http://www.statistik.uni-karlsruhe.de/download/tr_smoothly_truncated.pdf", "https://doi.org/10.1016%2Fj.jbankfin.2007.11.004"]}, "Substitution model": {"categories": ["Bioinformatics", "CS1 maint: Multiple names: authors list", "Computational phylogenetics", "Statistical genetics", "Stochastic models"], "title": "Substitution model", "method": "Substitution model", "url": "https://en.wikipedia.org/wiki/Substitution_model", "summary": "In biology, a substitution model describes the process from which a sequence of symbols changes into another set of traits. For example, in cladistics, each position in the sequence might correspond to a property of a species which can either be present or absent. The alphabet could then consist of \"0\" for absence and \"1\" for presence. Then the sequence 00110 could mean, for example, that a species does not have feathers or lay eggs, does have fur, is warm-blooded, and cannot breathe underwater. Another sequence 11010 would mean that a species has feathers, lays eggs, does not have fur, is warm-blooded, and cannot breathe underwater. In phylogenetics, sequences are often obtained by firstly obtaining a nucleotide or protein sequence alignment, and then taking the bases or amino acids at corresponding positions in the alignment as the characters. Sequences achieved by this might look like AGCGGAGCTTA and GCCGTAGACGC.\nSubstitution models are used for a number of things:\n\nConstructing evolutionary trees in phylogenetics or cladistics.\nSimulating sequences to test other methods and algorithms.", "images": [], "links": ["Alphabet (computer science)", "Amino acid", "Body size", "Cambrian explosion", "Cladistic", "Cladistics", "Codon", "Compositional bias", "Detailed balance", "Diagonalizable matrix", "Digital object identifier", "Evolutionary tree", "Gene expression", "Generation time", "Genome", "Kronecker delta", "Matrix (mathematics)", "Matrix exponential", "Maximum likelihood", "Metabolic rate", "Missense mutation", "Models of DNA evolution", "Molecular clock", "Motoo Kimura", "Natural selection", "Neutral theory of molecular evolution", "Nucleotide", "Nucleotide sequence", "Phylogenetics", "Point accepted mutation", "Primate", "Protein sequence", "Proteins", "PubMed Central", "PubMed Identifier", "Rodent", "Sequence alignment", "Sequence of symbols", "Simon Tavar\u00e9", "Speciation", "Species", "Statistical independence", "Time reversibility"], "references": ["http://linkinghub.elsevier.com/retrieve/pii/1055-7903(92)90017-B", "http://linkinghub.elsevier.com/retrieve/pii/S1055-7903(96)90012-3", "http://link.springer-ny.com/link/service/journals/00239/bibs/46n4p409.html", "http://www.cmb.usc.edu/people/stavare/STpapers-pdf/T86.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC46451", "http://www.ncbi.nlm.nih.gov/pubmed/11230536", "http://www.ncbi.nlm.nih.gov/pubmed/1342937", "http://www.ncbi.nlm.nih.gov/pubmed/1604319", "http://www.ncbi.nlm.nih.gov/pubmed/1630306", "http://www.ncbi.nlm.nih.gov/pubmed/3934395", "http://www.ncbi.nlm.nih.gov/pubmed/7288891", "http://www.ncbi.nlm.nih.gov/pubmed/7463489", "http://www.ncbi.nlm.nih.gov/pubmed/8336541", "http://www.ncbi.nlm.nih.gov/pubmed/8483925", "http://www.ncbi.nlm.nih.gov/pubmed/8673286", "http://www.ncbi.nlm.nih.gov/pubmed/9541535", "http://www.ncbi.nlm.nih.gov/pubmed/9656490", "http://www.ncbi.nlm.nih.gov/pubmed/9866200", "http://doi.org/10.1006%2Fmpev.1996.0012", "http://doi.org/10.1007%2FBF01731581", "http://doi.org/10.1007%2FBF01734359", "http://doi.org/10.1007%2FBF02101694", "http://doi.org/10.1007%2FPL00006320", "http://doi.org/10.1016%2F1055-7903(92)90017-B", "http://doi.org/10.1073%2Fpnas.90.9.4087", "http://doi.org/10.1093%2Fbioinformatics%2F8.3.275", "http://doi.org/10.1093%2Foxfordjournals.molbev.a003811", "http://doi.org/10.1093%2Foxfordjournals.molbev.a025892", "http://doi.org/10.1093%2Foxfordjournals.molbev.a025995", "http://doi.org/10.1126%2Fscience.1604319", "http://mbe.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=11230536", "http://mbe.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=9866200", "http://mbe.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=1630306", "http://mbe.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=8336541", "http://www.pnas.org/cgi/pmidlookup?view=long&pmid=8483925"]}, "Meta-analysis": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2018", "Articles with unsourced statements from September 2018", "CS1 maint: Multiple names: authors list", "Evidence-based practices", "Meta-analysis", "Systematic review", "Use dmy dates from March 2012", "Webarchive template wayback links", "Wikipedia articles needing clarification from April 2013", "Wikipedia articles with GND identifiers"], "title": "Meta-analysis", "method": "Meta-analysis", "url": "https://en.wikipedia.org/wiki/Meta-analysis", "summary": "A meta-analysis is a statistical analysis that combines the results of multiple scientific studies.\nThe basic tenet behind meta-analyses is that there is a common truth behind all conceptually similar scientific studies, but which has been measured with a certain error within individual studies. The aim then is to use approaches from statistics to derive a pooled estimate closest to the unknown common truth based on how this error is perceived. In essence, all existing methods yield a weighted average from the results of the individual studies and what differs is the manner in which these weights are allocated and also the manner in which the uncertainty is computed around the point estimate thus generated. In addition to providing an estimate of the unknown common truth, meta-analysis has the capacity to contrast results from different studies and identify patterns among study results, sources of disagreement among those results, or other interesting relationships that may come to light in the context of multiple studies.A key benefit of this approach is the aggregation of information leading to a higher statistical power and more robust point estimate than is possible from the measure derived from any individual study. However, in performing a meta-analysis, an investigator must make choices which can affect the results, including deciding how to search for studies, selecting studies based on a set of objective criteria, dealing with incomplete data, analyzing the data, and accounting for or choosing not to account for publication bias.Meta-analyses are often, but not always, important components of a systematic review procedure. For instance, a meta-analysis may be conducted on several clinical trials of a medical treatment, in an effort to obtain a better understanding of how well the treatment works. Here it is convenient to follow the terminology used by the Cochrane Collaboration, and use \"meta-analysis\" to refer to statistical methods of combining evidence, leaving other aspects of 'research synthesis' or 'evidence synthesis', such as combining information from qualitative studies, for the more general context of systematic reviews. A meta-analysis is a secondary source.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/d/da/Indirekt_j%C3%A4mf%C3%B6relse.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/0c/Integrated_Molecular_Meta-Analysis_of_1%2C000_Pediatric_High-Grade_and_Diffuse_Intrinsic_Pontine_Glioma_-_graphical_abstract.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/5/51/Example_of_a_symmetrical_funnel_plot_created_with_MetaXL_Sept_2015.jpg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/0/0e/Funnel_plot_depicting_asymmetry_Sept_2015.jpg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Academic clinical trials", "Accelerated failure time model", "Actuarial science", "Adaptive clinical trial", "Akaike information criterion", "Analysis of clinical trials", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Animal testing", "Animal testing on non-human primates", "Annals of Statistics", "Arithmetic mean", "Asymptotic theory (statistics)", "Attributable fraction among the exposed", "Attributable fraction for the population", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Base rate fallacy", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "British Medical Journal", "Canonical correlation", "Cartography", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Cherry picking (fallacy)", "Chi-squared test", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochrane Collaboration", "Cochrane Database of Systematic Reviews", "Cochran\u2013Mantel\u2013Haenszel statistics", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort study", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlation does not imply causation", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-sectional study", "Cross-validation (statistics)", "Cumulative incidence", "DNA microarray", "Data aggregation", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Diffuse intrinsic pontine glioma", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Ecological study", "Econometrics", "Economic", "Educational research", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental Protection Agency", "Environmental statistics", "Epidemiological methods", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation statistics", "Evidence-based medicine", "Experiment", "Exponential family", "Exponential smoothing", "Extrasensory Perception After Sixty Years", "Extrasensory perception", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "File drawer problem", "First-hitting-time model", "First-in-man study", "Forest plot", "Fourier analysis", "Frank L. Schmidt", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Funnel plot", "G-test", "Galbraith plot", "Gene V. Glass", "Gene expression", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Gideon J. Mellenbergh", "Glossary of clinical research", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "H. J. 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"https://web.archive.org/web/20111122083418/http://tobaccodocuments.org/pm/2047231315-1318.pdf", "https://web.archive.org/web/20121124154834/http://publish.uwo.ca/~elebel/documents/l&p(2011,rgp).pdf", "https://cran.r-project.org/web/packages/metansue/index.html", "https://www.wikidata.org/wiki/Q815382"]}, "Antecedent variable": {"categories": ["All stub articles", "Design of experiments", "Independence (probability theory)", "Regression analysis", "Statistics stubs"], "title": "Antecedent variable", "method": "Antecedent variable", "url": "https://en.wikipedia.org/wiki/Antecedent_variable", "summary": "In statistics and social sciences, an antecedent variable is a variable that can help to explain the apparent relationship (or part of the relationship) between other variables that are nominally in a cause and effect relationship. In a regression analysis, an antecedent variable would be one that influences both the independent variable and the dependent variable.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Causality", "Confounding variable", "Dependent variable", "Independent variable", "International Standard Book Number", "Intervening variable", "Latent variable", "Path analysis (statistics)", "Regression analysis", "Social sciences", "Statistics", "Variable (mathematics)"], "references": []}, "Arithmetic mean": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from July 2013", "Articles with unsourced statements from October 2018", "Means", "Use dmy dates from June 2013"], "title": "Arithmetic mean", "method": "Arithmetic mean", "url": "https://en.wikipedia.org/wiki/Arithmetic_mean", "summary": "In mathematics and statistics, the arithmetic mean ( , stress on third syllable of \"arithmetic\"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term \"arithmetic mean\" is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means, such as the geometric mean and the harmonic mean. \nIn addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology, and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.\nWhile the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influenced by outliers (values that are very much larger or smaller than most of the values). Notably, for skewed distributions, such as the distribution of income for which a few people's incomes are substantially greater than most people's, the arithmetic mean may not coincide with one's notion of \"middle\", and robust statistics, such as the median, may be a better description of central tendency.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/de/Comparison_mean_median_mode.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Angle", "Anthropology", "Arithmetic progression", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Data set", "Decomposition of time series", "Degree (angle)", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Distribution of income", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimating equations", "Euro coins", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet mean", "G-test", "General linear model", "Generalized linear model", "Generalized mean", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "HTML", "Harmonic mean", "Heteroscedasticity", "Histogram", "History", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-normal distribution", "Log-rank test", "Logistic regression", "Lognormal distribution", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "MathWorld", "Mathematics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean of circular quantities", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Microsoft Word", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "PDF", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Per capita income", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Radian", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistic", "Robust statistics", "Root mean squared error", "Run chart", "Sample mean and covariance", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewed distribution", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error of the mean", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Summary statistics", "Summation", "Summation operator", "Survey (statistics)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Text processing", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Unbiased estimate", "Unicode", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Viz.", "W. H. Freeman", "Wald test", "Wavelet", "Web browser", "Weighted average", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.fxsolver.com/browse/formulas/Arithmetic+Mean", "http://www.sengpielaudio.com/calculator-geommean.htm", "http://mathworld.wolfram.com/ArithmeticMean.html", "http://www.personal.psu.edu/ejp10/psu/gotunicode/statsym.html", "http://prospect.org/article/rich-right-and-facts-deconstructing-inequality-debate", "https://books.google.com/?id=bRUwgf_q5RsC"]}, "Base rate": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2016", "Bayesian statistics", "Epidemiology", "Machine learning", "Psychometrics"], "title": "Base rate", "method": "Base rate", "url": "https://en.wikipedia.org/wiki/Base_rate", "summary": "In probability and statistics, base rate generally refers to the (base) class probabilities unconditioned on featural evidence, frequently also known as prior probabilities. For example, if it were the case that 1% of the public were \"medical professionals\", and 99% of the public were not \"medical professionals\", then the base rate of medical professionals is simply 1%.\nIn the sciences, including medicine, the base rate is critical for comparison. It may at first seem impressive that 1000 people beat their winter cold while using 'Treatment X', until we look at the entire 'Treatment X' population and find that the base rate of success is only 1/100 (i.e. 100,000 people tried the treatment, but the other 99,000 people never really beat their winter cold). The treatment's effectiveness is clearer when such base rate information (i.e. \"1000 people... out of how many?\") is available. Note that controls may likewise offer further information for comparison; maybe the control groups, who were using no treatment at all, had their own base rate success of 5/100. Controls thus indicate that 'Treatment X' makes things worse, despite that initial proud claim about 1000 people.\nThe normative method for integrating base rates (prior probabilities) and featural evidence (likelihoods) is given by Bayes' rule.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Base rate fallacy", "Bayes' theorem", "Central bank", "Control group", "Keith Devlin", "Likelihood", "Medicine", "Prior probabilities", "Probability", "Reliability (statistics)", "Sciences", "Statistics", "Stethoscope"], "references": ["http://www.edge.org/responses/what-scientific-concept-would-improve-everybodys-cognitive-toolkit"]}, "Event (probability theory)": {"categories": ["All articles needing additional references", "Articles needing additional references from January 2018", "Commons category link from Wikidata", "Experiment (probability theory)"], "title": "Event (probability theory)", "method": "Event (probability theory)", "url": "https://en.wikipedia.org/wiki/Event_(probability_theory)", "summary": "In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. An event defines a complementary event, namely the complementary set (the event not occurring), and together these define a Bernoulli trial: did the event occur or not?\nTypically, when the sample space is finite, any subset of the sample space is an event (i.e. all elements of the power set of the sample space are defined as events). However, this approach does not work well in cases where the sample space is uncountably infinite. So, when defining a probability space it is possible, and often necessary, to exclude certain subsets of the sample space from being events (see Events in probabiliity spaces, below).", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png", "https://upload.wikimedia.org/wikipedia/commons/b/b0/Venn_A_subset_B.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayes' theorem", "Bernoulli trial", "Boole's inequality", "Borel measure", "Complementary event", "Conditional independence", "Conditional probability", "Elementary event", "Empty set", "Encyclopedia of Mathematics", "Euler diagram", "Experiment (probability theory)", "Independence (probability theory)", "Independent event", "International Standard Book Number", "Inverse image", "Joint probability", "Joint probability distribution", "Law of large numbers", "Law of total probability", "Lebesgue measure", "Map (mathematics)", "Marginal distribution", "Measure theory", "Michiel Hazewinkel", "Mizar system", "Nonmeasurable set", "Normal distribution", "Outcome (probability)", "Pathological (mathematics)", "Playing card", "Power set", "Prentice Hall", "Probability", "Probability axioms", "Probability distributions", "Probability measure", "Probability space", "Probability theory", "Proper subset", "Propositional formula", "Random variable", "Real numbers", "Sample space", "Set (mathematics)", "Sigma-algebra", "Singleton set", "Statistics", "Subset", "Tree diagram (probability theory)", "Uncountably infinite", "Venn diagram"], "references": ["http://mws.cs.ru.nl/mwiki/prob_1.html#M1", "https://www.amazon.com/Algebra-Trigonometry-Functions-Applications-Prentice/dp/0131657100", "https://books.google.com/books/about/Probability_Statistics_and_Random_Proces.html?id=GUJosCkbBywC", "https://books.google.com/books?id=_mayRBczVRwC&pg=PA18", "https://www.encyclopediaofmath.org/index.php?title=p/r077290"]}, "Topological data analysis": {"categories": ["All articles with style issues", "Applied mathematics", "Articles with short description", "Computational topology", "Data analysis", "Homology theory", "Wikipedia articles needing clarification from December 2015", "Wikipedia articles with style issues"], "title": "Topological data analysis", "method": "Topological data analysis", "url": "https://en.wikipedia.org/wiki/Topological_data_analysis", "summary": "In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools.\nThe initial motivation is to study the shape of data. TDA has combined algebraic topology and other tools from pure mathematics to allow mathematically rigorous study of \"shape\". The main tool is persistent homology, an adaptation of homology to point cloud data. Persistent homology has been applied to many types of data across many fields. Moreover, its mathematical foundation is also of theoretical importance. The unique features of TDA make it a promising bridge between topology and geometry.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6a/Illustration_of_Typical_Workflow_in_TDA.jpeg", "https://upload.wikimedia.org/wikipedia/commons/e/e4/Persistence_Diagram.png", "https://upload.wikimedia.org/wikipedia/commons/7/76/Topological_Barcode.png", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Algebraic geometry", "Algebraic topology", "Applied mathematics", "ArXiv", "Ayasdi", "Betti number", "Bibcode", "Category theory", "Cech complex", "Charles Epstein", "Complex network", "Computational topology", "Computer vision", "Confidence interval", "Data mining", "Digital object identifier", "Dimensionality reduction", "Discrete Morse theory", "Extended real number line", "Fiber (mathematics)", "Field (mathematics)", "Fr\u00e9chet mean", "Functor", "Fundamental theorem of finitely generated abelian groups", "Gabriel's theorem", "Gunnar Carlsson", "Heather Harrington", "Herbert Edelsbrunner", "Homology (mathematics)", "Initial and terminal objects", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Lipschitz continuity", "Lotka\u2013Volterra equations", "Machine learning", "Matroid", "Metric (mathematics)", "Morse theory", "Multidimensional scaling", "Multiset (abstract data type)", "Nerve of a covering", "Null hypothesis significance testing", "Persistent homology", "Point cloud", "Preordered set", "Principal component analysis", "PubMed Central", "PubMed Identifier", "R programming language", "Reeb graph", "Scientific visualization", "Self-similarity", "Shape analysis (digital geometry)", "Sheaf (mathematics)", "Simplicial complex", "Single-linkage clustering", "Size theory", "Spectral sequence", "Structure theorem for finitely generated modules over a principal ideal domain", "Topology", "Vietoris\u2013Rips complex", "Wasserstein metric", "\u010cech cohomology"], "references": ["http://www.birs.ca/events/2012/5-day-workshops/12w5081", "http://www.ayasdi.com", "http://www.ayasdi.com/blog/", "http://www.ayasdi.com/blog/bigdata/why-topological-data-analysis-works/", "http://www.ayasdi.com/resources/whitepaper/topology-and-topological-data-analysis/", "http://phat.googlecode.com/", "http://www.hindawi.com/journals/mpe/2013/815035/abs/", "http://intlpress.com/site/pub/files/_fulltext/journals/hha/2016/0018/0001/HHA-2016-0018-0001-a021.pdf", "http://www.nature.com/articles/srep01236?message-global=remove&WT.ec_id=SREP-639-20130301", "http://www.sciencedirect.com/science/article/pii/S0031320308000733", "http://www.sciencedirect.com/science/article/pii/S0166864113001892", "http://www.sciencedirect.com/science/article/pii/S0893965910004118", "http://www.sciencedirect.com/science/article/pii/S0925772112001435", "http://www.sciencedirect.com/science/article/pii/S1524070306000592", "http://onlinelibrary.wiley.com/doi/10.1002/cnm.2655/abstract", "http://onlinelibrary.wiley.com/doi/10.1002/jcc.23816/abstract", "http://onlinelibrary.wiley.com/doi/10.1002/mma.2704/abstract", "http://onlinelibrary.wiley.com/doi/10.1002/mma.3093/abstract", "http://onlinelibrary.wiley.com/doi/10.1111/j.1467-8659.2009.01516.x/abstract", "http://www.worldscientific.com/doi/abs/10.1142/S0218654305000761", "http://www.worldscientific.com/doi/pdf/10.1142/S0219498815500668", "http://adsabs.harvard.edu/abs/2009JSMTE..03..034H", "http://adsabs.harvard.edu/abs/2011InvPr..27a0101E", "http://adsabs.harvard.edu/abs/2011InvPr..27l4003D", "http://adsabs.harvard.edu/abs/2011InvPr..27l4005F", "http://adsabs.harvard.edu/abs/2011InvPr..27l4007M", "http://adsabs.harvard.edu/abs/2011PNAS..108.7265N", "http://adsabs.harvard.edu/abs/2012JMP....53g3516M", "http://adsabs.harvard.edu/abs/2013MMAS...36.1543C", "http://adsabs.harvard.edu/abs/2013NatSR...3E1236L", "http://adsabs.harvard.edu/abs/2013PNAS..11018566C", "http://adsabs.harvard.edu/abs/2015MMAS...38..617C", "http://adsabs.harvard.edu/abs/2015NatCo...6E7723T", "http://adsabs.harvard.edu/abs/2016arXiv160600199H", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.161.8956&rep=rep1&type=pdf", "http://www.math.upenn.edu/~ghrist/notes.html", "http://www.sas.upenn.edu/~vnanda/perseus/index.html", "http://www.lix.polytechnique.fr/~maks/papers/li-CVPR-14.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3084136", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3566620", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3831954", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4131872", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4223908", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4324100", "http://www.ncbi.nlm.nih.gov/pubmed/21482760", "http://www.ncbi.nlm.nih.gov/pubmed/23393618", "http://www.ncbi.nlm.nih.gov/pubmed/24170857", "http://www.ncbi.nlm.nih.gov/pubmed/24902720", "http://www.ncbi.nlm.nih.gov/pubmed/25401177", "http://www.ncbi.nlm.nih.gov/pubmed/25523342", 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"https://www.ias.edu/about/publications/ias-letter/articles/2013-summer/lesnick-topological-data-analysis", "https://www.ima.umn.edu/topology/", "https://project.inria.fr/gudhi/software/", "https://topology-tool-kit.github.io/", "https://www.researchgate.net/publication/267672645_The_Framed_Morse_complex_and_its_invariants", "https://www.researchgate.net/publication/327427685_Topological_Kernel_Learning", "https://web.archive.org/web/20151119021029/http://www.diva-portal.org/smash/record.jsf?pid=diva2:575329", "https://doi.org/10.1007/s00454-016-9763-9", "https://CRAN.R-project.org/package=TDAstats", "https://CRAN.R-project.org/package=ggplot2", "https://cran.r-project.org/web/packages/TDA/index.html"]}, "Medoid": {"categories": ["Cluster analysis", "Means"], "title": "Medoid", "method": "Medoid", "url": "https://en.wikipedia.org/wiki/Medoid", "summary": "Medoids are representative objects of a data set or a cluster with a data set whose average dissimilarity to all the objects in the cluster is minimal. Medoids are similar in concept to means or centroids, but medoids are always restricted to be members of the data set. Medoids are most commonly used on data when a mean or centroid cannot be defined, such as graphs. They are also used in contexts where the centroid is not representative of the dataset like in images and 3-D trajectories and gene expression (where while the data is sparse the medoid need not be). These are also of interest while wanting to find a representative using some distance other than squared euclidean distance (for instance in movie-ratings).\nFor some data sets there may be more than one medoid, as with medians.\nA common application of the medoid is the k-medoids clustering algorithm, which is similar to the k-means algorithm but works when a mean or centroid is not definable. This algorithm basically works as follows. First, a set of medoids is chosen at random. Second, the distances to the other points are computed. Third, data are clustered according to the medoid they are most similar to. Fourth, the medoid set is optimized via an iterative process.\nNote that a medoid is not equivalent to a median, a geometric median, or centroid. A median is only defined on 1-dimensional data, and it only minimizes dissimilarity to other points for a specific distance metric (Manhattan norm). A geometric median is defined in any dimension, but is not necessarily a point from within the original dataset.", "images": [], "links": ["Centroid", "Centroids", "Cluster analysis", "Data set", "Digital object identifier", "Euclidean distance", "Gene expression", "Geometric median", "K-means", "K-means algorithm", "K-medoids", "Mean", "Median", "Metric (mathematics)", "Multi-armed bandit", "Norm (mathematics)", "Peter Rousseeuw"], "references": ["http://doi.org/10.1080%2F0094965031000136012", "http://www.jstatsoft.org/v01/i04", "http://proceedings.mlr.press/v54/newling17a/newling17a.pdf", "https://github.com/EdwardRaff/JSAT/blob/master/JSAT/src/jsat/clustering/MEDDIT.java", "https://github.com/bagavi/Meddit", "https://github.com/idiap/trimed", "https://arxiv.org/abs/1711.00817"]}, "R v Adams": {"categories": ["1996 in British law", "1996 in case law", "All articles with unsourced statements", "Articles with unsourced statements from October 2012", "Court of Appeal of England and Wales cases", "English criminal case law", "Forensic statistics"], "title": "R v Adams", "method": "R v Adams", "url": "https://en.wikipedia.org/wiki/R_v_Adams", "summary": "R v Adams [1996] 2 Cr App R 467, [1996] Crim LR 898, CA and R v Adams [1998] 1 Cr App R 377, The Times, 3 November 1997, CA, are rulings that ousted explicit Bayesian statistics from the reasoning admissible before a jury in DNA cases.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/98/Royal_Coat_of_Arms_of_the_United_Kingdom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/9/98/20180809224607%21Royal_Coat_of_Arms_of_the_United_Kingdom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/9/98/20180809051945%21Royal_Coat_of_Arms_of_the_United_Kingdom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/9/98/20171004170431%21Royal_Coat_of_Arms_of_the_United_Kingdom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/9/98/20171004135718%21Royal_Coat_of_Arms_of_the_United_Kingdom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/9/98/20120912125553%21Royal_Coat_of_Arms_of_the_United_Kingdom.svg"], "links": ["Actus reus", "Adultery", "Alibi", "Animals", "Apostasy", "Appeal Court", "Arrest", "Arson", "Assassination", "Assault", "Attempt", "Automatism (law)", "BAILII", "Battery (crime)", "Bayes's theorem", "Bayes factor", "Bayesian statistics", "Begging", "Bestiality", "Bigamy", "Blackmail", "Bribery", "Burglary", "Causation (law)", "Censorship", "Child abuse", "Complicity", "Compounding a felony", "Concurrence", "Consent", "Conspiracy (criminal)", "Contract", "Corporate liability", "Corporate manslaughter", "Court of Appeal of England and Wales", "Crime", "Criminal Appeal Reports", "Criminal law", "Criminal negligence", "Cruelty to animals", "DNA", "DNA profile", "Defamation", "Defence of property", "Defense (legal)", "Defense of infancy", "Digital object identifier", "Diminished responsibility", "Dueling", "Duress", "Element (criminal law)", "Embezzlement", "English law", "Entrapment", "Evidence (law)", "Extortion", "False imprisonment", "False pretenses", "Felony", "Felony murder rule", "Fornication", "Fraud", "Gambling", "Guilt (law)", "Harassment", "Home invasion", "Homicide", "Identity parade", "Ignorantia juris non excusat", "Incest", "Inchoate offense", "Incitement", "Indecent exposure", "Infraction", "Innocence", "Insanity defense", "Intellectual property", "Intimidation", "Jury", "Justice", "Justification (jurisprudence)", "Kidnapping", "Larceny", "Malfeasance in office", "Manslaughter", "Masturbation", "Mayhem (crime)", "Mens rea", "Miscarriage of justice", "Misdemeanor", "Misprision of felony", "Mistake (criminal law)", "Mistake of law", "Murder", "Necessity (criminal law)", "Negligent homicide", "Obstruction of justice", "Odds", "Offence against the person", "Old Bailey", "Oxford University", "Payola", "Perjury", "Perverting the course of justice", "Peter Donnelly", "Pickpocketing", "Possession of stolen goods", "Prohibition", "Prohibition of drugs", "Property", "Property law", "Prostitution", "Provocation (legal)", "Public", "Questionnaire", "R v Adams (1957)", "Rape", "Reason", "Right of self-defense", "Right to privacy", "Robbery", "Sex and the law", "Sexual assault", "Significance (journal)", "Significance (magazine)", "Smoking ban", "Smuggling", "Sodomy", "Solicitation", "Statistical method", "Suicide", "Sumptuary law", "Tax evasion", "Terrorism", "Theft", "Tort", "Torture", "Trusts and estates", "Vicarious liability (criminal)", "Wildlife smuggling", "Will (law)"], "references": ["http://www.blackwell-synergy.com/doi/pdf/10.1111/j.1740-9713.2005.00089.x", "http://www.bailii.org/ew/cases/EWCA/Crim/1996/22.html", "http://www.bailii.org/ew/cases/EWCA/Crim/1996/2474.html", "http://www.bailii.org/ew/cases/EWCA/Crim/1997/2474.html", "http://www.bailii.org/ew/cases/EWCA/Crim/2006/222.html", "http://doi.org/10.1111%2Fj.1740-9713.2005.00089.x"]}, "Time series": {"categories": ["All articles lacking reliable references", "All articles with unsourced statements", "Articles lacking reliable references from September 2018", "Articles with unsourced statements from October 2017", "Commons category link from Wikidata", "Machine learning", "Mathematical and quantitative methods (economics)", "Statistical data types", "Time series", "Wikipedia articles with NDL identifiers"], "title": "Time series", "method": "Time series", "url": "https://en.wikipedia.org/wiki/Time_series", "summary": "A time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.\nTime series are very frequently plotted via line charts. Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements.\nTime series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values. While regression analysis is often employed in such a way as to test theories that the current values of one or more independent time series affect the current value of another time series, this type of analysis of time series is not called \"time series analysis\", which focuses on comparing values of a single time series or multiple dependent time series at different points in time. Interrupted time series analysis is the analysis of interventions on a single time series.\nTime series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility.)\nTime series analysis can be applied to real-valued, continuous data, discrete numeric data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the English language).", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Random-data-plus-trend-r2.png", "https://upload.wikimedia.org/wikipedia/commons/0/05/Tuberculosis_incidence_US_1953-2009.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", 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estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bayesloop", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Brain (journal)", "Breusch\u2013Godfrey test", "CRAN (R programming language)", "CRC Press", "CUSUM", "Cambridge University Press", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Change detection", "Chaos theory", "Chemometrics", "Chi-squared test", "Chirp", "Chirplet transform", "Classification (machine learning)", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Codomain", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Coherence (signal processing)", "Cointegration", "Communication engineering", "Communications engineering", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous wavelet transform", "Control chart", "Control engineering", "Correlation", "Correlation and dependence", "Correlation density", "Correlation dimension", "Correlation entropy", "Correlation integral", "Correlogram", "Count data", "Covariance", "Cram\u00e9r\u2013von Mises criterion", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-correlation function", "Cross-sectional data", "Cross-sectional study", "Cross-validation (statistics)", "Curve", "Curve fitting", "Cyclostationary process", "Data", "Data collection", "Data mining", "Data point", "Data type", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Dennis Gabor", "Density estimation", "Descriptive statistics", "Design of experiments", "Detrended fluctuation analysis", "Dickey\u2013Fuller test", "Digital filter", 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P. Box", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic analysis", "Harmonic mean", "Heteroscedasticity", "Heteroskedasticity", "Hidden Markov Model", "Hidden Markov Models", "Hidden Markov model", "Histogram", "Hjorth parameters", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Horizon graphs", "Hurst exponent", "IBM SPSS Statistics", "Index of dispersion", "Index set", "Interaction (statistics)", "International Standard Book Number", "Interpolation", "Interquartile range", "Interrupted time series", "Interval estimation", "Isotonic regression", "Jaan Kiusalaas", "Jackknife resampling", "James D. Hamilton", "James Durbin", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kalman filter", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov complexity", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "LetDaTalk", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line chart", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local flow", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "Lyapunov exponent", "M-estimator", "MATLAB", "MIT Press", "Machine Learning", "Machine learning", "Mahalanobis distance", "Mann\u2013Kendall test", "Mann\u2013Whitney U test", "Marginal predictability", "Markov switching multifractal", "Mathematical finance", "Maurice Priestley", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Meteorology", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minitab", "Minkowski distance", "Missing data", "Mixed model", "Mode (statistics)", "Model (abstract)", "Model selection", "Mollifier", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo method", "Moving average model", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National accounts", "Natural experiment", "Natural number", "Neil Gershenfeld", "Nelson\u2013Aalen estimator", "Newey\u2013West estimator", "Noise (physics)", "Non-parametric statistics", "Nonlinear autoregressive exogenous model", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Norbert Wiener", "Numerical analysis", "OCLC", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Oxford University Press", "Pandas (software)", "Panel analysis", "Panel data", "Parametric estimation", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pattern recognition", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase locking", "Phase synchronization", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial", "Polynomial interpolation", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prais\u2013Winsten estimation", "Prediction", "Prediction interval", "Predictive inference", "Princeton University Press", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Quality control", "Quantitative finance", "Quasi-experiment", "Questionnaire", "Queueing theory", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Random walk", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (mathematics)", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rational function", "Real number", "Recurrence plot", "Recurrence quantification analysis", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Rough path", "Rudolf E. K\u00e1lm\u00e1n", "Run chart", "R\u00e9nyi entropy", "SAS (software)", "SPSS", "SPSS Modeler", "S (programming language)", "Sample entropy", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled correlation", "Scatter plot", "Scientific control", "Scikit-learn", "Score test", "Seasonal adjustment", "Seasonality", "Seglearn", "Seismology", "Semiparametric regression", "Sequence", "Sequence analysis", "Serial dependence", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shewhart individuals control chart", "Short-time Fourier transform", "Sign language", "Sign test", "Signal processing", "Simple linear regression", "Simultaneous equations model", "Singular spectrum analysis", "Skewness", "Slycat", "Smoothing", "Social statistics", "Spatial analysis", "Spatial data analysis", "Spearman's rank correlation coefficient", "Special function", "Spectral band power", "Spectral density", "Spectral density estimation", "Spectral edge frequency", "Spectrum", "Speech recognition", "Spline interpolation", "Springer Science+Business Media", "Standard deviation", "Standard error", "State Space Model", "State space", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic", "Stochastic processes", "Stochastic simulation", "Stratified sampling", "Strict stationarity", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sunspots", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The Signal and the Noise", "Tides", "Time", "Time-domain", "Time-frequency analysis", "Time-frequency representation", "Time-series segmentation", "Time domain", "Time reversibility", "Time series database", "Time\u2013frequency representation", "Tolerance interval", "Total correlation", "Trend estimation", "U-statistic", "Uncertainty", "Unevenly spaced time series", "Uniformly most powerful test", "Univariate analysis", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wavelet analysis", "Weather forecasting", "Weka (machine learning)", "Whittle likelihood", "Wilcoxon signed-rank test", "Wolfram Language", "World War II", "Z-test"], "references": ["http://www.facm.ucl.ac.be/intranet/books/statistics/Prism-Regression-Book.unlocked.pdf", "http://bayesloop.com", "http://itfeature.com/time-series-analysis-and-forecasting/time-series-analysis-forecasting", "http://www.mathworks.com/help/matlab/data_analysis/time-series-objects.html", "http://wiki.pentaho.com/display/DATAMINING/Time+Series+Analysis+and+Forecasting+with+Weka", "http://www.sas.com/en_us/software/analytics/ets.html", "http://reference.wolfram.com/language/guide/TimeSeries.html", "http://statistik.mathematik.uni-wuerzburg.de/timeseries/", "http://www.nbb.cornell.edu/neurobio/land/PROJECTS/Complexity/", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.14.5597&rep=rep1&type=pdf", "http://www.ncbi.nlm.nih.gov/pubmed/17008335", "http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm", "http://survey.timeviz.net/", "http://survey.timeviz.net/:", "http://doi.org/10.1006%2Fnimg.1998.0391", "http://doi.org/10.1093%2Fbrain%2Fawl241", "http://doi.org/10.1109%2FIEMBS.2003.1280532", "http://doi.org/10.1109%2FTASSP.1978.1163055", "http://doi.org/10.1111%2Fj.1460-9568.2011.07987.x", "http://doi.org/10.1145%2F882082.882086", "http://earthpy.org/pandas-basics.html", "http://www.gaussianprocess.org/gpml/", "http://www.jstatsoft.org/v33/i05/paper", "http://www.nber.org/chapters/c2062.pdf", "http://www.worldcat.org/oclc/174825352", "https://github.com/dmbee/seglearn", "https://github.com/sandialabs/slycat", "https://www.gmdhshell.com/time-series-analysis-software", "https://books.google.com/books?id=SI-VqAT4_hYC", "https://books.google.com/books?id=UjnB0FIWv_AC&printsec=frontcover#v=onepage&q&f=false", "https://books.google.com/books?id=YlkgAwAAQBAJ&printsec=frontcover#v=onepage&q=%22curve%20fitting%22&f=false", "https://books.google.com/books?id=ba0hAQAAQBAJ&printsec=frontcover#v=onepage&q&f=false", "https://books.google.com/books?id=hhdVr9F-JfAC", "https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69", "https://books.google.com/books?id=rdJvXG1k3HsC&printsec=frontcover#v=onepage&q&f=false", "https://id.ndl.go.jp/auth/ndlna/00574724", "https://www.nbtwiki.net/doku.php?id=tutorial:power_spectra_wavelet_analysis_and_coherence", "https://sourceforge.net/projects/letdatalk/", "https://arxiv.org/pdf/1603.03788", "https://www.encyclopediaofmath.org/index.php/Time_series", "https://ieeexplore.ieee.org/abstract/document/5447930/", "https://cran.r-project.org/web/views/TimeSeries.html", "https://www.wikidata.org/wiki/Q186588"]}, "Frequentist inference": {"categories": ["Statistical inference"], "title": "Frequentist inference", "method": "Frequentist inference", "url": "https://en.wikipedia.org/wiki/Frequentist_inference", "summary": "Frequentist inference is a type of statistical inference that draws conclusions from sample data by emphasizing the frequency or proportion of the data. An alternative name is frequentist statistics. This is the inference framework in which the well-established methodologies of statistical hypothesis testing and confidence intervals are based. Other than frequentistic inference, the main alternative approach to statistical inference is Bayesian inference, while another is fiducial inference.\nWhile \"Bayesian inference\" is sometimes held to include the approach to inference leading to optimal decisions, a more restricted view is taken here for simplicity.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fiducial inference", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequency probability", "Frequentist probability", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "German tank problem", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independence (probability theory)", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability interpretations", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variate", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["https://www.jstor.org/stable/91337"]}, "Trend analysis": {"categories": ["Project management techniques", "Regression with time series structure", "Research methods"], "title": "Trend analysis", "method": "Trend analysis", "url": "https://en.wikipedia.org/wiki/Trend_analysis", "summary": "Trend analysis is the widespread practice of collecting information and attempting to spot a pattern. In some fields of study, the term \"trend analysis\" has more formally defined meanings.Although trend analysis is often used to predict future events, it could be used to estimate uncertain events in the past, such as how many ancient kings probably ruled between two dates, based on data such as the average years which other known kings reigned.\n\n", "images": [], "links": ["Adam Kilgarriff", "Archaisms", "Coolhunting", "Decomposition of time series", "Diachronic linguistics", "Econometric model", "Exponential smoothing", "Extrapolation", "Forecasting", "Google Trends", "Iowa State University", "Kendall rank correlation coefficient", "Moving average", "Neologisms", "Noise", "Project management", "Regression analysis", "Simple linear regression", "Sketch Engine", "Smoothing", "Statistics", "Technology forecasting", "Time series", "Timestamp", "Trend estimation", "Weather forecasting"], "references": ["http://www.investorwords.com/5068/trend_analysis.html", "http://www.abrachan.files.wordpress.com/2007/02/pmpreadyreckoner1.pdf", "http://www.seta.iastate.edu/", "http://hal.archives-ouvertes.fr/docs/00/60/12/61/PDF/TrendAnalysisGaryBenattar.pdf", "http://www.highereducation.org/reports/pubatt/", "https://github.com/TrustChainEG/mega-trends-and-trends-json", "https://www.sketchengine.co.uk/wp-content/uploads/Diacran_CL2015.pdf"]}, "Window function": {"categories": ["Commons category link is on Wikidata", "Digital signal processing", "Fourier analysis", "Signal estimation", "Types of functions"], "title": "Window function", "method": "Window function", "url": "https://en.wikipedia.org/wiki/Window_function", "summary": "In signal processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval, normally symmetric around the middle of the interval, usually near a maximum in the middle, and usually tapering away from the middle. Mathematically, when another function or waveform/data-sequence is \"multiplied\" by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the \"view through the window\". Equivalently, and in actual practice, the segment of data within the window is first isolated, and then only that data is multiplied by the window function values. Thus, tapering, not segmentation, is the main purpose of window functions.\nThe reasons for examining segments of a longer function include detection of transient events and time-averaging of frequency spectra. The duration of the segments is determined in each application by requirements like time and frequency resolution. But that method also changes the frequency content of the signal by an effect called spectral leakage. Window functions allow us to distribute the leakage spectrally in different ways, according to the needs of the particular application. There are many choices detailed in this article, but many of the differences are so subtle as to be insignificant in practice.\nIn typical applications, the window functions used are non-negative, smooth, \"bell-shaped\" curves. Rectangle, triangle, and other functions can also be used. A rectangular window does not modify the data segment at all. It's only for modelling purposes that we say it multiplies by 1 inside the window and by 0 outside. A more general definition of window functions does not require them to be identically zero outside an interval, as long as the product of the window multiplied by its argument is square integrable, and, more specifically, that the function goes sufficiently rapidly toward zero.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8f/8-point_Hann_windows.png", "https://upload.wikimedia.org/wikipedia/commons/5/5c/Comparison_of_symmetric_and_periodic_triangular_windows.png", "https://upload.wikimedia.org/wikipedia/commons/6/6d/Hanning.png", "https://upload.wikimedia.org/wikipedia/commons/0/0a/Processing_losses_for_3_window_functions.gif", "https://upload.wikimedia.org/wikipedia/commons/f/fb/Spectral_leakage_caused_by_%22windowing%22.svg", "https://upload.wikimedia.org/wikipedia/commons/7/78/Window_function_and_frequency_response_-_Approximate_confined_Gaussian_%28sigma_t_%3D_0.1%29.svg", "https://upload.wikimedia.org/wikipedia/commons/d/da/Window_function_and_frequency_response_-_Bartlett-Hann.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0a/Window_function_and_frequency_response_-_Blackman-Harris.svg", "https://upload.wikimedia.org/wikipedia/commons/b/bd/Window_function_and_frequency_response_-_Blackman-Nuttall.svg", "https://upload.wikimedia.org/wikipedia/commons/3/38/Window_function_and_frequency_response_-_Blackman.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a1/Window_function_and_frequency_response_-_Confined_Gaussian_%28sigma_t_%3D_0.1%29.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e5/Window_function_and_frequency_response_-_Cosine.svg", "https://upload.wikimedia.org/wikipedia/commons/8/85/Window_function_and_frequency_response_-_DPSS_%28alpha_%3D_2%29.svg", "https://upload.wikimedia.org/wikipedia/commons/4/48/Window_function_and_frequency_response_-_DPSS_%28alpha_%3D_3%29.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2d/Window_function_and_frequency_response_-_Dolph-Chebyshev_%28alpha_%3D_5%29.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a9/Window_function_and_frequency_response_-_Exponential_%2860dB_decay%29.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Window_function_and_frequency_response_-_Exponential_%28half_window_decay%29.svg", "https://upload.wikimedia.org/wikipedia/commons/0/05/Window_function_and_frequency_response_-_Gaussian_%28sigma_%3D_0.4%29.svg", "https://upload.wikimedia.org/wikipedia/commons/7/76/Window_function_and_frequency_response_-_Hamming_%28alpha_%3D_0.53836%29.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Window_function_and_frequency_response_-_Hann-Poisson_%28alpha_%3D_2%29.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b3/Window_function_and_frequency_response_-_Hann.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Window_function_and_frequency_response_-_Kaiser_%28alpha_%3D_2%29.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e7/Window_function_and_frequency_response_-_Kaiser_%28alpha_%3D_3%29.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d8/Window_function_and_frequency_response_-_Lanczos.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Window_function_and_frequency_response_-_Nuttall_%28continuous_first_derivative%29.svg", "https://upload.wikimedia.org/wikipedia/commons/4/48/Window_function_and_frequency_response_-_Parzen.svg", "https://upload.wikimedia.org/wikipedia/commons/9/97/Window_function_and_frequency_response_-_Planck-Bessel_%28epsilon_%3D_0.1%2C_alpha_%3D_4.45%29.svg", "https://upload.wikimedia.org/wikipedia/commons/3/34/Window_function_and_frequency_response_-_Planck-taper_%28epsilon_%3D_0.1%29.svg", "https://upload.wikimedia.org/wikipedia/commons/6/6a/Window_function_and_frequency_response_-_Rectangular.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5b/Window_function_and_frequency_response_-_Triangular.svg", "https://upload.wikimedia.org/wikipedia/commons/1/14/Window_function_and_frequency_response_-_Tukey_%28alpha_%3D_0.5%29.svg", "https://upload.wikimedia.org/wikipedia/commons/0/02/Window_function_and_frequency_response_-_Ultraspherical_%28mu_%3D_-0.5%29.svg", "https://upload.wikimedia.org/wikipedia/commons/1/17/Window_function_and_frequency_response_-_Welch.svg", "https://upload.wikimedia.org/wikipedia/commons/2/27/Window_function_and_frequency_response_-_flat_top.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f2/Window_functions_in_the_frequency_domain.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Airy function", "Alan V. Oppenheim", "Anisotropy", "Antenna (radio)", "Apodization", "ArXiv", "Asymptotically equal", "Autocorrelation", "B-spline", "Basis function", "Beamforming", "Bell Telephone Laboratories", "Bessel function", "Bibcode", "Boxcar function", "Bump function", "Curve fitting", "Derivative", "Diffraction", "Digital filters", "Digital object identifier", "Dirichlet kernel", "Discrete-time Fourier transform", "Discrete Fourier transform", "Dynamic range", "Eigenfunction", "Exponential function", "Filter design", "Finite impulse response", "Fourier transform", "Fredric J. Harris", "Frequency estimation", "Frequency spectrum", "Function (mathematics)", "Gaussian function", "Gaussian window", "Gravitational-wave astronomy", "Hann function", "Havercosine", "Hertz", "Hill climbing", "International Standard Book Number", "Interval (mathematics)", "Isotropy", "James Kaiser", "Julius von Hann", "Kaiser window", "Kernel (statistics)", "Kernel density estimation", "Kolmogorov\u2013Zurbenko filter", "Lanczos resampling", "Lip\u00f3t Fej\u00e9r", "M. S. Bartlett", "MATLAB", "Manifolds", "Modal analysis", "Modified Bessel function", "Modified discrete cosine transform", "Monthly Notices of the Royal Astronomical Society", "Multitaper", "Newton's method", "Noise floor", "Overlap\u2013add method", "Parabola", "Partitions of unity", "Piecewise", "Planck's law", "Power spectrum", "Quadratic polynomial", "Radial function", "Ralph Beebe Blackman", "Rectangular function", "Richard W. Hamming", "Ronald W. Schafer", "Short-time Fourier transform", "Signal processing", "Signal to noise ratio", "Sinc function", "Smooth function", "Spectral concentration problem", "Spectral leakage", "Square integrable", "Statistics", "Time-frequency representation", "Time\u2013frequency analysis", "Tukey window", "Ultraspherical polynomial", "Uniform norm", "Weighting", "Welch method", "White noise", "Window design method", "Window function", "Window function (SQL)"], "references": ["http://www.cg.tuwien.ac.at/research/vis/vismed/Windows/MasteringWindows.pdf", "http://www-mmsp.ece.mcgill.ca/Documents/Reports/2009/KabalR2009b.pdf", "http://www.bksv.com/doc/Bv0031.pdf", "http://www.dspguide.com/ch9/1.htm", "http://www.mathworks.com/help/signal/ref/hann.html", "http://www.mathworks.com/help/signal/ref/taylorwin.html", "http://www.mathworks.com/help/signal/ref/triang.html", "http://www.mathworks.com/help/toolbox/signal/ref/hann.html", "http://www.multi-instrument.com/doc/D1003/Evaluation_of_Various_Window_Functions_using_Multi-Instrument_D1003.pdf", "http://zone.ni.com/reference/en-XX/help/371361B-01/lvanlsconcepts/char_smoothing_windows/", "http://zone.ni.com/reference/en-XX/help/371361E-01/lvanlsconcepts/char_smoothing_windows/#Exact_Blackman", "http://practicalcryptography.com/miscellaneous/machine-learning/implementing-dolph-chebyshev-window/", "http://electronicsart.weebly.com/fftwindows.html", "http://mathworld.wolfram.com/BlackmanFunction.html", "http://edoc.mpg.de/395068", "http://adsabs.harvard.edu/abs/2004EJASP2004...63B", "http://adsabs.harvard.edu/abs/2005EJASP2005...44B", "http://adsabs.harvard.edu/abs/2010CQGra..27h4020M", "http://adsabs.harvard.edu/abs/2013MNRAS.429..589B", "http://web.mit.edu/xiphmont/Public/windows.pdf", "http://octave.sourceforge.net/signal/function/ultrwin.html", "http://arxiv.org/abs/1003.2939", "http://arxiv.org/abs/1210.2778", "http://doi.org/10.1002%2Fj.1538-7305.1970.tb01766.x", "http://doi.org/10.1007%2F978-1-4615-0327-9", "http://doi.org/10.1007%2F978-3-642-22389-1_24", "http://doi.org/10.1016%2Fj.sigpro.2014.03.033", "http://doi.org/10.1088%2F0264-9381%2F27%2F8%2F084020", "http://doi.org/10.1093%2Fmnras%2Fsts360", "http://doi.org/10.1109%2F19.137352", "http://doi.org/10.1109%2F19.31004", "http://doi.org/10.1109%2F29.17517", "http://doi.org/10.1109%2FPROC.1978.10837", "http://doi.org/10.1109%2FTASSP.1980.1163349", "http://doi.org/10.1109%2FTASSP.1981.1163506", "http://doi.org/10.1109%2FTAU.1967.1161901", "http://doi.org/10.1109%2Fiscas.2001.921012", "http://doi.org/10.1109%2Ftassp.1984.1164275", "http://doi.org/10.1155%2FASP.2005.1910", "http://doi.org/10.1155%2FS1110865704403114", "http://doi.org/10.7795%2F110.20121022aa", "http://www.hpmemoryproject.org/an/pdf/an_243.pdf", "http://www.labbookpages.co.uk/audio/firWindowing.html", "https://smile.amazon.com/Measurement-Power-Spectra-Communications-Engineering/dp/B0006AW1C4", "https://www.dsprelated.com/freebooks/sasp/Overlap_Add_OLA_STFT_Processing.html", "https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US6898235", "https://worldwide.espacenet.com/textdoc?DB=EPODOC&IDX=US7065150", "https://books.google.com/?id=JuJKu_0KDycC&pg=PA53&dq=define+%22window+function%22+nonzero+interval", "https://books.google.com/?id=V_JSAAAAMAAJ", "https://books.google.com/?id=aFDWuZZslUUC&pg=PA97&dq=apodization+function", "https://books.google.com/?id=duBQAAAAMAAJ&q=%22hamming+window%22+date:0-1970&dq=%22hamming+window%22+date:0-1970", "https://books.google.com/books?id=d6PLHcyejEIC&lpg=PA495&ots=tcBHi9Obfy&dq=image%20tapering%20tukey&pg=PA496#v=onepage&q&f=false", "https://www.mathworks.com/help/signal/ref/bohmanwin.html?s_tid=gn_loc_drop", "https://www.mathworks.com/help/signal/ref/flattopwin.html", "https://www.mathworks.com/help/signal/ref/sigwin.chebwin-class.html", "https://www.mathworks.com/help/signal/ug/generalized-cosine-windows.html", "https://link.springer.com/chapter/10.1007%2F978-0-387-48101-2_13#page-1", "https://ccrma.stanford.edu/~jos/filters/Zero_Phase_Filters_Even_Impulse.html", "https://ccrma.stanford.edu/~jos/sasp/Bartlett_Triangular_Window.html", "https://ccrma.stanford.edu/~jos/sasp/Blackman_Harris_Window_Family.html", "https://ccrma.stanford.edu/~jos/sasp/Dolph_Chebyshev_Window.html", "https://ccrma.stanford.edu/~jos/sasp/Gaussian_Window_Transform.html", "https://ccrma.stanford.edu/~jos/sasp/Hamming_Window.html", "https://ccrma.stanford.edu/~jos/sasp/Hann_Hanning_Raised_Cosine.html", "https://ccrma.stanford.edu/~jos/sasp/Hann_Poisson_Window.html", "https://ccrma.stanford.edu/~jos/sasp/Kaiser_DPSS_Windows_Compared.html", "https://ccrma.stanford.edu/~jos/sasp/Kaiser_Window.html", "https://ccrma.stanford.edu/~jos/sasp/Matlab_Gaussian_Window.html", "https://ccrma.stanford.edu/~jos/sasp/Poisson_Window.html", "https://ccrma.stanford.edu/~jos/sasp/Power_of_Cosine_Window_Family.html", "https://ccrma.stanford.edu/~jos/sasp/Quadratic_Interpolation_Spectral_Peaks.html", "https://ccrma.stanford.edu/~jos/sasp/Slepian_DPSS_Window.html", "https://ccrma.stanford.edu/~jos/sasp/Three_Term_Blackman_Harris_Window.html", "https://doi.org/10.1109%2FICASSP.2013.6638833", "https://commons.wikimedia.org/wiki/File:DFT-even_Hann_window_&_spectral_leakage.png"]}, "Data cleansing": {"categories": ["Business intelligence", "Data quality"], "title": "Data cleansing", "method": "Data cleansing", "url": "https://en.wikipedia.org/wiki/Data_cleansing", "summary": "Data cleansing or data cleaning is the process of detecting and correcting (or removing) corrupt or inaccurate records from a record set, table, or database and refers to identifying incomplete, incorrect, inaccurate or irrelevant parts of the data and then replacing, modifying, or deleting the dirty or coarse data. Data cleansing may be performed interactively with data wrangling tools, or as batch processing through scripting.\nAfter cleansing, a data set should be consistent with other similar data sets in the system. The inconsistencies detected or removed may have been originally caused by user entry errors, by corruption in transmission or storage, or by different data dictionary definitions of similar entities in different stores. Data cleaning differs from data validation in that validation almost invariably means data is rejected from the system at entry and is performed at the time of entry, rather than on batches of data.\n\nThe actual process of data cleansing may involve removing typographical errors or validating and correcting values against a known list of entities. The validation may be strict (such as rejecting any address that does not have a valid postal code) or fuzzy (such as correcting records that partially match existing, known records). Some data cleansing solutions will clean data by cross checking with a validated data set. A common data cleansing practice is data enhancement, where data is made more complete by adding related information. For example, appending addresses with any phone numbers related to that address. Data cleansing may also involve activities like, harmonization of data, and standardization of data. For example, harmonization of short codes (st, rd, etc.) to actual words (street, road, etcetera). Standardization of data is a means of changing a reference data set to a new standard, ex, use of standard codes.\n\n", "images": [], "links": ["Accuracy and precision", "Algorithm", "Alteryx", "Apache Spark", "Application programming interface", "Batch job", "Batch processing", "Cluster analysis", "Consistency", "Data (computing)", "Data analysis", "Data archaeology", "Data collection", "Data compression", "Data corruption", "Data curation", "Data degradation", "Data dictionary", "Data editing", "Data farming", "Data format management", "Data fusion", "Data integration", "Data integrity", "Data library", "Data loss", "Data management", "Data migration", "Data mining", "Data pre-processing", "Data preservation", "Data profiling", "Data quality", "Data recovery", "Data reduction", "Data redundancy", "Data retention", "Data science", "Data scraping", "Data scrubbing", "Data security", "Data set", "Data stewardship", "Data storage", "Data validation", "Data warehouse", "Data wrangling", "Database", "Digital object identifier", "Dirty data", "Extract, transform, load", "Fact table", "Foreign key", "Fuzzy logic", "Government", "Grammars", "IBM", "Information privacy", "Infrastructure", "Integrity", "Interactively", "International Standard Book Number", "Investment", "Iterative", "Jiawei Han", "Languages", "Mean", "Morgan Kaufmann", "Null character", "Open-source model", "OpenRefine", "Pandas (software)", "Paxata", "Postal code", "Python (programming language)", "R (programming language)", "Range (statistics)", "Record linkage", "Referential integrity", "Sanitization (classified information)", "Script (computing)", "Single customer view", "Standard deviation", "Statistical", "Storage record", "Table (database)", "Trifacta", "Typographical error", "Units of measurement", "Validity (statistics)"], "references": ["http://www.sciencedirect.com/science/article/pii/S0951832013000100", "http://www.dbis.informatik.hu-berlin.de/fileadmin/research/papers/techreports/2003-hub_ib_164-mueller.pdf", "http://lips.informatik.uni-leipzig.de/files/2000-45.pdf", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.98.8661&rep=rep1&type=pdf", "http://doi.org/10.1016%2Fj.ress.2012.12.021", "http://dplyr.tidyverse.org", "https://hioptimus.com", "https://web.archive.org/web/20100313055016/http://www.computerworld.com/s/article/78230/Data_Scrubbing", "https://web.archive.org/web/20171204114529/https://spotlessdata.com/blog/importance-data-cleansing-user-generated-content"]}, "Smoothing": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2012", "Articles with unsourced statements from September 2008", "Image processing", "Statistical charts and diagrams", "Time series", "Wikipedia articles needing page number citations from June 2012"], "title": "Smoothing", "method": "Smoothing", "url": "https://en.wikipedia.org/wiki/Smoothing", "summary": "In statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal. Smoothing may be used in two important ways that can aid in data analysis (1) by being able to extract more information from the data as long as the assumption of smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust. Many different algorithms are used in smoothing.\nSmoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways:\n\ncurve fitting often involves the use of an explicit function form for the result, whereas the immediate results from smoothing are the \"smoothed\" values with no later use made of a functional form if there is one;\nthe aim of smoothing is to give a general idea of relatively slow changes of value with little attention paid to the close matching of data values, while curve fitting concentrates on achieving as close a match as possible.\nsmoothing methods often have an associated tuning parameter which is used to control the extent of smoothing. Curve fitting will adjust any number of parameters of the function to obtain the 'best' fit.However, the terminology used across applications is mixed. For example, use of an interpolating spline fits a smooth curve exactly through the given data points and is sometimes called \"smoothing\".", "images": [], "links": ["Additive smoothing", "Algorithm", "Butterworth filter", "Computer vision", "Convolution", "Convolution kernel", "Curve fitting", "Data set", "Digital filter", "Edge preserving smoothing", "Exponential smoothing", "Filtering (signal processing)", "Function (mathematics)", "Graph cuts in computer vision", "Hat matrix", "Image processing", "International Standard Book Number", "Kalman filter", "Kernel smoother", "Kolmogorov\u2013Zurbenko filter", "Laplacian smoothing", "Linear transformation", "Local regression", "Low-pass filter", "Moving average", "Moving average (finance)", "Noise", "Numerical smoothing and differentiation", "Pattern", "Ramer\u2013Douglas\u2013Peucker algorithm", "Savitzky\u2013Golay smoothing filter", "Scale space", "Scatterplot smoothing", "Smoothing (disambiguation)", "Smoothing spline", "Smoothness", "Spline (mathematics)", "Statistical signal processing", "Statistical survey", "Statistics", "Stretched grid method", "Subdivision surface", "Vector (mathematics and physics)", "Window function"], "references": ["http://www.intechopen.com/books/smoothing-filtering-and-prediction-estimating-the-past-present-and-future", "http://terpconnect.umd.edu/~toh/spectrum/Smoothing.html", "http://www.stats.gla.ac.uk/steps/glossary/time_series.html"]}, "Breusch\u2013Godfrey test": {"categories": ["All articles with dead external links", "All articles with unsourced statements", "Articles with dead external links from November 2016", "Articles with permanently dead external links", "Articles with unsourced statements from November 2010", "Regression diagnostics", "Regression with time series structure", "Statistical tests", "Webarchive template wayback links"], "title": "Breusch\u2013Godfrey test", "method": "Breusch\u2013Godfrey test", "url": "https://en.wikipedia.org/wiki/Breusch%E2%80%93Godfrey_test", "summary": "In statistics, the Breusch\u2013Godfrey test, named after Trevor S. Breusch and Leslie G. Godfrey, is used to assess the validity of some of the modelling assumptions inherent in applying regression-like models to observed data series. In particular, it tests for the presence of serial correlation that has not been included in a proposed model structure and which, if present, would mean that incorrect conclusions would be drawn from other tests, or that sub-optimal estimates of model parameters are obtained if it is not taken into account. The regression models to which the test can be applied include cases where lagged values of the dependent variables are used as independent variables in the model's representation for later observations. This type of structure is common in econometric models.\nBecause the test is based on the idea of Lagrange multiplier testing, it is sometimes referred to as LM test for serial correlation.A similar assessment can be also carried out with the Durbin\u2013Watson test and the Ljung\u2013Box test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Pagan test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "EViews", "Econometric models", "Econometrica", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "G. S. Maddala", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent and dependent variables", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lagrange multiplier test", "Lehmann\u2013Scheff\u00e9 theorem", "Leslie G. Godfrey", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Python (programming language)", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "SAS (software)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Serial correlation", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Statsmodels", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Trevor S. Breusch", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.macrodados.com.br/English/help/Econometrics_Part3.htm", "http://statsmodels.sourceforge.net/devel/generated/statsmodels.stats.diagnostic.acorr_breush_godfrey.html?highlight=autocorrelation", "http://doi.org/10.1016%2F0378-3758(95)00039-9", "http://doi.org/10.1111%2Fj.1467-8454.1978.tb00635.x", "http://www.jstor.org/stable/1913829", "https://books.google.com/books?id=6qYcBQAAQBAJ&pg=PA159", "https://books.google.com/books?id=86rWI7WzFScC&pg=PA104", "https://books.google.com/books?id=zCym0GtuRE4C&pg=PA155", "https://www.stata.com/manuals/rregresspostestimationtimeseries.pdf", "https://web.archive.org/web/20140228210220/http://statsmodels.sourceforge.net/devel/generated/statsmodels.stats.diagnostic.acorr_breush_godfrey.html?highlight=autocorrelation#", "https://cran.r-project.org/web/packages/lmtest/index.html"]}, "Black\u2013Scholes": {"categories": ["1973 in economics", "All articles with dead external links", "All articles with unsourced statements", "Articles with dead external links from July 2018", "Articles with permanently dead external links", "Articles with unsourced statements from April 2012", "Articles with unsourced statements from November 2010", "Articles with unsourced statements from November 2013", "Equations", "Financial models", "Options (finance)", "Stochastic models", "Stock market"], "title": "Black\u2013Scholes model", "method": "Black\u2013Scholes", "url": "https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model", "summary": "The Black\u2013Scholes or Black\u2013Scholes\u2013Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black\u2013Scholes equation, one can deduce the Black\u2013Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price regardless of the risk of the security and its expected return (instead replacing the security's expected return with the risk-neutral rate). The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. It is widely used, although often with adjustments and corrections, by options market participants.Based on works previously developed by market researchers and practitioners, such as Louis Bachelier, Sheen Kassouf and Ed Thorp among others, Fischer Black and Myron Scholes demonstrated in the late 1960s that a dynamic revision of a portfolio removes the expected return of the security, thus inventing the risk neutral argument. In 1970, after they attempted to apply the formula to the markets and incurred financial losses due to lack of risk management in their trades, they decided to focus in their domain area, the academic environment. After three years of efforts, the formula named in honor of them for making it public, was finally published in 1973 in an article entitled \"The Pricing of Options and Corporate Liabilities\", in the Journal of Political Economy. Robert C. Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model, and coined the term \"Black\u2013Scholes options pricing model\". Merton and Scholes received the 1997 Nobel Memorial Prize in Economic Sciences for their work, the committee citing their discovery of the risk neutral dynamic revision as a breakthrough that separates the option from the risk of the underlying security. Although ineligible for the prize because of his death in 1995, Black was mentioned as a contributor by the Swedish Academy.The key idea behind the model is to hedge the option by buying and selling the underlying asset in just the right way and, as a consequence, to eliminate risk. This type of hedging is called \"continuously revised delta hedging\" and is the basis of more complicated hedging strategies such as those engaged in by investment banks and hedge funds.\nThe model's assumptions have been relaxed and generalized in many directions, leading to a plethora of models that are currently used in derivative pricing and risk management. It is the insights of the model, as exemplified in the Black\u2013Scholes formula, that are frequently used by market participants, as distinguished from the actual prices. These insights include no-arbitrage bounds and risk-neutral pricing (thanks to continuous revision). Further, the Black\u2013Scholes equation, a partial differential equation that governs the price of the option, enables pricing using numerical methods when an explicit formula is not possible.\nThe Black\u2013Scholes formula has only one parameter that cannot be directly observed in the market: the average future volatility of the underlying asset, though it can be found from the price of other options. Since the option value (whether put or call) is increasing in this parameter, it can be inverted to produce a \"volatility surface\" that is then used to calibrate other models, e.g. for OTC derivatives.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9f/Chicklet-currency.jpg", "https://upload.wikimedia.org/wikipedia/commons/e/e1/Crowd_outside_nyse.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f2/European_Call_Surface.png", "https://upload.wikimedia.org/wikipedia/commons/f/f2/Stockpricesimulation.jpg"], "links": ["Abstract Wiener space", "Activist shareholder", "Actuarial mathematics", "Algorithmic trading", "Alpha (investment)", "American option", "Amortising swap", "Andrew Kalotay", "Arbitrage", "Arbitrage pricing theory", "Asian option", "Asset-or-nothing call", "Asset swap", "Assets under management", "At-the-money", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Backspread", "Barrier option", "Basis swap", "Basket option", "Bear spread", "Berkshire Hathaway", "Bernoulli process", "Bessel process", "Beta (finance)", "Biased random walk on a graph", "Binary option", "Binomial options model", "Binomial options pricing model", "Birth\u2013death process", "Black's approximation", "Black Shoals", "Black model", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes equation", "Black\u2013Scholes formula", "Black\u2013Scholes model", "Bond (finance)", "Bond market", "Bond option", "Boolean network", "Boston University", "Box spread (options)", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian model of financial markets", "Bulk queue", "Bull spread", "Burkholder\u2013Davis\u2013Gundy inequalities", "Butterfly (options)", "B\u00fchlmann model", "Calendar spread", "Call option", "Cameron\u2013Martin formula", "Capital asset pricing model", "Capital structure", "Cash-or-nothing call", "Cauchy process", "Central limit theorem", "Chen model", "Chicago Board Options Exchange", "Chinese restaurant process", "Chooser option", "CiteSeerX", "Classical Wiener space", "Cliquet", "Closed-form expression", "Collar (finance)", "Collateralized debt obligation", "Commodity market", "Commodity trading advisor", "Commodore option", "Compound Poisson process", "Compound option", "Conditional probability", "Conditional variance swap", "Consistency", "Constant elasticity of variance model", "Constant maturity swap", "Constant proportion portfolio insurance", "Consumer debt", "Contact process (mathematics)", "Contango", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous compounding", "Continuous stochastic process", "Contract for difference", "Convergence of random variables", "Convergence trade", "Convertible arbitrage", "Coordinate transformation", "Corporate bond", "Correlation swap", "Covered call", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Credit-linked note", "Credit default option", "Credit default swap", "Credit derivative", "Credit spread (options)", "Cumulative distribution function", "Currency future", "Currency swap", "C\u00e0dl\u00e0g", "Datar\u2013Mathews method for real option valuation", "Day trading", "Debit spread", "Delta hedging", "Delta neutral", "Derivative", "Derivative (finance)", "Derivatives market", "Diagonal spread", "Differentiation (mathematics)", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discount factor", "Discrete-time stochastic process", "Distressed securities", "Dividend", "Dividend future", "Dividend swap", "Dividend yield", "Dol\u00e9ans-Dade exponential", "Donald Angus MacKenzie", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Drift rate", "Dynkin's formula", "Econometrics", "Edward O. Thorp", "Edward Thorp", "Emanuel Derman", "Empirical process", "Employee stock option", "Energy derivative", "Equation solving", "Equity-linked note", "Equity derivative", "Equity swap", "Ergodic theorem", "Ergodic theory", "Ergodicity", "European option", "Event-driven investing", "Exchangeable random variables", "Exercise (options)", "Exotic derivative", "Exotic option", "Expected value", "Expiration (options)", "Extreme value theory", "Family office", "Feller-continuous process", "Feller process", "Fence (finance)", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Financial economics", "Financial endowment", "Financial market", "Financial mathematics", "Finite difference methods for option pricing", "Fischer Black", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fixed-income relative-value investing", "Fixed income", "Fixed income arbitrage", "Fleming\u2013Viot process", "Fluid queue", "Force of interest", "Foreign-exchange option", "Foreign exchange derivative", "Foreign exchange market", "Foreign exchange swap", "Forward contract", "Forward market", "Forward price", "Forward rate", "Forward rate agreement", "Forward start option", "Fractional Brownian motion", "Freight derivative", "Frictionless market", "Fund derivative", "Fund governance", "Fund of funds", "Fundamental analysis", "Futures contract", "Fuzzy pay-off method for real option valuation", "G-network", "GARCH", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "George Szpiro", "Gibbs measure", "Girsanov theorem", "Global macro", "Government debt", "Great Recession", "Greeks (finance)", "Heat equation", "Heath\u2013Jarrow\u2013Morton framework", "Heaviside function", "Hedge (finance)", "Hedge Fund Standards Board", "Hedge fund", "Heston model", "Hidden Markov model", "High-frequency trading", "High-net-worth individual", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "INSEAD", "Ian Stewart (mathematician)", "Implied volatility", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Inflation derivative", "Inflation swap", "Institutional investor", "Insurance", "Interacting particle system", "Interest rate derivative", "Interest rate future", "Interest rate option", "Interest rate swap", "Intermarket Spread", "International Standard Book Number", "Investment bank", "Investment banking", "Iron butterfly (options strategy)", "Iron condor", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "It\u014d's lemma", "JSTOR", "John C. Hull", "Journal of Political Economy", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Lattice model (finance)", "Law of large numbers", "Law of the iterated logarithm", "Liquidity risk", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Log-normal distribution", "Long-Term Capital Management", "Long/short equity", "Lookback option", "Loop-erased random walk", "Louis Bachelier", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Managed futures account", "Margin (finance)", "Margrabe's formula", "Market neutral", "Market price of risk", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale pricing", "Martingale representation theorem", "Mathematical finance", "Mathematical model", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Measure (mathematics)", "Merchant bank", "Midas formula", "Mixing (mathematics)", "Money market", "Moneyness", "Monotonic function", "Monte Carlo methods for option pricing", "Monte Carlo option model", "Moran process", "Mortgage-backed security", "Mountain range (options)", "Moving-average model", "Multi-manager investment", "Municipal debt", "Myron Scholes", "Nassim Nicholas Taleb", "Nassim Taleb", "Neoclassical economics", "No-arbitrage bounds", "Nobel Memorial Prize in Economic Sciences", "Non-homogeneous Poisson process", "Normal backwardation", "Numerical method", "Numerical methods", "Num\u00e9raire", "Open interest", "Optimal stopping", "Option (finance)", "Option style", "Optional stopping theorem", "Options pricing", "Options spread", "Options strategy", "Ornstein\u2013Uhlenbeck process", "Out-of-the-money", "Overnight indexed swap", "Partial derivatives", "Partial differential equation", "Paul Wilmott", "Pension fund", "Percolation theory", "Peter L. Bernstein", "Piecewise deterministic Markov process", "Pin risk (options)", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Portfolio (finance)", "Potts model", "Power reverse dual-currency note", "Predictable process", "Prentice Hall", "Prime brokerage", "Probability density function", "Probability measure", "Probability theory", "Program trading", "Progressively measurable process", "Prokhorov's theorem", "Property derivative", "Proprietary trading", "Protective put", "Pull to par", "Put option", "Put\u2013call parity", "Quadratic equation", "Quadratic variation", "Queueing model", "Queueing theory", "Rainbow option", "Random dynamical system", "Random field", "Random graph", "Random walk", "Ratio spread", "Rational pricing", "Real options analysis", "Real options valuation", "Reflection principle (Wiener process)", "Regenerative process", "Relative value (economics)", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Riccardo Rebonato", "Risk-free interest rate", "Risk-neutral", "Risk-neutral measure", "Risk arbitrage", "Risk free rate", "Risk management", "Risk neutrality", "Risk process", "Risk reversal", "Robert C. Merton", "Root finding algorithm", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Securitization", "Security characteristic line", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sheen Kassouf", "Short (finance)", "Short selling", "Sigma-martingale", "Simulation", "Single-stock futures", "Skewness", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Slippage (finance)", "Snell envelope", "Sovereign wealth fund", "Sparre\u2013Anderson model", "Special situation", "Spot price", "Stable process", "Standard normal", "Standard normal distribution", "Stationary process", "Statistical arbitrage", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stochastic volatility", "Stock market", "Stock market crash", "Stock market index future", "Stopping time", "Straddle", "Strangle (options)", "Stratonovich integral", "Stress testing", "Strike price", "Structured finance", "Submartingale", "Supermartingale", "Superprocess", "Swap (finance)", "Swaption", "System on a chip", "Tail risk", "Tanaka equation", "Tax policy", "Taxation of private equity and hedge funds", "Technical analysis", "Telegraph process", "Terence Tao", "The Observer", "Time reversibility", "Time series", "Time series analysis", "Total return swap", "Transaction cost", "Trend following", "Trinomial tree", "Underlying", "Uniform integrability", "Usual hypotheses", "Valuation of options", "Vanilla option", "Vanna\u2013Volga pricing", "Variance gamma process", "Variance swap", "Vasicek model", "Vertical spread", "Volatility (finance)", "Volatility arbitrage", "Volatility risk", "Volatility skew", "Volatility smile", "Volatility surface", "Volatility swap", "Vulture fund", "Warrant (finance)", "Warren Buffett", "Weather derivative", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "Year-on-Year Inflation-Indexed Swap", "Yield curve", "Zero-Coupon Inflation-Indexed Swap", "Zero coupon swap", "Zvi Bodie"], "references": ["http://www.berkshirehathaway.com/letters/2008ltr.pdf", "http://www.ederman.com/new/docs/qf-Illusions-dynamic.pdf", "http://www.ederman.com/new/docs/risk-non_continuous_hedge.pdf", "http://edwardothorp.com/sitebuildercontent/sitebuilderfiles/thorpwilmottqfinrev2003.pdf", "http://www.espenhaug.com/black_scholes.html", "http://www.global-derivatives.com/index.php?option=com_content&task=view&id=14", "http://kalotay.com/sites/default/files/private/BlackScholes.pdf", "http://www.lifelong-learners.com/opt/com/SYL/s6node6.php", "http://www.ltnielsen.com/papers/understanding-nd1-and-nd2-risk-adjusted-probabilities-in-the-black-scholes-model", "http://www.ltnielsen.com/wp-content/uploads/Understanding.pdf", "http://www.merriam-webster.com/dictionary/scholes", "http://sss.sagepub.com/cgi/content/abstract/33/6/831", "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075", "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2115141", "http://www.wilmott.com/blogs/paul/index.cfm/2008/4/29/Science-in-Finance-IX-In-defence-of-Black-Scholes-and-Merton", "http://terrytao.wordpress.com/2008/07/01/the-black-scholes-equation/", "http://librarycatalogue.insead.edu/bib/972", "http://www.bus.lsu.edu/academics/finance/faculty/dchance/Instructional/TN99-02.pdf", "http://www.bus.lsu.edu/academics/finance/faculty/dchance/Instructional/TN98-01.pdf", "http://www.bus.lsu.edu/academics/finance/faculty/dchance/Instructional/TN98-02.pdf", "http://homepages.nyu.edu/~sl1544/KnownClosedForms.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.461.4099", "http://www.sjsu.edu/faculty/watkins/blacksch.htm", "http://www.physics.uci.edu/~silverma/bseqn/bs/bs.html", "http://www.affi.asso.fr/TPL_CODE/TPL_REVUE/PAR_TPL_IDENTIFIANT/53/193-publications.htm", "http://www.affi.asso.fr/TPL_CODE/TPL_REVUEARTICLEDOWNLOAD/PAR_TPL_IDENTIFIANT/187/193-publications.htm", "http://sourceforge.net/projects/chipricingmodel/", "http://finance.bi.no/~bernt/gcc_prog/recipes/recipes/node13.html", "http://finance.bi.no/~bernt/gcc_prog/recipes/recipes/node9.html#SECTION00920000000000000000", "http://finance.bi.no/~bernt/gcc_prog/recipes/recipes/node9.html", "http://brage.bibsys.no/nhh/bitstream/URN:NBN:no-bibsys_brage_22301/1/bjerksund%20petter%200902.pdf", "http://doi.org/10.1086%2F260062", "http://doi.org/10.1086%2F374404", "http://doi.org/10.1177%2F0306312703336002", "http://doi.org/10.2307%2F2328254", "http://doi.org/10.2307%2F3003143", "http://www.jstor.org/stable/3003143", "http://www.mayin.org/ajayshah/PDFDOCS/Shah1997_bms.pdf", "http://nobelprize.org/nobel_prizes/economics/laureates/1997/press.html", "http://planetmath.org/encyclopedia/AnalyticSolutionOfBlackScholesPDE.html", "http://www.bbc.co.uk/science/horizon/1999/midas.shtml", "https://github.com/OpenGamma/OG-Platform/blob/master/projects/OG-Analytics/src/main/java/com/opengamma/analytics/financial/model/volatility/surface/BlackScholesMertonImpliedVolatilitySurfaceModel.java", "https://code.google.com/p/black-scholes/", "https://docs.google.com/viewer?a=v&q=cache:ai5xEtbLxCIJ:centerforpbbefr.rutgers.edu/TaipeiPBFR%26D/01-16-09%2520papers/5-4%2520Greek%2520letters.doc+Derivations+and+Applications+of+Greek+Letters+%E2%80%93+Review+and+Integration&hl=en&pid=bl&srcid=ADGEEShU4q28apOYjO-BmqXOJTOHj2BG0BgnxtLn-ccCfh27FYlCDla0nspYCidFFFWiPfYjM2PTT0_109Lth79rFwKsenMFpawjU9BtpBSQO81hUj0OjG3owSKTyv6-VTziJ6tq5CNb&sig=AHIEtbREe6Jg8SlzylhuYC9xEoG0eG3dGg", "https://leventozturk.com/engineering/Black_Scholes/", "https://www.tastytrade.com/tt/shows/soom", "https://www.theguardian.com/science/2012/feb/12/black-scholes-equation-credit-crunch", "https://www.vcalc.com/wiki/vCalc/Black-Scholes", "https://www.wilmott.com/archives/830", "https://bret-blackford.github.io/black-scholes/", "https://archive.is/20121215011302/http://www.journals.uchicago.edu/AJS/journal/issues/v109n1/060259/brief/060259.abstract.html", "https://web.archive.org/web/*/http://www.bu.edu/econ/workingpapers/papers/RuffinoTreussardDT.pdf", "https://web.archive.org/web/20110710172106/http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/optiontheory.doc", "https://www.jstor.org/stable/1831029", "https://www.jstor.org/stable/3003143", "https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1997/press.html", "https://www.pbs.org/wgbh/nova/stockmarket/", "https://ideas.repec.org/a/bla/jfinan/v42y1987i2p301-20.html", "https://www.bbc.co.uk/news/magazine-17866646"]}, "Reliability (statistics)": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2010", "Commons category link from Wikidata", "Comparison of assessments", "Educational psychology research methods", "Engineering statistics", "Market research", "Psychometrics", "Reliability analysis", "Reliability engineering", "Survival analysis", "Use dmy dates from September 2010", "Webarchive template wayback links", "Wikipedia articles with GND identifiers"], "title": "Reliability (statistics)", "method": "Reliability (statistics)", "url": "https://en.wikipedia.org/wiki/Reliability_(statistics)", "summary": "Reliability in statistics and psychometrics is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions. \"It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are accurate, reproducible, and consistent from one testing occasion to another. That is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained. Various kinds of reliability coefficients, with values ranging between 0.00 (much error) and 1.00 (no error), are usually used to indicate the amount of error in the scores.\" For example, measurements of people's height and weight are often extremely reliable.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Accuracy and precision", "Carryover effect", "Classical test theory", "Coefficient of variation", "Consistency (statistics)", "Cronbach's alpha", "Digital object identifier", "Form (document)", "Homogeneity (statistics)", "Integrated Authority File", "Inter-rater reliability", "Internal consistency", "International Standard Book Number", "Intra-rater reliability", "Item-total correlation", "Item response theory", "Kuder\u2013Richardson Formula 20", "Levels of measurement", "Marketing Accountability Standards Board", "Pearson product-moment correlation coefficient", "Psychometrics", "Random error", "Reliability (disambiguation)", "Reliability engineering", "Reliability theory", "Reproducibility", "Spearman\u2013Brown prediction formula", "Statistics", "Systematic error", "Test-retest reliability", "Validity (statistics)", "Wayback Machine", "Weighing scales"], "references": ["http://www.socialresearchmethods.net/kb/reliable.php", "http://www.socialresearchmethods.net/kb/reltypes.php", "http://www.uncertainty-in-engineering.net", "http://www.visualstatistics.net/Statistics/Principal%20Components%20of%20Reliability/PCofReliability.asp", "http://www.visualstatistics.net/Statistics/Reliability%20Negative/Negative%20Reliability.asp", "http://doi.org/10.1007%2Fs00038-012-0416-3", "http://www.ncme.org/ncme/NCME/Resource_Center/Glossary/NCME/Resource_Center/Glossary1.aspx?hkey=4bb87415-44dc-4088-9ed9-e8515326a061#anchorR", "http://www.themasb.org/common-language-project/", "http://www.loopa.co.uk/internal-external-reliability-and-validity-in-psychology-aqa-a-explained-easily/", "https://d-nb.info/gnd/4213628-3", "https://web.archive.org/web/20130212100753/http://www.themasb.org/common-language-project/", "https://www.wikidata.org/wiki/Q18748"]}, "Levey\u2013Jennings chart": {"categories": ["All copied and pasted articles and sections", "Copied and pasted articles and sections with url provided from October 2014", "Laboratories", "Statistical process control"], "title": "Laboratory quality control", "method": "Levey\u2013Jennings chart", "url": "https://en.wikipedia.org/wiki/Laboratory_quality_control", "summary": "Laboratory quality control is designed to detect, reduce, and correct deficiencies in a laboratory's internal analytical process prior to the release of patient results, in order to improve the quality of the results reported by the laboratory. Quality control is a measure of precision, or how well the measurement system reproduces the same result over time and under varying operating conditions. Laboratory quality control material is usually run at the beginning of each shift, after an instrument is serviced, when reagent lots are changed, after calibration, and whenever patient results seem inappropriate. Quality control material should approximate the same matrix as patient specimens, taking into account properties such as viscosity, turbidity, composition, and color. It should be simple to use, with minimal vial to vial variability, because variability could be misinterpreted as systematic error in the method or instrument. It should be stable for long periods of time, and available in large enough quantities for a single batch to last at least one year. Liquid controls are more convenient than lyophilized controls because they do not have to be reconstituted minimizing pipetting error.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f6/Levy-Jennings_SampleChart.png", "https://upload.wikimedia.org/wikipedia/en/4/43/Copyright-problem_paste_2.svg"], "links": ["Levey-Jennings chart", "Process-behavior chart", "Quality assessment", "Quality assurance", "Quality control", "Shewhart chart", "Shewhart individuals control chart", "Standard deviation", "Westgard rules"], "references": ["http://www.westgard.com", "http://www.jasshpharma.net/about-us.html", "http://tools.wmflabs.org/dupdet/compare.php?url1=https://en.wikipedia.org/wiki/Laboratory_quality_control&url2=http://www.jasshpharma.net/about-us.html&minwords=3&minchars=13&removequotations=&removenumbers=", "https://tools.wmflabs.org/copyvios?lang=en&project=wikipedia&title=Laboratory_quality_control&url=http://www.jasshpharma.net/about-us.html"]}, "Dunn index": {"categories": ["Clustering criteria"], "title": "Dunn index", "method": "Dunn index", "url": "https://en.wikipedia.org/wiki/Dunn_index", "summary": "The Dunn index (DI) (introduced by J. C. Dunn in 1974) is a metric for evaluating clustering algorithms. This is part of a group of validity indices including the Davies\u2013Bouldin index or Silhouette index, in that it is an internal evaluation scheme, where the result is based on the clustered data itself. As do all other such indices, the aim is to identify sets of clusters that are compact, with a small variance between members of the cluster, and well separated, where the means of different clusters are sufficiently far apart, as compared to the within cluster variance. For a given assignment of clusters, a higher Dunn index indicates better clustering. One of the drawbacks of using this is the computational cost as the number of clusters and dimensionality of the data increase.", "images": [], "links": ["Apache Mahout", "Clustering algorithm", "Davies\u2013Bouldin index", "Digital object identifier", "Euclidean distance", "International Standard Serial Number", "MATLAB", "Manhattan distance", "R (programming language)", "Silhouette (clustering)"], "references": ["http://machaon.karanagai.com/validation_algorithms.html", "http://www.mathworks.com/matlabcentral/fileexchange/27859-dunns-index", "http://www.sciencedirect.com/science/article/pii/S0031320303002838", "http://mahout.apache.org/", "http://doi.org/10.1016%2Fj.patcog.2003.06.005", "http://doi.org/10.1080%2F01969727308546046", "http://doi.org/10.1080%2F01969727408546059", "http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=499469", "http://www.worldcat.org/issn/0022-0280", "https://dx.doi.org/10.1080/01969727408546059", "https://cran.r-project.org/web/packages/clv/clv.pdf"]}, "Numerical smoothing and differentiation": {"categories": ["Commons category link is on Wikidata", "Filter theory", "Signal estimation"], "title": "Savitzky\u2013Golay filter", "method": "Numerical smoothing and differentiation", "url": "https://en.wikipedia.org/wiki/Savitzky%E2%80%93Golay_filter", "summary": "A Savitzky\u2013Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the signal-to-noise ratio without greatly distorting the signal. This is achieved, in a process known as convolution, by fitting successive sub-sets of adjacent data points with a low-degree polynomial by the method of linear least squares. When the data points are equally spaced, an analytical solution to the least-squares equations can be found, in the form of a single set of \"convolution coefficients\" that can be applied to all data sub-sets, to give estimates of the smoothed signal, (or derivatives of the smoothed signal) at the central point of each sub-set. The method, based on established mathematical procedures, was popularized by Abraham Savitzky and Marcel J. E. Golay who published tables of convolution coefficients for various polynomials and sub-set sizes in 1964. Some errors in the tables have been corrected. The method has been extended for the treatment of 2- and 3-dimensional data.\nSavitzky and Golay's paper is one of the most widely cited papers in the journal Analytical Chemistry and is classed by that journal as one of its \"10 seminal papers\" saying \"it can be argued that the dawn of the computer-controlled analytical instrument can be traced to this article\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/06/4th_derivative.png", "https://upload.wikimedia.org/wikipedia/commons/0/01/Baseline_correction.png", "https://upload.wikimedia.org/wikipedia/commons/e/e5/FT_9_point_cubic_convolution_function.png", "https://upload.wikimedia.org/wikipedia/commons/8/89/Lissage_sg3_anim.gif", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lorentzian_and_derivative.gif", "https://upload.wikimedia.org/wikipedia/commons/d/db/Malonic_titration.png", "https://upload.wikimedia.org/wikipedia/commons/0/08/Resolution_enhancement.png", "https://upload.wikimedia.org/wikipedia/commons/4/44/SG_noise_reduction.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Abraham Savitzky", "Absorption band", "Analytical Chemistry (journal)", "Analytical chemistry", "Analytical solution", "Bibcode", "Cauchy distribution", "Chemical analysis", "Codomain", "Convolution", "Correlation and dependence", "Cramer's rule", "Degree (angle)", "Diagonal matrix", "Digital data", "Digital filter", "Digital object identifier", "Discrete Fourier transform", "Equivalence point", "Error propagation", "Faulhaber's formula", "Fourier transform", "Full width at half maximum", "Function (mathematics)", "GNU MPFR", "GNU Multiple Precision Arithmetic Library", "Gram polynomial", "Identity matrix", "Inflection point", "International Standard Book Number", "Interpolation", "Kernel smoother", "Linear least squares (mathematics)", "Local regression", "Low-pass filter", "Malonic acid", "Marcel J. E. Golay", "Matrix (mathematics)", "Maxima and minima", "Moving average", "Normal equations", "Numerical differentiation", "OCLC", "Objective function", "Open-source software", "Orthogonal polynomials", "Pascal (programming language)", "Polynomial", "PubMed Identifier", "Rational number", "Real-valued function", "Recursion", "Signal-to-noise ratio", "Smoothing", "Smoothing spline", "Spreadsheet", "Standard deviation", "Statistics", "Stencil (numerical analysis)", "Titration curve", "Variance", "Variance-covariance matrix", "Vector space"], "references": ["http://research.microsoft.com/en-us/um/people/jckrumm/SavGol/SavGol.htm", "http://www.users.waitrose.com/~robinjames/SG/SGhome.html", "http://adsabs.harvard.edu/abs/1955ApSpe...9...78G", "http://adsabs.harvard.edu/abs/1981ApSpe..35...88Z", "http://adsabs.harvard.edu/abs/1983ApSpe..37..515G", "http://adsabs.harvard.edu/abs/1985ApSRv..21..311D", "http://adsabs.harvard.edu/abs/2011Ana...136.2802L", "http://nsm1.nsm.iup.edu/jford/courses/CHEM421/Resources/CommentsOnTheSavitzkyGolayConvolutionMethodForLeastSquaresFitSmoothingAndDifferentiationOfDigitalData.pdf", "http://www.cecs.wright.edu/~phe/Research/DigitalSignalProcessing-05.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/21594244", "http://www.ncbi.nlm.nih.gov/pubmed/22324618", "http://www.ncbi.nlm.nih.gov/pubmed/23647149", "http://www.statistics4u.info/fundstat_eng/cc_filter_savgolay.html", "http://doi.org/10.1016%2Fj.dsp.2004.09.008", "http://doi.org/10.1016%2Fs0003-2670(00)00861-8", "http://doi.org/10.1021%2Fac00186a026", "http://doi.org/10.1021%2Fac00190a744", "http://doi.org/10.1021%2Fac00205a007", "http://doi.org/10.1021%2Fac00234a011", "http://doi.org/10.1021%2Fac002801q", "http://doi.org/10.1021%2Fac401048d", "http://doi.org/10.1021%2Fac50031a048", "http://doi.org/10.1021%2Fac50064a018", "http://doi.org/10.1021%2Fac60214a047", "http://doi.org/10.1021%2Fac60319a045", "http://doi.org/10.1039%2FC2AY05492B", "http://doi.org/10.1039%2Fc0an00751j", "http://doi.org/10.1080%2F05704928508060434", "http://doi.org/10.1366%2F000370255774634089", "http://doi.org/10.1366%2F0003702814731798", "http://doi.org/10.1366%2F0003702834634712", "http://doi.org/10.5281%2Fzenodo.1257898", "http://doi.org/10.5281%2Fzenodo.835283", "http://www.worldcat.org/oclc/1187948", "http://www.doc.ic.ac.uk/research/technicalreports/2006/DTR06-8.pdf", "https://books.google.com/books/about/Data_fitting_in_the_chemical_sciences.html?id=fRcvAQAAIAAJ", "https://books.google.com/books?id=UjnB0FIWv_AC", "https://sites.google.com/site/chandraacads/", "https://sites.google.com/site/chandraacads/resources/sg-filter/db", "https://books.google.comu/books?id=UjnB0FIWv_AC&lpg=PA147", "https://www.researchgate.net/publication/282647148", "https://archive.org/details/calculusofobserv031400mbp", "https://doi.org/10.5281/zenodo.1257898", "https://doi.org/10.5281/zenodo.835283", "https://books.google.co.uk/books?id=5dvvAAAAMAAJ&q="]}, "Mean signed difference": {"categories": ["All articles lacking sources", "All articles needing expert attention", "All pages needing cleanup", "All stub articles", "Articles lacking sources from April 2010", "Articles needing cleanup from April 2010", "Articles needing expert attention from May 2010", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Cleanup tagged articles without a reason field from April 2010", "Means", "Similarity and distance measures", "Statistics articles needing expert attention", "Statistics stubs", "Summary statistics", "Wikipedia pages needing cleanup from April 2010"], "title": "Mean signed deviation", "method": "Mean signed difference", "url": "https://en.wikipedia.org/wiki/Mean_signed_deviation", "summary": "In statistics, the mean signed difference, deviation, or error (MSD) is a sample statistic that summarises how well a set of estimates \n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n i\n \n \n \n \n {\\displaystyle {\\hat {\\theta }}_{i}}\n match the quantities \n \n \n \n \n \u03b8\n \n i\n \n \n \n \n {\\displaystyle \\theta _{i}}\n that they are supposed to estimate. It is one of a number of statistics that can be used to assess an estimation procedure, and it would often be used in conjunction with a sample version of the mean square error.\nFor example, suppose a linear regression model has been estimated over a sample of data, and is then used to extrapolate predictions of the dependent variable out of sample after the out-of-sample data points have become available. Then \n \n \n \n \n \u03b8\n \n i\n \n \n \n \n {\\displaystyle \\theta _{i}}\n would be the i-th out-of-sample value of the dependent variable, and \n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n i\n \n \n \n \n {\\displaystyle {\\hat {\\theta }}_{i}}\n would be its predicted value. The mean signed deviation is the average value of \n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n i\n \n \n \u2212\n \n \u03b8\n \n i\n \n \n .\n \n \n {\\displaystyle {\\hat {\\theta }}_{i}-\\theta _{i}.}", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Dependent variable", "Deviation (statistics)", "Forecasting", "Lead time", "Linear regression", "Mean absolute difference", "Mean absolute error", "Mean square error", "Statistic", "Statistics", "Time series analysis"], "references": []}, "Cox's theorem": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2017", "CS1 maint: Archived copy as title", "Probability interpretations", "Probability theorems", "Statistical theorems"], "title": "Cox's theorem", "method": "Cox's theorem", "url": "https://en.wikipedia.org/wiki/Cox%27s_theorem", "summary": "Cox's theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. This derivation justifies the so-called \"logical\" interpretation of probability, as the laws of probability derived by Cox's theorem are applicable to any proposition. Logical (a.k.a. objective Bayesian) probability is a type of Bayesian probability. Other forms of Bayesianism, such as the subjective interpretation, are given other justifications.", "images": [], "links": ["Aristotelian logic", "Associativity", "Bayesian probability", "Bayesian probability theory", "Common sense", "Conjunctive normal form", "Digital object identifier", "Disjunction", "Edwin Thompson Jaynes", "Formal system", "Functional equation", "Involution (mathematics)", "J\u00e1nos Acz\u00e9l (mathematician)", "Logic", "Logical conjunction", "Measure (mathematics)", "Monotonic function", "Negation", "Niels Henrik Abel", "Postulates", "Probability axioms", "Probability logic", "Probability theory", "Proposition", "Richard Threlkeld Cox", "Terrence L. Fine", "Theory of justification", "Uncertainty"], "references": ["http:ftp://ftp.nada.kth.se/pub/documents/Theory/Stefan-Arnborg/06arnborg.ps", "http:ftp://ftp.nada.kth.se/pub/documents/Theory/Stefan-Arnborg/06arnborg.pdf", "http:ftp://ftp.nada.kth.se/pub/documents/Theory/Stefan-Arnborg/fobshle.ps", "http:ftp://ftp.nada.kth.se/pub/documents/Theory/Stefan-Arnborg/fobshle.pdf", "http:ftp://ftp.nada.kth.se/pub/documents/Theory/Stefan-Arnborg/fobc1.ps", "http:ftp://ftp.nada.kth.se/pub/documents/Theory/Stefan-Arnborg/fobc1.pdf", "http://www.sciencedirect.com/science/journal/01968858", "http://omega.albany.edu:8008/JaynesBook.html", "http://bayes.wustl.edu/etj/prob/book.pdf", "http://doi.org/10.1016%2FS0888-613X(03)00051-3", "http://doi.org/10.1119%2F1.1990764", "http://www.jair.org/media/536/live-536-2054-jair.ps.Z", "http://www.jair.org/media/644/live-644-1840-jair.ps.Z", "http://projecteuclid.org/download/pdf_1/euclid.ba/1340369856", "https://web.archive.org/web/20160119131820/http://omega.albany.edu:8008/JaynesBook.html", "https://arxiv.org/abs/math.PR/0203249"]}, "Feller-continuous process": {"categories": ["Stochastic processes"], "title": "Feller-continuous process", "method": "Feller-continuous process", "url": "https://en.wikipedia.org/wiki/Feller-continuous_process", "summary": "In mathematics, a Feller-continuous process is a continuous-time stochastic process for which the expected value of suitable statistics of the process at a given time in the future depend continuously on the initial condition of the process. The concept is named after Croatian-American mathematician William Feller.", "images": [], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost surely", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bernt \u00d8ksendal", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Bounded function", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Croatia", "C\u00e0dl\u00e0g", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Expected value", "Extreme value theory", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "It\u014d diffusion", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Lipschitz continuity", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Mathematician", "Mathematics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Measurable function", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability space", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "William Feller"], "references": []}, "Bernstein\u2013von Mises theorem": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2018", "Bayesian inference", "Statistical theorems"], "title": "Bernstein\u2013von Mises theorem", "method": "Bernstein\u2013von Mises theorem", "url": "https://en.wikipedia.org/wiki/Bernstein%E2%80%93von_Mises_theorem", "summary": "In Bayesian inference, the Bernstein\u2013von Mises theorem provides the basis for the important result that the posterior distribution for unknown quantities in any problem is effectively asymptotically independent of the prior distribution (assuming it obeys Cromwell's rule) as the data sample grows large.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg"], "links": ["A. W. F. Edwards", "Admissible decision rule", "Almost surely", "Approximate Bayesian computation", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Conjugate prior", "Credible interval", "Cromwell's rule", "David A. Freedman (statistician)", "Empirical Bayes method", "Hyperparameter", "Hyperprior", "International Standard Book Number", "Joseph L. Doob", "Likelihood function", "Lorraine Schwartz (statistician)", "Lucien Le Cam", "Markov chain Monte Carlo", "Maximum a posteriori estimation", "Mode (statistics)", "Persi Diaconis", "Posterior distribution", "Posterior predictive distribution", "Posterior probability", "Principle of indifference", "Principle of maximum entropy", "Prior distribution", "Prior probability", "Probability interpretations", "Probability space", "Radical probabilism", "Richard von Mises", "S. N. Bernstein", "Schwarz criterion", "Statistics"], "references": []}, "Collider (epidemiology)": {"categories": ["Causal inference", "Epidemiology", "Graphical models", "Independence (probability theory)"], "title": "Collider (epidemiology)", "method": "Collider (epidemiology)", "url": "https://en.wikipedia.org/wiki/Collider_(epidemiology)", "summary": "In statistics and causal graphs, a variable is a collider when it is causally influenced by two or more variables. The causal variables influencing the collider are themselves not necessarily associated. The name \"collider\" reflects the fact that in graphical models, the arrow heads from variables that lead into the collider appear to \"collide\" on the node that is the collider. They are sometimes also referred to as inverted forks.\n\nThe result of having a collider in the path is that the collider blocks the association between the variables that influence it. Thus, the collider does not generate an unconditional association between the variables that determine it.\nConditioning on the collider via regression analysis, stratification, experimental design, or sample selection based on values of the collider \ncreate a non-causal association between X and Y (Berkson's paradox). In the terminology of causal graphs, conditioning on the colllider open the path between X and Y. This will introduce bias when estimating the causal association between X and Y, potentially introducing associations where there are none. Colliders can therefore undermine attempts to test causal theories.\nColliders are sometimes confused with confounder variables. Unlike colliders, confounder variables should be controlled for when estimating causal associations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c1/Collider%28statistics%29.png", "https://upload.wikimedia.org/wikipedia/commons/archive/c/c1/20151219213906%21Collider%28statistics%29.png"], "links": ["Berkson's paradox", "Causal graphs", "Causality", "Confounder", "Confounding", "Digital object identifier", "Directed acyclic graph", "Graphical model", "International Standard Book Number", "International Standard Serial Number", "Node (graph theory)", "OCLC", "Path analysis (statistics)", "Regression analysis", "Selection bias", "Simultaneous equations models", "Statistics"], "references": ["http://www.epidemiology.ch/history/PDF%20bg/Greenland,%20Pearl%20and%20Robins%201999%20causal%20diagrams%20for%20epidemiologic%20research.pdf", "http://doi.org/10.1016%2F0004-3702(86)90072-x", "http://doi.org/10.1097%2F00001648-199901000-00008", "http://www.worldcat.org/issn/1044-3983", "http://www.worldcat.org/oclc/484244020", "https://psyarxiv.com/t3qub"]}, "Intention to treat analysis": {"categories": ["CS1 maint: Archived copy as title", "Clinical research", "Clinical trials", "Epidemiology", "Experiments"], "title": "Intention-to-treat analysis", "method": "Intention to treat analysis", "url": "https://en.wikipedia.org/wiki/Intention-to-treat_analysis", "summary": "An intention-to-treat (ITT) analysis of the results of an experiment is based on the initial treatment assignment and not on the treatment eventually received. ITT analysis is intended to avoid various misleading artifacts that can arise in intervention research such as non-random attrition of participants from the study or crossover. ITT is also simpler than other forms of study design and analysis because it does not require observation of compliance status for units assigned to different treatments or incorporation of compliance into the analysis. Although ITT analysis is widely employed in published clinical trials, it can be incorrectly described and there are some issues with its application. Furthermore, there is no consensus on how to carry out an ITT analysis in the presence of missing outcome data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d6/WHO_Rod.svg"], "links": ["Academic clinical trials", "Adaptive clinical trial", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Attrition (medicine, epidemiology)", "BMJ", "Blind experiment", "CMAJ", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Compliance (medicine)", "Correlation does not imply causation", "Cross-sectional study", "Crossover study", "Cumulative incidence", "Design of experiments", "Digital object identifier", "Ecological study", "Epidemiological methods", "Evidence-based medicine", "Experiment", "First-in-man study", "Glossary of clinical research", "Hazard ratio", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Lost to follow-up", "Meta-analysis", "Missing data", "Morbidity", "Mortality rate", "Multicenter trial", "Nature Clinical Practice", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "Period prevalence", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (natural sciences)", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Random assignment", "Randomized controlled trial", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Scientific control", "Seeding trial", "Selection bias", "Specificity and sensitivity", "Survivorship bias", "Systematic review", "Type I and type II errors", "Vaccine trial", "Virulence"], "references": ["http://www.mja.com.au/", "http://www.mja.com.au/public/issues/179_08_201003/her10586_fm.html", "http://www.cmaj.ca/cgi/content/full/165/10/1339", "http://bmj.bmjjournals.com/cgi/content/full/319/7211/670", "http://www.jerrydallal.com/LHSP/itt.htm", "http://www.nature.com/glossary/clinicalpractice/", "http://www.nature.com/glossary/clinicalpractice/defDetails.do?uid=ncp_488", "http://people.bu.edu/mlava/ITT%20Workshop.pdf", "http://gateway.nlm.nih.gov/MeetingAbstracts/102214217.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC28218", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3055831", "http://www.ncbi.nlm.nih.gov/pubmed/10480822", "http://www.ncbi.nlm.nih.gov/pubmed/10822117", "http://www.ncbi.nlm.nih.gov/pubmed/21356072", "http://www.cochrane-net.org/openlearning/html/mod14-4.htm", "http://doi.org/10.1016%2FS0197-2456(00)00046-5", "http://doi.org/10.1136%2Fbmj.319.7211.670", "http://doi.org/10.1186%2F1745-6215-12-58", "http://www.plosone.org/article/info:doi%2F10.1371%2Fjournal.pone.0049163", "https://archive.is/20121223074651/http://www.medicine.ox.ac.uk/bandolier/booth/glossary/ITT.html", "https://web.archive.org/web/20131110154948/http://www.cochrane-net.org/openlearning/html/mod14-4.htm"]}, "List of fields of application of statistics": {"categories": ["Applied statistics", "Statistics-related lists"], "title": "List of fields of application of statistics", "method": "List of fields of application of statistics", "url": "https://en.wikipedia.org/wiki/List_of_fields_of_application_of_statistics", "summary": "Statistics is the mathematical science involving the collection, analysis and interpretation of data. A number of specialties have evolved to apply statistical and methods to various disciplines. Certain topics have \"statistical\" in their name but relate to manipulations of probability distributions rather than to statistical analysis.\n\nActuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries.\nAstrostatistics is the discipline that applies statistical analysis to the understanding of astronomical data.\nBiostatistics is a branch of biology that studies biological phenomena and observations by means of statistical analysis, and includes medical statistics.\nBusiness analytics is a rapidly developing business process that applies statistical methods to data sets (often very large) to develop new insights and understanding of business performance & opportunities\nChemometrics is the science of relating measurements made on a chemical system or process to the state of the system via application of mathematical or statistical methods.\nDemography is the statistical study of all populations. It can be a very general science that can be applied to any kind of dynamic population, that is, one that changes over time or space.\nEconometrics is a branch of economics that applies statistical methods to the empirical study of economic theories and relationships.\nEnvironmental statistics is the application of statistical methods to environmental science. Weather, climate, air and water quality are included, as are studies of plant and animal populations.\nEpidemiology is the study of factors affecting the health and illness of populations, and serves as the foundation and logic of interventions made in the interest of public health and preventive medicine.\nGeostatistics is a branch of geography that deals with the analysis of data from disciplines such as petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geography.\nMachine learning is the subfield of computer science that formulates algorithms in order to make predictions from data.\nOperations research (or operational research) is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems.\nPopulation ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment.\nPsychometrics is the theory and technique of educational and psychological measurement of knowledge, abilities, attitudes, and personality traits.\nQuality control reviews the factors involved in manufacturing and production; it can make use of statistical sampling of product items to aid decisions in process control or in accepting deliveries.\nQuantitative psychology is the science of statistically explaining and changing mental processes and behaviors in humans.\nReliability engineering is the study of the ability of a system or component to perform its required functions under stated conditions for a specified period of time\nStatistical finance, an area of econophysics, is an empirical attempt to shift finance from its normative roots to a positivist framework using exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets.\nStatistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.\nStatistical physics is one of the fundamental theories of physics, and uses methods of probability theory in solving physical problems.\nStatistical signal processing utilizes the statistical properties of signals to perform signal processing tasks.\nStatistical thermodynamics is the study of the microscopic behaviors of thermodynamic systems using probability theory and provides a molecular level interpretation of thermodynamic quantities such as work, heat, free energy, and entropy.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Astrostatistics", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biology", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Business analytics", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemistry", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computer science", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Demography", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Ecology", "Econometrics", "Economics", "Econophysics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Entropy", "Environment (biophysical)", "Environmental science", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finance", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geochemistry", "Geographic information system", "Geography", "Geometric mean", "Geostatistics", "Glossary of probability and statistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heat", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hydrogeology", "Hydrology", "Index of dispersion", "Insurance", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of statisticians", "List of statistics articles", "List of statistics journals", "List of statistics topics", "Lists of statistics topics", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Machine learning", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mechanics", "Median", "Median-unbiased estimator", "Medical statistics", "Meteorology", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normative economics", "Notation in probability and statistics", "Observational study", "Oceanography", "Official statistics", "One- and two-tailed tests", "Operations research", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Petroleum geology", "Physics", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population", "Population (statistics)", "Population ecology", "Population statistics", "Positivist", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Process control", "Proportional hazards model", "Psychometrics", "Quality control", "Quantitative psychology", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical finance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical mechanics", "Statistical model", "Statistical parameter", "Statistical physics", "Statistical power", "Statistical process control", "Statistical signal processing", "Statistical theory", "Statistical thermodynamics", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Thermodynamic free energy", "Thermodynamic system", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Work (thermodynamics)", "Z-test"], "references": []}, "Sequential analysis": {"categories": ["Design of experiments", "Sequential methods", "Statistical hypothesis testing", "Wikipedia articles needing page number citations from March 2011"], "title": "Sequential analysis", "method": "Sequential analysis", "url": "https://en.wikipedia.org/wiki/Sequential_analysis", "summary": "In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abraham Wald", "Accelerated failure time model", "Actuarial science", "Addison-Wesley", "Akaike information criterion", "Alan Turing", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Applied Mathematics Panel", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Banburismus", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bhaskar Kumar Ghosh", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bletchley Park", "Blind experiment", "Blocking (statistics)", "Bonferroni correction", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brian Randell", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Change detection", "Chemometrics", "Chi-squared test", "Christiaan Huygens", "Classified information", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Columbia University", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "David Blackwell", "David Siegmund", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Enigma machine", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gambler's ruin", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "George Alfred Barnard", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Haybittle\u2013Peto boundary", "Herman Chernoff", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis testing", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jacob Wolfowitz", "James Berger (statistician)", "Jarque\u2013Bera test", "Johansen test", "John Wiley and Sons", "Jonckheere's trend test", "Jones and Bartlett Publishers", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kenneth Arrow", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marcel Dekker", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Milton Friedman", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Null hypothesis", "OCLC", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Optimal stopping", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "PASS Sample Size Software", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Armitage", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Pocock boundary", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Pranab K. Sen", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential estimation", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Society for Industrial and Applied Mathematics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Springer-Verlag", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical analysis", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Step detection", "Stopping rule", "Stratified sampling", "Structural break", "Structural equation modeling", "Stuart Pocock", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Type 1 error", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "W. Allen Wallis", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "World War II", "Z-test"], "references": ["http://www.dictionaryofeconomics.com/article?id=pde2008_S000098", "http://onlinemarketr.com:", "http://ediss.sub.uni-hamburg.de/volltexte/2013/6152/pdf/Dissertation.pdf", "http://myweb.fsu.edu/ajeong/dat/", "http://www.ncbi.nlm.nih.gov/pubmed/23824994", "http://doi.org/10.1002%2Fsim.4780131308", "http://doi.org/10.1002%2Fsim.5893", "http://doi.org/10.1057%2F9780230226203.1513", "http://doi.org/10.1093%2Fbiomet%2F86.1.71", "http://doi.org/10.1214%2Faoms%2F1177731118", "http://doi.org/10.2307%2F1905525", "http://doi.org/10.2307%2F2530245", "http://doi.org/10.2307%2F2531959", "http://www.jstor.org/stable/1905525", "http://www.jstor.org/stable/2235829", "http://www.jstor.org/stable/2530245", "http://www.jstor.org/stable/2531959", "http://www.worldcat.org/issn/0006-3444", "http://www.worldcat.org/issn/1097-0258", "http://www.worldcat.org/oclc/553888945", "http://www.worldcat.org/oclc/900071609", "https://academic.oup.com/biomet/article-abstract/86/1/71/255103/Unbiased-estimation-following-a-group-sequential", "https://web.archive.org/web/20060501235736/http://garnet.fsu.edu/~ajeong/index.htm", "https://cran.r-project.org/web/packages/SPRT/SPRT.pdf"]}, "Raikov's theorem": {"categories": ["CS1 maint: Multiple names: authors list", "Characterization of probability distributions", "Probability theorems", "Statistical theorems"], "title": "Raikov's theorem", "method": "Raikov's theorem", "url": "https://en.wikipedia.org/wiki/Raikov%27s_theorem", "summary": "Raikov\u2019s theorem is a result in probability theory. It is well known that if each of two independent random variables \u03be1 and \u03be2 has a Poisson distribution, then their sum \u03be=\u03be1+\u03be2 has a Poisson distribution as well. It turns out that the converse is also valid .\n\n", "images": [], "links": ["Cram\u00e9r\u2019s decomposition theorem", "Independence (probability theory)", "Linnik's theorem", "Poisson distribution", "Probability theory", "Random variables", "Yuri Linnik"], "references": []}, "Multiple Indicator Cluster Survey": {"categories": ["Childhood", "Household surveys", "Social statistics data", "Statistical data agreements", "UNICEF", "Webarchive template wayback links"], "title": "Multiple Indicator Cluster Surveys", "method": "Multiple Indicator Cluster Survey", "url": "https://en.wikipedia.org/wiki/Multiple_Indicator_Cluster_Surveys", "summary": "The Multiple Indicator Cluster Surveys (MICS) are household surveys implemented by countries under the programme developed by the United Nations Children's Fund to provide internationally comparable, statistically rigorous data on the situation of children and women. The first round of surveys (MICS1) was carried out in over 60 countries in mainly 1995 and 1996 in response to the World Summit for Children and measurement of the mid-decade progress. A second round (MICS2) in 2000 increased the depth of the survey, allowing monitoring of a larger number of globally agreed indicators. A third round (MICS3) started in 2006 and aimed at producing data measuring progress also toward the Millennium Development Goals (MDGs), A World Fit for Children, and other major relevant international commitments. The fourth round, launched in 2009, aimed at most data collection conducted in 2010, but in reality most MICS4s were implemented in 2011 and even into 2012 and 2013. This represented a scale-up of frequency of MICS from UNICEF, now offering the survey programme on a three-year cycle. The fifth round, launched in 2012, was aimed at offering countries the tools to do the final MDG data collection. \nIn 2016, the sixth round was launched with an effort towards collecting baseline data for the new set of global goals and targets - the Sustainable Development Goals (SDGs). In early 2018, a total of more than 300 surveys have been completed in more than 100 countries.\nThe MICS is highly comparable to the Demographic and Health Survey (DHS) and the technical teams developing and supporting the surveys are in close collaboration.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9a/Flag_of_Afghanistan.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Flag_of_Albania.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Flag_of_Algeria.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9d/Flag_of_Angola.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1a/Flag_of_Argentina.svg", "https://upload.wikimedia.org/wikipedia/commons/d/dd/Flag_of_Azerbaijan.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2c/Flag_of_Bahrain.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Flag_of_Bangladesh.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ef/Flag_of_Barbados.svg", 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"https://upload.wikimedia.org/wikipedia/commons/9/9f/Flag_of_the_Dominican_Republic.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Flag_of_the_People%27s_Republic_of_China.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Flag_of_the_Philippines.svg", "https://upload.wikimedia.org/wikipedia/commons/9/92/Flag_of_the_Republic_of_the_Congo.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a0/Flag_of_the_Turks_and_Caicos_Islands.svg", "https://upload.wikimedia.org/wikipedia/commons/0/04/Flag_of_Gabon.svg", "https://upload.wikimedia.org/wikipedia/en/4/41/Flag_of_India.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9f/Flag_of_Saint_Lucia.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4f/Flag_of_Sao_Tome_and_Principe.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fd/Flag_of_Senegal.svg", "https://upload.wikimedia.org/wikipedia/commons/1/17/Flag_of_Sierra_Leone.svg", "https://upload.wikimedia.org/wikipedia/commons/3/38/Flag_of_Tanzania.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Flag_of_The_Gambia.svg", "https://upload.wikimedia.org/wikipedia/commons/8/84/Flag_of_Uzbekistan.svg"], "links": ["Afghanistan", "Albania", "Alcohol", "Algeria", "Angola", "Argentina", "Azerbaijan", "Bahrain", "Bangladesh", "Barbados", "Belarus", "Belize", "Benin", "Bhutan", "Birth", "Birth registration", "Bolivia", "Bosnia and Herzegovina", "Botswana", "Breastfeeding", "Burkina Faso", "Burundi", "CSPro", "Cameroon", "Central African Republic", "Chad", "Child", "Child Labour", "Child discipline", "Child mortality", "China", "Civil union", "Comoros", "Contraception", "Costa Rica", "Croatia", "Cuba", "Democratic Republic of the Congo", "Demographic and Health Surveys", "Disability", "Djibouti", "Domestic Violence", "Dominican Republic", "Drinking Water", "Early Childhood Development", "Education", "Egypt", "El Salvador", "Equatorial Guinea", "Eswatini", "Ethiopia", "Family planning", "Female Genital Mutilation", "Fertility", "Fiji", "Gabon", "Georgia (country)", "Ghana", "Guinea", "Guinea-Bissau", "Guyana", "HIV/AIDS", "Handwashing", "Honduras", "Human sexuality", "Immunisation", "India", "Indonesia", "Information and communications technology", "Insecticide treated net", "Iran", "Iraq", "Ivory Coast", "Jamaica", "Kazakhstan", "Kenya", "Kiribati", "Kosovo", "Kyrgyzstan", "Laos", "Lebanon", "Lesotho", "Liberia", "Libya", "Life satisfaction", "Madagascar", "Malawi", "Maldives", "Male circumcision", "Mali", "Malnutrition", "Marriage", "Mass Media", "Maternal Mortality", "Maternal health", "Mauritania", "Mexico", "Microsoft Excel", "Millennium Development Goals", "Moldova", "Mongolia", "Montenegro", "Mozambique", "Multidimensional Poverty Index", "Myanmar", "Nepal", "Newborn", "Niger", "Nigeria", "North Korea", "Oman", "Oxford Poverty and Human Development Initiative", "Pakistan", "Panama", "Paraguay", "Philippines", "Post-natal", "Qatar", "Questionnaires", "Republic of Macedonia", "Republic of the Congo", "Rwanda", "SPSS", "Saint Lucia", "Salt Iodisation", "Sanitation", "Senegal", "Serbia", "Sierra Leone", "Socialist Federal Republic of Yugoslavia", "Somalia", "South Sudan", "State of Palestine", "Statistical survey", "Statistics", "Sudan", "Suriname", "Sustainable Development Goals", "Syria", "S\u00e3o Tom\u00e9 and Pr\u00edncipe", "Tajikistan", "Tanzania", "Thailand", "The Gambia", "Tobacco", "Togo", "Trinidad and Tobago", "Tunisia", "Turkey", "Turkmenistan", "Turks and Caicos Islands", "UNICEF", "Ukraine", "United Nations Development Programme", "Uruguay", "Uzbekistan", "Vanuatu", "Venezuela", "Victimology", "Vietnam", "Wayback Machine", "Woman", "World Summit for Children", "Yemen", "Zambia", "Zimbabwe"], "references": ["http://54.92.12.252/files?job=W1siZiIsIjIwMTUvMDkvMTQvMTcvNTUvMzcvNTI2LzIwMTUwOTEyX01JQ1MyMF9XRUIucGRmIl1d&sha=da0e0b8ac785c628", "http://www.bbs.gov.bd/site/page/56067433-bdd2-4f62-b2df-7ac875659d64/Women-&-Children", "http://www.cso.gov.bw/templates/cso/file/File/bfhs_report.pdf", "http://www.dhsprogram.com", "http://www.sciencedirect.com/science/article/pii/S0145213411002353", "http://onlinelibrary.wiley.com/doi/10.1111/j.1467-8624.2011.01675.x/abstract", "http://ec.europa.eu/eurostat/web/income-and-living-conditions/overview", "http://www.who.int/bulletin/volumes/90/2/11-090886-ab/en/index.html", "http://www.who.int/tobacco/surveillance/survey/gats/en", "http://www.childmortality.org", "http://www.education-inequalities.org", "http://www.ggp-i.org", "http://www.ilo.org/ipec/ChildlabourstatisticsSIMPOC/lang--en/index.htm", "http://www.internationalsurveynetwork.org", "http://www.micscompiler.org", "http://www.odi.org/publications/9355-intra-household-inequalities-child-rights-wellbeing-barrier-progress", "http://www.papfam.org/", "http://smartmethodology.org", "http://unstats.un.org/iswghs", "http://data.unicef.org", "http://data.unicef.org/corecode/uploads/document6/uploaded_pdfs/corecode/ChildDiscipline_report_Eng_44.pdf", "http://mics.unicef.org", "http://mics.unicef.org/files?job=W1siZiIsIjIwMTUvMDEvMTkvMDcvMTAvNTcvMzIxL01JQ1NfV1MxXzEwMl9NSUNTX19fUGFzdF9fUHJlc2VudF9hbmRfRnV0dXJlLnBwdHgiXV0&sha=26e10bd88ba0610c", "http://mics.unicef.org/news_entries/46/CONCLUSION-OF-THE-MICS-FIELD-TEST-IN-BELIZE-AND-THE-WAY-FORWARD:-MICS6", "http://mics.unicef.org/news_entries/9", "http://mics.unicef.org/news_entries/90/Using-MICS-to-Understand-Emergencies:-MICS6", "http://mics.unicef.org/publications/reports-and-methodological-papers", "http://mics.unicef.org/surveys", "http://mics.unicef.org/tools", "http://www.unicef.org", "http://www.unicef.org/evaluation/files/UNICEF_Evaluation_of_the_Multiple_Indicator_Cluster_Surveys_Combined.pdf", "http://econ.worldbank.org/WBSITE/EXTERNAL/EXTDEC/EXTRESEARCH/EXTLSMS/0,,contentMDK:21610833~pagePK:64168427~piPK:64168435~theSitePK:3358997,00.html", "http://www.worldvaluessurvey.org/wvs.jsp", "http://www.ophi.org.uk", "https://www.ncbi.nlm.nih.gov/bookshelf/br.fcgi?book=malaria&part=A2416", "https://www.ncbi.nlm.nih.gov/bookshelf/br.fcgi?book=malaria", "https://web.archive.org/web/20080216075751/http://www.wssinfo.org/", "https://web.archive.org/web/20150402155955/http://data.unicef.org/corecode/uploads/document6/uploaded_pdfs/corecode/ChildDiscipline_report_Eng_44.pdf", "https://www.unicef.org/evaldatabase/index_14381.html", "https://www.unicef.org/evaldatabase/index_52700.html", "https://www.unicef.org/evaldatabase/index_76350.html"]}, "Engineering tolerance": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from January 2017", "Articles with unsourced statements from November 2012", "Engineering concepts", "Mechanical standards", "Metalworking terminology", "Metrology", "Quality", "Statistical deviation and dispersion", "Wikipedia articles with NDL identifiers"], "title": "Engineering tolerance", "method": "Engineering tolerance", "url": "https://en.wikipedia.org/wiki/Engineering_tolerance", "summary": "Engineering tolerance is the permissible limit or limits of variation in:\n\na physical dimension;\na measured value or physical property of a material, manufactured object, system, or service;\nother measured values (such as temperature, humidity, etc.);\nin engineering and safety, a physical distance or space (tolerance), as in a truck (lorry), train or boat under a bridge as well as a train in a tunnel (see structure gauge and loading gauge);\nin mechanical engineering the space between a bolt and a nut or a hole, etc..Dimensions, properties, or conditions may have some variation without significantly affecting functioning of systems, machines, structures, etc.\nA variation beyond the tolerance (for example, a temperature that is too hot or too cold) is said to be noncompliant, rejected, or exceeding the tolerance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/5/59/DINISO2768-2example.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f0/Limits_and_Fits.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/49/Mechanical_Tolerance_Definitions.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Air draft", "Allowance (engineering)", "Backlash (engineering)", "Boat", "Bridge", "Capacitor", "Civil engineering", "Design of experiments", "Dimension", "Distance", "Electronic color code", "Engineering", "Engineering fit", "Engineering tolerance", "Football (disambiguation)", "Genichi Taguchi", "Geometric dimensioning and tolerancing", "IT Grade", "Inductor", "International Standard Book Number", "Key relevance", "Loading gauge", "Machinery's Handbook", "Machining industry", "Manufacturing", "Margin of error", "Mechanical engineering", "Millimeter", "National Diet Library", "Normal distribution", "Nut (hardware)", "Ohm (unit)", "Overpass", "Physical property", "Precision engineering", "Probabilistic design", "Process capability", "Process capability index", "Process control", "Quality management system", "Railroad car", "Resistor", "Safety", "Sampling plan", "Screw", "Specification", "Specification (technical standard)", "Statistical interference", "Statistical process control", "Statistical tolerance", "Structure gauge", "Taguchi loss function", "Taguchi methods", "Tap and die", "Tolerance coning", "Tolerance interval", "Tolerance stacks", "Total Quality Management", "Train", "Tram", "Truck", "Tunnel", "Vehicle", "Verification and validation"], "references": ["http://biblion.epfl.ch/EPFL/theses/2007/3825/3825_abs.pdf", "http://www.mesys.ch/calc/tolerances.fcgi?lang=en", "http://www.engineersedge.com/tolerance_chart.htm", "http://www.amesweb.info/FitTolerance/FitTolerance.aspx", "http://www.iso.org/iso/iso_catalogue/catalogue_ics/catalogue_detail_ics.htm?csnumber=45975&ICS1=17&ICS2=40&ICS3=10", "http://www.roymech.co.uk/Useful_Tables/ISO_Tolerances/ISO_LIMITS.htm", "https://id.ndl.go.jp/auth/ndlna/00566663", "https://www.wikidata.org/wiki/Q950292"]}, "Ethical problems using children in clinical trials": {"categories": ["All articles covered by WikiProject Wikify", "All pages needing cleanup", "Articles covered by WikiProject Wikify from September 2009", "Articles with limited geographic scope from December 2010", "Articles with multiple maintenance issues", "Clinical research ethics", "Human subject research", "USA-centric", "Wikipedia introduction cleanup from September 2009"], "title": "Children in clinical research", "method": "Ethical problems using children in clinical trials", "url": "https://en.wikipedia.org/wiki/Children_in_clinical_research", "summary": "In health care, a clinical trial is a comparison test of a medication or other medical treatment (such as a medical device), versus a placebo (inactive look-alike), other medications or devices, or the standard medical treatment for a patient's condition.\nTo be ethical, researchers must obtain the full and voluntary informed consent of participating human subjects. If the subject is unable to consent for him/herself, researchers can seek consent from the subject's legally authorized representative. For a minor child this is typically a parent or guardian since as under the age of 18 cannot legally give consent to participate in a clinical trial.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/bd/Ambox_globe_content.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a9/Ritalin-SR-20mg-1000x1000.jpg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Abbreviated New Drug Application", "Aspirin", "Clinical trial", "Clinical trials", "Commission to Inquire into Child Abuse", "Comprehensive Drug Abuse Prevention and Control Act of 1970", "Controlled Substances Act", "Council for International Organizations of Medical Sciences", "Declaration of Helsinki", "Digital object identifier", "Drug Enforcement Administration", "Drug Price Competition and Patent Term Restoration Act", "Drug design", "Drug development", "Drug discovery", "Ethics", "Ethics in clinical research", "FDA Fast Track Development Program", "Federal Food, Drug, and Cosmetic Act", "Food and Drug Administration", "Good clinical practice", "Hatch-Waxman exemption", "Health care", "Human experimentation in the United States", "Informed consent", "Institute of Medicine", "Institutional Review Boards", "International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use", "Investigational new drug", "Ireland", "Marihuana Tax Act", "Medical device", "Medical ethics", "Medication", "Minor (law)", "NORML", "National Institutes of Health", "New drug application", "Off-label use", "Office for Human Research Protections", "Over-the-counter drugs", "Patent", "Pharmacovigilance", "Philosophy of Healthcare", "Placebo", "Prescription Drug Marketing Act", "Prescription drugs", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Research on Adverse Drug events And Reports", "Reye's syndrome", "Single Convention on Narcotic Drugs", "U.S. Food and Drug Administration", "United States Department of Health and Human Services", "United States Department of Justice", "University College Dublin", "Uppsala Monitoring Centre", "World Health Organization", "World Medical Association"], "references": ["http://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/CFRSearch.cfm?CFRPart=50", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4074620", "http://www.ncbi.nlm.nih.gov/pubmed/22891235", "http://www.dcya.gov.ie/documents/publications/20140716InterdepartReportMothBabyHomes.pdf", "http://www.independent.ie/irish-news/the-forgotten-children-of-irelands-hidden-scandal-26673545.html", "http://doi.org/10.1542/peds.2011-2910"]}, "Design of experiments": {"categories": ["All accuracy disputes", "All articles lacking reliable references", "All articles needing additional references", "All articles that may contain original research", "All articles with unsourced statements", "Articles lacking reliable references from September 2015", "Articles needing additional references from September 2015", "Articles that may contain original research from September 2015", "Articles with disputed statements from September 2015", "Articles with multiple maintenance issues", "Articles with unsourced statements from November 2011", "Articles with unsourced statements from September 2015", "CS1 maint: Multiple names: authors list", "Commons category link from Wikidata", "Design of experiments", "Experiments", "Industrial engineering", "Quantitative research", "Statistical process control", "Statistical theory", "Systems engineering", "Use dmy dates from July 2013", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Design of experiments", "method": "Design of experiments", "url": "https://en.wikipedia.org/wiki/Design_of_experiments", "summary": "The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe or explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation.\nIn its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as \"input variables\" or \"predictor variables.\" The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as \"output variables\" or \"response variables.\" The experimental design may also identify control variables that must be held constant to prevent external factors from affecting the results. Experimental design involves not only the selection of suitable independent, dependent, and control variables, but planning the delivery of the experiment under statistically optimal conditions given the constraints of available resources. There are multiple approaches for determining the set of design points (unique combinations of the settings of the independent variables) to be used in the experiment.\nMain concerns in experimental design include the establishment of validity, reliability, and replicability. For example, these concerns can be partially addressed by carefully choosing the independent variable, reducing the risk of measurement error, and ensuring that the documentation of the method is sufficiently detailed. Related concerns include achieving appropriate levels of statistical power and sensitivity.\nCorrectly designed experiments advance knowledge in the natural and social sciences and engineering. Other applications include marketing and policy making.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/1/17/Balance_%C3%A0_tabac_1850.JPG", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/9/94/Factorial_Design.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cc/Response_surface_metodology.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["5S (methodology)", "Abraham Wald", "Academic clinical trials", "Accelerated failure time model", "Actuarial science", "Adaptive clinical trial", "Adversarial collaboration", "Agricultural engineering", "Akaike information criterion", "Algebraic statistics", "Analysis of clinical trials", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Animal testing", "Animal testing on non-human primates", "Annals of Mathematical Statistics", "Antecedent variable", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Attributable fraction among the exposed", "Attributable fraction for the population", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bayesian statistics", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blind experiment", "Blinding (medicine)", "Block design", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Business process mapping", "C. R. Rao", "Canonical correlation", "Cartography", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Charles Sanders Peirce", "Charles Sanders Peirce bibliography", "Chemometrics", "Chi-squared test", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort study", "Cointegration", "Combinatorial design", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Computer experiment", "Confidence interval", "Confidentiality", "Confirmation bias", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Control plan", "Control variable", "Controlling for a variable", "Correlation and dependence", "Correlation does not imply causation", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-sectional study", "Cross-validation (statistics)", "Crossover study", "Cumulative incidence", "D. Raghavarao", "DMAIC", "Data collection", "David R. Cox", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Ecological study", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiological methods", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Evidence-based medicine", "Experiment", "Experimental unit", "Experiments", "Experimetrics", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial design", "Factorial experiment", "Failure mode and effects analysis", "Failure rate", "False positive", "Fan chart (statistics)", "First-hitting-time model", "First-in-man study", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frank Yates", "Frequency distribution", "Frequency domain", "Frequentist inference", "Frequentist statistics", "Friedman test", "G-test", "G. E. P. Box", "General linear model", "Generalized linear model", "Generalized randomized block design", "Genichi Taguchi", "Geographic information system", "Geometric mean", "Geostatistics", "Gertrude Mary Cox", "Gittins index", "Glossary of clinical research", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grey box model", "Grouped data", "HMS Salisbury (1746)", "Harmonic mean", "Harold Hotelling", "Hazard ratio", "Herbert Robbins", "Herman Chernoff", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human subject research", "Hypothesis", "Ian Hacking", "In vitro", "In vivo", "Incidence (epidemiology)", "Index of dispersion", "Indian Statistical Institute", "Industrial engineering", "Infectivity", "Informed consent", "Institutional review board", "Instrument effect", "Integrated Authority File", "Intention-to-treat analysis", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Intervening variable", "Isis (journal)", "Isotonic regression", "JSTOR", "Jack Kiefer (mathematician)", "Jackknife resampling", "Jagdish N. Srivastava", "James Lind (physician)", "Jarque\u2013Bera test", "Johansen test", "John Nelder", "Jonckheere's trend test", "Joseph Diaz Gergonne", "Joseph Jastrow", "Journal of the Royal Statistical Society", "KNKX", "Kaizen", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kirstine Smith", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lady tasting tea", "Latin hypercube sampling", "Latin square", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratios in diagnostic testing", "Lilliefors test", "Linear algebra", "Linear discriminant analysis", "Linear model", "Linear regression", "List of clinical research topics", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Longitudinal study", "Loss function", "Lp space", "M-estimator", "Manipulation checks", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement uncertainty", "Median", "Median-unbiased estimator", "Medical statistics", "Meta-analysis", "Method of moments (statistics)", "Methods engineering", "Minimisation (clinical trials)", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Morbidity", "Mortality rate", "Multi-armed bandit", "Multi-armed bandit problem", "Multi-vari chart", "Multicenter trial", "Multifactor design of experiments software", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Naturalistic observation", "Nelson\u2013Aalen estimator", "Nested case\u2013control study", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Official statistics", "One- and two-tailed tests", "One-factor-at-a-time method", "Open-label trial", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "P-hacking", "Pan balance", "Parametric statistics", "Pareto chart", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Peer-review", "Percentile", "Period prevalence", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plackett\u2013Burman design", "Plug-in principle", "Point estimation", "Point prevalence", "Poisson regression", "Poka-yoke", "Polynomial and rational function modeling", "Polynomial regression", "Population (statistics)", "Population Impact Measures", "Population statistics", "Posterior probability", "Power (statistics)", "Pre- and post-test probability", "Prediction interval", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Process capability", "Project charter", "Proportional hazards model", "Prospective cohort study", "Protocol (natural sciences)", "Protocol (science)", "Psychometrics", "PubMed Central", "PubMed Identifier", "Public Finance Review", "Publish or perish", "Quality control", "Quasi-experiment", "Quasi-experimental design", "Questionnaire", "Q\u2013Q plot", "R. A. Fisher", "R. C. Bose", "Radar chart", "Raj Chandra Bose", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative risk reduction", "Reliability (statistics)", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Reproducibility", "Resampling (statistics)", "Research design", "Response surface", "Response surface methodology", "Restricted randomization", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Robust parameter design (RPD)", "Robust regression", "Robust statistics", "Ronald Fisher", "Root cause analysis", "Rosemary A. Bailey", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Scurvy", "Seasonal adjustment", "Seeding trial", "Selection bias", "Semiparametric regression", "Sensitivity and specificity", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shrikhande S. S.", "Sign test", "Simple linear regression", "Simultaneous equations model", "Six Sigma", "Skewness", "Social statistics", "Society for Industrial and Applied Mathematics", "Spatial analysis", "Spearman's rank correlation coefficient", "Specificity and sensitivity", "Spectral density estimation", "Spurious relationship", "Standard (metrology)", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical analysis", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen M. Stigler", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survey sampling", "Survival analysis", "Survival function", "Survivorship bias", "System identification", "Systematic review", "Taguchi methods", "The Design of Experiments", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Vaccine trial", "Validity (statistics)", "Value stream mapping", "Variance", "Vector autoregression", "Virulence", "Vitriol", "Voice of the customer", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William G. Cochran", "William Gemmell Cochran", "Z-test", "Zero order (statistics)"], "references": ["http://psychclassics.yorku.ca/Peirce/small-diffs.htm", "http://fn.bmj.com/cgi/content/full/76/1/F64", "http://www.experiment-resources.com/replication-study.html", "http://pfr.sagepub.com", "http://pss.sagepub.com/content/22/11/1359.full", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1720613", "http://www.ncbi.nlm.nih.gov/pubmed/22006061", "http://www.ncbi.nlm.nih.gov/pubmed/9059193", "http://www.ncbi.nlm.nih.gov/pubmed/9519574", "http://www.itl.nist.gov/div898/handbook/", "http://www.itl.nist.gov/div898/handbook/pri/section1/pri1.htm", "http://www.itl.nist.gov/div898/handbook/pri/section3/pri3362.htm", "http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0025.PDF#page=222", "http://www.ams.org/mathscinet-getitem?mr=1013489", "http://arxiv.org/abs/0802.4381", "http://doi.org/10.1016%2Fj.automatica.2007.05.016", "http://doi.org/10.1086%2F354775", "http://doi.org/10.1086%2F383850", "http://doi.org/10.1086%2F444032", "http://doi.org/10.1090%2FS0002-9904-1952-09620-8", "http://doi.org/10.1109%2FMCS.2010.937677", "http://doi.org/10.1136%2Ffn.76.1.F64", "http://doi.org/10.1177%2F0956797611417632", "http://doi.org/10.1177%2F1091142110385210", "http://doi.org/10.1287%2Fopre.15.4.643", "http://www.jstor.org/stable/1085417", "http://www.jstor.org/stable/168276", "http://www.jstor.org/stable/234674", "http://www.kplu.org/post/science-trust-and-psychology-crisis", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Design+of+experiments", "http://www.worldcat.org/issn/0956-7976", "https://books.google.com/books?id=V7oIAAAAQAAJ&pg=PA126", "https://books.google.com/books?id=ZKMVAAAAYAAJ&jtp=604", "https://books.google.com/books?id=ZKMVAAAAYAAJ&jtp=705", "https://books.google.com/books?id=u8sWAQAAIAAJ&jtp=203", "https://books.google.com/books?id=u8sWAQAAIAAJ&jtp=470", "https://psmag.com/environment/statistically-significant-studies-arent-necessarily-significant-82832", "https://www.theguardian.com/science/head-quarters/2014/jun/10/physics-envy-do-hard-sciences-hold-the-solution-to-the-replication-crisis-in-psychology", "https://www.youtube.com/watch?v=hfdZabCVwzc", "https://d-nb.info/gnd/4078859-3", "https://osf.io", "https://id.ndl.go.jp/auth/ndlna/00574739", "https://archive.org/details/OperaMagistris", "https://archive.org/stream/popscimonthly12yoummiss#page/612/mode/1up", "https://archive.org/stream/popscimonthly12yoummiss#page/715/mode/1up", "https://archive.org/stream/popularsciencemo13newy#page/203/mode/1up", "https://archive.org/stream/popularsciencemo13newy#page/470/mode/1up", "https://www.wikidata.org/wiki/Q2334061"]}, "Expander walk sampling": {"categories": ["Sampling (statistics)"], "title": "Expander walk sampling", "method": "Expander walk sampling", "url": "https://en.wikipedia.org/wiki/Expander_walk_sampling", "summary": "In the mathematical discipline of graph theory, the expander walk sampling theorem states that sampling vertices in an expander graph by doing a random walk is almost as good as sampling the vertices independently from a uniform distribution.\nThe earliest version of this theorem is due to Ajtai, Koml\u00f3s & Szemer\u00e9di (1987), and the more general version is typically attributed to Gillman (1998).", "images": [], "links": ["Alexander Lubotzky", "Bit", "Derandomization", "Digital object identifier", "Expander graph", "Graph theory", "Mathematics", "Peter Sarnak", "Ramanujan graph", "Random walk", "Sample (statistics)", "Sampling (statistics)", "Statistical independence", "Uniform distribution (discrete)", "Vertex (graph theory)"], "references": ["http://citeseer.ist.psu.edu/gillman98chernoff.html", "http://doi.org/10.1137%2FS0097539794268765", "http://doi.org/10.1145%2F28395.28410", "http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.aoap/1028903453"]}, "Parameter identification problem": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from December 2009", "Estimation theory"], "title": "Parameter identification problem", "method": "Parameter identification problem", "url": "https://en.wikipedia.org/wiki/Parameter_identification_problem", "summary": "For a more technical treatment, see Identifiability.In statistics and econometrics, the parameter identification problem is the inability in principle to identify a best estimate of the value(s) of one or more parameters in a regression. This problem can occur in the estimation of multiple-equation econometric models where the equations have variables in common.\nMore generally, the term can be used to refer to any situation where a statistical model will invariably have more than one set of parameters that generate the same distribution of observations, meaning that multiple parametrizations are observationally equivalent.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2e/Supply_and_demand.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Damodar N. Gujarati", "Econometrica", "Econometrics", "Errors-in-variables model", "Estimation", "Fumio Hayashi", "Identifiability", "Instrumental variable", "International Standard Book Number", "JSTOR", "Jan Kmenta", "Mark Thoma", "Necessity and sufficiency", "Observational equivalence", "Order condition", "Parameter", "Rank condition", "Reduced form", "Regression analysis", "Simultaneous equations model", "Statistical model", "Statistics", "Supply and demand", "System of linear equations", "Tjalling Koopmans", "YouTube"], "references": ["http://www.jstor.org/stable/1905689", "https://books.google.com/books?id=Bxq7AAAAIAAJ&pg=PA660", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA200", "https://www.youtube.com/watch?v=WlOtUA8Rqw8&index=14&list=PLD15D38DC7AA3B737#t=57m47s"]}, "Conditional variance": {"categories": ["All stub articles", "Conditional probability", "Probability stubs", "Statistical deviation and dispersion", "Statistics stubs", "Theory of probability distributions"], "title": "Conditional variance", "method": "Conditional variance", "url": "https://en.wikipedia.org/wiki/Conditional_variance", "summary": "In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables.\nParticularly in econometrics, the conditional variance is also known as the scedastic function or skedastic function. Conditional variances are important parts of autoregressive conditional heteroskedasticity (ARCH) models.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg"], "links": ["Almost surely", "Autoregressive conditional heteroskedasticity", "Conditional density", "Conditional distribution", "Conditional expectation", "Discrete random variable", "Econometrics", "International Standard Book Number", "Law of total expectation", "Law of total variance", "Least-squares", "Mixed model", "Probability", "Probability theory", "Random effects model", "Random variable", "Statistics", "Variance"], "references": ["https://books.google.com/books?id=0x_vAAAAMAAJ&pg=PA151", "https://books.google.com/books?id=G0_HxBubGAwC&pg=PA342"]}, "Evolutionary data mining": {"categories": ["Data mining"], "title": "Evolutionary data mining", "method": "Evolutionary data mining", "url": "https://en.wikipedia.org/wiki/Evolutionary_data_mining", "summary": "Evolutionary data mining, or genetic data mining is an umbrella term for any data mining using evolutionary algorithms. While it can be used for mining data from DNA sequences, it is not limited to biological contexts and can be used in any classification-based prediction scenario, which helps \"predict the value ... of a user-specified goal attribute based on the values of other attributes.\" For instance, a banking institution might want to predict whether a customer's credit would be \"good\" or \"bad\" based on their age, income and current savings. Evolutionary algorithms for data mining work by creating a series of random rules to be checked against a training dataset. The rules which most closely fit the data are selected and are mutated. The process is iterated many times and eventually, a rule will arise that approaches 100% similarity with the training data. This rule is then checked against a test dataset, which was previously invisible to the genetic algorithm.", "images": [], "links": ["Academic journal", "Algorithm", "Ant colony optimization", "Artificial development", "Artificial intelligence", "Artificial life", "Bacterial Colony Optimization", "Bees algorithm", "CMA-ES", "Cellular evolutionary algorithm", "Convergence (evolutionary computing)", "Credit (finance)", "Cuckoo search", "DNA sequence", "Data analysis", "Data mining", "Database", "Dataset", "Differential evolution", "Digital organism", "Evolution", "Evolution strategy", "Evolutionary Computation (journal)", "Evolutionary algorithm", "Evolutionary computation", "Evolutionary multimodal optimization", "Evolutionary programming", "Evolutionary robotics", "Firefly algorithm", "Fitness approximation", "Fitness function", "Fitness landscape", "Gaussian adaptation", "Gene expression programming", "Genetic algorithm", "Genetic operators", "Genetic programming", "Grey Wolf Optimizer", "Harmony search", "Human-based evolutionary computation", "IEEE", "Interactive evolutionary computation", "International Standard Book Number", "Iteration", "Knowledge discovery", "Learning classifier system", "Machine learning", "Mating pool", "Memetic algorithm", "Metaheuristic", "Morgan Kaufmann", "Mutated", "Natural evolution strategy", "Neuroevolution", "No free lunch in search and optimization", "Normalization (statistics)", "Particle swarm optimization", "Pattern mining", "Pontif\u00edcia Universidade Cat\u00f3lica do Paran\u00e1", "Program synthesis", "Random", "Swarm intelligence", "Umbrella term"], "references": ["http://neuro.bstu.by/our/Data-mining/fereitas-ga.pdf", "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1255389&isnumber=28075"]}, "Lexis diagram": {"categories": ["Actuarial science", "All stub articles", "Commons category without a link on Wikidata", "Demography", "Statistical charts and diagrams", "Statistics stubs"], "title": "Lexis diagram", "method": "Lexis diagram", "url": "https://en.wikipedia.org/wiki/Lexis_diagram", "summary": "In demography (the branch of statistics that deals with the study of populations) a Lexis diagram (named after economist and social scientist Wilhelm Lexis) is a two dimensional diagram that is used to represent events (such as births or deaths) that occur to individuals belonging to different cohorts. Calendar time is usually represented on the horizontal axis, while age is represented on the vertical axis. In some textbooks the y-axis is plotted backwards, with age 0 at the top of the page and increasing downwards. However, other arrangements of the axes are also seen. As an example the death of an individual in 2009 at age 80 is represented by the point (2009,80); the cohort of all persons born in 1929 is represented by a diagonal line starting at (1929,0) and continuing through (1930,1) and so on.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e4/DL_CVds_11_V02.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Arabic", "Chinese language", "Cohort (statistics)", "Demography", "French language", "Russian language", "Spanish language", "Statistics", "United Nations Statistics Division", "Wilhelm Lexis"], "references": ["http://icampus.uclouvain.be/courses/LEXIS/document/index.htm", "http://www.demographic-research.org/Volumes/Vol4/3/4-3.pdf", "http://unstats.un.org/unsd/pubs/gesgrid.asp?id=325"]}, "A priori probability": {"categories": ["A priori", "Bayesian statistics", "Deductive reasoning", "Probability assessment"], "title": "A priori probability", "method": "A priori probability", "url": "https://en.wikipedia.org/wiki/A_priori_probability", "summary": "An a priori probability is a probability that is derived purely by deductive reasoning. One way of deriving a priori probabilities is the principle of indifference, which has the character of saying that, if there are N mutually exclusive and collectively exhaustive events and if they are equally likely, then the probability of a given event occurring is 1/N. Similarly the probability of one of a given collection of K events is K / N.\nOne disadvantage of defining probabilities in the above way is that it applies only to finite collections of events.\nIn Bayesian inference, \"uninformative priors\" or \"objective priors\" are particular choices of a priori probabilities.\nNote that \"prior probability\" is a broader concept.\nSimilar to the distinction in philosophy between a priori and a posteriori, in Bayesian inference a priori denotes general knowledge about the data distribution before making an inference, while a posteriori denotes knowledge that incorporates the results of making an inference.", "images": [], "links": ["A priori and a posteriori", "Bayesian inference", "Collectively exhaustive", "Deductive reasoning", "Degeneracy (mathematics)", "Elementary event", "Event (probability theory)", "International Standard Book Number", "Liouville's theorem (Hamiltonian)", "Mutually exclusive", "Principle of indifference", "Prior probability", "S-matrix", "Statistical mechanics", "Uncertainty relation"], "references": ["http://www.colorado.edu/Economics/morey/7818/7818readings.html", "http://link.aip.org/link/doi/10.1063/1.1477060", "https://books.google.com/books?id=Tmk7BAAAQBAJ&pg=PA109"]}, "Systematic review": {"categories": ["All articles with dead external links", "Articles to be expanded from May 2018", "Articles with dead external links from February 2018", "Articles with permanently dead external links", "CS1 errors: dates", "CS1 maint: Multiple names: authors list", "Commons category link from Wikidata", "Evidence-based practices", "Information science", "Meta-analysis", "Nursing research", "Review journals", "Systematic review", "Wikipedia articles needing page number citations from June 2012"], "title": "Systematic review", "method": "Systematic review", "url": "https://en.wikipedia.org/wiki/Systematic_review", "summary": "Systematic reviews are a type of literature review that uses systematic methods to collect secondary data, critically appraise research studies, and synthesize studies. Systematic reviews formulate research questions that are broad or narrow in scope, and identify and synthesize studies that directly relate to the systematic review question. They are designed to provide a complete, exhaustive summary of current evidence relevant to a research question. Systematic reviews of randomized controlled trials are key to the practice of evidence-based medicine, and a review of existing studies is often quicker and cheaper than embarking on a new study.\nAn understanding of systematic reviews, and how to implement them in practice, is highly recommended for professionals involved in the delivery of health care. Besides health interventions, systematic reviews may examine clinical tests, public health interventions, environmental interventions, social interventions, adverse effects, and economic evaluations. Systematic reviews are not limited to medicine and are quite common in all other sciences where data are collected, published in the literature, and an assessment of methodological quality for a precisely defined subject would be helpful.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/56/Extraction_machine.gif", "https://upload.wikimedia.org/wikipedia/commons/7/77/Open_Access_logo_PLoS_transparent.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/6/6c/Wiki_letter_w.svg"], "links": ["Academic clinical trials", "Adaptive clinical trial", "Adverse effects", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "AusAid", "Biomedical research", "Blind experiment", "Blobbogram", "Campbell Collaboration", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Centre for Evidence Based Medicine", "Citation index", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cochrane (organisation)", "Cochrane Collaboration", "Cochrane Library", "Cohort study", "Correlation does not imply causation", "Critical appraisal", "Cross-sectional study", "Cumulative incidence", "Database", "Design of experiments", "Digital object identifier", "EPPI-Centre", "Ecological study", "Economic evaluation", "Embase", "Epidemiological methods", "Evidence-Based Research", "Evidence-based medicine", "Evidence-based policy", "Experiment", "First-in-man study", "Forest plot", "Further research is needed", "Generalized model aggregation", "Gideon J. Mellenbergh", "Glossary of clinical research", "Grey literature", "Hazard ratio", "Health care", "Herman J. Ader", "Heterogeneity", "Impact factor", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Intention-to-treat analysis", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Literature review", "Living review", "Longitudinal study", "Medicine", "Meta-analysis", "Meta-narrative", "Morbidity", "Mortality rate", "Multicenter trial", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "Open access", "Overseas Development Institute", "Peer review", "Period prevalence", "Philosophical realism", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Preferred Reporting Items for Systematic Reviews and Meta-Analyses", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed", "PubMed Central", "PubMed Identifier", "Qualitative research", "Quantitative research", "Randomized controlled trial", "Relative risk reduction", "Reporting bias", "Reproducibility", "Research question", "Retrospective cohort study", "Review journal", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Scientific control", "Seeding trial", "Selection bias", "Social science", "Specificity and sensitivity", "Survivorship bias", "Systematic Reviews (journal)", "University of London", "University of York", "Vaccine trial", "Virulence", "Web of Science"], "references": ["http://www.cochranelibrary.com/", "http://linkinghub.elsevier.com/retrieve/pii/S0895435615000578", "http://www.iflscience.com/editors-blog/retraction-scientific-papers-fraud-or-bias-just-tip-iceberg", "http://retractionwatch.com/2015/03/26/biomed-central-retracting-43-papers-for-fake-peer-review/", "http://retractionwatch.com/2015/04/02/retraction-and-republication-for-lancet-resp-med-tracheostomy-paper/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1831728", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2539276", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2707010", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2888022", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC404509", "http://www.ncbi.nlm.nih.gov/pubmed/12701949", "http://www.ncbi.nlm.nih.gov/pubmed/15105329", "http://www.ncbi.nlm.nih.gov/pubmed/16053581", "http://www.ncbi.nlm.nih.gov/pubmed/17388659", "http://www.ncbi.nlm.nih.gov/pubmed/17638714", "http://www.ncbi.nlm.nih.gov/pubmed/19621070", "http://www.ncbi.nlm.nih.gov/pubmed/20021585", "http://www.ncbi.nlm.nih.gov/pubmed/23338737", "http://www.ncbi.nlm.nih.gov/pubmed/23398011", "http://www.ncbi.nlm.nih.gov/pubmed/24983062", "http://www.ncbi.nlm.nih.gov/pubmed/25271098", "http://www.ncbi.nlm.nih.gov/pubmed/25388685", "http://www.ncbi.nlm.nih.gov/pubmed/26041754", "http://www.ncbi.nlm.nih.gov/pubmed/7977286", "http://www.ncbi.nlm.nih.gov/pubmed/8124111", "http://www.cebm.net/index.aspx?o=1914", "http://www.campbellcollaboration.org/about_us/index.php", "http://www.campbellcollaboration.org/history/explore/background", "http://www.editorial-unit.cochrane.org/mecir", "http://handbook.cochrane.org", "http://tech.cochrane.org/revman", "http://www.cochrane.org/", "http://www.cochrane.org/about-us/our-logo", "http://www.cochrane.org/news/2015-impact-factor-released-cochrane-database-systematic-reviews", "http://doi.org/10.1002%2F14651858.MR000035.pub2", "http://doi.org/10.1016%2Fj.envsci.2014.05.010", "http://doi.org/10.1016%2Fj.jclinepi.2014.11.025", "http://doi.org/10.1017%2FS0266462303000163", "http://doi.org/10.1093%2Foxfordjournals.aje.a117324", "http://doi.org/10.1111%2F1467-8551.00375", "http://doi.org/10.1111%2Fj.1468-0009.2009.00578.x", "http://doi.org/10.1111%2Fjscm.12145", "http://doi.org/10.1111%2Fmedu.12092", "http://doi.org/10.1136%2Fbmj.308.6924.283", "http://doi.org/10.1136%2Fbmj.328.7446.1010", "http://doi.org/10.1136%2Fbmj.h2463", "http://doi.org/10.1258%2F1355819054308530", "http://doi.org/10.1371%2Fjournal.pmed.0040078", "http://doi.org/10.1371%2Fjournal.pmed.1000100", "http://doi.org/10.1590%2F1516-3180.2013.8150015", "http://doi.org/10.1590%2FS1516-31802012000600007", "http://doi.org/10.17226%2F13059", "http://doi.org/10.7326%2F0003-4819-147-4-200708210-00179", "http://getitglossary.org/term/systematic+review", "http://www.jstor.org/stable/25593645", "http://aje.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=7977286", "http://www.prisma-statement.org/", "http://www.prisma-statement.org/Endorsement/PRISMAEndorsers.aspx", "http://commons.wikimedia.org/wiki/File:What_are_systematic_reviews.ogg", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Systematic+review", "http://www.worldcat.org/issn/0895-4356", "http://eppi.ioe.ac.uk/", "http://www.york.ac.uk/inst/crd/", "http://www.odi.org.uk/resources/details.asp?id=6260&title=systematic-review-slrc-international-development-research-methods", "https://books.google.com/books?id=LCnOj4ZFyjkC&printsec=frontcover&hl=fr#v=onepage&q=%22Methodological%20quality%22&f=false", "https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=PureSearch&db=pubmed&details_term=%22Review%20Literature%22%5BMAJR%5D", "https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=mesh&list_uids=68012196&dopt=Full", "https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=mesh&list_uids=68016454&dopt=Full", "https://web.archive.org/web/20110406110628/http://www.cebm.net/index.aspx?o=1914", "https://web.archive.org/web/20140203232624/http://www.campbellcollaboration.org/about_us/index.php", "https://web.archive.org/web/20150616034557/http://www.cebma.org/wp-content/uploads/Pettigrew-Roberts-SR-in-the-Soc-Sc.pdf", "https://cccrg.cochrane.org/animated-storyboard-what-are-systematic-reviews", "https://doi.org/10.1111/jscm.12145", "https://www.york.ac.uk/media/crd/Systematic_Reviews.pdf"]}, "Epidemiology": {"categories": ["All articles with dead external links", "All articles with unsourced statements", "All pages needing factual verification", "Articles with dead external links from December 2016", "Articles with permanently dead external links", "Articles with unsourced statements from June 2015", "CS1 maint: Extra text: editors list", "Commons category link is on Wikidata", "Environmental social science", "Epidemiology", "Pages using div col with small parameter", "Public health", "Use dmy dates from January 2017", "Webarchive template wayback links", "Wikipedia articles needing factual verification from April 2011", "Wikipedia articles with GND identifiers", "Wikipedia articles with NARA identifiers", "Wikipedia articles with NDL identifiers"], "title": "Epidemiology", "method": "Epidemiology", "url": "https://en.wikipedia.org/wiki/Epidemiology", "summary": "Epidemiology is the study and analysis of the distribution (who, when, and where) and determinants of health and disease conditions in defined populations.\nIt is the cornerstone of public health, and shapes policy decisions and evidence-based practice by identifying risk factors for disease and targets for preventive healthcare. Epidemiologists help with study design, collection, and statistical analysis of data, amend interpretation and dissemination of results (including peer review and occasional systematic review). Epidemiology has helped develop methodology used in clinical research, public health studies, and, to a lesser extent, basic research in the biological sciences.Major areas of epidemiological study include disease causation, transmission, outbreak investigation, disease surveillance, forensic epidemiology, occupational epidemiology, screening, biomonitoring, and comparisons of treatment effects such as in clinical trials. Epidemiologists rely on other scientific disciplines like biology to better understand disease processes, statistics to make efficient use of the data and draw appropriate conclusions, social sciences to better understand proximate and distal causes, and engineering for exposure assessment.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d8/Nuvola_apps_package_favorite.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c7/Snow-cholera-map.jpg", "https://upload.wikimedia.org/wikipedia/commons/d/d6/WHO_Rod.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/commons/d/de/Tree_of_life_by_Haeckel.jpg"], "links": ["1854 Broad Street cholera outbreak", "Abiogenesis", "Academic clinical trials", "Accelerated failure time model", "Accuracy and precision", "Actuarial science", "Adaptation", "Adaptive clinical trial", "Age adjustment", "Akaike information criterion", "American Journal of Epidemiology", "Analysis of clinical trials", "Analysis of covariance", "Analysis of variance", "Anatomy", "Anderson Gray McKendrick", "Anderson\u2013Darling test", "Animal testing", "Animal testing on non-human primates", "Annals of Epidemiology", "Antiseptics", "Antonie van Leeuwenhoek", "Arithmetic mean", "Astrobiology", "Asymptomatic carrier", "Asymptotic theory (statistics)", "Atom", "Attributable fraction among the exposed", "Attributable fraction for the population", "Austin Bradford Hill", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Auxology", "Bachelor of Medicine and Surgery", "Bachelor of Science in Public Health", "Bar chart", "Basic research", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavior change (public health)", "Behavioural change theories", "Bias of an estimator", "Binomial regression", "Biochemistry", "Biocoenosis", "Biodiversity", "Biogeography", "Biohistory", "Bioinformatics", "Biological anthropology", "Biological classification", "Biological hazard", "Biological interaction", "Biological organisation", "Biological system", "Biology", "Biomarker", "Biomechanics", "Biomolecular complex", "Biomolecule", "Biomonitoring", "Biophysics", "Biosphere", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bloomberg School of Public Health", "Bootstrapping (statistics)", "Botany", "Box plot", "Box\u2013Jenkins method", "Bradford Hill criteria", "Breusch\u2013Godfrey test", "British Doctors Study", "British Medical Journal", "Broadwick Street", "Caerphilly Heart Disease Study", "Cancer", "Cancer Causes & Control", "Canonical correlation", "Carbohydrate", "Cardiovascular disease", "Carl Rogers Darnall", "Cartography", "Case-control study", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Categorical variable", "Causal inference", "Cell (biology)", "Cell biology", "Cell signaling", "Cell theory", "Cellular microbiology", "Census", "Centers for Disease Control and Prevention", "Central limit theorem", "Central tendency", "Centre for Research on the Epidemiology of Disasters (CRED)", "Chemical biology", "Chemical compound", "Chemometrics", "Chi-squared test", "Chief Medical Officer", "Child mortality", "Chronobiology", "Clinical Epidemiology", "Clinical Epidemiology (journal)", "Clinical endpoint", "Clinical epidemiology", "Clinical research", "Clinical study design", "Clinical surveillance", "Clinical trial", "Clinical trials", "Cluster (epidemiology)", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cognitive biology", "Cognitive epidemiology", "Cohen's kappa", "Cohort studies", "Cohort study", "Cointegration", "Community (ecology)", "Community health", "Completeness (statistics)", "Computational biology", "Computational epidemiology", "Confidence interval", "Conflict epidemiology", "Confounding", "Conservation biology", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlation does not imply causation", "Correlogram", "Council on Education for Public Health", "Count data", "Credible interval", "Crime statistics", "Critical community size", "Cross-correlation", "Cross-sectional study", "Cross-validation (statistics)", "Cultural competence in health care", "Cumulative incidence", "Cytogenetics", "Data collection", "David Clayton", "De contagione et contagiosis morbis", "Death", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Developmental biology", "Deviance (sociology)", "Diabetes", "Diagnosis", "Dickey\u2013Fuller test", "Diffusion of innovations", "Digital object identifier", "Disease diffusion mapping", "Disease informatics", "Disease surveillance", "Divergence (statistics)", "Doctor of Clinical Practice", "Doctor of Medicine", "Doctor of Nursing Practice", "Doctor of Osteopathic Medicine", "Doctor of Pharmacy", "Doctor of Philosophy", "Doctor of Physical Therapy", "Doctor of Podiatric Medicine", "Doctor of Public Health", "Doctor of Science", "Doctor of Social Work", "Doctor of Veterinary Medicine", "Durbin\u2013Watson statistic", "E-epidemiology", "Earliest known life forms", "Ecological niche", "Ecological study", "Ecology", "Econometrics", "Economic epidemiology", "Ecosystem", "Ecosystem ecology", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Embryology", "Emergency sanitation", "Emerging Themes in Epidemiology", "Empirical distribution function", "Endemic (epidemiology)", "Energy", "Engineering", "Engineering statistics", "Environmental epidemiology", "Environmental health", "Environmental statistics", "Enzyme", "Epidemic", "Epidemic model", "Epidemiological Transition", "Epidemiological methods", "Epidemiological study", "Epidemiology (disambiguation)", "Epidemiology (journal)", "Epidemiology and Infection", "Epidemiology of HIV/AIDS", "Epidemiology of asthma", "Epidemiology of attention deficit hyperactive disorder", "Epidemiology of autism", "Epidemiology of bed bugs", "Epidemiology of binge drinking", "Epidemiology of breast cancer", "Epidemiology of cancer", "Epidemiology of child psychiatric disorders", "Epidemiology of childhood obesity", "Epidemiology of depression", "Epidemiology of diabetes mellitus", "Epidemiology of domestic violence", "Epidemiology of herpes simplex", "Epidemiology of leprosy", "Epidemiology of malnutrition", "Epidemiology of motor vehicle collisions", "Epidemiology of obesity", "Epidemiology of periodontal diseases", "Epidemiology of pneumonia", "Epidemiology of representations", "Epidemiology of schizophrenia", "Epidemiology of snakebites", "Epidemiology of suicide", "Epidemiology of syphilis", "Epidemiology of tuberculosis", "Epigenetics", "Epizoology", "Epizootiology", "Errors and residuals in statistics", "Estimating equations", "Etiology", "European Centre for Disease Prevention and Control", "European Journal of Epidemiology", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Evidence-based medicine", "Evidence-based practice", "Evolution", "Evolutionary biology", "Evolutionary developmental biology", "Experiment", "Experimental epidemiology", "Exponential family", "Exponential smoothing", "Exposome", "Exposure Assessment", "Exposure assessment", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Family planning", "Fan chart (statistics)", "Fecal\u2013oral route", "First-hitting-time model", "First-in-man study", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Forensic epidemiology", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Freshwater biology", "Friedman test", "Function (biology)", "G-test", "Galen", "Gene flow", "General linear model", "Generalized linear model", "Genetic Epidemiology (journal)", "Genetic drift", "Genetic epidemiology", "Genetically modified food", "Genetics", "Genome-wide association study", "Genomics", "Geobiology", "Geographic information system", "Geometric mean", "Geostatistics", "Germ theory of disease", "Girolamo Fracastoro", "Global health", "Globalization and disease", "Glossary of biology", "Glossary of botanical terms", "Glossary of clinical research", "Glossary of ecology", "Glossary of plant morphology", "Glossary of rhetorical terms", "Good agricultural practice", "Good manufacturing practice", "Goodness of fit", "Granger causality", "Graphical model", "Great Plague of London", "Greek, Modern language", "Grouped data", "HACCP", "Haberdasher", "Habitat", "Hand washing", "Harmonic mean", "Hazard ratio", "Health Protection Agency", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health informatics", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Hepatitis C", "Heteroscedasticity", "Hippocrates", "Hispanic paradox", "Histogram", "Histology", "History of emerging infectious diseases", "Hodges\u2013Lehmann estimator", "Homeostasis", "Homoscedasticity", "Human biology", "Human factors and ergonomics", "Human nutrition", "Humorism", "Hungary", "Hygiene", "ISO 22000", "Iceland", "Ignaz Semmelweis", "Immunology", "In vitro", "In vivo", "Incidence (epidemiology)", "Index of dispersion", "Infant mortality", "Infection control", "Infections", "Infectious disease", "Infectivity", "Inference", "Information bias (epidemiology)", "Injury prevention", "Integrated Authority File", "Intention-to-treat analysis", "Interaction (statistics)", "Internal validity", "International Journal of Epidemiology", "International Society for Pharmacoepidemiology", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Janet Lane-Claypon", "Jarque\u2013Bera test", "Johansen test", "John Graunt", "John Snow (physician)", "Johns Hopkins University", "Jonckheere's trend test", "Joseph Lister", "Joseph Lister, 1st Baron Lister", "Journal of Clinical Epidemiology", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Life course approach", "Life science", "Life tables", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratios in diagnostic testing", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Lipid", "Lipidology", "List of clinical research topics", "List of epidemics", "List of fields of application of statistics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Logos", "London", "Longitudinal study", "Loss function", "Louis Pasteur", "Lp space", "Lung cancer", "M-estimator", "Macroevolution", "Macromolecule", "Mann\u2013Whitney U test", "Margaret Sanger", "Marine biology", "Mary Mallon", "Master of Public Health", "Master of Science", "Maternal health", "Mathematical and theoretical biology", "Mathematical modelling in epidemiology", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical Microbiology", "Medical anthropology", "Medical sociology", "Medical statistics", "Medicine", "Meiosis", "Mendelian randomization", "Mental health", "Meta-analysis", "Metabolism", "Method of moments (statistics)", "Methodology", "Methods engineering", "Miasma theory of disease", "Microbiology", "Microevolution", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Ministry of Health and Family Welfare", "Miquel Porta", "Missing data", "Mitosis", "Mixed model", "Mode (statistics)", "Model selection", "Molecular biology", "Molecular epidemiology", "Molecular pathological epidemiology", "Molecular pathology", "Molecule", "Moment (mathematics)", "Monotone likelihood ratio", "Morbidity", "Mortality rate", "Multicenter trial", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Mutation", "Mycology", "M\u00e9decins Sans Fronti\u00e8res", "Nanobiotechnology", "National Archives and Records Administration", "National Center for Biotechnology Information", "National Diet Library", "National accounts", "Natural experiment", "Natural selection", "Nelson\u2013Aalen estimator", "Neonatal tetanus", "Neontology", "Nested case\u2013control study", "Neuroepidemiology", "Neuroscience", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Notifiable disease", "Nucleic acid", "Null result", "Number needed to harm", "Number needed to treat", "Nutrition", "Nutritional epidemiology", "Obesity", "Observational study", "Occupational Health Science", "Occupational epidemiology", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Odds ratio", "Official statistics", "One- and two-tailed tests", "Open-label trial", "Open defecation", "Opinion poll", "Optimal decision", "Optimal design", "Oral hygiene", "Order statistic", "Ordinary least squares", "Organ (anatomy)", "Organelle", "Organic chemistry", "Organism", "Outbreak", "Outline of statistics", "Oxford University Press", "PRECEDE-PROCEED model", "Paleoepidemiology", "Paleontology", "Parametric statistics", "Parasitology", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pathogenesis", "Pathology", "Patient safety", "Patient safety organization", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Peer review", "Percentile", "Period prevalence", "Permutation test", "Peter Anton Schleisner", "Pharmaceutical policy", "Pharmacoepidemiology", "Pharmacology", "Pharmacovigilance", "Photosynthesis", "Phylogenetics", "Physiology", "Pie chart", "Pivotal quantity", "Plant disease epidemiology", "Plug-in principle", "Point estimation", "Point prevalence", "Poisson regression", "Population", "Population (statistics)", "Population Impact Measures", "Population ecology", "Population groups in biomedicine", "Population health", "Population statistics", "Positive deviance", "Post-transcriptional modification", "Posterior probability", "Power (statistics)", "Pre- and post-test probability", "Precision medicine", "Prediction interval", "Prevalence", "Prevalence of mental disorders", "Prevalence of teenage pregnancy", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Preventive Medicine (journal)", "Preventive healthcare", "Preventive nutrition", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Proceedings of the Royal Society of Medicine", "Professional degrees of public health", "Proportional hazards model", "Prospective cohort study", "Protein", "Protocol (science)", "Psychiatric epidemiology", "Psychology", "Psychometrics", "PubMed Central", "PubMed Identifier", "Public Health Agency of Canada", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Publicly funded health care", "Pulse oximeter", "Quality control", "Quantum biology", "Quarantine", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "ROC curve", "Race and health", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recall bias", "Regression analysis", "Regression model validation", "Regulation of gene expression", "Relative risk", "Relative risk reduction", "Reliability engineering", "Replication (statistics)", "Reproducibility", "Reproduction", "Reproductive health", "Resampling (statistics)", "Resource (biology)", "Retrospective cohort study", "Richard Doll", "Risk difference", "Risk factor", "Risk ratio", "Risk\u2013benefit ratio", "Robust regression", "Robust statistics", "Ronald Ross", "Run chart", "Safe sex", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling error", "Samuel Jay Crumbine", "Sander Greenland", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Screening (medicine)", "Seasonal adjustment", "Seeding trial", "Selection bias", "Semiparametric regression", "Sexually transmitted infection", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smallpox", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social epidemiology", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Social science", "Social statistics", "Sociobiology", "Sociology of health and illness", "Spatial analysis", "Spatial epidemiology", "Spearman's rank correlation coefficient", "Speciation", "Specificity and sensitivity", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical analysis", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Stress (medicine)", "Structural biology", "Structural break", "Structural equation modeling", "Student's t-test", "Study design", "Study of Health in Pomerania", "Sufficient statistic", "Surveillance", "Survey methodology", "Survival analysis", "Survival function", "Survivorship bias", "Syndemic", "Synthetic biology", "System identification", "Systematic review", "Systematics", "Systems biology", "Targeted Immunization Strategies", "Taxonomy (biology)", "Tele-epidemiology", "Teratology", "Theory of planned behavior", "Thomas Sydenham", "Time domain", "Time series", "Tissue (biology)", "Tobacco smoking", "Tolerance interval", "Toxicology", "Transmission (medicine)", "Transtheoretical model", "Trend estimation", "Tropical disease", "U-statistic", "Uniformly most powerful test", "United States Public Health Service", "Universities", "V-statistic", "Vaccination", "Vaccine trial", "Variance", "Vector autoregression", "Vector control", "Verona", "Vestmanna Islands", "Virology", "Virophysics", "Virulence", "Wald test", "Waterborne diseases", "Wavelet", "Wayback Machine", "Whitehall Study", "Whittle likelihood", "Wilcoxon signed-rank test", "World Health Organization", "World Toilet Organization", "Wu Youke", "Z-test", "Zoology", "Zoonoses"], "references": ["http://www.cred.be", "http://www.cjeb.ca/", "http://www.epidemiology.ch/history/PDF%20bg/Sackett%20DL%201979%20bias%20in%20analytic%20research.pdf", "http://www.epidemiology.ch/history/PeopleEpidemiologyLibrary.html", "http://www.epidemiology.ch/history/papers/SPM%2047(6)%20359-65%20Paneth%20et%20al.%20_%20Part%202.pdf", "http://baike.baidu.com/view/143117.htm", "http://www.biostatsresearch.com/repository/", "http://www.blackwellpublishing.com/journal.asp?ref=0269-5022", "http://jech.bmj.com", "http://www.bmj.com/about-bmj/resources-readers/publications/epidemiology-uninitiated", "http://2006.confex.com/uicc/uicc/techprogram/P7935.HTM", "http://www.duncan-associates.com/changing_concepts.pdf", "http://www.edwardtufte.com/tufte/hill", "http://www.epi-perspectives.com", "http://www.epi-perspectives.com/content/1/1/3", "http://www.epidem.com", "http://www.epidemiologicalnews.com", "http://www.ete-online.com/content/4/1/10", "http://samples.jbpub.com/9780763766221/66221_CH02_5398.pdf", "http://www.jsi.com/JSIInternet/About/snow.cfm", "http://global.oup.com/academic/product/a-dictionary-of-epidemiology-9780199976737?cc=us&lang=en", "http://www.riskanalytica.com/?q=node/70", "http://www.riskanalytica.com/?q=node/73", "http://www.riskanalytica.com/sites/riskanalytica.com/files/Canadian%20Cancer%20Abstract%2010%20June%202005.pdf", "http://statprob.com/encyclopedia/AndersonGrayMcKENDRICK.html", "http://eu.wiley.com/WileyCDA/WileyTitle/productCd-PDS.html", "http://krieger.jhu.edu/publichealth/", "http://www.ph.ucla.edu/epi/snow/fatherofepidemiology.html", "http://www.ph.ucla.edu/epi/snow/importance.html", "http://open.umich.edu/education/med/oernetwork/public-health/epidemiology/intro-epidemiology/2010", "http://ftp.ieg.csic.es/workshop/pdf/olofpaper.pdf", "http://dceg.cancer.gov/", "http://www.fjc.gov/public/pdf.nsf/lookup/sciman06.pdf/$file/sciman06.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1898525", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2841039", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3040598", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3492839", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3531829", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3571252", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3637979", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3678320", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3712261", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4002264", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC524370", "http://www.ncbi.nlm.nih.gov/pubmed/14283879", "http://www.ncbi.nlm.nih.gov/pubmed/15308962", "http://www.ncbi.nlm.nih.gov/pubmed/15507128", "http://www.ncbi.nlm.nih.gov/pubmed/20208016", "http://www.ncbi.nlm.nih.gov/pubmed/21036793", "http://www.ncbi.nlm.nih.gov/pubmed/21490505", "http://www.ncbi.nlm.nih.gov/pubmed/22056543", "http://www.ncbi.nlm.nih.gov/pubmed/22310693", "http://www.ncbi.nlm.nih.gov/pubmed/22522846", "http://www.ncbi.nlm.nih.gov/pubmed/22845482", "http://www.ncbi.nlm.nih.gov/pubmed/23230187", "http://www.ncbi.nlm.nih.gov/pubmed/23307060", "http://www.ncbi.nlm.nih.gov/pubmed/24001676", "http://www.ncbi.nlm.nih.gov/pubmed/30047858", "http://apps.who.int/medicinedocs/en/d/Js6170e/4.html", "http://www.who.int/topics/epidemiology/en/", "http://cebp.aacrjournals.org", "http://www.annualreviews.org/doi/full/10.1146/annurev.publhealth.22.1.189", "http://doi.org/10.1001%2Fjama.2013.280927", "http://doi.org/10.1001%2Fjama.2013.281501", "http://doi.org/10.1016%2Fj.bbcan.2011.10.005", "http://doi.org/10.1016%2Fj.hisfam.2009.08.004", "http://doi.org/10.1016%2Fj.plipres.2013.08.005", "http://doi.org/10.1038%2Fmodpathol.2012.214", "http://doi.org/10.1038%2Fmodpathol.2012.62", "http://doi.org/10.1038%2Fnm.2572", "http://doi.org/10.1038%2Fnrclinonc.2012.137", "http://doi.org/10.1046%2Fj.1526-0992.1999.09922.x", "http://doi.org/10.1080%2F1059924x.2018.1448734", "http://doi.org/10.1093%2Faje%2Fkws226", "http://doi.org/10.1093%2Fjnci%2Fdjq031", "http://doi.org/10.1097%2F01.ede.0000135174.63482.43", "http://doi.org/10.1097%2FEDE.0b013e31821b506e", "http://doi.org/10.1098%2Frstb.2012.0193", "http://doi.org/10.1136%2Fgut.2010.217182", "http://doi.org/10.1146%2Fannurev.publhealth.22.1.189", "http://doi.org/10.1158%2F2159-8290.cd-12-0424", "http://doi.org/10.1186%2F1742-5573-1-3", "http://doi.org/10.1586%2Ferm.12.46", "http://www.eurosurveillance.org", "http://epirev.oxfordjournals.org", "http://rstb.royalsocietypublishing.org/content/368/1614/20120193", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Epidemiology", "http://www.worldcat.org/issn/1059-924X", "http://www.economics.soton.ac.uk/staff/aldrich/Hardy%20and%20Magnello.pdf", "http://www.hpa.org.uk", "https://books.google.com/?id=E-OZbEmPSTkC&pg=PA93#v=onepage", "https://books.google.com/?id=RMDBh6gw1_UC&pg=PA24#v=onepage", "https://books.google.com/books?id=6DD1FKq6fFoC&lpg=PA323&pg=PA323#v=onepage&q=mathematical%20methods%20were%20introduced%20into%20epidemiology%2020th%20century%20ross", "https://books.google.com/books?id=Hgnnhu1ym-8C&dq=Morabia,+Alfredo.+ed.+(2004)+A+History+of+Epidemiologic+Methods&printsec=frontcover&source=bn", "https://skydrive.live.com/?cid=ec4d1867f6389ec0&id=EC4D1867F6389EC0!183", "https://www.springer.com/public+health/book/978-3-7643-6818-0", "https://catalog.archives.gov/id/10636962", "https://www.ncbi.nlm.nih.gov/books/NBK7993/", "https://d-nb.info/gnd/4015016-1", "https://id.ndl.go.jp/auth/ndlna/00561888", "https://web.archive.org/web/20071104183725/http://vlab.infotech.monash.edu.au/simulations/cellular-automata/epidemic/", "https://web.archive.org/web/20080227143925/http://www.fjc.gov/public/pdf.nsf/lookup/sciman06.pdf/$file/sciman06.pdf", "https://web.archive.org/web/20080523185244/http://www.epi-perspectives.com/content/1/1/3", "https://web.archive.org/web/20110726171127/http://www.iea-europe.org/index.htm", "https://web.archive.org/web/20110801204104/https://open.umich.edu/education/med/oernetwork/public-health/epidemiology/intro-epidemiology/2010", "https://web.archive.org/web/20110822114404/http://statprob.com/encyclopedia/AndersonGrayMcKENDRICK.html", "https://web.archive.org/web/20140202111153/http://www.riskanalytica.com/?q=node/73", "https://web.archive.org/web/20140202111300/http://www.riskanalytica.com/?q=node/70", "https://www.jstor.org/action/showPublication?journalCode=infeconthospepid", "https://www.npr.org/templates/story/story.php?storyId=3935461", "https://www.wikidata.org/wiki/Q133805"]}, "Disattenuation": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "Covariance and correlation", "Measurement", "Psychometrics"], "title": "Correction for attenuation", "method": "Disattenuation", "url": "https://en.wikipedia.org/wiki/Correction_for_attenuation", "summary": "Correction for attenuation is a statistical procedure, due to Spearman (1904), to \"rid a correlation coefficient from the weakening effect of measurement error\" (Jensen, 1998), a phenomenon known as regression dilution. In measurement and statistics, the correction is also called disattenuation. The correction assures that the correlation across data units (for example, people) between two sets of variables is estimated in a manner that accounts for error contained within the measurement of those variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Charles Spearman", "Classical test theory", "Correlation", "Cronbach's alpha", "Digital object identifier", "Errors-in-variables model", "Geometric mean", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Measurement", "Measurement error", "PubMed Central", "PubMed Identifier", "Random variable", "Rasch model", "Rasch model estimation", "Regression dilution", "Reliability (statistics)", "Statistical population", "Statistical unit", "Statistics"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5440056", "http://www.ncbi.nlm.nih.gov/pubmed/28481885", "http://pareonline.net/getvn.asp?v=8&n=11", "http://doi.org/10.1371%2Fjournal.pcbi.1005535", "http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005535", "http://www.rasch.org/rmt/rmt101g.htm", "http://www.worldcat.org/issn/1553-7358", "https://www.jstor.org/stable/1412159"]}, "Catastro of Ensenada": {"categories": ["1749 in Europe", "18th century in Spain", "Population statistics"], "title": "Catastro of Ensenada", "method": "Catastro of Ensenada", "url": "https://en.wikipedia.org/wiki/Catastro_of_Ensenada", "summary": "In 1749 a large-scale census and statistical investigation was conducted in the Crown of Castile (15.000 places including Galicia and Andalusia, but not including the Basque provinces, Navarre or the Crown of Aragon). It included population, territorial properties, buildings, cattle, offices, all kinds of revenue and trades, and even geographical information from each place. It was encouraged by king Ferdinand VI of Spain and his minister the Marquis of Ensenada, and is known today as the Catastro of Ensenada.\nThe general answers of each place to the 40 questions of the Catastro produced a huge volume of documentation that affords historians an opportunity to analyze the economy, the society, the practices of the se\u00f1or\u00edo system (manorialism) and environmental data from 18th-century Spain. It is the best statistical register of the pre-statistical age of the Ancien R\u00e9gime in Europe.\nToday the word catastro means \u201cregister of the properties\u201d, but the etymology comes from \u201cenquire\u201d. In the 18th century there was a distinction between a catastro, which was made by central officers who traveled to the places to enquire, and the amillaramiento, which was made by local authorities.", "images": [], "links": ["Alcabala", "Ancien R\u00e9gime", "Basque Country (autonomous community)", "Capitalism", "Census", "Ciento", "Clergy", "Council of Castile", "Council of Indies", "Crown of Aragon", "Crown of Castile", "Esquilache Riots", "Ferdinand VI of Spain", "Feudalism", "Free trade", "French Revolution", "General Archive of Simancas", "International Standard Book Number", "Ja\u00e9n (Spanish province)", "Manorialism", "Marquis of Ensenada", "Mercantilism", "Military order (society)", "Millones", "Nobility", "Peninsular Spain", "Physiocratic", "Portable Document Format", "Se\u00f1or\u00edo", "Tercias reales", "Tithe", "Treasury"], "references": ["http://pares.mcu.es/Catastro/", "http://www.catastro.meh.es/esp/publicaciones1.asp#menu6", "https://books.google.com/books?id=6iBjNgAACAAJ"]}, "Stopped process": {"categories": ["Stochastic processes"], "title": "Stopped process", "method": "Stopped process", "url": "https://en.wikipedia.org/wiki/Stopped_process", "summary": "In mathematics, a stopped process is a stochastic process that is forced to assume the same value after a prescribed (possibly random) time.", "images": [], "links": ["Brownian motion", "Filtration (abstract algebra)", "Hitting time", "Killed process", "Mathematics", "Measurable space", "Probability space", "Roulette", "Stochastic process", "Stopping rule"], "references": []}, "Trend stationary": {"categories": ["All articles needing additional references", "Articles needing additional references from December 2010", "CS1 maint: Archived copy as title", "Pages with citations having bare URLs", "Pages with citations lacking titles", "Time series"], "title": "Trend stationary", "method": "Trend stationary", "url": "https://en.wikipedia.org/wiki/Trend_stationary", "summary": "In the statistical analysis of time series, a stochastic process is trend stationary if an underlying trend (function solely of time) can be removed, leaving a stationary process. The trend does not have to be linear.\nConversely, if the process requires differencing to be made stationary, then it is called difference stationary and possesses one or more unit roots. Those two concepts may sometimes be confused, but while they share many properties, they are different in many aspects. It is possible for a time series to be non-stationary, yet have no unit root and be trend-stationary. In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent impact on the mean (i.e. no convergence over time).", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Decomposition of time series", "Errors and residuals in statistics", "Exponential growth", "Gross domestic product", "Journal of Monetary Economics", "KPSS test", "Linear regression", "Log-linear modeling", "Natural logarithm", "Real number", "Stationary process", "Statistics", "Stochastic process", "Time series", "Trend estimation", "Unit root", "White noise"], "references": ["http://economics.about.com/od/economicsglossary/g/trends.htm", "http://www.wiso.uni-hamburg.de/fileadmin/wiso_vwl_iwk/paper/gdptrend.pdf", "http://www.econ.ku.dk/metrics/Econometrics2_05_II/Slides/08_unitroottests_2pp.pdf", "http://www.duke.edu/~rnau/411diff.htm", "http://pages.stern.nyu.edu/~churvich/Forecasting/Handouts/UnitRoot.pdf", "http://www.uh.edu/~dpapell/realgdp.pdf", "http://www.stats.ox.ac.uk/~burke/Autocorrelation/Non-Stationary%20Series.pdf", "https://web.archive.org/web/20110708110539/http://www.wiso.uni-hamburg.de/fileadmin/wiso_vwl_iwk/paper/gdptrend.pdf"]}, "Observational study": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2010", "CS1 maint: Multiple names: authors list", "Design of experiments", "Observational study", "Statistical data types"], "title": "Observational study", "method": "Observational study", "url": "https://en.wikipedia.org/wiki/Observational_study", "summary": "In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws inferences from a sample to a population where the independent variable is not under the control of the researcher because of ethical concerns or logistical constraints. One common observational study is about the possible effect of a treatment on subjects, where the assignment of subjects into a treated group versus a control group is outside the control of the investigator. This is in contrast with experiments, such as randomized controlled trials, where each subject is randomly assigned to a treated group or a control group.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abortion \u2013 breast cancer hypothesis", "Academic clinical trials", "Accelerated failure time model", "Actuarial science", "Adaptive clinical trial", "Akaike information criterion", "Analysis of clinical trials", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Animal testing", "Animal testing on non-human primates", "Arithmetic mean", "Asymptotic theory (statistics)", "Attributable fraction among the exposed", "Attributable fraction for the population", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Case-control study", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochrane Collaboration", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort study", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Control group", "Correlation and dependence", "Correlation does not imply causation", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-sectional study", "Cross-validation (statistics)", "Cumulative incidence", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Difference-in-differences", "Digital object identifier", "Divergence (statistics)", "Doug Altman", "Durbin\u2013Watson statistic", "Ecological study", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiological methods", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Ethics", "Evidence-based medicine", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "First-in-man study", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of clinical research", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hazard ratio", "Healthcare", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "In vitro", "In vivo", "Incidence (epidemiology)", "Index of dispersion", "Infectivity", "Instrumental variable", "Intention-to-treat analysis", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratios in diagnostic testing", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of clinical research topics", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Longitudinal study", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Matching (statistics)", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Meta-analysis", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Morbidity", "Mortality rate", "Multicenter trial", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Center for Complementary and Integrative Health", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nested case\u2013control study", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null result", "Number needed to harm", "Number needed to treat", "Odds ratio", "Official statistics", "One- and two-tailed tests", "Open-label trial", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Panel analysis", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Period prevalence", "Permutation test", "Peter C. G\u00f8tzsche", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Point prevalence", "Poisson regression", "Population (statistics)", "Population Impact Measures", "Population statistics", "Posterior probability", "Power (statistics)", "Pre- and post-test probability", "Prediction interval", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Propensity score matching", "Proportional hazards model", "Prospective cohort study", "Protocol (science)", "Psychology", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quantitative research", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression discontinuity", "Regression model validation", "Relative risk reduction", "Reliability engineering", "Replication (statistics)", "Reproducibility", "Resampling (statistics)", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Seeding trial", "Selection bias", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smoking ban", "Social science", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Specificity and sensitivity", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Strengthening the reporting of observational studies in epidemiology", "Structural break", "Structural equation modeling", "Stuart Pocock", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Survivorship bias", "System identification", "Systematic review", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Vaccine trial", "Variance", "Vector autoregression", "Virulence", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://nccih.nih.gov/research/blog/observational-secondary", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2020495", "http://www.ncbi.nlm.nih.gov/pubmed/17941714", "http://www.ncbi.nlm.nih.gov/pubmed/24782322", "http://www.itl.nist.gov/div898/handbook/", "http://doi.org/10.1002%2F14651858.MR000034.pub2", "http://doi.org/10.1371%2Fjournal.pmed.0040296", "http://www.strobe-statement.org", "https://web.archive.org/web/20160427111413/http://www.medicine.ox.ac.uk:80/bandolier/booth/glossary/observ.html"]}, "Maxwell speed distribution": {"categories": ["Continuous distributions", "Gases", "James Clerk Maxwell", "Normal distribution", "Pages using deprecated image syntax", "Particle distributions", "Wikipedia articles needing clarification from June 2018"], "title": "Maxwell\u2013Boltzmann distribution", "method": "Maxwell speed distribution", "url": "https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution", "summary": "In physics (in particular in statistical mechanics), the Maxwell\u2013Boltzmann distribution is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. \nIt was first defined and used for describing particle speeds in idealized gases, where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment. \nThe term \"particle\" in this context refers to gaseous particles only (atoms or molecules), and the system of particles is assumed to have reached thermodynamic equilibrium.\nThe energies of such particles follow what is known as Maxwell-Boltzmann statistics, and the statistical distribution of speeds is derived by equating particle energies with kinetic energy.\nMathematically, the Maxwell\u2013Boltzmann distribution is the chi distribution with three degrees of freedom (the components of the velocity vector in Euclidean space), with a scale parameter measuring speeds in units proportional to the square root of \n \n \n \n T\n \n /\n \n m\n \n \n {\\displaystyle T/m}\n (the ratio of temperature and particle mass).The Maxwell\u2013Boltzmann distribution is a result of the kinetic theory of gases, which provides a simplified explanation of many fundamental gaseous properties, including pressure and diffusion. \nThe Maxwell\u2013Boltzmann distribution applies fundamentally to particle velocities in three dimensions, but turns out to depend only on the speed (the magnitude of the velocity) of the particles. \nA particle speed probability distribution indicates which speeds are more likely: a particle will have a speed selected randomly from the distribution, and is more likely to be within one range of speeds than another.\nThe kinetic theory of gases applies to the classical ideal gas, which is an idealization of real gases. In real gases, there are various effects (e.g., van der Waals interactions, vortical flow, relativistic speed limits, and quantum exchange interactions) that can make their speed distribution different from the Maxwell\u2013Boltzmann form. \nHowever, rarefied gases at ordinary temperatures behave very nearly like an ideal gas and the Maxwell speed distribution is an excellent approximation for such gases. \nIdeal plasmas, which are ionized gases of sufficiently low density, frequently also have particle distributions that are partially or entirely Maxwellian.The distribution was first derived by Maxwell in 1860 on heuristic grounds. \nBoltzmann later, in the 1870s, carried out significant investigations into the physical origins of this distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/98/Maxwell-Boltzmann_distribution_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/1/19/Maxwell-Boltzmann_distribution_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/0/01/MaxwellBoltzmann-en.svg"], "links": ["ARGUS distribution", "Adiabatic index", "Air", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Atmospheric chemistry", "Atoms", "Avogadro constant", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Boltzmann's constant", "Boltzmann constant", "Boltzmann distribution", "Boltzmann factor", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Collision", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Darwin\u2013Fowler method", "Davis distribution", "Degenerate distribution", "Degrees of freedom", "Delaporte distribution", "Derivative", "Diffusion", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Equipartition theorem", "Erlang distribution", "Error function", "Euclidean space", "Ewens's sampling formula", "Excess kurtosis", "Exchange interaction", "Expectation value", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gas constant", "Gas in a box", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "H-theorem", "Half-logistic distribution", "Half-normal distribution", "Harald J. W. Mueller-Kirsten", "Heat capacity", "Helium", "Holtsmark distribution", "Hotelling's T-squared distribution", "Humidity", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Ideal gas", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "James Clerk Maxwell", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kinetic energy", "Kinetic theory of gases", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Ludwig Boltzmann", "L\u00e9vy distribution", "Magnitude (mathematics)", "Marchenko\u2013Pastur distribution", "Mathworld", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell-Boltzmann statistics", "Maxwell\u2013Boltzmann statistics", "Maxwell\u2013J\u00fcttner distribution", "Microstate (statistical mechanics)", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Molecule", "Molecules", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noble gas", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normalizing constant", "Ordinary differential equation", "Oxygen", "Parabolic fractal distribution", "Pareto distribution", "Partition function (statistical mechanics)", "Pearson distribution", "Phase-type distribution", "Physics", "Plasma (physics)", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Pressure", "Probability density function", "Probability distribution", "Proportionality (mathematics)", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantum Boltzmann equation", "Quantum mechanics", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rarefied", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Room temperature", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Special relativity", "Specific heat", "Speed", "Speed of sound", "Spherical coordinate system", "Spherical coordinates", "Stable distribution", "Statistical mechanics", "Statistical thermodynamics", "Student's t-distribution", "Support (mathematics)", "Thermodynamic equilibrium", "Thermodynamic temperature", "Tracy\u2013Widom distribution", "Translation (physics)", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Van der Waals interaction", "Variance", "Variance-gamma distribution", "Velocity", "Voigt profile", "Volume element", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Vortex", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "World Scientific", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://demonstrations.wolfram.com/TheMaxwellSpeedDistribution/", "http://adsabs.harvard.edu/abs/2017SHPMP..57...53G", "http://arxiv.org/abs/1702.01411", "http://doi.org/10.1016%2Fj.shpsb.2017.01.001", "https://books.google.com/books?id=6C0R1qpAk7EC&pg=SA2-PA278", "https://books.google.com/books?id=HLxV-IKYO5IC&pg=PA352", "https://books.google.com/books?id=QF6iMewh4KMC", "https://books.google.com/books?id=QF6iMewh4KMC&pg=PA434", "https://www.biodiversitylibrary.org/item/20012#page/37/mode/1up", "https://www.biodiversitylibrary.org/item/53795#page/33/mode/1up"]}, "Simulated annealing": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from December 2009", "Articles with inconsistent citation formats", "Articles with unsourced statements from June 2011", "Metaheuristics", "Monte Carlo methods", "Optimization algorithms and methods"], "title": "Simulated annealing", "method": "Simulated annealing", "url": "https://en.wikipedia.org/wiki/Simulated_annealing", "summary": "Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to alternatives such as gradient descent.\nThe name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. Both are attributes of the material that depend on its thermodynamic free energy. Heating and cooling the material affects both the temperature and the thermodynamic free energy.\nThe simulation of annealing can be used to find an approximation of a global minimum for a function with a large number of variables.This notion of slow cooling implemented in the simulated annealing algorithm is interpreted as a slow decrease in the probability of accepting worse solutions as the solution space is explored. Accepting worse solutions is a fundamental property of metaheuristics because it allows for a more extensive search for the global optimal solution. In general, the simulated annealing algorithms work as follows. At each time step, the algorithm randomly selects a solution close to the current one, measures its quality, and then decides to move to it or to stay with the current solution based on either one of two probabilities between which it chooses on the basis of the fact that the new solution is better or worse than the current one. During the search, the temperature is progressively decreased from an initial positive value to zero and affects the two probabilities: at each step, the probability of moving to a better new solution is either kept to 1 or is changed towards a positive value; instead, the probability of moving to a worse new solution is progressively changed towards zero.\nThe simulation can be performed either by a solution of kinetic equations for density functions or by using the stochastic sampling method. The method is an adaptation of the Metropolis\u2013Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, published by N. Metropolis et al. in 1953.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/Hill_Climbing_with_Simulated_Annealing.gif", "https://upload.wikimedia.org/wikipedia/commons/8/82/SimulatedAnnealingFast.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/8d/SimulatedAnnealingSlow.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/10/Travelling_salesman_problem_solved_with_simulated_annealing.gif", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Adaptive simulated annealing", "Amorphous solid", "Annealing (metallurgy)", "Ant colony optimization", "ArXiv", "Automatic label placement", "Bibcode", "Brute-force search", "Colour", "Combinatorial optimization", "Constraint satisfaction", "Convex programming", "Cross-entropy method", "Crystalline solid", "Digital object identifier", "Drainage basin", "Dual-phase evolution", "Function (mathematics)", "Genetic algorithms", "Global optimization", "Global optimum", "Gradient descent", "Graduated optimization", "Graph cuts in computer vision", "Greedy algorithm", "Hamiltonian (quantum mechanics)", "Harmony search", "Heuristic", "Hill climbing", "Hill climbing algorithm", "Infinite-dimensional optimization", "Integer programming", "Intelligent water drops algorithm", "Internal energy", "International Standard Book Number", "JSTOR", "LIONsolver", "Local optimum", "Markov chain", "Metaheuristic", "Metropolis\u2013Hastings algorithm", "Molecular dynamics", "Monte Carlo method", "Multidisciplinary optimization", "Multiobjective optimization", "Nicholas Metropolis", "Nonlinear programming", "Optimization (mathematics)", "Optimization problem", "Parallel tempering", "Particle filter", "Particle swarm optimization", "Permutation", "Physical system", "Pixel", "Place and route", "Potential energy", "Probabilistic", "Probabilistic algorithm", "Procedural parameter", "PubMed Central", "PubMed Identifier", "Quadratic programming", "Quantum annealing", "Robust optimization", "Solution space", "State transition", "Steepest descent", "Stochastic gradient descent", "Stochastic optimization", "Stochastic programming", "Stochastic tunneling", "Tabu search", "Thermodynamic equilibrium", "Thermodynamic state", "Traveling salesman problem", "Travelling salesman problem", "Uniform distribution (continuous)"], "references": ["http://www.foibg.com/ijita/vol01-09/ijita-fv06.htm", "http://www.heatonresearch.com/aifh/vol1/tsp_anneal.html", "http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=10548&objectType=file", "http://apps.nrbook.com/empanel/index.html#pg=549", "http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9868.2006.00553.x/abstract", "http://adsabs.harvard.edu/abs/1953JChPh..21.1087M", "http://adsabs.harvard.edu/abs/1981AcCrA..37..742K", "http://adsabs.harvard.edu/abs/1983Sci...220..671K", "http://adsabs.harvard.edu/abs/2003PhLA..317..415D", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4912009", "http://www.ncbi.nlm.nih.gov/pubmed/17813860", "http://www.ncbi.nlm.nih.gov/pubmed/27150349", "http://arxiv.org/abs/cond-mat/0212648", "http://doi.org/10.1007%2FBF00202749", "http://doi.org/10.1007%2FBF00940812", "http://doi.org/10.1016%2Fj.physleta.2003.08.070", "http://doi.org/10.1016%2Fj.ympev.2016.05.001", "http://doi.org/10.1063%2F1.1699114", "http://doi.org/10.1107%2FS0108767385000563", "http://doi.org/10.1107%2FS0567739481001630", "http://doi.org/10.1109%2F34.295910", "http://doi.org/10.1111%2Fj.1467-9868.2006.00553.x", "http://doi.org/10.1126%2Fscience.220.4598.671", "http://www.jstor.org/stable/1690046", "https://arstechnica.com/science/news/2009/12/uncertainty-hovers-over-claim-googles-using-quantum-computer.ars"]}, "Balance equation": {"categories": ["Articles with inconsistent citation formats", "Queueing theory"], "title": "Balance equation", "method": "Balance equation", "url": "https://en.wikipedia.org/wiki/Balance_equation", "summary": "In probability theory, a balance equation is an equation that describes the probability flux associated with a Markov chain in and out of states or set of states.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival theorem", "BCMP network", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Cambridge University Press", "Chemical equation", "Continuous-time Markov chain", "Continuous time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Detailed balance", "Digital object identifier", "Discrete time Markov chains", "Equation", "Equilibrium distribution", "Erlang (unit)", "Erlang distribution", "Erol Gelenbe", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "Frank Kelly (mathematician)", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "International Standard Book Number", "JSTOR", "Jackson network", "James R. Norris", "K.M. Chandy", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markov chain", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Peter G. Harrison", "Peter Whittle (mathematician)", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations", "Transition rate matrix"], "references": ["http://www.springerlink.com/content/g013851405418642/", "http://portal.acm.org/citation.cfm?id=322009", "http://doi.org/10.1007/bf02033315", "http://doi.org/10.1145/321879.321887", "http://doi.org/10.1145/322003.322009", "http://doi.org/10.1287/opre.46.6.927", "http://doi.org/10.2307/3211921", "http://doi.org/10.2307/3214781", "http://www.jstor.org/stable/222945", "http://www.jstor.org/stable/3211921", "http://www.jstor.org/stable/3214781", "http://www.statslab.cam.ac.uk/~frank/BOOKS/kelly_book.html", "http://www.statslab.cam.ac.uk/~james/Markov/"]}, "Equiprobable": {"categories": ["All articles lacking sources", "All articles needing expert attention", "Articles lacking sources from August 2009", "Articles needing expert attention from February 2009", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Philosophy articles needing expert attention", "Philosophy of statistics", "Probability interpretations", "Statistics articles needing expert attention"], "title": "Equiprobability", "method": "Equiprobable", "url": "https://en.wikipedia.org/wiki/Equiprobability", "summary": "Equiprobability is a property for a collection of events that each have the same probability of occurring. In statistics and probability theory it is applied in the discrete uniform distribution and the equidistribution theorem for rational numbers. If there are \n \n \n \n n\n \n \n {\\textstyle n}\n events under consideration, the probability of each occurring is \n \n \n \n \n \n 1\n n\n \n \n .\n \n \n {\\textstyle {\\frac {1}{n}}.}\n \nIn philosophy it corresponds to a concept that allows one to assign equal probabilities to outcomes when they are judged to be equipossible or to be \"equally likely\" in some sense. The best-known formulation of the rule is Laplace's principle of indifference (or principle of insufficient reason), which states that, when \"we have no other information than\" that exactly \n \n \n \n N\n \n \n {\\displaystyle N}\n mutually exclusive events can occur, we are justified in assigning each the probability \n \n \n \n \n \n 1\n N\n \n \n .\n \n \n {\\textstyle {\\frac {1}{N}}.}\n This subjective assignment of probabilities is especially justified for situations such as rolling dice and lotteries since these experiments carry a symmetry structure, and one's state of knowledge must clearly be invariant under this symmetry.\nA similar argument could lead to the seemingly absurd conclusion that the sun is as likely to rise as to not rise tomorrow morning. However, the conclusion that the sun is equally likely to rise as it is to not rise is only absurd when additional information is known, such as the laws of gravity and the sun's history. Similar applications of the concept are effectively instances of circular reasoning, with \"equally likely\" events being assigned equal probabilities, which means in turn that they are equally likely. Despite this, the notion remains useful in probabilistic and statistical modeling.\nIn Bayesian probability, one needs to establish prior probabilities for the various hypotheses before applying Bayes' theorem. One procedure is to assume that these prior probabilities have some symmetry which is typical of the experiment, and then assign a prior which is proportional to the Haar measure for the symmetry group: this generalization of equiprobability is known as the principle of transformation groups and leads to misuse of equiprobability as a model for incertitude.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["A priori probability", "Aequiprobabilism", "Bayes' theorem", "Bayesian probability", "Circular reasoning", "Dice", "Discrete uniform distribution", "Epistemic probability", "Equidistribution theorem", "Equipossible", "Haar measure", "Information content", "Information gain", "Invariant (mathematics)", "Laplace", "Laplacian smoothing", "Lottery", "Mutually exclusive", "Philosophy", "Principle of indifference", "Principle of transformation groups", "Prior probabilities", "Probability", "Probability theory", "Scientific modelling", "Statistics", "Subjective probability", "Symmetry group", "Uniform distribution (continuous)", "Uninformative prior"], "references": ["http://www.stats.org.uk/probability/classical.html"]}, "Normal variance-mean mixture": {"categories": ["Compound probability distributions", "Continuous distributions"], "title": "Normal variance-mean mixture", "method": "Normal variance-mean mixture", "url": "https://en.wikipedia.org/wiki/Normal_variance-mean_mixture", "summary": "In probability theory and statistics, a normal variance-mean mixture with mixing probability density \n \n \n \n g\n \n \n {\\displaystyle g}\n is the continuous probability distribution of a random variable \n \n \n \n Y\n \n \n {\\displaystyle Y}\n of the form\n\n \n \n \n Y\n =\n \u03b1\n +\n \u03b2\n V\n +\n \u03c3\n \n \n V\n \n \n X\n ,\n \n \n {\\displaystyle Y=\\alpha +\\beta V+\\sigma {\\sqrt {V}}X,}\n where \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n , \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n and \n \n \n \n \u03c3\n >\n 0\n \n \n {\\displaystyle \\sigma >0}\n are real numbers, and random variables \n \n \n \n X\n \n \n {\\displaystyle X}\n and \n \n \n \n V\n \n \n {\\displaystyle V}\n are independent, \n \n \n \n X\n \n \n {\\displaystyle X}\n is normally distributed with mean zero and variance one, and \n \n \n \n V\n \n \n {\\displaystyle V}\n is continuously distributed on the positive half-axis with probability density function \n \n \n \n g\n \n \n {\\displaystyle g}\n . The conditional distribution of \n \n \n \n Y\n \n \n {\\displaystyle Y}\n given \n \n \n \n V\n \n \n {\\displaystyle V}\n is thus a normal distribution with mean \n \n \n \n \u03b1\n +\n \u03b2\n V\n \n \n {\\displaystyle \\alpha +\\beta V}\n and variance \n \n \n \n \n \u03c3\n \n 2\n \n \n V\n \n \n {\\displaystyle \\sigma ^{2}V}\n . A normal variance-mean mixture can be thought of as the distribution of a certain quantity in an inhomogeneous population consisting of many different normal distributed subpopulations. It is the distribution of the position of a Wiener process (Brownian motion) with drift \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n and infinitesimal variance \n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n {\\displaystyle \\sigma ^{2}}\n observed at a random time point independent of the Wiener process and with probability density function \n \n \n \n g\n \n \n {\\displaystyle g}\n . An important example of normal variance-mean mixtures is the generalised hyperbolic distribution in which the mixing distribution is the generalized inverse Gaussian distribution.\nThe probability density function of a normal variance-mean mixture with mixing probability density \n \n \n \n g\n \n \n {\\displaystyle g}\n is\n\n \n \n \n f\n (\n x\n )\n =\n \n \u222b\n \n 0\n \n \n \u221e\n \n \n \n \n 1\n \n 2\n \u03c0\n \n \u03c3\n \n 2\n \n \n v\n \n \n \n exp\n \u2061\n \n (\n \n \n \n \u2212\n (\n x\n \u2212\n \u03b1\n \u2212\n \u03b2\n v\n \n )\n \n 2\n \n \n \n \n 2\n \n \u03c3\n \n 2\n \n \n v\n \n \n \n )\n \n g\n (\n v\n )\n \n d\n v\n \n \n {\\displaystyle f(x)=\\int _{0}^{\\infty }{\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}v}}}\\exp \\left({\\frac {-(x-\\alpha -\\beta v)^{2}}{2\\sigma ^{2}v}}\\right)g(v)\\,dv}\n and its moment generating function is\n\n \n \n \n M\n (\n s\n )\n =\n exp\n \u2061\n (\n \u03b1\n s\n )\n \n \n M\n \n g\n \n \n \n (\n \n \u03b2\n s\n +\n \n \n 1\n 2\n \n \n \n \u03c3\n \n 2\n \n \n \n s\n \n 2\n \n \n \n )\n \n ,\n \n \n {\\displaystyle M(s)=\\exp(\\alpha s)\\,M_{g}\\left(\\beta s+{\\frac {1}{2}}\\sigma ^{2}s^{2}\\right),}\n where \n \n \n \n \n M\n \n g\n \n \n \n \n {\\displaystyle M_{g}}\n is the moment generating function of the probability distribution with density function \n \n \n \n g\n \n \n {\\displaystyle g}\n , i.e.\n\n \n \n \n \n M\n \n g\n \n \n (\n s\n )\n =\n E\n \n (\n \n exp\n \u2061\n (\n s\n V\n )\n \n )\n \n =\n \n \u222b\n \n 0\n \n \n \u221e\n \n \n exp\n \u2061\n (\n s\n v\n )\n g\n (\n v\n )\n \n d\n v\n .\n \n \n {\\displaystyle M_{g}(s)=E\\left(\\exp(sV)\\right)=\\int _{0}^{\\infty }\\exp(sv)g(v)\\,dv.}", "images": [], "links": ["Conditional distribution", "Continuous probability distribution", "Generalised hyperbolic distribution", "Generalized inverse Gaussian distribution", "Independence (probability theory)", "Mixture density", "Moment generating function", "Normal-inverse Gaussian distribution", "Normal distribution", "Probability density function", "Probability theory", "Statistics", "Wiener process"], "references": []}, "Cross-sectional data": {"categories": ["Cross-sectional analysis", "Statistical data types"], "title": "Cross-sectional data", "method": "Cross-sectional data", "url": "https://en.wikipedia.org/wiki/Cross-sectional_data", "summary": "Cross-sectional data, or a cross section of a study population, in statistics and econometrics is a type of data collected by observing many subjects (such as individuals, firms, countries, or regions) at the same point of time, or without regard to differences in time. Analysis of cross-sectional data usually consists of comparing the differences among the subjects.\nFor example, if we want to measure current obesity levels in a population, we could draw a sample of 1,000 people randomly from that population (also known as a cross section of that population), measure their weight and height, and calculate what percentage of that sample is categorized as obese. This cross-sectional sample provides us with a snapshot of that population, at that one point in time. Note that we do not know based on one cross-sectional sample if obesity is increasing or decreasing; we can only describe the current proportion.\nCross-sectional data differs from time series data, in which the same small-scale or aggregate entity is observed at various points in time. Another type of data, panel data (or longitudinal data), combines both cross-sectional and time series data ideas and looks at how the subjects (firms, individuals, etc.) change over time. Panel data differs from pooled cross-sectional data across time, because it deals with the observations on the same subjects in different times whereas the latter observes different subjects in different time periods. Panel analysis uses panel data to examine changes in variables over time and differences in variables between the subjects.\nIn a rolling cross-section, both the presence of an individual in the sample and the time at which the individual is included in the sample are determined randomly. For example, a political poll may decide to interview 1000 individuals. It first selects these individuals randomly from the entire population. It then assigns a random date to each individual. This is the random date that the individual will be interviewed, and thus included in the survey.Cross-sectional data can be used in cross-sectional regression, which is regression analysis of cross-sectional data. For example, the consumption expenditures of various individuals in a fixed month could be regressed on their incomes, accumulated wealth levels, and their various demographic features to find out how differences in those features lead to differences in consumers\u2019 behavior.\n\n", "images": [], "links": ["Aggregate data", "Consumption (economics)", "Cross-sectional regression", "Cross-sectional study", "Data set", "Demographics", "Econometrics", "International Standard Book Number", "Panel analysis", "Panel data", "Regression analysis", "Statistics", "Study population", "Time series"], "references": ["http://www.press.umich.edu/pdf/0472099213-ch7.pdf"]}, "Beta function": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "Gamma and related functions", "Special hypergeometric functions", "Wikipedia articles with NDL identifiers"], "title": "Beta function", "method": "Beta function", "url": "https://en.wikipedia.org/wiki/Beta_function", "summary": "In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by\n\n \n \n \n \n B\n \n (\n x\n ,\n y\n )\n =\n \n \u222b\n \n 0\n \n \n 1\n \n \n \n t\n \n x\n \u2212\n 1\n \n \n (\n 1\n \u2212\n t\n \n )\n \n y\n \u2212\n 1\n \n \n \n d\n t\n \n \n {\\displaystyle \\mathrm {B} (x,y)=\\int _{0}^{1}t^{x-1}(1-t)^{y-1}\\,dt}\n for Re x > 0, Re y > 0.\nThe beta function was studied by Euler and Legendre and was given its name by Jacques Binet; its symbol \u0392 is a Greek capital beta rather than the similar Latin capital B or the Greek lowercase \u03b2.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4d/Beta_function_contour_plot.png", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Abramowitz and Stegun", "Adrien-Marie Legendre", "Analytic continuation", "B", "Beta-binomial distribution", "Beta (letter)", "Beta distribution", "Beta function", "Beta function (disambiguation)", "Binomial coefficient", "Binomial distribution", "Cartesian coordinates", "Computer algebra system", "Contour plot", "Convolution", "Cumulative distribution function", "Digamma function", "Digital Library of Mathematical Functions", "Dirichlet distribution", "Dover Publications", "Encyclopedia of Mathematics", "Euler integral (disambiguation)", "Factorial", "Frank W. J. Olver", "GNU Octave", "Gabriele Veneziano", "Gamma function", "Greek alphabet", "Incomplete gamma function", "International Standard Book Number", "Irene Stegun", "Jacobi sum", "Jacobian matrix and determinant", "Jacques Philippe Marie Binet", "Latin alphabet", "Leonhard Euler", "MATLAB", "Mathematica", "Mathematical Reviews", "Mathematics", "Michiel Hazewinkel", "Microsoft Excel", "Milton Abramowitz", "National Diet Library", "Negative binomial distribution", "N\u00f6rlund\u2013Rice integral", "PlanetMath", "Pochhammer contour", "Preferential attachment", "Python (programming language)", "R (programming language)", "Random variable", "Richard Askey", "S matrix", "SciPy", "Special function", "Spreadsheet", "Stirling's approximation", "String theory", "Symmetric function", "Truncated power function", "Uniform distribution (continuous)", "Urn problem", "Volume of an n-ball", "Yule\u2013Simon distribution"], "references": ["http://www.math.sfu.ca/~cbm/aands/page_258.htm", "http://apps.nrbook.com/empanel/index.html?pg=256", "http://functions.wolfram.com", "http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized", "http://www.plouffe.fr/simon/math/Artin%20E.%20The%20Gamma%20Function%20(1931)(23s).pdf", "http://dlmf.nist.gov/5.12", "http://dlmf.nist.gov/8.17", "http://www.ams.org/mathscinet-getitem?mr=2723248", "http://planetmath.org/?op=getobj&from=objects&id=6206", "https://id.ndl.go.jp/auth/ndlna/00560632", "https://web.archive.org/web/20070120151547/http://www.danielsoper.com/statcalc/calc36.aspx", "https://web.archive.org/web/20070120151557/http://www.danielsoper.com/statcalc/calc37.aspx", "https://www.encyclopediaofmath.org/index.php?title=p/b015960", "https://www.wikidata.org/wiki/Q468881"]}, "Fano factor": {"categories": ["Statistical deviation and dispersion", "Statistical ratios"], "title": "Fano factor", "method": "Fano factor", "url": "https://en.wikipedia.org/wiki/Fano_factor", "summary": "In statistics, the Fano factor, like the coefficient of variation, is a measure of the dispersion of a probability distribution of a Fano noise. It is named after Ugo Fano, an Italian American physicist.\nThe Fano factor is defined as\n\n \n \n \n F\n =\n \n \n \n \u03c3\n \n W\n \n \n 2\n \n \n \n \u03bc\n \n W\n \n \n \n \n ,\n \n \n {\\displaystyle F={\\frac {\\sigma _{W}^{2}}{\\mu _{W}}},}\n where \n \n \n \n \n \u03c3\n \n W\n \n \n 2\n \n \n \n \n {\\displaystyle \\sigma _{W}^{2}}\n is the variance and \n \n \n \n \n \u03bc\n \n W\n \n \n \n \n {\\displaystyle \\mu _{W}}\n is the mean of a random process in some time window W. The Fano factor can be viewed as a kind of noise-to-signal ratio; it is a measure of the reliability with which the random variable could be estimated from a time window that on average contains several random events.\nFor a Poisson process, the variance in the count equals the mean count, so F = 1 (normalization).\nIf the time window is chosen to be infinity, the Fano factor is similar to the variance-to-mean ratio (VMR) which in statistics is also known as the index of dispersion.", "images": [], "links": ["Bibcode", "Cadmium zinc telluride", "Coefficient of variation", "Digital object identifier", "Fano noise", "Full width at half maximum", "Index of dispersion", "International Standard Book Number", "Neuroscience", "Particle detector", "Poisson process", "Probability distribution", "Random event", "Random process", "Random variable", "Statistical dispersion", "Statistics", "Ugo Fano", "Variance", "Variance-to-mean ratio"], "references": ["http://adsabs.harvard.edu/abs/1947PhRv...72...26F", "http://adsabs.harvard.edu/abs/1980PhRvB..22.5565A", "http://adsabs.harvard.edu/abs/1984NIMPA.227..311K", "http://adsabs.harvard.edu/abs/2008ITNS...55.2637D", "http://doi.org/10.1016%2F0168-9002(84)90139-6", "http://doi.org/10.1103%2FPhysRev.72.26", "http://doi.org/10.1103%2FPhysRevB.22.5565", "http://doi.org/10.1109%2FTNS.2008.2003075", "http://doi.org/10.1557%2FPROC-487-101"]}, "Gaussian process emulator": {"categories": ["Bayesian statistics", "Ensemble learning", "Statistical randomness", "Statistics articles needing expert attention"], "title": "Gaussian process emulator", "method": "Gaussian process emulator", "url": "https://en.wikipedia.org/wiki/Gaussian_process_emulator", "summary": "In statistics, Gaussian process emulator is one name for a general type of statistical model that has been used in contexts where the problem is to make maximum use of the outputs of a complicated (often non-random) computer-based simulation model. Each run of the simulation model is computationally expensive and each run is based on many different controlling inputs. The variation of the outputs of the simulation model is expected to vary reasonably smoothly with the inputs, but in an unknown way.\nThe overall analysis involves two models: the simulation model, or \"simulator\", and the statistical model, or \"emulator\", which notionally emulates the unknown outputs from the simulator.\nThe Gaussian process emulator model treats the problem from the viewpoint of Bayesian statistics. In this approach, even though the output of the simulation model is fixed for any given set of inputs, the actual outputs are unknown unless the computer model is run and hence can be made the subject of a Bayesian analysis. The main element of the Gaussian process emulator model is that it models the outputs as a Gaussian process on a space that is defined by the model inputs. The model includes a description of the correlation or covariance of the outputs, which enables the model to encompass the idea that differences in the output will be small if there are only small differences in the inputs. Automatic Emulators have been proposed in the literature, where the sequence of inputs is chosen adaptively.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian analysis", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bayesian statistics", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computer experiment", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian process", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Science", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1007%2F978-3-319-59126-1_37", "http://mucm.aston.ac.uk/MUCM/MUCMToolkit/index.php?page=MetaFirstExample.html", "http://www.tonyohagan.co.uk/academic/abs/val6.html", "https://link.springer.com/chapter/10.1007/978-3-319-59126-1_37", "https://doi.org/10.1007%2F978-3-319-59126-1_37"]}, "Root mean square fluctuation": {"categories": ["All articles needing additional references", "Articles needing additional references from January 2017", "Statistical deviation and dispersion", "Statistical mechanics"], "title": "Mean squared displacement", "method": "Root mean square fluctuation", "url": "https://en.wikipedia.org/wiki/Mean_squared_displacement", "summary": "In statistical mechanics, the mean squared displacement (MSD, also mean square displacement, average squared displacement, or mean square fluctuation) is a measure of the deviation of the position of a particle with respect to a reference position over time. It is the most common measure of the spatial extent of random motion, and can be thought of as measuring the portion of the system \"explored\" by the random walker. In the realm of biophysics and environmental engineering, the Mean Squared Displacement is measured over time to determine if a particle is spreading solely due to diffusion, or if an advective force is also contributing. Another relevant concept, the Variance-Related Diameter (VRD, which is twice the square root of MSD), is also used in studying the transportation and mixing phenomena in the realm of environmental engineering. It prominently appears in the Debye\u2013Waller factor (describing vibrations within the solid state) and in the Langevin equation (describing diffusion of a Brownian particle). The MSD is defined as\n\n \n \n \n \n \n M\n S\n D\n \n \n \u2261\n \u27e8\n (\n x\n \u2212\n \n x\n \n 0\n \n \n \n )\n \n 2\n \n \n \u27e9\n =\n \n \n 1\n N\n \n \n \n \u2211\n \n n\n =\n 1\n \n \n N\n \n \n (\n \n x\n \n n\n \n \n (\n t\n )\n \u2212\n \n x\n \n n\n \n \n (\n 0\n )\n \n )\n \n 2\n \n \n \n \n {\\displaystyle {\\rm {MSD}}\\equiv \\langle (x-x_{0})^{2}\\rangle ={\\frac {1}{N}}\\sum _{n=1}^{N}(x_{n}(t)-x_{n}(0))^{2}}\n where N is the number of particles to be averaged, \n \n \n \n \n x\n \n n\n \n \n (\n 0\n )\n =\n \n x\n \n 0\n \n \n \n \n {\\displaystyle x_{n}(0)=x_{0}}\n is the reference position of each particle, \n \n \n \n \n x\n \n n\n \n \n (\n t\n )\n \n \n {\\displaystyle x_{n}(t)}\n is the position of each particle in determined time t.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Advection", "Atmospheric dispersion modeling", "Biophysics", "Brownian motion", "Characteristic function (probability theory)", "Cumulant", "Cumulant generating function", "Debye\u2013Waller factor", "Deviation (statistics)", "Diffusion", "Diffusion equation", "Digital object identifier", "Environmental engineering", "Full width at half maximum", "International Standard Book Number", "International Standard Serial Number", "Langevin equation", "Mean squared error", "Moment-generating function", "Neutron scattering", "OCLC", "Photon correlation spectroscopy", "Probability density function", "PubMed Central", "PubMed Identifier", "Random walk", "Root-mean-square deviation of atomic positions", "Statistical mechanics"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3897181", "http://www.ncbi.nlm.nih.gov/pubmed/24446482", "http://doi.org/10.1080%2F10473289.1990.10466761", "http://doi.org/10.1083%2Fjcb.201307172", "http://jcb.rupress.org/content/204/2/231", "http://www.worldcat.org/issn/0021-9525", "http://www.worldcat.org/issn/1047-3289", "http://www.worldcat.org/oclc/983391285", "https://dx.doi.org/10.1080/10473289.1990.10466761", "https://www.worldcat.org/oclc/983391285"]}, "Total correlation": {"categories": ["Covariance and correlation", "Information theory", "Probability theory"], "title": "Total correlation", "method": "Total correlation", "url": "https://en.wikipedia.org/wiki/Total_correlation", "summary": "In probability theory and in particular in information theory, total correlation (Watanabe 1960) is one of several generalizations of the mutual information. It is also known as the multivariate constraint (Garner 1962) or multiinformation (Studen\u00fd & Vejnarov\u00e1 1999). It quantifies the redundancy or dependency among a set of n random variables.", "images": [], "links": ["Bit", "Cluster analysis", "Digital object identifier", "Dual total correlation", "Feature selection", "Information entropy", "Information theory", "Interaction information", "Joint entropy", "Kullback\u2013Leibler divergence", "Multivariate mutual information", "Mutual information", "Probability theory", "Random variable"], "references": ["https://arxiv.org/abs/cs/0308002v1", "https://arxiv.org/abs/q-bio.QM/0406015", "https://doi.org/10.1029%2F2009WR008953"]}, "Log-linear model": {"categories": ["All articles lacking sources", "Articles lacking sources from July 2012", "Log-linear models"], "title": "Log-linear model", "method": "Log-linear model", "url": "https://en.wikipedia.org/wiki/Log-linear_model", "summary": "A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression. That is, it has the general form\n\n \n \n \n exp\n \u2061\n \n (\n \n c\n +\n \n \u2211\n \n i\n \n \n \n w\n \n i\n \n \n \n f\n \n i\n \n \n (\n X\n )\n \n )\n \n \n \n {\\displaystyle \\exp \\left(c+\\sum _{i}w_{i}f_{i}(X)\\right)}\n ,in which the fi(X) are quantities that are functions of the variables X, in general a vector of values, while c and the wi stand for the model parameters.\nThe term may specifically be used for:\n\nA log-linear plot or graph, which is a type of semi-log plot.\nPoisson regression for contingency tables, a type of generalized linear model.The specific applications of log-linear models are where the output quantity lies in the range 0 to \u221e, for values of the independent variables X, or more immediately, the transformed quantities fi(X) in the range \u2212\u221e to +\u221e. This may be contrasted to logistic models, similar to the logistic function, for which the output quantity lies in the range 0 to 1. Thus the contexts where these models are useful or realistic often depends on the range of the values being modelled.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Boltzmann distribution", "Function (mathematics)", "General linear model", "Generalized linear model", "Linear combination", "Linear regression", "Log-linear analysis", "Logarithm", "Logistic function", "Mathematical model", "Multivariate analysis", "Parameter", "Poisson regression", "Semi-log plot"], "references": []}, "Sample space": {"categories": ["All articles needing additional references", "Articles needing additional references from November 2010", "Experiment (probability theory)"], "title": "Sample space", "method": "Sample space", "url": "https://en.wikipedia.org/wiki/Sample_space", "summary": "In probability theory, the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set. It is common to refer to a sample space by the labels S, \u03a9, or U (for \"universal set\").\nFor example, if the experiment is tossing a coin, the sample space is typically the set {head, tail}. For tossing two coins, the corresponding sample space would be {(head,head), (head,tail), (tail,head), (tail,tail)}, commonly written {HH, HT, TH, TT}. If the sample space is unordered, it becomes {{head,head}, {head,tail}, {tail,tail}}.\nFor tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6} (in which the result of interest is the number of pips facing up).A well-defined sample space is one of three basic elements in a probabilistic model (a probability space); the other two are a well-defined set of possible events (a sigma-algebra) and a probability assigned to each event (a probability measure function).", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a1/Brass_thumbtack.jpg", "https://upload.wikimedia.org/wikipedia/commons/e/e8/Coin_tossing.JPG", "https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abstraction", "Bayes' theorem", "Bias of an estimator", "Boole's inequality", "Cartesian product", "Complementary event", "Conditional independence", "Conditional probability", "Dice", "Element (mathematics)", "Elementary event", "Equally likely outcomes", "Event (probability theory)", "Experiment (probability theory)", "Independence (probability theory)", "International Standard Book Number", "Joint probability distribution", "Law of large numbers", "Law of total probability", "Marginal distribution", "Measure (mathematics)", "Outcome (probability)", "Parameter space", "Playing card", "Prentice Hall", "Probability", "Probability axioms", "Probability measure", "Probability space", "Probability theory", "Random variable", "Sample (statistics)", "Set (mathematics)", "Set notation", "Sigma-algebra", "Simple random sample", "Space (mathematics)", "Statistical population", "Statistics", "Suit (cards)", "Thumb tack", "Tree diagram (probability theory)", "Trial and error", "Universe (mathematics)", "Venn diagram", "W. H. Freeman and Company", "\u03a3-algebra"], "references": ["http://bcs.whfreeman.com/yates2e/", "http://www-math.bgsu.edu/~albert/m115/probability/sample_space.html", "http://stats.oecd.org/glossary/detail.asp?ID=3855", "https://ocw.mit.edu/resources/res-6-012-introduction-to-probability-spring-2018/part-i-the-fundamentals", "https://people.richland.edu/james/lecture/m170/ch05-int.html", "https://web.archive.org/web/20050209001108/http://bcs.whfreeman.com/yates2e/"]}, "Probabilistic design": {"categories": ["CS1 maint: Multiple names: authors list", "Design", "Engineering statistics", "Quality"], "title": "Probabilistic design", "method": "Probabilistic design", "url": "https://en.wikipedia.org/wiki/Probabilistic_design", "summary": "Probabilistic design is a discipline within engineering design. It deals primarily with the consideration of the effects of random variability upon the performance of an engineering system during the design phase. Typically, these effects are related to quality and reliability. Thus, probabilistic design is a tool that is mostly used in areas that are concerned with quality and reliability. For example, product design, quality control, systems engineering, machine design, civil engineering (particularly useful in limit state design) and manufacturing. It differs from the classical approach to design by assuming a small probability of failure instead of using the safety factor. \n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/1/1b/Interference_Forces.jpg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": [".design", "AIGA", "Accelerated failure time model", "Activity-centered design", "Actuarial science", "Adaptive web design", "Advertising", "Aesthetics", "Affective design", "Agile software development", "Akaike information criterion", "Algorithm design", "Algorithms-Aided Design (AAD)", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Applied arts", "Architect-led design\u2013build", "Architectural lighting design", "Architectural model", "Architecture", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Automotive design", "Automotive suspension design", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Blueprint", "Boiler design", "Book design", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Brainstorming", "Breusch\u2013Godfrey test", "Building design", "C-K theory", "CMF design", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Ceramic art", "Chartered Society of Designers", "Chemometrics", "Chi-squared test", "Circuit design", "Civil engineering", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Communication design", "Community design", "Completeness (statistics)", "Comprehensive layout", "Computer-aided design", "Computer-aided garden design", "Computer-aided industrial design", "Computer-automated design", "Concept-oriented design", "Concept art", "Conceptual design", "Confidence interval", "Configuration design", "Confounding", "Contextual design", "Contingency table", "Continuous design", "Continuous probability distribution", "Control chart", "Corporate design", "Correlation and dependence", "Correlogram", "Corrugated box design", "Costume design", "Count data", "Cradle-to-cradle design", "Creative industries", "Creative problem-solving", "Creativity techniques", "Credible interval", "Crime statistics", "Critical design", "Cross-correlation", "Cross-validation (statistics)", "Cultural icon", "Data collection", "Database design", "Decomposition of time series", "Defensive design", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design", "Design Council", "Design Research Society", "Design and Industries Association", "Design around", "Design brief", "Design by committee", "Design by contract", "Design change", "Design choice", "Design classic", "Design closure", "Design computing", "Design controls", "Design director", "Design education", "Design elements and principles", "Design engineer", "Design fiction", "Design firm", "Design flow (EDA)", "Design for All (in ICT)", "Design for Six Sigma", "Design for X", "Design for assembly", "Design for behaviour change", "Design for manufacturability", "Design for testing", "Design history", "Design knowledge", "Design language", "Design leadership", "Design life", "Design load", "Design management", "Design marker", "Design methods", "Design museum", "Design of experiments", "Design paradigm", "Design patent", "Design pattern", "Design quality indicator", "Design rationale", "Design research", "Design review", "Design science", "Design specification", "Design strategy", "Design studio", "Design technology", "Design theory", "Design thinking", "Design tool", "Designer", "Design\u2013bid\u2013build", "Design\u2013build", "Dickey\u2013Fuller test", "Divergence (statistics)", "Domain-driven design", "Drug design", "Durbin\u2013Watson statistic", "Ecodesign", "Ecological design", "Econometrics", "Effect size", "Efficiency (statistics)", "Electric guitar design", "Electrical system design", "Electronic design automation", "Elliptical distribution", "Empathic design", "Empirical distribution function", "Employee experience design", "Energy neutral design", "Engineering", "Engineering design", "Engineering design process", "Engineering statistics", "Engineering system", "Enterprise architecture", "Environmental design", "Environmental impact design", "Environmental statistics", "Epidemiology", "Error-tolerant design", "Errors and residuals in statistics", "Estimating equations", "European Design Award", "Exhibit design", "Experience design", "Experiential interior design", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure mode and effects analysis", "Failure rate", "Fan chart (statistics)", "Fashion design", "Fashion design copyright", "Fault-tolerant design", "Film title design", "Filter design", "First-hitting-time model", "Floral design", "Flowchart", "Forest plot", "Fourier analysis", "Framework-oriented design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Functional design", "Furniture", "Futures studies", "G-test", "Game art design", "Game design", "Garden design", "General linear model", "Generalized linear model", "Generative Design", "Geodesign", "Geographic information system", "Geometric mean", "Geostatistics", "German Design Award", "Geschmacksmuster", "Glass art", "Good Design Award (Chicago)", "Good Design Award (Japan)", "Goodness of fit", "Granger causality", "Graphex", "Graphic design", "Graphical model", "Grouped data", "Hardware interface design", "Harmonic mean", "Healthy community design", "Heteroscedasticity", "High-level design", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hotel design", "IF product design award", "Icon design", "Illustration", "Immersive design", "Index of dispersion", "Industrial design", "Industrial design right", "Industrial design rights in the European Union", "Information design", "Innovation Management", "Instructional design", "Integrated circuit design", "Integrated design", "Integrated topside design", "Intelligence-based design", "Intelligent design", "Interaction (statistics)", "Interaction design", "Interior architecture", "Interior design", "International Forum Design", "International Standard Book Number", "Interquartile range", "Interval estimation", "Interval finite element", "Isotonic regression", "Iterative design", "Jackknife resampling", "James Dyson Award", "Jarque\u2013Bera test", "Jewelry design", "Job design", "Johansen test", "Jonckheere's trend test", "KISS principle", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Keyline design", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Landscape architecture", "Landscape design", "Latin hypercube sampling", "Lean Startup", "Lehmann\u2013Scheff\u00e9 theorem", "Level design", "Lighting designer", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Limit state design", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Low-level design", "Lp space", "M-estimator", "Machine design", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mechanism design", "Median", "Median-unbiased estimator", "Medical statistics", "Metadesign", "Method of moments (statistics)", "Methods engineering", "Mind map", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mockup", "Mode (statistics)", "Model selection", "Modular design", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo method", "Motion graphic design", "Motorcycle design", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New Wave (design)", "New product development", "News design", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuclear weapon design", "Nucleic acid design", "OODA Loop", "Object-oriented design", "Observational study", "Official statistics", "One- and two-tailed tests", "Open-design movement", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Organization design", "Outline of design", "Outline of statistics", "Packaging and labeling", "Parametric design", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Participatory design", "Partition of sums of squares", "Passive solar building design", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Philosophy of design", "Photographic lens design", "Photography", "Physical design (electronics)", "Pie chart", "Pivotal quantity", "Platform-based design", "Plug-in principle", "Point estimation", "Poisson regression", "Policy-based design", "Population (statistics)", "Population statistics", "Postage stamp design", "Posterior probability", "Power (statistics)", "Power network design (IC)", "Prediction interval", "Prince Philip Designers Prize", "Principal component analysis", "Print design", "Prior probability", "Privacy by Design", "Probability distribution", "Process-centered design", "Process design", "Process simulation", "Processor design", "Product design", "Product design specification", "Production design", "Propagation of error", "Property designer", "Proportional hazards model", "Protein design", "Prototype", "Psychometrics", "Public art", "Public interest design", "Quality control", "Quality function deployment", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rational design", "Regenerative design", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Research-based design", "Research design", "Responsibility-driven design", "Responsive web design", "Retail design", "Robust regression", "Robust statistics", "Robustification", "Run chart", "STEAM fields", "Safe-life design", "Safety factor", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scenic design", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sensory design", "Service design", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signage", "Simple linear regression", "Simultaneous equations model", "Sketch (drawing)", "Skewness", "Slow design", "Social design", "Social statistics", "Software design", "Sonic interaction design", "Sound design", "Spacecraft design", "Spatial analysis", "Spatial design", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical interference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Storyboard", "Strategic design", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Sustainable design", "Sustainable furniture design", "Sustainable landscape architecture", "System identification", "Systemic Design", "Systems Oriented Design", "Systems design", "TRIZ", "Tableless web design", "Technical drawing", "Textile design", "The Design Society", "Theory of constraints", "Time domain", "Time series", "Tolerance interval", "Top-down and bottom-up design", "Traffic sign design", "Transformation design", "Transgenerational design", "Trend estimation", "Type design", "Typography", "U-statistic", "Uniformly most powerful test", "Unintelligent design", "Universal design", "Urban design", "Usage-centered design", "Use-centered design", "User-centered design", "User experience design", "User innovation", "User interface design", "V-statistic", "Value-driven design", "Value sensitive design", "Variance", "Vector autoregression", "Video design", "Video game design", "Virtual home design software", "Visual merchandising", "Visualization (computer graphics)", "Wald test", "Wavelet", "Web design", "Web design program", "Website wireframe", "Whittle likelihood", "Wicked problem", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ndaportal.com/non-deterministic-approaches-handbook.html", "http://grassmannalgebra.info/probabilisticdesign", "http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA365683", "http://www.fpl.fs.fed.us/documnts/fplrp/fplrp302.pdf"]}, "F-distribution": {"categories": ["All articles with unsourced statements", "Analysis of variance", "Articles with unsourced statements from March 2014", "Continuous distributions", "Pages using deprecated image syntax"], "title": "F-distribution", "method": "F-distribution", "url": "https://en.wikipedia.org/wiki/F-distribution", "summary": "In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher\u2013Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/74/F-distribution_pdf.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8e/F_dist_cdf.svg"], "links": ["ARGUS distribution", "Abramowitz and Stegun", "Analysis of variance", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biometrika", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Chow test", "Circular distribution", "Circular uniform distribution", "Cochran's theorem", "Compound Poisson distribution", "Confluent hypergeometric function", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-statistics", "F-test", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Frequentist", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "George W. Snedecor", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independence (probability theory)", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irene Stegun", "Irwin\u2013Hall distribution", "JSTOR", "Jeffreys prior", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Library of Congress Control Number", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mathematical Reviews", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Milton Abramowitz", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral F-distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Null distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Population genetics", "Positive integer", "Prior probability", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Random variate", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Regularized incomplete beta function", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Ronald Fisher", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Statistics", "Student's t-distribution", "Support (mathematics)", "Test statistic", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks' lambda distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.math.sfu.ca/~cbm/aands/page_946.htm", "http://www.statlect.com/F_distribution.htm", "http://jeff560.tripod.com/f.html", "http://lccn.loc.gov/64-60036", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda3665.htm", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm", "http://www.waterlog.info/f-test.htm", "http://www.ams.org/mathscinet-getitem?mr=0167642", "https://lccn.loc.gov/65012253", "https://www.jstor.org/stable/2335882"]}, "MinHash": {"categories": ["Clustering criteria", "Hash functions", "Hashing", "Probabilistic data structures"], "title": "MinHash", "method": "MinHash", "url": "https://en.wikipedia.org/wiki/MinHash", "summary": "In computer science and data mining, MinHash (or the min-wise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating how similar two sets are. The scheme was invented by Andrei Broder (1997), and initially used in the AltaVista search engine to detect duplicate web pages and eliminate them from search results.\nIt has also been applied in large-scale clustering problems, such as clustering documents by the similarity of their sets of words.\n\n", "images": [], "links": ["Alan M. Frieze", "AltaVista", "Andrei Broder", "ArXiv", "Association for Computing Machinery", "Association rule learning", "Bias of an estimator", "Bibcode", "Bloom filter", "Chernoff bound", "Cluster analysis", "Communications of the ACM", "Computer science", "Cosine distance", "Count-min sketch", "Data mining", "Digital object identifier", "Disjoint sets", "Document clustering", "Edith Cohen", "Euclidean vector", "Exponential distribution", "Google", "Google News", "Hamming distance", "Hash function", "IEEE", "Information Processing Letters", "International Standard Book Number", "International Standard Serial Number", "Intersection (set theory)", "Inverse transform sampling", "Jaccard index", "Jeffrey Ullman", "Ji\u0159\u00ed Matou\u0161ek (mathematician)", "Linear time", "Locality-sensitive hashing", "Locality sensitive hashing", "Logical matrix", "MapReduce", "Michael Mitzenmacher", "Michael Saks (mathematician)", "Nearest neighbor search", "Permutation", "Piotr Indyk", "Probability", "Rajeev Motwani", "Random permutation", "Random variable", "RefSeq", "SimHash", "Similarity measure", "Simple random sample", "Symposium on Theory of Computing", "Union (set theory)", "Universal hashing", "Variance", "W-shingling"], "references": ["http://infoscience.epfl.ch/record/99373/files/Henzinger06.pdf", "http://gatekeeper.dec.com/ftp/pub/dec/SRC/publications/broder/positano-final-wpnums.pdf", "http://static.googleusercontent.com/media/research.google.com/en//pubs/archive/33026.pdf", "http://www.cs.columbia.edu/~coms699812/lecture1.pdf", "http://adsabs.harvard.edu/abs/2012arXiv1206.2082B", "http://arxiv.org/abs/1206.2082", "http://www.bmva.org/bmvc/2008/papers/119.pdf", "http://doi.org/10.1002%2Frsa.10101", "http://doi.org/10.1016%2FS0020-0190(99)00163-5", "http://doi.org/10.1038%2Fnbt.3238", "http://doi.org/10.1109%2F69.908981", "http://doi.org/10.1109%2FSEQUEN.1997.666900", "http://doi.org/10.1145%2F1148170.1148222", "http://doi.org/10.1145%2F1242572.1242592", "http://doi.org/10.1145%2F1242572.1242610", "http://doi.org/10.1145%2F1282280.1282359", "http://doi.org/10.1145%2F1327452.1327494", "http://doi.org/10.1145%2F276698.276781", "http://doi.org/10.1145%2F509907.509965", "http://doi.org/10.1186%2Fs13059-016-0997-x", "http://www.worldcat.org/issn/1474-760X", "http://www.worldcat.org/issn/1546-1696", "https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/36928.pdf", "https://www.nature.com/articles/nbt.3238", "https://sourmash.readthedocs.io/en/latest/", "https://arxiv.org/abs/1602.08393", "https://arxiv.org/abs/1809.04052", "https://doi.org/10.1186/s13059-016-0997-x"]}, "Surrogate model": {"categories": ["Design of experiments", "Mathematical modeling", "Numerical analysis", "Scientific modeling"], "title": "Surrogate model", "method": "Surrogate model", "url": "https://en.wikipedia.org/wiki/Surrogate_model", "summary": "A surrogate model is an engineering method used when an outcome of interest cannot be easily directly measured, so a model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the air flow around the wing for different shape variables (length, curvature, material, ..). For many real world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and what-if analysis become impossible since they require thousands or even millions of simulation evaluations.\nOne way of alleviating this burden is by constructing approximation models, known as surrogate models, response surface models, metamodels or emulators, that mimic the behavior of the simulation model as closely as possible while being computationally cheap(er) to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), solely the input-output behavior is important. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points. This approach is also known as behavioral modeling or black-box modeling, though the terminology is not always consistent. When only a single design variable is involved, the process is known as curve fitting.\nThough using surrogate models in lieu of experiments and simulations in engineering design is more common, surrogate modelling may be used in many other areas of science where there are expensive experiments and/or function evaluations.", "images": [], "links": ["Artificial neural networks", "CMA-ES", "Computer experiment", "Conceptual model", "Curve fitting", "Design of experiments", "Evolutionary algorithms", "Fitness approximation", "Genetic algorithm", "Gradient-Enhanced Kriging (GEK)", "Kriging", "Linear approximation", "OptiY", "Orthogonal transform", "Radial basis function", "Response surface", "Response surface methodology", "Space-mapping", "Space mapping", "Support vector machine", "Surrogate data", "Surrogate endpoint", "Wei Shyy"], "references": ["http://sumowiki.intec.ugent.be", "http://www.wiley.com//legacy/wileychi/forrester/terms.html", "http://jmlr.csail.mit.edu/papers/volume11/gorissen10a/gorissen10a.pdf", "http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7423860&action=search&sortType=&rowsPerPage=&searchField=Search_All&matchBoolean=true&queryText=(%22Document%20Title%22:simplicity%20in%20asm)", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1262727", "http://www.ep.liu.se/ecp/063/074/ecp11063074.pdf", "https://github.com/SMTorg/SMT", "https://hal.inria.fr/file/index/docid/493921/filename/ACM-ES.pdf"]}, "Ordered probit": {"categories": ["All articles to be expanded", "All stub articles", "Articles to be expanded from February 2017", "Articles using small message boxes", "Categorical regression models", "Statistics stubs"], "title": "Ordered probit", "method": "Ordered probit", "url": "https://en.wikipedia.org/wiki/Ordered_probit", "summary": "In statistics, ordered probit is a whole of the widely used probit analysis to the case of more than two outcomes of an ordinal dependent variable (a dependent variable for which the potential values have a natural ordering, as in poor, fair, good, excellent). Similarly, the widely used logit method also has a counterpart ordered logit. Ordered probit, like ordered logit, is a particular method of ordinal regression.\nFor example, in clinical research, the effect a drug may have on a patient may be modeled with ordered probit regression. Independent variables may include the use or non-use of the drug as well as control variables such as age and details from medical history such as whether the patient suffers from high blood pressure, heart disease, etc. The dependent variable would be ranked from the following list: complete cure, relieve symptoms, no effect, deteriorate condition, death.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Clinical research", "Dependent variable", "Digital object identifier", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Logit", "Maximum likelihood", "Mean and predicted response", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordinal data", "Ordinal regression", "Ordinary least squares", "Partial least squares regression", "Peter Kennedy (economist)", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Weighted least squares", "William Greene (economist)"], "references": ["http://doi.org/10.1017%2FS0266466600010781"]}, "Tukey\u2013Kramer method": {"categories": ["Analysis of variance", "Multiple comparisons", "Statistical tests"], "title": "Tukey's range test", "method": "Tukey\u2013Kramer method", "url": "https://en.wikipedia.org/wiki/Tukey%27s_range_test", "summary": "Tukey's range test, also known as the Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test, is a single-step multiple comparison procedure and statistical test. It can be used on raw data or in conjunction with an ANOVA (post-hoc analysis) to find means that are significantly different from each other. Named after John Tukey, it compares all possible pairs of means, and is based on a studentized range distribution (q) (this distribution is similar to the distribution of t from the t-test. See below). The Tukey HSD tests should not be confused with the Tukey Mean Difference tests (also known as the Bland\u2013Altman diagram).\nTukey's test compares the means of every treatment to the means of every other treatment; that is, it applies simultaneously to the set of all pairwise comparisons\n\n \n \n \n \n \u03bc\n \n i\n \n \n \u2212\n \n \u03bc\n \n j\n \n \n \n \n \n {\\displaystyle \\mu _{i}-\\mu _{j}\\,}\n and identifies any difference between two means that is greater than the expected standard error. The confidence coefficient for the set, when all sample sizes are equal, is exactly \n \n \n \n 1\n \u2212\n \u03b1\n \n \n {\\displaystyle 1-\\alpha }\n for any \n \n \n \n 0\n \u2264\n \u03b1\n \u2264\n 1\n \n \n {\\displaystyle 0\\leq \\alpha \\leq 1}\n . For unequal sample sizes, the confidence coefficient is greater than 1 \u2212 \u03b1. In other words, the Tukey method is conservative when there are unequal sample sizes.", "images": [], "links": ["ANOVA", "Biometrics (journal)", "Bland\u2013Altman plot", "Central limit theorem", "Clyde Kramer", "Confidence coefficient", "Confidence interval", "Cumulative distribution function", "Digital object identifier", "Family-wise error rate", "Familywise error rate", "Homoscedasticity", "JSTOR", "John Tukey", "Multiple comparison", "Newman\u2013Keuls method", "Normal distribution", "Null hypothesis", "Post-hoc analysis", "Quantile function", "R (programming language)", "Sample mean", "Set (mathematics)", "Standard error", "Standard error (statistics)", "Statistical independence", "Statistical test", "Student's t-distribution", "Studentized range", "Studentized range distribution", "T-test", "Type I error"], "references": ["http://faculty.vassar.edu/lowry/ch14pt2.html", "http://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm", "http://doi.org/10.1016%2Fj.jns.2013.01.016", "http://www.jstor.org/stable/3001913", "https://web.archive.org/web/20081017161620/http://faculty.vassar.edu/lowry/ch14pt2.html"]}, "Anscombe transform": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2013", "Normal distribution", "Poisson distribution", "Statistical data transformation"], "title": "Anscombe transform", "method": "Anscombe transform", "url": "https://en.wikipedia.org/wiki/Anscombe_transform", "summary": "In statistics, the Anscombe transform, named after Francis Anscombe, is a variance-stabilizing transformation that transforms a random variable with a Poisson distribution into one with an approximately standard Gaussian distribution. The Anscombe transform is widely used in photon-limited imaging (astronomy, X-ray) where images naturally follow the Poisson law. The Anscombe transform is usually used to pre-process the data in order to make the standard deviation approximately constant. Then denoising algorithms designed for the framework of additive white Gaussian noise are used; the final estimate is then obtained by applying an inverse Anscombe transformation to the denoised data.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/bb/Anscombe_stabilized_stdev.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/bb/20110307111343%21Anscombe_stabilized_stdev.svg"], "links": ["Additive white Gaussian noise", "Bias of an estimator", "Bibcode", "Box\u2013Cox transformation", "Closed-form expression", "Digital object identifier", "Francis Anscombe", "Frank Anscombe", "International Standard Book Number", "Inverse function", "JSTOR", "John Tukey", "Linear map", "Noise reduction", "Normal distribution", "Photon-limited imaging", "Poisson distribution", "Random variable", "Standard deviation", "Statistics", "Variance-stabilizing transformation"], "references": ["http://adsabs.harvard.edu/abs/2001ISPM...18...30S", "http://adsabs.harvard.edu/abs/2011ITIP...20...99M", "http://adsabs.harvard.edu/abs/2011ITIP...20.2697M", "http://adsabs.harvard.edu/abs/2013ITIP...22...91M", "http://doi.org/10.1093%2Fbiomet%2F35.3-4.246", "http://doi.org/10.1093%2Fbiomet%2F75.4.803", "http://doi.org/10.1109%2F79.916319", "http://doi.org/10.1109%2FTIP.2010.2056693", "http://doi.org/10.1109%2FTIP.2011.2121085", "http://doi.org/10.1109%2FTIP.2012.2202675", "http://doi.org/10.1214%2Faoms%2F1177729756", "http://www.jstor.org/stable/2236611", "http://www.jstor.org/stable/2332343"]}, "Ergodicity": {"categories": ["All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from July 2014", "Ergodic theory", "Wikipedia articles that are too technical from July 2014"], "title": "Ergodicity", "method": "Ergodicity", "url": "https://en.wikipedia.org/wiki/Ergodicity", "summary": "In probability theory, an ergodic dynamical system is one that, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states in its phase space. In physics the term implies that a system satisfies the ergodic hypothesis of thermodynamics.\nA random process is ergodic if its time average is the same as its average over the probability space, known in the field of thermodynamics as its ensemble average. The state of an ergodic process after a long time is nearly independent of its initial state.The term \"ergodic\" was derived from the Greek words \u03ad\u03c1\u03b3\u03bf\u03bd (ergon: \"work\") and \u03bf\u03b4\u03cc\u03c2 (odos: \"path,\" \"way\"). It was chosen by Ludwig Boltzmann while he was working on a problem in statistical mechanics. The branch of mathematics that studies ergodic systems is known as Ergodic theory.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Borel measure", "Digital object identifier", "Dynamical system", "Ensemble average", "Ergodic (disambiguation)", "Ergodic hypothesis", "Ergodic theory", "Flow (mathematics)", "Garrett Birkhoff", "George David Birkhoff", "Independence (probability theory)", "International Standard Book Number", "Irreducible representation", "JSTOR", "Leonidas Alaoglu", "Lp space", "Ludwig Boltzmann", "Markov chain", "Mathematical Reviews", "Measure-preserving dynamical system", "Measure-preserving transformation", "Mixing (mathematics)", "Phase space", "Physics", "Prime number", "Probability space", "Probability theory", "PubMed Central", "PubMed Identifier", "Random process", "Spectral decomposition", "Springer Science+Business Media", "Symmetric difference", "Symmetric matrix", "Thermal noise", "Thermodynamics"], "references": ["http://www.math.unc.edu/Faculty/petersen/erg3.doc", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076138", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1077986", "http://www.ncbi.nlm.nih.gov/pubmed/16577406", "http://www.ncbi.nlm.nih.gov/pubmed/16588311", "http://www.staff.science.uu.nl/~kraai101/lecturenotes2009.pdf", "http://www.ams.org/mathscinet-getitem?mr=0002026", "http://doi.org/10.1073%2Fpnas.17.2.656", "http://doi.org/10.1073%2Fpnas.25.12.628", "http://doi.org/10.2307%2F1969004", "http://www.jstor.org/stable/1969004", "http://www.jstor.org/stable/86016", "http://www.jstor.org/stable/87048", "http://www.pnas.org/content/17/12/656.full.pdf", "http://www.pnas.org/content/25/12/628.full.pdf", "https://books.google.com/books?id=OXkg-LvRgjUC&pg=PA271"]}, "Intra-rater reliability": {"categories": ["All stub articles", "Comparison of assessments", "Psychometrics", "Statistics stubs"], "title": "Intra-rater reliability", "method": "Intra-rater reliability", "url": "https://en.wikipedia.org/wiki/Intra-rater_reliability", "summary": "In statistics, intra-rater reliability is the degree of agreement among repeated administrations of a diagnostic test performed by a single rater. Intra-rater reliability and inter-rater reliability are aspects of test validity.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Inter-rater reliability", "Rating (pharmaceutical industry)", "Reliability (statistics)", "Repeatability", "Statistics", "Test-retest reliability", "Test validity"], "references": ["http://www.medicine.mcgill.ca/strokengine-assess/definitions-en.html", "http://www.outcomesdatabase.org/show/category/id/8"]}, "Local convex hull": {"categories": ["Spatial data analysis"], "title": "Local convex hull", "method": "Local convex hull", "url": "https://en.wikipedia.org/wiki/Local_convex_hull", "summary": "Local convex hull (LoCoH) is a method for estimating size of the home range of an animal or a group of animals (e.g. a pack of wolves, a pride of lions, or herd of buffaloes), and for constructing a utilization distribution. The latter is a probability distribution that represents the probabilities of finding an animal within a given area of its home range at any point in time; or, more generally, at points in time for which the utilization distribution has been constructed. In particular, different utilization distributions can be constructed from data pertaining to particular periods of a diurnal or seasonal cycle.\nUtilization distributions are constructed from data providing the location of an individual or several individuals in space at different points in time by associating a local distribution function with each point and then summing and normalizing these local distribution functions to obtain a distribution function that pertains to the data as a whole. If the local distribution function is a parametric distribution, such as a symmetric bivariate normal distribution then the method is referred to as a kernel method, but more correctly should be designated as a parametric kernel method. On the other hand, if the local kernel element associated with each point is a local convex polygon constructed from the point and its k-1 nearest neighbors, then the method is nonparametric and referred to as a k-LoCoH or fixed point LoCoH method. This is in contrast to r-LoCoH (fixed radius) and a-LoCoH (adaptive radius) methods.\nIn the case of LoCoH utilization distribution constructions, the home range can be taken as the outer boundary of the distribution (i.e. the 100th percentile). In the case of utilization distributions constructed from unbounded kernel elements, such as bivariate normal distributions, the utilization distribution is itself unbounded. In this case the most often used convention is to regard the 95th percentile of the utilization distribution as the boundary of the home range.\nTo construct a k-LoCoH utilization distribution:\n\nLocate the k \u2212 1 nearest neighbors for each point in the dataset.\nConstruct a convex hull for each set of nearest neighbors and the original data point.\nMerge these hulls together from smallest to largest.\nDivide the merged hulls into isopleths where the 10% isopleth contains 10% of the original data points, the 100% isopleth contains all the points, etc.In this sense, LoCoH methods are a generalization of the home range estimator method based on constructing the minimum convex polygon (MCP) associated with the data. The LoCoH method has a number of advantages over parametric kernel methods. In particular:\n\nAs more data are added, the estimates of the home range become more accurate than for bivariate normal kernel constructions.\nLoCoH handles 'sharp' features such as lakes and fences much better than parametric kernel constructions.\nAs mentioned above, the home range is a finite region without having to resort to an ad-hoc choice, such as the 95th percentile to obtain bounded region.LoCoH has a number of implementations including a LoCoH Web Application.\nLoCoH was formerly known as k-NNCH, for k-nearest neighbor convex hulls. It has recently been shown that the a-LoCoH is the best of the three LoCoH methods mentioned above (see Getz et al. in the references below).", "images": [], "links": ["Bivariate normal distribution", "Convex polygon", "Digital object identifier", "Home range", "Minimum convex polygon", "Probability distribution", "Utilization distribution"], "references": ["http://www.cnr.berkeley.edu/~getz/Reprints04/Getz&WilmersEcoG_SF_04.pdf", "http://www.cnr.berkeley.edu/~getz/Reprints06/GetzEtAlPLoSLoCoH07.pdf", "http://tlocoh.r-forge.r-project.org/", "https://web.archive.org/web/20060912083122/http://locoh.cnr.berkeley.edu/", "https://doi.org/10.1186%2F2051-3933-1-2", "https://doi.org/10.1371%2Fjournal.pone.0000207"]}, "Normal-scaled inverse gamma distribution": {"categories": ["All articles to be expanded", "All articles with empty sections", "Articles to be expanded from July 2010", "Articles using small message boxes", "Articles with empty sections from July 2010", "Continuous distributions", "Multivariate continuous distributions", "Normal distribution", "Pages using deprecated image syntax"], "title": "Normal-inverse-gamma distribution", "method": "Normal-scaled inverse gamma distribution", "url": "https://en.wikipedia.org/wiki/Normal-inverse-gamma_distribution", "summary": "In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions. It is a family of conjugate priors of a normal distribution with unknown mean and variance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/48/Normal-inverse-gamma.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Covariance matrix", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Determinant", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse gamma distribution", "Inverse matrix gamma distribution", "Invertible matrix", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix (mathematics)", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate Student distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Precision (statistics)", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scalar (mathematics)", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": []}, "Knightian uncertainty": {"categories": ["All articles needing additional references", "Articles needing additional references from August 2014", "Probability interpretations", "Risk"], "title": "Knightian uncertainty", "method": "Knightian uncertainty", "url": "https://en.wikipedia.org/wiki/Knightian_uncertainty", "summary": "In economics, Knightian uncertainty is a lack of any quantifiable knowledge about some possible occurrence, as opposed to the presence of quantifiable risk (e.g., that in statistical noise or a parameter's confidence interval). The concept acknowledges some fundamental degree of ignorance, a limit to knowledge, and an essential unpredictability of future events.\nKnightian uncertainty is named after University of Chicago economist Frank Knight (1885\u20131972), who distinguished risk and uncertainty in his work Risk, Uncertainty, and Profit:\n\"Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.... The essential fact is that 'risk' means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating.... It will appear that a measurable uncertainty, or 'risk' proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all.\"In this matter Knight's own views were widely shared by key economists in the 1920s and 1930s who played a key role distinguishing the effects of risk from uncertainty. They were particularly concerned with the different impact on human behavior as economic agents. Entrepreneurs invest for quantifiable risk and return; savers may mistrust potential future inflation.\nWhilst Frank Knight's seminal book elaborated the problem, his focus was on avoiding intervention in markets. Work on estimating and mitigating uncertainty was continued by G. L. S. Shackle who later followed up with Potential Surprise Theory \nHowever, the concept is largely informal and there is no single best formal system of probability and belief to represent Knightian uncertainty. Economists and management scientists continue to look at practical methodologies for decision under different types of uncertainty.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Ambiguity aversion", "Black swan theory", "Common cause and special cause", "Economics", "Ellsberg paradox", "Frank Knight", "G. L. S. Shackle", "International Standard Book Number", "Nassim Nicholas Taleb", "Personal computer", "Philosophy of probability", "Probability interpretations", "Risk", "Uncertainty", "Uninformative prior", "University of Chicago", "Utility theory"], "references": ["https://archive.org/details/riskuncertaintyp00knigrich"]}, "Dynamic factor": {"categories": ["Time series"], "title": "Dynamic factor", "method": "Dynamic factor", "url": "https://en.wikipedia.org/wiki/Dynamic_factor", "summary": "In econometrics, a dynamic factor (also known as a diffusion index) is a series which measures the co-movement of many time series. It is used in certain macroeconomic models.\nFormally\n\n \n \n \n \n X\n \n t\n \n \n =\n \n \u039b\n \n t\n \n \n \n F\n \n t\n \n \n +\n \n e\n \n t\n \n \n ,\n \n \n {\\displaystyle X_{t}=\\Lambda _{t}F_{t}+e_{t},}\n where \n \n \n \n \n F\n \n t\n \n \n =\n (\n \n f\n \n t\n \n \n \u22a4\n \n \n ,\n \u2026\n ,\n \n f\n \n t\n \u2212\n q\n \n \n \u22a4\n \n \n )\n \n \n {\\displaystyle F_{t}=(f_{t}^{\\top },\\dots ,f_{t-q}^{\\top })}\n is the vector of lagged factors of the variables in the \n \n \n \n T\n \u00d7\n N\n \n \n {\\displaystyle T\\times N}\n matrix \n \n \n \n \n X\n \n t\n \n \n \n \n {\\displaystyle X_{t}}\n (T is the number of observations and N is the number of variables), \n \n \n \n \n \u039b\n \n t\n \n \n \n \n {\\displaystyle \\Lambda _{t}}\n are the factor loadings, and \n \n \n \n \n e\n \n t\n \n \n \n \n {\\displaystyle e_{t}}\n is the factor error.", "images": [], "links": ["Co-movement", "Econometrics", "Error", "Macroeconomic model", "Matrix (mathematics)", "Monthly Labor Review", "Time series", "Variable (mathematics)", "Vector space"], "references": ["http://www.bls.gov/opub/mlr/1990/04/art3full.pdf"]}, "Markov chain": {"categories": ["All accuracy disputes", "All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from February 2012", "Articles that may be too long from February 2017", "Articles with disputed statements from March 2015", "Articles with unsourced statements from March 2009", "Articles with unsourced statements from March 2012", "CS1 maint: Archived copy as title", "CS1 maint: Extra text: authors list", "CS1 maint: Multiple names: authors list", "Graph theory", "Markov models", "Markov processes", "Webarchive template wayback links", "Wikipedia articles with GND identifiers", "Wikipedia articles with content forks"], "title": "Markov chain", "method": "Markov chain", "url": "https://en.wikipedia.org/wiki/Markov_chain", "summary": "A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.In probability theory and related fields, a Markov process, named after the Russian mathematician Andrey Markov, is a stochastic process that satisfies the Markov property (sometimes characterized as \"memorylessness\"). Roughly speaking, a process satisfies the Markov property if one can make predictions for the future of the process based solely on its present state just as well as one could knowing the process's full history, hence independently from such history; i.e., conditional on the present state of the system, its future and past states are independent.\nA Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless of the nature of time), but it is also common to define a Markov chain as having discrete time in either countable or continuous state space (thus regardless of the state space).Markov studied Markov processes in the early 20th century, publishing his first paper on the topic in 1906. Random walks based on integers and the gambler's ruin problem are examples of Markov processes. Some variations of these processes were studied hundreds of years earlier in the context of independent variables. Two important examples of Markov processes are the Wiener process, also known as the Brownian motion process, and the Poisson process, which are considered the most important and central stochastic processes in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after 1906, in various settings. These two processes are Markov processes in continuous time, while random walks on the integers and the gambler's ruin problem are examples of Markov processes in discrete time.Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, exchange rates of currencies, storage systems such as dams, and population growths of certain animal species. The algorithm known as PageRank, which was originally proposed for the internet search engine Google, is based on a Markov process.Markov processes are the basis for general stochastic simulation methods known as Gibbs sampling and Markov chain Monte Carlo. Furthermore, they are used for simulating random objects with specific probability distributions, and have found extensive application in Bayesian statistics.The adjective Markovian is used to describe something that is related to a Markov process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/70/AAMarkov.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/9/95/Finance_Markov_chain_example_state_space.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a6/Financial_Markov_process.svg", "https://upload.wikimedia.org/wikipedia/commons/0/07/Intensities_vs_transition_probabilities.svg", "https://upload.wikimedia.org/wikipedia/commons/d/da/Markov_Chains_prediction_on_50_discrete_steps..png", "https://upload.wikimedia.org/wikipedia/commons/8/86/Markov_Chains_prediction_on_n%3D3..png", "https://upload.wikimedia.org/wikipedia/commons/f/f3/Markov_chain_extremly_simple1.png", "https://upload.wikimedia.org/wikipedia/commons/2/2b/Markovkate_01.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0b/Mchain_simple_corrected_C1.png", "https://upload.wikimedia.org/wikipedia/commons/5/5b/Mvchain_approx_C2.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9a/Transition_graph_pac-man.png", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["A Mathematical Theory of Communication", "Absorbing Markov chain", "Abstract Wiener space", "Actuarial mathematics", "Agner Krarup Erlang", "Alexander Pushkin", "Algorithmic composition", "Andrei Kolmogorov", "Andrey Markov", "Arithmetic coding", "AstroTurf", "Authoritarian", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Base stealing", "Bayesian inference", "Bayesian statistics", "Bear market", "Bernoulli process", "Bernoulli scheme", "Bessel process", "Biased random walk on a graph", "Bibcode", "Bioinformatics", "Bipartite graph", "Birth-death process", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Bull market", "Bunt (baseball)", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Capitalism", "Cauchy process", "Central limit theorem", "Chapman\u2013Kolmogorov equation", "Chen model", "Chinese restaurant process", "CiteSeerX", "Classical Wiener space", "Claude Shannon", "Compound Poisson process", "Conditional probability", "Conditional probability distribution", "Connected component (graph theory)", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time Markov process", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous or discrete variable", "Continuous stochastic process", "Convergence of random variables", "Copolymer", "Countable set", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Credit rating agency", "Cruise control", "Csound", "C\u00e0dl\u00e0g", "Dam", "Das Kapital", "Data compression", "Defective matrix", "Democratic regime", "Detailed balance", "Diagonal matrix", "Diffusion equation", "Diffusion process", "Digital object identifier", "Directed acyclic graph", "Directed graph", "Dirichlet process", "Discrete-time stochastic process", "Dissociated press", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynamics of Markovian particles", "Dynkin's formula", "Econometrics", "Economic development", "Edmund F. Robertson", "Eigendecomposition", "Eigenvalue", "Eigenvector", "Element (mathematics)", "Empirical process", "Encyclopedia of Mathematics", "Entropy encoding", "Epithelial cell", "Equivalence class", "Equivalence relation", "Ergodic", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Eugene Dynkin", "Eugene Onegin", "Examples of Markov chains", "Exchange rate", "Exchangeable random variables", "Expected value", "Exponent", "Exponential distribution", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Finite-state machine", "Finite group", "Finite set", "First-order differential equation", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Forward equation", "Fractional Brownian motion", "Francis Galton", "Frobenius norm", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gambler's ruin", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "General equilibrium", "Genetic drift", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Google", "Google search engine", "Greatest common divisor", "Harris chain", "Heath\u2013Jarrow\u2013Morton framework", "Henry William Watson", "Hertz", "Heston model", "Hi Ho! Cherry-O", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Identity matrix", "If and only if", "In silico", "Independence (probability theory)", "Independent and identically distributed random variables", "Indexed family", "Infinitesimal generator (stochastic processes)", "Information entropy", "Information theory", "Inner product space", "Integers", "Integrated Authority File", "Interacting particle system", "International Standard Book Number", "International Standard Serial Number", "Invariant measure", "Ion channel", "Ir\u00e9n\u00e9e-Jules Bienaym\u00e9", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Iverson bracket", "J. L. Doob", "J. Laurie Snell", "JSTOR", "James D. Hamilton", "James R. Norris", "John G. Kemeny", "John J. O'Connor (mathematician)", "Jordan normal form", "Joseph O'Rourke (professor)", "Journal of Econometrics", "Jump diffusion", "Jump process", "Karl Marx", "Kelly's lemma", "Kolmogorov's criterion", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kronecker delta", "Kunita\u2013Watanabe inequality", "LIBOR market model", "LZ77 and LZ78", "Large deviation principle", "Large deviations theory", "Lattice QCD", "Laurent E. Calvet", "Law of large numbers", "Law of the iterated logarithm", "Lempel\u2013Ziv\u2013Markov chain algorithm", "Leslie matrix", "List of inequalities", "List of stochastic processes topics", "Little-o notation", "Local martingale", "Local time (mathematics)", "Locally interacting Markov chains", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "MIDI", "MacTutor History of Mathematics archive", "Machine learning", "Main diagonal", "Malliavin calculus", "Marginal distribution", "Mark V. Shaney", "Markov additive process", "Markov blanket", "Markov chain Monte Carlo", "Markov chain approximation method", "Markov chain geostatistics", "Markov chain mixing time", "Markov chains on a measurable state space", "Markov decision process", "Markov information source", "Markov model", "Markov process", "Markov property", "Markov random field", "Markov switching multifractal", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical Reviews", "Mathematical finance", "Mathematical statistics", "Matrix (mathematics)", "Matrix exponential", "Maurice Fr\u00e9chet", "Max (software)", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Memorylessness", "Michaelis-Menten kinetics", "Michaelis\u2013Menten kinetics", "Michiel Hazewinkel", "Middle class", "Mixing (mathematics)", "Moran process", "Motoo Kimura", "Motor vehicle", "Moving-average model", "Natural language generation", "Natural numbers", "Non-homogeneous Poisson process", "Norbert Wiener", "Norm (mathematics)", "Number line", "OCLC", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Oxford English Dictionary", "PageRank", "Parody generator", "Path-dependent", "Pattern recognition", "Paul Ehrenfest", "Pavel Nekrasov", "Percolation theory", "Periodic function", "Perron\u2013Frobenius theorem", "Phase-type distribution", "Phrase (music)", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Political", "Population dynamics", "Population genetics", "Population process", "Posterior distribution", "Potts model", "Predictable process", "Probability theory", "Probability vector", "Progressively measurable process", "Prokhorov's theorem", "PubMed Central", "PubMed Identifier", "Quadratic variation", "Quantum Markov chain", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Reinforcement learning", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Right stochastic matrix", "Risk process", "Ruin theory", "Russia", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semi-Markov process", "Semigroup", "Semimartingale", "Sequence", "Serial dependence", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snakes and Ladders", "Snell envelope", "Society for Industrial and Applied Mathematics", "Software", "Sparre\u2013Anderson model", "Speech recognition", "Stable process", "Standard simplex", "State diagram", "State estimation", "State space", "State transition", "Stationary probability distribution", "Stationary process", "Statistical mechanics", "Statistical model", "Statistics", "Steric effects", "Stochastic analysis", "Stochastic cellular automata", "Stochastic cellular automaton", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic matrix", "Stochastic model", "Stochastic process", "Stochastic row vector", "Stopping time", "Stratonovich integral", "Submartingale", "SuperCollider", "Superlattice", "Supermartingale", "Superprocess", "Sydney Chapman (mathematician)", "System of linear equations", "System on a chip", "Tanaka equation", "Tatyana Ehrenfest", "Telegraph process", "Telescoping Markov chain", "Thermodynamics", "Time-homogeneous Markov chain", "Time-independent matrix", "Time reversibility", "Time series", "Time series analysis", "Transition rate matrix", "Uniform integrability", "Unit vector", "University of St Andrews", "Usual hypotheses", "Variable-order Markov model", "Variance gamma process", "Vasicek model", "Viterbi algorithm", "Wayback Machine", "Weak law of large numbers", "White noise", "Wiener process", "Wiener 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Data sets that are so large that traditional data processing applications are inadequate to deal with them are known as big data.In the open data discipline, data set is the unit to measure the information released in a public open data repository. The European Open Data portal aggregates more than half a million data sets. In this field other definitions have been proposed but currently there is not an official one. 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Both of these models are fitted to time series data either to better understand the data or to predict future points in the series (forecasting). ARIMA models are applied in some cases where data show evidence of non-stationarity, where an initial differencing step (corresponding to the \"integrated\" part of the model) can be applied one or more times to eliminate the non-stationarity.The AR part of ARIMA indicates that the evolving variable of interest is regressed on its own lagged (i.e., prior) values. The MA part indicates that the regression error is actually a linear combination of error terms whose values occurred contemporaneously and at various times in the past. The I (for \"integrated\") indicates that the data values have been replaced with the difference between their values and the previous values (and this differencing process may have been performed more than once). The purpose of each of these features is to make the model fit the data as well as possible.\nNon-seasonal ARIMA models are generally denoted ARIMA(p,d,q) where parameters p, d, and q are non-negative integers, p is the order (number of time lags) of the autoregressive model, d is the degree of differencing (the number of times the data have had past values subtracted), and q is the order of the moving-average model. Seasonal ARIMA models are usually denoted ARIMA(p,d,q)(P,D,Q)m, where m refers to the number of periods in each season, and the uppercase P,D,Q refer to the autoregressive, differencing, and moving average terms for the seasonal part of the ARIMA model.When two out of the three terms are zeros, the model may be referred to based on the non-zero parameter, dropping \"AR\", \"I\" or \"MA\" from the acronym describing the model. 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"Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Julia language", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Lag operator", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Linear combination", "Linear regression", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Long-range dependence", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "MATLAB", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematica", "Mathematical finance", "Mathematical model", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Microsoft", "Mixing (mathematics)", "Moran process", "Moving-average model", "NCSS (statistical software)", "Non-homogeneous Poisson process", "Normal distribution", "Optional stopping theorem", "Order of integration", "Ornstein\u2013Uhlenbeck process", "Parameter", "Partial autocorrelation", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Python (programming language)", "Quadratic variation", "Queueing model", "Queueing theory", "R (programming language)", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Root-mean-square deviation", "Ruby (programming language)", "Ruin theory", "SABR volatility model", "SAP AG", "SAP ERP", "SAS (software)", "SPSS", "SQL Server Analysis Services", "Sample-continuous process", "Sanov's theorem", "Scala (programming language)", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stata", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Unit root", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wide-sense stationary", "Wide sense stationary", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "X-12-ARIMA"], "references": ["http://www.mathworks.com/help/econ/arimaclass.html", "http://www.mathworks.com/help/econ/regarimaclass.html", "http://www.mathworks.com/products/econometrics/", "http://ncss.wpengine.netdna-cdn.com/wp-content/themes/ncss/pdf/Procedures/NCSS/ARIMA-Box-Jenkins.pdf", "http://ncss.wpengine.netdna-cdn.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Automatic_ARMA.pdf", "http://ncss.wpengine.netdna-cdn.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Autocorrelations.pdf", "http://www.safetoolboxes.com", "http://www.safetoolboxes.com/howto_fitarimamodel.html", "http://www.safetoolboxes.com/howto_transformtimeseries.html", "http://help.sap.com/saphelp_45b/helpdata/en/35/8a524b52060634e10000009b38f9b9/content.htm", "http://reference.wolfram.com/mathematica/ref/ARIMAProcess.html", "http://people.duke.edu/~rnau/411arim.htm", "http://people.duke.edu/~rnau/411arim.htm#arima010", "http://search.r-project.org/R/library/stats/html/arima.html", "https://github.com/JuliaStats/TimeModels.jl", "https://github.com/sryza/spark-timeseries", "https://support.sas.com/documentation/cdl/en/etsug/63939/HTML/default/viewer.htm#etsug_tffordet_sect016.htm", "https://web.archive.org/web/20160205235259/http://www.census.gov/srd/www/x12a/", "https://www.otexts.org/fpp/8/1", "https://www.otexts.org/fpp/8/7", "https://www.otexts.org/fpp/8/9", "https://pypi.python.org/pypi/statsmodels", "https://cran.r-project.org/web/packages/forecast/index.html", "https://cran.r-project.org/web/views/TimeSeries.html", "https://rubygems.org/gems/statsample-timeseries", "https://www.tol-project.org/"]}, "Limiting density of discrete points": {"categories": ["All articles needing expert attention", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Information theory", "Mathematics articles needing expert attention", "Theory of probability distributions"], "title": "Limiting density of discrete points", "method": "Limiting density of discrete points", "url": "https://en.wikipedia.org/wiki/Limiting_density_of_discrete_points", "summary": "In information theory, the limiting density of discrete points is an adjustment to the formula of Claude Shannon for differential entropy.\nIt was formulated by Edwin Thompson Jaynes to address defects in the initial definition of differential entropy.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["Change of variables", "Claude Shannon", "Differential entropy", "Edwin Thompson Jaynes", "Entropy", "Information theory", "International Standard Book Number", "Kullback\u2013Leibler divergence"], "references": ["http://bayes.wustl.edu/etj/articles/brandeis.pdf", "http://bayes.wustl.edu/etj/articles/prior.pdf"]}, "Generalized chi-squared distribution": {"categories": ["Continuous distributions"], "title": "Generalized chi-squared distribution", "method": "Generalized chi-squared distribution", "url": "https://en.wikipedia.org/wiki/Generalized_chi-squared_distribution", "summary": "In probability theory and statistics, the specific name generalized chi-squared distribution (also generalized chi-square distribution) arises in relation to one particular family of variants of the chi-squared distribution. There are several other such variants for which the same term is sometimes used, or which clearly are generalizations of the chi-squared distribution, and which are treated elsewhere: some are special cases of the family discussed here, for example the noncentral chi-squared distribution and the gamma distribution, while the generalized gamma distribution is outside this family. The type of generalisation of the chi-squared distribution that is discussed here is of importance because it arises in the context of the distribution of statistical estimates in cases where the usual statistical theory does not hold. For example, if a predictive model is fitted by least squares but the model errors have either autocorrelation or heteroscedasticity, then a statistical analysis of alternative model structures can be undertaken by relating changes in the sum of squares to an asymptotically valid generalized chi-squared distribution. More specifically, the distribution can be defined in terms of a quadratic form derived from a multivariate normal distribution.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Asymptotic distribution", "Autocorrelation", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biometrika", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Complex normal distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Estimation", "Ewens's sampling formula", "Explained sum of squares", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fourier analysis", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized gamma distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heteroscedasticity", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Least squares", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "MIMO", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Positive-definite matrix", "Predictive modelling", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quadratic form (statistics)", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Renewal theory", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Signal processing", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard normal", "Statistical independence", "Statistical theory", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wireless", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.statsresearch.co.nz/robert/QF.htm", "http://kth.diva-portal.org/smash/get/diva2:402940/FULLTEXT01"]}, "Central tendency": {"categories": ["Probability theory", "Summary statistics"], "title": "Central tendency", "method": "Central tendency", "url": "https://en.wikipedia.org/wiki/Central_tendency", "summary": "In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution. It may also be called a center or location of the distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s.The most common measures of central tendency are the arithmetic mean, the median and the mode. A central tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote \"the tendency of quantitative data to cluster around some central value.\"The central tendency of a distribution is typically contrasted with its dispersion or variability; dispersion and central tendency are the often characterized properties of distributions. Analysts may judge whether data has a strong or a weak central tendency based on its dispersion.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average absolute deviation", "Averages", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calculus of variations", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Centrality", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Coercive function", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convex function", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric median", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "International Statistical Institute", "Interquartile mean", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum deviation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Midhinge", "Midrange", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiplicative inverse", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric skew", "Nonparametric statistics", "Normal distribution", "Nth root", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-norm", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quadratic mean", "Quality control", "Quartile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Root mean square", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simplex", "Simplicial depth", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Strictly convex", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Trimean", "Truncated mean", "Tukey median", "U-statistic", "Uniformly most powerful test", "Unimodal distribution", "V-statistic", "Variance", "Variation ratio", "Vector autoregression", "Wald test", "Wavelet", "Weighted arithmetic mean", "Whittle likelihood", "Wilcoxon signed-rank test", "Winsorized mean", "Z-test"], "references": []}, "Khmaladze transformation": {"categories": ["All Wikipedia articles needing clarification", "All articles with incomplete citations", "All articles with unsourced statements", "Articles with incomplete citations from August 2013", "Articles with unsourced statements from August 2013", "Empirical process", "Theory of probability distributions", "Transforms", "Wikipedia articles needing clarification from September 2008"], "title": "Khmaladze transformation", "method": "Khmaladze transformation", "url": "https://en.wikipedia.org/wiki/Khmaladze_transformation", "summary": "In statistics, the Khmaladze transformation is a mathematical tool used in constructing convenient goodness of fit tests for hypothetical distribution functions. More precisely, suppose \n \n \n \n \n X\n \n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n \n \n {\\displaystyle X_{1},\\ldots ,X_{n}}\n are i.i.d., possibly multi-dimensional, random observations generated from an unknown probability distribution. A classical problem in statistics is to decide how well a given hypothetical distribution function \n \n \n \n F\n \n \n {\\displaystyle F}\n , or a given hypothetical parametric family of distribution functions \n \n \n \n {\n \n F\n \n \u03b8\n \n \n :\n \u03b8\n \u2208\n \u0398\n }\n \n \n {\\displaystyle \\{F_{\\theta }:\\theta \\in \\Theta \\}}\n , fits the set of observations. The Khmaladze transformation allows us to construct goodness of fit tests with desirable properties. It is named after Estate V. Khmaladze.\nConsider the sequence of empirical distribution functions \n \n \n \n \n F\n \n n\n \n \n \n \n {\\displaystyle F_{n}}\n based on a sequence of i.i.d random variables, \n \n \n \n \n X\n \n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n \n \n {\\displaystyle X_{1},\\ldots ,X_{n}}\n , as n increases. Suppose \n \n \n \n F\n \n \n {\\displaystyle F}\n is the hypothetical distribution function of each \n \n \n \n \n X\n \n i\n \n \n \n \n {\\displaystyle X_{i}}\n . To test whether the choice of \n \n \n \n F\n \n \n {\\displaystyle F}\n is correct or not, statisticians use the normalized difference,\n\n \n \n \n \n v\n \n n\n \n \n (\n x\n )\n =\n \n \n n\n \n \n [\n \n F\n \n n\n \n \n (\n x\n )\n \u2212\n F\n (\n x\n )\n ]\n .\n \n \n {\\displaystyle v_{n}(x)={\\sqrt {n}}[F_{n}(x)-F(x)].}\n This \n \n \n \n \n v\n \n n\n \n \n \n \n {\\displaystyle v_{n}}\n , as a random process in \n \n \n \n x\n \n \n {\\displaystyle x}\n , is called the empirical process. Various functionals of \n \n \n \n \n v\n \n n\n \n \n \n \n {\\displaystyle v_{n}}\n are used as test statistics. The change of the variable \n \n \n \n \n v\n \n n\n \n \n (\n x\n )\n =\n \n u\n \n n\n \n \n (\n t\n )\n \n \n {\\displaystyle v_{n}(x)=u_{n}(t)}\n , \n \n \n \n t\n =\n F\n (\n x\n )\n \n \n {\\displaystyle t=F(x)}\n transforms to the so-called uniform empirical process \n \n \n \n \n u\n \n n\n \n \n \n \n {\\displaystyle u_{n}}\n . The latter is an empirical processes based on independent random variables \n \n \n \n \n U\n \n i\n \n \n =\n F\n (\n \n X\n \n i\n \n \n )\n \n \n {\\displaystyle U_{i}=F(X_{i})}\n , which are uniformly distributed on \n \n \n \n [\n 0\n ,\n 1\n ]\n \n \n {\\displaystyle [0,1]}\n if the \n \n \n \n \n X\n \n i\n \n \n \n \n {\\displaystyle X_{i}}\n s do indeed have distribution function \n \n \n \n F\n \n \n {\\displaystyle F}\n .\nThis fact was discovered and first utilized by Kolmogorov (1933), Wald and Wolfowitz (1936) and Smirnov (1937) and, especially after Doob (1949) and Anderson and Darling (1952), it led to the standard rule to choose test statistics based on \n \n \n \n \n v\n \n n\n \n \n \n \n {\\displaystyle v_{n}}\n . That is, test statistics \n \n \n \n \u03c8\n (\n \n v\n \n n\n \n \n ,\n F\n )\n \n \n {\\displaystyle \\psi (v_{n},F)}\n are defined (which possibly depend on the \n \n \n \n F\n \n \n {\\displaystyle F}\n being tested) in such a way that there exists another statistic \n \n \n \n \u03c6\n (\n \n u\n \n n\n \n \n )\n \n \n {\\displaystyle \\varphi (u_{n})}\n derived from the uniform empirical process, such that \n \n \n \n \u03c8\n (\n \n v\n \n n\n \n \n ,\n F\n )\n =\n \u03c6\n (\n \n u\n \n n\n \n \n )\n \n \n {\\displaystyle \\psi (v_{n},F)=\\varphi (u_{n})}\n . Examples are\n\n \n \n \n \n sup\n \n x\n \n \n \n |\n \n \n v\n \n n\n \n \n (\n x\n )\n \n |\n \n =\n \n sup\n \n t\n \n \n \n |\n \n \n u\n \n n\n \n \n (\n t\n )\n \n |\n \n ,\n \n \n sup\n \n x\n \n \n \n \n \n \n |\n \n \n v\n \n n\n \n \n (\n x\n )\n \n |\n \n \n \n a\n (\n F\n (\n x\n )\n )\n \n \n \n =\n \n sup\n \n t\n \n \n \n \n \n \n |\n \n \n u\n \n n\n \n \n (\n t\n )\n \n |\n \n \n \n a\n (\n t\n )\n \n \n \n \n \n {\\displaystyle \\sup _{x}|v_{n}(x)|=\\sup _{t}|u_{n}(t)|,\\quad \\sup _{x}{\\frac {|v_{n}(x)|}{a(F(x))}}=\\sup _{t}{\\frac {|u_{n}(t)|}{a(t)}}}\n and\n\n \n \n \n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n \n v\n \n n\n \n \n 2\n \n \n (\n x\n )\n \n d\n F\n (\n x\n )\n =\n \n \u222b\n \n 0\n \n \n 1\n \n \n \n u\n \n n\n \n \n 2\n \n \n (\n t\n )\n \n d\n t\n .\n \n \n {\\displaystyle \\int _{-\\infty }^{\\infty }v_{n}^{2}(x)\\,dF(x)=\\int _{0}^{1}u_{n}^{2}(t)\\,dt.}\n For all such functionals, their null distribution (under the hypothetical \n \n \n \n F\n \n \n {\\displaystyle F}\n ) does not depend on \n \n \n \n F\n \n \n {\\displaystyle F}\n , and can be calculated once and then used to test any \n \n \n \n F\n \n \n {\\displaystyle F}\n .\nHowever, it is only rarely that one needs to test a simple hypothesis, when a fixed \n \n \n \n F\n \n \n {\\displaystyle F}\n as a hypothesis is given. Much more often, one needs to verify parametric hypotheses where the hypothetical \n \n \n \n F\n =\n \n F\n \n \n \u03b8\n \n n\n \n \n \n \n \n \n {\\displaystyle F=F_{\\theta _{n}}}\n , depends on some parameters \n \n \n \n \n \u03b8\n \n n\n \n \n \n \n {\\displaystyle \\theta _{n}}\n , which the hypothesis does not specify and which have to be estimated from the sample \n \n \n \n \n X\n \n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n \n \n {\\displaystyle X_{1},\\ldots ,X_{n}}\n itself.\nAlthough the estimators \n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n n\n \n \n \n \n {\\displaystyle {\\hat {\\theta }}_{n}}\n , most commonly converge to true value of \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n , it was discovered that the parametric, or estimated, empirical process\n\n \n \n \n \n \n \n \n v\n ^\n \n \n \n \n n\n \n \n (\n x\n )\n =\n \n \n n\n \n \n [\n \n F\n \n n\n \n \n (\n x\n )\n \u2212\n \n F\n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n n\n \n \n \n \n (\n x\n )\n ]\n \n \n {\\displaystyle {\\hat {v}}_{n}(x)={\\sqrt {n}}[F_{n}(x)-F_{{\\hat {\\theta }}_{n}}(x)]}\n differs significantly from \n \n \n \n \n v\n \n n\n \n \n \n \n {\\displaystyle v_{n}}\n and that the transformed process \n \n \n \n \n \n \n \n u\n ^\n \n \n \n \n n\n \n \n (\n t\n )\n =\n \n \n \n \n v\n ^\n \n \n \n \n n\n \n \n (\n x\n )\n \n \n {\\displaystyle {\\hat {u}}_{n}(t)={\\hat {v}}_{n}(x)}\n , \n \n \n \n t\n =\n \n F\n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n n\n \n \n \n \n (\n x\n )\n \n \n {\\displaystyle t=F_{{\\hat {\\theta }}_{n}}(x)}\n has a distribution for which the limit distribution, as \n \n \n \n n\n \u2192\n \u221e\n \n \n {\\displaystyle n\\to \\infty }\n , is dependent on the parametric form of \n \n \n \n \n F\n \n \u03b8\n \n \n \n \n {\\displaystyle F_{\\theta }}\n and on the particular estimator \n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n n\n \n \n \n \n {\\displaystyle {\\hat {\\theta }}_{n}}\n and, in general, within one parametric family, on the value of \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n .\nFrom mid-1950s to the late-1980s, much work was done to clarify the situation and understand the nature of the process \n \n \n \n \n \n \n \n v\n ^\n \n \n \n \n n\n \n \n \n \n {\\displaystyle {\\hat {v}}_{n}}\n .\nIn 1981, and then 1987 and 1993, Khmaladze suggested to replace the parametric empirical process \n \n \n \n \n \n \n \n v\n ^\n \n \n \n \n n\n \n \n \n \n {\\displaystyle {\\hat {v}}_{n}}\n by its martingale part \n \n \n \n \n w\n \n n\n \n \n \n \n {\\displaystyle w_{n}}\n only.\n\n \n \n \n \n \n \n \n v\n ^\n \n \n \n \n n\n \n \n (\n x\n )\n \u2212\n \n K\n \n n\n \n \n (\n x\n )\n =\n \n w\n \n n\n \n \n (\n x\n )\n \n \n {\\displaystyle {\\hat {v}}_{n}(x)-K_{n}(x)=w_{n}(x)}\n where \n \n \n \n \n K\n \n n\n \n \n (\n x\n )\n \n \n {\\displaystyle K_{n}(x)}\n is the compensator of \n \n \n \n \n \n \n \n v\n ^\n \n \n \n \n n\n \n \n (\n x\n )\n \n \n {\\displaystyle {\\hat {v}}_{n}(x)}\n . Then the following properties of \n \n \n \n \n w\n \n n\n \n \n \n \n {\\displaystyle w_{n}}\n were established:\n\nAlthough the form of \n \n \n \n \n K\n \n n\n \n \n \n \n {\\displaystyle K_{n}}\n , and therefore, of \n \n \n \n \n w\n \n n\n \n \n \n \n {\\displaystyle w_{n}}\n , depends on \n \n \n \n \n F\n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n n\n \n \n \n \n (\n x\n )\n \n \n {\\displaystyle F_{{\\hat {\\theta }}_{n}}(x)}\n , as a function of both \n \n \n \n x\n \n \n {\\displaystyle x}\n and \n \n \n \n \n \u03b8\n \n n\n \n \n \n \n {\\displaystyle \\theta _{n}}\n , the limit distribution of the time transformed process\n \n \n \n \n \u03c9\n \n n\n \n \n (\n t\n )\n =\n \n w\n \n n\n \n \n (\n x\n )\n ,\n t\n =\n \n F\n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n n\n \n \n \n \n (\n x\n )\n \n \n {\\displaystyle \\omega _{n}(t)=w_{n}(x),t=F_{{\\hat {\\theta }}_{n}}(x)}\n is that of standard Brownian motion on \n \n \n \n [\n 0\n ,\n 1\n ]\n \n \n {\\displaystyle [0,1]}\n , i.e., is again standard and independent of the choice of \n \n \n \n \n F\n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n n\n \n \n \n \n \n \n {\\displaystyle F_{{\\hat {\\theta }}_{n}}}\n .The relationship between \n \n \n \n \n \n \n \n v\n ^\n \n \n \n \n n\n \n \n \n \n {\\displaystyle {\\hat {v}}_{n}}\n and \n \n \n \n \n w\n \n n\n \n \n \n \n {\\displaystyle w_{n}}\n and between their limits, is one to one, so that the statistical inference based on \n \n \n \n \n \n \n \n v\n ^\n \n \n \n \n n\n \n \n \n \n {\\displaystyle {\\hat {v}}_{n}}\n or on \n \n \n \n \n w\n \n n\n \n \n \n \n {\\displaystyle w_{n}}\n are equivalent, and in \n \n \n \n \n w\n \n n\n \n \n \n \n {\\displaystyle w_{n}}\n , nothing is lost compared to \n \n \n \n \n \n \n \n v\n ^\n \n \n \n \n n\n \n \n \n \n {\\displaystyle {\\hat {v}}_{n}}\n .\nThe construction of innovation martingale \n \n \n \n \n w\n \n n\n \n \n \n \n {\\displaystyle w_{n}}\n could be carried over to the case of vector-valued \n \n \n \n \n X\n \n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n \n \n {\\displaystyle X_{1},\\ldots ,X_{n}}\n , giving rise to the definition of the so-called scanning martingales in \n \n \n \n \n \n R\n \n \n d\n \n \n \n \n {\\displaystyle \\mathbb {R} ^{d}}\n .For a long time the transformation was, although known, still not used. Later, the work of researchers like Koenker, Stute, Bai, Koul, Koening, and others made it popular in econometrics and other fields of statistics.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Annals of Mathematical Statistics", "Annals of Statistics", "Cumulative distribution function", "Digital object identifier", "Empirical distribution function", "Empirical process", "Estate V. Khmaladze", "Functional (mathematics)", "Goodness of fit", "Hira L. Koul", "I.i.d.", "JSTOR", "Jushan Bai", "Null distribution", "Parametric family", "Probability distribution", "Roger Koenker", "Statistics", "Uniform distribution (continuous)", "Winfried Stute"], "references": ["http://doi.org/10.1007/978-3-642-04898-2_325", "http://doi.org/10.1137/1126027", "http://doi.org/10.1214/aoms/1177728538", "http://doi.org/10.1214/aoms/1177729437", "http://doi.org/10.1214/aos/1176349152", "http://www.jstor.org/stable/2236876", "http://www.jstor.org/stable/2242262"]}, "Mean preserving spread": {"categories": ["Decision theory", "Theory of probability distributions"], "title": "Mean-preserving spread", "method": "Mean preserving spread", "url": "https://en.wikipedia.org/wiki/Mean-preserving_spread", "summary": "In probability and statistics, a mean-preserving spread (MPS) is a change from one probability distribution A to another probability distribution B, where B is formed by spreading out one or more portions of A's probability density function or probability mass function while leaving the mean (the expected value) unchanged. As such, the concept of mean-preserving spreads provides a stochastic ordering of equal-mean gambles (probability distributions) according to their degree of risk; this ordering is partial, meaning that of two equal-mean gambles, it is not necessarily true that either is a mean-preserving spread of the other. A is said to be a mean-preserving contraction of B if B is a mean-preserving spread of A.\nRanking gambles by mean-preserving spreads is a special case of ranking gambles by second-order stochastic dominance \u2013 namely, the special case of equal means: If B is a mean-preserving spread of A, then A is second-order stochastically dominant over B; and the converse holds if A and B have equal means.\nIf B is a mean-preserving spread of A, then B has a higher variance than A and the expected values of A and B are identical; but the converse is not in general true, because the variance is a complete ordering while ordering by mean-preserving spreads is only partial.", "images": [], "links": ["Andreu Mas-Colell", "Contraposition", "Cumulative distribution function", "Digital object identifier", "Expected utility hypothesis", "Expected value", "Google Books", "International Standard Book Number", "Joseph Stiglitz", "Journal of Economic Theory", "Michael Rothschild", "Partially ordered set", "Probability and statistics", "Probability density function", "Probability distribution", "Probability mass function", "Random variable", "Review of Economic Studies", "Risk", "Risk (statistics)", "Stochastic dominance", "Stochastic ordering"], "references": ["http://doi.org/10.1016%2F0022-0531(70)90038-4", "http://doi.org/10.2307%2F2298068", "https://books.google.com/books?id=KGtegVXqD8wC&pg=PA197"]}, "Multinomial probit": {"categories": ["All articles needing additional references", "All articles to be expanded", "Articles needing additional references from July 2015", "Articles to be expanded from February 2017", "Articles using small message boxes", "Regression analysis", "Statistical classification"], "title": "Multinomial probit", "method": "Multinomial probit", "url": "https://en.wikipedia.org/wiki/Multinomial_probit", "summary": "In statistics and econometrics, the multinomial probit model is a generalization of the probit model used when there are several possible categories that the dependent variable can fall into. As such, it is an alternative to the multinomial logit model as one method of multiclass classification. It is not to be confused with the multivariate probit model, which is used to model correlated binary outcomes for more than one independent variable.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Blood pressure", "Body-mass index", "Categorical distribution", "Dependent variable", "Discrete choice", "Econometrics", "Error variable", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Heteroscedasticity", "Independence of irrelevant alternatives", "Independent variable", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Latent variable model", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Mean and predicted response", "Mixed logit", "Mixed model", "Multiclass classification", "Multilevel model", "Multinomial logit", "Multivariate probit model", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistical model", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Weighted least squares", "William Greene (economist)"], "references": []}, "Survivorship bias": {"categories": ["All articles needing additional references", "All articles with specifically marked weasel-worded phrases", "All articles with unsourced statements", "Articles needing additional references from April 2017", "Articles needing additional references from December 2017", "Articles needing additional references from September 2018", "Articles with specifically marked weasel-worded phrases from June 2017", "Articles with unsourced statements from April 2017", "Articles with unsourced statements from September 2010", "Articles with unsourced statements from September 2018", "Bias", "Cognitive biases", "Informal fallacies", "Sampling (statistics)", "Webarchive template wayback links"], "title": "Survivorship bias", "method": "Survivorship bias", "url": "https://en.wikipedia.org/wiki/Survivorship_bias", "summary": "Survivorship bias or survival bias is the logical error of concentrating on the people or things that made it past some selection process and overlooking those that did not, typically because of their lack of visibility. This can lead to false conclusions in several different ways. It is a form of selection bias.\nSurvivorship bias can lead to overly optimistic beliefs because failures are ignored, such as when companies that no longer exist are excluded from analyses of financial performance. It can also lead to the false belief that the successes in a group have some special property, rather than just coincidence (correlation proves causality). For example, if three of the five students with the best college grades went to the same high school, that can lead one to believe that the high school must offer an excellent education. This could be true, but the question cannot be answered without looking at the grades of all the other students from that high school, not just the ones who \"survived\" the top-five selection process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/98/Survivorship-bias.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abraham Wald", "Academic bias", "Academic clinical trials", "Acquiescence bias", "Adaptive clinical trial", "Alpha (investment)", "Analysis of clinical trials", "Anchoring", "Animal testing", "Animal testing on non-human primates", "Artifact (error)", "Attentional bias", "Attributable fraction among the exposed", "Attributable fraction for the population", "Attribution bias", "Authority bias", "Automation bias", "Backtesting", "Belief bias", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Blind experiment", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Cherry picking", "Choice-supportive bias", "Clades", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Cohort study", "Confirmation bias", "Congruence bias", "Correlation does not imply causation", "Cross-sectional study", "Cultural bias", "Cumulative incidence", "Debiasing", "Design of experiments", "Digital object identifier", "Diogenes", "Distinction bias", "Dunning\u2013Kruger effect", "EHarmony", "Ecological study", "Econometrics", "Egocentric bias", "Emotional bias", "Epidemiological methods", "Evidence-based medicine", "Experiment", "Extra-sensory perception", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Fads and Fallacies in the Name of Science", "False advertising", "Finance", "First-in-man study", "Fooled by Randomness", "Forecast bias", "Fundamental attribution error", "Funding bias", "Genetic divergence", "Glossary of clinical research", "Halo effect", "Hazard ratio", "Healthy user bias", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "Impact bias", "Improbability", "In-group favoritism", "In vitro", "In vivo", "Incidence (epidemiology)", "Inductive bias", "Infectivity", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "Intention-to-treat analysis", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Joseph Banks Rhine", "Lead time bias", "Length time bias", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "List of cognitive biases", "List of memory biases", "Logical error", "Longitudinal study", "Martin Gardner", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "Multiple comparisons problem", "Mutual fund", "Nassim Taleb", "Negativity bias", "Nested case\u2013control study", "Net bias", "Normalcy bias", "Null hypothesis", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Omission bias", "Omitted-variable bias", "Open-label trial", "Operational research", "Optimism bias", "Outcome bias", "Overengineering", "Overton window", "PLoS Med", "Parapsychology", "Participation bias", "Period prevalence", "Planned obsolescence", "Point prevalence", "Population Impact Measures", "Post hoc ergo propter hoc", "Pre- and post-test probability", "Precision bias", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Pro-innovation bias", "Prospective cohort study", "Protocol (science)", "Psychology", "PubMed Central", "PubMed Identifier", "Publication bias", "Push of the past", "Randomized controlled trial", "Recall bias", "Relative risk reduction", "Reporting bias", "Reproducibility", "Response bias", "Restraint bias", "Retrospective cohort study", "Review of Financial Studies", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "S&P 500", "Sampling bias", "Scientific American", "Scientific control", "Scientist", "Seeding trial", "Selection bias", "Selection principle", "Self-selection bias", "Self-serving bias", "Social comparison bias", "Social desirability bias", "Specificity and sensitivity", "Spectrum bias", "Statistical", "Statistically significant", "Status quo bias", "Systematic error", "Systematic review", "Systemic bias", "Telepath", "Terminal velocity", "Texas sharpshooter fallacy", "The Black Swan (Taleb book)", "The Straight Dope", "Time-saving bias", "Trade secret", "Trait ascription bias", "United States news media and the Vietnam War", "University of Waterloo", "Vaccine trial", "Verification bias", "Virulence", "Von Restorff effect", "Washington Post", "Wayback Machine", "Wet bias", "White hat bias", "Zener cards", "Zero-risk bias"], "references": ["http://www.petplace.com/cats/highrise-syndrome-in-cats/page1.aspx", "http://www.scientificamerican.com/article/how-the-survivor-bias-distorts-reality/", "http://www.straightdope.com/classics/a5_190.html", "http://www.ocf.berkeley.edu/~barneye/kitty.html", "http://www4.ncsu.edu/~swu6/documents/A_Reprint_Plane_Vulnerability.pdf", "http://people.ucsc.edu/~msmangel/Wald.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182327", "http://www.ncbi.nlm.nih.gov/pubmed/16060722", "http://www.ncbi.nlm.nih.gov/pubmed/3692980", "http://doi.org/10.1016%2FS0169-5347(02)02491-6", "http://doi.org/10.1093%2Frfs%2F9.4.1097", "http://doi.org/10.1111%2F1365-2745.12815", "http://doi.org/10.1371%2Fjournal.pmed.0020124", "http://doi.org/10.2307%2F2288257", "http://www.jstor.org/stable/2288257", "http://www.worldcat.org/issn/0022-0477", "http://www.worldcat.org/issn/0169-5347", "https://www.bloomberg.com/bw/articles/2014-08-11/success-stories-how-survivorship-bias-tricks-entrepreneurs", "https://www.bloomberg.com/news/articles/2014-08-11/success-stories-how-survivorship-bias-tricks-entrepreneurs", "https://www.forbes.com/sites/carminegallo/2012/12/06/high-tech-dropouts-misinterpret-steve-jobs-advice/", "https://www.theatlantic.com/business/archive/2013/03/the-myth-of-the-successful-college-dropout-why-it-could-make-millions-of-young-americans-poorer/273628/", "https://www.washingtonpost.com/wp-dyn/content/article/2007/05/12/AR2007051201350.html", "https://onlinelibrary.wiley.com/doi/10.1111/evo.13593", "https://web.archive.org/web/20070712033200/http://www.ocf.berkeley.edu/~barneye/kitty.html"]}, "Moving average representation": {"categories": ["Statistical theorems", "Time series", "Wikipedia articles needing clarification from December 2015"], "title": "Wold's theorem", "method": "Moving average representation", "url": "https://en.wikipedia.org/wiki/Wold%27s_theorem", "summary": "In statistics, Wold's decomposition or the Wold representation theorem (not to be confused with the Wold theorem that is the discrete-time analog of the Wiener\u2013Khinchin theorem), named after Herman Wold, says that every covariance-stationary time series \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n can be written as the sum of two time series, one deterministic and one stochastic.\nFormally\n\n \n \n \n \n Y\n \n t\n \n \n =\n \n \u2211\n \n j\n =\n 0\n \n \n \u221e\n \n \n \n b\n \n j\n \n \n \n \u03b5\n \n t\n \u2212\n j\n \n \n +\n \n \u03b7\n \n t\n \n \n ,\n \n \n {\\displaystyle Y_{t}=\\sum _{j=0}^{\\infty }b_{j}\\varepsilon _{t-j}+\\eta _{t},}\n where:\n\n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n is the time series being considered,\n \n \n \n \n \u03b5\n \n t\n \n \n \n \n {\\displaystyle \\varepsilon _{t}}\n is an uncorrelated sequence which is the innovation process to the process \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n \u2013 that is, a white noise process that is input to the linear filter \n \n \n \n {\n \n b\n \n j\n \n \n }\n \n \n {\\displaystyle \\{b_{j}\\}}\n .\n \n \n \n b\n \n \n {\\displaystyle b}\n is the possibly infinite vector of moving average weights (coefficients or parameters)\n \n \n \n \n \u03b7\n \n t\n \n \n \n \n {\\displaystyle \\eta _{t}}\n is a deterministic time series, such as one represented by a sine wave.The moving average coefficients have these properties:\n\nStable, that is square summable \n \n \n \n \n \u2211\n \n j\n =\n 1\n \n \n \u221e\n \n \n \n |\n \n \n b\n \n j\n \n \n \n \n |\n \n \n 2\n \n \n \n \n {\\displaystyle \\sum _{j=1}^{\\infty }|b_{j}|^{2}}\n < \n \n \n \n \u221e\n \n \n {\\displaystyle \\infty }\n \nCausal (i.e. there are no terms with j < 0)\nMinimum delay\nConstant (\n \n \n \n \n b\n \n j\n \n \n \n \n {\\displaystyle b_{j}}\n independent of t)\nIt is conventional to define \n \n \n \n \n b\n \n 0\n \n \n =\n 1\n \n \n {\\displaystyle b_{0}=1}\n This theorem can be considered as an existence theorem: any stationary process has this seemingly special representation. Not only is the existence of such a simple linear and exact representation remarkable, but even more so is the special nature of the moving average model. Imagine creating a process that is a moving average but not satisfying these properties 1\u20134. For example, the coefficients \n \n \n \n \n b\n \n j\n \n \n \n \n {\\displaystyle b_{j}}\n could define an acausal and non-minimum delay model. Nevertheless the theorem assures the existence of a causal minimum delay moving average that exactly represents this process. How this all works for the case of causality and the minimum delay property is discussed in Scargle (1981), where an extension of the Wold Decomposition is discussed.\nThe usefulness of the Wold Theorem is that it allows the dynamic evolution of a variable \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n to be approximated by a linear model. If the innovations \n \n \n \n \n \u03b5\n \n t\n \n \n \n \n {\\displaystyle \\varepsilon _{t}}\n are independent, then the linear model is the only possible representation relating the observed value of \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n to its past evolution. However, when \n \n \n \n \n \u03b5\n \n t\n \n \n \n \n {\\displaystyle \\varepsilon _{t}}\n is merely an uncorrelated but not independent sequence, then the linear model exists but it is not the only representation of the dynamic dependence of the series. In this latter case, it is possible that the linear model may not be very useful, and there would be a nonlinear model relating the observed value of \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n to its past evolution. However, in practical time series analysis, it is often the case that only linear predictors are considered, partly on the grounds of simplicity, in which case the Wold decomposition is directly relevant.\nThe Wold representation depends on an infinite number of parameters, although in practice they usually decay rapidly. The autoregressive model is an alternative that may have only a few coefficients if the corresponding moving average has many. These two models can be combined into an autoregressive-moving average (ARMA) model, or an autoregressive-integrated-moving average (ARIMA) model if non-stationarity is involved. See Scargle (1981) and references there; in addition this paper gives an extension of the Wold Theorem that allows more generality for the moving average (not necessarily stable, causal, or minimum delay) accompanied by a sharper characterization of the innovation (identically and independently distributed, not just uncorrelated). This extension allows the possibility of models that are more faithful to physical or astrophysical processes, and in particular can sense \u2033the arrow of time.\u2033", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive model", "Autoregressive moving average model", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dynamical system", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Herman Wold", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Innovation (signal processing)", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jeffrey Scargle", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear filter", "Linear model", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marc Nerlove", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Whittle (mathematician)", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Theodore Wilbur Anderson", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uncorrelated", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wiener\u2013Khinchin theorem", "Wilcoxon signed-rank test", "Wold decomposition", "Z-test"], "references": []}, "Tornqvist index": {"categories": ["All articles with dead external links", "Articles with dead external links from July 2018", "Articles with permanently dead external links", "Price index theory", "Webarchive template wayback links"], "title": "T\u00f6rnqvist index", "method": "Tornqvist index", "url": "https://en.wikipedia.org/wiki/T%C3%B6rnqvist_index", "summary": "In economics, the T\u00f6rnqvist index is a price or quantity index. In practice, T\u00f6rnqvist index values are calculated for consecutive periods, then these are strung together, or \"chained\". Thus, the core calculation does not refer to a single base year.", "images": [], "links": ["Aggregation problem", "Arithmetic average", "Bank of Finland", "Chained dollars", "Cost curve", "Divisia index", "Economics", "Fisher index", "Geometric mean", "International Monetary Fund", "International Standard Book Number", "Leo T\u00f6rnqvist", "List of price index formulas", "Logarithm", "Multifactor productivity", "Natural logarithms", "Organisation for Economic Co-operation and Development", "Price index", "Production function", "Quantity index", "Statistics New Zealand", "Translog", "United States Chained Consumer Price Index", "Vector notation", "Wayback Machine", "Weighted"], "references": ["http://www.pc.gov.au/research/productivity/estimates-trends/methodology", "http://stats.bls.gov/hom/homch10.pdf", "http://www.bls.gov/cpi/super_paris.pdf", "http://www.bls.gov/mfp/mprover.htm", "http://www.ers.usda.gov/publications/tb1872/tb1872d.pdf", "http://www2.stats.govt.nz/domino/external/omni/omni.nsf/wwwglsry/tornqvist+index+and+other+log-change+index+numbers", "http://www.imf.org/external/np/sta/tegppi/gloss.pdf", "http://stats.oecd.org/glossary/detail.asp?ID=2711", "http://econpapers.repec.org/RePEc:eee:ecolet:v:76:y:2002:i:2:p:251-258", "https://web.archive.org/web/20100615153935/http://www.ers.usda.gov/publications/tb1872/tb1872d.pdf", "https://web.archive.org/web/20110928000903/http://www.pc.gov.au/research/productivity/estimates-trends/methodology", "https://web.archive.org/web/20131224111339/http://www2.stats.govt.nz/domino/external/omni/omni.nsf/wwwglsry/tornqvist+index+and+other+log-change+index+numbers", "https://www.jstor.org/stable/view/1924361"]}, "Indecomposable distribution": {"categories": ["Types of probability distributions", "Wikipedia articles needing clarification from January 2017"], "title": "Indecomposable distribution", "method": "Indecomposable distribution", "url": "https://en.wikipedia.org/wiki/Indecomposable_distribution", "summary": "In probability theory, an indecomposable distribution is a probability distribution that cannot be represented as the distribution of the sum of two or more non-constant independent random variables: Z \u2260 X + Y. If it can be so expressed, it is decomposable: Z = X + Y. If, further, it can be expressed as the distribution of the sum of two or more independent identically distributed random variables, then it is divisible: Z = X1 + X2.", "images": [], "links": ["Absolute continuity", "Argumentum a fortiori", "Bernoulli distribution", "Binomial distribution", "Chi-squared distribution", "Cochran's theorem", "Cram\u00e9r\u2019s decomposition theorem", "Discrete uniform distribution", "Geometric distribution", "Independent identically distributed", "Infinite divisibility (probability)", "Infinitely divisible distribution", "Khinchin's theorem on the factorization of distributions", "Negative binomial distribution", "Normal distribution", "Probability density function", "Probability distribution", "Probability theory", "Random variable", "Stable distribution", "Statistical independence", "Uniform distribution (continuous)"], "references": []}, "Random assignment": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from May 2016", "Articles needing additional references from May 2016", "Articles with multiple maintenance issues", "CS1 errors: external links", "CS1 maint: Multiple names: authors list", "Causal inference", "Design of experiments", "Experiments", "Pages with citations having bare URLs", "Pages with citations lacking titles"], "title": "Random assignment", "method": "Random assignment", "url": "https://en.wikipedia.org/wiki/Random_assignment", "summary": "Random assignment or random placement is an experimental technique for assigning human participants or animal subjects to different groups in an experiment (e.g., a treatment group versus a control group) using randomization, such as by a chance procedure (e.g., flipping a coin) or a random number generator. This ensures that each participant or subject has an equal chance of being placed in any group. Random assignment of participants helps to ensure that any differences between and within the groups are not systematic at the outset of the experiment. Thus, any differences between groups recorded at the end of the experiment can be more confidently attributed to the experimental procedures or treatment.\nRandom assignment, blinding, and controlling are key aspects of the design of experiments, because they help ensure that the results are not spurious or deceptive via confounding. This is why randomized controlled trials are vital in clinical research, especially ones that can be double-blinded and placebo-controlled.\nMathematically, there are distinctions between randomization, pseudorandomization, and quasirandomization, as well as between random number generators and pseudorandom number generators. How much these differences matter in experiments (such as clinical trials) is a matter of trial design and statistical rigor, which affect evidence grading. Studies done with pseudo- or quasirandomization are usually given nearly the same weight as those with true randomization but are viewed with a bit more caution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Animal testing", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Charles Sanders Peirce", "Charles Sanders Peirce bibliography", "Chemometrics", "Chi-squared test", "Clinical research", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Coin flipping", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Dorota Dabrowska", "Double-blinded", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental design", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human subject research", "Ian Hacking", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isis (journal)", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Joseph Jastrow", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Levels of evidence", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Low-discrepancy sequence", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Placebo-controlled", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Pseudorandom number generator", "Pseudorandomness", "Psychometrics", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random effect", "Random number generation", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Ronald A. Fisher", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen M. Stigler", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Systematic error", "Taguchi methods", "Terence Speed", "The Design of Experiments", "Time domain", "Time series", "Tolerance interval", "Treatment and control groups", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://psychclassics.yorku.ca/Peirce/small-diffs.htm", "http://www.australiabesttutors.com/Help-with-Assignment", "http://www.ncbi.nlm.nih.gov/pubmed/9519574", "http://www.socialresearchmethods.net/kb/random.php", "http://www.ams.org/mathscinet-getitem?mr=1013489", "http://www.ams.org/mathscinet-getitem?mr=1092986", "http://doi.org/10.1086%2F354775", "http://doi.org/10.1086%2F383850", "http://doi.org/10.1086%2F444032", "http://doi.org/10.1214%2Fss%2F1177012031", "http://www.jstor.org/stable/234674", "http://www.researchtool.org"]}, "Sparse binary polynomial hashing": {"categories": ["All stub articles", "Bayesian statistics", "Spam filtering", "Statistics stubs"], "title": "Sparse binary polynomial hashing", "method": "Sparse binary polynomial hashing", "url": "https://en.wikipedia.org/wiki/Sparse_binary_polynomial_hashing", "summary": "Sparse binary polynomial hashing (SBPH) is a generalization of Bayesian spam filtering that can match mutating phrases as well as single words. SBPH is a way of generating a large number of features from an incoming text automatically, and then using statistics to determine the weights for each of those features in terms of their predictive values for spam/nonspam evaluation.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Bayesian spam filtering", "Statistics"], "references": ["http://crm114.sourceforge.net/docs/CRM114_paper.html"]}, "Regression diagnostic": {"categories": ["All stub articles", "Regression diagnostics", "Statistics stubs"], "title": "Regression diagnostic", "method": "Regression diagnostic", "url": "https://en.wikipedia.org/wiki/Regression_diagnostic", "summary": "In statistics, a regression diagnostic is one of a set of procedures available for regression analysis that seek to assess the validity of a model in any of a number of different ways. This assessment may be an exploration of the model's underlying statistical assumptions, an examination of the structure of the model by considering formulations that have fewer, more or different explanatory variables, or a study of subgroups of observations, looking for those that are either poorly represented by the model (outliers) or that have a relatively large effect on the regression model's predictions.\nA regression diagnostic may take the form of a graphical result, informal quantitative results or a formal statistical hypothesis test, each of which provides guidance for further stages of a regression analysis.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Breusch\u2013Godfrey test", "Breusch\u2013Pagan test", "Chow test", "Cook's distance", "DFFITS", "Dependent and independent variables", "F test", "Goldfeld\u2013Quandt test", "Homoscedastic", "Homoscedasticity", "International Standard Book Number", "Lack-of-fit sum of squares", "Leverage (statistics)", "Linear regression", "Normal distribution", "Normal probability plot", "Ordinary least squares", "Outlier", "PRESS statistic", "Park test", "Partial leverage", "Partial regression plot", "Partial residual plot", "Ramsey RESET test", "Regression analysis", "Regression validation", "Statistical assumption", "Statistical hypothesis test", "Statistics", "Structural break test", "Student's t test", "White test"], "references": []}, "SPSS Clementine": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from December 2008", "Articles with unsourced statements from November 2012", "Data mining and machine learning software", "Proprietary commercial software for Linux"], "title": "SPSS Modeler", "method": "SPSS Clementine", "url": "https://en.wikipedia.org/wiki/SPSS_Modeler", "summary": "IBM SPSS Modeler is a data mining and text analytics software application from IBM. It is used to build predictive models and conduct other analytic tasks. It has a visual interface which allows users to leverage statistical and data mining algorithms without programming. One of its main aims from the outset was to get rid of unnecessary complexity in data transformations, and to make complex predictive models very easy to use. The first version incorporated decision trees (ID3), and neural networks (backprop), which could both be trained without underlying knowledge of how those techniques worked.\nIBM SPSS Modeler was originally named Clementine by its creators, Integral Solutions Limited. This name continued for a while after SPSS's acquisition of the product. SPSS later changed the name to SPSS Clementine, and then later to PASW Modeler. Following IBM's 2009 acquisition of SPSS, the product was renamed IBM SPSS Modeler, its current name.", "images": ["https://upload.wikimedia.org/wikipedia/en/0/0b/IBM_SPSS_Modeler_Logo.jpg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/6/6c/SPSS_Modeler_Sample_Stream.png"], "links": ["ADMB", "Analyse-it", "Artificial Intelligence", "BMDP", "BV4.1 (software)", "Business intelligence", "CSPro", "Commercial software", "Comparison of statistical packages", "Cross-platform", "Cross Industry Standard Process for Data Mining", "CumFreq", "Customer analytics", "Customer relationship management", "DAP (software)", "Data Desk", "Data mining", "Dataplot", "EViews", "Epi Info", "Forecasting", "Fraud detection", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Graphical user interface", "Gretl", "H2O (software)", "IBM", "International Standard Book Number", "JASP", "JMP (statistical software)", "JMulTi", "Java (programming language)", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Linux", "List of statistical packages", "MATLAB", "MKS Toolkit", "MLwiN", "Mac OS X", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Open-source software", "OpenBUGS", "OpenVMS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Pop11", "Poplog", "Predictive Models", "Predictive analytics", "Programming language", "Proprietary software", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "Risk management", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Inc.", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "Sensemaking", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Social network analysis", "Software categories", "Software developer", "Software license", "Software release life cycle", "Solaris (operating system)", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "StatsDirect", "Sussex University", "TSP (econometrics software)", "Text analytics", "The Unscrambler", "UNISTAT", "Unix", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http:ftp://public.dhe.ibm.com/software/analytics/spss/documentation/modeler/15.0/en/UsersGuide.pdf", "http:ftp://ftp.software.ibm.com/software/analytics/spss/support/Modeler/Documentation/14/UserManual/CRISP-DM.pdf", "http://store.elsevier.com/product.jsp?isbn=9780123747655&pagename=search", "http://www.forrester.com/pimages/rws/reprints/document/80281/oid/1-KRB1C8", "http://public.dhe.ibm.com/common/ssi/ecm/en/imw14303usen/IMW14303USEN.PDF", "http://public.dhe.ibm.com/common/ssi/ecm/en/ytw03085usen/YTW03085USEN.PDF", "http://www-01.ibm.com/software/analytics/spss/12/patient-outcomes/", "http://www-01.ibm.com/software/analytics/spss/products/modeler/", "http://www-01.ibm.com/software/success/cssdb.nsf/CS/KKMH-88U29V?OpenDocument&Site=default&cty=en_us", "http://www-01.ibm.com/software/success/cssdb.nsf/cs/STRD-8LJJGH?OpenDocument&Site=spss&cty=en_us", "http://intelligent-enterprise.informationweek.com/showArticle.jhtml;jsessionid=NJTHOD3PYRWU3QE1GHOSKHWATMY32JVN?articleID=216500162", "http://www.cs.bham.ac.uk/research/projects/poplog/isl-docs/1999-AISBQ-TheStoryofClementine.pdf", "http://www.timeshighereducation.co.uk/story.asp?storyCode=154315§ioncode=26", "https://www.apponfly.com/en/ibm-spss-modeler", "https://developer.ibm.com/predictiveanalytics/2016/03/15/announcing-ibm-spss-modeler-18/", "https://developer.ibm.com/predictiveanalytics/2017/06/20/ibm-spss-modeler-18-1-coding-free-open-source-seamless-weather-data-optimization-integration-text-analytics-big-data/", "https://www.ibm.com/products/spss-modeler"]}, "Examples of Markov chains": {"categories": ["All articles needing additional references", "Articles needing additional references from June 2016", "Markov models", "Mathematical examples"], "title": "Examples of Markov chains", "method": "Examples of Markov chains", "url": "https://en.wikipedia.org/wiki/Examples_of_Markov_chains", "summary": "This page contains examples of Markov chains in action.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/7a/Markov_Chain_weather_model_matrix_as_a_graph.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Absorbing Markov chain", "Blackjack", "Dice", "Eigenvalue", "Eigenvector", "Interacting particle system", "International Standard Book Number", "Mark V. Shaney", "Markov chain", "Random walk", "Snakes and ladders", "Stochastic cellular automata", "Stochastic matrix"], "references": ["http://www.bewersdorff-online.de/amonopoly/", "https://www.math.drexel.edu/~jwd25/LM_SPRING_07/lectures/Markov.html"]}, "Unseen species problem": {"categories": ["Biostatistics", "Ecology"], "title": "Unseen species problem", "method": "Unseen species problem", "url": "https://en.wikipedia.org/wiki/Unseen_species_problem", "summary": "The unseen species problem is commonly referred to in ecology and deals with the estimation of the number of species represented in an ecosystem that were not observed by samples. It more specifically relates to how many new species would be discovered if more samples were taken in an ecosystem. The study of the unseen species problem was started in the early 1940s by Alexander Corbet. He spent 2 years in Malaya trapping butterflies, and was curious how many new species he would discover if he spent another 2 years trapping. Many different estimation methods have been developed to determine how many new species would be discovered given more samples. The unseen species problem also applies more broadly, as the estimators can be used to estimate any new elements of a set not previously found in samples. An example of this is determining how many words William Shakespeare knew based on all of his written works. The unseen species problem can be broken down mathematically as follows:\nIf \n \n \n \n n\n \n \n {\\textstyle n}\n independent samples are taken, \n \n \n \n \n X\n \n n\n \n \n \u225c\n \n X\n \n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n \n \n {\\textstyle X^{n}\\triangleq X_{1},\\ldots ,X_{n}}\n , and then if \n \n \n \n m\n \n \n {\\textstyle m}\n more independent samples were taken, the number of unseen species that will be discovered by the additional samples is given bywith \n \n \n \n \n X\n \n n\n +\n 1\n \n \n m\n +\n n\n \n \n \u225c\n \n X\n \n n\n +\n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n +\n m\n \n \n \n \n {\\textstyle X_{n+1}^{m+n}\\triangleq X_{n+1},\\ldots ,X_{n+m}}\n being the second set of \n \n \n \n m\n \n \n {\\displaystyle m}\n samples.\nIn the early 1940s Alexander Steven Corbet spent 2 years in Malaya trapping butterflies. He kept track of how many species he observed, and how many members of each species were captured. For example, he captured only 2 members of 74 different species. When he returned to the United Kingdom, he approached statistician Ronald Fisher, and asked how many new species of butterflies he could expect to catch if he went trapping for another two years. In essence, Corbet was asking how many species he observed zero times.Fisher responded with a simple estimation: for an additional 2 years of trapping, Corbet could expect to capture 75 new species. He did this using a simple summation (data provided by Orlitsky in Table 1 below in the Example section):Here, \n \n \n \n \n \u03c6\n \n i\n \n \n \n \n {\\textstyle \\varphi _{i}}\n corresponds to the number of individual species which were observed \n \n \n \n i\n \n \n {\\textstyle i}\n times. Fisher's sum was later confirmed by Good\u2013Toulmin.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/6/61/Unseen_Species_Example.png"], "links": ["Alexander Steven Corbet", "ArXiv", "Digital object identifier", "Euler transform", "Exponential function", "German tank problem", "International Standard Serial Number", "JSTOR", "Logarithm", "PubMed Central", "Ronald Fisher", "Species discovery curve", "William Shakespeare"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2169286", "http://arxiv.org/abs/1511.07428", "http://arxiv.org/archive/math.ST", "http://doi.org/10.1073/pnas.1607774113", "http://doi.org/10.1093/biomet/43.1-2.45", "http://doi.org/10.1098/rspb.2007.0464", "http://doi.org/10.2307/2335721", "http://www.jstor.org/stable/2335721", "http://www.pnas.org/cgi/doi/10.1073/pnas.1607774113", "http://www.worldcat.org/issn/0006-3444", "https://academic.oup.com/biomet/article/43/1-2/45/334874", "https://www.researchgate.net/publication/6373629"]}, "Gauss's inequality": {"categories": ["Probabilistic inequalities"], "title": "Gauss's inequality", "method": "Gauss's inequality", "url": "https://en.wikipedia.org/wiki/Gauss%27s_inequality", "summary": "In probability theory, Gauss's inequality (or the Gauss inequality) gives an upper bound on the probability that a unimodal random variable lies more than any given distance from its mode.\nLet X be a unimodal random variable with mode m, and let \u03c4 2 be the expected value of (X \u2212 m)2. (\u03c4 2 can also be expressed as (\u03bc \u2212 m)2 + \u03c3 2, where \u03bc and \u03c3 are the mean and standard deviation of X.) Then for any positive value of k,\n\n \n \n \n Pr\n (\n \u2223\n X\n \u2212\n m\n \u2223>\n k\n )\n \u2264\n \n \n {\n \n \n \n \n \n (\n \n \n \n 2\n \u03c4\n \n \n 3\n k\n \n \n \n )\n \n \n 2\n \n \n \n \n \n if \n \n k\n \u2265\n \n \n \n 2\n \u03c4\n \n \n 3\n \n \n \n \n \n \n \n 1\n \u2212\n \n \n k\n \n \u03c4\n \n \n 3\n \n \n \n \n \n \n \n \n if \n \n 0\n \u2264\n k\n \u2264\n \n \n \n 2\n \u03c4\n \n \n 3\n \n \n \n .\n \n \n \n \n \n \n \n \n {\\displaystyle \\Pr(\\mid X-m\\mid >k)\\leq {\\begin{cases}\\left({\\frac {2\\tau }{3k}}\\right)^{2}&{\\text{if }}k\\geq {\\frac {2\\tau }{\\sqrt {3}}}\\\\[6pt]1-{\\frac {k}{\\tau {\\sqrt {3}}}}&{\\text{if }}0\\leq k\\leq {\\frac {2\\tau }{\\sqrt {3}}}.\\end{cases}}}\n The theorem was first proved by Carl Friedrich Gauss in 1823.", "images": [], "links": ["American Statistician", "Carl Friedrich Gauss", "Chebyshev's inequality", "Digital object identifier", "Expected value", "Gaussian correlation inequality", "Gaussian isoperimetric inequality", "JSTOR", "Mode (statistics)", "Probability theory", "Random variable", "Standard deviation", "Unimodal", "Vysochanski\u00ef\u2013Petunin inequality"], "references": ["http://www.answers.com/topic/gauss-inequality", "http://doi.org/10.2307%2F2684253", "http://doi.org/10.2307%2F2684690", "http://www.jstor.org/stable/2684253", "http://www.jstor.org/stable/2684690"]}, "Bayesian multivariate linear regression": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "Bayesian inference", "Single-equation methods (econometrics)"], "title": "Bayesian multivariate linear regression", "method": "Bayesian multivariate linear regression", "url": "https://en.wikipedia.org/wiki/Bayesian_multivariate_linear_regression", "summary": "In statistics, Bayesian multivariate linear regression is a\nBayesian approach to multivariate linear regression, i.e. linear regression where the predicted outcome is a vector of correlated random variables rather than a single scalar random variable. A more general treatment of this approach can be found in the article MMSE estimator.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Bayesian inference", "Bayesian linear regression", "Dependent variable", "Design matrix", "Discrete choice", "Dummy variable (statistics)", "Errors-in-variables models", "Errors and residuals in statistics", "Explanatory variable", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "George E. P. Box", "Goodness of fit", "International Standard Book Number", "Inverse-Wishart distribution", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Journal of the Royal Statistical Society. Series B (Methodological)", "Kronecker product", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "Local regression", "Logistic regression", "MMSE estimator", "Matrix normal distribution", "Mean and predicted response", "Mixed logit", "Mixed model", "Moore\u2013Penrose pseudoinverse", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate linear regression", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Normal distribution", "Ordered logit", "Ordered probit", "Ordinary least squares", "Outer product", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Pseudoinverse", "Quantile regression", "Random effects model", "Random variable", "Real-valued", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Row vector", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistics", "Studentized residual", "The Annals of Mathematical Statistics", "Tikhonov regularization", "Total least squares", "Vectorization (mathematics)", "Weighted least squares"], "references": ["http://www.jstor.org/stable/2238083", "http://www.jstor.org/stable/2984424"]}, "Binomial proportion confidence interval": {"categories": ["All articles needing additional references", "Articles needing additional references from July 2017", "CS1 French-language sources (fr)", "Statistical approximations", "Statistical intervals", "Webarchive template wayback links"], "title": "Binomial proportion confidence interval", "method": "Binomial proportion confidence interval", "url": "https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval", "summary": "In statistics, a binomial proportion confidence interval is a confidence interval for the probability of success calculated from the outcome of a series of success\u2013failure experiments (Bernoulli trials). In other words, a binomial proportion confidence interval is an interval estimate of a success probability p when only the number of experiments n and the number of successes nS are known. \nThere are several formulas for a binomial confidence interval, but all of them rely on the assumption of a binomial distribution. In general, a binomial distribution applies when an experiment is repeated a fixed number of times, each trial of the experiment has two possible outcomes (success and failure), the probability of success is the same for each trial, and the trials are statistically independent. Because the binomial distribution is a discrete probability distribution (i.e., not continuous) and difficult to calculate for large numbers of trials, a variety of approximations are used to calculate this confidence interval, all with their own tradeoffs in accuracy and computational intensity.\nA simple example of a binomial distribution is the set of various possible outcomes, and their probabilities, for the number of heads observed when a coin is flipped ten times. The observed binomial proportion is the fraction of the flips that turn out to be heads. Given this observed proportion, the confidence interval for the true probability of the coin landing on heads is a range of possible proportions, which may or may not contain the true proportion. A 95% confidence interval for the proportion, for instance, will contain the true proportion 95% of the times that the procedure for constructing the confidence interval is employed.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Abraham Wald", "Bernoulli trial", "Beta distribution", "Binomial distribution", "Central limit theorem", "CiteSeerX", "Cohen's h", "Coin flipping", "Confidence interval", "Continuity correction", "Coverage probability", "Credible interval", "Cumulative distribution function", "Digital object identifier", "Discrete probability distribution", "Edwin Bidwell Wilson", "Egon Pearson", "Estimation theory", "F-distribution", "International Standard Serial Number", "JSTOR", "Jeffreys prior", "Lawrence D. Brown", "Mathematical Reviews", "Non-informative prior", "Normal distribution", "Pearson's chi-squared test", "Pierre-Simon Laplace", "Population proportion", "Posterior distribution", "Probit", "PubMed Identifier", "Quantile", "R (programming language)", "Rule of three (statistics)", "Score test", "Standard normal distribution", "Statistically independent", "Statistics", "Statistics in Medicine (journal)", "T. Tony Cai", "Wald test", "Wayback Machine", "Yates's correction for continuity", "Zentralblatt MATH"], "references": ["http://www.measuringusability.com/papers/sauro-lewisHFES.pdf", "http://www.pmean.com/01/zeroevents.html", "http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Confidence_Intervals/", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.3025", "http://www.ncbi.nlm.nih.gov/pubmed/9595616", "http://www.zoologia.hu/qp/Reiczigel_conf_int.pdf", "http://www.ams.org/mathscinet-getitem?mr=1628435", "http://www.ams.org/mathscinet-getitem?mr=1861069", "http://www.childrensmercy.org/stats/", "http://doi.org/10.1002%2F(SICI)1097-0258(19980430)17:8%3C857::AID-SIM777%3E3.0.CO;2-E", "http://doi.org/10.1002%2Fsim.1320", "http://doi.org/10.1016%2FS0010-4825(03)00019-2", "http://doi.org/10.1016%2Fj.jspi.2004.01.005", "http://doi.org/10.1080%2F01621459.1927.10502953", "http://doi.org/10.1080%2F09296174.2013.799918", "http://doi.org/10.1093%2Fbiomet%2F26.4.404", "http://doi.org/10.1214%2F14-EJS909", "http://doi.org/10.1214%2Fss%2F1009213286", "http://doi.org/10.2307%2F2685469", "http://www.jstor.org/stable/2276774", "http://www.jstor.org/stable/2685469", "http://projecteuclid.org/euclid.ejs/1402927499", "http://www.worldcat.org/issn/1935-7524", "http://zbmath.org/?format=complete&q=an:1059.62533", "http://www.ucl.ac.uk/english-usage/staff/sean/resources/binomialpoisson.pdf", "https://books.google.com/books?id=ooBLvgAACAAJ", "https://web.archive.org/web/20111015182854/http://www.childrensmercy.org/stats/", "https://cran.r-project.org/web/packages/binom/index.html"]}, "Mean absolute percentage error": {"categories": ["All articles needing additional references", "Articles needing additional references from December 2009", "Statistical deviation and dispersion"], "title": "Mean absolute percentage error", "method": "Mean absolute percentage error", "url": "https://en.wikipedia.org/wiki/Mean_absolute_percentage_error", "summary": "The mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics, for example in trend estimation. It usually expresses accuracy as a percentage, and is defined by the formula:\n\n \n \n \n \n \n M\n \n \n =\n \n \n \n 100\n %\n \n n\n \n \n \n \u2211\n \n t\n =\n 1\n \n \n n\n \n \n \n |\n \n \n \n \n A\n \n t\n \n \n \u2212\n \n F\n \n t\n \n \n \n \n A\n \n t\n \n \n \n \n |\n \n ,\n \n \n {\\displaystyle {\\mbox{M}}={\\frac {100\\%}{n}}\\sum _{t=1}^{n}\\left|{\\frac {A_{t}-F_{t}}{A_{t}}}\\right|,}\n where At is the actual value and Ft is the forecast value.\nThe difference between At and Ft is divided by the actual value At again. The absolute value in this calculation is summed for every forecasted point in time and divided by the number of fitted points n. Multiplying by 100% makes it a percentage error.\nAlthough the concept of MAPE sounds very simple and convincing, it has major drawbacks in practical application \nIt cannot be used if there are zero values (which sometimes happens for example in demand data) because there would be a division by zero.\nFor forecasts which are too low the percentage error cannot exceed 100%, but for forecasts which are too high there is no upper limit to the percentage error.\nWhen MAPE is used to compare the accuracy of prediction methods it is biased in that it will systematically select a method whose forecasts are too low. This little-known but serious issue can be overcome by using an accuracy measure based on the ratio of the predicted to actual value (called the Accuracy Ratio), this approach leads to superior statistical properties and leads to predictions which can be interpreted in terms of the geometric mean.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Least absolute deviations", "Mean Absolute Scaled Error", "Mean Directional Accuracy (MDA)", "Mean absolute error", "Mean percentage error", "Statistics", "Symmetric Mean Absolute Percentage Error", "Symmetric mean absolute percentage error", "Trend estimation"], "references": ["http://robjhyndman.com/hyndsight/smape", "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2635088", "http://www.gestiondeoperaciones.net/proyeccion-de-demanda/error-porcentual-absoluto-medio-mape-en-un-pronostico-de-demanda/", "https://www.sciencedirect.com/science/article/pii/S0169207016000121/", "https://arxiv.org/pdf/1605.02541.pdf"]}, "Trispectrum": {"categories": ["All articles lacking sources", "All articles needing expert attention", "Articles lacking sources from December 2009", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Mathematics articles needing expert attention", "Nonlinear time series analysis"], "title": "Trispectrum", "method": "Trispectrum", "url": "https://en.wikipedia.org/wiki/Trispectrum", "summary": "In mathematics, in the area of statistical analysis, the trispectrum is a statistic used to search for nonlinear interactions. The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the traditional power spectrum. The Fourier transform of C4 (t1, t2, t3) (fourth-order cumulant-generating function) is called the trispectrum or trispectral density.\nThe trispectrum T(f1,f2,f3) falls into the category of higher-order spectra, or polyspectra, and provides supplementary information to the power spectrum. The trispectrum is a three-dimensional construct. The symmetries of the trispectrum allow a much reduced support set to be defined, contained within the following verticies, where 1 is the Nyquist frequency. (0,0,0) (1/2,1/2,-1/2) (1/3,1/3,0) (1/2,0,0) (1/4,1/4,1/4). The plane containing the points (1/6,1/6,1/6) (1/4,1/4,0) (1/2,0,0) divides this volume into an inner and an outer region. A stationary signal will have zero strength (statistically) in the outer region. The trispectrum support is divided into regions by the plane identified above and by the (f1,f2) plane. Each region has different requirements in terms of the bandwidth of signal required for non-zero values.\nIn the same way that the bispectrum identifies contributions to a signal's skewness as a function of frequency triples, the trispectrum identifies contributions to a signal's kurtosis as a function of frequency quadruplets.\nThe trispectrum has been used to investigate the domains of applicability of maximum kurtosis phase estimation used in the deconvolution of seismic data to find layer structure.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Autocorrelation function", "Bispectrum", "Cumulant", "Fourier transform", "Kurtosis", "Nonlinear interaction", "Nyquist frequency", "Polyspectra", "Power spectrum", "Skewness", "Statistical analysis", "Symmetry"], "references": []}, "Two-way analysis of variance": {"categories": ["All articles needing expert attention", "Analysis of variance", "Articles needing expert attention from January 2012", "Articles needing expert attention with no reason or talk parameter", "Statistics articles needing expert attention"], "title": "Two-way analysis of variance", "method": "Two-way analysis of variance", "url": "https://en.wikipedia.org/wiki/Two-way_analysis_of_variance", "summary": "In statistics, the two-way analysis of variance (ANOVA) is an extension of the one-way ANOVA that examines the influence of two different categorical independent variables on one continuous dependent variable. The two-way ANOVA not only aims at assessing the main effect of each independent variable but also if there is any interaction between them.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg"], "links": ["Analysis of variance", "Andrew Gelman", "ArXiv", "Cambridge University Press", "Categorical variable", "Contingency table", "Continuous function", "Data set", "Degrees of freedom (statistics)", "Dependent variable", "Digital object identifier", "Errors and residuals in statistics", "Experimental design", "F test", "Frank Yates", "General linear model", "George Casella", "Histogram", "Homoscedasticity", "Hypothesis testing", "Identifiability", "Independence (probability theory)", "Independent variables", "Institute of Mathematical Statistics", "Interaction (statistics)", "International Standard Book Number", "JSTOR", "Linear combination", "Main effect", "Mixed model", "Multilevel model", "Multivariate analysis of variance", "Normal distribution", "One-way ANOVA", "One-way analysis of variance", "Partition of sums of squares", "Probability theory", "PubMed Central", "Random variable", "Repeated measures", "Ronald Fisher", "Springer Science+Business Media", "Statistical Methods for Research Workers", "Statistical Science", "Statistical noise", "Statistical significance", "Statistics", "Tukey's test of additivity", "Yasunori Fujikoshi"], "references": ["http://www.sciencedirect.com/science/article/pii/0012365X9390410U", "http://onlinelibrary.wiley.com/doi/10.1002/gepi.21744/abstract", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4009698", "http://arxiv.org/abs/1106.2895", "http://www.cambridge.org/us/academic/subjects/statistics-probability/statistical-theory-and-methods/data-analysis-using-regression-and-multilevelhierarchical-models", "http://doi.org/10.1002/gepi.21744", "http://doi.org/10.1016/0012-365X(93)90410-U", "http://doi.org/10.1080/01621459.1934.10502686", "http://doi.org/10.1214/009053604000001048", "http://doi.org/10.1214/10-sts337", "http://www.jstor.org/stable/2278459", "http://projecteuclid.org/euclid.aos/1112967698", "http://projecteuclid.org/euclid.ss/1307626554", "https://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-75964-7"]}, "Cram\u00e9r\u2013Rao bound": {"categories": ["Articles containing proofs", "Estimation theory", "Statistical inequalities"], "title": "Cram\u00e9r\u2013Rao bound", "method": "Cram\u00e9r\u2013Rao bound", "url": "https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound", "summary": "In estimation theory and statistics, the Cram\u00e9r\u2013Rao bound (CRB), Cram\u00e9r\u2013Rao lower bound (CRLB), Cram\u00e9r\u2013Rao inequality, Frechet\u2013Darmois\u2013Cram\u00e9r\u2013Rao inequality, or information inequality expresses a lower bound on the variance of unbiased estimators of a deterministic (fixed, though unknown) parameter. This term is named in honor of Harald Cram\u00e9r, Calyampudi Radhakrishna Rao, Maurice Fr\u00e9chet and Georges Darmois all of whom independently derived this limit to statistical precision in the 1940s.In its simplest form, the bound states that the variance of any unbiased estimator is at least as high as the inverse of the Fisher information. An unbiased estimator which achieves this lower bound is said to be (fully) efficient. Such a solution achieves the lowest possible mean squared error among all unbiased methods, and is therefore the minimum variance unbiased (MVU) estimator. However, in some cases, no unbiased technique exists which achieves the bound. This may occur even when an MVU estimator exists.\nThe Cram\u00e9r\u2013Rao bound can also be used to bound the variance of biased estimators of given bias. In some cases, a biased approach can result in both a variance and a mean squared error that are below the unbiased Cram\u00e9r\u2013Rao lower bound; see estimator bias.", "images": [], "links": ["Bias of an estimator", "Brascamp\u2013Lieb inequality", "C. R. Rao", "Calcutta Mathematical Society", "Cauchy\u2013Schwarz inequality", "Chain rule", "Chapman\u2013Robbins bound", "Continuously differentiable", "Covariance", "Covariance matrix", "Efficiency (statistics)", "Estimation theory", "Estimator", "Estimator bias", "Expected value", "Fisher information", "Fisher information matrix", "Georges Darmois", "Harald Cram\u00e9r", "International Standard Book Number", "Jacobian matrix", "Kullback's inequality", "Likelihood function", "Mathematical Reviews", "Maurice Ren\u00e9 Fr\u00e9chet", "Mean squared error", "Minimum variance unbiased", "Moment about the mean", "Multiplicative inverse", "Multivariate normal distribution", "Natural logarithm", "Normal distribution", "OCLC", "Positive semidefinite matrix", "Probability density function", "Random variable", "Scalar (mathematics)", "Score (statistics)", "Statistic", "Statistics", "Trace (matrix)", "Variance", "Vector space"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0015748", "http://www.worldcat.org/oclc/174244259", "http://www.worldcat.org/oclc/185436716", "https://archive.is/20121215055105/http://www4.utsouthwestern.edu/wardlab/fandplimittool.asp"]}, "Impulse response": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2011", "Control theory", "Time domain analysis"], "title": "Impulse response", "method": "Impulse response", "url": "https://en.wikipedia.org/wiki/Impulse_response", "summary": "In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system).\nIn all these cases, the dynamic system and its impulse response may be actual physical objects, or may be mathematical systems of equations describing such objects.\nSince the impulse function contains all frequencies, the impulse response defines the response of a linear time-invariant system for all frequencies.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ec/Impulse.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Adaptive filter", "Broadband", "Complex plane", "Consumption (economics)", "Continuous-time", "Control theory", "Convolution", "Convolution reverb", "Digital signal processing", "Dirac's delta function", "Dirac delta function", "Discount factor", "Discrete-time", "Duhamel's principle", "Dynamic stochastic general equilibrium", "Dynamic system", "Dynamic systems", "Economic Modelling", "Economics", "Employment", "Endogeneity (economics)", "Exogenous", "F. Alton Everest", "Fiscal policy", "Fourier analysis", "Frequency domain", "Frequency response", "Function (mathematics)", "Fundamental solution", "GDP", "Gibbs phenomenon", "Government spending", "Green's function", "Helmut L\u00fctkepohl", "Independent variable", "International Standard Book Number", "Inverse Laplace transform", "Investment", "James D. Hamilton", "Kronecker delta", "K\u00fcssner effect", "LTI system theory", "Laplace transform", "Linear response function", "Linear time-invariant system", "Linear transformation", "Loudspeaker", "Maximum length sequence", "Model (macroeconomics)", "Monetary base", "Monetary policy", "Moving average model", "Partial differential operator", "Point spread function", "Pre-echo", "Production function", "Pulse (signal processing)", "Radar", "Shock (economics)", "Signal processing", "Step response", "System analysis", "Tax rate", "Time constant", "Time domain", "Total factor productivity", "Transfer function", "Transient (oscillation)", "Transient response", "Ultrasound imaging", "Unit impulse function", "Utility", "Variation of parameters", "Vector autoregression"], "references": ["http://www.acoustics.hut.fi/projects/poririrs/", "https://books.google.com/books?id=q6w7AAAAMAAJ&q=%22impulse+response%22+%22loudspeaker+testing%22&dq=%22impulse+response%22+%22loudspeaker+testing%22&pgis=1", "https://books.google.com/books?id=sgwg1Vwm9VUC&pg=RA1-PA510&dq=%22impulse+response%22+loudspeaker+testing", "https://ideas.repec.org/a/eee/ecmode/v36y2014icp18-22.html"]}, "Nelson\u2013Aalen estimator": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "Life insurance", "Reliability engineering", "Survival analysis"], "title": "Nelson\u2013Aalen estimator", "method": "Nelson\u2013Aalen estimator", "url": "https://en.wikipedia.org/wiki/Nelson%E2%80%93Aalen_estimator", "summary": "The Nelson\u2013Aalen estimator is a non-parametric estimator of the cumulative hazard rate function in case of censored data or incomplete data. It is used in survival theory, reliability engineering and life insurance to estimate the cumulative number of expected events. An \"event\" can be the failure of a non-repairable component, the death of a human being, or any occurrence for which the experimental unit remains in the \"failed\" state (e.g., death) from the point at which it changed on. The estimator is given by\n\n \n \n \n \n \n \n H\n ~\n \n \n \n (\n t\n )\n =\n \n \u2211\n \n \n t\n \n i\n \n \n \u2264\n t\n \n \n \n \n \n d\n \n i\n \n \n \n n\n \n i\n \n \n \n \n ,\n \n \n {\\displaystyle {\\tilde {H}}(t)=\\sum _{t_{i}\\leq t}{\\frac {d_{i}}{n_{i}}},}\n with \n \n \n \n \n d\n \n i\n \n \n \n \n {\\displaystyle d_{i}}\n the number of events at \n \n \n \n \n t\n \n i\n \n \n \n \n {\\displaystyle t_{i}}\n and \n \n \n \n \n n\n \n i\n \n \n \n \n {\\displaystyle n_{i}}\n the total individuals at risk at \n \n \n \n \n t\n \n i\n \n \n \n \n {\\displaystyle t_{i}}\n .The curvature of the Nelson\u2013Aalen estimator gives an idea of the hazard rate shape. A concave shape is an indicator for infant mortality while a convex shape indicates wear out mortality.\nIt can be used for example when testing the homogeneity of Poisson processes.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bathtub curve", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Censoring (statistics)", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hazard rate", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Life insurance", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson process", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.statsdirect.com/help/survival_analysis/kaplan.htm", "http://tkchen.wordpress.com/2008/09/21/kaplan-meier-and-nelson-aalen-estimators/", "http://doi.org/10.1016%2Fj.gloplacha.2010.03.006", "https://books.google.com/books?id=7tdcCol9mNEC&pg=PA141"]}, "Champernowne distribution": {"categories": ["Continuous distributions"], "title": "Champernowne distribution", "method": "Champernowne distribution", "url": "https://en.wikipedia.org/wiki/Champernowne_distribution", "summary": "In statistics, the Champernowne distribution is a symmetric, continuous probability distribution, describing random variables that take both positive and negative values. It is a generalization of the logistic distribution that was introduced by D. G. Champernowne. Champernowne developed the distribution to describe the logarithm of income.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "D. G. Champernowne", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Fisk distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized logistic distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://doi.org/10.2307%2F1907644", "http://doi.org/10.2307%2F1909287", "http://doi.org/10.2307%2F2227127", "http://www.jstor.org/stable/1907644", "http://www.jstor.org/stable/2227127", "https://books.google.com/books?id=7wLGjyB128IC&lpg=PA241&dq=Champernowne%20distribution&pg=PA240#v=onepage&q=Champernowne%20distribution&f=false"]}, "Dimension reduction": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from June 2017", "Articles needing additional references from November 2010", "Articles with unsourced statements from June 2017", "Articles with unsourced statements from September 2017", "Dimension reduction", "Machine learning", "Wikipedia articles needing clarification from September 2017"], "title": "Dimensionality reduction", "method": "Dimension reduction", "url": "https://en.wikipedia.org/wiki/Dimensionality_reduction", "summary": "In statistics, machine learning, and information theory, dimensionality reduction or dimension reduction is the process of reducing the number of random variables under consideration by obtaining a set of principal variables. It can be divided into feature selection and feature extraction.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Anomaly detection", "ArXiv", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Backpropagation", "Bayesian network", "Bias-variance dilemma", "Bibcode", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "CUR matrix approximation", "Canonical correlation analysis", "Circumstellar disks", "Cluster analysis", "Cold start (computing)", "Collaborative filtering", "Collaborative search engine", "Collective intelligence", "Combinatorial optimization", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Content discovery platform", "Convolutional neural network", "Correlation and dependence", "Covariance", "Curse of dimensionality", "DBSCAN", "Data analysis", "Data mining", "Data transformation (statistics)", "Decision support system", "Decision tree learning", "DeepDream", "Deep learning", "Diffusion map", "Digital object identifier", "Dimensional reduction", "Eigenvalue, eigenvector and eigenspace", "Embedding", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature (machine learning)", "Feature engineering", "Feature extraction", "Feature learning", "Feature projection", "Feature selection", "Gated recurrent unit", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "GroupLens Research", "Hidden Markov model", "Hierarchical clustering", "High-dimensional space", "Hyperparameter optimization", "Implicit data collection", "Independent component analysis", "Information gain in decision trees", "Information theory", "International Conference on Machine Learning", "International Standard Book Number", "Isomap", "Item-item collaborative filtering", "Johnson\u2013Lindenstrauss lemma", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kernel PCA", "Kernel trick", "Latent semantic analysis", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Local tangent space alignment", "Locality sensitive hashing", "Locally linear embedding", "Logistic regression", "Long short-term memory", "Long tail", "MIT Press", "Machine Learning (journal)", "Machine learning", "Manifold learning", "Matrix (mathematics)", "Matrix factorization (recommender systems)", "Maximally informative dimensions", "Maximum variance unfolding", "Mean-shift", "Methods of detecting exoplanets", "MinHash", "MovieLens", "Multidimensional scaling", "Multifactor dimensionality reduction", "Multilayer perceptron", "Multilinear PCA", "Multilinear subspace learning", "Music Genome Project", "Mutual information", "Naive Bayes classifier", "Nature (journal)", "Nearest neighbor search", "Netflix Prize", "Neural network", "Neuroscience", "Non-negative matrix factorization", "Nonlinear dimensionality reduction", "OPTICS algorithm", "Occam learning", "Online machine learning", "Outline of machine learning", "Perceptron", "Preference elicitation", "Principal component analysis", "Probably approximately correct learning", "Product finder", "PubMed Identifier", "Q-learning", "Random forest", "Random projection", "Recommender system", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance", "Relevance vector machine", "Restricted Boltzmann machine", "Sammon mapping", "Sebastian Seung", "Self-organizing map", "Semantic mapping (statistics)", "Semi-supervised learning", "Semidefinite embedding", "Semidefinite programming", "Similarity search", "Singular value decomposition", "Social loafing", "Star (classification)", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Statistics", "Structured prediction", "Sufficient dimension reduction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Tensor", "Time series", "Topological data analysis", "U-Net", "Unsupervised learning", "VLDB conference", "Vapnik\u2013Chervonenkis theory", "Weighted correlation network analysis"], "references": ["http://www.dsp.utoronto.ca/~haiping/Publication/SurveyMSL_PR2011.pdf", "http://papers.nips.cc/paper/1861-algorithms-for-non-negative-matrix-factorization.pdf", "http://rielac.cujae.edu.cu/index.php/rieac/article/download/478/278", "http://bingweb.binghamton.edu/~hhu1/paper/Hu2010Dimensionality.pdf", "http://www.cs.columbia.edu/~jebara/papers/spe-icml09.pdf", "http://adsabs.harvard.edu/abs/1999Natur.401..788L", "http://adsabs.harvard.edu/abs/2000Sci...290.2323R", "http://adsabs.harvard.edu/abs/2007AJ....133..734B", "http://adsabs.harvard.edu/abs/2018ApJ...852..104R", "http://jmlr.csail.mit.edu/papers/special/feature03.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.1422", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.1478", "http://citeseerx.ist.psu.edu/viewdoc/versions?doi=10.1.1.8.5098", "http://www.cs.toronto.edu/~roweis/lle", "http://bioinfo-out.curie.fr/projects/elmap/", "http://www.ncbi.nlm.nih.gov/pubmed/10548103", "http://www.ncbi.nlm.nih.gov/pubmed/11125150", "http://arxiv.org/abs/1612.06037", "http://arxiv.org/abs/1712.10317", "http://arxiv.org/abs/astro-ph/0606170", "http://arxiv.org/archive/astro-ph.IM", "http://doi.org/10.1007%2F978-1-4615-5725-8_7", "http://doi.org/10.1016%2Fj.patcog.2011.01.004", "http://doi.org/10.1038%2F44565", "http://doi.org/10.1086%2F510127", "http://doi.org/10.1109%2FIACC.2016.16", "http://doi.org/10.1126%2Fscience.290.5500.2323", "http://doi.org/10.1137%2Fs1064827502419154", "http://doi.org/10.1145%2F1553374.1553494", "http://doi.org/10.1145%2F502512.502546", "http://doi.org/10.1162%2Fneco.2006.18.10.2509", "http://doi.org/10.3847%2F1538-4357%2Faaa1f2", "http://doi.org/10.5772%2F16863", "http://dx.doi.org/10.1137/s1064827502419154", "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7544805&isnumber=7544788", "https://hal.archives-ouvertes.fr/hal-01575345/document", "https://web.archive.org/web/20040411051530/http://isomap.stanford.edu/", "https://arxiv.org/list/cs.LG/recent", "https://dx.doi.org/10.1016/j.eswa.2015.06.025", "https://dx.doi.org/10.1162/089976600300014980"]}, "Idealised population": {"categories": ["Population genetics", "Statistical genetics"], "title": "Idealised population", "method": "Idealised population", "url": "https://en.wikipedia.org/wiki/Idealised_population", "summary": "In population genetics an idealised population is one that can be described using a number of simplifying assumptions. Models of idealised populations are either used to make a general point, or they are fit to data on real populations for which the assumptions may not hold true. For example, coalescent theory is used to fit data to models of idealised populations. The most common idealized population in population genetics is described in the Wright-Fisher model after Sewall Wright and Ronald Fisher (1922, 1930) and (1931). Wright-Fisher populations have constant size, and their members can mate and reproduce with any other member. Another example is a Moran model, which has overlapping generations, rather than the non-overlapping generations of the Fisher-Wright model. The complexities of real populations can cause their behavior to match an idealised population with an effective population size that is very different from the census population size of the real population. For sexual diploids, idealized populations will have genotype frequencies related to the allele frequencies according to Hardy-Weinberg equilibrium.\n\n", "images": [], "links": ["Archaic human admixture with modern humans", "Binomial square principle", "Coalescent theory", "Computer program", "Digital object identifier", "Diploids", "Effective population", "Effective population size", "Generation", "Genetic diversity", "Genetic drift", "Joe Roman", "Population", "Population genetics", "PubMed Central", "Reproduce", "Ronald Fisher", "Science (journal)", "Sewall Wright", "Sex ratio", "Sexual intercourse", "Simulation", "Stephen Palumbi", "Stephen R. Palumbi", "Stepping stone model"], "references": ["http://www.animalplanet.com/wild-animals/darwin-survive-game.htm/", "http://darwin.eeb.uconn.edu/simulations/drift.html/", "http://evolution.gs.washington.edu/popgen/popg.html/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1764933", "http://doi.org/10.1098%2Frstb.2006.1926", "http://doi.org/10.1126%2Fscience.1084524", "https://mcbi.marine-conservation.org/publications/pub_pdfs/Roman_Palumbi_2003.pdf"]}, "Sobel test": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2012", "Regression analysis", "Statistical tests", "Wikipedia articles needing clarification from May 2012"], "title": "Sobel test", "method": "Sobel test", "url": "https://en.wikipedia.org/wiki/Sobel_test", "summary": "In statistics, the Sobel test is a method of testing the significance of a mediation effect. The test is based on the work of Michael E. Sobel, a statistics professor at Columbia University in New York, NY, and is an application of the delta method. In mediation, the relationship between the independent variable and the dependent variable is hypothesized to be an indirect effect that exists due to the influence of a third variable (the mediator). As a result when the mediator is included in a regression analysis model with the independent variable, the effect of the independent variable is reduced and the effect of the mediator remains significant. The Sobel test is basically a specialized t test that provides a method to determine whether the reduction in the effect of the independent variable, after including the mediator in the model, is a significant reduction and therefore whether the mediation effect is statistically significant.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/8/8b/Basic_Mediation_Diagram.png", "https://upload.wikimedia.org/wikipedia/en/6/65/Sobel_Test_Venn_Diagram.png"], "links": ["Bootstrapping (statistics)", "Delta method", "Digital object identifier", "International Standard Serial Number", "Mediation (statistics)", "Michael E. Sobel", "Normal distribution", "PubMed Central", "PubMed Identifier", "Regression analysis", "Statistics", "T test"], "references": ["http://www.public.asu.edu/~davidpm/ripl/maloy.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2819363", "http://www.ncbi.nlm.nih.gov/pubmed/18697684", "http://www.ncbi.nlm.nih.gov/pubmed/3806354", "http://doi.org/10.1037/0022-3514.51.6.1173", "http://doi.org/10.1037/1082-989X.7.1.83", "http://doi.org/10.1177/0193841X8100500502", "http://doi.org/10.1207/s15327906mbr3901_4", "http://doi.org/10.1214/aoms/1177730442", "http://doi.org/10.2307/270723", "http://doi.org/10.2307/270922", "http://doi.org/10.2307/271084", "http://doi.org/10.3758/BRM.40.3.879", "http://www.worldcat.org/issn/1939-1463"]}, "Canopy clustering algorithm": {"categories": ["Algorithms and data structures stubs", "All stub articles", "Cluster analysis algorithms", "Computer science stubs"], "title": "Canopy clustering algorithm", "method": "Canopy clustering algorithm", "url": "https://en.wikipedia.org/wiki/Canopy_clustering_algorithm", "summary": "The canopy clustering algorithm is an unsupervised pre-clustering algorithm introduced by Andrew McCallum, Kamal Nigam and Lyle Ungar in 2000. It is often used as preprocessing step for the K-means algorithm or the Hierarchical clustering algorithm. It is intended to speed up clustering operations on large data sets, where using another algorithm directly may be impractical due to the size of the data set.\nThe algorithm proceeds as follows, using two thresholds \n \n \n \n \n T\n \n 1\n \n \n \n \n {\\displaystyle T_{1}}\n (the loose distance) and \n \n \n \n \n T\n \n 2\n \n \n \n \n {\\displaystyle T_{2}}\n (the tight distance), where \n \n \n \n \n T\n \n 1\n \n \n >\n \n T\n \n 2\n \n \n \n \n {\\displaystyle T_{1}>T_{2}}\n .\nBegin with the set of data points to be clustered.\nRemove a point from the set, beginning a new 'canopy' containing this point.\nFor each point left in the set, assign it to the new canopy if its distance to the first point of the canopy is less than the loose distance \n \n \n \n \n T\n \n 1\n \n \n \n \n {\\displaystyle T_{1}}\n .\nIf the distance of the point is additionally less than the tight distance \n \n \n \n \n T\n \n 2\n \n \n \n \n {\\displaystyle T_{2}}\n , remove it from the original set.\nRepeat from step 2 until there are no more data points in the set to cluster.\nThese relatively cheaply clustered canopies can be sub-clustered using a more expensive but accurate algorithm.An important note is that individual data points may be part of several canopies. As an additional speed-up, an approximate and fast distance metric can be used for 3, where a more accurate and slow distance metric can be used for step 4.\nSince the algorithm uses distance functions and requires the specification of distance thresholds, its applicability for high-dimensional data is limited by the curse of dimensionality. Only when a cheap and approximative \u2013 low-dimensional \u2013 distance function is available, the produced canopies will preserve the clusters produced by K-means.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f7/Binary_tree.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/f/f7/20110216185700%21Binary_tree.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/f/f7/20090116232339%21Binary_tree.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/f/f7/20051231213046%21Binary_tree.svg"], "links": ["Algorithm", "Andrew McCallum", "Computer cluster", "Curse of dimensionality", "Data clustering", "Data set", "Data structure", "Digital object identifier", "Hierarchical clustering", "K-means algorithm"], "references": ["http://www.kamalnigam.com/papers/canopy-kdd00.pdf", "http://courses.cs.washington.edu/courses/cse590q/04au/slides/DannyMcCallumKDD00.ppt", "https://mahout.apache.org/users/clustering/canopy-clustering.html", "https://doi.org/10.1145%2F347090.347123"]}, "Interval estimation": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2009", "Statistical intervals"], "title": "Interval estimation", "method": "Interval estimation", "url": "https://en.wikipedia.org/wiki/Interval_estimation", "summary": "In statistics, interval estimation is the use of sample data to calculate an interval of plausible values of an unknown population parameter; this is in contrast to point estimation, which gives a single value. Jerzy Neyman (1937) identified interval estimation (\"estimation by interval\") as distinct from point estimation (\"estimation by unique estimate\"). In doing so, he recognized that then-recent work quoting results in the form of an estimate plus-or-minus a standard deviation indicated that interval estimation was actually the problem statisticians really had in mind.\nThe most prevalent forms of interval estimation are:\n\nconfidence intervals (a frequentist method); and\ncredible intervals (a Bayesian method).Other common approaches to interval estimation, which are encompassed by statistical theory, are:\n\nTolerance intervals\nPrediction intervals - used mainly in Regression Analysis\nLikelihood intervalsThere is another approach to statistical inference, namely fiducial inference, that also considers interval estimation. Non-statistical methods that can lead to interval estimates include fuzzy logic.\nAn interval estimate is one type of outcome of a statistical analysis. Some other types of outcome are point estimates and decisions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algorithmic inference", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behrens\u2013Fisher problem", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Coverage probability", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decision Theory", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fiducial inference", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentism", "Frequentist inference", "Friedman test", "Fuzzy logic", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Induction (philosophy)", "Interaction (statistics)", "Interquartile range", "Interval (mathematics)", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Philosophy of statistics", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population parameter", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Predictive inference", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression Analysis", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statisticians", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["https://www.jstor.org/stable/91337"]}, "Skellam distribution": {"categories": ["Discrete distributions", "Pages using deprecated image syntax", "Poisson distribution"], "title": "Skellam distribution", "method": "Skellam distribution", "url": "https://en.wikipedia.org/wiki/Skellam_distribution", "summary": "The Skellam distribution is the discrete probability distribution of the difference \n \n \n \n \n N\n \n 1\n \n \n \u2212\n \n N\n \n 2\n \n \n \n \n {\\displaystyle N_{1}-N_{2}}\n of two statistically independent random variables \n \n \n \n \n N\n \n 1\n \n \n \n \n {\\displaystyle N_{1}}\n and \n \n \n \n \n N\n \n 2\n \n \n ,\n \n \n {\\displaystyle N_{2},}\n each Poisson-distributed with respective expected values \n \n \n \n \n \u03bc\n \n 1\n \n \n \n \n {\\displaystyle \\mu _{1}}\n and \n \n \n \n \n \u03bc\n \n 2\n \n \n \n \n {\\displaystyle \\mu _{2}}\n It is useful in describing the statistics of the difference of two images with simple photon noise, as well as describing the point spread distribution in sports where all scored points are equal, such as baseball, hockey and soccer.\nThe distribution is also applicable to a special case of the difference of dependent Poisson random variables, but just the obvious case where the two variables have a common additive random contribution which is cancelled by the differencing: see Karlis & Ntzoufras (2003) for details and an application.\nThe probability mass function for the Skellam distribution for a difference \n \n \n \n K\n =\n \n N\n \n 1\n \n \n \u2212\n \n N\n \n 2\n \n \n \n \n {\\displaystyle K=N_{1}-N_{2}}\n between two independent Poisson-distributed random variables with means \n \n \n \n \n \u03bc\n \n 1\n \n \n \n \n {\\displaystyle \\mu _{1}}\n and \n \n \n \n \n \u03bc\n \n 2\n \n \n \n \n {\\displaystyle \\mu _{2}}\n is given by:\n\n \n \n \n p\n (\n k\n ;\n \n \u03bc\n \n 1\n \n \n ,\n \n \u03bc\n \n 2\n \n \n )\n =\n Pr\n {\n K\n =\n k\n }\n =\n \n e\n \n \u2212\n (\n \n \u03bc\n \n 1\n \n \n +\n \n \u03bc\n \n 2\n \n \n )\n \n \n \n \n (\n \n \n \n \u03bc\n \n 1\n \n \n \n \u03bc\n \n 2\n \n \n \n \n )\n \n \n k\n \n /\n \n 2\n \n \n \n I\n \n k\n \n \n (\n 2\n \n \n \n \u03bc\n \n 1\n \n \n \n \u03bc\n \n 2\n \n \n \n \n )\n \n \n {\\displaystyle p(k;\\mu _{1},\\mu _{2})=\\Pr\\{K=k\\}=e^{-(\\mu _{1}+\\mu _{2})}\\left({\\mu _{1} \\over \\mu _{2}}\\right)^{k/2}I_{k}(2{\\sqrt {\\mu _{1}\\mu _{2}}})}\n where Ik(z) is the modified Bessel function of the first kind. Since k is an integer we have that Ik(z)=I|k|(z).", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a9/Skellam_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a9/20130310001214%21Skellam_distribution.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Asymptotic expansion", "Balding\u2013Nichols model", "Baseball", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bessel function", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Big O notation", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Convolution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulant", "Cumulant-generating function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Ice hockey", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "John Gordon Skellam", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the Royal Statistical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Moment-generating function", "Moment (mathematics)", "Moment about the mean", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Photon noise", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability-generating function", "Probability distribution", "Probability mass function", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soccer", "Soliton distribution", "Spread betting", "Stable distribution", "Statistically independent", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://store.doverpublications.com/0486612724.html", "http://stat-athens.aueb.gr/~jbn/papers/paper11.htm", "https://doi.org/10.1111%2F1467-9884.00366", "https://www.jstor.org/stable/2980526", "https://www.jstor.org/stable/2981372"]}, "Mathematical modelling of infectious disease": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2012", "Articles with unsourced statements from July 2017", "CS1 maint: Date format", "Epidemiology", "Mathematical and theoretical biology", "Medical statistics", "Vaccination"], "title": "Mathematical modelling of infectious disease", "method": "Mathematical modelling of infectious disease", "url": "https://en.wikipedia.org/wiki/Mathematical_modelling_of_infectious_disease", "summary": "Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic and help inform public health interventions. Models use some basic assumptions and mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programmes. The modelling can help in deciding which intervention/s to avoid and which to trial.\n\n", "images": [], "links": ["2009 flu pandemic vaccine", "ALVAC-CEA vaccine", "ATC code J07", "Adenovirus vaccine", "Advisory Committee on Immunization Practices", "Alternative vaccination schedule", "Anderson Gray McKendrick", "Andrew Wakefield", "Androvax", "Anthrax vaccines", "Antigenic shift", "Artificial induction of immunity", "Atmospheric model", "Attenuated vaccine", "BCG vaccine", "Basic reproduction number", "Bibcode", "Biopsychosocial model", "Brucellosis vaccine", "Business process modelling", "Cancer vaccine", "Catastrophe modeling", "Causes of death", "Cedillo v. Secretary of Health and Human Services", "Cellular model", "Cervarix", "Chemical process modeling", "Chemical transport model", "Chikungunya vaccine", "Cholera vaccine", "Climate model", "Clinical trial", "Compartmental models in epidemiology", "Conjugate vaccine", "Construction and management simulation", "Crime mapping", "Critical community size", "Cytomegalovirus vaccine", "DNA vaccination", "DPT vaccine", "DTaP-IPV-HepB", "DTaP-IPV/Hib", "Daniel Bernoulli", "Data visualization", "Dengue vaccine", "Digital object identifier", "Diphtheria vaccine", "Disease eradication", "Drug resistance", "Dryvax", "Ebola vaccine", "Economic model", "Ecosystem model", "Endemic (epidemiology)", "Energy modeling", "Epidemic", "Epidemiological", "Epidemiology", "Epstein\u2013Barr virus vaccine", "Eradication of infectious diseases", "Every Child by Two", "Evolution", "Exponential growth", "Force of infection", "GAVI Alliance", "Gardasil", "Geologic modelling", "Germ theory", "Groundwater model", "HIV vaccine", "HPV vaccines", "Hantavirus vaccine", "Helminthiasis", "Hepatitis A vaccine", "Hepatitis B vaccine", "Hepatitis C vaccine", "Hepatitis E vaccine", "Herd immunity", "Heterologous vaccine", "Hexavalent vaccine", "Hib vaccine", "Hookworm vaccine", "Host (biology)", "Hydrological modelling", "Hydrological transport model", "Immune system", "Immunity (medical)", "Immunization", "Immunologic adjuvant", "Inactivated vaccine", "Infection", "Infection reservoir", "Infectious disease", "Infectious diseases", "Influenza vaccine", "Inoculation", "Input-output model", "Integrated assessment modelling", "International Standard Book Number", "JSTOR", "Japanese encephalitis vaccine", "John Graunt", "Kermack\u2013McKendrick theory", "Landscape epidemiology", "Law of mass action", "Leptospirosis vaccine", "Life expectancy", "List of computer simulation software", "List of vaccine ingredients", "List of vaccine topics", "List of withdrawn drugs", "Live attenuated influenza vaccine", "Live vector vaccine", "Lyme disease vaccine", "MMRV vaccine", "MMR vaccine", "MMR vaccine controversy", "Malaria vaccine", "Mathematical modeling", "Mathematical models", "MeNZB", "Measles vaccine", "Meningococcal vaccine", "Metabolic network modelling", "Modelling biological systems", "Modular Ocean Model", "Mumps vaccine", "Mumpsvax", "National Childhood Vaccine Injury Act", "Next-generation matrix", "NicVAX", "NmVac4-A/C/Y/W-135", "Numerical data", "Ovandrotone albumin", "PROSTVAC", "Pandemrix", "Parameter", "Pathogen", "Pentavalent vaccine", "Peptide vaccine", "Pertussis vaccine", "Phases of clinical research", "Phylodynamics", "Plague vaccine", "Plants", "Pneumococcal conjugate vaccine", "Pneumococcal polysaccharide vaccine", "Pneumococcal vaccine", "Polio vaccine", "Poliomyelitis eradication", "Population dynamics", "Population genetics", "Population model", "Population pyramid", "Pox party", "Protein structure prediction", "Protein subunit", "PubMed Identifier", "Public health", "Q fever vaccine", "RTS,S", "R (programming language)", "Rabies vaccine", "Reed\u2013Frost model", "Rinderpest", "Risk factor", "Ronald Ross", "Rotavirus vaccine", "Rubella vaccine", "Sabin polio vaccine", "Salk polio vaccine", "Schistosomiasis vaccine", "Scientific modelling", "Sexual network", "Smallpox", "Smallpox eradication", "Smallpox vaccine", "Social structure", "Spatial epidemiology", "Steady state", "Strain (biology)", "Susceptible", "Systems theory", "Systems thinking", "TA-CD", "TA-NIC", "Tetanus vaccine", "Thiomersal controversy", "Tick-borne encephalitis vaccine", "Timeline of vaccines", "Toxoid", "Transitive property", "Transmission (medicine)", "Transmission risks and rates", "Trypanosomiasis vaccine", "Tuberculosis vaccines", "Ty21a", "Typhoid vaccine", "Typhus vaccine", "Vaccination", "Vaccination policy", "Vaccination schedule", "Vaccine", "Vaccine Adverse Event Reporting System", "Vaccine Safety Datalink", "Vaccine controversies", "Vaccine court", "Vaccine injury", "Vaccine trial", "Vaccines for Children Program", "Varicella vaccine", "Vi capsular polysaccharide vaccine", "Virulence", "Virus-like particle", "Visual analytics", "WHO", "WHO Model List of Essential Medicines", "Wildfire modeling", "William Hamer", "Yellow fever vaccine", "Zoster vaccine"], "references": ["http://anintroductiontoinfectiousdiseasemodelling.com/", "http://apmonitor.com/wiki/index.php/Apps/MeaslesVirus", "http://adsabs.harvard.edu/abs/1927RSPSA.115..700K", "http://www.ncbi.nlm.nih.gov/pubmed/18533288", "http://www.ncbi.nlm.nih.gov/pubmed/9336095", "http://model-builder.sourceforge.net/", "http://doi.org/10.1038%2Fnrmicro1845", "http://doi.org/10.1098%2Frspa.1927.0118", "http://www.eclipse.org/stem/", "http://www.gleamviz.org/", "http://catalog.hathitrust.org/Record/001587831", "http://www.jstor.org/stable/94815", "https://www.amazon.com/Infectious-Diseases-Humans-Dynamics-Control/dp/019854040X/ref=sr_1_1?s=books&ie=UTF8&qid=1532296195&sr=1-1&keywords=anderson+and+may+infectious+diseases+of+humans", "https://CRAN.R-project.org/package=surveillance"]}, "Topic model": {"categories": ["All articles with dead external links", "Articles with dead external links from July 2018", "Articles with permanently dead external links", "Corpus linguistics", "Latent variable models", "Statistical natural language processing"], "title": "Topic model", "method": "Topic model", "url": "https://en.wikipedia.org/wiki/Topic_model", "summary": "In machine learning and natural language processing, a topic model is a type of statistical model for discovering the abstract \"topics\" that occur in a collection of documents. Topic modeling is a frequently used text-mining tool for discovery of hidden semantic structures in a text body. Intuitively, given that a document is about a particular topic, one would expect particular words to appear in the document more or less frequently: \"dog\" and \"bone\" will appear more often in documents about dogs, \"cat\" and \"meow\" will appear in documents about cats, and \"the\" and \"is\" will appear equally in both. A document typically concerns multiple topics in different proportions; thus, in a document that is 10% about cats and 90% about dogs, there would probably be about 9 times more dog words than cat words. The \"topics\" produced by topic modeling techniques are clusters of similar words. A topic model captures this intuition in a mathematical framework, which allows examining a set of documents and discovering, based on the statistics of the words in each, what the topics might be and what each document's balance of topics is.\nTopic models are also referred to as probabilistic topic models, which refers to statistical algorithms for discovering the latent semantic structures of an extensive text body. In the age of information, the amount of the written material we encounter each day is simply beyond our processing capacity. Topic models can help to organize and offer insights for us to understand large collections of unstructured text bodies. Originally developed as a text-mining tool, topic models have been used to detect instructive structures in data such as genetic information, images, and networks. They also have applications in other fields such as bioinformatics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/70/Topic_model_scheme.webm", "https://upload.wikimedia.org/wikipedia/commons/archive/7/70/20170329164712%21Topic_model_scheme.webm", "https://upload.wikimedia.org/wikipedia/commons/archive/7/70/20170329163155%21Topic_model_scheme.webm"], "links": ["AI-complete", "American Civil War", "Andrew Ng", "ArXiv", "Automated essay scoring", "Automated online assistant", "Automatic identification and data capture", "Automatic summarization", "Bag-of-words model", "Bibcode", "BigARTM", "Bigram", "Bioinformatics", "Chatbot", "Collocation extraction", "Compound term processing", "Computer-assisted reviewing", "Computer-assisted translation", "Concept mining", "Concordancer", "Coreference", "David Blei", "Digital object identifier", "Dirichlet distribution", "Example-based machine translation", "Explicit semantic analysis", "Gensim", "Grammar checker", "Hierarchical Dirichlet process", "Interactive fiction", "International Standard Book Number", "Journal of Machine Learning Research", "Latent Dirichlet allocation", "Latent semantic analysis", "Lemmatisation", "Machine learning", "Machine translation", "Mallet (software project)", "Method of moments (statistics)", "Michael I. Jordan", "Multi-document summarization", "N-gram", "Named-entity recognition", "Natural language generation", "Natural language processing", "Natural language understanding", "Natural language user interface", "Non-negative matrix factorization", "Ontology learning", "Optical character recognition", "PNAS", "Pachinko allocation", "Parsing", "Part-of-speech tagging", "Pennsylvania Gazette", "Predictive text", "Probabilistic latent semantic indexing", "PubMed Central", "PubMed Identifier", "Question answering", "Richmond Times-Dispatch", "Rule-based machine translation", "STTM", "Sentence extraction", "Sentiment analysis", "Shallow parsing", "Singular value decomposition", "Speech corpus", "Speech recognition", "Speech synthesis", "Spell checker", "Statistical model", "Stemming", "Stop words", "Syntax guessing", "Terminology extraction", "Text corpus", "Text mining", "Text segmentation", "Text simplification", "Trigram", "Truecasing", "Voice user interface", "Word-sense disambiguation"], "references": ["http://www.psypress.com/books/details/9780805854183/", "http://radimrehurek.com/gensim/", "http://vimeo.com/13597441", "http://toolsfortext.wordpress.com/", "http://topicmodels.west.uni-koblenz.de/ckling/tmt/svd_ap.html", "http://www.cs.berkeley.edu/~christos/ir.ps", "http://www.cs.brown.edu/~th/papers/Hofmann-SIGIR99.pdf", "http://www.cs.columbia.edu/~blei/papers/BleiLafferty2009.pdf", "http://mimno.infosci.cornell.edu/topics.html", "http://adsabs.harvard.edu/abs/2004PNAS..101.5228G", "http://jmlr.csail.mit.edu/papers/v3/blei03a.html", "http://nlp.stanford.edu/software/tmt/tmt-0.4/", "http://www.perseus.tufts.edu/~amahoney/02-jocch-mimno.pdf", "http://www.ics.uci.edu/~newman/pubs/JASIST_Newman.pdf", "http://psiexp.ss.uci.edu/research/papers/SteyversGriffithsLSABookFormatted.pdf", "http://mallet.cs.umass.edu/", "http://mith.umd.edu/topic-modeling-in-the-humanities-an-overview/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC387300", "http://www.ncbi.nlm.nih.gov/pubmed/14872004", "http://www.matthewjockers.net/2010/03/19/whos-your-dh-blog-mate-match-making-the-day-of-dh-bloggers-with-topic-modeling/", "http://elcid.demon.nl/form.html", "http://www.aclweb.org/anthology/W/W11/W11-15.pdf#page=108", "http://arxiv.org/abs/0708.3601", "http://arxiv.org/abs/1204.1956", "http://www.common-place.org/vol-06/no-02/tales/", "http://doi.org/10.1002%2Fasi.20342", "http://doi.org/10.1073%2Fpnas.0307752101", "http://doi.org/10.1145%2F2133806.2133826", "http://doi.org/10.1145%2F2160165.2160168", "http://doi.org/10.1162%2Fjmlr.2003.3.4-5.993", "http://doi.org/10.1214%2F07-AOAS114", "http://journalofdigitalhumanities.org/2-1/topic-modeling-a-basic-introduction-by-megan-r-brett/", "http://programminghistorian.org/lessons/topic-modeling-and-mallet/", "http://www.proustarchive.org/wp-trackback.php?p=60", "https://github.com/AmazaspShumik/sklearn-bayes/blob/master/skbayes/decomposition_models/gibbs_lda_cython.pyx", "https://github.com/AmazaspShumik/sklearn-bayes/blob/master/ipython_notebooks_tutorials/decomposition_models/example_lda.ipynb", "https://github.com/bigartm/bigartm", "https://github.com/datquocnguyen/jLDADMM", "https://github.com/ericproffitt/TopicModelsVB.jl", "https://github.com/lettier/lda-topic-modeling", "https://github.com/qiang2100/STTM", "https://lettier.com/projects/lda-topic-modeling/", "https://www.youtube.com/watch?v=1wcX4fEdNUo", "https://www.youtube.com/watch?v=8nBE5Qm8y6I", "https://www.academia.edu/5508141/Discovery_of_Emergent_Issues_and_Controversies_in_Anthropology_Using_Text_Mining_Topic_Modeling_and_Social_Network_Analysis_of_Microblog_Content", "https://cacm.acm.org/magazines/2012/4/147361-probabilistic-topic-models/fulltext", "https://web.archive.org/web/20101214074049/http://www.cs.brown.edu/~th/papers/Hofmann-SIGIR99.pdf", "https://web.archive.org/web/20121002061418/http://www.cs.princeton.edu/~blei/topicmodeling.html", "https://web.archive.org/web/20130624013706/http://www.psypress.com/books/details/9780805854183/", "https://cran.r-project.org/package=topicmodels"]}, "Naive Bayes classifier": {"categories": ["All articles lacking in-text citations", "All articles to be expanded", "All articles with unsourced statements", "Articles lacking in-text citations from May 2009", "Articles to be expanded from August 2014", "Articles using small message boxes", "Articles with unsourced statements from December 2014", "Bayesian statistics", "Classification algorithms", "Statistical classification"], "title": "Naive Bayes classifier", "method": "Naive Bayes classifier", "url": "https://en.wikipedia.org/wiki/Naive_Bayes_classifier", "summary": "In machine learning, naive Bayes classifiers are a family of simple \"probabilistic classifiers\" based on applying Bayes' theorem with strong (naive) independence assumptions between the features.\nNaive Bayes has been studied extensively since the 1950s. It was introduced under a different name into the text retrieval community in the early 1960s, and remains a popular (baseline) method for text categorization, the problem of judging documents as belonging to one category or the other (such as spam or legitimate, sports or politics, etc.) with word frequencies as the features. With appropriate pre-processing, it is competitive in this domain with more advanced methods including support vector machines. It also finds application in automatic medical diagnosis.Naive Bayes classifiers are highly scalable, requiring a number of parameters linear in the number of variables (features/predictors) in a learning problem. Maximum-likelihood training can be done by evaluating a closed-form expression, which takes linear time, rather than by expensive iterative approximation as used for many other types of classifiers.\nIn the statistics and computer science literature, naive Bayes models are known under a variety of names, including simple Bayes and independence Bayes. All these names reference the use of Bayes' theorem in the classifier's decision rule, but naive Bayes is not (necessarily) a Bayesian method.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["AODE", "Algorithm", "Andrew Ng", "Anomaly detection", "Apache Mahout", "Artificial Intelligence: A Modern Approach", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bag of words", "Bayes' theorem", "Bayes classifier", "Bayesian network", "Bayesian probability", "Bayesian spam filtering", "Bernoulli distribution", "Bias-variance dilemma", "Boolean data type", "Boosted trees", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Chain rule (probability)", "CiteSeerX", "Closed-form expression", "Cluster analysis", "Computational learning theory", "Computer science", "Conditional independence", "Conditional probability", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "Correlation and dependence", "Curse of dimensionality", "DBSCAN", "Data mining", "Decision rule", "Decision tree learning", "DeepDream", "Deep learning", "Digital object identifier", "Dimensionality reduction", "Discretization error", "Discretization of continuous features", "Document classification", "E-mail", "Efficacy", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature engineering", "Feature learning", "Feature vector", "Gated recurrent unit", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "Histogram", "IMSL Numerical Libraries", "Independence (probability theory)", "Independent component analysis", "Information retrieval", "International Conference on Machine Learning", "International Standard Book Number", "International Standard Serial Number", "Iterative method", "Joint probability", "Journal of Machine Learning Research", "Journal of the ACM", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Laplace smoothing", "Learning to rank", "Lidstone smoothing", "Likelihood", "Likelihood function", "Linear classifier", "Linear discriminant analysis", "Linear regression", "Linear time", "List of datasets for machine-learning research", "Local outlier factor", "Log-likelihood ratio", "Logarithm", "Logistic function", "Logistic regression", "Logit", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Marvin Minsky", "Maximum-likelihood estimation", "Maximum a posteriori", "Maximum likelihood", "Mean-shift", "Medical diagnosis", "Michael I. Jordan", "Microsoft Excel", "Mixture model", "Multilayer perceptron", "Multinomial distribution", "Multinomial logistic regression", "NLTK", "Non-negative matrix factorization", "Nonparametric", "Normal distribution", "OPTICS algorithm", "Occam learning", "Odds", "Online machine learning", "Orange (software)", "Outline of machine learning", "Perceptron", "Peter Norvig", "Principal component analysis", "Probabilistic classifier", "Probability model", "Probably approximately correct learning", "Proportionality (mathematics)", "Pseudocount", "Q-learning", "Random forest", "Random forests", "Random naive Bayes", "Recurrent neural network", "Regression analysis", "Regularization (mathematics)", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Scikit-learn", "Self-organizing map", "Semi-supervised learning", "Sigmoid curve", "Softmax function", "Spam filtering", "Spamming", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical independence", "Statistical learning theory", "Statistics", "Structured prediction", "Stuart J. Russell", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Take-the-best heuristic", "Temporal difference learning", "Text categorization", "Tf\u2013idf", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory", "Variance", "Visual Basic for Applications", "Weka (machine learning)"], "references": ["http://www.cs.unb.ca/profs/hzhang/publications/FLAIRS04ZhangH.pdf", "http://papers.nips.cc/paper/2020-on-discriminative-vs-generative-classifiers-a-comparison-of-logistic-regression-and-naive-bayes", "http://www.biomedcentral.com/1471-2105/7/514", "http://www.research.ibm.com/people/r/rish/papers/RC22230.pdf", "http://www.kamalnigam.com/papers/emcat-aaai98.pdf", "http://www.kamalnigam.com/papers/multinomial-aaaiws98.pdf", "http://www.springerlink.com/content/u8w306673m1p866k/", "http://cmp.felk.cvut.cz/cmp/software/stprtool/", "http://people.csail.mit.edu/jrennie/ifile/", "http://people.csail.mit.edu/~jrennie/papers/icml03-nb.pdf", "http://citeseer.ist.psu.edu/domingos97optimality.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.122.5901", "http://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html", "http://mallet.cs.umass.edu/", "http://machinelearning.wustl.edu/mlpapers/paper_files/icml2005_Niculescu-MizilC05.pdf", "http://classifier4j.sourceforge.net/", "http://downloads.sourceforge.net/naivebayesclass/NaiveBayesDemo.xls?use_mirror=osdn", "http://jbnc.sourceforge.net/", "http://nclassifier.sourceforge.net/", "http://www.cs.waikato.ac.nz/~eibe/pubs/FrankAndBouckaertPKDD06new.pdf", "http://doi.org/10.1007%2Fs10994-005-4258-6", "http://doi.org/10.1145%2F1102351.1102430", "http://doi.org/10.1145%2F321075.321084", "http://doi.org/10.2307%2F1403452", "http://tunedit.org/results?d=UCI/&a=bayes", "http://www.worldcat.org/issn/0306-7734", "http://eprints.fri.uni-lj.si/154/01/PKDD_camera_mozina.pdf", "https://github.com/Tradeshift/blayze", "https://arxiv.org/list/cs.LG/recent"]}, "Wigner semicircle distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2017", "Continuous distributions", "Pages using deprecated image syntax"], "title": "Wigner semicircle distribution", "method": "Wigner semicircle distribution", "url": "https://en.wikipedia.org/wiki/Wigner_semicircle_distribution", "summary": "The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution supported on the interval [\u2212R, R] the graph of whose probability density function f is a semicircle of radius R centered at (0, 0) and then suitably normalized (so that it is really a semi-ellipse):\n\n \n \n \n f\n (\n x\n )\n =\n \n \n 2\n \n \u03c0\n \n R\n \n 2\n \n \n \n \n \n \n \n \n R\n \n 2\n \n \n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n \n \n {\\displaystyle f(x)={2 \\over \\pi R^{2}}{\\sqrt {R^{2}-x^{2}\\,}}\\,}\n for \u2212R \u2264 x \u2264 R, and f(x) = 0 if |x| > R.\nThis distribution arises as the limiting distribution of eigenvalues of many random symmetric matrices as the size of the matrix approaches infinity.\nIt is a scaled beta distribution, more precisely, if Y is beta distributed with parameters \u03b1 = \u03b2 = 3/2, then X = 2RY \u2013 R has the above Wigner semicircle distribution.\nA higher-dimensional generalization is a parabolic distribution in three dimensional space, namely the marginal distribution function of a spherical (parametric) distribution\n \n \n \n \n f\n \n X\n ,\n Y\n ,\n Z\n \n \n (\n x\n ,\n y\n ,\n z\n )\n =\n \n \n 3\n \n 4\n \u03c0\n \n \n \n ,\n \n \n \n x\n \n 2\n \n \n +\n \n y\n \n 2\n \n \n +\n \n z\n \n 2\n \n \n \u2264\n 1\n ,\n \n \n {\\displaystyle f_{X,Y,Z}(x,y,z)={\\frac {3}{4\\pi }},\\qquad \\qquad x^{2}+y^{2}+z^{2}\\leq 1,}\n \n\n \n \n \n \n f\n \n X\n \n \n (\n x\n )\n =\n \n \u222b\n \n \u2212\n \n \n 1\n \u2212\n \n y\n \n 2\n \n \n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n +\n \n \n 1\n \u2212\n \n y\n \n 2\n \n \n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n \n \u222b\n \n \u2212\n \n \n 1\n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n +\n \n \n 1\n \u2212\n \n x\n \n 2\n \n \n \n \n \n \n \n \n \n 3\n \n d\n \n y\n \n \n 4\n \u03c0\n \n \n \n =\n 3\n (\n 1\n \u2212\n \n x\n \n 2\n \n \n )\n \n /\n \n 4.\n \n \n {\\displaystyle f_{X}(x)=\\int _{-{\\sqrt {1-y^{2}-x^{2}}}}^{+{\\sqrt {1-y^{2}-x^{2}}}}\\int _{-{\\sqrt {1-x^{2}}}}^{+{\\sqrt {1-x^{2}}}}{\\frac {3\\mathrm {d} y}{4\\pi }}=3(1-x^{2})/4.}\n \nNote that R=1.\nWhile Wigner's semicircle distribution pertains to the distribution of eigenvalues, Wigner surmise deals with the probability density of the differences between consecutive eigenvalues.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/53/WignerS_distribution_CDF.svg", "https://upload.wikimedia.org/wikipedia/commons/6/66/WignerS_distribution_PDF.svg"], "links": ["ARGUS distribution", "Abramowitz and Stegun", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bessel function", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Catalan number", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chebyshev polynomials", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulant", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Eigenvalues", "Elliptical distribution", "Eric W. Weisstein", "Erlang distribution", "Eugene Wigner", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Free Poisson distribution", "Free probability", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "If and only if", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kesten\u2013McKay measure", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Moment (mathematics)", "Moment generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "N-sphere", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Noncrossing partition", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normalizing constant", "Number theory", "Orthogonal polynomials", "Parabolic fractal distribution", "Pareto distribution", "Partition of a set", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Radius", "Raised cosine distribution", "Random matrices", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Sato\u2013Tate conjecture", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner surmise", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.math.sfu.ca/~cbm/aands/page_360.htm", "http://www.math.sfu.ca/~cbm/aands/page_376.htm", "http://mathworld.wolfram.com/StruveFunction.html", "http://mathworld.wolfram.com/WignersSemicircleLaw.html", "http://www.dtic.upf.edu/~alozano/papers/ThesisIlaria.pdf", "http://doi.org/10.1109%2FAPS.2011.5996900", "http://doi.org/10.1109%2FRADAR.2017.7944181", "http://ieeexplore.ieee.org/document/7944181/", "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5996900"]}, "Tsallis distribution": {"categories": ["Probability distributions with non-finite variance", "Statistical mechanics", "Types of probability distributions"], "title": "Tsallis distribution", "method": "Tsallis distribution", "url": "https://en.wikipedia.org/wiki/Tsallis_distribution", "summary": "In statistics, a Tsallis distribution is a probability distribution derived from the maximization of the Tsallis entropy under appropriate constraints. There are several different families of Tsallis distributions, yet different sources may reference an individual family as \"the Tsallis distribution\". The q-Gaussian is a generalization of the Gaussian in the same way that Tsallis entropy is a generalization of standard Boltzmann\u2013Gibbs entropy or Shannon entropy. Similarly, if the domain of the variable is constrained to be positive in the maximum entropy procedure, the q-exponential distribution is derived.\nThe Tsallis distributions have been applied to problems in the fields of statistical mechanics, geology, anatomy, astronomy, economics, finance, and machine learning. The distributions are often used for their heavy tails.\nNote that Tsallis distributions are obtained as Box-Cox transformation over usual distributions, with deformation parameter \n \n \n \n \u03bb\n =\n 1\n \u2212\n q\n \n \n {\\displaystyle \\lambda =1-q}\n . This deformation transforms exponentials into q-exponentials.", "images": [], "links": ["Anatomy", "Astronomy", "Box-Cox transformation", "Constantino Tsallis", "David Cox (statistician)", "Digital object identifier", "Economics", "Entropy (information theory)", "Entropy (statistical thermodynamics)", "Finance", "Geology", "George E. P. Box", "Heavy tails", "International Standard Serial Number", "JSTOR", "Journal of the Royal Statistical Society", "Machine learning", "Mathematical Reviews", "Maximum entropy probability distribution", "Normal distribution", "Probability distribution", "Q-Gaussian", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Statistical mechanics", "Statistics", "Tsallis entropy", "Tsallis statistics"], "references": ["http://e1.newcastle.edu.au/coffee/pubs/wp/2007/07-10.pdf", "http://www.cscs.umich.edu/~crshalizi/notebooks/tsallis.html", "http://www.ams.org/mathscinet-getitem?mr=0192611", "http://www.jstor.org/stable/2984418", "https://doi.org/10.1016%2Fj.physa.2011.07.052", "https://doi.org/10.1186%2F1029-242X-2012-226", "https://doi.org/10.3390%2Fe16105377", "https://www.worldcat.org/search?fq=x0:jrnl&q=n2:0378-4371"]}, "Sign test": {"categories": ["Nonparametric statistics", "Statistical tests"], "title": "Sign test", "method": "Sign test", "url": "https://en.wikipedia.org/wiki/Sign_test", "summary": "The sign test is a statistical method to test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment. Given pairs of observations (such as weight pre- and post-treatment) for each subject, the sign test determines if one member of the pair (such as pre-treatment) tends to be greater than (or less than) the other member of the pair (such as post-treatment).\nThe paired observations may be designated x and y. For comparisons of paired observations (x,y), the sign test is most useful if comparisons can only be expressed as x > y, x = y, or x < y. If, instead, the observations can be expressed as numeric quantities (x = 7, y = 18), or as ranks (rank of x = 1st, rank of y = 8th), then the paired t-test\nor the Wilcoxon signed-rank test will usually have greater power than the sign test to detect consistent differences.\nIf X and Y are quantitative variables, the sign test can be used to test the hypothesis that the difference between the X and Y has zero median, assuming continuous distributions of the two random variables X and Y, in the situation when we can draw paired samples from X and Y.The sign test can also test if the median of a collection of numbers is significantly greater than or less than a specified value. For example, given a list of student grades in a class, the sign test can determine if the median grade is significantly different from, say, 75 out of 100.\nThe sign test is a non-parametric test which makes very few assumptions about the nature of the distributions under test \u2013 this means that it has very general applicability but may lack the statistical power of the alternative tests.\nThe two conditions for the paired-sample sign test are that a sample must be randomly selected from each population, and the samples must be dependent, or paired. \nIndependent samples cannot be meaningfully paired. Since the test is nonparametric, the samples need not come from normally distributed populations. Also, the test works for left-tailed, right-tailed, and two-tailed tests.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic relative efficiency", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Binomial test", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "History of statistics", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis test", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jean D. Gibbons", "Johansen test", "John Arbuthnot", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Median test", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric test", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal scale", "Ordinary least squares", "Outline of statistics", "P-value", "Paired difference test", "Paired t-test", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Platykurtic distribution", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.real-statistics.com/non-parametric-tests/sign-test/", "https://books.google.com/books?id=CIxgAwAAQBAJ&pg=SA3-PA7", "https://books.google.com/books?id=ObUcBQAAQBAJ&pg=PA281", "https://onlinecourses.science.psu.edu/stat414/node/318"]}, "Delaporte distribution": {"categories": ["CS1 French-language sources (fr)", "CS1 German-language sources (de)", "Compound probability distributions", "Discrete distributions", "Pages using deprecated image syntax"], "title": "Delaporte distribution", "method": "Delaporte distribution", "url": "https://en.wikipedia.org/wiki/Delaporte_distribution", "summary": "The Delaporte distribution is a discrete probability distribution that has received attention in actuarial science. It can be defined using the convolution of a negative binomial distribution with a Poisson distribution. Just as the negative binomial distribution can be viewed as a Poisson distribution where the mean parameter is itself a random variable with a gamma distribution, the Delaporte distribution can be viewed as a compound distribution based on a Poisson distribution, where there are two components to the mean parameter: a fixed component, which has the \n \n \n \n \u03bb\n \n \n {\\displaystyle \\lambda }\n parameter, and a gamma-distributed variable component, which has the \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n and \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n parameters. The distribution is named for Pierre Delaporte, who analyzed it in relation to automobile accident claim counts in 1959, although it appeared in a different form as early as 1934 in a paper by Rolf von L\u00fcders, where it was called the Formel II distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/94/DelaporteCDF.svg", "https://upload.wikimedia.org/wikipedia/commons/6/63/DelaportePMF.svg"], "links": ["ARGUS distribution", "Actuarial science", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biometrika", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Compound distribution", "Convolution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harry Panjer", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "John Wiley & Sons", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "Library of Congress Control Number", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Norman Lloyd Johnson", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Probability mass function", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Samuel Kotz", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://lccn.loc.gov/2007041696", "http://doi.org/10.1002%2F9780470012505.tad027", "http://doi.org/10.1007%2FBF02432340", "http://doi.org/10.1093%2Fbiomet%2F26.1-2.108", "http://www.jstor.org/stable/2332055"]}, "Ljung\u2013Box test": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from June 2011", "Articles with unsourced statements from June 2011", "Time domain analysis", "Time series statistical tests", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Ljung\u2013Box test", "method": "Ljung\u2013Box test", "url": "https://en.wikipedia.org/wiki/Ljung%E2%80%93Box_test", "summary": "The Ljung\u2013Box test (named for Greta M. Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the \"overall\" randomness based on a number of lags, and is therefore a portmanteau test.\nThis test is sometimes known as the Ljung\u2013Box Q test, and it is closely connected to the Box\u2013Pierce test (which is named after George E. P. Box and David A. Pierce). In fact, the Ljung\u2013Box test statistic was described explicitly in the paper that led to the use of the Box-Pierce statistic, and from which that statistic takes its name. The Box-Pierce test statistic is a simplified version of the Ljung\u2013Box statistic for which subsequent simulation studies have shown poor performance.\nThe Ljung\u2013Box test is widely applied in econometrics and other applications of time series analysis. A similar assessment can be also carried out with the Breusch\u2013Godfrey test and the Durbin\u2013Watson test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Answers.com", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Critical region", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fumio Hayashi", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George E. P. Box", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Greta M. Ljung", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Portmanteau test", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Python (programming language)", "Q-statistic", "Quality control", "Quantile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Randomness", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical test", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wald\u2013Wolfowitz runs test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.answers.com/topic/box-pierce-statistic", "http://www.nist.gov", "http://doi.org/10.1080%2F01621459.1970.10481180", "http://doi.org/10.1093%2Fbiomet%2F65.2.297", "http://www.jstor.org/stable/2284333", "https://stat.ethz.ch/R-manual/R-devel/library/stats/html/box.test.html", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA142", "https://books.google.com/books?id=Tc4RPwAACAAJ&pg=PA69", "https://books.google.com/books?id=VHB4OSAmwcUC&pg=PA35", "https://books.google.com/books?id=shWtvsFbxlkC&pg=PA162", "https://www.statsmodels.org/dev/generated/statsmodels.stats.diagnostic.acorr_ljungbox.html"]}, "Vysochanski\u00ef\u2013Petunin inequality": {"categories": ["Probabilistic inequalities", "Statistical inequalities"], "title": "Vysochanskij\u2013Petunin inequality", "method": "Vysochanski\u00ef\u2013Petunin inequality", "url": "https://en.wikipedia.org/wiki/Vysochanskij%E2%80%93Petunin_inequality", "summary": "In probability theory, the Vysochanskij\u2013Petunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variable's mean, or equivalently an upper bound for the probability that it lies further away. The sole restrictions on the distribution are that it be unimodal and have finite variance. (This implies that it is a continuous probability distribution except at the mode, which may have a non-zero probability.)\nThe theorem applies even to heavily skewed distributions and puts bounds on how much of the data is, or is not, \"in the middle.\"", "images": [], "links": ["Chebyshev's inequality", "Continuous probability distribution", "Control chart", "Expected value", "Gauss's inequality", "Mode (statistics)", "Probability", "Probability distribution", "Probability theory", "Random variable", "Rule of three (statistics)", "Standard deviation", "Symmetric distribution", "Unimodal function", "Variance", "Yuri Petunin"], "references": ["http://m.njit.edu/CAMS/Technical_Reports/CAMS02_03/report4.pdf"]}, "Effect size": {"categories": ["All articles needing expert attention", "All articles that are too technical", "All articles with incomplete citations", "Articles needing expert attention from February 2014", "Articles needing expert attention from May 2011", "Articles needing expert attention with no reason or talk parameter", "Articles with incomplete citations from November 2012", "Articles with multiple maintenance issues", "Clinical research", "Educational psychology research methods", "Effect size", "Inconsistent articles", "Mathematical and quantitative methods (economics)", "Medical statistics", "Meta-analysis", "Pharmaceutical industry", "Statistical hypothesis testing", "Statistics articles needing expert attention", "Wikipedia articles needing page number citations from August 2016", "Wikipedia articles that are too technical from February 2014", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from June 2014"], "title": "Effect size", "method": "Effect size", "url": "https://en.wikipedia.org/wiki/Effect_size", "summary": "In statistics, an effect size is a quantitative measure of the magnitude of a phenomenon. Examples of effect sizes are the correlation between two variables, the regression coefficient in a regression, the mean difference, or even the risk with which something happens, such as how many people survive after a heart attack for every one person that does not survive. For most types of effect size, a larger absolute value always indicates a stronger effect, with the main exception being if the effect size is an odds ratio. Effect sizes complement statistical hypothesis testing, and play an important role in power analyses, sample size planning, and in meta-analyses. They are the first item (magnitude) in the MAGIC criteria for evaluating the strength of a statistical claim.\nEspecially in meta-analysis, where the purpose is to combine multiple effect sizes, the standard error (S.E.) of the effect size is of critical importance. The S.E. of the effect size is used to weigh effect sizes when combining studies, so that large studies are considered more important than small studies in the analysis. The S.E. of the effect size is calculated differently for each type of effect size, but generally only requires knowing the study's sample size (N), or the number of observations in each group (n's).\nReporting effect sizes or estimates thereof (effect estimate [EE], estimate of effect) is considered good practice when presenting empirical research findings in many fields. The reporting of effect sizes facilitates the interpretation of the substantive, as opposed to the statistical, significance of a research result. Effect sizes are particularly prominent in social science and in medical research (where size of treatment effect is important). Relative and absolute measures of effect size convey different information, and can be used complementarily. A prominent task force in the psychology research community made the following recommendation:\n\nAlways present effect sizes for primary outcomes...If the units of measurement are meaningful on a practical level (e.g., number of cigarettes smoked per day), then we usually prefer an unstandardized measure (regression coefficient or mean difference) to a standardized measure (r or d).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/1/15/Cohens_d_4panel.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA", "Abelson's paradox", "Absolute value", "Academic Press", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average treatment effect", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Case-control study", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's d", "Cohen's h", "Cohen's kappa", "Cohort study", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Cram\u00e9r's V (statistics)", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimating sample sizes", "Estimation statistics", "Estimator", "Expected value", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gamma function", "Gaussian", "Gene V. Glass", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harald Cram\u00e9r", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Ingram Olkin", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iverson bracket", "Jackknife resampling", "Jacob Cohen (statistician)", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Applied Psychology", "Journal of Consulting and Clinical Psychology", "Journal of Educational Statistics", "Journal of Educational and Behavioral Statistics", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Larry Hedges", "Larry V. Hedges", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mahalanobis distance", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean (statistics)", "Median", "Median-unbiased estimator", "Medical research", "Medical statistics", "Meta-analysis", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multiple regression", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Noncentral F distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Noncentrality parameter", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Norman Cliff", "Nuisance variable", "Observational study", "Odds ratio", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "P-value", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares path modeling", "Partition of sums of squares", "Pearson correlation", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perceptual and Motor Skills", "Permutation test", "Phenomenon", "Phi coefficient", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point-biserial correlation coefficient", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Pooled standard deviation", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychological Bulletin", "Psychological Methods", "Psychometrics", "PubMed Central", "PubMed Identifier", "Publication bias", "Quality control", "Quantile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative risk", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Risk difference", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling error", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social science", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Squared multiple correlation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "Taguchi methods", "Test statistic", "The Journal of General Psychology", "The MAGIC criteria", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-factor", "Z-test"], "references": ["http://davidmlane.com/hyperstat/effect_size.html", "http://effectsizefaq.com/", "http://www.ipsychexpts.com/brand_et_al_(2011).pdf", "http://itfeature.com/testing-of-hypothesis/effect-size-for-dependent-sample-t-test", "http://mtbradley.com/brandbradelybeststoicapdf.pdf", "http://jeb.sagepub.com/content/25/2/101.full.pdf+html", "http://journals.sagepub.com/doi/10.1177/147470491301100511", "http://cps.nova.edu/marker/olejnik2003.pdf", "http://www.stat.uiowa.edu/~rlenth/Power/", "http://digitalcommons.wayne.edu/coe_tbf/13/", "http://digitalcommons.wayne.edu/coe_tbf/17/", "http://digitalcommons.wayne.edu/jmasm/vol8/iss2/26/", "http://digitalcommons.wayne.edu/jmasm/vol8/iss2/26/.pdf", "http://www.eric.ed.gov/ERICWebPortal/contentdelivery/servlet/ERICServlet?accno=ED433353", "http://www.eric.ed.gov/ERICWebPortal/custom/portlets/recordDetails/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=ED433353&ERICExtSearch_SearchType_0=no&accno=ED433353", "http://ies.ed.gov/ncser/pubs/20133000/pdf/20133000.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1114127", "http://www.ncbi.nlm.nih.gov/pubmed/17944619", "http://www.ncbi.nlm.nih.gov/pubmed/18556917", "http://www.ncbi.nlm.nih.gov/pubmed/18557680", "http://www.ncbi.nlm.nih.gov/pubmed/19271844", "http://www.ncbi.nlm.nih.gov/pubmed/19565683", "http://www.ncbi.nlm.nih.gov/pubmed/26199055", "http://www.ncbi.nlm.nih.gov/pubmed/9784470", "http://davidakenny.net/doc/statbook/chapter_13.pdf", "http://www.statpower.net/Steiger%20Biblio/Steiger04.pdf", "http://www.bobmcgrath.org/Pubs/When_effect_sizes_disagree.pdf", "http://doi.org/10.1002%2Fejsp.2420020412", "http://doi.org/10.1007%2FBF02289138", "http://doi.org/10.1016%2Fj.shpsc.2015.06.003", "http://doi.org/10.1037%2F0003-066X.54.8.594", "http://doi.org/10.1037%2F0022-006X.62.2.281", "http://doi.org/10.1037%2F0033-2909.111.2.361", "http://doi.org/10.1037%2F0033-2909.112.1.155", "http://doi.org/10.1037%2F0033-2909.114.3.494", "http://doi.org/10.1037%2F1082-989x.11.4.386", "http://doi.org/10.1037%2F1082-989x.13.2.99", "http://doi.org/10.1037%2F1082-989x.8.4.434", "http://doi.org/10.1037%2F1082-989x.9.2.164", "http://doi.org/10.1037%2Fa0014270", "http://doi.org/10.1037%2Fa0028086", "http://doi.org/10.1037%2Fa0034745", "http://doi.org/10.1080%2F00221309.2010.520360", "http://doi.org/10.1111%2Fj.1469-185X.2007.00027.x", "http://doi.org/10.1136%2Fbmj.317.7166.1155a", "http://doi.org/10.1177%2F0013164401614002", "http://doi.org/10.1177%2F147470491301100511", "http://doi.org/10.22237%2Fjmasm%2F1051747860", "http://doi.org/10.2466%2F11.IT.3.1", "http://doi.org/10.2466%2FPMS.106.2.645-649", "http://doi.org/10.3102%2F10769986006002107", "http://doi.org/10.3102%2F10769986025002101", "http://www.jstatsoft.org/v20/i08/paper", "http://www.tqmp.org/Content/vol05-1/p025/p025.pdf", "https://books.google.com/books?id=2v9zDAsLvA0C&pg=PP1", "https://books.google.com/books?id=5obZnfK5pbsC&pg=PP1", "https://books.google.com/books?id=EdqhQgAACAAJ&pg=PP1", "https://books.google.com/books?id=JEoNB_2NONQC&pg=PP1", "https://books.google.com/books?id=bmwhcJqq01cC&pg=PP1", "https://www.academia.edu/16420844/Measuring_Effectiveness", "https://web.archive.org/web/20081217175012/http://mtbradley.com/brandbradelybeststoicapdf.pdf", "https://web.archive.org/web/20110927074709/http://www.uccs.edu/~faculty/lbecker/es.htm"]}, "Stein's lemma": {"categories": ["All articles needing additional references", "Articles needing additional references from January 2011", "Probability theorems", "Statistical theorems"], "title": "Stein's lemma", "method": "Stein's lemma", "url": "https://en.wikipedia.org/wiki/Stein%27s_lemma", "summary": "Stein's lemma, named in honor of Charles Stein, is a theorem of probability theory that is of interest primarily because of its applications to statistical inference \u2014 in particular, to James\u2013Stein estimation and empirical Bayes methods \u2014 and its applications to portfolio choice theory. The theorem gives a formula for the covariance of one random variable with the value of a function of another, when the two random variables are jointly normally distributed.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Absolute value", "Charles Stein (statistician)", "Covariance", "Digital object identifier", "Empirical Bayes method", "Expected value", "Exponential family", "Integration by parts", "James\u2013Stein estimation", "Joint normal distribution", "Modern portfolio theory", "Normal distribution", "Probability density function", "Probability theory", "Proof of Stein's example", "Random variable", "Statistical inference", "Stein's method", "Taylor expansions for the moments of functions of random variables", "Theorem", "Variance"], "references": ["http://doi.org/10.1016%2Fj.jmva.2007.05.006", "http://doi.org/10.1111%2Fj.1539-6975.2008.00265.x"]}, "Cosmic variance": {"categories": ["Physical cosmology", "Statistical deviation and dispersion"], "title": "Cosmic variance", "method": "Cosmic variance", "url": "https://en.wikipedia.org/wiki/Cosmic_variance", "summary": "The term cosmic variance is the statistical uncertainty inherent in observations of the universe at extreme distances. It has three different but closely related meanings:\n\nIt is sometimes used, incorrectly, to mean sample variance - the difference between different finite samples of the same parent population. Such differences follow a Poissonian distribution, and in this case the term sample variance should be used instead.\nIt is sometimes used, mainly by cosmologists, to mean the uncertainty because we can only observe one realization of all the possible observable universes. For example, we can only observe one Cosmic Microwave Background, so the measured positions of the peaks in the Cosmic Microwave Background spectrum, integrated over the visible sky, are limited by the fact that only one spectrum is observable from Earth. The observable universe viewed from another Galaxy will have the peaks in slightly different places, while remaining consistent with the same physical laws, inflation, etc. This second meaning may be regarded as a special case of the third meaning.\nThe most widespread use, to which the rest of this article refers, reflects the fact that measurements are affected by cosmic large-scale structure, so a measurement of any region of sky (viewed from Earth) may differ from a measurement of a different region of sky (also viewed from Earth) by an amount that may be much greater than the sample variance.This most widespread use of the term is based on the idea that it is only possible to observe part of the universe at one particular time, so it is difficult to make statistical statements about cosmology on the scale of the entire universe, as the number of observations (sample size) must be too small.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5c/Earth-moon.jpg", "https://upload.wikimedia.org/wikipedia/commons/e/e9/Gravitational_inverse-square_law.png", "https://upload.wikimedia.org/wikipedia/commons/3/3c/Ilc_9yr_moll4096.png", "https://upload.wikimedia.org/wikipedia/commons/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg", "https://upload.wikimedia.org/wikipedia/commons/6/6f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.svg", "https://upload.wikimedia.org/wikipedia/commons/0/00/Crab_Nebula.jpg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["2dF Galaxy Redshift Survey", "AMiBA", "ARCADE", "Accelerating expansion of the universe", "Age of the universe", "Alan Guth", "Albert Einstein", "Alexander Friedmann", "Alexei Starobinsky", "American Astronomical Society", "Andrei Linde", "Anthropic principle", "ArXiv", "Archeops", "Arcminute Cosmology Bolometer Array Receiver", "Arcminute Microkelvin Imager", "Arno Allan Penzias", "Astrophysical Journal", "Atacama B-Mode Search", "Atacama Cosmology Telescope", "Atacama Pathfinder Experiment", "Australia Telescope Compact Array", "BICEP and Keck Array", "BOOMERanG experiment", "Baryonic matter", "Berkeley-Illinois-Maryland Association", "Bibcode", "Big Bang", "Big Bang nucleosynthesis", "Big Bounce", "Big Crunch", "Big Rip", "Big bang", "Brian Schmidt", "COSMOSOMAS", "China", "Chronology of the universe", "Cold dark matter", "Cosmic Anisotropy Polarization Mapper", "Cosmic Anisotropy Telescope", "Cosmic Background Explorer", "Cosmic Background Imager", "Cosmic Microwave Background", "Cosmic Variance (blog)", "Cosmic background radiation", "Cosmic inflation", "Cosmic infrared background", "Cosmic microwave background", "Cosmic microwave background radiation", "Cosmic neutrino background", "Cosmology Large Angular Scale Surveyor", "Dark Ages (cosmology)", "Dark Energy Survey", "Dark energy", "Dark matter", "Dark radiation", "Degree Angular Scale Interferometer", "Diffusion damping", "Digital object identifier", "Discovery of cosmic microwave background radiation", "Edwin Hubble", "Energy", "Euclid (spacecraft)", "Evolutionary biology", "Expansion of the universe", "France", "Friedmann equations", "Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker metric", "Future of an expanding universe", "Galaxies", "Galaxy cluster", "Galaxy filament", "Galaxy formation and evolution", "Galaxy group", "Galileo Galilei", "General relativity", "George F. R. Ellis", "George Gamow", "George Smoot", "Georges Lema\u00eetre", "Grand unification epoch", "Gravitational wave background", "Hadron epoch", "Hannes Alfv\u00e9n", "Heat death of the universe", "History of the Big Bang theory", "Hot dark matter", "Hubble's law", "Illustris project", "India", "Inflation (cosmology)", "Inhomogeneous cosmology", "Isaac Newton", "John C. Mather", "J\u00fcrgen Ehlers", "Lambda-CDM model", "Large Scale Polarization Explorer - STRIP", "Large Scale Polarization Explorer - Short Wavelength Instrument for the Polarization Explorer", "Large Synoptic Survey Telescope", "Large quasar group", "Lepton epoch", "List of cosmic microwave background experiments", "List of cosmologists", "LiteBIRD", "Local Group", "Marc Aaronson", "Millimeter Anisotropy eXperiment IMaging Array", "Mobile Anisotropy Telescope", "Nicholas B. Suntzeff", "Nicolaus Copernicus", "OVRO", "Observable universe", "Observational cosmology", "POLARBEAR", "Particle horizon", "Paul Steinhardt", "Phantom energy", "Philosophy", "Photon epoch", "Physical cosmology", "Physical laws", "Planck (spacecraft)", "Planck epoch", "Poisson distribution", "Poissonian distribution", "Probability distribution", "QMAP", "QUIET", "QUIJOTE CMB Experiment", "QUaD", "Quantum mechanics", "Quark epoch", "Qubic experiment", "Quintessence (physics)", "RELIKT-1", "Radiation", "Ralph Asher Alpher", "Random", "Rashid Sunyaev", "Recombination (cosmology)", "Redshift", "Reionization", "Religious interpretations of the Big Bang theory", "Richard C. Tolman", "Robert H. Dicke", "Robert Woodrow Wilson", "Roger Penrose", "Sachs\u2013Wolfe effect", "Sample size", "Sample variance", "Saskatoon experiment", "Shape of the universe", "Sloan Digital Sky Survey", "Somnath Bharadwaj", "South Pole Telescope", "Spherical harmonic", "Spider (polarimeter)", "Statistical sample", "Statistics", "Stephen Hawking", "Structure formation", "Sunyaev\u2013Zel'dovich Array", "Sunyaev\u2013Zel'dovich effect", "Supercluster", "Tenerife Experiment", "The E and B Experiment", "Thomson scattering", "Timeline of cosmic microwave background astronomy", "Timeline of cosmological theories", "Titius\u2013Bode law", "TopHat (telescope)", "Ultimate fate of the universe", "Uncertainty", "United States", "Universe", "Variance", "Vera Rubin", "Very Small Array", "Void (astronomy)", "WMAP", "Warm dark matter", "Wilkinson Microwave Anisotropy Probe", "Willem de Sitter", "Yakov Borisovich Zel'dovich"], "references": ["http://adsabs.harvard.edu/abs/2004ApJ...600L.171S", "http://adsabs.harvard.edu/abs/2004PhRvD..70f3504P", "http://www.aas.org/publications/baas/v37n4/aas207/1366.htm", "http://arXiv.org/abs/astro-ph/0305562", "http://arxiv.org/abs/astro-ph/0309071", "http://arxiv.org/abs/astro-ph/0402173", "http://doi.org/10.1086%2F378628", "http://doi.org/10.1103%2FPhysRevD.70.063504", "http://www.iop.org/EJ/article/1538-4357/600/2/L171/17416.html", "https://web.archive.org/web/20080102081508/http://www.aas.org/publications/baas/v37n4/aas207/1366.htm"]}, "Cunningham function": {"categories": ["All stub articles", "Special hypergeometric functions", "Statistical approximations", "Statistics stubs"], "title": "Cunningham function", "method": "Cunningham function", "url": "https://en.wikipedia.org/wiki/Cunningham_function", "summary": "In statistics, the Cunningham function or Pearson\u2013Cunningham function \u03c9m,n(x) is a generalisation of a special function introduced by Pearson (1906) and studied in the form here by Cunningham (1908). It can be defined in terms of the confluent hypergeometric function U, by\n\n \n \n \n \n \n \u03c9\n \n m\n ,\n n\n \n \n (\n x\n )\n =\n \n \n \n e\n \n \u2212\n x\n +\n \u03c0\n i\n (\n m\n \n /\n \n 2\n \u2212\n n\n )\n \n \n \n \u0393\n (\n 1\n +\n n\n \u2212\n m\n \n /\n \n 2\n )\n \n \n \n U\n (\n m\n \n /\n \n 2\n \u2212\n n\n ,\n 1\n +\n m\n ,\n x\n )\n .\n \n \n \n {\\displaystyle \\displaystyle \\omega _{m,n}(x)={\\frac {e^{-x+\\pi i(m/2-n)}}{\\Gamma (1+n-m/2)}}U(m/2-n,1+m,x).}\n The function was studied by Cunningham in the context of a multivariate generalisation of the Edgeworth expansion for approximating a probability density function based on its (joint) moments. In a more general context, the function is related to the solution of the constant-coefficient diffusion equation, in one or more dimensions.The function \u03c9m,n(x) is a solution of the differential equation for X:\n\n \n \n \n x\n \n X\n \u2033\n \n +\n (\n x\n +\n 1\n +\n m\n )\n \n X\n \u2032\n \n +\n (\n n\n +\n \n \n \n 1\n 2\n \n \n \n m\n +\n 1\n )\n X\n .\n \n \n {\\displaystyle xX''+(x+1+m)X'+(n+{\\tfrac {1}{2}}m+1)X.}\n The special function studied by Pearson is given, in his notation by,\n\n \n \n \n \n \u03c9\n \n 2\n n\n \n \n (\n x\n )\n =\n \n \u03c9\n \n 0\n ,\n n\n \n \n (\n x\n )\n .\n \n \n {\\displaystyle \\omega _{2n}(x)=\\omega _{0,n}(x).}", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Abramowitz and Stegun", "Cambridge University Press", "Confluent hypergeometric function", "Diffusion equation", "Digital object identifier", "Edgeworth expansion", "International Standard Book Number", "International Standard Serial Number", "Irene Stegun", "JSTOR", "Karl Pearson", "Library of Congress Control Number", "Mathematical Reviews", "Milton Abramowitz", "Moment (mathematics)", "Probability density function", "Statistics"], "references": ["http://www.math.sfu.ca/~cbm/aands/page_510.htm", "http://lccn.loc.gov/64-60036", "http://www.ams.org/mathscinet-getitem?mr=0167642", "http://doi.org/10.1098/rspa.1908.0085", "http://www.jstor.org/stable/93061", "http://www.worldcat.org/issn/0950-1207", "https://lccn.loc.gov/65012253"]}, "Quartile coefficient of dispersion": {"categories": ["All stub articles", "Statistical deviation and dispersion", "Statistical ratios", "Statistics stubs"], "title": "Quartile coefficient of dispersion", "method": "Quartile coefficient of dispersion", "url": "https://en.wikipedia.org/wiki/Quartile_coefficient_of_dispersion", "summary": "In statistics, the quartile coefficient of dispersion is a descriptive statistic which measures dispersion and which is used to make comparisons within and between data sets. \nThe statistic is easily computed using the first (Q1) and third (Q3) quartiles for each data set. The quartile coefficient of dispersion is:\n\n \n \n \n \n \n \n \n Q\n \n 3\n \n \n \u2212\n \n Q\n \n 1\n \n \n \n \n \n Q\n \n 3\n \n \n +\n \n Q\n \n 1\n \n \n \n \n \n .\n \n \n {\\displaystyle {Q_{3}-Q_{1} \\over Q_{3}+Q_{1}}.}", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Coefficient of variation", "Digital object identifier", "Quartile", "Statistical dispersion", "Statistics"], "references": ["http://doi.org/10.1016/j.csda.2005.05.007"]}, "Statistical shape analysis": {"categories": ["Computer vision", "Spatial data analysis", "Statistical data types"], "title": "Statistical shape analysis", "method": "Statistical shape analysis", "url": "https://en.wikipedia.org/wiki/Statistical_shape_analysis", "summary": "Statistical shape analysis is an analysis of the geometrical properties of some given set of shapes by statistical methods. For instance, it could be used to quantify differences between male and female gorilla skull shapes, normal and pathological bone shapes, leaf outlines with and without herbivory by insects, etc. Important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate mean shapes from (possibly random) samples, to estimate shape variability within samples, to perform clustering and to test for differences between shapes. One of the main methods used is principal component analysis (PCA). Statistical shape analysis has applications in various fields, including medical imaging, computer vision, computational anatomy, sensor measurement, and geographical profiling.", "images": [], "links": ["Active shape model", "ArXiv", "Bayesian Estimation of Templates in Computational Anatomy", "Bayesian model of computational anatomy", "Bibcode", "Computational anatomy", "Computer vision", "D'Arcy Thompson", "David George Kendall", "Deformation (engineering)", "Diffeomorphism", "Digital object identifier", "Force (physics)", "Fred Bookstein", "Geometric data analysis", "Geometric morphometrics in anthropology", "Geometry", "Image registration", "International Standard Book Number", "International Standard Serial Number", "Kent distribution", "Landmark point", "Large Deformation Diffeomorphic Metric Mapping", "Large deformation diffeomorphic metric mapping", "Ley lines", "Mapping (mathematics)", "Medical imaging", "On Growth and Form", "Pathology", "Point distribution model", "Principal component analysis", "Procrustes analysis", "PubMed Central", "PubMed Identifier", "Shape", "Shape analysis (disambiguation)", "Statistical", "Voxel-based morphometry"], "references": ["http://www.worldscientific.com/doi/abs/10.1142/S2339547814500010", "http://adsabs.harvard.edu/abs/1996ITIP....5.1435C", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4041578", "http://www.ncbi.nlm.nih.gov/pubmed/17761438", "http://www.ncbi.nlm.nih.gov/pubmed/18290061", "http://www.ncbi.nlm.nih.gov/pubmed/24904924", "http://www.ncbi.nlm.nih.gov/pubmed/26221678", "http://dl.acm.org/citation.cfm?id=309082.309089", "http://arxiv.org/abs/1305.1150", "http://doi.org/10.1007%2Fs10851-013-0490-z", "http://doi.org/10.1016%2Fj.neuroimage.2007.07.007", "http://doi.org/10.1016%2Fj.patcog.2003.07.008", "http://doi.org/10.1023%2Fb:visi.0000043755.93987.aa", "http://doi.org/10.1109%2F83.536892", "http://doi.org/10.1142%2FS2339547814500010", "http://www.worldcat.org/issn/0033-569X", "http://www.worldcat.org/issn/1011-2499", "http://www.worldcat.org/issn/1053-8119", "http://www.worldcat.org/issn/1057-7149", "http://www.worldcat.org/issn/2339-5478", "https://github.com/stnava/ANTs/blob/master/Scripts/antsIntroduction.sh", "https://sites.google.com/site/tomvercauteren/software", "https://www.openaire.eu/search/publication?articleId=dedup_wf_001::ea7b28db1d4570e248acdffb6211d98d", "https://www.nitrc.org/projects/lddmm-volume/", "https://www.independent.co.uk/news/obituaries/professor-david-kendall-398453.html"]}, "Mean absolute scaled error": {"categories": ["All accuracy disputes", "All articles lacking reliable references", "Articles lacking reliable references from April 2011", "Articles with disputed statements from September 2018", "Point estimation performance", "Statistical deviation and dispersion", "Time series", "Wikipedia articles needing clarification from April 2011"], "title": "Mean absolute scaled error", "method": "Mean absolute scaled error", "url": "https://en.wikipedia.org/wiki/Mean_absolute_scaled_error", "summary": "In statistics, the mean absolute scaled error (MASE) is a measure of the accuracy of forecasts . It was proposed in 2005 by statistician Rob J. Hyndman and Professor of Decision Sciences Anne B. Koehler, who described it as a \"generally applicable measurement of forecast accuracy without the problems seen in the other measurements.\" The mean absolute scaled error has favorable properties when compared to other methods for calculating forecast errors, such as root-mean-square-deviation, and is therefore recommended for determining comparative accuracy of forecasts.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Accuracy", "Digital object identifier", "Forecast error", "Forecasting", "International Standard Book Number", "Mean absolute error", "Mean absolute percentage error", "Mean squared error", "Rob J. Hyndman", "Root-mean-square deviation", "Root-mean-square error", "Scale invariance", "Statistics", "Test set"], "references": ["http://robjhyndman.com/papers/foresight.pdf", "http://www.sciencedirect.com/science/article/pii/0169207093900793", "http://www.sciencedirect.com/science/article/pii/S0169207015000448", "http://doi.org/10.1016%2F0169-2070(93)90079-3", "http://doi.org/10.1016%2Fj.ijforecast.2015.03.008", "https://doi.org/10.1016%2Fj.ijforecast.2006.03.001", "https://www.otexts.org/fpp/2/5"]}, "Survey data collection": {"categories": ["All articles with unsourced statements", "All pages needing cleanup", "Articles needing cleanup from January 2012", "Articles with sections that need to be turned into prose from January 2012", "Articles with unsourced statements from April 2017", "Survey methodology"], "title": "Survey data collection", "method": "Survey data collection", "url": "https://en.wikipedia.org/wiki/Survey_data_collection", "summary": "With the application of probability sampling in the 1930s, surveys became a standard tool for empirical research in social sciences, marketing, and official statistics. The methods involved in survey data collection are any of a number of ways in which data can be collected for a statistical survey. These are methods that are used to collect information from a sample of individuals in a systematic way. First there was the change from traditional paper-and-pencil interviewing (PAPI) to computer-assisted interviewing (CAI). Now, face-to-face surveys (CAPI), telephone surveys (CATI), and mail surveys (CASI, CSAQ) are increasingly replaced by web surveys.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/66/US_Navy_030618-N-2893B-001_Information_Technician_1st_Class_Annette_Leasure_takes_a_few_minutes_to_fill_out_the_BUPERS_Online_Uniform_Survey_Questionnaire.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Assessment (disambiguation)", "CATI", "Comparison of survey software", "Custom online panel", "Data collection", "Data collection system", "Digital object identifier", "ESOMAR", "Empirical research", "European Social Survey", "Gideon J. Mellenbergh", "Herman J. Ad\u00e8r", "International Standard Book Number", "Internet", "Marketing", "Mode effect", "Multitrait-multimethod matrix", "QuestBack", "Response rate (survey)", "Sampling (statistics)", "Sampling frame", "Social sciences", "Survey methodology"], "references": ["http://homepage.univie.ac.at/andreas.hergovich/php/reaching_the_mobile_respondent_soc.sci.comp.rev.pdf", "http://www.forecastingprinciples.com/paperpdf/Class%20of%20Mail.pdf", "http://www.forecastingprinciples.com/paperpdf/Monetary%20Incentives.pdf", "http://home.magpi.com/case-study/evaluating-cash-transfers-in-guatemala/", "http://home.magpi.com/more-data-for-less-money/", "http://www.onepointglobal.com/MobileSurveys/SMSsurveys", "http://www.questback.com/online-customer-surveys", "http://surveyanyplace.com/why-mobile-surveys/", "http://www.press.uchicago.edu/ucp/books/book/distributed/S/bo22196267.html", "http://marketing.wharton.upenn.edu/ideas/pdf/Armstrong/EstimatingNonresponseBias.pdf", "http://www.surveysoftware.info/en/", "http://doi.org/10.1086%2F268203", "http://doi.org/10.1177%2F0894439309353099", "http://doi.org/10.18148%2Fsrm%2F2010.v4i3.4278", "http://doi.org/10.18148%2Fsrm%2F2013.v7i1.5098", "http://doi.org/10.18148%2Fsrm%2F2013.v7i3.5458", "http://doi.org/10.2307%2F3150783", "http://www.surveypractice.org/index.php/SurveyPractice/article/view/250", "https://academic.oup.com/jcmc/article/10/3/JCMC1034/4614509", "https://journals.sub.uni-hamburg.de/giga/jpla/article/viewArticle/903", "https://ojs.ub.uni-konstanz.de/srm/article/view/4278", "https://ojs.ub.uni-konstanz.de/srm/article/view/5098", "https://ojs.ub.uni-konstanz.de/srm/article/view/5458", "https://web.archive.org/web/20100620200022/http://marketing.wharton.upenn.edu/ideas/pdf/Armstrong/EstimatingNonresponseBias.pdf", "https://web.archive.org/web/20140208043428/http://surveyanyplace.com/why-mobile-surveys/", "https://dx.doi.org/10.5334/bar.h", "https://www.webcitation.org/6cTYw0aQt?url=http://www.questback.com/online-customer-surveys", "https://www.mrs.org.uk/ijmr_article/article/104501"]}, "Distance sampling": {"categories": ["All stub articles", "Demography", "Environmental statistics", "Sampling techniques", "Sociology stubs", "Statistics stubs"], "title": "Distance sampling", "method": "Distance sampling", "url": "https://en.wikipedia.org/wiki/Distance_sampling", "summary": "Distance sampling is a widely used group of closely related methods for estimating the density and/or abundance of populations. The main methods are based on line transects or point transects. In this method of sampling, the data collected are the distances of the objects being surveyed from these randomly placed lines or points, and the objective is to estimate the average density of the objects within a region.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/1/15/Vista_Login_Manager_Cropped.svg"], "links": ["Abundance (ecology)", "International Standard Book Number", "Point transect", "Population", "Population density", "Sociology", "Statistics", "Transect"], "references": ["http://www.colostate.edu/Dept/coopunit/download.html", "http://www.ruwpa.st-and.ac.uk/distance.book/dist_encyc_env.pdf", "https://web.archive.org/web/20090409112605/http://www.creem.st-and.ac.uk:80/tiago/webpages/distancesamplingreferences.html"]}, "Cumulative accuracy profile": {"categories": ["Articles created via the Article Wizard", "Mathematical modeling"], "title": "Cumulative accuracy profile", "method": "Cumulative accuracy profile", "url": "https://en.wikipedia.org/wiki/Cumulative_accuracy_profile", "summary": "The cumulative accuracy profile (CAP) is used in data science to visualize the discriminative power of a model. The CAP of a model represents the cumulative number of positive outcomes along the y-axis versus the corresponding cumulative number of a classifying parameter along the x-axis. The CAP is distinct from the receiver operating characteristic (ROC), which plots the true-positive rate against the false-positive rate.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2d/CAP_profiles.jpg"], "links": ["False-positive rate", "Receiver operating characteristic", "True-positive rate"], "references": ["http://www.statoo.ch/jss09/presentations/Calabrese.pdf", "http://www.rogermstein.com/wp-content/uploads/SobehartKeenanStein2000.pdf", "https://www.bundesbank.de/Redaktion/EN/Downloads/Publications/Discussion_Paper_2/2003/2003_10_01_dkp_01.pdf?__blob=publication"]}, "Asymptotic equipartition property": {"categories": ["Information theory", "Statistical theorems"], "title": "Asymptotic equipartition property", "method": "Asymptotic equipartition property", "url": "https://en.wikipedia.org/wiki/Asymptotic_equipartition_property", "summary": "In information theory, the asymptotic equipartition property (AEP) is a general property of the output samples of a stochastic source. It is fundamental to the concept of typical set used in theories of compression.\nRoughly speaking, the theorem states that although there are many series of results that may be produced by a random process, the one actually produced is most probably from a loosely defined set of outcomes that all have approximately the same chance of being the one actually realized. (This is a consequence of the law of large numbers and ergodic theory.) Although there are individual outcomes which have a higher probability than any outcome in this set, the vast number of outcomes in the set almost guarantees that the outcome will come from the set. One way of intuitively understanding the property is through Cram\u00e9r's large deviation theorem, which states that the probability of a large deviation from mean decays exponentially with the number of samples. Such results are studied in large deviations theory; intuitively, it is the large deviations that would violate equipartition, but these are unlikely.\nIn the field of pseudorandom number generation, a candidate generator of undetermined quality whose output sequence lies too far outside the typical set by some statistical criteria is rejected as insufficiently random. Thus, although the typical set is loosely defined, practical notions arise concerning sufficient typicality.", "images": [], "links": ["A Mathematical Theory of Communication", "Almost sure", "Almost surely", "Bandwidth (signal processing)", "Bijection", "Borel\u2013Cantelli lemma", "Brockway McMillan", "Category theoretic", "Claude E. Shannon", "Claude Shannon", "Convergence in probability", "Cram\u00e9r's large deviation theorem", "Data compression", "David J. C. MacKay", "Differential entropy", "Earth mover's distance", "Entropy", "Entropy rate", "Ergodic theory", "Gromov", "Independent identically distributed random variables", "Information theory", "Injective correspondence", "International Standard Book Number", "Isomorphism", "Large deviations theory", "Law of large numbers", "Leo Breiman", "L\u00e9vy's martingale convergence theorem", "Markov's inequality", "Measurable", "Noisy-channel coding theorem", "Noisy channel coding theorem", "Partially defined map", "Probability space", "Product (category theory)", "Pseudorandom number generator", "Source coding theorem", "Stationary ergodic process", "Stationary process", "Stochastic process", "Terminal object", "Time-invariant", "Time series", "Typical set", "Wasserstein metric"], "references": ["http://www-isl.stanford.edu/~cover/papers/paper83.pdf", "http://www.ihes.fr/~gromov/PDF/structre-serch-entropy-july5-2012.pdf", "https://web.archive.org/web/20160217105359/http://www.inference.phy.cam.ac.uk/mackay/itila/book.html"]}, "Variance-gamma distribution": {"categories": ["Continuous distributions"], "title": "Variance-gamma distribution", "method": "Variance-gamma distribution", "url": "https://en.wikipedia.org/wiki/Variance-gamma_distribution", "summary": "The variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the gamma distribution. The tails of the distribution decrease more slowly than the normal distribution. It is therefore suitable to model phenomena where numerically large values are more probable than is the case for the normal distribution. Examples are returns from financial assets and turbulent wind speeds. The distribution was introduced in the financial literature by Madan and Seneta. The variance-gamma distributions form a subclass of the generalised hyperbolic distributions.\nThe fact that there is a simple expression for the moment generating function implies that simple expressions for all moments are available. The class of variance-gamma distributions is closed under convolution in the following sense. If \n \n \n \n \n X\n \n 1\n \n \n \n \n {\\displaystyle X_{1}}\n and \n \n \n \n \n X\n \n 2\n \n \n \n \n {\\displaystyle X_{2}}\n are independent random variables that are variance-gamma distributed with the same values of the parameters \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n and \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n , but possibly different values of the other parameters, \n \n \n \n \n \u03bb\n \n 1\n \n \n \n \n {\\displaystyle \\lambda _{1}}\n , \n \n \n \n \n \u03bc\n \n 1\n \n \n \n \n {\\displaystyle \\mu _{1}}\n and \n \n \n \n \n \u03bb\n \n 2\n \n \n ,\n \n \n {\\displaystyle \\lambda _{2},}\n \n \n \n \n \n \u03bc\n \n 2\n \n \n \n \n {\\displaystyle \\mu _{2}}\n , respectively, then \n \n \n \n \n X\n \n 1\n \n \n +\n \n X\n \n 2\n \n \n \n \n {\\displaystyle X_{1}+X_{2}}\n is variance-gamma distributed with parameters \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n , \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n , \n \n \n \n \n \u03bb\n \n 1\n \n \n +\n \n \u03bb\n \n 2\n \n \n \n \n {\\displaystyle \\lambda _{1}+\\lambda _{2}}\n and \n \n \n \n \n \u03bc\n \n 1\n \n \n +\n \n \u03bc\n \n 2\n \n \n \n \n {\\displaystyle \\mu _{1}+\\mu _{2}}\n .\nThe variance-gamma distribution can also be expressed in terms of three inputs parameters (C,G,M) denoted after the initials of its founders. If the \"C\", \n \n \n \n \u03bb\n \n \n {\\displaystyle \\lambda }\n here, parameter is integer then the distribution has a closed form 2-EPT distribution. See 2-EPT Probability Density Function. Under this restriction closed form option prices can be derived.\nIf \n \n \n \n \u03b1\n =\n 1\n \n \n {\\displaystyle \\alpha =1}\n , \n \n \n \n \u03bb\n =\n 1\n \n \n {\\displaystyle \\lambda =1}\n and \n \n \n \n \u03b2\n =\n 0\n \n \n {\\displaystyle \\beta =0}\n , the distribution becomes a Laplace distribution with scale parameter \n \n \n \n b\n =\n 1\n \n \n {\\displaystyle b=1}\n . As long as \n \n \n \n \u03bb\n =\n 1\n \n \n {\\displaystyle \\lambda =1}\n , alternative choices of \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n and \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n will produce distributions related to the Laplace distribution, with skewness, scale and location depending on the other parameters.See also Variance gamma process.", "images": [], "links": ["2-EPT probability density function", "ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous probability distribution", "Convolution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture density", "Mixture distribution", "Modified Bessel function of the second kind", "Moment-generating function", "Moment (mathematics)", "Moment generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normal variance-mean mixture", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance gamma process", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": []}, "Alternative hypothesis": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2011", "Statistical hypothesis testing"], "title": "Alternative hypothesis", "method": "Alternative hypothesis", "url": "https://en.wikipedia.org/wiki/Alternative_hypothesis", "summary": "In statistical hypothesis testing,\nthe alternative hypothesis (or maintained hypothesis or research hypothesis) and the null hypothesis are the two rival hypotheses which are compared by a statistical hypothesis test.\nIn the domain of science two rival hypotheses can be compared by explanatory power and predictive power.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Explanatory power", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jacob Cohen (statistician)", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Neyman\u2013Pearson lemma", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Predictive power", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1037%2F0003-066X.45.12.1304"]}, "Mean absolute difference": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from November 2010", "Articles with unsourced statements from October 2010", "Scale statistics", "Similarity and distance measures", "Statistical deviation and dispersion", "Summary statistics", "Theory of probability distributions"], "title": "Mean absolute difference", "method": "Mean absolute difference", "url": "https://en.wikipedia.org/wiki/Mean_absolute_difference", "summary": "The mean absolute difference (univariate) is a measure of statistical dispersion equal to the average absolute difference of two independent values drawn from a probability distribution. A related statistic is the relative mean absolute difference, which is the mean absolute difference divided by the arithmetic mean, and equal to twice the Gini coefficient.\nThe mean absolute difference is also known as the absolute mean difference (not to be confused with the absolute value of the mean signed difference) and the Gini mean difference (GMD). The mean absolute difference is sometimes denoted by \u0394 or as MD.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Absolute difference", "Absolute value", "Arithmetic mean", "Bernoulli distribution", "Beta function", "Coefficient of variation", "Corrado Gini", "Cumulative distribution function", "Degrees of freedom (statistics)", "Digital object identifier", "Discrete probability distribution", "Distance standard deviation", "E-statistic", "Estimator", "Expected value", "Exponential distribution", "Gamma distribution", "Gini coefficient", "Independent and identically distributed random variables", "JSTOR", "L-moment", "L-scale", "Law of total expectation", "Lorenz curve", "Mean absolute deviation", "Mean absolute error", "Mean deviation (disambiguation)", "Mean signed difference", "Normal distribution", "Pareto distribution", "Probability density function", "Probability distribution", "Quantile function", "Random variables", "Shlomo Yitzhaki (economics)", "Standard deviation", "Statistical dispersion", "Student's t-distribution", "Uniform distribution (continuous)"], "references": ["http:ftp://metron.sta.uniroma1.it/RePEc/articoli/2003-2-285-316.pdf", "http://economics.dal.ca/RePEc/dal/wparch/howgini.pdf", "http://doi.org/10.1002%2F(SICI)1099-1255(199703)12:2%3C133::AID-JAE433%3E3.0.CO;2-H", "http://doi.org/10.1093%2Fbiomet%2F28.3-4.428", "http://doi.org/10.1214%2Faoms%2F1177729346", "http://doi.org/10.2307%2F2223319", "http://www.jstor.org/stable/2223319"]}, "Resentful demoralization": {"categories": ["All stub articles", "Design of experiments", "Sociology stubs"], "title": "Resentful demoralization", "method": "Resentful demoralization", "url": "https://en.wikipedia.org/wiki/Resentful_demoralization", "summary": "Resentful demoralization is an issue in controlled experiments in which those in the control group become resentful of not receiving the experimental treatment. Alternatively, the experimental group could be resentful of the control group, if the experimental group perceive its treatment as inferior.\nThey may become angry, depressed, uncooperative, or non-compliant. This may lead to significant systematic differences in the outcome of the control group, obscuring the results of the study and threatening their validity.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/15/Vista_Login_Manager_Cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/15/20120521043933%21Vista_Login_Manager_Cropped.svg"], "links": ["Clinical trial", "Compliance (medicine)", "Control group", "Controlled experiment", "Randomized controlled trial", "Resentment", "Sociology", "Validity (statistics)"], "references": ["http://mrw.interscience.wiley.com/emrw/9780470013199/esbs/article/bsa561/current/abstract"]}, "Multivariate normal distribution": {"categories": ["All articles with dead external links", "All articles with unsourced statements", "Articles with dead external links from December 2017", "Articles with permanently dead external links", "Articles with unsourced statements from July 2012", "Continuous distributions", "Exponential family distributions", "Multivariate continuous distributions", "Normal distribution", "Pages using deprecated image syntax", "Stable distributions", "Webarchive template webcite links", "Wikipedia articles needing clarification from April 2018"], "title": "Multivariate normal distribution", "method": "Multivariate normal distribution", "url": "https://en.wikipedia.org/wiki/Multivariate_normal_distribution", "summary": "In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8e/MultivariateNormal.png", "https://upload.wikimedia.org/wikipedia/commons/5/57/Multivariate_Gaussian.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARGUS distribution", "Absolute continuity", "Accelerated failure time model", "Actuarial science", "Affine function", "Affine transformation", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Apache Maven", "ArXiv", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Best linear unbiased prediction", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Biased estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bit", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Box\u2013Muller transform", "Breusch\u2013Godfrey test", "Burr distribution", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Characteristic function (probability theory)", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Cholesky decomposition", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Complex normal distribution", "Compound Poisson distribution", "Confidence interval", "Confidence region", "Confounding", "Conjugate prior", "Conjugate transpose", "Contingency table", "Continuous probability distribution", "Control chart", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation (statistics)", "Correlation and dependence", "Correlogram", "Count data", "Countably infinite", "Covariance matrix", "Cram\u00e9r\u2013Rao bound", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Dagum distribution", "Data collection", "Data set", "Davis distribution", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Determinant", "Diagonal matrix", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Disintegration theorem", "Divergence (statistics)", "Dot product", "Durbin\u2013Watson statistic", "E (mathematical constant)", "Econometrics", "Effect size", "Efficiency (statistics)", "Eigendecomposition", "Eigendecomposition of a matrix", "Ellipse", "Ellipsoid", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Estimation of covariance matrices", "Estimator", "Euclidean norm", "Ewens's sampling formula", "Expected value", "Experiment", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's z-distribution", "Fisher information", "Fisher information matrix", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian copula", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "Geostatistics", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harmonic mean", "Hermitian matrices", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hoyt distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypersphere", "Hypoexponential distribution", "Index of dispersion", "Information entropy", "Interaction (statistics)", "International Air Transport Association airport code", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse Mills ratio", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "Isserlis\u2019 theorem", "Jackknife resampling", "Jarque\u2013Bera test", "Jerome H. Friedman", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kullback\u2013Leibler divergence", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Larry rafsky", "Lebesgue measure", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "MVN", "Mahalanobis distance", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Marginal distribution", "Matrix-exponential distribution", "Matrix (math)", "Matrix gamma distribution", "Matrix inverse", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Mean vector", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mixture model", "Mode (statistics)", "Model selection", "Moment-generating function", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo method", "Mount Vernon Airport", "Multinomial distribution", "Multiple comparisons", "Multiple linear regression", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Mutual information", "Nakagami distribution", "Nat (unit)", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Norm (mathematics)", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normally distributed and uncorrelated does not imply independent", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "Pairwise independence", "Parabolic fractal distribution", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Polar coordinates", "Poly-Weibull distribution", "Population (statistics)", "Population statistics", "Positive-definite matrix", "Positive semi-definite matrix", "Posterior probability", "Power (statistics)", "Precision (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability theory", "Proportional hazards model", "Pseudo-determinant", "Psychometrics", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quantile function", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrix", "Random variable", "Random vector", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rice distribution", "Robust regression", "Robust statistics", "Rotation matrix", "Run chart", "Sample covariance matrix", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Schur complement", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Singular matrix", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable distribution", "Standard deviation", "Standard error", "Standard normal", "Standard score", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Sum of normally distributed random variables", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Tracy\u2013Widom distribution", "Transpose", "Trend estimation", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "Univariate", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "WebCite", "Weibull distribution", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://amath.colorado.edu/courses/7400/2010Spr/lecture9.pdf", "http://fourier.eng.hmc.edu/e161/lectures/gaussianprocess/node7.html", "http://web.mit.edu/6.041/www/LECTURE/lec22.pdf", "http://stanford.edu/~jduchi/projects/general_notes.pdf", "http://www.math.uiuc.edu/~r-ash/Stat/StatLec21-25.pdf", "http://finzi.psych.upenn.edu/usr/share/doc/library/shotGroups/html/hoyt.html", "http://www.lri.fr/~hansen/cmatutorial.pdf", "http://www.ism.ac.jp/editsec/aism/pdf/016_1_0135.pdf", "http://arxiv.org/abs/1603.04166", "http://doi.org/10.1007%2F978-0-387-98144-4", "http://doi.org/10.1007%2F978-1-4613-9655-0", "http://doi.org/10.1007%2FBF02613322", "http://doi.org/10.1007%2FBF02868568", "http://doi.org/10.1007%2Fs00362-002-0119-6", "http://doi.org/10.1016%2F0047-259X(91)90031-V", "http://doi.org/10.1093%2Fbiomet%2F57.3.519", "http://doi.org/10.1093%2Fbiomet%2F65.2.263", "http://doi.org/10.1109%2F18.30996", "http://doi.org/10.1109%2F34.6789", "http://doi.org/10.1109%2FWSC.2008.473608", "http://doi.org/10.1109%2FWSC.2015.7408202", "http://doi.org/10.1111%2Frssb.12162", "http://doi.org/10.1214%2Faos%2F1176344722", "http://doi.org/10.2307%2F2318494", "https://www.springer.com/statistics/computational+statistics/book/978-3-642-01688-2", "https://web.archive.org/web/20100331114258/http://www.lri.fr/~hansen/cmatutorial.pdf", "https://ieeexplore.ieee.org/document/4736085/", "https://ieeexplore.ieee.org/document/7408202/", "https://cran.r-project.org/web/packages/TruncatedNormal/", "https://www.webcitation.org/6HPbX5thy?url=http://amath.colorado.edu/courses/7400/2010Spr/lecture9.pdf", "https://upload.wikimedia.org/wikipedia/commons/a/a2/Cumulative_function_n_dimensional_Gaussians_12.2013.pdf"]}, "Box plot": {"categories": ["Commons category link is on Wikidata", "Statistical charts and diagrams", "Statistical outliers"], "title": "Box plot", "method": "Box plot", "url": "https://en.wikipedia.org/wiki/Box_plot", "summary": "In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles. Box plots may also have lines extending vertically from the boxes (whiskers) indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and-whisker diagram. Outliers may be plotted as individual points.\nBox plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution (though Tukey's boxplot assumes symmetry for the whiskers and normality for their length). The spacings between the different parts of the box indicate the degree of dispersion (spread) and skewness in the data, and show outliers. In addition to the points themselves, they allow one to visually estimate various L-estimators, notably the interquartile range, midhinge, range, mid-range, and trimean. Box plots can be drawn either horizontally or vertically. Box plots received their name from the box in the middle.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2b/Box-Plot_mit_Interquartilsabstand.png", "https://upload.wikimedia.org/wikipedia/commons/5/55/Box-Plot_mit_Min-Max_Abstand.png", "https://upload.wikimedia.org/wikipedia/commons/1/1a/Boxplot_vs_PDF.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2b/Fourboxplots.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Michelsonmorley-boxplot.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Addison-Wesley", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bagplot", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Candlestick chart", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "CiteSeerX", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Five-number summary", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Functional boxplot", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Tukey", "John W. Tukey", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kernel density estimation", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-estimator", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Medcouple", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michelson\u2013Morley experiment", "Mid-range", "Midhinge", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Rousseeuw", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quartile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Seven-number summary", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The American Statistician", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Trimean", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Violin plot", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://stat.ethz.ch/R-manual/R-devel/library/grDevices/html/boxplot.stats.html", "http://www.purplemath.com/modules/boxwhisk3.htm", "http://www.r-statistics.com/2011/03/beeswarm-boxplot-and-plotting-it-with-r/", "http://www.physics.csbsju.edu/stats/box2.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.90.9812", "http://doi.org/10.1016%2Fj.csda.2007.11.008", "http://doi.org/10.2307%2F2683468", "http://doi.org/10.2307%2F2685133", "http://doi.org/10.2307%2F2685173", "http://doi.org/10.2307%2F2686061", "http://www.jstor.org/stable/2683468", "http://www.jstor.org/stable/2685133", "http://www.jstor.org/stable/2685173", "http://www.jstor.org/stable/2686061", "https://web.archive.org/web/20171001193540/http://boxplot.bio.ed.ac.uk/"]}, "Safety in numbers": {"categories": ["CS1 errors: dates", "CS1 maint: Multiple names: authors list", "Crowd psychology", "Cycling safety", "Evolutionary biology", "Statistical laws"], "title": "Safety in numbers", "method": "Safety in numbers", "url": "https://en.wikipedia.org/wiki/Safety_in_numbers", "summary": "Safety in numbers is the hypothesis that, by being part of a large physical group or mass, an individual is less likely to be the victim of a mishap, accident, attack, or other bad event. Some related theories also argue (and can show statistically) that mass behaviour (by becoming more predictable and \"known\" to other people) can reduce accident risks, such as in traffic safety \u2013 in this case, the safety effect creates an actual reduction of danger, rather than just a redistribution over a larger group.", "images": [], "links": ["Accident", "Antipredator adaptation", "Brown fur seal", "Correlation does not imply causation", "Critical Mass (cycling)", "Cyclist", "Digital object identifier", "Flocking (behavior)", "Great white shark", "JSTOR", "Jenny Morton", "London Congestion Charge", "Pedestrian", "Predator", "Predator satiation", "PubMed Central", "PubMed Identifier", "Reuben Smeed", "Safety in Numbers (disambiguation)", "Selfish herd theory", "Shanthi Ameratunga", "Shoaling and schooling", "Smeed's law", "Transportation (journal)", "W.D. Hamilton"], "references": ["http://www.acrs.org.au/publications/journalscurrentandbackissues.html", "http://ip.bmjjournals.com/cgi/content/full/9/3/205", "http://www.cycle-helmets.com/hpja_2005_1_robinson.pdf", "http://www.sciencedirect.com/science/article/pii/S0001457509000876", "http://springerlink.com/content/u64017227p1g5445/fulltext.pdf", "http://www.vejpark2.kk.dk/publikationer/pdf/464_Cykelregnskab_UK.%202006.pdf", "http://www.vejdirektoratet.dk/pdf/cykelrapport/009-018Chapter03.pdf", "http://policy.rutgers.edu/faculty/pucher/MakingWalkingAndCyclingSafer_TQ2000.pdf", "http://factfinder.census.gov", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1731007", "http://www.ncbi.nlm.nih.gov/pubmed/10868762", "http://www.ncbi.nlm.nih.gov/pubmed/12067108", "http://www.ncbi.nlm.nih.gov/pubmed/12966006", "http://www.ncbi.nlm.nih.gov/pubmed/16389930", "http://www.ncbi.nlm.nih.gov/pubmed/19540975", "http://www.ncbi.nlm.nih.gov/pubmed/20159059", "http://www.ncbi.nlm.nih.gov/pubmed/21806731", "http://www.ncbi.nlm.nih.gov/pubmed/5104951", "http://www.ncbi.nlm.nih.gov/pubmed/8397652", "http://www.nyc.gov/html/dot/downloads/pdf/commuter_cycling_indicator_and_data_2009.pdf", "http://ww.fietsberaad.nl/library/repository/bestanden/CyclingintheNetherlands2009.pdf", "http://www.nzta.govt.nz/resources/research/reports/289/docs/289.pdf", "http://www.nzta.govt.nz/resources/research/reports/389/docs/389.pdf", "http://doi.org/10.1007%2Fs11116-007-9133-9", "http://doi.org/10.1016%2F0001-4575(93)90001-D", "http://doi.org/10.1016%2F0022-5193(71)90189-5", "http://doi.org/10.1016%2FS0001-4575(01)00043-4", "http://doi.org/10.1016%2FS0001-4575(99)00090-1", "http://doi.org/10.1016%2Fj.aap.2009.04.009", "http://doi.org/10.1016%2Fj.aap.2009.08.019", "http://doi.org/10.1016%2Fj.aap.2011.09.045", "http://doi.org/10.1016%2Fj.aap.2013.12.016", "http://doi.org/10.1016%2Fj.anbehav.2008.01.016", "http://doi.org/10.1016%2Fj.cub.2012.05.008", "http://doi.org/10.1016%2Fj.ssci.2010.07.016", "http://doi.org/10.1016%2Fj.tranpol.2009.03.004", "http://doi.org/10.1071%2Fhe05047", "http://doi.org/10.1111%2Fj.1753-6405.2011.00731.x", "http://doi.org/10.1136%2Fip.9.3.205", "http://doi.org/10.2307%2F2984177", "http://doi.org/10.3141%2F1818-16", "http://doi.org/10.3141%2F1878-09", "http://doi.org/10.3141%2F1982-20", "http://doi.org/10.3141%2F2198-06", "http://doi.org/10.3141%2F2236-09", "http://www.jstor.org/stable/2984177", "http://www.norden.org/pub/sk/showpub.asp?pubnr=2005:556", "http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w129p3.pdf", "http://www.avhandlingar.se/avhandling/ff9fdd701a/", "http://www.tfl", "http://www.thisislondon.co.uk/standard/article-23434443-details/Number+of+cyclists+treated+for+serious+injuries+doubles/article.do", "http://www.trl.co.uk/online_store/reports_publications/trl_reports/cat_road_user_safety/report_collisions_involving_pedal_cyclists_on_britain_s_roads_establishing_the_causes_.htm", "http://www.tfl.gov.uk/assets/downloads/businessandpartners/cycling-action-plan.pdf", "http://www.tfl.gov.uk/assets/downloads/businessandpartners/cycling-in-london-final-october-2008.pdf", "http://www.tfl.gov.uk/assets/downloads/corporate/ThirdAnnualReportFinal.pdf"]}, "Tukey's lambda distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax", "Probability distributions with non-finite variance", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Tukey lambda distribution", "method": "Tukey's lambda distribution", "url": "https://en.wikipedia.org/wiki/Tukey_lambda_distribution", "summary": "Formalized by John Tukey, the Tukey lambda distribution is a continuous, symmetric probability distribution defined in terms of its quantile function. It is typically used to identify an appropriate distribution (see the comments below) and not used in statistical models directly.\nThe Tukey lambda distribution has a single shape parameter, \u03bb, and as with other probability distributions, it can be transformed with a location parameter, \u03bc, and a scale parameter, \u03c3. Since the general form of probability distribution can be expressed in terms of the standard distribution, the subsequent formulas are given for the standard form of the function.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/25/Several_samples_of_the_pdfs_of_the_Tukey_lambda_distributions.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["ARGUS distribution", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Concave function", "Continuous uniform distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Copyright status of work by the U.S. government", "Correlation", "Cumulative distribution function", "Dagum distribution", "Data set", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Histogram", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "John Tukey", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the Royal Statistical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "L-moments", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "National Institute of Standards and Technology", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "PPCC plot", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Reflection symmetry", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical model", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.itl.nist.gov/div898/handbook/eda/section3/eda366f.htm", "http://www.nist.gov", "http://arxiv.org/abs/0903.1592", "http://arxiv.org/abs/math/0701405", "http://doi.org/10.1016%2Fj.csda.2007.06.021", "http://doi.org/10.2307%2F2283943", "http://www.jstor.org/stable/2283943"]}, "Pseudocount": {"categories": ["All articles to be merged", "All articles with unsourced statements", "Articles to be merged from July 2018", "Articles with unsourced statements from December 2013", "Categorical data", "Probability theory", "Statistical natural language processing", "Wikipedia articles needing clarification from October 2018"], "title": "Additive smoothing", "method": "Pseudocount", "url": "https://en.wikipedia.org/wiki/Additive_smoothing", "summary": "In statistics, additive smoothing, also called Laplace smoothing (not to be confused with Laplacian smoothing as used in image processing), or Lidstone smoothing, is a technique used to smooth categorical data. Given an observation \n \n \n \n \n \n \n x\n \n \n =\n \n \n \u27e8\n \n \n x\n \n 1\n \n \n ,\n \n \n x\n \n 2\n \n \n ,\n \n \u2026\n ,\n \n \n x\n \n d\n \n \n \n \u27e9\n \n \n \n \n \n {\\textstyle \\scriptstyle {\\mathbf {x} \\ =\\ \\left\\langle x_{1},\\,x_{2},\\,\\ldots ,\\,x_{d}\\right\\rangle }}\n from a multinomial distribution with \n \n \n \n \n \n N\n \n \n \n \n {\\textstyle \\scriptstyle {N}}\n trials, a \"smoothed\" version of the data gives the estimator:\n\n \n \n \n \n \n \n \n \u03b8\n ^\n \n \n \n \n i\n \n \n =\n \n \n \n \n x\n \n i\n \n \n +\n \u03b1\n \n \n N\n +\n \u03b1\n d\n \n \n \n \n (\n i\n =\n 1\n ,\n \u2026\n ,\n d\n )\n ,\n \n \n {\\displaystyle {\\hat {\\theta }}_{i}={\\frac {x_{i}+\\alpha }{N+\\alpha d}}\\qquad (i=1,\\ldots ,d),}\n where the \"pseudocount\" \u03b1 > 0 is a smoothing parameter. \u03b1 = 0 corresponds to no smoothing. (This parameter is explained in \u00a7 Pseudocount below.) Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability (relative frequency) \n \n \n \n \n \n \n \n x\n \n i\n \n \n N\n \n \n \n \n \n {\\textstyle \\scriptstyle {\\frac {x_{i}}{N}}}\n , and the uniform probability \n \n \n \n \n \n \n 1\n d\n \n \n \n \n \n {\\textstyle \\scriptstyle {\\frac {1}{d}}}\n . Invoking Laplace's rule of succession, some authors have argued that \u03b1 should be 1 (in which case the term add-one smoothing is also used), though in practice a smaller value is typically chosen.\nFrom a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a symmetric Dirichlet distribution with parameter \u03b1 as a prior distribution. In the special case where the number of categories is 2, this is equivalent to using a Beta distribution as the conjugate prior for the parameters of Binomial distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20161219000653%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20071115071721%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20070702231905%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20070702215640%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20070404041444%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20070316075541%21Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/0/0f/20060817065722%21Mergefrom.svg"], "links": ["0 (number)", "Artificial neural network", "Bag of words model", "Bayesian average", "Bayesian inference", "Beta distribution", "Binomial distribution", "Categorical data", "Categorical distribution", "Cromwell's rule", "Density estimation", "Dirichlet distribution", "Discrete uniform distribution", "Empirical probability", "Estimator", "Event (probability theory)", "Expected value", "George James Lidstone", "Halting problem", "Hidden Markov model", "Image processing", "International Standard Book Number", "Jeffreys prior", "Laplacian smoothing", "Machine learning", "Model (abstract)", "Multinomial distribution", "Naive Bayes classifier", "PPM compression algorithm", "Parameter", "Pierre-Simon Laplace", "Posterior distribution", "Prediction by partial matching", "Principle of indifference", "Prior distribution", "Prior probability", "Probability", "Recommender system", "Relative frequency", "Relevance feedback", "Rule of Succession", "Rule of succession", "Sample (statistics)", "Shrinkage estimator", "Smoothing", "Statistics", "Sunrise problem"], "references": ["http://www.aclweb.org/anthology/P/P96/P96-1041.pdf", "http://dl.acm.org/citation.cfm?id=2809471", "http://dl.acm.org/citation.cfm?id=2934737", "https://www.youtube.com/watch?v=qRJ3GKMOFrE#t=4124", "https://archive.is/20130419033054/http://www.soe.ucsc.edu/research/compbio/html_format_papers/tr-95-11/node30.html", "https://web.archive.org/web/20040909153902/http://www.soe.ucsc.edu/research/compbio/html_format_papers/tr-95-11/node8.html"]}, "Mixed data sampling": {"categories": ["All stub articles", "Econometric modeling", "Econometrics stubs", "Statistical forecasting", "Time series models"], "title": "Mixed-data sampling", "method": "Mixed data sampling", "url": "https://en.wikipedia.org/wiki/Mixed-data_sampling", "summary": "Mixed-data sampling (MIDAS) is an econometric regression or filtering method developed by Ghysels et al. There is now a substantial literature on MIDAS regressions and their applications, including Andreou et al. (2010), and especially Andreou et al. (2013).A simple regression example has the independent variable appearing at a higher frequency than the dependent variable:\n\n \n \n \n \n y\n \n t\n \n \n =\n \n \u03b2\n \n 0\n \n \n +\n \n \u03b2\n \n 1\n \n \n B\n (\n \n L\n \n 1\n \n /\n \n m\n \n \n ;\n \u03b8\n )\n \n x\n \n t\n \n \n (\n m\n )\n \n \n +\n \n \u03b5\n \n t\n \n \n (\n m\n )\n \n \n ,\n \n \n {\\displaystyle y_{t}=\\beta _{0}+\\beta _{1}B(L^{1/m};\\theta )x_{t}^{(m)}+\\varepsilon _{t}^{(m)},}\n where y is the dependent variable, x is the regressor, m denotes the frequency \u2013 for instance if y is yearly \n \n \n \n \n x\n \n t\n \n \n (\n 4\n )\n \n \n \n \n {\\displaystyle x_{t}^{(4)}}\n is quarterly \u2013 \n \n \n \n \u03b5\n \n \n {\\displaystyle \\varepsilon }\n is the disturbance and \n \n \n \n B\n (\n \n L\n \n 1\n \n /\n \n m\n \n \n ;\n \u03b8\n )\n \n \n {\\displaystyle B(L^{1/m};\\theta )}\n is a lag distribution, for instance the Beta function or the Almon Lag.\nThe regression models can be viewed in some cases as substitutes for the Kalman filter when applied in the context of mixed frequency data. Bai, Ghysels and Wright (2010) examine the relationship between MIDAS regressions and Kalman filter state space models applied to mixed frequency data. In general, the latter involve a system of equations, whereas in contrast MIDAS\nregressions involve a (reduced form) single equation. As a consequence, MIDAS regressions might be less efficient, but also less prone to specification errors. In cases where the MIDAS regression is only an approximation, the approximation errors tend to be small.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170527191524%21Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170519203409%21Emoji_u1f4c8.svg"], "links": ["ARMAX", "Beta function", "Dependent variable", "Distributed lag", "Econometric", "Econometric Reviews", "Econometrics", "Eric Ghysels", "Independent variable", "Kalman filter"], "references": ["http://www.mathworks.com/matlabcentral/fileexchange/45150-midas-regression/", "http://www.unc.edu/~eghysels/", "https://mpiktas.github.io/midasr//"]}, "Nonlinear regression": {"categories": ["Regression analysis"], "title": "Nonlinear regression", "method": "Nonlinear regression", "url": "https://en.wikipedia.org/wiki/Nonlinear_regression", "summary": "In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c9/Segmented_linear_regression_graph_showing_yield_of_mustard_plants_vs_soil_salinity_in_Haryana%2C_India%2C_1987%E2%80%931988.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Michaelis-Menten_saturation_curve_of_an_enzyme_reaction.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c9/Segmented_linear_regression_graph_showing_yield_of_mustard_plants_vs_soil_salinity_in_Haryana%2C_India%2C_1987%E2%80%931988.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Approximation theory", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bias (statistics)", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calibration curve", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational statistics", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Crop yield", "Cross-correlation", "Cross-validation (statistics)", "Curve fitting", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Dependent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete choice", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors-in-variables model", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential function", "Exponential smoothing", "Exponentiation", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fixed effects model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian function", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "Guess value", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent variable", "Independent variables", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iteratively reweighted least squares", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least-angle regression", "Least absolute deviations", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "Lineweaver\u2013Burk plot", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local maximum", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logarithmic growth", "Logistic regression", "Lorenz curve", "Loss function", "Lp space", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michaelis-Menten kinetics", "Michaelis\u2013Menten", "Michaelis\u2013Menten kinetics", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-linear least squares", "Non-negative least squares", "Nonparametric regression", "Nonparametric statistics", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Optimization (mathematics)", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal component regression", "Prior probability", "Probabilistic design", "Probability distribution", "Probit model", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effects model", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regularized least squares", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Ridge regression", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "SegReg", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Soil salinity", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Systematic error", "Taylor series", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Trend estimation", "Trigonometric functions", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.waterlog.info/pdf/analysis.pdf", "http://www.waterlog.info/pdf/regtxt.pdf", "http://www.waterlog.info/segreg.htm", "http://doi.org/10.1002%2Ffor.3980140502"]}, "Stem-and-leaf display": {"categories": ["Exploratory data analysis", "Statistical charts and diagrams"], "title": "Stem-and-leaf display", "method": "Stem-and-leaf display", "url": "https://en.wikipedia.org/wiki/Stem-and-leaf_display", "summary": "A stem-and-leaf display or stem-and-leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. They evolved from Arthur Bowley's work in the early 1900s, and are useful tools in exploratory data analysis. Stemplots became more commonly used in the 1980s after the publication of John Tukey's book on exploratory data analysis in 1977. The popularity during those years is attributable to their use of monospaced (typewriter) typestyles that allowed computer technology of the time to easily produce the graphics. Modern computers' superior graphic capabilities have meant these techniques are less often used.\nA stem-and-leaf display is also called a stemplot, but the latter term often refers to another chart type. A simple stem plot may refer to plotting a matrix of y values onto a common x axis, and identifying the common x value with a vertical line, and the individual y values with symbols on the line.\nUnlike histograms, stem-and-leaf displays retain the original data to at least two significant digits, and put the data in order, thereby easing the move to order-based inference and non-parametric statistics.\nA basic stem-and-leaf display contains two columns separated by a vertical line. The left column contains the stems and the right column contains the leaves.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e4/Stem-and-leaf_time_tables_in_Japanese_train_stations.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Arthur Bowley", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Dot plot (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Information graphics", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Japan", "Jarque\u2013Bera test", "Johansen test", "John Tukey", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minatomirai Station", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monospaced", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Observations", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Place value", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Public transport timetable", "Quality control", "Quantitative data", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Yokohama", "Z-test"], "references": ["http://www.mathworks.com/help/matlab/ref/stem.html", "http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.stem"]}, "Cochran's theorem": {"categories": ["All articles needing additional references", "Articles needing additional references from July 2011", "Characterization of probability distributions", "Statistical theorems"], "title": "Cochran's theorem", "method": "Cochran's theorem", "url": "https://en.wikipedia.org/wiki/Cochran%27s_theorem", "summary": "In statistics, Cochran's theorem, devised by William G. Cochran, is a theorem used to justify results relating to the probability distributions of statistics that are used in the analysis of variance.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Analysis of covariance", "Analysis of variance", "Arithmetic mean", "Basis (linear algebra)", "Basu's theorem", "Bayesian experimental design", "Bayesian linear regression", "Blind experiment", "Blocking (statistics)", "Box\u2013Behnken design", "Central composite design", "Characteristic function (probability theory)", "Chi-squared distribution", "Comparing means", "Completely randomized design", "Confounding", "Contrast (statistics)", "Covariate", "Cram\u00e9r\u2019s decomposition theorem", "Crossover study", "Degrees of freedom (statistics)", "Design of experiments", "Digital object identifier", "Effect size", "Eigenvalue", "Experiment", "Experimental unit", "External validity", "F-distribution", "Factorial experiment", "Fourier transform", "Fractional factorial design", "Generalized randomized block design", "Glossary of experimental design", "Graeco-Latin square", "Hierarchical Bayes model", "Hierarchical linear modeling", "Identity matrix", "Independence (probability)", "Infinite divisibility (probability)", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "JSTOR", "Jahrbuch \u00fcber die Fortschritte der Mathematik", "Latin hypercube sampling", "Latin square", "Linear regression", "List of statistics articles", "Mathematical Proceedings of the Cambridge Philosophical Society", "Matrix diagonalization", "Maximum likelihood", "Mixed model", "Multiple comparison", "Multivariate analysis of variance", "Multivariate normal distribution", "Normal distribution", "Nuisance variable", "Optimal design", "Ordinary least squares", "Orthogonal array", "Orthogonal matrix", "Orthogonality", "Outline of statistics", "Plackett-Burman design", "Polynomial and rational function modeling", "Positive-semidefinite matrix", "Probability distribution", "Quadratic form", "Random assignment", "Random effect", "Random variable", "Random vector", "Randomization", "Randomized block design", "Randomized controlled trial", "Rank (linear algebra)", "Repeated measures design", "Replication (statistics)", "Response surface methodology", "Restricted randomization", "Roy C. Geary", "Sample size", "Sample variance", "Scientific control", "Scientific method", "Sequential analysis", "Sequential probability ratio test", "Standard normal", "Statistical inference", "Statistical model", "Statistics", "Student's t-distribution", "Symmetric matrices", "Taguchi methods", "Theorem", "Validity (statistics)", "William G. Cochran", "William Gemmell Cochran"], "references": ["http://www.stat.columbia.edu/~yangfeng/slides/cochran's-theorem.pdf", "http://doi.org/10.1017%2FS0305004100016595", "http://doi.org/10.2307%2F2983669", "http://www.jstor.org/stable/2983669", "http://zbmath.org/?format=complete&q=an:63.1090.03"]}, "Sinusoidal model": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from February 2008", "Articles with unsourced statements from February 2008", "Regression models", "Regression with time series structure", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Sinusoidal model", "method": "Sinusoidal model", "url": "https://en.wikipedia.org/wiki/Sinusoidal_model", "summary": "In statistics, signal processing, and time series analysis, a sinusoidal model to approximate a sequence Yi is:\n\n \n \n \n \n Y\n \n i\n \n \n =\n C\n +\n \u03b1\n sin\n \u2061\n (\n \u03c9\n \n T\n \n i\n \n \n +\n \u03d5\n )\n +\n \n E\n \n i\n \n \n \n \n {\\displaystyle Y_{i}=C+\\alpha \\sin(\\omega T_{i}+\\phi )+E_{i}}\n where C is constant defining a mean level, \u03b1 is an amplitude for the sine wave, \u03c9 is the frequency, Ti is a time variable, \u03c6 is the phase, and Ei is the error sequence in approximating the sequence Yi by the model. This sinusoidal model can be fit using nonlinear least squares; to obtain a good fit, nonlinear least squares routines may require good starting values for the constant, the amplitude, and the frequency.\nFitting a model with a single sinusoid is a special case of least-squares spectral analysis.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Amplitude", "Complex demodulation", "Copyright status of work by the U.S. government", "Errors and residuals in statistics", "Frequency", "Histogram", "Lag plot", "Least-squares spectral analysis", "Least squares", "Mean", "Model validation", "National Institute of Standards and Technology", "Nonlinear least squares", "Normal distribution", "Normal probability plot", "Outliers", "Periodogram", "Phase (waves)", "Root mean square", "Run sequence plot", "Signal processing", "Sine wave", "Spectral density estimation", "Statistical model", "Statistics", "Time series analysis", "Trend estimation"], "references": ["http://fr.scribd.com/doc/14674814/Regressions-et-equations-integrales", "http://www.itl.nist.gov/div898/handbook/eda/section4/eda425.htm", "http://www.nist.gov"]}, "V-statistic": {"categories": ["Asymptotic theory (statistics)", "Estimation theory"], "title": "V-statistic", "method": "V-statistic", "url": "https://en.wikipedia.org/wiki/V-statistic", "summary": "V-statistics are a class of statistics named for Richard von Mises who developed their asymptotic distribution theory in a fundamental paper in 1947. V-statistics are closely related to U-statistics (U for \"unbiased\") introduced by Wassily Hoeffding in 1948. A V-statistic is a statistical function (of a sample) defined by a particular statistical functional of a probability distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic distribution", "Asymptotic normality", "Asymptotic theory", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central Limit Theorem", "Central limit theorem", "Central moment", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Cram\u00e9r\u2013von-Mises criterion", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Differentiable function", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Richard von Mises", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard normal", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taylor series", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Variance", "Vector autoregression", "Wald test", "Wassily Hoeffding", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1016%2F0047-259X(77)90083-5", "http://doi.org/10.1214%2Faoms%2F1177729341", "http://doi.org/10.1214%2Faoms%2F1177730196", "http://doi.org/10.1214%2Faoms%2F1177730385", "http://www.jstor.org/stable/2235637", "http://www.jstor.org/stable/2235734", "http://www.jstor.org/stable/2236587"]}, "Generalized inverse Gaussian distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from February 2012", "Continuous distributions", "Exponential family distributions", "Pages using deprecated image syntax"], "title": "Generalized inverse Gaussian distribution", "method": "Generalized inverse Gaussian distribution", "url": "https://en.wikipedia.org/wiki/Generalized_inverse_Gaussian_distribution", "summary": "In probability theory and statistics, the generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions with probability density function\n\n \n \n \n f\n (\n x\n )\n =\n \n \n \n (\n a\n \n /\n \n b\n \n )\n \n p\n \n /\n \n 2\n \n \n \n \n 2\n \n K\n \n p\n \n \n (\n \n \n a\n b\n \n \n )\n \n \n \n \n x\n \n (\n p\n \u2212\n 1\n )\n \n \n \n e\n \n \u2212\n (\n a\n x\n +\n b\n \n /\n \n x\n )\n \n /\n \n 2\n \n \n ,\n \n x\n >\n 0\n ,\n \n \n {\\displaystyle f(x)={\\frac {(a/b)^{p/2}}{2K_{p}({\\sqrt {ab}})}}x^{(p-1)}e^{-(ax+b/x)/2},\\qquad x>0,}\n where Kp is a modified Bessel function of the second kind, a > 0, b > 0 and p a real parameter. It is used extensively in geostatistics, statistical linguistics, finance, etc. This distribution was first proposed by \u00c9tienne Halphen. \nIt was rediscovered and popularised by Ole Barndorff-Nielsen, who called it the generalized inverse Gaussian distribution. It is also known as the Sichel distribution, after Herbert Sichel. Its statistical properties are discussed in Bent J\u00f8rgensen's lecture notes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/88/GIG_distribution_pdf.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Georges Henri Halphen", "Geostatistics", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Herbert Sichel", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Infinite divisibility (probability)", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "John Wiley & Sons", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mathematical Reviews", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Modified Bessel function", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normal variance-mean mixture", "Ole Barndorff-Nielsen", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0648107", "http://www.ams.org/mathscinet-getitem?mr=1299979", "http://doi.org/10.1061%2F(ASCE)1084-0699(1999)4:3(189)"]}, "Errors-in-variables models": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from November 2015", "Regression models"], "title": "Errors-in-variables models", "method": "Errors-in-variables models", "url": "https://en.wikipedia.org/wiki/Errors-in-variables_models", "summary": "In statistics, errors-in-variables models or measurement error models are regression models that account for measurement errors in the independent variables. In contrast, standard regression models assume that those regressors have been measured exactly, or observed without error; as such, those models account only for errors in the dependent variables, or responses.\n\nIn the case when some regressors have been measured with errors, estimation based on the standard assumption leads to inconsistent estimates, meaning that the parameter estimates do not tend to the true values even in very large samples. For simple linear regression the effect is an underestimate of the coefficient, known as the attenuation bias. In non-linear models the direction of the bias is likely to be more complicated.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3b/Visualization_of_errors-in-variables_linear_regression.png"], "links": ["Attenuation bias", "Bayesian linear regression", "Bayesian multivariate linear regression", "Berkson error model", "Biometrika", "Characteristic function (probability theory)", "Consistent estimator", "Continuous and discrete variables", "Cumulant", "Data collection", "Data set", "Deconvolution", "Deming regression", "Dependent variables", "Digital object identifier", "Discrete choice", "Dummy variable (statistics)", "Econometric Theory", "Econometrica", "Edgeworth series", "Errors and residuals in statistics", "Fixed effects model", "Fourier transform", "Function (mathematics)", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Generalized method of moments", "Goodness of fit", "Hadamard product (matrices)", "Heteroscedasticity", "Identifiability", "Identifiability condition", "Identifiable", "Importance sampling", "Independence (probability theory)", "Independent variables", "Instrumental variables", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jan Kmenta", "Jerry Hausman", "Journal of Econometrics", "Journal of Economic Perspectives", "Journal of Multivariate Analysis", "Kernel (statistics)", "Latent variable", "Latent variable model", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear model", "Linear regression", "Local regression", "Logistic regression", "Mark Thoma", "Maximum likelihood", "Mean and predicted response", "Measurement errors", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "NLLS", "Nadaraya\u2013Watson estimator", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Nuisance parameter", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal regression", "Parameter", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Proceedings of the Royal Irish Academy", "Proxy (statistics)", "Quantile regression", "Random effects model", "Regression analysis", "Regression dilution", "Regression model", "Regression model validation", "Regularized least squares", "Reliability (statistics)", "Review of Economics and Statistics", "Robust regression", "Scalar (mathematics)", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Standard normal", "Statistical unit", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Type I and type II errors", "Weighted least squares", "YouTube"], "references": ["http://escholarship.bc.edu/cgi/viewcontent.cgi?article=1433&context=econ_papers", "http://doi.org/10.1006%2Fjmva.1998.1741", "http://doi.org/10.1016%2F0304-4076(80)90032-9", "http://doi.org/10.1016%2F0304-4076(95)01789-5", "http://doi.org/10.1016%2FS0304-4076(02)00120-3", "http://doi.org/10.1016%2Fj.jspi.2007.05.048", "http://doi.org/10.1017%2FS0266466604206028", "http://doi.org/10.1017%2Fs0266466602183101", "http://doi.org/10.1093%2Fbiomet%2F78.3.451", "http://doi.org/10.1111%2Fb.9781405106764.2003.00013.x", "http://doi.org/10.1111%2Fj.1468-0262.2004.00477.x", "http://doi.org/10.1146%2Fannurev-economics-080315-015058", "http://doi.org/10.1162%2F003465301753237704", "http://doi.org/10.1257%2Fjep.15.4.57", "http://doi.org/10.2307%2F1907835", "http://doi.org/10.2307%2F1913020", "http://doi.org/10.2307%2F1914166", "http://www.jstor.org/stable/1907835", "http://www.jstor.org/stable/1913020", "http://www.jstor.org/stable/1914166", "http://www.jstor.org/stable/20488436", "http://www.jstor.org/stable/2337015", "http://www.jstor.org/stable/2696516", "http://www.jstor.org/stable/3211757", "http://www.jstor.org/stable/3533649", "http://www.jstor.org/stable/3598849", "http://www.jstor.org/stable/4615738", "http://mathsdemo.cf.ac.uk/maths/resources/Gillard_Tech_Report.pdf", "https://books.google.com/books?id=9kBx5CPZCqkC&pg=PA41", "https://books.google.com/books?id=Bxq7AAAAIAAJ&pg=PA346", "https://books.google.com/books?id=JJkWAQAAMAAJ", "https://books.google.com/books?id=Nalc0DkAJRYC&pg=PA1", "https://books.google.com/books?id=Nalc0DkAJRYC&pg=PA184", "https://books.google.com/books?id=Nalc0DkAJRYC&pg=PA2", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA7", "https://books.google.com/books?id=UXucAQAAQBAJ&pg=PA300", "https://books.google.com/books?id=xs55E7FsMHMC&pg=PA162", "https://www.youtube.com/watch?v=brTmzHE9Gvw&index=11&list=PLD15D38DC7AA3B737&t=22m52s", "https://pure.uvt.nl/ws/files/5280778/BPA5621179.pdf", "https://ideas.repec.org/a/anr/reveco/v8y2016p341-377.html", "https://ideas.repec.org/p/ifs/cemmap/41-12.html"]}, "Game of chance": {"categories": ["Game terminology", "Games of chance"], "title": "Game of chance", "method": "Game of chance", "url": "https://en.wikipedia.org/wiki/Game_of_chance", "summary": "A game of chance is a game whose outcome is strongly influenced by some randomizing device, and upon which contestants may choose to wager money or anything of monetary value. Common devices used include dice, spinning tops, playing cards, roulette wheels, or numbered balls drawn from a container. A game of chance may have some skill element to it, however, chance generally plays a greater role in determining the outcome than skill. A game of skill, on the other hand, also may have elements of chance, but with skill playing a greater role in determining the outcome.\nAny game of chance that involves anything of monetary value is gambling.\nGambling is known in nearly all human societies, even though many have passed laws restricting it. Early people used the knucklebones of sheep as dice. Some people develop a psychological addiction to gambling, and will risk even food and shelter to continue.\nSome games of chance may also involve a certain degree of skill. This is especially true where the player or players have decisions to make based upon previous or incomplete knowledge, such as blackjack. In other games like roulette and punto banco (baccarat) the player may only choose the amount of bet and the thing he/she wants to bet on; the rest is up to chance, therefore these games are still considered games of chance with small amount of skills required. The distinction between 'chance' and 'skill' is relevant because in some countries chance games are illegal or at least regulated, but skill games are not.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/0/06/Playing_roulette%2C_Las_Vegas%2C_Nevada_%2874663%29.jpg", "https://upload.wikimedia.org/wikipedia/commons/e/ec/Wiktionary-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Advance-deposit wagering", "Advantage gambling", "Asian handicap", "Baccarat (card game)", "Betting on horse racing", "Betting strategy", "Big Six wheel", "Bingo (United Kingdom)", "Blackjack", "Bola tangkas", "Card counting", "Cardroom", "Casino", "Casino game", "Craps", "Crimp (gambling)", "Dice", "Dice control", "Double or nothing", "Due Column betting", "Edmund Bergler", "Even money", "Faro (card game)", "Gambler's ruin", "Gambling", "Gambling mathematics", "Game", "Game classification", "Game of skill", "Gaming law", "Guessing game", "Handicapping", "High roller", "Keno", "Knucklebones", "Labouch\u00e8re system", "List of bets", "List of casinos", "List of types of games", "Lottery", "Lottery betting", "Ludomania", "Mahjong", "Martingale (betting system)", "Mathematics of bookmaking", "Medal game", "Mini-Baccarat", "Monty Hall problem", "Natural (gambling)", "Online casino", "Pachinko", "Pai gow", "Pai gow poker", "Party game", "Playing card", "Poker", "Poker probability", "Problem gambling", "Progressive jackpot", "Racino", "Randomness", "Riverboat casino", "Role-playing game", "Roulette", "Rummy", "Russian roulette", "Scratchcard", "Sheep", "Shill", "Sic bo", "Skill", "Slot machine", "Spinning top", "Sport", "Sports betting", "Stochastic process", "Strategy game", "Street game", "Table game", "Table limit", "Tabletop game", "Trente et Quarante", "Video game", "Video poker"], "references": ["http://casinoobserver.com/baccarat-strategy.htm", "http://www.hopital-marmottan.fr/articles/jeupatho.php", "https://www.nytimes.com/2012/08/25/opinion/poker-an-american-pastime-and-a-game-of-skill.html", "https://www.nytimes.com/2016/08/04/sports/new-york-fantasy-sports-law-opens-door-for-more-gambling.html", "https://www.setthings.com/en/gambling-and-chance/"]}, "GenStat": {"categories": ["All articles lacking reliable references", "All articles with a promotional tone", "All stub articles", "Articles lacking reliable references from November 2012", "Articles with a promotional tone from November 2016", "Articles with multiple maintenance issues", "Biostatistics", "Fortran software", "Pages using Infobox software with unknown parameters", "Statistical software", "Wikipedia articles with possible conflicts of interest from November 2016", "Windows-only software", "Windows software stubs"], "title": "Genstat", "method": "GenStat", "url": "https://en.wikipedia.org/wiki/Genstat", "summary": "Genstat (General Statistics) is a statistical software package with data analysis capabilities, particularly in the field of agriculture.Since 1968, it has been developed by many scientific experts in Rothamsted Research, and has a user-friendly interface, professional modular design, excellent linear mixed models and graphic functions. Leading Genstat\u2019s continued development and distribution is VSN International (VSNi), which is owned by The Numerical Algorithms Group and Rothamsted Research.\nGenstat is used in a number of research areas, including plant science, forestry, animal science, and medicine, and is recognized by several world-class universities and enterprises.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f5/Genstat_interface.gif", "https://upload.wikimedia.org/wikipedia/commons/4/41/Statistical_methods_in_Genstat.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Unbalanced_scales.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ee/Windows_logo_%E2%80%93_2012_%28dark_blue%29.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ADMB", "ANOVA", "ASReml", "Agriculture", "Analyse-it", "Animal science", "BMDP", "BV4.1 (software)", "Biology", "Box plot", "CSPro", "Chi-squared test", "Classification trees", "Cluster analysis", "Cluster sampling", "Commercial software", "Comparison of statistical packages", "Correspondence analysis", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "Digital object identifier", "Discriminant analysis (in marketing)", "EViews", "Ecology", "Engineering", "Epi Info", "Factor analysis", "Factorial experiment", "Finance", "Food science", "Forestry", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "Generalized additive model", "Generalized linear mixed model", "Generalized linear model", "Genetics", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "Hierarchical generalized linear model", "Histogram", "Industry", "Irregular grid", "JASP", "JMP (statistical software)", "JMulTi", "John Nelder", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Line graph of a hypergraph", "List of statistical packages", "Logistic regression", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "Mathematics", "MedCalc", "Medicine", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Mixed model", "Modular design", "Multivariate analysis of variance", "NCSS (statistical software)", "Natural environment", "Nonparametric statistics", "Numerical Algorithms Group", "One-way analysis of variance", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Partial least squares regression", "Pharmaceutical drug", "Plant science", "Polar plot", "Principal component analysis", "Principal coordinates analysis", "Probability distribution", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Regression analysis", "Regular grid", "Reml", "Revolution Analytics", "Rothamsted Research", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "Scatter plot", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "Six Sigma", "SmartPLS", "Software", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistical hypothesis testing", "Statistical package", "Statistics", "StatsDirect", "Stratified sampling", "Student's t-test", "TSP (econometrics software)", "The Unscrambler", "Time series", "Two-way analysis of variance", "UNISTAT", "Variogram", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.agronomix.com/Corporate/GenStat.aspx", "http://doi.org/10.1002%2Fwics.32", "http://www2.warwick.ac.uk/services/ldc/researchers/opportunities/development_support/mathstats/additional_resources/software_list/genstat/", "http://www.vsni.co.uk/", "http://www.vsni.co.uk/software/Genstat", "http://www.vsni.co.uk/software/Genstat/", "https://genstat.kb.vsni.co.uk/article-categories/whats_new/"]}, "Barnes interpolation": {"categories": ["Interpolation", "Spatial data analysis"], "title": "Barnes interpolation", "method": "Barnes interpolation", "url": "https://en.wikipedia.org/wiki/Barnes_interpolation", "summary": "Barnes interpolation, named after Stanley L. Barnes, is the interpolation of unstructured data points from a set of measurements of an unknown function in two dimensions into an analytic function of two variables. An example of a situation where the Barnes scheme is important is in weather forecasting where measurements are made wherever monitoring stations may be located, the positions of which are constrained by topography. Such interpolation is essential in data visualisation, e.g. in the construction of contour plots or other representations of analytic surfaces.\n\n", "images": [], "links": ["Analytic function", "Bibcode", "Cluster analysis", "Complete spatial randomness", "Contour plot", "Digital object identifier", "Distance weighting", "Gaussian function", "Interpolation", "Spectral response", "Synoptic chart", "Topography", "Weather forecasting"], "references": ["http://www.bom.gov.au/bmrc/mdev/expt/rainanal/rainanal.shtml", "http://ams.allenpress.com/perlserv/?request=get-abstract&doi=10.1175/1520-0450(1964)003%3C0396:ATFMDI%3E2.0.CO%3B2", "http://adsabs.harvard.edu/abs/1964JApMe...3..396B", "http://doi.org/10.1175%2F1520-0450(1964)003%3C0396:ATFMDI%3E2.0.CO;2", "https://archive.is/20120722172541/http://www.bom.gov.au/bmrc/mdev/expt/rainanal/rainanal.shtml"]}, "Random compact set": {"categories": ["Random dynamical systems", "Statistical randomness"], "title": "Random compact set", "method": "Random compact set", "url": "https://en.wikipedia.org/wiki/Random_compact_set", "summary": "In mathematics, a random compact set is essentially a compact set-valued random variable. Random compact sets are useful in the study of attractors for random dynamical systems.", "images": [], "links": ["Almost surely", "Borel sigma algebra", "Compact space", "Complete space", "Georges Matheron", "I.i.d.", "Mathematics", "Measurable function", "Metric space", "Probability space", "Random closed set", "Random dynamical system", "Random variable", "Separable space", "Sigma algebra"], "references": []}, "Least-angle regression": {"categories": ["All articles needing expert attention", "All articles that are too technical", "All articles with unsourced statements", "Articles needing additional categories from April 2018", "Articles needing expert attention from April 2018", "Articles with unsourced statements from August 2009", "Regression variable selection", "Wikipedia articles that are too technical from April 2018"], "title": "Least-angle regression", "method": "Least-angle regression", "url": "https://en.wikipedia.org/wiki/Least-angle_regression", "summary": "In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani.Suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates. Then the LARS algorithm provides a means of producing an estimate of which variables to include, as well as their coefficients.\nInstead of giving a vector result, the LARS solution consists of a curve denoting the solution for each value of the L1 norm of the parameter vector. The algorithm is similar to forward stepwise regression, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one's correlations with the residual.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b7/Larsdiabetes.png", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/6/6c/Wiki_letter_w.svg"], "links": ["ArXiv", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bradley Efron", "Cross-validation (statistics)", "Digital object identifier", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "High-dimensional statistics", "High dimensional data", "Isotonic regression", "Iteratively reweighted least squares", "L1 norm", "Lasso (statistics)", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Mathematical Reviews", "Mean and predicted response", "Mixed logit", "Mixed model", "Model selection", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Python (language)", "Quantile regression", "R (language)", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Robert Tibshirani", "Robust regression", "SAS (software)", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistics", "Stepwise regression", "Studentized residual", "Tikhonov regularization", "Total least squares", "Trevor Hastie", "Weighted least squares"], "references": ["http://statweb.stanford.edu/~imj/WEBLIST/2004/LarsAnnStat04.pdf", "http://statweb.stanford.edu/~tibs/ftp/lars.pdf", "http://statweb.stanford.edu/~tibs/lasso/simple.html", "http://www.ams.org/mathscinet-getitem?mr=2060166", "http://arxiv.org/abs/math/0406456", "http://doi.org/10.1214%2F009053604000000067", "http://scikit-learn.org/stable/modules/linear_model.html#least-angle-regression", "https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_glmselect_a0000000242.htm", "https://cran.r-project.org/web/packages/lars/index.html"]}, "Ascertainment bias": {"categories": ["All articles lacking reliable references", "Articles lacking reliable references from November 2014", "Bias", "CS1 maint: Multiple names: authors list", "Design of experiments", "Misuse of statistics", "Sampling (statistics)", "Wikipedia articles needing clarification from August 2014"], "title": "Sampling bias", "method": "Ascertainment bias", "url": "https://en.wikipedia.org/wiki/Sampling_bias", "summary": "In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population are less likely to be included than others. It results in a biased sample, a non-random sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling.\nMedical sources sometimes refer to sampling bias as ascertainment bias. Ascertainment bias has basically the same definition, but is still sometimes classified as a separate type of bias.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c9/Acid2compliancebyusage.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/7/70/Ascertainment_bias.png", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["Academic bias", "Accident (fallacy)", "Acid2", "Acquiescence bias", "Alf Landon", "Ambiguity", "Anchoring", "Anecdotal evidence", "Animistic fallacy", "ArXiv", "Argument from analogy", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "Autosomal recessive", "Base rate fallacy", "Begging the question", "Belief bias", "Bell System", "Berkson's fallacy", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Cave painting", "Censored regression model", "Ceremonial burial", "Cherry picking", "Cherry picking (fallacy)", "Chicago Tribune", "Choice-supportive bias", "Cholecystitis", "Circular analysis", "Circular reasoning", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Comorbidity", "Complex question", "Confirmation bias", "Confounding", "Congruence bias", "Conjunction fallacy", "Continuum fallacy", "Converse accident", "Correlation does not imply causation", "Correlative-based fallacies", "Cultural bias", "Debiasing", "Demarcation Problem", "Denying the correlative", "Dewey Defeats Truman", "Digital object identifier", "Distinction bias", "Double-barreled question", "Double counting (fallacy)", "Dunning\u2013Kruger effect", "Dyslexia", "Ecological fallacy", "Egocentric bias", "Emotional bias", "Equivocation", "External validity", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Fallacies of illicit transference", "Fallacy", "Fallacy of accent", "Fallacy of composition", "Fallacy of division", "Fallacy of the single cause", "False attribution", "False dilemma", "False equivalence", "False precision", "Faulty generalization", "File drawer problem", "Fold change", "Forecast bias", "Franklin Roosevelt", "Friendship paradox", "Fundamental attribution error", "Funding bias", "Furtive fallacy", "Gallup poll", "Gambler's fallacy", "George Gallup", "Halo effect", "Harry S. Truman", "Healthy user bias", "Heterozygote", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "How to Lie with Statistics", "Human migration", "Impact bias", "Impression management", "In-group favoritism", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "Intellectual disability", "Internal validity", "International Standard Book Number", "Internet Explorer", "Inverse gambler's fallacy", "Lead time bias", "Leading question", "Length time bias", "Lies, damned lies, and statistics", "List of cognitive biases", "List of fallacies", "List of memory biases", "Literary Digest", "Loaded language", "Loaded question", "Loki's Wager", "Malmquist bias", "McNamara fallacy", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mendelian inheritance", "Mere-exposure effect", "Midden", "Misleading graph", "Misuse of statistics", "Moving the goalposts", "National Center for Health Statistics", "Negativity bias", "Net bias", "Nirvana fallacy", "No true Scotsman", "Non-response bias", "Normalcy bias", "Omission bias", "Omitted-variable bias", "Online and phone-in polls", "Optimism bias", "Outcome bias", "Overmatching", "Overton window", "Overwhelming exception", "Parameter", "Participation bias", "Phone survey", "Post hoc ergo propter hoc", "Precision bias", "Prehistory", "President-elect", "Pro-innovation bias", "PubMed Identifier", "Publication bias", "Questionable cause", "Quoting out of context", "Recall bias", "Regression fallacy", "Reification (fallacy)", "Reporting bias", "Research ethics", "Response bias", "Restraint bias", "Sampling (statistics)", "Sampling probability", "Scientific fraud", "Secundum quid", "Selection bias", "Self-selection bias", "Self-serving bias", "Slippery slope", "Slothful induction", "Social Register", "Social comparison bias", "Social desirability bias", "Society for Academic Emergency Medicine", "Sorites paradox", "Spectrum bias", "Statistic", "Statistical population", "Statistics", "Status quo bias", "Suppressed correlative", "Survivorship bias", "Syntactic ambiguity", "Systematic error", "Systemic bias", "Telephone directory", "Texas sharpshooter fallacy", "Time-saving bias", "Trait ascription bias", "Truncated regression model", "United States news media and the Vietnam War", "United States presidential election, 1936", "United States presidential election, 1948", "Vagueness", "Verification bias", "Von Restorff effect", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://www.tdx.cat/bitstream/handle/10803/7140/tars.pdf?sequence=1", "http://www.medilexicon.com/medicaldictionary.php?t=10080", "http://www.medilexicon.com/medicaldictionary.php?t=10087", "http://medical-dictionary.thefreedictionary.com/Sample+bias", "http://medical.webends.com/kw/Selection%20Bias", "http://www.cs.nyu.edu/~mohri/postscript/bias.pdf", "http://www.cs.nyu.edu/~mohri/pub/nsmooth.pdf", "http://www.uh.edu/engines/epi1199.htm", "http://web.utk.edu/~orme00/articles/Cuddeback_et_al.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/9504213", "http://arxiv.org/abs/0805.2775", "http://doi.org/10.1007%2F978-3-540-87987-9_8", "http://doi.org/10.1016%2FS0145-2134(97)00131-2", "http://doi.org/10.1016%2Fj.tcs.2013.09.027", "http://doi.org/10.1300%2FJ079v30n03_02", "http://doi.org/10.2307%2F2095230", "http://elearning.saem.org/sites/default/files/issuu/libraries/Panacek_Error_And_Bias_In_Clinical_Research_syllabus_1.pdf", "https://books.google.com/books?id=EBq63uyt87QC", "https://books.google.com/books?id=WY5qAAAAMAAJ", "https://books.google.com/books?id=f0IDHvLiWqUC", "https://www.w3schools.com/browsers/browsers_stats.asp", "https://www.cdc.gov/nchs/about/otheract/minority/minority.htm"]}, "Population dynamics": {"categories": ["All articles lacking in-text citations", "All articles with dead external links", "Articles lacking in-text citations from July 2012", "Articles with dead external links from December 2017", "Articles with permanently dead external links", "Environmental controversies", "Fisheries science", "Human overpopulation", "Population ecology", "Population models", "Social dynamics", "Wikipedia articles needing page number citations from November 2017"], "title": "Population dynamics", "method": "Population dynamics", "url": "https://en.wikipedia.org/wiki/Population_dynamics", "summary": "Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them (such as birth and death rates, and by immigration and emigration). Example scenarios are ageing populations, population growth, or population decline.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3f/Jellyfish_population_trends_by_LME.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/10/Logical_deterministic_individual-based_cellular_automata_model_of_interspecific_competition_for_a_single_limited_resource.gif", "https://upload.wikimedia.org/wikipedia/commons/b/bf/Logical_deterministic_individual-based_cellular_automata_model_of_single_species_population_growth.gif", "https://upload.wikimedia.org/wikipedia/commons/7/70/Planetary_boundaries.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["7 Billion Actions", "A Modest Proposal", "Ageing population", "Allee effect", "An Essay on the Principle of Population", "Andrey Korotayev", "Arditi\u2013Ginzburg equations", "Benjamin Gompertz", "Biocapacity", "Biocenosis", "Biodiversity loss", "Biodiversity threats", "Biological organisation", "Biological system", "Biology", "Biome", "Biomolecular complex", "Biomolecule", "Biosphere", "Birth control", "Birth rate", "Bloomberg Innovation Index", "Carrying capacity", "Cell (biology)", "Classic Maya collapse", "Cleaner production", "Climate change", "Climate change mitigation", "Climate engineering", "Computer game", "Computer simulation", "Control theory", "Death rate", "Deep ecology", "Defaunation", "Deforestation", "Delayed density dependence", "Demographic economics", "Demographics", "Demography", "Derivative", "Desalination", "Desertification", "Deterministic chaos", "Digital object identifier", "Dispatchable generation", "Divorce demography", "Dynamical systems", "Earth's energy budget", "Ecocide", "Ecological engineering", "Ecosystem", "Education Index", "Emigration", "Environment (biophysical)", "Environmental degradation", "Environmental engineering", "Environmental impact assessment", "Environmental impact of agriculture", "Environmental impact of aviation", "Environmental impact of biodiesel", "Environmental impact of cleaning agents", "Environmental impact of cocoa production", "Environmental impact of concrete", "Environmental impact of electricity generation", "Environmental impact of fishing", "Environmental impact of irrigation", "Environmental impact of meat production", "Environmental impact of mining", "Environmental impact of nanotechnology", "Environmental impact of nuclear power", "Environmental impact of paint", "Environmental impact of paper", "Environmental impact of pesticides", "Environmental impact of pharmaceuticals and personal care products", "Environmental impact of plastics", "Environmental impact of reservoirs", "Environmental impact of roads", "Environmental impact of shipping", "Environmental impact of the coal industry", "Environmental impact of the energy industry", "Environmental impact of the oil shale industry", "Environmental impact of the petroleum industry", "Environmental impact of tourism", "Environmental impact of transport", "Environmental impact of war", "Environmental impact of wind power", "Environmental issue", "Environmental issues with coral reefs", "Environmental mitigation", "Erosion", "Evolutionary game theory", "F.J. Richards", "Family planning", "Fertility and intelligence", "Fisheries", "Food security", "Freshwater cycle", "Genetic pollution", "Global warming", "Green Revolution", "Green belt", "Habitat destruction", "Health", "Holocene extinction", "Homeostasis", "How Much Land Does a Man Need?", "Human Development Index", "Human Poverty Index", "Human impact on the environment", "Human impact on the nitrogen cycle", "Human migration", "Human overpopulation", "Human population growth", "Human population planning", "I = PAT", "Immigration", "Indirect land use change impacts of biofuels", "Industrial ecology", "Industrialisation", "Industrialization", "Innovation Union Scoreboard", "International Conference on Population and Development", "International Innovation Index", "International Standard Book Number", "Jellyfish", "John Maynard Smith", "Land degradation", "Land reclamation", "Land surface effects on climate", "Land use", "Life sciences", "Linguistic diversity index", "List of African countries by population", "List of Arab countries by population", "List of Asian countries by population", "List of Caribbean countries by population", "List of Eurasian countries by population", "List of European Union member states by population", "List of European countries by population", "List of Latin American countries by population", "List of Middle Eastern countries by population", "List of North American countries by population", "List of Oceanian countries by population", "List of South American countries by population", "List of cities proper by population", "List of continents by population", "List of countries and dependencies by population", "List of countries and dependencies by population density", "List of countries by HIV/AIDS adult prevalence rate", "List of countries by Human Development Index", "List of countries by Official Development Assistance received", "List of countries by Sen social welfare function", "List of countries by age at first marriage", "List of countries by age structure", "List of countries by body mass index", "List of countries by dependency ratio", "List of countries by employment rate", "List of countries by future population (United Nations, medium fertility variant)", "List of countries by health expenditure covered by government", "List of countries by imports", "List of countries by income equality", "List of countries by inequality-adjusted HDI", "List of countries by infant and under-five mortality rates", "List of countries by irrigated land area", "List of countries by labour force", "List of countries by life expectancy", "List of countries by literacy rate", "List of countries by maternal mortality rate", "List of countries by median age", "List of countries by natural increase", "List of countries by net migration rate", "List of countries by number of households", "List of countries by past and future population", "List of countries by past life expectancy", "List of countries by past population (United Nations, estimates)", "List of countries by percentage of population living in poverty", "List of countries by percentage of population suffering from undernourishment", "List of countries by population (United Nations)", "List of countries by population growth rate", "List of countries by population in 1000", "List of countries by population in 1500", "List of countries by population in 1600", "List of countries by population in 1700", "List of countries by population in 1800", "List of countries by population in 1900", "List of countries by population in 1907", "List of countries by population in 1939", "List of countries by population in 1989", "List of countries by population in 2000", "List of countries by population in 2005", "List of countries by population in 2010", "List of countries by public sector", "List of countries by real population density based on food growing capacity", "List of countries by sex ratio", "List of countries by student skills", "List of countries by suicide rate", "List of countries by tertiary education attainment", "List of countries by the number of billionaires", "List of countries by total health expenditure per capita", "List of countries by unemployment rate", "List of countries by urban population", "List of countries by women's average years in school", "List of countries in the Americas by population", "List of countries ranked by ethnic and cultural diversity level", "List of development aid country donors", "List of environmental issues", "List of international rankings", "List of islands by population", "List of member states of the Commonwealth of Nations by population", "List of metropolitan areas by population", "List of national capitals by population", "List of population milestones by country", "List of sovereign states and dependencies by total fertility rate", "List of sovereign states and dependent territories by birth rate", "List of sovereign states and dependent territories by immigrant population", "List of sovereign states and dependent territories by mortality rate", "List of states by population in 1 CE", "List of top international rankings by country", "List of urban areas by population", "Lists by country", "Lists of countries and territories", "Logistic function", "Logistics", "Lotka-Volterra equations", "Lotka\u2013Volterra equation", "Ludwig von Bertalanffy", "MIMO", "MMORPG", "Macromolecule", "Malthus", "Malthusian catastrophe", "Malthusian growth model", "Manufacturing", "Mathematical biology", "Mathematical modelling in epidemiology", "Matrix population models", "Maximum sustainable yield", "Megacity", "Megalopolis", "Millionaire", "Minimum viable population", "Mitigation banking", "Mortality rate", "Nature reserve", "Nicholson\u2013Bailey model", "Observations Concerning the Increase of Mankind, Peopling of Countries, etc.", "Ocean acidification", "Off-roading", "One-child policy", "Operating Manual for Spaceship Earth", "Optimum population", "Organ (anatomy)", "Organelle", "Organic farming", "Organism", "Oscillation", "Overconsumption", "Overdrafting", "Overexploitation", "Overfishing", "Overgrazing", "Overpopulation", "Overshoot (population)", "Ozone depletion", "Particulates", "Pest insect population dynamics", "Peter Turchin", "Phosphorus cycle", "Physiological density", "Pierre Fran\u00e7ois Verhulst", "Planetary boundaries", "Pollution", "Population", "Population Action International", "Population Connection", "Population Control: Real Costs, Illusory Benefits", "Population Matters", "Population Research Institute", "Population and Development Review", "Population and Environment", "Population and housing censuses by country", "Population biology", "Population cycle", "Population decline", "Population density", "Population dynamics of fisheries", "Population ecology", "Population ethics", "Population genetics", "Population growth", "Population growth rate", "Population model", "Population modeling", "Population momentum", "Population pyramid", "Population statistics", "Programme for the International Assessment of Adult Competencies", "Progress in International Reading Literacy Study", "Projections of population growth", "PubMed Central", "PubMed Identifier", "Quarry", "R/K selection theory", "Reforestation", "Refuge (ecology)", "Reproductive rights", "Resource depletion", "Restoration ecology", "Ricker model", "Runaway climate change", "Scarcity", "Scenarios", "Sigmoid curve", "SimCity (1989 video game)", "Simon Hopkins", "Single-input single-output system", "Social and environmental impact of palm oil", "Societal collapse", "Starvation", "Stockpiling antiviral medications for pandemic influenza", "Sustainable consumption", "Sustainable development", "System dynamics", "The Limits to Growth", "The Population Bomb", "The Skeptical Environmentalist", "The Ultimate Resource", "Tissue (biology)", "Trends in International Mathematics and Science Study", "Two-child policy", "Ultima Online", "United Nations Population Fund", "Urban reforestation", "Urban sprawl", "Urbanization", "Urbanization by country", "Voluntary Human Extinction Movement", "Waste", "Waste minimisation", "Water degradation", "Water scarcity", "Water supply network", "Wildlife management", "World3", "World Intellectual Property Indicators", "World Population Day", "World Population Foundation", "World energy consumption", "World energy resources", "World population", "World population milestones", "Zero population growth"], "references": ["http://www.thomas-brey.de/science/virtualhandbook", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3758828", "http://www.ncbi.nlm.nih.gov/pubmed/23949368", "http://www.ncbi.nlm.nih.gov/pubmed/27755756", "http://doi.org/10.1007%2Fs10750-012-1039-7", "http://doi.org/10.1007%2Fs10867-013-9329-5", "http://doi.org/10.1016%2Fj.apm.2012.07.030", "http://doi.org/10.1093%2Ficesjms%2Ffss192", "http://doi.org/10.1603%2F0046-225X-34.4.938", "http://doi.org/10.1890%2F15-1295", "https://psmag.com/sometimes-even-bad-models-make-better-decisions-than-people-4956bade3990#.qv2oz7gd2", "https://mpra.ub.uni-muenchen.de/6557/"]}, "Pareto analysis": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from July 2010", "Articles with unsourced statements from July 2009", "Problem solving methods", "Quality", "Statistical charts and diagrams", "Vilfredo Pareto"], "title": "Pareto analysis", "method": "Pareto analysis", "url": "https://en.wikipedia.org/wiki/Pareto_analysis", "summary": "Pareto analysis is a formal technique useful where many possible courses of action are competing for attention. In essence, the problem-solver estimates the benefit delivered by each action, then selects a number of the most effective actions that deliver a total benefit reasonably close to the maximal possible one.Pareto analysis is a creative way of looking at causes of problems because it helps stimulate thinking and organize thoughts. However, it can be limited by its exclusion of possibly important problems which may be small initially, but which grow with time. It should be combined with other analytical tools such as failure mode and effects analysis and fault tree analysis for example.This technique helps to identify the top portion of causes that need to be addressed to resolve the majority of problems. Once the predominant causes are identified, then tools like the Ishikawa diagram or Fish-bone Analysis can be used to identify the root causes of the problems. While it is common to refer to pareto as \"80/20\" rule, under the assumption that, in all situations, 20% of causes determine 80% of problems, this ratio is merely a convenient rule of thumb and is not nor should it be considered an immutable law of nature.\nThe application of the Pareto analysis in risk management allows management to focus on those risks that have the most impact on the project.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6a/Pareto_analysis.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["80/20 rule", "Failure mode and effects analysis", "Fault tree analysis", "Ishikawa diagram", "Pareto chart", "Pareto distribution", "Pareto interpolation"], "references": ["http://www.pmhut.com/project-risk-and-risk-management", "http://erc.msh.org/quality/pstools/pspareto.cfm", "https://web.archive.org/web/20120208180732/http://erc.msh.org/quality/pstools/pspareto.cfm"]}, "Randomized decision rule": {"categories": ["Decision theory", "Statistical inference"], "title": "Randomised decision rule", "method": "Randomized decision rule", "url": "https://en.wikipedia.org/wiki/Randomised_decision_rule", "summary": "In statistical decision theory, a randomised decision rule or mixed decision rule is a decision rule that associates probabilities with deterministic decision rules. In finite decision problems, randomised decision rules define a risk set which is the convex hull of the risk points of the nonrandomised decision rules.\nAs nonrandomised alternatives always exist to randomised Bayes rules, randomisation is not needed in Bayesian statistics, although frequentist statistical theory sometimes requires the use of randomised rules to satisfy optimality conditions such as minimax, most notably when deriving confidence intervals and hypothesis tests about discrete probability distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/92/Riskset_admissible_smaller.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e1/Riskset_bayes2_smaller.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a8/Riskset_bayes3_smaller.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Riskset_bayes_smaller.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c0/Riskset_minimax2.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1a/Riskset_minimax3.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7f/Riskset_minimax_smaller.svg"], "links": ["Admissible decision rule", "Bayes risk", "Bayesian statistics", "Bernoulli distribution", "Binomial proportion confidence interval", "Confidence intervals", "Continuous uniform distribution", "Convex hull", "Decision rule", "Decision theory", "Digital object identifier", "Discrete probability distribution", "Egon Pearson", "Experiment (probability theory)", "Frequentist statistics", "Hypothesis testing", "International Standard Book Number", "Likelihood ratio test", "Linear programming", "Loss function", "Minimax", "Mixed strategy", "Neyman-Pearson lemma", "Null hypothesis", "Probability distribution", "Randomness test", "Risk function"], "references": ["http://users.stat.ufl.edu/~aa/articles/agresti_gottard_2005.pdf", "http://doi.org/10.1214%2F088342305000000403"]}, "Multiple-try Metropolis": {"categories": ["Markov chain Monte Carlo", "Monte Carlo methods"], "title": "Multiple-try Metropolis", "method": "Multiple-try Metropolis", "url": "https://en.wikipedia.org/wiki/Multiple-try_Metropolis", "summary": "Multiple-try Metropolis (MTM) is a sampling method that is a modified form of the Metropolis-Hastings method, first presented by Liu, Liang, and Wong in 2000.\nIt is designed to help the sampling trajectory converge faster,\nby increasing both the step size and the acceptance rate.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["ArXiv", "Chi distribution", "Detailed balance", "Digital object identifier", "International Standard Serial Number", "Markov chain Monte Carlo", "Metropolis-Hastings", "Metropolis\u2013Hastings algorithm", "Multivariate normal distribution", "Probability distribution", "Proposal function", "Sampling method"], "references": ["http://linkinghub.elsevier.com/retrieve/pii/S1051200418300149", "http://www.sciencedirect.com/science/article/pii/S0167715212001514", "http://www.sciencedirect.com/science/article/pii/S0167947313003605", "http://www.sciencedirect.com/science/article/pii/S0304414911002791", "http://arxiv.org/abs/1006.0621", "http://arxiv.org/abs/1011.1170", "http://arxiv.org/abs/1112.4048", "http://arxiv.org/abs/1201.0646", "http://doi.org/10.1007/s00180-013-0429-2", "http://doi.org/10.1007/s11222-006-9009-4", "http://doi.org/10.1007/s11222-011-9301-9", "http://doi.org/10.1016/j.csda.2013.10.007", "http://doi.org/10.1016/j.dsp.2018.01.004", "http://doi.org/10.1016/j.spa.2011.11.004", "http://doi.org/10.1016/j.spl.2012.04.008", "http://www.worldcat.org/issn/0943-4062", "http://www.worldcat.org/issn/0960-3174", "https://link.springer.com/article/10.1007/s00180-013-0429-2", "https://link.springer.com/article/10.1007/s11222-006-9009-4", "https://link.springer.com/article/10.1007/s11222-011-9301-9", "https://www.jstor.org/stable/2669532"]}, "Consensus-based assessment": {"categories": ["Comparison of assessments", "Psychological testing"], "title": "Consensus-based assessment", "method": "Consensus-based assessment", "url": "https://en.wikipedia.org/wiki/Consensus-based_assessment", "summary": "Consensus-based assessment expands on the common practice of consensus decision-making and the theoretical observation that expertise can be closely approximated by large numbers of novices or journeymen. It creates a method for determining measurement standards for very ambiguous domains of knowledge, such as emotional intelligence, politics, religion, values and culture in general. From this perspective, the shared knowledge that forms cultural consensus can be assessed in much the same way as expertise or general intelligence.", "images": [], "links": ["Collective intelligence", "Consensus", "Consensus decision-making", "Consensus democracy", "Consensus theory of truth", "Correlation", "Emotional Intelligence", "Emotional intelligence", "Factor analysis", "General intelligence factor", "Intelligence", "Libertarian socialism", "Likert scale", "Participation (decision making)", "Polder model", "Principal components analysis", "Q methodology", "Rubric (academic)", "Social representations", "Unanimity", "William Stephenson (psychologist)"], "references": ["http://www.axiopole.com/pdf/Managing_collective_intelligence.pdf", "http://www.randomhouse.com/features/wisdomofcrowds/index.html", "http://www.smartmobs.com/"]}, "Environmental statistics": {"categories": ["All stub articles", "Applied statistics", "Environment stubs", "Environmental statistics", "Statistics stubs"], "title": "Environmental statistics", "method": "Environmental statistics", "url": "https://en.wikipedia.org/wiki/Environmental_statistics", "summary": "Environment statistics is the application of statistical methods to environmental science. It covers procedures for dealing with questions concerning both the natural environment in its undisturbed state and the interaction of humanity with the environment. Thus weather, climate, air and water quality are included, as are studies of plant and animal populations.\nThe United Nations Framework for the Development of Environment Statistics (FDES) defines the scope of environment statistics as follows:\nThe scope of environment statistics covers biophysical aspects of the environment and those aspects of the socio-economic system that directly influence and interact with the environment.\nThe scope of environment, social and economic statistics overlap. It is not easy \u2013 or necessary \u2013 to draw a clear line dividing these areas. Social and economic statistics that describe processes or activities with a direct impact on, or direct interaction with, the environment are used widely in environment statistics. They are within the scope of the FDES.\nSources of data for environmental statistics are varied and include: surveys related to human populations and the environment, records from agencies managing environmental resources, maps and images, equipment used to examine the environment, and research studies around the world. A primary component of the data is direct observation, although most environmental statistics use a variety of sources.Environmental statistics covers a number of types of study:\nBaseline studies to document the present state of an environment to provide background in case of unknown changes in the future;\nTargeted studies to describe the likely impact of changes being planned or of accidental occurrences;\nRegular monitoring to attempt to detect changes in the environment.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/3/30/Leaf.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Coordination of Information on the Environment", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environment (biophysical)", "Environmental science", "Environmental studies", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://unstats.un.org/unsd/environment/FDES/FDES-2015-supporting-tools/FDES.pdf"]}, "Variance inflation factor": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from July 2010", "Articles with unsourced statements from July 2010", "Pages with DOIs inactive since 2018", "Regression diagnostics", "Statistical deviation and dispersion", "Statistical ratios"], "title": "Variance inflation factor", "method": "Variance inflation factor", "url": "https://en.wikipedia.org/wiki/Variance_inflation_factor", "summary": "In statistics, the variance inflation factor (VIF) is the ratio of variance in a model with multiple terms, divided by the variance of a model with one term alone. It quantifies the severity of multicollinearity in an ordinary least squares regression analysis. It provides an index that measures how much the variance (the square of the estimate's standard deviation) of an estimated regression coefficient is increased because of collinearity.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Coefficient of determination", "Design matrix", "Digital object identifier", "Errors and residuals in statistics", "International Standard Book Number", "Linear model", "Linear regression", "Multicollinearity", "Ordinary least squares", "Orthogonal", "Python (programming language)", "R (programming language)", "Residual sum of squares", "Root-mean-square deviation", "Schur complement", "Standard deviation", "Standard error (statistics)", "Statistics", "Variance"], "references": ["http://doi.org/10.1080%2F00401706.1970.10488699", "http://doi.org/10.1111%2Fj.2041-210X.2009.00001x", "http://www.statsmodels.org", "https://cran.r-project.org/package=car", "https://cran.r-project.org/package=olsrr"]}, "Freedman\u2013Diaconis rule": {"categories": ["All stub articles", "Infographics", "Rules of thumb", "Statistical charts and diagrams", "Statistics stubs", "Wikipedia articles needing clarification from June 2017"], "title": "Freedman\u2013Diaconis rule", "method": "Freedman\u2013Diaconis rule", "url": "https://en.wikipedia.org/wiki/Freedman%E2%80%93Diaconis_rule", "summary": "In statistics, the Freedman\u2013Diaconis rule can be used to select the width of the bins to be used in a histogram. It is named after David A. Freedman and Persi Diaconis. \nFor a set of empirical measurements sampled from some probability distribution, the Freedman-Diaconis rule is designed to minimize the difference between the area under the empirical probability distribution and the area under the theoretical probability distribution.The general equation for the rule is:\n\n \n \n \n \n Bin width\n \n =\n 2\n \n \n \n \n \n IQR\n \n (\n x\n )\n \n \n \n n\n \n 3\n \n \n \n \n \n \n \n {\\displaystyle {\\text{Bin width}}=2\\,{{\\text{IQR}}(x) \\over {\\sqrt[{3}]{n}}}}\n where \n \n \n \n IQR\n \u2061\n (\n x\n )\n \n \n {\\displaystyle \\operatorname {IQR} (x)}\n is the interquartile range of the data and \n \n \n \n n\n \n \n {\\displaystyle n}\n is the number of observations in the sample \n \n \n \n x\n .\n \n \n {\\displaystyle x.}", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["CiteSeerX", "David A. Freedman", "David Freedman (statistician)", "Digital object identifier", "Histogram", "Integral", "International Standard Serial Number", "Interquartile range", "Persi Diaconis", "Portable Document Format", "Probability distribution", "Statistics"], "references": ["http://robjhyndman.com/papers/sturges.pdf", "http://www.springerlink.com/content/mp364022824748n3/fulltext.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.220", "http://doi.org/10.1002%2Fwics.35", "http://doi.org/10.1007%2FBF01025868", "http://doi.org/10.1051%2Fps:2006001", "http://www.numdam.org/item?id=PS_2006__10__24_0", "http://www.worldcat.org/issn/0178-8051"]}, "Freidlin\u2013Wentzell theorem": {"categories": ["Asymptotic analysis", "Large deviations theory", "Probability theorems", "Statistical theorems", "Stochastic differential equations"], "title": "Freidlin\u2013Wentzell theorem", "method": "Freidlin\u2013Wentzell theorem", "url": "https://en.wikipedia.org/wiki/Freidlin%E2%80%93Wentzell_theorem", "summary": "In mathematics, the Freidlin\u2013Wentzell theorem is a result in the large deviations theory of stochastic processes. Roughly speaking, the Freidlin\u2013Wentzell theorem gives an estimate for the probability that a (scaled-down) sample path of an It\u014d diffusion will stray far from the mean path. This statement is made precise using rate functions. The Freidlin\u2013Wentzell theorem generalizes Schilder's theorem for standard Brownian motion.\n\n", "images": [], "links": ["Alexander D. Wentzell", "Banach space", "Brownian motion", "Closed set", "International Standard Book Number", "It\u014d diffusion", "Large deviations theory", "Lipschitz continuity", "Mark Freidlin", "Mathematical Reviews", "Mathematics", "Open set", "Rate function", "Schilder's theorem", "Sobolev space", "Stochastic differential equation", "Stochastic process", "Supremum norm", "Vector field"], "references": ["https://mathscinet.ams.org/mathscinet-getitem?mr=1619036", "https://mathscinet.ams.org/mathscinet-getitem?mr=1652127"]}, "Coefficient of determination": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2017", "Least squares", "Regression diagnostics", "Statistical ratios", "Wikipedia articles needing page number citations from April 2012"], "title": "Coefficient of determination", "method": "Coefficient of determination", "url": "https://en.wikipedia.org/wiki/Coefficient_of_determination", "summary": "In statistics, the coefficient of determination, denoted R2 or r2 and pronounced \"R squared\", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).\nIt is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.There are several definitions of R2 that are only sometimes equivalent. One class of such cases includes that of simple linear regression where r2 is used instead of R2. When an intercept is included, then r2 is simply the square of the sample correlation coefficient (i.e., r) between the observed outcomes and the observed predictor values. If additional regressors are included, R2 is the square of the coefficient of multiple correlation. In both such cases, the coefficient of determination ranges from 0 to 1.\nThere are cases where the computational definition of R2 can yield negative values, depending on the definition used. This can arise when the predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data. Even if a model-fitting procedure has been used, R2 may still be negative, for example when linear regression is conducted without including an intercept, or when a non-linear function is used to fit the data. In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular criterion. Since the most general definition of the coefficient of determination is also known as the Nash\u2013Sutcliffe model efficiency coefficient, this last notation is preferred in many fields, because denoting a goodness-of-fit indicator that can vary from -\u221e to 1 (i.e., it can yield negative values) with a squared letter is confusing.\nWhen evaluating the goodness-of-fit of simulated (Ypred) vs. measured (Yobs) values, it is not appropriate to base this on the R2 of the linear regression (i.e., Yobs= m\u00b7Ypred + b). The R2 quantifies the degree of any linear correlation between Yobs and Ypred, while for the goodness-of-fit evaluation only one specific linear correlation should be taken into consideration: Yobs = 1\u00b7Ypred + 0 (i.e., the 1:1 line).", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/86/Coefficient_of_Determination.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Okuns_law_quarterly_differences.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e9/Thiel-Sen_estimator.svg"], "links": ["ANOVA", "Bias of an estimator", "Biometrika", "Coefficient of correlation", "Coefficient of multiple correlation", "Coefficient of multiple determination", "Coefficient of variation", "Correlation", "Correlation does not imply causation", "Damodar N. Gujarati", "Degrees of freedom (statistics)", "Dependent variable", "Digital object identifier", "Effect size", "Errors and residuals in statistics", "Explained sum of squares", "Explained variation", "Explanatory variable", "F-test", "Feature selection", "Fraction of variance unexplained", "Generalized least squares", "Goodness of fit", "Granger causality", "Henri Theil", "Hydrology", "Hypotheses", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Jan Kmenta", "Kitchen sink regression", "Least-squares", "Least squares", "Likelihood ratio test", "Linear regression", "Logistic regression", "Lurking variable", "Maximum Likelihood", "Maximum likelihood", "McGraw Hill", "Mean squared error", "Metric prefix", "Monotonic function", "Multicollinearity", "Multiple regression", "Nash\u2013Sutcliffe model efficiency coefficient", "Norm (mathematics)", "Normalization (statistics)", "Okun's law", "Omitted-variable bias", "Ordinary least squares", "Outlier", "Partial correlation", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Prediction", "Proportional reduction in loss", "Regression analysis", "Regression intercept", "Regression model validation", "Regressor", "Residual sum of squares", "Residuals (statistics)", "Root-mean-square deviation", "Root mean square deviation", "Sewall Wright", "Simple linear regression", "Simple regression", "Standard deviation", "Statistic", "Statistical model", "Statistics", "Sufficient condition", "Sum of squared residuals", "Test statistic", "The American Statistician", "Theil\u2013Sen estimator", "Total sum of squares", "Variance", "Weighted least squares"], "references": ["http://www.cesarzamudio.com/uploads/1/7/9/1/17916581/nagelkerke_n.j.d._1991_-_a_note_on_a_general_definition_of_the_coefficient_of_determination.pdf", "http://itfeature.com/correlation-and-regression-analysis/coefficient-of-determination", "http://www.originlab.com/doc/Origin-Help/LR-Algorithm", "http://stats.stackexchange.com/questions/7775/r-implementation-of-coefficient-of-partial-determination", "http://www.tandfonline.com/doi/abs/10.1080/00031305.1994.10476036", "http://doi.org/10.1016%2FS0304-4076(96)01818-0", "http://doi.org/10.1016%2Fj.jhydrol.2012.12.004", "http://doi.org/10.1029%2F1998WR900018", "http://doi.org/10.1080%2F00031305.1990.10475731", "http://doi.org/10.1093%2Fbiomet%2F78.3.691", "http://doi.org/10.1177%2F1094428106292901", "http://doi.org/10.2307%2F2683704", "http://www.jstor.org/stable/2337038", "http://www.jstor.org/stable/2683704", "http://www.worldcat.org/issn/1094-4281", "https://www.mathworks.com/help/matlab/data_analysis/linear-regression.html#bswinlz"]}, "Simfit": {"categories": ["All stub articles", "Free statistical software", "Regression and curve fitting software", "Science software stubs", "Statistics stubs"], "title": "SimFiT", "method": "Simfit", "url": "https://en.wikipedia.org/wiki/SimFiT", "summary": "Simfit is a free Open Source Windows package for simulation, curve fitting, statistics, and plotting, using a library of models or user-defined equations. Simfit has been in continuous development for many years by Bill Bardsley of the University of Manchester. Although it is written for Windows, it can easily be installed and used on Linux machines via WINE.\nSimfit is developed using Silverfrost Limited's FTN95 Fortran Compiler and is currently featured on their website as a showcased application. The graphical functionality in Simfit has been released as a Fortran library called Simdem which allows the programmer to produce charts and graphs with just a few lines of Fortran. A version of Simdem is shipped with the Windows version of the NAG Fortran Builder.A Spanish-language version of Simfit is maintained by a team in Salamanca.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/7/75/Science-symbol-2.svg"], "links": ["ADMB", "Analyse-it", "Association for Computing Machinery", "BMDP", "BV4.1 (software)", "CSPro", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "Digital object identifier", "EViews", "Epi Info", "Freeware", "GAUSS (software)", "GNU AGPL", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Numerical analysis", "Open-source software", "OpenBUGS", "Open source", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "Salamanca", "Scientific software", "SegReg", "SigmaStat", "SigmaXL", "Silverfrost FTN95", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistics", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "University of Manchester", "WinBUGS", "Wine (software)", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.silverfrost.com", "http://www.silverfrost.com/37/ftn95/ftn95_showcase.aspx", "http://simfit.usal.es/", "http://doi.org/10.1145%2F1279941.1279943", "http://www.simfit.manchester.ac.uk/simdem.html", "http://www.simfit.org.uk/"]}, "Test\u2013retest reliability": {"categories": ["Metrology", "Psychometrics", "Reliability analysis"], "title": "Repeatability", "method": "Test\u2013retest reliability", "url": "https://en.wikipedia.org/wiki/Repeatability", "summary": "Repeatability or test\u2013retest reliability is the closeness of the agreement between the results of successive measurements of the same measurand carried \nout under the same conditions of measurement. In other words, the measurements are taken by a single person or instrument on the same item, under the same conditions, and in a short period of time. A less-than-perfect test\u2013retest reliability causes test\u2013retest variability. Such variability can be caused by, for example, intra-individual variability and intra-observer variability. A measurement may be said to be repeatable when this variation is smaller than a pre-determined acceptance criterion.\nTest\u2013retest variability is practically used, for example, in medical monitoring of conditions. In these situations, there is often a predetermined \"critical difference\", and for differences in monitored values that are smaller than this critical difference, the possibility of pre-test variability as a sole cause of the difference may be considered in addition to, for examples, changes in diseases or treatments.", "images": [], "links": ["Absolute difference", "Accuracy", "Accuracy and precision", "Carryover effect", "Correlation", "Digital object identifier", "Internal consistency", "International Standard Book Number", "Intra-individual variability", "Intra-observer variability", "Measurements", "Measuring instrument", "Medical monitoring", "Monitoring (medicine)", "PubMed Central", "PubMed Identifier", "Reliability (statistics)", "Reproducibility", "Standard deviation", "Statistical variability"], "references": ["http://www.isixsigma.com/tools-templates/measurement-systems-analysis-msa-gage-rr/attribute-agreement-analysis-defect-databases/", "http://learnoilanalysis.com/how-can-results-for-the-same-sample-be-different/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1836738", "http://www.ncbi.nlm.nih.gov/pubmed/2503170", "http://www.socialresearchmethods.net/kb/reltypes.php", "http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf", "http://doi.org/10.1136%2Fbmj.298.6689.1659", "http://www-users.york.ac.uk/~mb55/meas/ba.htm", "https://www.nist.gov/pml/nist-technical-note-1297"]}, "JMP (statistical software)": {"categories": ["Data-centric programming languages", "Data analysis software", "Data visualization software", "Good articles", "High-level programming languages", "Numerical analysis software for MacOS", "Time series software"], "title": "JMP (statistical software)", "method": "JMP (statistical software)", "url": "https://en.wikipedia.org/wiki/JMP_(statistical_software)", "summary": "JMP (pronounced \"jump\") is a suite of computer programs for statistical analysis developed by the JMP business unit of SAS Institute. It was launched in 1989 to take advantage of the graphical user interface introduced by the Macintosh. It has since been significantly rewritten and made available for the Windows operating system. JMP is used in applications such as Six Sigma, quality control, and engineering, design of experiments, as well as for research in science, engineering, and social sciences.\nThe software can be purchased in any of five configurations: JMP, JMP Pro, JMP Clinical, JMP Genomics and the JMP Graph Builder App for the iPad. JMP can be automated with its proprietary scripting language, JSL. The software is focused on exploratory visual analytics, where users investigate and explore data. These explorations can also be verified by hypothesis testing, data mining, or other analytic methods. In addition, discoveries made through graphical exploration can lead to a designed experiment that can be both designed and analyzed with JMP.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/23/%E0%A6%9C%E0%A6%BE%E0%A6%AE%E0%A7%8D%E0%A6%AA_%E0%A6%B2%E0%A7%8B%E0%A6%97%E0%A7%8B.png", "https://upload.wikimedia.org/wikipedia/en/6/68/JMP_data_displays.png", "https://upload.wikimedia.org/wikipedia/en/9/94/Symbol_support_vote.svg", "https://upload.wikimedia.org/wikipedia/en/a/a3/Version_1.0_of_JMP_1989.png", "https://upload.wikimedia.org/wikipedia/en/2/25/Wildtrack_FIT_JMP.png"], "links": ["ADMB", "Analyse-it", "Apple Macintosh", "BMDP", "BV4.1 (software)", "Biomarkers", "CSPro", "Clinical trials", "Commercial software", "Comparison of statistical packages", "Computer program", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Data mining", "Data processing", "Dataplot", "Design of experiments", "Digital object identifier", "EViews", "Epi Info", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "Genomics", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "Hypothesis testing", "Information visualization", "International Standard Book Number", "International Standard Serial Number", "JASP", "JMulTi", "John Sall", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Macintosh", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Multivariate analysis", "NCSS (statistical software)", "Online analytical processing", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Proprietary software", "Public-domain software", "Quality control", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SAS Institute", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SQL", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "Six Sigma", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistical analysis", "Statistical package", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "Visual analytics", "WinBUGS", "Windows", "Wizard (software)", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.computerworld.com/article/2527824/business-intelligence/billionaire-sas-co-founder-keeps-on-coding.html", "http://www.drdobbs.com/tools/228200027?queryText=SAS%2BJMP", "http://www.google.com/translate?hl=en&ie=UTF8&sl=auto&tl=en&u=http://www.diarioti.com/noticia/SAS_lanza_JMP_8_para_Mac/24733", "http://www.information-management.com/issues/20030601/6798-1.html", "http://www.informationweek.com/news/200000512", "http://jmp.com", "http://www.jmp.com/", "http://www.jmp.com/about/newsletters/jmpercable/pdf/25_winter_2009.pdf", "http://www.jmp.com/en_us/about.html", "http://www.jmp.com/software/jmp10/jmp-graph-builder-for-ipad.shtml", "http://www.jmp.com/support/downloads/pdf/jmp9/jmp9_new_features.pdf", "http://jtonedm.com/2011/08/10/first-look-jmp-pro/", "http://jtonedm.com/2016/11/10/first-look-sas-jmp-13-and-jmp-pro-13/", "http://blogs.sas.com/jmp/", "http://support.sas.com/resources/papers/proceedings12/277-2012.pdf", "http://www2.sas.com/proceedings/sugi30/210-30.pdf", "http://scientificcomputing.com/articles-DA-JMP-9-A-Really-New-Version-051211.aspx", "http://www.scientificcomputing.com/article-da-JMP8-Continuous-Improvement-051509.aspx", "http://www.scientificcomputing.com/articles/2014/11/jmp-11-remarkable-statistics-graphics-and-integration", "http://www.scientificcomputing.com/articles/2016/01/jmp-pro-12-best-keeps-getting-better", "http://www.scientificcomputing.com/jmp-7-one-of-the-best-just-got.aspx", "http://www.tandfonline.com/doi/abs/10.1198/000313002753631402?journalCode=utas20#preview", "http://www.tandfonline.com/doi/pdf/10.1198/jcgs.2011.204c", "http://analytics.ncsu.edu/sesug/2000/s-61.pdf", "http://analytics.ncsu.edu/sesug/2011/JP03.Okerson.pdf", "http://www.niu.edu/clas/awards/awards_2010/honorees/sall.shtml", "http://cwhonors.org/viewCaseStudy2010.asp?NominationID=132&Username=hlsu", "http://doi.org/10.1002%2Fpst.460", "http://doi.org/10.1002%2Fwics.162", "http://doi.org/10.1021%2Fci00006a600", "http://doi.org/10.1198%2F000313002753631402", "http://doi.org/10.1198%2Fjcgs.2011.204c", "http://www.macstats.org/reviews/jmp.html", "http://www.orms-today.org/orms-2-07/frswr.html", "http://www.pharmasug.org/proceedings/2012/DG/PharmaSUG-2012-DG01.pdf", "http://www.phusewiki.org/docs/2011%20Papers/PP06%20paper.pdf", "http://www.sascommunity.org/wiki/Main_Page", "http://www.worldcat.org/issn/0003-1305", "http://www.worldcat.org/issn/1539-1604", "http://www.worldcat.org/issn/1549-9596", "https://451research.com/report-short?entityId=90656", "https://books.google.com/books?id=T_mJXz7xzo8C&pg=PA392", "https://books.google.com/books?id=Wd6p3YrbDi8C", "https://books.google.com/books?id=iCTlfWYOmzcC&pg=PA61", "https://books.google.com/books?id=k1QgAQAAMAAJ", "https://books.google.com/books?id=oOb3ejkFiIUC", "https://books.google.com/books?id=xdg9nkBFh1UC&pg=PA23", "https://link.springer.com.prox.lib.ncsu.edu/content/pdf/10.1007%2F978-0-387-09823-4_65", "https://archive.is/20130126070615/http://www.informationweek.com/news/200000512", "https://web.archive.org/web/20111105125748/http://cwhonors.org/viewCaseStudy2010.asp?NominationID=132&Username=hlsu", "https://web.archive.org/web/20121205173316/http://www.niu.edu/clas/awards/awards_2010/honorees/sall.shtml"]}, "Markov kernel": {"categories": ["Markov processes"], "title": "Markov kernel", "method": "Markov kernel", "url": "https://en.wikipedia.org/wiki/Markov_kernel", "summary": "In probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that plays the role, in the general theory of Markov processes, that the transition matrix does in the theory of Markov processes with a finite state space.", "images": [], "links": ["Borel set", "Conditional expectation", "Digital object identifier", "Finite set", "Galton\u2013Watson process", "Independent and identically distributed random variables", "Indicator function", "International Standard Book Number", "Markov process", "Measurable function", "Measurable space", "Measure (mathematics)", "Power set", "Probability measure", "Probability theory", "Random variable", "Sigma-algebra", "Simple random walk", "State space", "Stochastic matrix", "Transition kernel"], "references": ["http://doi.org/10.1007%2F978-1-4471-5361-0", "http://doi.org/10.1007%2F978-1-4613-9308-5"]}, "Probability bounds analysis": {"categories": ["Mathematical analysis", "Probability bounds analysis", "Use dmy dates from April 2013", "Webarchive template wayback links"], "title": "Probability bounds analysis", "method": "Probability bounds analysis", "url": "https://en.wikipedia.org/wiki/Probability_bounds_analysis", "summary": "Probability bounds analysis (PBA) is a collection of methods of uncertainty propagation for making qualitative and quantitative calculations in the face of uncertainties of various kinds. It is used to project partial information about random variables and other quantities through mathematical expressions. For instance, it computes sure bounds on the distribution of a sum, product, or more complex function, given only sure bounds on the distributions of the inputs. Such bounds are called probability boxes, and constrain cumulative probability distributions (rather than densities or mass functions).\nThis bounding approach permits analysts to make calculations without requiring overly precise assumptions about parameter values, dependence among variables, or even distribution shape. Probability bounds analysis is essentially a combination of the methods of standard interval analysis and classical probability theory. Probability bounds analysis gives the same answer as interval analysis does when only range information is available. It also gives the same answers as Monte Carlo simulation does when information is abundant enough to precisely specify input distributions and their dependencies. Thus, it is a generalization of both interval analysis and probability theory.\nThe diverse methods comprising probability bounds analysis provide algorithms to evaluate mathematical expressions when there is uncertainty about the input values, their dependencies, or even the form of mathematical expression itself. The calculations yield results that are guaranteed to enclose all possible distributions of the output variable if the input p-boxes were also sure to enclose their respective distributions. In some cases, a calculated p-box will also be best-possible in the sense that\nthe bounds could be no tighter without excluding some of the possible\ndistributions.\nP-boxes are usually merely bounds on possible distributions. The bounds often also enclose distributions that are not themselves possible. For instance, the set of probability distributions that could result from adding random values without the independence assumption from two (precise) distributions is generally a proper subset of all the distributions enclosed by the p-box computed for the sum. That is, there are distributions within the output p-box that could not arise under any dependence between the two input distributions. The output p-box will, however, always contain all distributions that are possible, so long as the input p-boxes were sure to enclose their respective underlying distributions. This property often suffices for use in risk analysis and other fields requiring calculations under uncertainty.", "images": [], "links": ["AND gate", "Aerospace engineering", "Andrey Markov", "Applications of p-boxes and probability bounds analysis", "Ariane 5", "Bayesian sensitivity analysis", "Biosecurity", "Boolean function", "Brownfield land", "CSIRO", "Calcasieu River", "Chebyshev", "Chebyshev inequality", "Chemical reactor", "Climate change", "Comonotonicity", "Convolution", "Convolution of probability distributions", "Copula (probability theory)", "Cost estimation models", "Countermonotonicity", "Cumulative distribution function", "Curse of dimensionality", "Digital object identifier", "Endangered species", "Environmental impact assessment", "Extinction", "Failure analysis", "Finite element method", "Fracking", "Frechet inequalities", "George Boole", "Groundwater", "Groundwater model", "Heavy metal (chemistry)", "Henry E. Kyburg, Jr.", "Housatonic River", "Importance sampling", "Imprecise probability", "Insectivore", "International Standard Book Number", "Interval (mathematics)", "Interval analysis", "Interval arithmetic", "Invasive species", "Ironworks", "John Maynard Keynes", "Kolmogorov", "Latin hypercube", "Leadbeater's possum", "Logical conjunction", "Logical disjunction", "Markov inequality", "Mathematical programming", "Maurice Ren\u00e9 Fr\u00e9chet", "Mercury (element)", "Monte Carlo simulation", "NP-hard", "Northern spotted owl", "Nuclear stockpile", "OR gate", "Olympic Peninsula", "Ordinary differential equation", "Pest (organism)", "Pesticide", "Pharmacokinetics", "Polychlorinated biphenyl", "Positive quadrant dependence", "Probabilistic logic", "Probabilistic risk assessment", "Probability box", "Probability density function", "Probability mass function", "Probability theory", "Queueing theory", "Real number", "Regulatory Toxicology and Pharmacology", "Reliability engineering", "Risk analysis", "Robust Bayes analysis", "Salinity in Australia", "Second-order Monte Carlo simulation", "Sensitivity analysis", "Soil contamination", "Structural analysis", "Subset", "Superfund", "Supersonic nozzle", "The Laws of Thought", "Uncertainty quantification", "United States Environmental Protection Agency", "Upper and lower bounds", "Verification and validation", "Verified computing", "Volatile organic compound", "Water pollution", "Water treatment", "Wayback Machine"], "references": ["http://www.depi.vic.gov.au/__data/assets/pdf_file/0013/333112/ARI-Technical-Report-163-The-use-of-probability-bounds-analysis-for-characterising-and-propagating-uncertainty-in-species-sensitivity-distributions.pdf", "http://www.depi.vic.gov.au/__data/assets/pdf_file/0017/333116/ARI-Technical-Report-164-Uncertainty-propagation-in-population-level-salinity-risk-models.pdf", "http://www.dl.begellhouse.com/download/article/340d23ed5c6d1633/IJUQ-3562.pdf", "http://authors.elsevier.com/sd/article/S0888613X04001112", "http://www.inderscience.com/search/index.php?action=record&rec_id=44292&prevQuery=&ps=10&m=or", "http://www.informaworld.com/smpp/content~db=all~content=a727073280~frm=abslink", "http://www.ramas.com/depend.pdf", "http://www.ramas.com/pbawhite.pdf", "http://www.ramas.com/unabridged.zip", "http://www.sciencedirect.com/science/journal/aip/08883270", "http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V5X-482MG17-3&_user=10&_coverDate=12/31/1995&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1690824265&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=35a304a0cd02672e067639a29e6b114a&searchtype=a", "http://opus.kobv.de/ubp/volltexte/2005/561/", "http://www.srl.gatech.edu/Members/jaughenbaugh/papers_presentations/2007-01-1480.pdf", "http://ualr.edu/jdberleant/intprob/", "http://www.cs.utep.edu/vladik/2000/tr00-17.pdf", "http://www.caee.utexas.edu/prof/tonon/Publications/Papers/Paper%20P%202005-6%20Probability%20bounds%20for%20systems%20with%20random%20set%20input.pdf", "http://www.brgm.fr/publication/pubDetailRapportSP.jsp?id=RSP-BRGM/RP-54099-FR", "http://www.univ-orleans.fr/mapmo/membres/baudrit/consoil05.pdf", "http://www.epa.gov/ne/ge/", "http://www.epa.gov/region6/6sf/louisiana/calcasieu/la_calcasieu_calcri.html", "http://www.epa.gov/superfund/health/conmedia/soil/index.htm", "http://doi.org/10.1016%2F0004-3702(94)90102-3", "http://doi.org/10.1201%2Fb19094-339", "http://www.gutenberg.org/etext/15114", "http://www.sipta.org/", "http://www.sipta.org/documentation/interval_prob/kyburg.pdf", "http://www.sipta.org/isipta07/proceedings/papers/s032.pdf", "http://www.eng.nus.edu.sg/civil/REC2010/documents/papers/013.pdf", "https://www.ncbi.nlm.nih.gov/pubmed/25976918", "https://web.archive.org/web/20110120051527/http://www.epa.gov/region6/6sf/louisiana/calcasieu/la_calcasieu_calcri.html", "https://web.archive.org/web/20110722073459/http://www.ramas.com/unabridged.zip", "https://web.archive.org/web/20120210155925/http://www.sandia.gov/epistemic/", "https://web.archive.org/web/20120321204134/http://www.caee.utexas.edu/prof/tonon/Publications/Papers/Paper%20P%202005-6%20Probability%20bounds%20for%20systems%20with%20random%20set%20input.pdf", "https://doi.org/10.1002%2Fieam.1661", "https://doi.org/10.1016%2Fj.ymssp.2012.03.001", "https://doi.org/10.1016%2Fj.ymssp.2012.03.014", "https://doi.org/10.1016%2Fj.ymssp.2012.08.012", "https://doi.org/10.1504%2FIJRS.2008.022079", "https://doi.org/10.1615%2FInt.J.UncertaintyQuantification.2012003562"]}, "Karhunen\u2013Lo\u00e8ve theorem": {"categories": ["All articles to be expanded", "Articles to be expanded from July 2010", "Articles using small message boxes", "Probability theorems", "Signal estimation", "Statistical theorems"], "title": "Karhunen\u2013Lo\u00e8ve theorem", "method": "Karhunen\u2013Lo\u00e8ve theorem", "url": "https://en.wikipedia.org/wiki/Karhunen%E2%80%93Lo%C3%A8ve_theorem", "summary": "In the theory of stochastic processes, the Karhunen\u2013Lo\u00e8ve theorem (named after Kari Karhunen and Michel Lo\u00e8ve), also known as the Kosambi\u2013Karhunen\u2013Lo\u00e8ve theorem is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval. The transformation is also known as Hotelling transform and eigenvector transform, and is closely related to principal component analysis (PCA) technique widely used in image processing and in data analysis in many fields.Stochastic processes given by infinite series of this form were first considered by Damodar Dharmananda Kosambi. There exist many such expansions of a stochastic process: if the process is indexed over [a, b], any orthonormal basis of L2([a, b]) yields an expansion thereof in that form. The importance of the Karhunen\u2013Lo\u00e8ve theorem is that it yields the best such basis in the sense that it minimizes the total mean squared error.\nIn contrast to a Fourier series where the coefficients are fixed numbers and the expansion basis consists of sinusoidal functions (that is, sine and cosine functions), the coefficients in the Karhunen\u2013Lo\u00e8ve theorem are random variables and the expansion basis depends on the process. In fact, the orthogonal basis functions used in this representation are determined by the covariance function of the process. One can think that the Karhunen\u2013Lo\u00e8ve transform adapts to the process in order to produce the best possible basis for its expansion.\nIn the case of a centered stochastic process {Xt}t \u2208 [a, b] (centered means E[Xt] = 0 for all t \u2208 [a, b]) satisfying a technical continuity condition, Xt admits a decomposition\n\n \n \n \n \n X\n \n t\n \n \n =\n \n \u2211\n \n k\n =\n 1\n \n \n \u221e\n \n \n \n Z\n \n k\n \n \n \n e\n \n k\n \n \n (\n t\n )\n \n \n {\\displaystyle X_{t}=\\sum _{k=1}^{\\infty }Z_{k}e_{k}(t)}\n where Zk are pairwise uncorrelated random variables and the functions ek are continuous real-valued functions on [a, b] that are pairwise orthogonal in L2([a, b]). It is therefore sometimes said that the expansion is bi-orthogonal since the random coefficients Zk are orthogonal in the probability space while the deterministic functions ek are orthogonal in the time domain. The general case of a process Xt that is not centered can be brought back to the case of a centered process by considering Xt \u2212 E[Xt] which is a centered process.\nMoreover, if the process is Gaussian, then the random variables Zk are Gaussian and stochastically independent. This result generalizes the Karhunen\u2013Lo\u00e8ve transform. An important example of a centered real stochastic process on [0, 1] is the Wiener process; the Karhunen\u2013Lo\u00e8ve theorem can be used to provide a canonical orthogonal representation for it. In this case the expansion consists of sinusoidal functions.\nThe above expansion into uncorrelated random variables is also known as the Karhunen\u2013Lo\u00e8ve expansion or Karhunen\u2013Lo\u00e8ve decomposition. The empirical version (i.e., with the coefficients computed from a sample) is known as the Karhunen\u2013Lo\u00e8ve transform (KLT), principal component analysis, proper orthogonal decomposition (POD), empirical orthogonal functions (a term used in meteorology and geophysics), or the Hotelling transform.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128143823%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128140726%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110427033551%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110424212543%21Wiki_letter_w_cropped.svg"], "links": ["Adaptive optics", "Additive white Gaussian noise", "ArXiv", "Bibcode", "Brownian bridge", "Brownian motion", "Convergence of random variables", "Cosine", "Covariance function", "Damodar Dharmananda Kosambi", "Digital object identifier", "Empirical orthogonal functions", "Entropy (information theory)", "Fourier series", "Functional derivative", "Gaussian process", "Geophysics", "Harold Hotelling", "Harvey Mudd College", "Integral equation", "International Standard Book Number", "Karhunen\u2013Lo\u00e8ve transform", "Kari Karhunen", "Linear operator", "Mathematical Reviews", "Maximum likelihood", "Mean squared error", "Mean vector", "Mercer's theorem", "Meteorology", "Michel Lo\u00e8ve", "Neyman\u2013Pearson lemma", "Orthogonal function", "Orthogonality principle", "Orthonormal basis", "Polynomial chaos", "Principal component analysis", "Probability space", "Proper orthogonal decomposition", "Random variable", "Sine", "Singular Value Decomposition", "Statistic", "Stochastic process", "Stochastically independent", "Trigonometric function", "Uncorrelated", "Variance", "Wiener process", "Wiener\u2013Hopf equation"], "references": ["http://reference.wolfram.com/mathematica/ref/KarhunenLoeveDecomposition.html", "http://adsabs.harvard.edu/abs/1996JOSAA..13.1218D", "http://adsabs.harvard.edu/abs/2007JMP....48j3503J", "http://adsabs.harvard.edu/abs/2011IJEST...1....5S", "http://fourier.eng.hmc.edu/e161/lectures/klt/klt.html", "http://fourier.eng.hmc.edu/e161/lectures/klt/node3.html", "http://www.ams.org/mathscinet-getitem?mr=0009816", "http://arxiv.org/abs/math-ph/0701056", "http://doi.org/10.1063%2F1.2793569", "http://doi.org/10.1109%2Fjetcas.2011.2138250", "http://doi.org/10.1364%2FJOSAA.13.001218", "http://openlibrary.org/books/OL1865197M/Stochastic_finite_elements", "http://openlibrary.org/books/OL21138080M/Probability_random_processes_and_estimation_theory_for_engineers"]}, "Sally Clark": {"categories": ["1964 births", "2003 in law", "2007 deaths", "Alcohol-related deaths in England", "All articles with dead external links", "All articles with unsourced statements", "Alumni of the University of Southampton", "Articles with dead external links from May 2011", "Articles with hCards", "Articles with unsourced statements from January 2017", "CS1 maint: Archived copy as title", "English law", "English solicitors", "Forensic statistics", "History of mental health in the United Kingdom", "Overturned convictions in England", "People educated at South Wilts Grammar School for Girls", "People from Devizes", "People from Hatfield Peverel", "People from Wilmslow", "Use dmy dates from August 2015", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with VIAF identifiers"], "title": "Sally Clark", "method": "Sally Clark", "url": "https://en.wikipedia.org/wiki/Sally_Clark", "summary": "Sally Clark (August 1964 \u2013 15 March 2007) was an English solicitor who, in November 1999, became the victim of a miscarriage of justice when she was found guilty of the murder of her two infant sons.\nClark's first son died suddenly in December 1996 within a few weeks of his birth, and in January 1998 her second died in a similar manner. A month later, she was arrested and tried for both of the deaths. The prosecution case relied on significantly flawed statistical evidence presented by paediatrician Professor Sir Roy Meadow, who testified that the chance of two children from an affluent family suffering sudden infant death syndrome was 1 in 73 million. He had arrived at this figure erroneously by squaring 1 in 8500, as being the likelihood of a cot death in similar circumstances. The Royal Statistical Society later issued a statement arguing that there was \"no statistical basis\" for Meadow's claim, and expressing its concern at the \"misuse of statistics in the courts\".Clark was convicted in November 1999. The convictions were upheld on appeal in October 2000, but overturned in a second appeal in January 2003, after it emerged that Dr Alan Williams, the prosecution forensic pathologist who examined both of her babies, had incompetently failed to disclose microbiological reports that suggested the second of her sons had died of natural causes. She was released from prison having served more than three years of her sentence. Journalist Geoffrey Wansell called Clark's experience \"one of the great miscarriages of justice in modern British legal history\". As a result of her case, the Attorney-General ordered a review of hundreds of other cases, and two other women had their convictions overturned. Clark's experience caused her to develop serious psychiatric problems and she died in her home in March 2007 from alcohol poisoning.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9a/Johnny-automatic-scales-of-justice.svg", "https://upload.wikimedia.org/wikipedia/en/a/ae/Flag_of_the_United_Kingdom.svg", "https://upload.wikimedia.org/wikipedia/en/6/69/P_vip.svg"], "links": ["Acute alcohol intoxication", "Addleshaw Booth & Co", "Alcohol poisoning", "Angela Cannings", "Attorney General for England and Wales", "BAILII", "BBC News", "Bayes' theorem", "Bayes Theorem", "Bullwood Hall (HM Prison)", "Cheshire", "Citibank", "City University, London", "City of London", "Coralie Colmez", "Court of Appeal of England and Wales", "Criminal Cases Review Commission", "Crown Court", "David Southall", "Death by natural causes", "Devizes", "Digital object identifier", "Donna Anthony", "Ebury Press", "Expert witness", "General Medical Council", "Grand National", "Hatfield Peverel", "High Court of Justice", "Hockley", "Home Office", "Ian McEwan", "International Standard Book Number", "John Batt", "Jury", "Leila Schneps", "Library of Congress Control Number", "Life imprisonment", "Lloyds Bank (historic)", "Lord Chancellor", "Lucia de Berk", "Manchester", "Mandatory sentence", "Marilyn Stowe", "Meadow's law", "Miscarriage of justice", "Peter Donnelly", "Post-natal depression", "Priory Clinic", "Prosecutor's fallacy", "PubMed Central", "PubMed Identifier", "Queen's Counsel", "Robin Spencer", "Roy Meadow", "Royal Statistical Society", "Salford University", "Salisbury", "Sally Clark (disambiguation)", "Solicitor", "South Wilts Grammar School for Girls", "Southampton University", "Staphylococcus aureus", "Styal (HM Prison)", "Sudden infant death syndrome", "The Children Act (novel)", "The Guardian", "The Times", "Trupti Patel", "University of Leeds", "Virtual International Authority File", "Wilmslow", "Wiltshire Constabulary", "WorldCat"], "references": ["http://bmj.bmjjournals.com/cgi/content/full/330/7504/1347", "http://www.geoffreywansell.com/SallyClark.html", "http://www.ted.com/tedtalks/tedtalksplayer.cfm?key=p_donnelly", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2078654", "http://www.ncbi.nlm.nih.gov/pubmed/18006978", "http://www.richardwebster.net/cotdeaths.html", "http://www.bailii.org/ew/cases/EWCA/Crim/2000/54.html", "http://www.bailii.org/ew/cases/EWCA/Crim/2003/1020.html", "http://doi.org/10.1136%2Fbmj.39398.639525.DB", "http://www.gmc-uk.org/gmp_2001.pdf_25416526.pdf", "http://www.gmc-uk.org/good_medical_practice_july_1998.pdf_25416527.pdf", "http://plus.maths.org/issue21/features/clark/index.html", "http://www.cse.salford.ac.uk/profiles/profile.php?profile=R.Hill", "http://www.cse.salford.ac.uk/staff/RHill/ppe_5601.pdf", "http://news.bbc.co.uk/1/hi/england/essex/7082411.stm", "http://news.bbc.co.uk/1/hi/uk/6460669.stm", "http://news.bbc.co.uk/2/hi/uk_news/england/essex/7082411.stm", "http://society.guardian.co.uk/children/story/0,1074,1541102,00.html", "http://www.timesonline.co.uk/tol/comment/obituaries/article1533755.ece", "http://www.rss.org.uk/Images/PDF/influencing-change/rss-use-statistical-evidence-court-cases-2002.pdf", "http://www.rss.org.uk/uploadedfiles/documentlibrary/744.pdf", "http://www.sallyclark.org.uk/", "https://www.theguardian.com/science/2006/oct/28/uknews1", "https://www.theguardian.com/society/2005/jul/06/NHS.uknews", "https://www.theguardian.com/society/2007/sep/06/childrensservices.health", "https://www.theguardian.com/uk_news/story/0,,2036295,00.html", "https://www.theguardian.com/uk_news/story/0,,2038232,00.html", "https://id.loc.gov/authorities/names/nb2005015500", "https://web.archive.org/web/20070320200507/http://news.independent.co.uk/uk/legal/article2368993.ece", "https://web.archive.org/web/20110824151124/http://www.rss.org.uk/uploadedfiles/documentlibrary/744.pdf", "https://web.archive.org/web/20150924022745/http://www.gmc-uk.org/gmp_2001.pdf_25416526.pdf", "https://web.archive.org/web/20150924022746/http://www.gmc-uk.org/good_medical_practice_july_1998.pdf_25416527.pdf", "https://viaf.org/viaf/16744957", "https://www.wikidata.org/wiki/Q3544105", "https://www.worldcat.org/identities/containsVIAFID/16744957", "https://www.telegraph.co.uk/news/obituaries/1545933/Sally-Clark.html"]}, "Ordered logit": {"categories": ["All articles to be expanded", "Articles to be expanded from February 2017", "Articles using small message boxes", "Logistic regression"], "title": "Ordered logit", "method": "Ordered logit", "url": "https://en.wikipedia.org/wiki/Ordered_logit", "summary": "In statistics, the ordered logit model (also ordered logistic regression or proportional odds model), is an ordinal regression model\u2014that is, a regression model for ordinal dependent variables\u2014first considered by Peter McCullagh. For example, if one question on a survey is to be answered by a choice among \"poor\", \"fair\", \"good\", and \"excellent\", and the purpose of the analysis is to see how well that response can be predicted by the responses to other questions, some of which may be quantitative, then ordered logistic regression may be used. It can be thought of as an extension of the logistic regression model that applies to dichotomous dependent variables, allowing for more than two (ordered) response categories.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Censoring (statistics)", "Consistency (statistics)", "Dependent variable", "Dichotomous", "Discrete choice", "Errors-in-variables models", "Errors and residuals", "Errors and residuals in statistics", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jeffrey Wooldridge", "Joseph Hilbe", "Journal of the Royal Statistical Society", "Least-angle regression", "Least absolute deviations", "Least squares", "Levels of measurement", "Likert scale", "Linear combination", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Maximum likelihood", "Mean and predicted response", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Odds", "Ordered probit", "Ordinal regression", "Ordinary least squares", "Partial least squares regression", "Peter McCullagh", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Weighted least squares", "William Greene (economist)"], "references": ["http://www.pmean.com/04/OrdinalLogistic.html", "http://data.princeton.edu/wws509/stata/c6s5.html", "http://www.jstor.org/stable/2984952", "https://books.google.com/books?id=hSs3AgAAQBAJ&pg=PA655", "https://books.google.com/books?id=lV3DIdV0F9AC&pg=PA119", "https://stats.idre.ucla.edu/stata/dae/ordered-logistic-regression"]}, "TPL Tables": {"categories": ["Pages using Infobox software with unknown parameters", "Statistical software"], "title": "TPL Tables", "method": "TPL Tables", "url": "https://en.wikipedia.org/wiki/TPL_Tables", "summary": "TPL Tables is a cross tabulation system used to generate statistical tables for analysis or publication.", "images": [], "links": ["Bureau of Labor Statistics", "Comma-separated values", "Comma Separated Values", "Comoros Islands", "Cross tabulation", "Data analysis", "HTML", "Linux", "Microsoft Windows", "Operating system", "PDF", "People's Republic of China", "PostScript", "Proprietary software", "Software categories", "Software developer", "Software license", "Software release life cycle", "Table Producing Language", "Unix"], "references": ["http://www.qqqsoft.com/html/download/index.html", "http://qqqsoftware.com/", "http://qqqsoftware.com", "http://www.qqqsoftware.com", "http://portal.acm.org/citation.cfm?id=1115964", "http://portal.acm.org/citation.cfm?id=800182.810390", "http://unstats.un.org/unsd/publication/unint/DP_UN_INT_81_041_1.pdf", "https://web.archive.org/web/20070517080104/http://www.pc-axis.scb.se/"]}, "Stability (probability)": {"categories": ["Stability (probability)", "Theory of probability distributions"], "title": "Stability (probability)", "method": "Stability (probability)", "url": "https://en.wikipedia.org/wiki/Stability_(probability)", "summary": "In probability theory, the stability of a random variable is the property that a linear combination of two independent copies of the variable has the same distribution, up to location and scale parameters. The distributions of random variables having this property are said to be \"stable distributions\". Results available in probability theory show that all possible distributions having this property are members of a four-parameter family of distributions. The article on the stable distribution describes this family together with some of the properties of these distributions.\nThe importance in probability theory of \"stability\" and of the stable family of probability distributions is that they are \"attractors\" for properly normed sums of independent and identically distributed random variables.\nImportant special cases of stable distributions are the normal distribution, the Cauchy distribution and the L\u00e9vy distribution. For details see stable distribution.", "images": [], "links": ["Absolutely continuous", "Cauchy distribution", "Characteristic function (probability theory)", "Convolution", "Extreme value theory", "Generalized extreme value distribution", "Geometric distribution", "Geometric stable distribution", "Indecomposable distribution", "Independent and identically distributed", "Infinite divisibility", "Infinitely divisible", "International Standard Book Number", "Location parameter", "L\u00e9vy distribution", "Normal distribution", "Probability distribution", "Probability theory", "Random variable", "Scale parameter", "Stability postulate", "Stable distribution", "Statistical independence", "Unimodal", "Univariate distribution"], "references": []}, "Average treatment effect": {"categories": ["Estimation theory", "Experiments", "Medical statistics"], "title": "Average treatment effect", "method": "Average treatment effect", "url": "https://en.wikipedia.org/wiki/Average_treatment_effect", "summary": "The average treatment effect (ATE) is a measure used to compare treatments (or interventions) in randomized experiments, evaluation of policy interventions, and medical trials. The ATE measures the difference in mean (average) outcomes between units assigned to the treatment and units assigned to the control. In a randomized trial (i.e., an experimental study), the average treatment effect can be estimated from a sample using a comparison in mean outcomes for treated and untreated units. However, the ATE is generally understood as a causal parameter (i.e., an estimate or property of a population) that a researcher desires to know, defined without reference to the study design or estimation procedure. Both observational studies and experimental study designs with random assignment may enable one to estimate an ATE in a variety of ways.", "images": [], "links": ["Causal", "Causality", "Central tendency", "Confounding", "Counterfactual conditional", "Covariate", "Dependent and independent variables", "Difference in differences", "Digital object identifier", "Economics", "Estimator", "Experiment", "International Standard Book Number", "JSTOR", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society, Series A", "Law of large numbers", "Local IV", "Matching (statistics)", "Mean", "Natural experiment", "Observational study", "Paired difference test", "Political science", "Probability distribution", "Psychology", "Quasi-experiment", "Random assignment", "Randomized trial", "Regression analysis", "Regression discontinuity design", "Rubin causal model", "Statistical inference", "Statistical population", "Study design"], "references": ["http://doi.org/10.1080%2F01621459.1986.10478354", "http://doi.org/10.1111%2Fj.1467-985X.2007.00527.x", "http://www.jstor.org/stable/2289064"]}, "CHAID": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2010", "Classification algorithms", "Decision trees", "Market research", "Market segmentation", "Statistical algorithms", "Statistical classification"], "title": "Chi-square automatic interaction detection", "method": "CHAID", "url": "https://en.wikipedia.org/wiki/Chi-square_automatic_interaction_detection", "summary": "Chi-square automatic interaction detection (CHAID) is a decision tree technique, based on adjusted significance testing (Bonferroni testing). The technique was developed in South Africa and was published in 1980 by Gordon V. Kass, who had completed a PhD thesis on this topic. CHAID can be used for prediction (in a similar fashion to regression analysis, this version of CHAID being originally known as XAID) as well as classification, and for detection of interaction between variables. CHAID is based on a formal extension of the United States' AID (Automatic Interaction Detection) and THAID (THeta Automatic Interaction Detection) procedures of the 1960s and 1970s, which in turn were extensions of earlier research, including that performed in the UK in the 1950s.\nIn practice, CHAID is often used in the context of direct marketing to select groups of consumers and predict how their responses to some variables affect other variables, although other early applications were in the field of medical and psychiatric research.\nLike other decision trees, CHAID's advantages are that its output is highly visual and easy to interpret. Because it uses multiway splits by default, it needs rather large sample sizes to work effectively, since with small sample sizes the respondent groups can quickly become too small for reliable analysis.\nOne important advantage of CHAID over alternatives such as multiple regression is that it is non-parametric.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Bonferroni testing", "Chi-squared distribution", "Decision tree learning", "Direct marketing", "Journal of the American Statistical Association", "Latent class model", "Market segment", "Multiple comparisons", "Regression analysis", "Structural equation modeling"], "references": ["https://ideas.repec.org/c/boc/bocode/s457752.html", "https://ideas.repec.org/c/boc/bocode/s457932.html"]}, "Geometric data analysis": {"categories": ["All articles with dead external links", "Articles with dead external links from January 2018", "Articles with permanently dead external links", "Geometry", "Multivariate statistics", "Spatial data analysis"], "title": "Geometric data analysis", "method": "Geometric data analysis", "url": "https://en.wikipedia.org/wiki/Geometric_data_analysis", "summary": "Geometric data analysis comprises geometric aspects of image analysis, pattern analysis and shape analysis or the approach of multivariate statistics that treats arbitrary data sets as clouds of points in n-dimensional space. This includes topological data analysis, cluster analysis, inductive data analysis, correspondence analysis, multiple correspondence analysis, principal components analysis and fr:Iconographie des corr\u00e9lations.", "images": [], "links": ["Algebraic statistics", "Cluster analysis", "Combinatorial data analysis", "Computational anatomy", "Correspondence analysis", "Geometry", "Image analysis", "Inductive data analysis", "International Standard Book Number", "J\u00f6rg Blasius", "Multiple correspondence analysis", "Multivariate statistics", "Pattern analysis", "Principal components analysis", "Shape analysis (digital geometry)", "Structured data analysis (statistics)", "Topological data analysis"], "references": ["http://math.u-bourgogne.fr/IMB/chazal/Intrinsic_distances.pdf", "https://www.amazon.com/Differential-Geometry-Statistics-Monographs-Probability/dp/0412398605", "https://books.google.com/books?id=wvaH1QxyBFoC"]}, "Philosophy of statistics": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Applied philosophy", "Articles lacking in-text citations from November 2010", "Articles with unsourced statements from July 2016", "Ethics and statistics", "Philosophy of statistics", "Wikipedia articles needing clarification from July 2016"], "title": "Philosophy of statistics", "method": "Philosophy of statistics", "url": "https://en.wikipedia.org/wiki/Philosophy_of_statistics", "summary": "The philosophy of statistics involves the meaning, justification, utility, use and abuse of statistics and its methodology, and ethical and epistemological issues involved in the consideration of choice and interpretation of data and methods of statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Bayesian inference", "Bradley Efron", "Causality", "Confidence Interval", "Correlation", "Data", "Data analysis", "Data transformation (statistics)", "Digital object identifier", "Epistemological", "Epistemology", "Ethical", "Ethics", "Evidence", "Experimental design", "Foundations of statistics", "Frequentist", "History of statistics", "I. J. Good", "Ian Hacking", "Inductive reasoning", "International Standard Book Number", "JSTOR", "Leonard Jimmie Savage", "Logical deduction", "Meaning (philosophy of language)", "Medical", "Methodology", "Model selection", "Nonparametric statistics", "Optimization (mathematics)", "Parametric statistics", "Philosophy of probability", "Philosophy of science", "Probability distribution", "SIAM Review", "Sample size", "Scientific American", "Scientific method", "Sir David Cox (statistician)", "Statistical Science", "Statistical inference", "Statistical literacy", "Statistics", "Theodore Porter", "Theoretical statistics", "Theory of justification", "Theory of measurement", "Utility"], "references": ["http://plato.stanford.edu/entries/statistics/", "http://www-stat.stanford.edu/~ckirby/brad/other/Article1977.pdf", "http://doi.org/10.1093/bjps/xv.57.1", "http://doi.org/10.1137/1021092", "http://doi.org/10.1214/ss/1009213726", "http://doi.org/10.1214/ss/1177012754", "http://www.jstor.org/stable/2245388", "http://www.jstor.org/stable/685624", "https://www.springer.com/us/book/9783662486368"]}, "Procedural confound": {"categories": ["All articles with unsourced statements", "Analysis of variance", "Articles with short description", "Articles with unsourced statements from April 2012", "Causal inference", "Design of experiments"], "title": "Confounding", "method": "Procedural confound", "url": "https://en.wikipedia.org/wiki/Confounding", "summary": "In statistics, a confounder (also confounding variable, confounding factor or lurking variable) is a variable that influences both the dependent variable and independent variable causing a spurious association. Confounding is a causal concept, and as such, cannot be described in terms of correlations or associations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/Confounding.PNG", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b8/Simple_Confounding_Case.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alaska", "American Journal of Epidemiology", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anecdotal evidence", "Antidepressant", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Berkson's paradox", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Case-control study", "Categorical variable", "Causal inference", "Causality", "Cause", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort study", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding Factor (games company)", "Confounding factor", "Confusion", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Donald Rubin", "Double blinding", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiological method", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Health", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Judea Pearl", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Leslie Kish", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Lippincott Williams & Wilkins", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Medieval Latin", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New England Journal of Medicine", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational studies", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Peer review", "Percentile", "Permutation test", "Pesticide", "Pie chart", "Pivotal quantity", "Placebo effect", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Risk assessment", "Risk ratio", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "SSRI", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific Reports", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sherry L Mayrent", "Sign test", "Simple linear regression", "Simpson's Paradox", "Simpson's paradox", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratification (statistics)", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tricyclic antidepressant", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.une.edu.au/WebStat/unit_materials/c1_behavioural_science_research/confounds.html", "http://adsabs.harvard.edu/abs/2014NatSR...4E6085L", "http://ftp.cs.ucla.edu/pub/stat_ser/R256.pdf", "http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1009818", "http://www.ncbi.nlm.nih.gov/pubmed/11565527", "http://arxiv.org/abs/1304.0564", "http://doi.org/10.1037%2Fh0037350", "http://doi.org/10.1038%2Fsrep06085", "http://doi.org/10.1056%2Fnejm200109203451211", "http://doi.org/10.1093%2Faje%2F154.3.276", "http://doi.org/10.1093%2Fije%2F15.3.413", "http://doi.org/10.1136%2Fjech.2010.112565", "http://doi.org/10.1136%2Foem.46.8.505", "http://doi.org/10.1214%2F12-aos1058", "http://doi.org/10.1214%2Fss%2F1009211805"]}, "Barnardisation": {"categories": ["All stub articles", "Information privacy", "Statistics stubs", "Survey methodology"], "title": "Barnardisation", "method": "Barnardisation", "url": "https://en.wikipedia.org/wiki/Barnardisation", "summary": "Barnardisation is a method of disclosure control for tables of counts that involves randomly adding or subtracting 1 from some cells in the table.\nIt is named after Professor George Alfred Barnard (1915\u20132002), a professor of mathematics at the University of Essex.\nIn the United Kingdom, barnardisation is sometimes employed by public agencies in order to enable them to provide information for statistical purposes without infringing the information privacy rights of the individuals to whom the information relates. The question whether barnardisation may fall short of the complete anonymisation of data and the status of barnardised data under the complex provisions of the Data Protection Act 1998 were considered by the House of Lords in the case of Common Services Agency v Scottish Information Commissioner [2008] 1 WLR 1550, the above case is also reported at All ER 2008 (4) 851.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Data Protection Act 1998", "George Alfred Barnard", "Information privacy", "Judicial functions of the House of Lords", "Mathematics", "Office For National Statistics", "Statistics", "United Kingdom", "University of Essex"], "references": ["http://www.ons.gov.uk/ons/guide-method/best-practice/disclosure-control-of-health-statistics/working-paper-3--risk-management.pdf"]}, "Markov chain mixing time": {"categories": ["Markov processes"], "title": "Markov chain mixing time", "method": "Markov chain mixing time", "url": "https://en.wikipedia.org/wiki/Markov_chain_mixing_time", "summary": "In probability theory, the mixing time of a Markov chain is the time until the Markov chain is \"close\" to its steady state distribution.\nMore precisely, a fundamental result about Markov chains is that a finite state irreducible aperiodic chain has a unique stationary distribution \u03c0 and, regardless of the initial state, the time-t distribution of the chain converges to \u03c0 as t tends to infinity. Mixing time refers to any of several variant formalizations of the idea: how large must t be until the time-t distribution is approximately \u03c0 ? One variant, variation distance mixing time, is defined as the smallest t such that\n\n \n \n \n \n |\n \n Pr\n (\n \n X\n \n t\n \n \n \u2208\n A\n )\n \u2212\n \u03c0\n (\n A\n )\n \n |\n \n \u2264\n 1\n \n /\n \n 4\n \n \n {\\displaystyle |\\Pr(X_{t}\\in A)-\\pi (A)|\\leq 1/4}\n for all subsets A of states and all initial states. This is the sense in which Dave Bayer and Persi Diaconis (1992) proved that the number of riffle shuffles needed to mix an ordinary 52 card deck is 7. Mathematical theory focuses on how mixing times change as a function of the size of the structure underlying the chain. For an n-card deck, the number of riffle shuffles needed grows as 1.5 log (n) / log (2). The most developed theory concerns randomized algorithms for #P-Complete algorithmic counting problems such as the number of graph colorings of a given n vertex graph. Such problems can, for sufficiently large number of colors, be answered using the Markov chain Monte Carlo method and showing that the mixing time grows only as n log (n) (Jerrum 1995). This example and the shuffling example possess the rapid mixing property, that the mixing time grows at most polynomially fast in log (number of states of the chain). Tools for proving rapid mixing include arguments based on conductance and the method of coupling. In broader uses of the Markov chain Monte Carlo method, rigorous justification of simulation results would require a theoretical bound on mixing time, and many interesting practical cases have resisted such theoretical analysis.", "images": [], "links": ["Conductance (probability)", "Coupling (probability)", "Dave Bayer", "Digital object identifier", "Graph coloring", "International Standard Book Number", "JSTOR", "Markov chain", "Markov chain Monte Carlo", "Markov chains", "Mathematical Reviews", "Mixing (mathematics)", "Monte Carlo method", "Persi Diaconis", "Probability distribution", "Probability theory", "Randomized algorithms", "Sharp-P-complete", "Shuffle", "Steady state"], "references": ["http://stat-www.berkeley.edu/users/aldous/RWG/book.html", "http://darkwing.uoregon.edu/~dlevin/MARKOV/", "http://www.ams.org/mathscinet-getitem?mr=1161056", "http://www.ams.org/mathscinet-getitem?mr=1201590", "http://www.ams.org/mathscinet-getitem?mr=1369061", "http://www.ams.org/mathscinet-getitem?mr=2466937", "http://doi.org/10.1002%2Frsa.3240070205", "http://doi.org/10.1007%2F978-1-4612-0323-0", "http://doi.org/10.1214%2Faoap%2F1177005705", "http://www.jstor.org/stable/2959752", "https://web.archive.org/web/20040921020230/http://stat-www.berkeley.edu/users/aldous/RWG/book.html"]}, "Variation ratio": {"categories": ["Statistical deviation and dispersion", "Statistical ratios", "Summary statistics for categorical data"], "title": "Variation ratio", "method": "Variation ratio", "url": "https://en.wikipedia.org/wiki/Variation_ratio", "summary": "The variation ratio is a simple measure of statistical dispersion in nominal distributions; it is the simplest measure of qualitative variation.\nIt is defined as the proportion of cases which are not in the mode category:\n\n \n \n \n \n v\n \n :=\n 1\n \u2212\n \n \n \n f\n \n m\n \n \n N\n \n \n ,\n \n \n {\\displaystyle \\mathbf {v} :=1-{\\frac {f_{m}}{N}},}\n where fm is the frequency (number of cases) of the mode, and N is the total number of cases. While a simple measure, it is notable in that some texts and guides suggest or imply that the dispersion of nominal measurements cannot be ascertained. It is defined for instance by (Freeman 1965).\nJust as with the range or standard deviation, the larger the variation ratio, the more differentiated or dispersed the data are; and the smaller the variation ratio, the more concentrated and similar the data are. \nFor example, a group which is 55% female and 45% male has a proportion of 0.55 females and therefore variation ratio of (1.0- 0.55) = 0.45; and is more dispersed in terms of gender than a group which is 95% female and has a variation ratio of only 0.05. Similarly, a group which is 25% Catholic (where Catholic is the modal religious preference) has a variation ratio of 0.75 and is much more dispersed religiously than a group which is 85% Catholic and has a variation ratio of only 0.15.", "images": [], "links": ["Mode (statistics)", "Nominal distribution", "Qualitative variation", "Range (statistics)", "Standard deviation", "Statistical dispersion"], "references": []}, "Tyranny of averages": {"categories": ["All stub articles", "Misuse of statistics", "Statistics stubs"], "title": "Tyranny of averages", "method": "Tyranny of averages", "url": "https://en.wikipedia.org/wiki/Tyranny_of_averages", "summary": "The tyranny of averages is a phrase used in applied statistics to describe the often overlooked fact that the mean does not provide any information about the shape of the probability distribution of a data set or skewness, and that decisions or analysis based on only the mean\u2014as opposed to median and standard deviation\u2014may be faulty.\nA UN Development Program press release discusses a real-world example:\nA new report launched 1 July [2005] warns that in Asia and the Pacific, the rising prosperity and fast growth in populous countries like China and India is hiding widespread extreme poverty in the Least Developed Countries (LDCs). The result is potentially very debilitating to development efforts in the 14 Asia-Pacific LDCs.\nThis \u201ctyranny of averages\u201d to which the report refers tends to mask the stark contrast between the Asia-Pacific LDCs\u2019 sluggish economies and the success of their far more populous neighbours.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Applied statistics", "Law of averages", "Law of large numbers", "Mean", "Median", "Probability distribution", "Skewness", "Standard deviation", "Statistics", "Trimean", "United Nations", "United Nations Development Programme"], "references": ["http://www.undp.org.af/News/2005/docs/20050704_pr_voices_ldcs_publication.pdf", "https://www.jstor.org/stable/2377539"]}, "Polychoric correlation": {"categories": ["Psychometrics", "Summary statistics", "Summary statistics for contingency tables"], "title": "Polychoric correlation", "method": "Polychoric correlation", "url": "https://en.wikipedia.org/wiki/Polychoric_correlation", "summary": "In statistics, polychoric correlation is a technique for estimating the correlation between two theorised normally distributed continuous latent variables, from two observed ordinal variables. Tetrachoric correlation is a special case of the polychoric correlation applicable when both observed variables are dichotomous. These names derive from the polychoric and tetrachoric series which are used for estimation of these correlations. These series were mathematical expansions once but not anymore.", "images": [], "links": ["Correlation", "Factor analysis", "Latent variable", "Level of measurement", "Normal distribution", "Personality test", "Rating scale", "Statistical survey", "Statistics"], "references": ["http://www.john-uebersax.com/stat/tetra.htm", "http://www.john-uebersax.com/stat/xpc.htm", "http://support.sas.com/documentation/cdl/en/procstat/67528/HTML/default/viewer.htm#procstat_corr_syntax01.htm", "https://support.sas.com/documentation/cdl/en/procstat/65543/HTML/default/viewer.htm#procstat_corr_details14.htm", "https://www.statmodel.com/", "https://web.archive.org/web/20160327054012/http://web.missouri.edu/~kolenikovs/stata/", "https://cran.r-project.org/web/packages/polycor/", "https://cran.r-project.org/web/packages/psych/index.html"]}, "Stationary process": {"categories": ["Signal processing", "Stochastic processes"], "title": "Stationary process", "method": "Stationary process", "url": "https://en.wikipedia.org/wiki/Stationary_process", "summary": "In mathematics and statistics, a stationary process (a.k.a. a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over time.\nSince stationarity is an assumption underlying many statistical procedures used in time series analysis, non-stationary data is often transformed to become stationary. The most common cause of violation of stationarity is a trend in the mean, which can be due either to the presence of a unit root or of a deterministic trend. In the former case of a unit root, stochastic shocks have permanent effects, and the process is not mean-reverting. In the latter case of a deterministic trend, the process is called a trend stationary process, and stochastic shocks have only transitory effects after which the variable tends toward a deterministically evolving (non-constant) mean.\nA trend stationary process is not strictly stationary, but can easily be transformed into a stationary process by removing the underlying trend, which is solely a function of time. Similarly, processes with one or more unit roots can be made stationary through differencing. An important type of non-stationary process that does not include a trend-like behavior is a cyclostationary process, which is a stochastic process that varies cyclically with time.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e1/Stationarycomparison.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algorithm", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Augmented Dickey-Fuller test", "Autocorrelation", "Autocovariance", "Autoregressive", "Autoregressive conditional heteroskedasticity", "Autoregressive moving average model", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli scheme", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bochner's theorem", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Circulant matrix", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous time", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Cyclostationary process", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete-time stochastic process", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Eigenfunction", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Ergodicity", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential function", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Filter (signal processing)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fourier series", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hilbert space", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jef Caers", "Johansen test", "Joint distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "LTI system theory", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear", "Linear discriminant analysis", "Linear operator", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "L\u00e9vy process", "M-estimator", "Mann\u2013Whitney U test", "Marginal distribution", "Mathematics", "Maurice Priestley", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean reversion (finance)", "Median", "Median-unbiased estimator", "Medical statistics", "Mehrdad Honarkhah", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving average model", "Muhammad Sahimi", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal increments", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Pejman Tahmasebi", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random process", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal processing", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary ergodic process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical regularity", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic process", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Time-invariant", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "Trend stationary", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "Unit root", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "White noise", "Whittle likelihood", "Wiener\u2013Khinchin theorem", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://eom.springer.de/s/s086360.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4253861", "http://www.ncbi.nlm.nih.gov/pubmed/25245522", "http://journals.aps.org/pre/abstract/10.1103/PhysRevE.91.032401", "http://doi.org/10.1007%2Fs11004-010-9276-7", "http://doi.org/10.1016%2Fj.brainres.2014.09.035", "http://doi.org/10.1103%2FPhysRevE.91.032401", "https://www.otexts.org/fpp/8/1"]}, "Maximal ergodic theorem": {"categories": ["All stub articles", "Ergodic theory", "Probability stubs", "Probability theorems", "Theorems in dynamical systems"], "title": "Maximal ergodic theorem", "method": "Maximal ergodic theorem", "url": "https://en.wikipedia.org/wiki/Maximal_ergodic_theorem", "summary": "The maximal ergodic theorem is a theorem in ergodic theory, a discipline within mathematics.\nSuppose that \n \n \n \n (\n X\n ,\n \n \n B\n \n \n ,\n \u03bc\n )\n \n \n {\\displaystyle (X,{\\mathcal {B}},\\mu )}\n is a probability space, that \n \n \n \n T\n :\n X\n \u2192\n X\n \n \n {\\displaystyle T:X\\to X}\n is a (possibly noninvertible) measure-preserving transformation, and that \n \n \n \n f\n \u2208\n \n L\n \n 1\n \n \n (\n \u03bc\n )\n \n \n {\\displaystyle f\\in L^{1}(\\mu )}\n . Define \n \n \n \n \n f\n \n \u2217\n \n \n \n \n {\\displaystyle f^{*}}\n by\n\n \n \n \n \n f\n \n \u2217\n \n \n =\n \n sup\n \n N\n \u2265\n 1\n \n \n \n \n 1\n N\n \n \n \n \u2211\n \n i\n =\n 0\n \n \n N\n \u2212\n 1\n \n \n f\n \u2218\n \n T\n \n i\n \n \n .\n \n \n {\\displaystyle f^{*}=\\sup _{N\\geq 1}{\\frac {1}{N}}\\sum _{i=0}^{N-1}f\\circ T^{i}.}\n Then the maximal ergodic theorem states that\n\n \n \n \n \n \u222b\n \n \n f\n \n \u2217\n \n \n >\n \u03bb\n \n \n f\n \n d\n \u03bc\n \u2265\n \u03bb\n \u22c5\n \u03bc\n {\n \n f\n \n \u2217\n \n \n >\n \u03bb\n }\n \n \n {\\displaystyle \\int _{f^{*}>\\lambda }f\\,d\\mu \\geq \\lambda \\cdot \\mu \\{f^{*}>\\lambda \\}}\n for any \u03bb \u2208 R.\nThis theorem is used to prove the point-wise ergodic theorem.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg"], "links": ["ArXiv", "Digital object identifier", "Ergodic theorem", "Ergodic theory", "International Standard Book Number", "Mathematics", "Measure-preserving transformation", "Probability", "Probability space", "Theorem"], "references": ["http://arxiv.org/abs/math/0004070", "http://doi.org/10.1214/074921706000000266"]}, "Pignistic probability": {"categories": ["Decision theory", "Probability interpretations"], "title": "Pignistic probability", "method": "Pignistic probability", "url": "https://en.wikipedia.org/wiki/Pignistic_probability", "summary": "In decision theory, a pignistic probability is a probability that a rational person will assign to an option when required to make a decision. \nA person may have, at one level certain beliefs or a lack of knowledge, or uncertainty, about the options and their actual likelihoods. However, when it is necessary to make a decision (such as deciding whether to place a bet), the behaviour of the rational person would suggest that the person has assigned a set of regular probabilities to the options. These are the pignistic probabilities.\nThe term was coined by Philippe Smets, and stems from the Latin pignus, a bet. He contrasts the pignistic level, where one might take action, with the credal level, where one interprets the state of the world:\n\nThe transferable belief model is based on the assumption that beliefs manifest themselves at two mental levels: the \u2018credal\u2019 level where beliefs are entertained and the \u2018pignistic\u2019 level where beliefs are used to make decisions (from \u2018credo\u2019 I believe and \u2018pignus\u2019 a bet, both in Latin). Usually these two levels are not distinguished and probability functions are used to quantify beliefs at both levels. The justification for the use of probability functions is usually linked to \u201crational\u201d behavior to be held by an ideal agent involved in some decision contexts.A pignistic probability transform will calculate these pignistic probabilities from a structure that describes belief structures.", "images": [], "links": ["Decision theory", "Gambling", "Paris", "Philippe Smets", "Probability", "Stockholm", "Transferable belief model"], "references": ["http://iridia.ulb.ac.be/~psmets/Data-Fusion.pdf"]}, "Rankit": {"categories": ["Normal distribution", "Statistical charts and diagrams"], "title": "Rankit", "method": "Rankit", "url": "https://en.wikipedia.org/wiki/Rankit", "summary": "In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data. They are primarily used in the normal probability plot, a graphical technique for normality testing.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2c/Normal_probability_plot.gif"], "links": ["Chester Ittner Bliss", "Expected value", "Graphical technique", "Independent identically-distributed random variables", "Normal distribution", "Normal probability plot", "Normality test", "Order statistic", "Probability distribution", "Probit", "Q-Q plot", "Scatter plot", "Standard normal distribution", "Statistics", "Variance"], "references": ["http://www.itl.nist.gov/div898/handbook/eda/section3/normprpl.htm"]}, "Inverse matrix gamma distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2012", "Continuous distributions", "Multivariate continuous distributions", "Random matrices"], "title": "Inverse matrix gamma distribution", "method": "Inverse matrix gamma distribution", "url": "https://en.wikipedia.org/wiki/Inverse_matrix_gamma_distribution", "summary": "In statistics, the inverse matrix gamma distribution is a generalization of the inverse gamma distribution to positive-definite matrices. It is a more general version of the inverse Wishart distribution, and is used similarly, e.g. as the conjugate prior of the covariance matrix of a multivariate normal distribution or matrix normal distribution. The compound distribution resulting from compounding a matrix normal with an inverse matrix gamma prior over the covariance matrix is a generalized matrix t-distribution.This reduces to the inverse Wishart distribution with \n \n \n \n \u03b2\n =\n 2\n ,\n \u03b1\n =\n \n \n n\n 2\n \n \n \n \n {\\displaystyle \\beta =2,\\alpha ={\\frac {n}{2}}}\n .", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Compound distribution", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Covariance matrix", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized matrix t-distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse Wishart distribution", "Inverse gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix (mathematics)", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate gamma function", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Positive-definite matrix", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale matrix", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": []}, "Inverse-Wishart distribution": {"categories": ["Conjugate prior distributions", "Continuous distributions", "Exponential family distributions", "Multivariate continuous distributions"], "title": "Inverse-Wishart distribution", "method": "Inverse-Wishart distribution", "url": "https://en.wikipedia.org/wiki/Inverse-Wishart_distribution", "summary": "In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices. In Bayesian statistics it is used as the conjugate prior for the covariance matrix of a \nmultivariate normal distribution.\nWe say \n \n \n \n \n X\n \n \n \n {\\displaystyle \\mathbf {X} }\n follows an inverse Wishart distribution, denoted as \n \n \n \n \n X\n \n \u223c\n \n \n \n W\n \n \n \n \u2212\n 1\n \n \n (\n \n \n \u03a8\n \n \n ,\n \u03bd\n )\n \n \n {\\displaystyle \\mathbf {X} \\sim {\\mathcal {W}}^{-1}({\\mathbf {\\Psi } },\\nu )}\n , if its inverse \n \n \n \n \n \n X\n \n \n \u2212\n 1\n \n \n \n \n {\\displaystyle \\mathbf {X} ^{-1}}\n has a Wishart distribution \n \n \n \n \n \n W\n \n \n (\n \n \n \n \u03a8\n \n \n \n \u2212\n 1\n \n \n ,\n \u03bd\n )\n \n \n {\\displaystyle {\\mathcal {W}}({\\mathbf {\\Psi } }^{-1},\\nu )}\n . Important identities have been derived for Inverse-Wishart distribution.", "images": [], "links": ["ARGUS distribution", "Academic Press", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Complex inverse Wishart distribution", "Compound Poisson distribution", "Conformable matrix", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverse multivariate gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kanti V. Mardia", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Marginalize out", "Matrix-exponential distribution", "Matrix (mathematics)", "Matrix gamma distribution", "Matrix inverse", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate gamma function", "Multivariate normal", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Positive-definite matrix", "Prior knowledge for pattern recognition", "Prior probability", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real numbers", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale matrix", "Scaled inverse chi-squared distribution", "Schur complement", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Trace (linear algebra)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Univariate", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.sciencedirect.com/science/article/pii/0047259X79900563", "http://arxiv.org/abs/1311.0634", "http://doi.org/10.1016%2F0047-259x(79)90056-3", "http://doi.org/10.1109%2Ftcbb.2013.143", "http://doi.org/10.1111%2Fj.1467-9892.2010.00686.x", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6654120&tag=1", "https://www.amazon.com/Bayesian-Analysis-Chapman-Statistical-Science/dp/1439840954"]}, "Monte Carlo methods for option pricing": {"categories": ["Monte Carlo methods in finance", "Options (finance)"], "title": "Monte Carlo methods for option pricing", "method": "Monte Carlo methods for option pricing", "url": "https://en.wikipedia.org/wiki/Monte_Carlo_methods_for_option_pricing", "summary": "In mathematical finance, a Monte Carlo option model uses Monte Carlo methods to calculate the value of an option with multiple sources of uncertainty or with complicated features. The first application to option pricing was by Phelim Boyle in 1977 (for European options). In 1996, M. Broadie and P. Glasserman showed how to price Asian options by Monte Carlo. In 2001 F. A. Longstaff and E. S. Schwartz developed a practical Monte Carlo method for pricing American-style options.\n\n", "images": [], "links": ["American option", "Amortising swap", "Asian option", "Asian options", "Asset swap", "BOPM", "Backspread", "Backward induction", "Barrier option", "Basis swap", "Basket option", "Bear spread", "Binary option", "Binomial options pricing model", "Black model", "Black\u2013Scholes", "Black\u2013Scholes model", "Bond (finance)", "Bond option", "Bond valuation", "Box spread (options)", "Bruno Dupire", "Buffon's needle", "Bull spread", "Butterfly (options)", "Calendar spread", "Call option", "Cholesky decomposition", "Chooser option", "Claremont Graduate University", "Cliquet", "Closed-form expression", "Collar (finance)", "Collateralized debt obligation", "Collateralized mortgage obligation", "Commodity markets", "Commodore option", "Comparison of risk analysis Microsoft Excel add-ins", "Compound option", "Conditional variance swap", "Constant maturity swap", "Constant proportion portfolio insurance", "Consumer debt", "Contango", "Contract for difference", "Convergence (mathematics)", "Corporate bond", "Correlation", "Correlation swap", "Covered call", "Credit-linked note", "Credit default option", "Credit default swap", "Credit derivative", "Credit spread (options)", "Currency future", "Currency swap", "Datar\u2013Mathews method for real option valuation", "Debit spread", "Derivative (finance)", "Derivatives market", "Diagonal spread", "Digital object identifier", "Dividend future", "Dividend swap", "Eduardo Schwartz", "Employee stock option", "Energy derivative", "Equity-linked note", "Equity derivative", "Equity swap", "European option", "Exchange rate", "Exercise (options)", "Exotic derivative", "Exotic derivatives", "Exotic option", "Expected value", "Expiration (options)", "Fence (finance)", "Financial economics", "Finite difference methods for option pricing", "Fixed income", "Foreign-exchange option", "Foreign exchange derivative", "Foreign exchange swap", "Forward contract", "Forward market", "Forward price", "Forward rate", "Forward rate agreement", "Forward start option", "Francis Longstaff", "Frank J. Fabozzi", "Freight derivative", "Fund derivative", "Futures contract", "Geometric Brownian motion", "Georges-Louis Leclerc, Comte de Buffon", "Government debt", "Great Recession", "Greeks (finance)", "HEC Lausanne", "Heston model", "Inflation", "Inflation derivative", "Inflation swap", "Interest rate", "Interest rate derivative", "Interest rate future", "Interest rate option", "Interest rate swap", "Intermarket Spread", "International Standard Book Number", "Iron butterfly (options strategy)", "Iron condor", "Joint probability", "Jump process", "Lattice model (finance)", "Least squares regression", "Lognormal distribution", "Lookback option", "Louisiana State University", "Margin (finance)", "Margrabe's formula", "Mathematical finance", "Mean reverting process", "Moneyness", "Monte Carlo method", "Monte Carlo methods in finance", "Mortgage-backed security", "Mountain range (options)", "Municipal debt", "Normal backwardation", "Normal distribution", "Norwegian School of Management", "Numerical methods", "Oklahoma State University\u2013Stillwater", "Open interest", "Option (finance)", "Option style", "Option time value", "Options spread", "Options strategy", "Overnight indexed swap", "Parameter", "Path dependence", "Peter Jaeckel", "Phelim Boyle", "Pin risk (options)", "Power reverse dual-currency note", "Present value", "Probability distribution", "Property derivative", "Protective put", "Put option", "Put\u2013call parity", "Rainbow option", "Random", "Random sampling", "Ratio spread", "Rational pricing", "Real options", "Real options analysis", "Real options valuation", "Risk-free interest rate", "Risk neutrality", "Risk reversal", "Short-rate model", "Short rate model", "Simulation", "Single-stock futures", "Slippage (finance)", "Springer-Verlag", "Stanislaw Ulam", "State prices", "Statistical parameter", "Stochastic process", "Stochastic volatility", "Stock", "Stock market index future", "Straddle", "Strangle (options)", "Strike price", "Swap (finance)", "Swaption", "Tax policy", "Total return swap", "Trinomial tree", "Underlying", "Underlying instrument", "Valuation of options", "Vanilla option", "Vanna\u2013Volga pricing", "Variance swap", "Vertical spread", "Volatility (finance)", "Volatility swap", "Warrant (finance)", "Weather derivative", "Year-on-Year Inflation-Indexed Swap", "Yield curve", "Zero-Coupon Inflation-Indexed Swap", "Zero coupon swap"], "references": ["http://marcoagd.usuarios.rdc.puc-rio.br/faq4.html", "http://25yearsofprogramming.com/blog/20070412c-montecarlostockprices.htm", "http://www.erasmusenergy.com/downloadattachment.php?aId=4b0d2207d4169ee155591c70efa19c63&articleId=139", "http://www.fea.com/resources/pdf/swaptions.pdf", "http://www.global-derivatives.com/index.php?option=com_content&task=view&id=26#MCS", "http://www.global-derivatives.com/maths/k-o.php", "http://www.kamakuraco.com/Blog/tabid/231/EntryId/347/Pitfalls-in-Asset-and-Liability-Management-One-Factor-Term-Structure-Models.aspx", "http://www.quantnotes.com/publications/papers/Fink-montecarlo.pdf", "http://www.riskglossary.com/link/monte_carlo_method.htm", "http://www.savvysoft.com/treevsmontecarlo.htm", "http://www.smartquant.com/references/MonteCarlo/mc6.pdf", "http://www.columbia.edu/~mnb2/broadie/Assets/bg_ms_1996.pdf", "http://www.bus.lsu.edu/academics/finance/faculty/dchance/Instructional/TN96-03.pdf", "http://www.math.nyu.edu/research/carrp/papers/pdf/hjm.pdf", "http://spears.okstate.edu/home/tlk/legacy/fin5883/notes6_s05.doc", "http://spears.okstate.edu/home/tlk/legacy/fin5883/notes7_s05.doc", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.194.9001", "http://finance-old.bi.no/~bernt/gcc_prog/recipes/recipes/node12.html", "http://repositories.cdlib.org/anderson/fin/1-01/", "http://doi.org/10.1016%2F0304-405x(77)90005-8", "http://doi.org/10.1093%2Frfs%2F14.1.113", "http://doi.org/10.1287%2Fmnsc.42.2.269", "http://www.realoptions.org/papers2005/Cortazar_GU052RealOptionsParis.pdf", "http://ideas.repec.org/a/eee/jfinec/v4y1977i3p323-338.html", "https://books.google.com/books?id=wF8yVzLI6EYC&pg=PA138&lpg=PA138&dq=cmo+valuation+fabozzi+simulation&source=bl&ots=zSvgwSKm2V&sig=lW48IuS6CEQAch0f-uGVyHdIg3A&hl=en&ei=tcfATqPPB8SKhQfGovGzBA&sa=X&oi=book_result&ct=result&resnum=4&ved=0CC4Q6AEwAw#v=onepage&q&f=false"]}, "Online NMF": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2015", "CS1 maint: Explicit use of et al.", "CS1 maint: Multiple names: authors list", "Linear algebra", "Machine learning algorithms", "Matrix theory"], "title": "Non-negative matrix factorization", "method": "Online NMF", "url": "https://en.wikipedia.org/wiki/Non-negative_matrix_factorization", "summary": "Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms or muscular activity, non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.\nNMF finds applications in such fields as astronomy, computer vision, document clustering, chemometrics, audio signal processing, recommender systems, and bioinformatics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f2/Fractional_Residual_Variances_comparison%2C_PCA_and_NMF.pdf", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/NMF.png", "https://upload.wikimedia.org/wikipedia/commons/e/e8/Restricted_Boltzmann_machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["1980s", "Acta Neuropathologica", "Active set", "Algorithm", "Amnon Shashua", "Andrzej Cichocki", "Anomaly detection", "ArXiv", "Artificial neural network", "Artificial neural networks", "Association for Computing Machinery", "Association rule learning", "Astronomy", "Astronomy & Astrophysics", "Atmospheric Environment (journal)", "Audio signal processing", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Bibcode", "Bioinformatics", "Bioinformatics (journal)", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Chemometrics", "Chemometrics and Intelligent Laboratory Systems", "Chinese Science Bulletin", "Circumstellar disks", "CiteSeerX", "Cluster analysis", "Cluster indicator", "Collaborative filtering", "Computational Intelligence and Neuroscience", "Computational and Mathematical Organization Theory", "Computational learning theory", "Computer vision", "Conditional random field", "Conference on Neural Information Processing Systems", "Convex combination", "Convolutional neural network", "DBSCAN", "DNA methylation", "Data clustering", "Data mining", "Data stream", "Decision tree learning", "DeepDream", "Deep learning", "Digital object identifier", "Dimension reduction", "Dimensionality reduction", "Document-term matrix", "Edward A. 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Lawton"], "references": ["http:ftp://ftp.kyb.tuebingen.mpg.de/pub/mpi-memos/pdf/nmftr.pdf", "http://books.nips.cc/papers/files/nips18/NIPS2005_0203.pdf", "http://books.nips.cc/papers/files/nips24/NIPS2011_1189.pdf", "http://papers.nips.cc/paper/1861-algorithms-for-non-negative-matrix-factorization.pdf", "http://papers.nips.cc/paper/2672-exponential-family-harmoniums-with-an-application-to-information-retrieval", "http://cslt.riit.tsinghua.edu.cn:8081/homepages/wangd/public/pdf/cnsc-tsp.pdf", "http://www.hindawi.com/journals/cin/2009/785152.abs.html", "http://research.microsoft.com/pubs/119077/DNMF.pdf", "http://www.sciencedirect.com/science/article/pii/S0024379511002199#", "http://www.springerlink.com/index/7285V70531634264.pdf", "http://www.mpi-inf.mpg.de/~rgemulla/publications/rj10481rev.pdf", "http://www2.imm.dtu.dk/pubdb/views/publication_details.php?id=5666", "http://www.cs.cmu.edu/~enron/", "http://www.columbia.edu/~jwp2128/Teaching/E4903/papers/nmf_nature.pdf", "http://www.cs.duke.edu/~ychen/Phoenix_TNSM.pdf", "http://users.cis.fiu.edu/~taoli/pub/NMFpLSIequiv.pdf", "http://www.cc.gatech.edu/~hpark/papers/2011_paper_hpscbook_ntf.pdf", "http://www.cc.gatech.edu/~hpark/papers/simax-nmf.pdf", "http://www.cc.gatech.edu/~jingu/docs/2011_paper_sisc_nmf.pdf", "http://adsabs.harvard.edu/abs/1982ITNS...29.1310D", "http://adsabs.harvard.edu/abs/1989AtmEn..23.2289S", "http://adsabs.harvard.edu/abs/1995AtmEn..29.1705A", "http://adsabs.harvard.edu/abs/1999Natur.401..788L", "http://adsabs.harvard.edu/abs/2006ChSBu..51....7L", "http://adsabs.harvard.edu/abs/2007AJ....133..734B", "http://adsabs.harvard.edu/abs/2008ISPM...25R.142C", "http://adsabs.harvard.edu/abs/2008PLSCB...4E0029D", "http://adsabs.harvard.edu/abs/2009ApJ...694L.148L", "http://adsabs.harvard.edu/abs/2012ApJ...755L..28S", "http://adsabs.harvard.edu/abs/2012ITSP...60.2882G", "http://adsabs.harvard.edu/abs/2012MNRAS.427..948A", "http://adsabs.harvard.edu/abs/2012PLoSO...746331T", "http://adsabs.harvard.edu/abs/2012arXiv1212.4777A", "http://adsabs.harvard.edu/abs/2013ITSP...61...44W", "http://adsabs.harvard.edu/abs/2015A&A...581A..24W", "http://adsabs.harvard.edu/abs/2016ApJ...824..117P", "http://adsabs.harvard.edu/abs/2018ApJ...852..104R", "http://jialu.cs.illinois.edu/paper/sdm2013-liu.pdf", "http://jmlr.csail.mit.edu/proceedings/papers/v28/arora13.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.136.3837", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.8281", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.21.24", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.300.2851", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.301.1771", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.9135", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.407.318", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.419.798", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.3485", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.707.7348", "http://rio.ecs.umass.edu/mnilpub/papers/ecmlpkdd2014-yin.pdf", "http://ranger.uta.edu/~chqding/papers/NMF-SDM2005.pdf", "http://www.cs.utexas.edu/~cjhsieh/nmf_kdd11.pdf", "http://cosco.hiit.fi/Articles/ecml02.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2447881", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2688815", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3245233", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3487913", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3588146", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4313078", "http://www.ncbi.nlm.nih.gov/pubmed/10548103", "http://www.ncbi.nlm.nih.gov/pubmed/11989846", "http://www.ncbi.nlm.nih.gov/pubmed/15946864", "http://www.ncbi.nlm.nih.gov/pubmed/17298233", "http://www.ncbi.nlm.nih.gov/pubmed/17483501", "http://www.ncbi.nlm.nih.gov/pubmed/17716011", "http://www.ncbi.nlm.nih.gov/pubmed/18654623", "http://www.ncbi.nlm.nih.gov/pubmed/18785855", 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"https://arxiv.org/pdf/cs/0202009", "https://dx.doi.org/10.1109/IJCNN.2004.1381036"]}, "Whittle likelihood": {"categories": ["Frequency-domain analysis", "Normal distribution", "Signal estimation", "Statistical inference", "Statistical models", "Statistical signal processing", "Time series", "Time series models"], "title": "Whittle likelihood", "method": "Whittle likelihood", "url": "https://en.wikipedia.org/wiki/Whittle_likelihood", "summary": "In statistics, Whittle likelihood is an approximation to the likelihood function of a stationary Gaussian time series. It is named after the mathematician and statistician Peter Whittle, who introduced it in his PhD thesis in 1951.\nIt is commonly utilized in time series analysis and signal processing for parameter estimation and signal detection.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian 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"Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete Fourier transform", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fourier domain", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian distribution", "Gaussian process", "General linear model", "Generalized linear model", "Geographic information system", 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"Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Whittle (mathematician)", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Power spectral density", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling theorem", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal processing", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spectral leakage", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical signal processing", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Student-t distribution", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "White noise", "Wilcoxon signed-rank test", "Window function", "Z-test"], "references": ["http://www.stat.colostate.edu/statresearch/stattechreports.html", "http://adsabs.harvard.edu/abs/1992PhRvD..46.5236F", "http://adsabs.harvard.edu/abs/2011CQGra..28a5010R", "http://adsabs.harvard.edu/abs/2011PhRvD..84l2004R", "http://adsabs.harvard.edu/abs/2015PhRvD..92f4011E", "http://www4.stat.ncsu.edu/~sghosal/papers/specden.pdf", "http://people.stern.nyu.edu/churvich/TimeSeries/Handouts/Whittle.pdf", "http://arxiv.org/abs/0804.3853", "http://arxiv.org/abs/1109.0442", "http://arxiv.org/abs/1506.00185", "http://arxiv.org/abs/gr-qc/9209010", "http://doi.org/10.1002%2F0471667196.ess0753", "http://doi.org/10.1007%2F978-1-4612-0667-5_7", "http://doi.org/10.1080%2F03610910600880203", "http://doi.org/10.1088%2F0264-9381%2F28%2F1%2F015010", "http://doi.org/10.1093%2Fbiomet%2F91.1.211", "http://doi.org/10.1103%2FPhysRevD.46.5236", "http://doi.org/10.1103%2FPhysRevD.84.122004", "http://doi.org/10.1103%2FPhysRevD.92.064011", "http://doi.org/10.1109%2FTIT.1960.1057571", "http://doi.org/10.1198%2F016214504000000557"]}, "Pareto principle": {"categories": ["Adages", "All articles with unsourced statements", "Articles with unsourced statements from January 2008", "CS1 maint: Uses authors parameter", "Commons category link is on Wikidata", "Rules of thumb", "Statistical laws", "Statistical principles", "Tails of probability distributions", "Vilfredo Pareto", "Webarchive template wayback links"], "title": "Pareto principle", "method": "Pareto principle", "url": "https://en.wikipedia.org/wiki/Pareto_principle", "summary": "The Pareto principle (also known as the 80/20 rule, the law of the vital few, or the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes. Management consultant Joseph M. Juran suggested the principle and named it after Italian economist Vilfredo Pareto, who noted the 80/20 connection while at the University of Lausanne in 1896, as published in his first work, Cours d'\u00e9conomie politique. Essentially, Pareto showed that approximately 80% of the land in Italy was owned by 20% of the population.\nIt is an axiom of business management that \"80% of sales come from 20% of clients\". Richard Koch authored the book, The 80/20 Principle, which illustrated some practical applications of the Pareto principle in business management and life.Mathematically, the 80/20 rule is roughly followed by a power law distribution (also known as a Pareto distribution) for a particular set of parameters, and many natural phenomena have been shown empirically to exhibit such a distribution.The Pareto principle is only tangentially related to Pareto efficiency. Pareto developed both concepts in the context of the distribution of income and wealth among the population.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/11/Peas_in_pods_-_Studio.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["1% rule (Internet culture)", "10/90 gap", "Agent-based social simulation", "Baseball", "Benford's law", "Broken windows", "Brush fire", "COCOMO", "Computer science", "Contact tracing", "Decentralised system", "Derek J. de Solla Price", "Digital object identifier", "Diminishing returns", "Distribution of income", "Dunedin Multidisciplinary Health and Development Study", "Economist", "Elephant flow", "Epidemic", "Free-to-play", "Gini index", "Hoover index", "Income inequality metrics", "International Standard Book Number", "Joseph M. Juran", "Joshua M. Epstein", "Keystone species", "Logistics", "Long tail", "Lowell Arthur", "MIT Press", "Management consultant", "Mathematical economics", "Megadiverse countries", "Microsoft", "Nassim Taleb", "Ninety-ninety rule", "Normal distribution", "Occupational health and safety", "Optimization (computer science)", "Pareto chart", "Pareto distribution", "Pareto efficiency", "Pareto index", "Pareto priority index", "Parkinson's law", "Pea", "Per Bak", "Power law", "Principle of least effort", "Profit risk", "PubMed Identifier", "Rank-size distribution", "Richard Koch", "Robert Axtell", "Six Sigma", "Stop-and-frisk", "Sturgeon's law", "Sugarscape", "Super-spreader", "The Black Swan (Taleb book)", "The Guardian", "The New York Times", "Theil index", "Time management", "Total quality management", "University of Lausanne", "Vilfredo Pareto", "Vitality curve", "Wayback Machine", "Wealth concentration", "Wins Above Replacement", "Zipf's law"], "references": ["http://www.ryerson.ca/woodcock/", "http://management.about.com/cs/generalmanagement/a/Pareto081202.htm", "http://buildthefire.com/pareto-principle-accomplishing-goals-with-purpose/", "http://www.crn.com/news/security/18821726/microsofts-ceo-80-20-rule-applies-to-bugs-not-just-features.htm", "http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html", "http://speedendurance.com/2008/11/20/training-and-the-80-20-rule-of-paretos-principle/", "http://www.ncbi.nlm.nih.gov/pubmed/16292292", "http://www.ncbi.nlm.nih.gov/pubmed/16292310", "http://www.uscg.mil/hq/cg5/cg5211/docs/RBDM_Files/PDF/RBDM_Guidelines/Volume%202/Volume%202-Chapter%206.pdf", "http://doi.org/10.1002%2F(SICI)1097-4571(199007)41:5%3C368::AID-ASI8%3E3.0.CO;2-C", "http://doi.org/10.1016%2F0094-1190(80)90043-1", "http://doi.org/10.1016%2FS0165-1765(01)00524-9", "http://doi.org/10.1016%2Fj.econlet.2005.08.020", "http://doi.org/10.1038%2F438293a", "http://doi.org/10.1038%2Fnature04153", "http://doi.org/10.1080%2F00401706.1986.10488093", "http://www.poorcity.richcity.org/calculator/?quantiles=82.4,17.6%7C17.6,82.4", "http://hdr.undp.org/en/reports/global/hdr1992/chapters/", "https://www.beyondtheboxscore.com/2010/6/4/1501048/applying-the-parento-principle-80", "https://www.entrepreneur.com/article/229294", "https://books.google.com/?id=xXvelSs2caQC", "https://www.nytimes.com/2008/03/03/business/03juran.html", "https://www.pinnacle.com/en/betting-articles/betting-strategy/the-pareto-principle-of-prediction", "https://www.scribd.com/doc/3664882/The-8020-Principle-The-Secret-to-Success-by-Achieving-More-with-Less", "https://www.theguardian.com/science/2016/dec/12/high-social-cost-adults-can-be-identified-from-as-young-as-three-says-study", "https://www.wsj.com/articles/top-20-of-americans-will-pay-87-of-income-tax-1523007001", "https://books.google.co.in/books?id=QtVmCgAAQBAJ&pg=PA8&lpg=PA8&dq=The+Pareto+principle+has+many+applications+in+quality+control&source=bl&ots=qFmwW19c5q&sig=4f0n7ESBCiqhG5xY7ri0NXX5fD0&hl=en&sa=X&ved=0ahUKEwiFo4_YpN7YAhULNbwKHeEQA044ChDoAQg0MAI#v=onepage&q=The%20Pareto%20principle%20has%20many%20applications%20in%20quality%20control&f=false", "https://web.archive.org/web/20080528063231/http://www.ma.hw.ac.uk/~des/HWM00-26.pdf", "https://web.archive.org/web/20090802002952/http://www.projo.com/opinion/contributors/content/CT_weinberg27_07-27-09_HQF0P1E_v15.3f89889.html", "https://web.archive.org/web/20170906182706/http://www.nytimes.com/2008/03/03/business/03juran.html", "https://arxiv.org/PS_cache/cond-mat/pdf/0412/0412004v3.pdf", "https://www.heritage.org/poverty-and-inequality/report/the-rich-pay-more-taxes-top-20-percent-pay-record-share-income-taxes"]}, "Experimental design diagram": {"categories": ["All articles needing additional references", "All stub articles", "Articles needing additional references from August 2007", "Design of experiments", "Science stubs"], "title": "Experimental design diagram", "method": "Experimental design diagram", "url": "https://en.wikipedia.org/wiki/Experimental_design_diagram", "summary": "Experimental Design Diagram (EDD) is a diagram used in science classrooms to design an experiment. This diagram helps to identify the essential components of an experiment. It includes a title, the research hypothesis and null hypothesis, the independent variable, the levels of the independent variable, the number of trials, the dependent variable, the operational definition of the dependent variable and the constants.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/75/Science-symbol-2.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Constant (mathematics)", "Dependent variable", "Design of experiments", "Diagram", "Experiment", "Hypothesis", "Independent variable"], "references": []}, "Etemadi's inequality": {"categories": ["Probabilistic inequalities", "Statistical inequalities"], "title": "Etemadi's inequality", "method": "Etemadi's inequality", "url": "https://en.wikipedia.org/wiki/Etemadi%27s_inequality", "summary": "In probability theory, Etemadi's inequality is a so-called \"maximal inequality\", an inequality that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound. The result is due to Nasrollah Etemadi.\n\n", "images": [], "links": ["Chebyshev's inequality", "Expected value", "Finite set", "Independent random variables", "Inequality (mathematics)", "International Standard Book Number", "JSTOR", "Kolmogorov's inequality", "Mathematical Reviews", "Nasrollah Etemadi", "Partial sum", "Probability", "Probability space", "Probability theory", "Sankhya (journal)"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0844022", "http://www.jstor.org/stable/25050536"]}, "Hammersley\u2013Clifford theorem": {"categories": ["All stub articles", "Markov networks", "Probability stubs", "Probability theorems", "Statistical theorems", "Wikipedia articles needing clarification from April 2016"], "title": "Hammersley\u2013Clifford theorem", "method": "Hammersley\u2013Clifford theorem", "url": "https://en.wikipedia.org/wiki/Hammersley%E2%80%93Clifford_theorem", "summary": "The Hammersley\u2013Clifford theorem is a result in probability theory, mathematical statistics and statistical mechanics, that gives necessary and sufficient conditions under which a strictly positive probability distribution can be represented as a Markov network (also known as a Markov random field). It is the fundamental theorem of random fields. It states that a probability distribution that has a strictly positive mass or density satisfies one of the Markov properties with respect to an undirected graph G if and only if it is a Gibbs random field, that is, its density can be factorized over the cliques (or complete subgraphs) of the graph.\nThe relationship between Markov and Gibbs random fields was initiated by Roland Dobrushin and Frank Spitzer in the context of statistical mechanics. The theorem is named after John Hammersley and Peter Clifford who proved the equivalence in an unpublished paper in 1971. Simpler proofs using the inclusion\u2013exclusion principle were given independently by Geoffrey Grimmett, Preston and Sherman in 1973, with a further proof by Julian Besag in 1974.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e6/Neighborhood_Intersections.png", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/en/7/7b/A_simple_Markov_network.png", "https://upload.wikimedia.org/wikipedia/en/f/f7/Merging_two_factorizations_of_a_positive_mass_function.png"], "links": ["Bulletin of the London Mathematical Society", "Complete graph", "Conditional independence", "Conditional random field", "Digital object identifier", "Frank Spitzer", "Geoffrey Grimmett", "Gibbs random field", "Inclusion\u2013exclusion principle", "International Standard Book Number", "JSTOR", "John Hammersley", "Journal of the Royal Statistical Society, Series B", "Julian Besag", "Markov network", "Markov random field", "Mathematical Reviews", "Mathematical statistics", "Peter Clifford (statistician)", "Probability", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Roland Dobrushin", "Statistical mechanics", "University of Washington"], "references": ["http://repository.upenn.edu/cis_papers/159/", "http://ssli.ee.washington.edu/courses/ee512/handout2.pdf", "http://www.idi.ntnu.no/~helgel/thesis/forelesning.pdf", "http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=TPRBAU000013000002000197000001&idtype=cvips&gifs=yes", "http://www.ams.org/mathscinet-getitem?mr=0321185", "http://www.ams.org/mathscinet-getitem?mr=0329039", "http://www.ams.org/mathscinet-getitem?mr=0373208", "http://www.ams.org/mathscinet-getitem?mr=0405645", "http://www.ams.org/mathscinet-getitem?mr=1064553", "http://doi.org/10.1007/BF02761538", "http://doi.org/10.1112/blms/5.1.81", "http://doi.org/10.1137/1113026", "http://doi.org/10.2307/1426035", "http://doi.org/10.2307/2317621", "http://www.jstor.org/stable/1426035", "http://www.jstor.org/stable/2317621", "http://www.jstor.org/stable/2984812", "http://www.statslab.cam.ac.uk/~grg/books/hammfest/3-pdc.ps", "http://www.statslab.cam.ac.uk/~grg/books/hammfest/hamm-cliff.pdf", "http://www.statslab.cam.ac.uk/~grg/books/jmh.html", "http://www.statslab.cam.ac.uk/~grg/books/pgs.html"]}, "History of statistics": {"categories": ["All articles lacking reliable references", "All articles with unsourced statements", "Articles lacking reliable references from February 2012", "Articles with unsourced statements from February 2012", "Articles with unsourced statements from July 2012", "Articles with unsourced statements from May 2012", "Articles with unsourced statements from September 2010", "Commons category link is on Wikidata", "History of probability and statistics", "History of science by discipline", "Pages using web citations with no URL", "Webarchive template wayback links", "Wikipedia articles needing page number citations from May 2012"], "title": "History of statistics", "method": "History of statistics", "url": "https://en.wikipedia.org/wiki/History_of_statistics", "summary": "The history of statistics in the modern sense dates from the mid-17th century, with the term statistics itself coined in 1749 in German, although there have been changes to the interpretation of the word over time. The development of statistics is intimately connected on the one hand with the development of sovereign states, particularly European states following the Peace of Westphalia (1648); and the other hand with the development of probability theory, which put statistics on a firm theoretical basis; see History of probability.\nIn early times, the meaning was restricted to information about states, particularly demographics such as population. This was later extended to include all collections of information of all types, and later still it was extended to include the analysis and interpretation of such data. In modern terms, \"statistics\" means both sets of collected information, as in national accounts and temperature records, and analytical work which requires statistical inference. Statistical activities are often associated with models expressed using probabilities, hence the connection with probability theory. The large requirements of data processing have made statistics a key application of computing; see history of computing hardware. A number of statistical concepts have an important impact on a wide range of sciences. These include the design of experiments and approaches to statistical inference such as Bayesian inference, each of which can be considered to have their own sequence in the development of the ideas underlying modern statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/33/Bendixen_-_Carl_Friedrich_Gau%C3%9F%2C_1828.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/77/James_lind.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/18/Karl_Pearson%2C_1910.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/89/Laplace_distribution_pdf.png", "https://upload.wikimedia.org/wikipedia/commons/2/24/Libr0310.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e3/Pierre-Simon_Laplace.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/46/R._A._Fischer.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/84/Sir_William_Petty.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/13/Statistical_Society_of_London_-_1837_logo.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["Abraham De Moivre", "Abraham Wald", "Abraham de Moivre", "Accelerated failure time model", "Actuarial science", "Adolphe Quetelet", "Adrien-Marie Legendre", "Agricultural science", "Akaike information criterion", "Al-Kindi", "Alan Turing", "Aleksandr Lyapunov", "Analysis of covariance", "Analysis of variance", "Ancillary statistic", "Anders Hald", "Anders Nicolai Ki\u00e6r", "Anderson\u2013Darling test", "Andrey Kolmogorov", "Anil Kumar Gain", "Annals of Mathematical Statistics", "Antoine Augustin Cournot", "Applied statistics", "Arithmetic mean", "Ars Conjectandi", "Arthur Lyon Bowley", "Asymptotic theory (statistics)", "Augustus De Morgan", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Axiom", "B.O. Koopman", "Ball (mathematics)", "Bar chart", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernstein\u2013von Mises theorem", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biology", "Biometrics (journal)", "Biometrika", "Biometry", "Biostatistics", "Biplot", "Blaise Pascal", "Blinding (medicine)", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Bradley Efron", "Breusch\u2013Godfrey test", "Bruno de Finetti", "Byzantine science", "C. R. Rao", "C. S. Peirce", "Canonical correlation", "Carl Friedrich Gauss", "Cartography", "Categorical variable", "Celestial mechanics", "Census", "Censuses", "Central limit theorem", "Central tendency", "Ceres (dwarf planet)", "Charles Booth (philanthropist)", "Charles Sanders Peirce", "Charles Sanders Peirce bibliography", "Charles Spearman", "Charles Stein (statistician)", "Chemometrics", "Chi-squared test", "Christiaan Huygens", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational problem", "Computational statistics", "Computer", "Computer science", "Confidence interval", "Confounding", "Conjugate prior", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime rates", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cryptologia", "Daniel Bernoulli", "Data", "Data collection", "David R. Cox", "David Salsburg", "Decision science", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic", "Demographic statistics", "Demographics", "Demography", "Dennis Lindley", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete uniform distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dwarf planet", "Econometrics", "Economics", "Edgeworth expansion", "Edgeworth series", "Edmund F. Robertson", "Edward Wright (mathematician)", "Edwin Thompson Jaynes", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Empirical distribution function", "Encyclop\u00e6dia Britannica 2006 Ultimate Reference Suite DVD", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "European science in the Middle Ages", "Evolution", "Experiment", "Experimental psychology", "Exponential family", "Exponential smoothing", "F-test", "F distribution", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fiducial inference", "First-hitting-time model", "Fisher's z-distribution", "Fisher information", "Florence Nightingale", "Forest plot", "Founders of statistics", "Fourier analysis", "Francis Galton", "Francis Ysidro Edgeworth", "Frank P. Ramsey", "Frank Yates", "Frequency analysis", "Frequency distribution", "Frequency domain", "Frequentist", "Frequentist inference", "Frequentist statistics", "Friedman test", "Friedrich Bessel", "G-test", "Games of chance", "Gauss", "Gaussian distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George Boole", "George E. P. Box", "Geostatistics", "German language", "Gerolamo Cardano", "Gertrude Mary Cox", "Giovanni Schiaparelli", "Giovanni Villani", "Goodness of fit", "Gottfried Achenwall", "Granger causality", "Graphical model", "Grouped data", "Gustav Theodor Fechner", "Harald Cram\u00e9r", "Harmonic mean", "Harold Jeffreys", "Herbert Robbins", "Herman Chernoff", "Hermann Laurent", "Heteroscedasticity", "Histogram", "Historiography of science", "History", "History of Florence", "History of agricultural science", "History of algebra", "History of anatomy", "History of anthropology", "History of astronomy", "History of biology", "History of botany", "History of calculus", "History of chemistry", "History of combinatorics", "History of computer science", "History of computing hardware", "History of ecology", "History of economic thought", "History of engineering", "History of evolutionary thought", "History of geography", "History of geology", "History of geometry", "History of geophysics", "History of linguistics", "History of logic", "History of materials science", "History of mathematics", "History of medicine", "History of natural science", "History of neurology and neurosurgery", "History of neuroscience", "History of nutrition", "History of paleontology", "History of pathology", "History of pharmacy", "History of physics", "History of political science", "History of probability", "History of pseudoscience", "History of psychology", "History of science", "History of science and technology in Africa", "History of science and technology in China", "History of science and technology in the Indian subcontinent", "History of science in classical antiquity", "History of science in early cultures", "History of science in the Renaissance", "History of sociology", "History of sustainability", "History of technology", "History of the Peloponnesian War", "History of the social sciences", "History of trigonometry", "History of veterinary medicine", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Howard Raiffa", "Human sex ratio", "Hypothesis", "I.J. Good", "Ian Hacking", "Index of dispersion", "Inductive logic", "Inductive reasoning", "Information science", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse probability", "Isis (journal)", "Isotonic regression", "Italian language", "JSTOR", "Jackknife resampling", "Jakob Bernoulli", "James Lind (physician)", "James Whitbread Lee Glaisher", "Jarque\u2013Bera test", "Jerzy Neyman", "Johann Heinrich Lambert", "Johansen test", "John Arbuthnot", "John Graunt", "John J. O'Connor (mathematician)", "John Lawes", "John Maynard Keynes", "John Tukey", "Jonckheere's trend test", "Joseph Diaz Gergonne", "Joseph Jastrow", "Joseph Louis Lagrange", "Joseph Priestley", "Jos\u00e9-Miguel Bernardo", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society", "Jupiter", "Jurisprudence", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kirstine Smith", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lady tasting tea", "Laplace", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "Leonard Jimmie Savage", "Libration", "Life table", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line chart", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of national and international statistical services", "List of statisticians", "List of statistics articles", "List of timelines", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logarithmic distribution", "Logistic regression", "London", "Loss function", "Lp space", "M-estimator", "MacTutor History of Mathematics archive", "Machine learning", "Mahalanobis distance", "Mann\u2013Whitney U test", "Markov chain Monte Carlo", "Marriage rates", "Mathematical Reviews", "Mathematical science", "Mathematical statistics", "Mathematics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement", "Median", "Median-unbiased estimator", "Medical statistics", "Medicine", "Method of least squares", "Method of moments (statistics)", "Methods engineering", "Minimisation (clinical trials)", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moon", "Mortality rate", "Multi-armed bandit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New Latin", "Non-parametric test", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Nuova Cronica", "Observational study", "Official statistics", "One- and two-tailed tests", "Operations research", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Oxford University", "P-value", "Pafnuty Chebyshev", "Parabolic distribution", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Peace of Westphalia", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Peirce's criterion", "Percentile", "Permutation test", "Philosophical Transactions of the Royal Society of London", "Pie chart", "Pierre-Simon Laplace", "Pierre de Fermat", "Pivotal quantity", "Platea", "Plug-in principle", "Point estimation", "Poisson regression", "Politician", "Polynomial regression", "Population", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prasanta Chandra Mahalanobis", "Prediction interval", "Principal component analysis", "Principle of insufficient reason", "Principle of maximum entropy", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Public administration", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Raised cosine distribution", "Random assignment", "Random sampling", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Ratio estimator", "Regression analysis", "Regression model validation", "Reliability (statistics)", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Richard Dedekind", "Richard von Mises", "Robert Adrain", "Robert Schlaifer", "Robust regression", "Robust statistics", "Roger Cotes", "Roger Joseph Boscovich", "Roman Empire", "Romanticism in science", "Ronald A. Fisher", "Ronald Fisher", "Rothamsted Experimental Station", "Rothamsted Research Station", "Royal Mint", "Royal Statistical Society", "Run chart", "S. N. Bernstein", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Kotz", "Saturn", "Scale parameter", "Scatter plot", "Science in the medieval Islamic world", "Scientific Revolution", "Scientific control", "Scientific method", "Score test", "Scurvy", "Seasonal adjustment", "Seebohm Rowntree", "Semicircle", "Semiparametric regression", "Sequential analysis", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance test", "Simon Singh", "Simon Stevin", "Simple linear regression", "Simultaneous equations model", "Sir John Sinclair", "Sir John Sinclair, 1st Baronet", "Skewness", "Social statistics", "Society for Industrial and Applied Mathematics", "Sociology", "Sociology of the history of science", "Sovereign state", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "State (polity)", "Stationary process", "Statistic", "Statistical Account of Scotland", "Statistical Accounts of Scotland", "Statistical Methods for Research Workers", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical mechanics", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen M. Stigler", "Stephen Stigler", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficiency (statistics)", "Sufficient statistic", "Suicide rates", "Survey methodology", "Survival analysis", "Survival function", "Sylvestre Lacroix", "System identification", "Temperature record", "The American Statistician", "The Correlation between Relatives on the Supposition of Mendelian Inheritance", "The Design of Experiments", "The Doctrine of Chances", "The Genetical Theory of Natural Selection", "The Lady Tasting Tea", "The code book : the science of secrecy from ancient Egypt to quantum cryptography", "Theory (mathematical logic)", "Theory of errors", "Thermodynamics", "Thomas Bayes", "Thomas Simpson", "Thorvald N. Thiele", "Thucydides", "Time domain", "Time series", "Timeline", "Timeline of probability and statistics", "Tobias Mayer", "Tolerance interval", "Trend estimation", "Trial of the Pyx", "Triangular distribution", "Tycho Brahe", "Type I and type II errors", "U-statistic", "Udny Yule", "Uniform distribution (continuous)", "Uniformly most powerful test", "University College London", "University of Cambridge", "University of St Andrews", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Walter A. Shewhart", "Walter Frank Raphael Weldon", "Wavelet", "Wayback Machine", "Westminster Abbey", "Whittle likelihood", "Wiktionary", "Wilcoxon signed-rank test", "Wilhelm Lexis", "William Gosset", "William Petty", "William Playfair", "William Sealey Gosset", "William Sealy Gosset", "Z-test"], "references": ["http://psychclassics.yorku.ca/Peirce/small-diffs.htm", "http://fn.bmj.com/cgi/content/full/76/1/F64", "http://jeff560.tripod.com/b.html", "http://jeff560.tripod.com/mathsym.html", "http://jeff560.tripod.com/stat.html", "http://www.stat.berkeley.edu/~census/521.pdf", "http://ba.stat.cmu.edu/journal/2006/vol01/issue01/fienberg.pdf", "http://ba.stat.cmu.edu/journal/2008/vol03/issue01/aldrich.pdf", "http://www.stat.ufl.edu/~aa/articles/agresti_hitchcock_2005.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1720613", "http://www.ncbi.nlm.nih.gov/pubmed/9059193", "http://www.ncbi.nlm.nih.gov/pubmed/9519574", "http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0025.PDF#page=222", "http://www.jehps.net/indexang.html", "http://www.jehps.net/publications.htm", "http://www.stat.auckland.ac.nz/~iase/publications/17/3I2_BERN.pdf", "http://www.ams.org/mathscinet-getitem?mr=1013489", "http://doi.org/10.1007%2FBF00485695", "http://doi.org/10.1007%2Fs10260-005-0121-y", "http://doi.org/10.1016%2FS0169-7161(05)25002-2", "http://doi.org/10.1080%2F14786440009463897", "http://doi.org/10.1080%2F14786440109462720", "http://doi.org/10.1086%2F354775", "http://doi.org/10.1086%2F383850", "http://doi.org/10.1086%2F444032", "http://doi.org/10.1090%2FS0002-9904-1952-09620-8", "http://doi.org/10.1098%2Frstl.1710.0011", "http://doi.org/10.1136%2Ffn.76.1.F64", "http://doi.org/10.1214%2Fss%2F1009212409", "http://doi.org/10.1214%2Fss%2F1177012580", "http://doi.org/10.1287%2Fopre.15.4.643", "http://doi.org/10.2307%2F2331929", "http://doi.org/10.2307%2F2528399", "http://doi.org/10.2307%2F2682986", "http://doi.org/10.2307%2F2684625", "http://doi.org/10.3102%2F00028312003003223", "http://or.journal.informs.org/cgi/content/abstract/15/4/643", "http://www.jstor.org/stable/1161806", "http://www.jstor.org/stable/168276", "http://www.jstor.org/stable/234674", "http://www.jstor.org/stable/2528399", "http://www.jstor.org/stable/2682986", "http://www.jstor.org/stable/2684625", "http://www.jstor.org/stable/27956805", "http://projecteuclid.org/euclid.ss/1089808283", "http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm", "http://www.economics.soton.ac.uk/staff/aldrich/Probability%20Earliest%20Uses.htm", "http://www-history.mcs.st-andrews.ac.uk/Biographies/Jeffreys.html", "http://www.york.ac.uk/depts/maths/histstat", "http://www.york.ac.uk/depts/maths/histstat/arbuthnot.pdf", "https://books.google.com/books?id=8Y71m9yoK6UC", "https://books.google.com/books?id=M7yvkERHIIMC&lpg=PA225&pg=PA225#v=onepage", "https://books.google.com/books?id=jYFRAAAAMAAJ", "https://mathscinet.ams.org/mathscinet-getitem?mr=2082155", "https://web.archive.org/web/20140906190025/http://ba.stat.cmu.edu/journal/2008/vol03/issue01/aldrich.pdf", "https://web.archive.org/web/20140910070556/http://ba.stat.cmu.edu/journal/2006/vol01/issue01/fienberg.pdf", "https://doi.org/10.1214%2F088342304000000053", "https://www.jstor.org/stable/2342192", "https://www.jstor.org/stable/2965467"]}, "Fixed effects model": {"categories": ["All articles needing additional references", "All articles to be merged", "Analysis of variance", "Articles needing additional references from September 2009", "Articles to be merged from October 2017", "Articles with multiple maintenance issues", "Regression models"], "title": "Fixed effects model", "method": "Fixed effects model", "url": "https://en.wikipedia.org/wiki/Fixed_effects_model", "summary": "In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities. This is in contrast to random effects models and mixed models in which all or some of the model parameters are considered as random variables. In many applications including econometrics and biostatistics a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a random effects model in which the group means are a random sample from a population. Generally, data can be grouped according to several observed factors. The group means could be modeled as fixed or random effects for each grouping. In a fixed effects model each group mean is a group-specific fixed quantity.\nIn panel data where longitudinal observations exist for the same subject, fixed effects represent the subject-specific means. In panel data analysis the term fixed effects estimator (also known as the within estimator) is used to refer to an estimator for the coefficients in the regression model including those fixed effects (one time-invariant intercept for each subject).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ArXiv", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bibcode", "Biometrics (journal)", "Biostatistics", "Chamberlain's approach to unobserved effects models", "Coefficient", "Consistent estimator", "Control variable", "Digital object identifier", "Discrete choice", "Durbin\u2013Wu\u2013Hausman test", "Dynamic unobserved effects model", "Econometrics", "Efficiency (statistics)", "Endogeneity (econometrics)", "Errors-in-variables models", "Errors and residuals in statistics", "Estimator", "First-Difference Estimator", "First difference", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Marc Nerlove", "Mean and predicted response", "Mixed logit", "Mixed model", "Multicollinearity", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Panel data", "Parameter", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistical model", "Statistics", "Statistics in Medicine (journal)", "Studentized residual", "Tikhonov regularization", "Total least squares", "Variance-covariance matrix", "Weighted least squares"], "references": ["http://adsabs.harvard.edu/abs/2018ApJ...857L...9R", "http://pmrc.uga.edu/TR2000-7.pdf", "http://teaching.sociology.ul.ie/DCW/confront/node45.html", "http://arxiv.org/abs/1803.06776", "http://doi.org/10.1002%2Fsim.3478", "http://doi.org/10.3847%2F2041-8213%2Faab7f5", "http://www.jstor.org/stable/2529876", "http://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm", "https://books.google.com/books?id=2eZpoAZnu9UC&pg=PA36", "https://books.google.com/books?id=Zf0gCwxC9ocC&pg=PA717", "https://books.google.com/books?id=i9iPG7C3EP4C&pg=PA95"]}, "Lp space": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from November 2015", "Banach spaces", "Function spaces", "Mathematical series", "Measure theory", "Normed spaces", "Wikipedia articles needing page number citations from April 2016"], "title": "Lp space", "method": "Lp space", "url": "https://en.wikipedia.org/wiki/Lp_space", "summary": "In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910).\nLp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces.\nBecause of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces are used also in the theoretical discussion of problems in physics, statistics, finance, engineering, and other disciplines.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/03/Astroid.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1f/Lp_space_animation.gif", "https://upload.wikimedia.org/wikipedia/commons/d/d4/Vector-p-Norms_qtl1.svg"], "links": ["Absolute convergence", "Absolute value", "Absolutely continuous", "Abuse of terminology", "Almost everywhere", "Astroid", "Axiom of dependent choice", "Ba space", "Baire property", "Banach", "Banach space", "Birnbaum\u2013Orlicz space", "Bochner space", "Borel algebra", "Bounded operator", "Bounded sequence", "C*-algebra", "Cauchy\u2013Schwarz inequality", "Central tendency", "Chebyshev distance", "Clarkson's inequalities", "Closed graph theorem", "Commutative", "Complete space", "Complex number", "Compressed sensing", "Computer science", "Convergence in measure", "Convergence in probability", "Counting measure", "Cumulative distribution function", "David Donoho", "Density on a manifold", "Digital object identifier", "Dual space", "Edward Charles Titchmarsh", "Elastic net regularization", "Encyclopedia of Mathematics", "Essential supremum", "Euclidean norm", "F-space", "Fourier series", "Fourier transform", "Frigyes Riesz", "Function (mathematics)", "Function space", "Functional analysis", "Hahn\u2013Banach theorem", "Hardy space", "Hardy\u2013Littlewood maximal operator", "Harmonic analysis", "Harmonic series (mathematics)", "Hausdorff\u2013Young inequality", "Henri Lebesgue", "Hilbert space", "Hilbert transform", "Homogeneous function", "H\u00f6lder's inequality", "H\u00f6lder mean", "H\u00f6lder space", "Improper integral", "Indicator function", "Information theory", "Integral", "International Standard Book Number", "Isometry", "Isomorphism", "Kernel (set theory)", "L-infinity", "LASSO", "Lebesgue integrable", "Lebesgue integral", "Lebesgue integration", "Locally bounded", "Locally convex", "Locally integrable function", "Lorentz space", "Lp sum", "Manhattan distance", "Marcinkiewicz interpolation", "Markov's inequality", "Mathematical Reviews", "Mathematics", "McGraw-Hill", "Mean", "Measurable function", "Measure space", "Median", "Metric space", "Metrization theorem", "Michiel Hazewinkel", "Minkowski distance", "Minkowski inequality", "Muckenhoupt weights", "Multiplication operator", "Natural number", "Nicolas Bourbaki", "Nigel Kalton", "Norm (mathematics)", "Normed vector space", "OCLC", "Open set", "Operator norm", "Paul L\u00e9vy (mathematician)", "Periodic functions", "Physics", "Pontryagin duality", "Quadratically integrable function", "Quantum mechanics", "Quasi-norm", "Quotient space (topology)", "Radon\u2013Nikodym theorem", "Real number", "Reflexive space", "Riemann integral", "Riesz-Fischer theorem", "Riesz\u2013Thorin theorem", "Root mean square", "Saharon Shelah", "Scientific computing", "Seminorm", "Sequence", "Sequence space", "Series (mathematics)", "Sigma-finite", "Signal processing", "Singular integrals", "Standard deviation", "Statistical dispersion", "Statistics", "Stochastic calculus", "Subadditivity", "Superellipse", "Supremum", "Taxicab geometry", "Theory of Linear Operations", "Tikhonov regularization", "Topological space", "Topological vector space", "Triangle inequality", "Uniformly convex space", "Unit circle", "Vector space", "Von Neumann algebra", "Walter Rudin", "Zermelo\u2013Fraenkel set theory", "Zero to the power of zero"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0801221", "http://www.ams.org/mathscinet-getitem?mr=0808777", "http://www.ams.org/mathscinet-getitem?mr=0920371", "http://www.ams.org/mathscinet-getitem?mr=0924157", "http://doi.org/10.1007%2F978-94-015-7758-8", "http://doi.org/10.1007%2FBF01457637", "http://doi.org/10.1017%2FCBO9780511662447", "http://doi.org/10.2307%2F2322503", "http://planetmath.org/ProofThatLpSpacesAreComplete", "http://www.worldcat.org/oclc/13064804", "https://www.encyclopediaofmath.org/index.php?title=p/l057910"]}, "OpenBUGS": {"categories": ["Free Bayesian statistics software", "Monte Carlo software", "Numerical programming languages", "Pages using Infobox software with unknown parameters", "Use dmy dates from January 2012"], "title": "OpenBUGS", "method": "OpenBUGS", "url": "https://en.wikipedia.org/wiki/OpenBUGS", "summary": "OpenBUGS is a software application for the Bayesian analysis of complex statistical models using Markov chain Monte Carlo (MCMC) methods. OpenBUGS is the open source variant of WinBUGS (Bayesian inference Using Gibbs Sampling). It runs under Windows and Linux, as well as from inside the R statistical package. Versions from v3.0.7 onwards have been designed to be at least as efficient and reliable as WinBUGS over a range of test applications.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20161201223606%21Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20120912121406%21Blue_pencil.svg"], "links": ["ADMB", "Analyse-it", "BMDP", "BUGS language", "BV4.1 (software)", "Bayesian analysis", "Bayesian inference", "CSPro", "Commercial software", "Comparison of statistical packages", "Complex system", "Component Pascal", "Computing platform", "Conditional distribution", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "Digital object identifier", "EViews", "Epi Info", "Executable", "File size", "Freeware", "GAUSS (software)", "GNU General Public License", "GNU Octave", "Gardens Point Component Pascal", "GenStat", "Gibbs sampling", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "IA-32", "JASP", "JMP (statistical software)", "JMulTi", "Java (programming language)", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "Library (computer science)", "Linux", "List of statistical packages", "MATLAB", "MLwiN", "MacOS", "Maple (software)", "Markov chain Monte Carlo", "Mathcad", "Mathematica", "MedCalc", "Megabyte", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Open-source software", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Parsing", "Posterior probability", "Programming language", "PubMed Identifier", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "R programming language", "Repository (version control)", "Revolution Analytics", "S-PLUS", "S-Plus", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "S programming language", "SageMath", "Sample (statistics)", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software application", "Software categories", "Software developer", "Software license", "Software release life cycle", "Software versioning", "Source code", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistical model", "Statistical package", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "Unix", "WinBUGS", "Wine (software)", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/19630097", "http://openbugs.net", "http://openbugs.net/w/OpenBUGS_3_2_3?action=AttachFile&do=get&target=OpenBUGS-3.2.3.tar.gz", "http://www.openbugs.net", "http://www.openbugs.net/w/OpenVsWin", "http://www.openbugs.net/w/Overview", "http://doi.org/10.1002%2Fsim.3680", "http://www.mrc-bsu.cam.ac.uk/bugs/documentation/Download/manual05.pdf", "https://www.wikidata.org/wiki/Q7095741#P1324"]}, "Score test": {"categories": ["All articles to be expanded", "All articles with empty sections", "Articles to be expanded from June 2008", "Articles using small message boxes", "Articles with empty sections from June 2008", "Statistical tests", "Wikipedia articles needing clarification from March 2011"], "title": "Score test", "method": "Score test", "url": "https://en.wikipedia.org/wiki/Score_test", "summary": "Rao's score test, also known as the score test or the Lagrange multiplier test (LM test) in econometrics, is a statistical test of a simple null hypothesis that a parameter of interest \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n is equal to some particular value \n \n \n \n \n \u03b8\n \n 0\n \n \n \n \n {\\displaystyle \\theta _{0}}\n . It is the most powerful test when the true value of \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n is close to \n \n \n \n \n \u03b8\n \n 0\n \n \n \n \n {\\displaystyle \\theta _{0}}\n . The main advantage of the score test is that it does not require an estimate of the information under the alternative hypothesis or unconstrained maximum likelihood. This constitutes a potential advantage in comparison to other tests, such as the Wald test and the generalized likelihood ratio test (GLRT). This makes testing feasible when the unconstrained maximum likelihood estimate is a boundary point in the parameter space.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "C. R. Rao", "C R Rao", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher information", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Neyman\u2013Pearson lemma", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Proportional hazards models", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score (statistics)", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical test", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sup-LM test", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T statistic", "Taylor series", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Type I error", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1016%2FS0378-3758(00)00343-8", "http://doi.org/10.1016%2FS1573-4412(84)02005-5"]}, "Fixed effects estimation": {"categories": ["All articles needing additional references", "All articles to be merged", "Analysis of variance", "Articles needing additional references from September 2009", "Articles to be merged from October 2017", "Articles with multiple maintenance issues", "Regression models"], "title": "Fixed effects model", "method": "Fixed effects estimation", "url": "https://en.wikipedia.org/wiki/Fixed_effects_model", "summary": "In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities. This is in contrast to random effects models and mixed models in which all or some of the model parameters are considered as random variables. In many applications including econometrics and biostatistics a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a random effects model in which the group means are a random sample from a population. Generally, data can be grouped according to several observed factors. The group means could be modeled as fixed or random effects for each grouping. In a fixed effects model each group mean is a group-specific fixed quantity.\nIn panel data where longitudinal observations exist for the same subject, fixed effects represent the subject-specific means. In panel data analysis the term fixed effects estimator (also known as the within estimator) is used to refer to an estimator for the coefficients in the regression model including those fixed effects (one time-invariant intercept for each subject).", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ArXiv", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bibcode", "Biometrics (journal)", "Biostatistics", "Chamberlain's approach to unobserved effects models", "Coefficient", "Consistent estimator", "Control variable", "Digital object identifier", "Discrete choice", "Durbin\u2013Wu\u2013Hausman test", "Dynamic unobserved effects model", "Econometrics", "Efficiency (statistics)", "Endogeneity (econometrics)", "Errors-in-variables models", "Errors and residuals in statistics", "Estimator", "First-Difference Estimator", "First difference", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Marc Nerlove", "Mean and predicted response", "Mixed logit", "Mixed model", "Multicollinearity", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Panel data", "Parameter", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model", "Regression model validation", "Regularized least squares", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistical model", "Statistics", "Statistics in Medicine (journal)", "Studentized residual", "Tikhonov regularization", "Total least squares", "Variance-covariance matrix", "Weighted least squares"], "references": ["http://adsabs.harvard.edu/abs/2018ApJ...857L...9R", "http://pmrc.uga.edu/TR2000-7.pdf", "http://teaching.sociology.ul.ie/DCW/confront/node45.html", "http://arxiv.org/abs/1803.06776", "http://doi.org/10.1002%2Fsim.3478", "http://doi.org/10.3847%2F2041-8213%2Faab7f5", "http://www.jstor.org/stable/2529876", "http://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm", "https://books.google.com/books?id=2eZpoAZnu9UC&pg=PA36", "https://books.google.com/books?id=Zf0gCwxC9ocC&pg=PA717", "https://books.google.com/books?id=i9iPG7C3EP4C&pg=PA95"]}, "Precision (statistics)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2016", "Bayesian statistics", "Statistical deviation and dispersion"], "title": "Precision (statistics)", "method": "Precision (statistics)", "url": "https://en.wikipedia.org/wiki/Precision_(statistics)", "summary": "In statistics, precision is the reciprocal of the variance, and the precision matrix (also known as concentration matrix) is the matrix inverse of the covariance matrix. Some particular statistical models define the term precision differently.\nOne particular use of the precision matrix is in the context of Bayesian analysis of the multivariate normal distribution: for example, Bernardo & Smith prefer to parameterise the multivariate normal distribution in terms of the precision matrix, rather than the covariance matrix, because of certain simplifications that then arise.\nIn general, statisticians prefer to use the dual term variability rather than precision. Variability is the amount of imprecision.", "images": [], "links": ["Bayesian analysis", "Carl Friedrich Gauss", "Covariance matrix", "International Standard Book Number", "Matrix inverse", "Multiplicative inverse", "Multivariate normal distribution", "Statistical variability", "Statistics", "Variance"], "references": ["http://jeff560.tripod.com/m.html"]}, "Spatial statistics": {"categories": ["All articles with specifically marked weasel-worded phrases", "All articles with unsourced statements", "Articles with short description", "Articles with specifically marked weasel-worded phrases from February 2018", "Articles with unsourced statements from August 2014", "Articles with unsourced statements from December 2010", "Articles with unsourced statements from February 2013", "Cartography", "Commons category link is on Wikidata", "Geographic data and information", "Geography", "Geostatistics", "Mathematical and quantitative methods (economics)", "Spatial data analysis", "Statistical data types", "Webarchive template wayback links", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from June 2014"], "title": "Spatial analysis", "method": "Spatial statistics", "url": "https://en.wikipedia.org/wiki/Spatial_analysis", "summary": "Spatial analysis or spatial statistics includes any of the formal techniques which study entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques, many still in their early development, using different analytic approaches and applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, to chip fabrication engineering, with its use of \"place and route\" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is the technique applied to structures at the human scale, most notably in the analysis of geographic data.\nComplex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research. The most fundamental of these is the problem of defining the spatial location of the entities being studied.\nClassification of the techniques of spatial analysis is difficult because of the large number of different fields of research involved, the different fundamental approaches which can be chosen, and the many forms the data can take.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c8/Britain-fractal-coastline-100km.png", "https://upload.wikimedia.org/wikipedia/commons/7/78/Britain-fractal-coastline-200km.png", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Britain-fractal-coastline-50km.png", "https://upload.wikimedia.org/wikipedia/commons/1/15/Bubonic_plague-en.svg", "https://upload.wikimedia.org/wikipedia/commons/8/83/Jubilee_Campus_MMB_%C2%AB24_Nottingham_Geospatial_Building.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/08/Manhattan_distance.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d1/Q-fig2.jpg", "https://upload.wikimedia.org/wikipedia/commons/c/c7/Snow-cholera-map.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/commons/2/29/Minard.png"], "links": ["1854 Broad Street cholera outbreak", "Ade Olufeko", "Adolphe Quetelet", "Agent-based model", "Alan MacEachren", "Algorithm", "Analysis", "ArXiv", "Arthur H. Robinson", "Artificial neural networks", "Aspect (geography)", "Astronomy", "August Kekul\u00e9", "Autocorrelation", "Bang Wong", "Bayesian hierarchical modeling", "Ben Shneiderman", "Benoit Mandelbrot", "Bibcode", "Biogeography", "Biological data visualization", "Biology", "Botany", "Boundary problem (in spatial analysis)", "Bruce H. McCormick", "Cartography", "Cellular automata", "Charles Joseph Minard", "Chart", "Chartjunk", "Chemical imaging", "Christopher R. Johnson", "CiteSeerX", "Clifford A. Pickover", "Cluster (epidemiology)", "Complete spatial randomness", "Complex adaptive systems", "Computational geometry", "Computer graphics", "Computer graphics (computer science)", "Computer science", "Cosmos", "Crime mapping", "DE-9IM", "Data mining", "Data visualization", "Database", "Diagram", "Digital cartography", "Digital object identifier", "Ecological fallacy", "Ecology", "Economics", "Edward Tufte", "Eigenvalues and eigenvectors", "Engineering drawing", "Epidemiology", "Ethology", "Euclidean distance", "Exploratory data analysis", "Extrapolation domain analysis", "Factor analysis", "Fernanda Vi\u00e9gas", "Florence Nightingale", "Flow visualization", "Fractal", "Fractals", "Fraser Stoddart", "Fuzzy architectural spatial analysis", "GIS", "Gaspard Monge", "Gaussian processes", "Geary's C", "GeoComputation", "Geodemographic segmentation", "Geographic", "Geographic data", "Geographic information science", "Geographic information system", "Geographic information systems", "Geoinformatics", "Geology", "Geomatics", "Geometric", "George Furnas", "George G. Robertson", "Geospatial intelligence", "Geospatial predictive modeling", "Geospatial topology", "Geovisualization", "Getis's G", "Gradient", "Graph drawing", "Graph of a function", "Graphic design", "Graphic organizer", "Gravity model", "Hanspeter Pfister", "Heterogeneity", "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", "Howard Wainer", "Hydrology", "Ideogram", "Imaging science", "Infographic", "Information science", "Information visualization", "International Standard Book Number", "International Standard Serial Number", "Inverse distance weighting", "Jacques Bertin", "Jock D. Mackinlay", "John Snow (physician)", "Jubilee Campus", "Karl Wilhelm Pohlke", "Kriging", "Landscape ecology", "Lawrence J. Rosenblum", "List of spatial analysis software", "Local regression", "London", "Manuel Lima", "Map", "Marco A. Janssen", "Markov Chain Monte Carlo", "Martin M. Wattenberg", "Mathematical diagram", "Mathematical statistics", "Mathematics", "Measurement", "Medical imaging", "Mental image", "Michael Friendly", "Michael Maltz", "Miriah Meyer", "Misleading graph", "Modifiable areal unit problem", "Molecular graphics", "Moran's I", "Neuroimaging", "Nigel Holmes", "OCLC", "Open Geospatial Consortium", "Operations research", "Otto Neurath", "Pat Hanrahan", "Patent drawing", "Photograph", "Pictogram", "Pixel", "Plot (graphics)", "PubMed Central", "PubMed Identifier", "Public Safety", "Regression-Kriging", "Regression analysis", "Remote sensing", "Rudolf Modley", "Sampling (statistics)", "Scale invariance", "Scale invariant", "Schematic", "Scientific modelling", "Scientific technique", "Scientific visualization", "Skeletal formula", "Software visualization", "Spatial association", "Spatial autocorrelation", "Spatial database", "Spatial decision support system", "Spatial econometrics", "Spatial epidemiology", "Spatial interpolation", "Spatial relation", "Standard deviational ellipse", "Statistical analysis", "Statistical graphics", "Statistics", "Stuart Card", "Suitability analysis", "Surveying", "Table (information)", "Tamara Munzner", "Taxicab geometry", "Technical drawing", "Technical illustration", "Thomas A. DeFanti", "Tobler's first law of geography", "Topological", "University of Nottingham", "User interface", "User interface design", "Visibility", "Visibility analysis", "Visual analytics", "Visual culture", "Visual perception", "Visualization (computer graphics)", "Visualization (graphics)", "Volume cartography", "Volume rendering", "Wayback Machine", "William Playfair"], "references": ["http://www.ryerson.ca/graduate/programs/spatial/index.html", "http://www.artechhouse.com/International/Books/Geospatial-Computing-in-Mobile-Devices-2159.aspx", "http://www.collinsdictionary.com/dictionary/english/geospatial", "http://dictionary.reference.com/browse/geospatial", "http://www.spatialanalysisonline.com/", "http://www.receiver.vodafone.com/the-geospatial-web", "http://adsabs.harvard.edu/abs/2015PhRvE..91c2401T", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.109.1825", "http://www.ncgia.ucsb.edu/", "http://www.icpsr.umich.edu/CrimeStat", "http://www-ohp.univ-paris1.fr", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2741335", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4936159", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5927603", "http://www.ncbi.nlm.nih.gov/pubmed/19750209", "http://www.ncbi.nlm.nih.gov/pubmed/20503184", "http://www.ncbi.nlm.nih.gov/pubmed/25871117", "http://www.ncbi.nlm.nih.gov/pubmed/27387921", "http://www.ncbi.nlm.nih.gov/pubmed/29720777", "http://eprints.maynoothuniversity.ie/6102/1/MC_gwr%201998.pdf", "http://rgdoi.net/10.13140/2.1.1560.2247", "http://www.ai-geostats.org/", "http://arxiv.org/abs/1406.7343", "http://www.bioversityinternational.org/index.php?id=244&tx_news_pi1%5Bnews%5D=1256&cHash=110ef499ad0d2d17abb48849909f1356", "http://doi.org/10.1007%2Fs10596-012-9287-1", "http://doi.org/10.1007%2Fs11004-010-9276-7", "http://doi.org/10.1007%2Fs11242-015-0471-3", "http://doi.org/10.1016%2FS0198-9715(01)00014-X", "http://doi.org/10.1016%2FS1470-160X(02)00052-3", "http://doi.org/10.1016%2Fj.compenvurbsys.2017.06.003", "http://doi.org/10.1016%2Fj.ecolind.2016.02.052", "http://doi.org/10.1016%2Fj.eiar.2012.06.007", "http://doi.org/10.1016%2Fs0198-9715(01)00047-3", "http://doi.org/10.1068%2Fa301905", "http://doi.org/10.1068%2Fb240235", "http://doi.org/10.1080%2F01621459.2015.1044091", "http://doi.org/10.1080%2F02693798708927820", "http://doi.org/10.1080%2F02693799308901936", "http://doi.org/10.1080%2F02723638.2015.1096118", "http://doi.org/10.1080%2F0965431042000312424", "http://doi.org/10.1103%2FPhysRevE.91.032401", "http://doi.org/10.1111%2F1467-8306.9302004", "http://doi.org/10.1111%2F1467-9671.00017", "http://doi.org/10.1111%2Fj.1461-0248.2004.00568.x", "http://doi.org/10.1111%2Fj.1467-8306.2004.09402005.x", "http://doi.org/10.1111%2Fj.1467-9671.1997.tb00010.x", "http://doi.org/10.1111%2Fj.1467-9868.2008.00663.x", "http://doi.org/10.1111%2Fj.1745-7939.1971.tb00636.x", "http://doi.org/10.1177%2F0042098016686493", "http://doi.org/10.1186%2Fs12936-016-1395-2", "http://doi.org/10.13140%2F2.1.1560.2247", "http://doi.org/10.1890%2F09-1359.1", "http://doi.org/10.4081%2Fgh.2010.196", "http://www.icaci.org", "http://www.worldcat.org/issn/1461-0248", "http://www.worldcat.org/oclc/973767077", "http://sasi.group.shef.ac.uk/", "https://sites.google.com/site/commissionofica/", "https://www.e-education.psu.edu/sgam/node/214", "https://web.archive.org/web/20110919052807/http://www.drs.wisc.edu/documents/articles/curtis/cesoc977/Anselin1995.pdf", "https://web.archive.org/web/20111002151826/http://www.receiver.vodafone.com/the-geospatial-web"]}, "Accuracy paradox": {"categories": ["All stub articles", "Statistical paradoxes", "Statistics stubs"], "title": "Accuracy paradox", "method": "Accuracy paradox", "url": "https://en.wikipedia.org/wiki/Accuracy_paradox", "summary": "The accuracy paradox is the paradoxical finding that accuracy is not a good metric for predictive models when classifying in predictive analytics. This is because a simple model may have a high level of accuracy but be too crude to be useful. For example, if the incidence of category A is dominant, being found in 99% of cases, then predicting that every case is category A will have an accuracy of 99%. Precision and recall are better measures in such cases.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Accuracy", "Binary classification", "Digital object identifier", "International Standard Book Number", "Paradox", "Precision and recall", "Predictive analytics", "Predictive model", "Statistics"], "references": ["http://doi.org/10.1117%2F12.785623", "https://www.utwente.nl/en/eemcs/trese/graduation_projects/2009/Abma.pdf"]}, "Statistical population": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2017", "Statistical theory"], "title": "Statistical population", "method": "Statistical population", "url": "https://en.wikipedia.org/wiki/Statistical_population", "summary": "In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker). A common aim of statistical analysis is to produce information about some chosen population.In statistical inference, a subset of the population (a statistical sample) is chosen to represent the population in a statistical analysis. The ratio of the size of this statistical sample to the size of the population is called a sampling fraction. If a sample is chosen properly, characteristics of the entire population that the sample is drawn from can be estimated from corresponding characteristics of the sample.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bimodal distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Data collection system", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimating equations", "Estimation theory", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Galaxy", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Infinite set", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "MathWorld", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Milky Way", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mixture model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Overdispersion", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Poker", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling fraction", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Star", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Statistics.com", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Subset", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "W. H. Freeman and Company", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.statistics.com/glossary&term_id=281", "http://www.statistics.com/glossary&term_id=812", "http://bcs.whfreeman.com/yates2e/", "http://mathworld.wolfram.com/Population.html", "http://www.socialresearchmethods.net/kb/sampstat.htm", "https://web.archive.org/web/20050209001108/http://bcs.whfreeman.com/yates2e/"]}, "Baseball statistics": {"categories": ["All articles needing additional references", "All articles that may contain original research", "Articles needing additional references from October 2018", "Articles that may contain original research from November 2018", "Baseball statistics"], "title": "Baseball statistics", "method": "Baseball statistics", "url": "https://en.wikipedia.org/wiki/Baseball_statistics", "summary": "Baseball statistics play an important role in evaluating the progress of a player or team.\nSince the flow of a baseball game has natural breaks to it, and normally players act individually rather than performing in clusters, the sport lends itself to easy record-keeping and statistics. Statistics have been kept for professional baseball since the creation of the National League and American League, now part of Major League Baseball.\nMany statistics are also available from outside Major League Baseball, from leagues such as the National Association of Professional Base Ball Players and the Negro Leagues, although the consistency of whether these records were kept, of the standards with respect to which they were calculated, and of their accuracy has varied.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/9/92/Baseball.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["20\u201320\u201320 club", "3,000 hit club", "3,000 strikeout club", "300 save club", "300 win club", "30\u201330 club", "40\u201340 club", "500 home run club", "50 home run club", "Abbreviation", "Adjusted ERA+", "Alan Schwarz", "American League", "Appeal play", "Assist (baseball)", "Assist (baseball statistics)", "At bat", "At bats per home run", "Backstop (baseball)", "Balk", "Baltimore chop", "Base on balls", "Base running", "Base runs", "Baseball", "Baseball (ball)", "Baseball Encyclopedia", "Baseball awards", "Baseball bat", "Baseball cap", "Baseball clothing and equipment", "Baseball doughnut", "Baseball field", "Baseball glove", "Baseball park", "Baseball positioning", "Baseball positions", "Baseball rules", "Baseball scorekeeping", "Baseball stirrups", "Baseball uniform", "Bases loaded", "Bases on balls per 9 innings pitched", "Bat flip", "Batter's box", "Batter's eye", "Batting (baseball)", "Batting average (baseball)", "Batting average on balls in play", "Batting cage", "Batting glove", "Batting helmet", "Batting order (baseball)", "Batting park factor", "Beanball", "Bench-clearing brawl", "Bench jockey", "Blocking the plate", "Blown save", "Breaking ball", "Brushback pitch", "Bullpen", "Bunt (baseball)", "Catch (baseball)", "Catcher's ERA", "Caught stealing", "Changeup", "Checked swing", "Chinese home run", "Cleanup hitter", "Complete game", "Component ERA", "Computer", "Contact play", "Count (baseball)", "Cricket", "Curveball", "Cy Young Award", "Dead ball", "Defense-Independent Component ERA", "Defense independent pitching statistics", "Defensive Indifference", "Defensive Runs Saved", "Defensive indifference", "Designated hitter", "Digital object identifier", "Document", "Double (baseball)", "Double play", "Double plays", "Double switch (baseball)", "Dugout (baseball)", "Earned run", "Earned run average", "Eephus", "Equivalent average", "Error (baseball)", "Error (baseball statistics)", "Extra-base hit", "Extra base hit", "Extra innings", "Extrapolated Runs", "Fangraphs", "Fastball", "Fielder's choice", "Fielding independent pitching", "Fielding percentage", "Fifth infielder", "Force play", "Foul ball", "Foul pole", "Foul territory", "Foul tip", "Fourth out", "Full count", "Game-winning RBI", "Game score", "Games behind", "Games finished", "Games in relief", "Games pitched", "Games played", "Games started", "Glossary of baseball", "Golden sombrero", "Grand slam (baseball)", "Gross Production Average", "Ground ball fly ball ratio", "Ground rule double", "Ground rules", "Hank Aaron Award", "Hat-trick", "Henry Chadwick (writer)", "Hidden ball trick", "Hit (baseball)", "Hit and run (baseball)", "Hit by pitch", "Hits allowed", "Hits allowed per 9 innings pitched", "Hitting for the cycle", "Hitting streak", "Hold (baseball)", "Hold (baseball statistics)", "Home run", "Home runs allowed", "Home runs per hit", "Home runs per nine innings", "Hy Turkin", "Immaculate inning", "In-between hop", "In flight", "Infield", "Infield fly rule", "Infield hit", "Infield shift", "Inherited runners", "Inherited runs allowed", "Inning", "Innings pitched", "Inside-the-park home run", "Inside pitching", "Intentional base on balls", "Interference (baseball)", "Interleague play", "International Standard Book Number", "Isolated Power", "Isolated power", "Jockstrap", "K/9IP", "Knuckleball", "Leadoff hitter", "Left on base", "Lefty-righty switch", "Line drive", "List of Major League Baseball annual ERA leaders", "List of Major League Baseball annual doubles leaders", "List of Major League Baseball annual fielding errors leaders", "List of Major League Baseball annual home run leaders", "List of Major League Baseball annual putouts leaders", "List of Major League Baseball annual runs batted in leaders", "List of Major League Baseball annual runs scored leaders", "List of Major League Baseball annual saves leaders", "List of Major League Baseball annual shutout leaders", "List of Major League Baseball annual stolen base leaders", "List of Major League Baseball annual strikeout leaders", "List of Major League Baseball annual triples leaders", "List of Major League Baseball annual wins leaders", "List of Major League Baseball awards", "List of Major League Baseball batting champions", "List of Major League Baseball career ERA leaders", "List of Major League Baseball career OPS leaders", "List of Major League Baseball career WHIP leaders", "List of Major League Baseball career assists leaders", "List of Major League Baseball career at-bat leaders", "List of Major League Baseball career bases on balls allowed leaders", "List of Major League Baseball career bases on balls leaders", "List of Major League Baseball career batters faced leaders", "List of Major League Baseball career batting average leaders", "List of Major League Baseball career complete games leaders", "List of Major League Baseball career doubles leaders", "List of Major League Baseball career extra base hits leaders", "List of Major League Baseball career fielding errors as a catcher leaders", "List of Major League Baseball career fielding errors as a center fielder leaders", "List of Major League Baseball career fielding errors as a first baseman leaders", "List of Major League Baseball career fielding errors as a left fielder leaders", "List of Major League Baseball career fielding errors as a second baseman leaders", "List of Major League Baseball career fielding errors as a shortstop leaders", "List of Major League Baseball career fielding errors as a third baseman leaders", "List of Major League Baseball career fielding errors as an outfielder leaders", "List of Major League Baseball career fielding errors leaders", "List of Major League Baseball career games finished leaders", "List of Major League Baseball career games played leaders", "List of Major League Baseball career games started leaders", "List of Major League Baseball career hit batsmen leaders", "List of Major League Baseball career hit by pitch leaders", "List of Major League Baseball career hits leaders", "List of Major League Baseball career home run leaders", "List of Major League Baseball career innings pitched leaders", "List of Major League Baseball career intentional bases on balls leaders", "List of Major League Baseball career losses leaders", "List of Major League Baseball career on-base percentage leaders", "List of Major League Baseball career passed balls leaders", "List of Major League Baseball career plate appearance leaders", "List of Major League Baseball career putouts as a catcher leaders", "List of Major League Baseball career putouts as a center fielder leaders", "List of Major League Baseball career putouts as a first baseman leaders", "List of Major League Baseball career putouts as a left fielder leaders", "List of Major League Baseball career putouts as a pitcher leaders", "List of Major League Baseball career putouts as a right fielder leaders", "List of Major League Baseball career putouts as a second baseman leaders", "List of Major League Baseball career putouts as a shortstop leaders", "List of Major League Baseball career putouts as a third baseman leaders", "List of Major League Baseball career putouts as an outfielder leaders", "List of Major League Baseball career putouts leaders", "List of Major League Baseball career records", "List of Major League Baseball career runs batted in leaders", "List of Major League Baseball career runs scored leaders", "List of Major League Baseball career shutout leaders", "List of Major League Baseball career singles leaders", "List of Major League Baseball career slugging percentage leaders", "List of Major League Baseball career stolen bases leaders", "List of Major League Baseball career strikeout leaders", "List of Major League Baseball career strikeouts by batters leaders", "List of Major League Baseball career times on base leaders", "List of Major League Baseball career total bases leaders", "List of Major League Baseball career triples leaders", "List of Major League Baseball career wild pitches leaders", "List of Major League Baseball career wins leaders", "List of Major League Baseball doubles records", "List of Major League Baseball hit records", "List of Major League Baseball home run records", "List of Major League Baseball individual streaks", "List of Major League Baseball longest losing streaks", "List of Major League Baseball longest winning streaks", "List of Major League Baseball managers by wins", "List of Major League Baseball no-hitters", "List of Major League Baseball perfect games", "List of Major League Baseball pitchers who have thrown an immaculate inning", "List of Major League Baseball players to hit for the cycle", "List of Major League Baseball players with a .400 batting average in a season", "List of Major League Baseball progressive career hits leaders", "List of Major League Baseball progressive career home runs leaders", "List of Major League Baseball progressive single-season home run leaders", "List of Major League Baseball record breakers by season", "List of Major League Baseball records considered unbreakable", "List of Major League Baseball runs batted in records", "List of Major League Baseball runs records", "List of Major League Baseball single-game grand slam leaders", "List of Major League Baseball single-game hits leaders", "List of Major League Baseball single-game home run leaders", "List of Major League Baseball single-game records", "List of Major League Baseball single-game runs batted in leaders", "List of Major League Baseball single-game runs scored leaders", "List of Major League Baseball single-game strikeout leaders", "List of Major League Baseball single-inning runs batted in leaders", "List of Major League Baseball single-inning strikeout leaders", "List of Major League Baseball single-season records", "List of Major League Baseball single-season triples leaders", "List of Major League Baseball stolen base records", "List of Major League Baseball triple plays", "List of Major League Baseball triples records", "List of Major League Baseball wins records", "Losing streak (sports)", "Loss (baseball)", "Lou Proctor", "MLB Most Valuable Player Award", "MLB Rookie of the Year Award", "Macmillan Publishing", "Major League Baseball", "Major League Baseball consecutive games played streaks", "Major League Baseball titles leaders", "Major League Baseball titles streaks", "Moonshot (baseball)", "NERD (sabermetrics)", "National Association of Professional Base Ball Players", "National League", "Negro League", "No-hitter", "Obstruction (baseball)", "Official Baseball Rules", "On-base percentage", "On-base plus slugging", "On-deck", "Opponents batting average", "Out (baseball)", "Out of zone plays made", "Outfield", "Outline of baseball", "Pace of play", "Passed ball", "Paul Adomites", "Pepper (baseball)", "Perfect game", "Pete Palmer", "Pickoff", "Pitch (baseball)", "Pitch clock", "Pitch count", "Pitchers of record", "Pitching (baseball)", "Pitching machine", "Pitchout", "Plate appearance", "Plate appearances per strikeout", "Platoon system", "Power finesse ratio", "Professional baseball", "Pull hitter", "Putout", "Pythagorean expectation", "Quality of pitch", "Quality start", "Quick pitch", "Range factor", "Rawlings Gold Glove Award", "Retrosheet", "Run (baseball)", "Run average", "Run batted in", "Rundown", "Runner in scoring position", "Runs batted in", "Runs created", "Runs produced", "Sabermetric", "Sabermetrics", "Sacrifice bunt", "Sacrifice fly", "Sacrifice hit", "Safe (baseball)", "Save (baseball)", "Save opportunity", "Scoring position", "Scout (sport)", "Screwball", "Secondary average", "Series (baseball)", "Seventh-inning stretch", "Shagging (baseball)", "Shin guard", "Shutout (baseball)", "Shutouts in baseball", "Silver Slugger Award", "Single (baseball)", "Slap bunt", "Slide (baseball)", "Slider", "Slugging average", "Slugging percentage", "Slump (sports)", "Small ball (baseball)", "Society for American Baseball Research", "Softball", "Speed Score", "Spitball", "Sports league", "Squeeze play (baseball)", "Starting pitcher", "Statistics", "Stolen base", "Stolen base percentage", "Strike out", "Strike zone", "Strikeout", "Strikeout-to-walk ratio", "Strikeouts", "Strikeouts per 9 innings pitched", "Striking out the side", "Sweet spot (sports)", "Switch hitter", "Tag out", "Tag up", "Time of pitch", "Times on base", "Tom Tango", "Total Baseball", "Total average", "Total bases", "Total batters faced", "Total chances", "Triple (baseball)", "Triple Crown (baseball)", "Triple crown (baseball)", "Triple play", "Triple play (baseball)", "Ultimate zone rating", "Unassisted triple play", "Uncaught third strike", "Uniform number (Major League Baseball)", "Value over replacement player", "WOBA", "Walk-off home run", "Walk-to-strikeout ratio", "Walk percentage", "Walks plus hits per inning pitched", "Wall climb", "Warning track", "Wheel play", "Wild pitch", "Win (baseball)", "Win Shares", "Win probability added", "Win shares", "Winning percentage", "Winning streak (sports)", "Wins Above Replacement", "Wins above replacement", "Win\u2013loss record (pitching)"], "references": ["http://www.baseball-almanac.com/", "http://www.fangraphs.com/library/index.php/pitching/lob/", "http://mlb.mlb.com/mlb/official_info/baseball_basics/abbreviations.jsp", "http://mlb.mlb.com/stats/historical/leaders.jsp?c_id=mlb&baseballScope=mlb&statType=1&sortByStat=All&timeFrame=1&timeSubFrame=2004", "http://doi.org/10.2307%2F2685280", "http://www.retrosheet.org/", "https://www.baseball-reference.com/"]}, "Mean square weighted deviation": {"categories": ["All articles covered by WikiProject Wikify", "All articles with too few wikilinks", "Articles covered by WikiProject Wikify from August 2016", "Articles with too few wikilinks from August 2016", "Geochronological dating methods", "Statistical deviation and dispersion"], "title": "Reduced chi-squared statistic", "method": "Mean square weighted deviation", "url": "https://en.wikipedia.org/wiki/Reduced_chi-squared_statistic", "summary": "In statistics, the reduced chi-squared statistic is used extensively in goodness of fit testing. It is also known as mean square weighted deviation (MSWD) in isotopic dating and variance of unit weight in the context of weighted least squares.Its square root is called regression standard error, standard error of the regression, or standard error of the equation\n(see Ordinary least squares#Reduced chi-squared)", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e1/Ambox_wikify.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/e/e1/20121002130016%21Ambox_wikify.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/e/e1/20110517152050%21Ambox_wikify.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/e/e1/20101207003759%21Ambox_wikify.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/e/e1/20101207003359%21Ambox_wikify.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/e/e1/20080429230220%21Ambox_wikify.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/e/e1/20080429225941%21Ambox_wikify.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/e/e1/20080429225545%21Ambox_wikify.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/e/e1/20080429225007%21Ambox_wikify.svg"], "links": ["Chi-squared distribution", "Degree of freedom (statistics)", "Deviation (statistics)", "Digital object identifier", "Geochronology", "Goodness of fit", "Helium", "International Standard Book Number", "Isotopic dating", "Ordinary least squares", "Rasch Model", "Standard deviation", "Thorium", "Uranium", "Variance", "Weighted arithmetic mean", "Weighted least squares"], "references": ["http://www.physics.csbsju.edu/stats/chi_fit.html", "http://neutrons2.ornl.gov/workshops/sns_hfir_users/posters/Laub_Chi-Square_Data_Fitting.pdf", "https://books.google.com.br/books?id=AbEVDAAAQBAJ&lpg=PA135&dq=reduced%20chi-squared%20in%20regression&pg=PA107#v=onepage&q&f=false", "https://books.google.com.br/books?id=GcILAQAAQBAJ&lpg=PA109&dq=reduced%20chi-squared%20per%20degree%20of%20freedom&pg=PA109#v=onepage&q&f=false", "https://books.google.com.br/books?id=GhGAlryfy6cC&lpg=PA224&dq=reduced%20chi-squared%20per%20degree%20of%20freedom&pg=PA169#v=onepage&q&f=false", "https://books.google.com.br/books?id=HXF02H8USjIC&lpg=PA264&dq=reduced%20chi-squared%20per%20degree%20of%20freedom&pg=PA264#v=onepage&q&f=false", "https://books.google.com.br/books?id=MjNwWUY8jx4C&lpg=PA333&dq=variance%20of%20unit%20weight&pg=PA301#v=onepage&q&f=false", "https://books.google.com.br/books?id=n3bvCAAAQBAJ&lpg=PA162&dq=variance%20of%20unit%20weight&pg=PA162#v=onepage&q&f=false", "https://doi.org/10.1144%2F0016-76492008-117", "https://cran.r-project.org/doc/contrib/Faraway-PRA.pdf", "https://www.rasch.org/rmt/rmt162f.htm"]}, "Taguchi methods": {"categories": ["All articles with minor POV problems", "All articles with unsourced statements", "Articles containing Japanese-language text", "Articles with minor POV problems from September 2015", "Articles with unsourced statements from June 2010", "Articles with unsourced statements from October 2011", "Articles with unsourced statements from September 2017", "CS1 errors: external links", "CS1 maint: Multiple names: authors list", "Design of experiments", "Manufacturing", "Pages with citations lacking titles", "Quality", "Quality control", "Systems engineering"], "title": "Taguchi methods", "method": "Taguchi methods", "url": "https://en.wikipedia.org/wiki/Taguchi_methods", "summary": "Taguchi methods (Japanese: \u30bf\u30b0\u30c1\u30e1\u30bd\u30c3\u30c9) are statistical methods, or sometimes called robust design methods, developed by Genichi Taguchi to improve the quality of manufactured goods, and more recently also applied to engineering, biotechnology, marketing and advertising. Professional statisticians have welcomed the goals and improvements brought about by Taguchi methods, particularly by Taguchi's development of designs for studying variation, but have criticized the inefficiency of some of Taguchi's proposals.Taguchi's work includes three principal contributions to statistics:\n\nA specific loss function\nThe philosophy of off-line quality control; and\nInnovations in the design of experiments.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Analytic studies", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calyampudi Radhakrishna Rao", "Canonical correlation", "Carbon dioxide", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Convergence (mathematics)", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Creativity", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "David Hume", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Detail design", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Donald J. Wheeler", "Durbin\u2013Watson statistic", "Econometrics", "Economist", "Effect size", "Efficiency (statistics)", "Electrochemical cell", "Elliptical distribution", "Empirical distribution function", "Engineering", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "Externalities", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gauss\u2013Markov theorem", "General linear model", "Generalized linear model", "Generalized randomized block design", "Genichi Taguchi", "Geographic information system", "Geometric mean", "George E. P. Box", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Higher-order statistics", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Idiosyncratic", "Index of dispersion", "Industrial engineering", "Innovation", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Japanese language", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laser engraving", "Latin hypercube sampling", "Latin square", "Law of large numbers", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Loss functions", "Lp space", "M-estimator", "Machine", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monotonic function", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Neil Sloane", "Nelson\u2013Aalen estimator", "Nicholas Logothetis", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nonprobability sampling", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Parametric statistics", "Pareto principle", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Private cost", "Probabilistic design", "Probability distribution", "Problem of induction", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Public economics", "Quality control", "Quality costs", "Quality engineering", "Quality management", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R. A. Fisher", "Radar chart", "Random assignment", "Random effect", "Random variables", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real analytic", "Reality", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust parameter design (RPD)", "Robust regression", "Robust statistics", "Robustification", "Ronald A. Fisher", "Run chart", "Sales process engineering", "Sample mean", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Saturated array", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal-to-noise ratio", "Simple linear regression", "Simple random sample", "Simultaneous equations model", "Six sigma", "Skewness", "Social cost", "Social statistics", "Society for Industrial and Applied Mathematics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistician", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi loss function", "Taylor series", "Time domain", "Time series", "Tolerance (engineering)", "Tolerance interval", "Tragedy of the commons", "Trend estimation", "U-statistic", "Unbiased estimator", "Uncorrelated", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Voltage", "W. Edwards Deming", "Wald test", "Walter A. Shewhart", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ua.ac.be/main.aspx?c=peter.goos", "http://users.telenet.be/peter.goos/springer.htm", "http://www.ec-securehost.com/SIAM/CL50.html", "http://neilsloane.com/doc/design.pdf", "http://neilsloane.com/doc/doeh.pdf", "http://neilsloane.com/doc/meatball.pdf", "http://www.us.oup.com/us/catalog/general/subject/Mathematics/ProbabilityStatistics/~~/dmlldz11c2EmY2k9OTc4MDE5OTI5NjYwNg==", "http://support.sas.com/publishing/bbu/companion_site/index_author.html#tobias", "http://www3.interscience.wiley.com/journal/117927543/abstract", "http://www.math.uni-augsburg.de/stochastik/pukelsheim/", "http://www.ncbi.nlm.nih.gov/pubmed/18320563", "http://www.eng.tau.ac.il/~bengal/Eco_Design.pdf", "http://www.eng.tau.ac.il/~bengal/Journal%20Paper.pdf", "http://doi.org/10.1002%2Fbiot.200700201", "http://doi.org/10.1016%2FS0032-9592(03)00207-3", "http://doi.org/10.1016%2Fj.jmatprotec.2008.03.021", "http://doi.org/10.1080%2F00401706.1992.10484904", "http://doi.org/10.2307%2F1269331", "http://stats.lse.ac.uk/atkinson/", "http://www.lse.ac.uk/collections/cats/People/HenryPage.htm", "http://www.maths.manchester.ac.uk/~adonev/", "https://books.google.com/books?id=5ZcfDZUJ4F8C", "https://books.google.com/books?id=oIHsrw6NBmoC", "https://www.springer.com/series/694", "https://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-95515-5"]}, "One- and two-tailed tests": {"categories": ["Statistical tests"], "title": "One- and two-tailed tests", "method": "One- and two-tailed tests", "url": "https://en.wikipedia.org/wiki/One-_and_two-tailed_tests", "summary": "In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value may be more than or less than the reference value, for example, whether a test taker may score above or below the historical average. \nA one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, for example, whether a machine produces more than one-percent defective products. Alternative names are one-sided and two-sided tests; the terminology \"tail\" is used because the extreme portions of distributions, where observations lead to rejection of the null hypothesis, are small and often \"tail off\" toward zero as in the normal distribution or \"bell curve\", pictured on the right.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8e/Chi-square_distributionCDF-English.png", "https://upload.wikimedia.org/wikipedia/commons/9/96/DisNormal06.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/0/00/P-value_Graph.png", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli trial", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Checking whether a coin is fair", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Critical values", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness-of-fit", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John E. Freund", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lady tasting tea", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "Paired difference test", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile function", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance testing", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Methods for Research Workers", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "The Design of Experiments", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://edr.sagepub.com/content/20/9/13.short", "http://www.sciencedirect.com/science/article/pii/S0003347298907564", "http://doi.org/10.1080%2F14786440009463897", "http://www.economics.soton.ac.uk/staff/aldrich/1900.pdf", "https://drive.google.com/file/d/0B76EXfrQqs3ha255TkliQk1ONEE/view"]}, "Mean and predicted response": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "Regression analysis"], "title": "Mean and predicted response", "method": "Mean and predicted response", "url": "https://en.wikipedia.org/wiki/Mean_and_predicted_response", "summary": "In linear regression, mean response and predicted response are values of the dependent variable calculated from the regression parameters and a given value of the independent variable. The values of these two responses are the same, but their calculated variances are different.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Analysis of covariance", "Analysis of variance", "Approximation theory", "Bayesian experimental design", "Bayesian linear regression", "Bayesian multivariate linear regression", "Binomial regression", "Calibration curve", "Chebyshev nodes", "Chebyshev polynomials", "Computational statistics", "Confidence interval", "Confounding", "Correlation and dependence", "Covariance matrix", "Curve fitting", "Design of experiments", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "Explanatory variable", "Fixed effects model", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Growth curve (statistics)", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Kendall tau rank correlation coefficient", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "List of statistics articles", "Local regression", "Logistic regression", "Mallows's Cp", "Minimum mean-square error", "Mixed logit", "Mixed model", "Model selection", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate analysis of variance", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Optimal design", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson product-moment correlation coefficient", "Poisson regression", "Polynomial regression", "Prediction interval", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Rank correlation", "Regression analysis", "Regression model validation", "Regularized least squares", "Response surface methodology", "Response variable", "Ridge regression", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Spearman's rank correlation coefficient", "Statistical model", "Statistics", "Stepwise regression", "Straight line fitting", "Studentized residual", "System identification", "Tikhonov regularization", "Total least squares", "Weighted least squares"], "references": []}, "Odds": {"categories": ["All articles needing additional references", "All articles needing expert attention", "All articles that are too technical", "All articles with unsourced statements", "Articles needing additional references from May 2018", "Articles needing expert attention from March 2016", "Articles with unsourced statements from May 2016", "CS1 maint: Explicit use of et al.", "CS1 maint: Multiple names: authors list", "Randomness", "Statistical ratios", "Use dmy dates from September 2010", "Wagering", "Wikipedia articles that are too technical from March 2016"], "title": "Odds", "method": "Odds", "url": "https://en.wikipedia.org/wiki/Odds", "summary": "Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics. In statistics, the odds for or odds of some event reflect the likelihood that the event will take place, while odds against reflect the likelihood that it will not. In gambling, the odds are the ratio of payoff to stake, and do not necessarily reflect exactly the probabilities. Odds are expressed in several ways (see below), and sometimes the term is used incorrectly to mean simply the probability of an event. Conventionally, gambling odds are expressed in the form \"X to Y\", where X and Y are numbers, and it is implied that the odds are odds against the event on which the gambler is considering wagering. In both gambling and statistics, the 'odds' are a numerical expression of the likelihood of some possible event.\nIn gambling, odds represent the ratio between the amounts staked by parties to a wager or bet. Thus, odds of 6 to 1 mean the first party (normally a bookmaker) stakes six times the amount staked by the second party. In simplest terms, 6 to 1 odds means if you bet a dollar (the \"1\" in the expression), and you win you get paid six dollars (the \"6\" in the expression), or 6 x 1. If you bet two dollars you would be paid twelve dollars, or 6 x 2. If you bet three dollars and win, you would be paid eighteen dollars, or 6 x 3. If you bet one hundred dollars and win you would be paid six hundred dollars, or 6 x 100. If you lose any of those bets you would lose the dollar, or two dollars, or three dollars, or one hundred dollars.\nIn statistics, the odds for an event E are defined as a simple function of the probability of that possible event E. One drawback of expressing the uncertainty of this possible event as odds for is that to regain the probability requires a calculation. The natural way to interpret odds for (without calculating anything) is as the ratio of events to non-events in the long run. A simple example is that the (statistical) odds for rolling a three with a fair die (one of a pair of dice) are 1 to 5. This is because, if one rolls the die many times, and keeps a tally of the results, one expects 1 three event for every 5 times the die does not show three (i.e., a 1, 2, 4, 5 or 6). For example, if we roll the fair die 600 times, we would very much expect something in the neighborhood of 100 threes, and 500 of the other five possible outcomes. That is a ratio of 100 to 500, or simply 1 to 5. To express the (statistical) odds against, the order of the pair is reversed. Hence the odds against rolling a three with a fair die are 5 to 1. The probability of rolling a three with a fair die is the single number 1/6, roughly 0.17.\nThe gambling and statistical uses of odds are closely interlinked. If a bet is a fair one, then the odds offered to the gamblers will perfectly reflect relative probabilities. A fair bet that a fair die will roll a three will pay the gambler $5 for a $1 wager (and return the bettor his or her wager) in the case of a three and nothing in any other case. The terms of the bet are fair, because on average, five rolls result in something other than a three, at a cost of $5, for every roll that results in a three and a net payout of $5. The profit and the expense exactly offset one another and so there is no advantage to gambling over the long run. If the odds being offered to the gamblers do not correspond to probability in this way then one of the parties to the bet has an advantage over the other. Casinos, for example, offer odds that place themselves at an advantage, which is how they guarantee themselves a profit and survive as businesses. The fairness of a particular gamble is more clear in a game involving relatively pure chance, such as the ping-pong ball method used in state lotteries in the United States. It is much harder to judge the fairness of the odds offered in a wager on a sporting event such as a football match.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Alternative rock", "ArXiv", "Australia", "Average", "Bayes factor", "Bayesian statistics", "Bernoulli trial", "Betting exchanges", "Bookmaker", "Calculation", "Canada", "Cardano", "Casino", "Chess handicap", "Circular transform", "Clinical trial", "Coin toss", "Colon (punctuation)", "Denominator", "Dice", "Equally likely outcomes", "Europe", "Even money", "Event (probability theory)", "Expected value", "Fair value", "Football", "Fraction (mathematics)", "Galton box", "Gambler", "Gambling", "Gaming mathematics", "Heads or tails", "Henry IV, Part II", "Horse racing", "Hyphen", "Index (economics)", "Integer", "Intuition", "Intuition (knowledge)", "Ireland", "Log-odds", "Logistic regression", "Logit", "Lowest common denominator", "Match race", "Mathematics of bookmaking", "Moneyline odds", "Multiplicative inverse", "M\u00f6bius transformation", "New Zealand", "Numerator", "Odds (band)", "Odds against", "Odds algorithm", "Odds ratio", "Optimal stopping", "Outcome (probability)", "Overround", "Parabolic transform", "Parlay (gambling)", "Polymath", "Probability", "Probability theory", "Profit margin", "Proposition", "Random variable", "Ratio", "Rational number", "Rebecca Goldin", "Sample space", "Sharply multiply transitive", "Slash (punctuation)", "Sports information service", "Spread betting", "Statistical association football predictions", "Statistician", "Statistics", "Symbol", "Table tennis", "The Odds Against", "Uncertainty", "United Kingdom", "United States", "Unity (mathematics)", "Vernacular", "Vigorish", "William Shakespeare"], "references": ["http://betstarter.com/sportsbetting/Fractionalodds.asp#3", "http://www.goal.com/en/news/2994/betting/2011/01/10/2101368/betting-school-understanding-fractional-decimal-betting-odds", "http://www.powerball.com/powerball/pb_prizes.asp", "http://www.soccerwidow.com/betting-advice/betting-terminology/understanding-betting-odds-moneyline-fractional-decimal/", "http://mathworld.wolfram.com/Odds.html", "http://www.wolframalpha.com/input/?i=Poker+Probabilities", "http://zcodebettingsystem.com/odds-worth-betting-review/", "http://www.columbia.edu/~pg2113/index_files/Gorroochurn-Some%20Laws.pdf", "http://www.amstat.org/publications/jse/v20n3/fulton.pdf", "http://arxiv.org/abs/1710.02824", "http://www.stats.org/stories/2008/odds_ratios_april4_2008.html", "http://ubplj.org/index.php/jpm/article/view/987/968", "https://blogabet.com/betting-guide/betting-basics/betting-odds-explained", "https://ed.ted.com/on/cTH8zSi7#digdeeper", "https://m.wbx.com/Help.aspx?IC=50176&S=&ID=20012", "https://www.wired.com/wiredscience/2010/10/exoplanet-stats/", "https://web.archive.org/web/20140402082613/http://betstarter.com/SportsBetting/FractionalOdds.asp/", "https://web.archive.org/web/20140502002250/https://m.wbx.com/Help.aspx?IC=50176&S=&ID=20012", "https://web.archive.org/web/20140714143749/http://stats.org/stories/2008/odds_ratios_april4_2008.html"]}, "Multitrait-multimethod matrix": {"categories": ["Psychometrics", "Validity (statistics)"], "title": "Multitrait-multimethod matrix", "method": "Multitrait-multimethod matrix", "url": "https://en.wikipedia.org/wiki/Multitrait-multimethod_matrix", "summary": "The multitrait-multimethod (MTMM) matrix is an approach to examining construct validity developed by Campbell and Fiske (1959). It organizes convergent and discriminant validity evidence for comparison of how a measure relates to other measures.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6c/Psi2.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/6c/20101113061943%21Psi2.svg"], "links": ["Abnormal psychology", "Applied behavior analysis", "Applied psychology", "Basic science (psychology)", "Behavioral neuroscience", "Behavioural genetics", "Big Five personality traits", "Clinical psychology", "Cognitive psychology", "Cognitivism (psychology)", "Community psychology", "Comparative psychology", "Confirmatory factor analysis", "Construct (philosophy of science)", "Construct validity", "Consumer behaviour", "Convergent validity", "Counseling psychology", "Critical psychology", "Cross-cultural psychology", "Cultural psychology", "Developmental psychology", "Differential psychology", "Discriminant validity", "Donald T. Campbell", "Donald W. Fiske", "Educational psychology", "Environmental psychology", "European Social Survey", "Evolutionary psychology", "Experimental psychology", "Forensic psychology", "Health psychology", "History of psychology", "Human factors and ergonomics", "Humanistic psychology", "Index of psychology articles", "Industrial and organizational psychology", "Legal psychology", "List of important publications in psychology", "List of psychological research methods", "List of psychological schools", "List of psychologists", "List of psychology disciplines", "List of psychology organizations", "List of psychotherapies", "Mathematical psychology", "Medical psychology", "Military psychology", "Music psychology", "Neuropsychology", "Occupational health psychology", "Outline of psychology", "Personality psychology", "Political psychology", "Positive psychology", "Psychology", "Psychology of religion", "Quantitative psychology", "School psychology", "Social psychology", "Sport psychology", "Strong inference", "Subfields of psychology", "Timeline of psychology", "Traffic psychology"], "references": ["http://gim.med.ucla.edu/FacultyPages/Hays/utils/"]}, "M/M/c queue": {"categories": ["Single queueing nodes"], "title": "M/M/c queue", "method": "M/M/c queue", "url": "https://en.wikipedia.org/wiki/M/M/c_queue", "summary": "In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang\u2013C model) is a multi-server queueing model. In Kendall's notation it describes a system where arrivals form a single queue and are governed by a Poisson process, there are c servers and job service times are exponentially distributed. It is a generalisation of the M/M/1 queue which considers only a single server. The model with infinitely many servers is the M/M/\u221e queue.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4c/Mmc-statespace.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Adversarial queueing network", "Arrival theorem", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "BCMP network", "Balance equation", "Bene\u0161 method", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burke's theorem", "Burkholder\u2013Davis\u2013Gundy inequalities", "Buzen's algorithm", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Communications in Statistics. 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This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms or muscular activity, non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.\nNMF finds applications in such fields as astronomy, computer vision, document clustering, chemometrics, audio signal processing, recommender systems, and bioinformatics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f2/Fractional_Residual_Variances_comparison%2C_PCA_and_NMF.pdf", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/NMF.png", "https://upload.wikimedia.org/wikipedia/commons/e/e8/Restricted_Boltzmann_machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["1980s", "Acta Neuropathologica", "Active set", "Algorithm", "Amnon Shashua", "Andrzej Cichocki", "Anomaly detection", "ArXiv", "Artificial neural network", "Artificial neural networks", "Association for Computing Machinery", "Association rule learning", "Astronomy", "Astronomy & Astrophysics", "Atmospheric Environment (journal)", "Audio signal processing", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Bibcode", "Bioinformatics", "Bioinformatics (journal)", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Chemometrics", "Chemometrics and Intelligent Laboratory Systems", "Chinese Science Bulletin", "Circumstellar disks", "CiteSeerX", "Cluster analysis", "Cluster indicator", "Collaborative filtering", "Computational Intelligence and Neuroscience", "Computational and Mathematical Organization Theory", "Computational learning theory", "Computer vision", "Conditional random field", "Conference on Neural Information Processing Systems", "Convex combination", "Convolutional neural network", "DBSCAN", "DNA methylation", "Data clustering", "Data mining", "Data stream", "Decision tree learning", "DeepDream", "Deep learning", "Digital object identifier", "Dimension reduction", "Dimensionality reduction", "Document-term matrix", "Edward A. 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"https://arxiv.org/pdf/cs/0202009", "https://dx.doi.org/10.1109/IJCNN.2004.1381036"]}, "Cost-of-living index": {"categories": ["Price index theory", "Price indices"], "title": "Cost-of-living index", "method": "Cost-of-living index", "url": "https://en.wikipedia.org/wiki/Cost-of-living_index", "summary": "A cost-of-living index is a theoretical price index that measures relative cost of living over time or regions. It is an index that measures differences in the price of goods and services, and allows for substitutions with other items as prices vary.There are many different methodologies that have been developed to approximate cost-of-living indexes. A Kon\u00fcs index is a type of cost-of-living index that uses an expenditure function such as one used in assessing expected compensating variation. The expected indirect utility is equated in both periods.", "images": [], "links": ["ACCRA Cost of Living Index", "Bureau of Labor Statistics", "Compensating variation", "Consumer price index", "Cost of living", "Good (economics)", "Indirect utility", "Kon\u00fcs index", "List of price index formulas", "Price index", "Public good", "Service (economics)", "Substitute good", "U.S. Bureau of Labor Statistics Division of Information Services", "U.S. Department of Labor", "United States Consumer Price Index", "Utility"], "references": ["http://www.bls.gov/bls/glossary.htm", "http://www.bls.gov/cpi/cpifaq.htm#Question_4", "http://www.ilo.org/public/english/bureau/stat/download/cpi/ch17.pdf"]}, "Risk function": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2018", "Loss functions", "Optimal decisions"], "title": "Loss function", "method": "Risk function", "url": "https://en.wikipedia.org/wiki/Loss_function", "summary": "In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some \"cost\" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its negative (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized.\nIn statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economics, for example, this is usually economic cost or regret. In classification, it is the penalty for an incorrect classification of an example. In actuarial science, it is used in an insurance context to model benefits paid over premiums, particularly since the works of Harald Cram\u00e9r in the 1920s. In optimal control, the loss is the penalty for failing to achieve a desired value. In financial risk management, the function is mapped to a monetary loss.\nIn classical statistics (both frequentist and Bayesian), a loss function is typically treated as something of a background mathematical convention. Critics such as W. Edwards Deming and Nassim Nicholas Taleb have argued that loss functions require much greater attention than they have traditionally been given and that loss functions used in real world decision making need to reflect actual empirical experience. They argue that real-world loss functions are often very different from the smooth, symmetric ones used by classical convention, and are often highly asymmetric, nonlinear, and discontinuous.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abraham Wald", "Absolute deviation", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bayesian regret", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Closed-form expression", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational neuroscience", "Confidence interval", "Confounding", "Contingency table", "Continuous function", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decision rule", "Decision theory", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Differentiable function", "Digital object identifier", "Discounted maximum loss", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Economic cost", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Event (probability theory)", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Financial risk management", "First-hitting-time model", "First-order condition", "Fitness function", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist", "Frequentist inference", "Friedman test", "Function space", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harald Cram\u00e9r", "Harmonic mean", "Heteroscedasticity", "Hinge loss", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "I.i.d.", "Index of dispersion", "Indicator function", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Invariant estimator", "Isotonic regression", "Jackknife resampling", "James Berger (statistician)", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "L2 norm", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Leonard J. Savage", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear-quadratic regulator", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss functions for classification", "Lp space", "M-estimator", "Machine learning", "Mann\u2013Whitney U test", "Mathematical Reviews", "Mathematical optimization", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean integrated squared error", "Mean squared error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimax", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Morbidity", "Morris H. DeGroot", "Mortality rate", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Nassim Nicholas Taleb", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Norm (mathematics)", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal control", "Optimal decision", "Optimal design", "Optimization algorithm", "Optimization problem", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parameter estimation", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pierre-Simon Laplace", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior distribution", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability measure", "Profit function", "Proportional hazards model", "Psychometrics", "Public health", "Quadratic form", "Quadratic function", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real number", "Regression analysis", "Regression model validation", "Regret (decision theory)", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Reward function", "Risk-loving", "Risk aversion", "Risk neutral", "Robust regression", "Robust statistics", "Run chart", "Safety engineering", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Scoring rule", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social Science Research Network", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical risk", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic control", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Support (measure theory)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Utility", "Utility function", "V-statistic", "Variance", "Vector autoregression", "Von Neumann-Morgenstern utility function", "W. Edwards Deming", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://ssrn.com/abstract=889323", "http://www.ams.org/mathscinet-getitem?mr=0804611", "http://www.ams.org/mathscinet-getitem?mr=1835885", "http://www.ams.org/mathscinet-getitem?mr=2288194", "http://doi.org/10.1007%2F0-387-71599-1", "http://doi.org/10.1016%2Fj.ijforecast.2009.10.008", "https://www.encyclopediaofmath.org/index.php?title=R/r082490"]}, "Uncertainty": {"categories": ["All articles with unsourced statements", "All articles with vague or ambiguous time", "Articles that may be too long from November 2017", "Articles using small message boxes", "Articles with attributed pull quotes", "Articles with unsourced statements from November 2017", "Articles with unsourced statements from September 2014", "Assumption", "CS1 maint: Archived copy as title", "Cognition", "Commons category link from Wikidata", "Concepts in epistemology", "Doubt", "Experimental physics", "Measurement", "Probability", "Probability interpretations", "Prospect theory", "Vague or ambiguous time from November 2017", "Webarchive template wayback links"], "title": "Uncertainty", "method": "Uncertainty", "url": "https://en.wikipedia.org/wiki/Uncertainty", "summary": "Uncertainty is a situation which involves imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable and/or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, psychology, sociology, engineering, metrology, meteorology, ecology and information science.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8b/Blank_Fork.png", "https://upload.wikimedia.org/wikipedia/commons/7/7b/Uncertainty.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Accuracy and precision", "Actuarial science", "Agnosticism", "Ambiguity", "American Journal of Botany", "Applied Information Economics", "Approximation", "Belief", "Bibcode", "Brady Haran", "CODATA", "Calibrated probability assessment", "Cambridge University Press", "Causality", "Certainty", "Chemical element", "Cognitive psychology", "Confidence interval", "Decision theory", "Dempster\u2013Shafer theory", "Dennis Lindley", "Determinism", "Digital object identifier", "Doubt", "EMBO Rep.", "Ecology", "Economics", "Effectuation", "Engineering", "Entrepreneurship", "Epistemology", "Error", "Error bar", "Expectation (epistemic)", "Fallibilism", "Fatalism", "Finance", "Financial market", "Frank Knight", "Frank Luntz", "Further research is needed", "Fuzzy logic", "Fuzzy set theory", "Gambling", "Game", "Game theory", "Global warming", "Hamlet", "Heisenberg uncertainty principle", "Heuristics", "Hypothesis", "ISO", "IUPAC", "Ignorance", "Information", "Information deficit model", "Information entropy", "Information science", "Information theory", "Insurance", "International Standard Book Number", "Interval finite element", "Itzhak Gilboa", "Jean-Jacques Laffont", "John Quiggin", "John Wiley & Sons", "Joseph Halpern", "Knightian uncertainty", "Laziness", "List of elements by atomic mass", "Lotfi A. Zadeh", "MIT Press", "Margin of error", "Martin Creed", "Measurement uncertainty", "Measuring instruments", "Meteorology", "Metereology", "Metrology", "Michael Smithson (author)", "Morphological analysis (problem-solving)", "NIST", "National Institute for Standards and Technology", "Nihilism", "Normal distribution", "Optimization", "Partially observable", "Peter Norvig", "Philosophy", "Physics", "Physics Today", "Presupposition (philosophy)", "Probabilities", "Probability", "Probability density function", "Probability distribution", "Probability theory", "Proof (truth)", "Propagation of uncertainty", "Psychology", "PubMed Central", "PubMed Identifier", "Quantum mechanics", "Random variables", "Randomness", "Risk", "Scenario optimization", "Schr\u00f6dinger's cat", "Science journalism", "Scientific consensus", "Scientific modelling", "Scientific theory", "Sebastian Thrun", "Sigma", "Significant figure", "Significant figures", "Skepticism", "Sociology", "Solipsism", "Springer-Verlag", "Standard deviation", "Standard error (statistics)", "Statistical", "Statistical mechanics", "Statistics", "Stochastic", "Stochastic optimization", "Subjective logic", "Surprisal", "Systematic error", "The Scientist (magazine)", "Theory", "Theory of justification", "Truth", "Udacity", "Uncertainty (film)", "Uncertainty principle", "Uncertainty propagation", "Uncertainty quantification", "Uncertainty tolerance", "University of Chicago", "University of Nottingham", "Vagueness", "Variance", "Volatility, uncertainty, complexity and ambiguity", "Wayback Machine", "Weather forecast"], "references": ["http://www.fasor.com/iso25/bibliography_of_uncertainty.htm", "http://www.sixtysymbols.com/videos/uncertainty.htm", "http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470539399.html", "http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470539399,descCd-tableOfContents.html", "http://www.uncertainty.de", "http://www.uncertainty.de/p97_s.pdf", "http://adsabs.harvard.edu/abs/2011PhT....64j..48S", "http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=7640", "http://strategic.mit.edu", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2002561", "http://www.ncbi.nlm.nih.gov/pubmed/17906667", "http://physics.nist.gov/Pubs/guidelines/contents.html", "http://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html", "http://www.scielo.org.mx/pdf/poli/n48/n48a2.pdf", "http://www.cambridge.org/aus/catalogue/catalogue.asp?isbn=9780521622448", "http://doi.org/10.1007%2FBF00486156", "http://doi.org/10.1007%2FBF03178705", "http://doi.org/10.1038%2Fsj.embor.7401072", "http://doi.org/10.1063%2Fpt.3.1296", "http://doi.org/10.1177%2F016224399602100302", "http://doi.org/10.3732%2Fajb.0900041", "http://understandinguncertainty.org/", "https://books.google.com/books/p/harvard?id=7r484x3HVu4C&printsec=find&pg=PR5=#v=onepage&q&f=false", "https://books.google.com/books/p/harvard?id=8wwbolpmLH8C&printsec=find&pg=PR7#v=onepage&q&f=false", "https://books.google.com/books?hl=en&lr=&id=UFAkkGaY1x4C&oi=fnd&pg=PR5&ots=Jm_WeKJYwO&sig=JeG1WGp5GhVHyHiUD9DWmWzLfwg#v=onepage&q&f=false", "https://books.google.com/books?id=_R54pqQWvPYC&pg=PR7lpg=PR7&dq=&source=bl&ots=6oKu2mnosK&sig=br2OLdOohXfbBB9UT5icGmj0imo&hl=en&ei=5Ow6TYq1DML6lwe61eCCBw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCwQ6AEwAw#v=onepage&q&f=false", "https://books.google.com/books?id=nqRlDQAAQBAJ&printsec=frontcover#v=onepage&q&f=false", "https://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-24419924-0", "https://www.udacity.com/wiki/cs271/unit1_notes", "https://icme.hpc.msstate.edu/mediawiki/index.php/Category:Uncertainty", "https://web.archive.org/web/20111016021440/http://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html", "https://web.archive.org/web/20111122171459/http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470539399.html", "https://web.archive.org/web/20120125171634/http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=7640", "https://web.archive.org/web/20130427210148/http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470539399,descCd-tableOfContents.html", "https://web.archive.org/web/20150926183351/https://icme.hpc.msstate.edu/mediawiki/index.php/Category:Uncertainty"]}, "Sinkov statistic": {"categories": ["All articles needing expert attention", "All stub articles", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Computational linguistics", "Cryptographic attacks", "Statistical natural language processing", "Statistics articles needing expert attention", "Statistics stubs"], "title": "Sinkov statistic", "method": "Sinkov statistic", "url": "https://en.wikipedia.org/wiki/Sinkov_statistic", "summary": "Sinkov statistics, also known as log-weight statistics, is a specialized field of statistics that was developed by Abraham Sinkov, while working for the small Signal Intelligence Service organization, the primary mission of which was to compile codes and ciphers for use by the U.S. Army. The mathematics involved include modular arithmetic, a bit of number theory, some linear algebra of two dimensions with matrices, some combinatorics, and a little statistics. Sinkov did not explain the theoretical underpinnings of his statistics, or characterized its distribution, nor did he give a decision procedure for accepting or rejecting candidate plaintexts on the basis of their S1 scores. The situation becomes more difficult when comparing strings of different lengths because Sinkov does not explain how the distribution of his statistics changes with length, especially when applied to higher-order grams. As for how to accept or reject a candidate plaintext, Sinkov simply said to try all possibilities and to pick the one with the highest S1 value. Although the procedure works for some applications, it is inadequate for applications that require on-line decisions. Furthermore, it is desirable to have a meaningful interpretation of the S1 values.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg"], "links": ["Abraham Sinkov", "Cipher", "Code", "Combinatorics", "Distribution (mathematics)", "Linear algebra", "Mathematics", "Matrix (mathematics)", "Modular arithmetic", "Number theory", "Plaintext", "Signal Intelligence Service", "Statistics", "String (computer science)", "United States Army"], "references": ["http://web.cecs.pdx.edu/~bart/decrypter/gs93.pdf", "https://www.amazon.co.uk/Elementary-Cryptanalysis-Mathematical-Approach-Library/dp/0883856220"]}, "Discrete probability distribution": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles with unsourced statements", "Articles lacking in-text citations from July 2011", "Articles needing additional references from July 2011", "Articles with multiple maintenance issues", "Articles with unsourced statements from March 2018", "Mathematical and quantitative methods (economics)", "Probability distributions", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers"], "title": "Probability distribution", "method": "Discrete probability distribution", "url": "https://en.wikipedia.org/wiki/Probability_distribution", "summary": "In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. For instance, if the random variable X is used to denote the outcome of a coin toss (\"the experiment\"), then the probability distribution of X would take the value 0.5 for X = heads, and 0.5 for X = tails (assuming the coin is fair). Examples of random phenomena can include the results of an experiment or survey.\nA probability distribution is defined in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed. The sample space may be the set of real numbers or a higher-dimensional vector space, or it may be a list of non-numerical values; for example, the sample space of a coin flip would be {heads, tails} .\nProbability distributions are generally divided into two classes. A discrete probability distribution (applicable to the scenarios where the set of possible outcomes is discrete, such as a coin toss or a roll of dice) can be encoded by a discrete list of the probabilities of the outcomes, known as a probability mass function. On the other hand, a continuous probability distribution (applicable to the scenarios where the set of possible outcomes can take on values in a continuous range (e.g. real numbers), such as the temperature on a given day) is typically described by probability density functions (with the probability of any individual outcome actually being 0). The normal distribution is a commonly encountered continuous probability distribution. More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures.\nA probability distribution whose sample space is the set of real numbers is called univariate, while a distribution whose sample space is a vector space is called multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution (a joint probability distribution) gives the probabilities of a random vector \u2013 a list of two or more random variables \u2013 taking on various combinations of values. Important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is a commonly encountered multivariate distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/1/12/Dice_Distribution_%28bar%29.svg", "https://upload.wikimedia.org/wikipedia/commons/8/85/Discrete_probability_distrib.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fb/Discrete_probability_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/6/64/Mixed_probability_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e8/Normal_probability_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARGUS distribution", "Absolute continuity", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Almost surely", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Antiderivative", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Cache language model", "Cambridge University Press", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central moment", "Central tendency", "Characteristic function (probability theory)", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Chi squared distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinant", "Complement (set theory)", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confounding", "Conjugate prior", "Contingency table", "Continuous and discrete variables", "Continuous function", "Continuous probability distribution", "Continuous time", "Continuous uniform distribution", "Control chart", "Convex combination", "Convex subset", "Convolution", "Conway\u2013Maxwell\u2013Poisson distribution", "Copula (statistics)", "Correlation and dependence", "Correlogram", "Count data", "Countable", "Countable set", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulative distribution function", "Dagum distribution", "Data collection", "Davis distribution", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dice", "Dickey\u2013Fuller test", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Disjoint set", "Distribution (disambiguation)", "Distribution (mathematics)", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical probability", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Event (probability theory)", "Ewens's sampling formula", "Expected value", "Experiment", "Experiment (probability theory)", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finite set", "First-hitting-time model", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "Fundamental particles", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Genetic variability", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "Geostatistics", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Half-open interval", "Harmonic mean", "Heavy-tailed distribution", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent (statistics)", "Index of dispersion", "Indicator function", "Infinitesimal", "Infinity", "Integral", "Integration (mathematics)", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval (mathematics)", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Jump discontinuity", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kinetic theory of gases", "Kirkwood approximation", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Lebesgue integration", "Lebesgue measure", "Lehmann\u2013Scheff\u00e9 theorem", "Library of Congress Control Number", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Limit (mathematics)", "Linear combination", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistical topics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Measurable function", "Measurable space", "Measure theory", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment-generating function", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo method", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate hypergeometric distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "National Diet Library", "National accounts", "Natural experiment", "Natural exponential family", "Natural language processing", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Non-negative definite", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Number", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outcome (probability)", "Outline of statistics", "Parabolic fractal distribution", "Paradox", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Polya urn scheme", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Power law", "Precision (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability-generating function", "Probability density function", "Probability mass function", "Probability measure", "Probability space", "Probability theory", "Proportional hazards model", "Pseudo-random number sampling", "Pseudorandom number generator", "Pseudorandomness", "Psychometrics", "PubMed Identifier", "Pushforward measure", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quantile function", "Quantum mechanical", "Quasi-experiment", "Quasiprobability distribution", "Questionnaire", "Q\u2013Q plot", "R-squared", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrix", "Random variable", "Random variate", "Random vector", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Randomness", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raw moment", "Rayleigh distribution", "Real numbers", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rice distribution", "Rician fading", "Riemann\u2013Stieltjes integral", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sample space", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Sampling without replacement", "Scalar (mathematics)", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singleton (mathematics)", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Springer Publishing", "Stable distribution", "Standard deviation", "Standard error", "Standard normal", "Standardized moment", "Stationary process", "Statistic", "Statistical Language Model", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic processes", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Student's t distribution", "Sufficient statistic", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "Symmetric probability distribution", "System identification", "Time domain", "Time series", "Tolerance interval", "Tracy\u2013Widom distribution", "Trend estimation", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Uniformly most powerful test", "Univariate distribution", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Vector space", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "Weibull distribution", "Weighted average", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://threeplusone.com/FieldGuide.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/25059432", "http://doi.org/10.1016%2Fj.ejmp.2014.05.002", "https://id.loc.gov/authorities/subjects/sh85038545", "https://id.ndl.go.jp/auth/ndlna/00564751", "https://www.encyclopediaofmath.org/index.php?title=p/p074900", "https://www.wikidata.org/wiki/Q200726"]}, "Stress majorization": {"categories": ["Dimension reduction", "Graph drawing", "Mathematical analysis", "Mathematical optimization"], "title": "Stress majorization", "method": "Stress majorization", "url": "https://en.wikipedia.org/wiki/Stress_majorization", "summary": "Stress majorization is an optimization strategy used in multidimensional scaling (MDS) where, for a set of n m-dimensional data items, a configuration X of n points in r(<<m)-dimensional space is sought that minimizes the so-called stress function \n \n \n \n \u03c3\n (\n X\n )\n \n \n {\\displaystyle \\sigma (X)}\n . Usually r is 2 or 3, i.e. the (n x r) matrix X lists points in 2- or 3-dimensional Euclidean space so that the result may be visualised (i.e. an MDS plot). The function \n \n \n \n \u03c3\n \n \n {\\displaystyle \\sigma }\n is a cost or loss function that measures the squared differences between ideal (\n \n \n \n m\n \n \n {\\displaystyle m}\n -dimensional) distances and actual distances in r-dimensional space. It is defined as:\n\n \n \n \n \u03c3\n (\n X\n )\n =\n \n \u2211\n \n i\n <\n j\n \u2264\n n\n \n \n \n w\n \n i\n j\n \n \n (\n \n d\n \n i\n j\n \n \n (\n X\n )\n \u2212\n \n \u03b4\n \n i\n j\n \n \n \n )\n \n 2\n \n \n \n \n {\\displaystyle \\sigma (X)=\\sum _{i<j\\leq n}w_{ij}(d_{ij}(X)-\\delta _{ij})^{2}}\n where \n \n \n \n \n w\n \n i\n j\n \n \n \u2265\n 0\n \n \n {\\displaystyle w_{ij}\\geq 0}\n is a weight for the measurement between a pair of points \n \n \n \n (\n i\n ,\n j\n )\n \n \n {\\displaystyle (i,j)}\n , \n \n \n \n \n d\n \n i\n j\n \n \n (\n X\n )\n \n \n {\\displaystyle d_{ij}(X)}\n is the euclidean distance between \n \n \n \n i\n \n \n {\\displaystyle i}\n and \n \n \n \n j\n \n \n {\\displaystyle j}\n and \n \n \n \n \n \u03b4\n \n i\n j\n \n \n \n \n {\\displaystyle \\delta _{ij}}\n is the ideal distance between the points (their separation) in the \n \n \n \n m\n \n \n {\\displaystyle m}\n -dimensional data space. Note that \n \n \n \n \n w\n \n i\n j\n \n \n \n \n {\\displaystyle w_{ij}}\n can be used to specify a degree of confidence in the similarity between points (e.g. 0 can be specified if there is no information for a particular pair).\nA configuration \n \n \n \n X\n \n \n {\\displaystyle X}\n which minimizes \n \n \n \n \u03c3\n (\n X\n )\n \n \n {\\displaystyle \\sigma (X)}\n gives a plot in which points that are close together correspond to points that are also close together in the original \n \n \n \n m\n \n \n {\\displaystyle m}\n -dimensional data space.\nThere are many ways that \n \n \n \n \u03c3\n (\n X\n )\n \n \n {\\displaystyle \\sigma (X)}\n could be minimized. For example, Kruskal recommended an iterative steepest descent approach. However, a significantly better (in terms of guarantees on, and rate of, convergence) method for minimizing stress was introduced by Jan de Leeuw. De Leeuw's iterative majorization method at each step minimizes a simple convex function which both bounds \n \n \n \n \u03c3\n \n \n {\\displaystyle \\sigma }\n from above and touches the surface of \n \n \n \n \u03c3\n \n \n {\\displaystyle \\sigma }\n at a point \n \n \n \n Z\n \n \n {\\displaystyle Z}\n , called the supporting point. In convex analysis such a function is called a majorizing function. This iterative majorization process is also referred to as the SMACOF algorithm (\"Scaling by MAjorizing a COmplicated Function\").", "images": [], "links": ["Cauchy-Schwarz", "Convex analysis", "Digital object identifier", "Euclidean distance", "Euclidean space", "Graph drawing", "Hessian matrix", "International Symposium on Graph Drawing", "Jan de Leeuw", "Joseph Kruskal", "Loss function", "MDS plot", "Matrix trace", "Multidimensional scaling", "Optimization (mathematics)", "Patrick Groenen", "Steepest descent"], "references": ["http://doi.org/10.1007/BF02289565", "http://doi.org/10.1007/s001800100077", "http://doi.org/10.1145/264645.264657"]}, "Kernel (statistics)": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles with unsourced statements", "Articles lacking in-text citations from May 2012", "Articles needing additional references from May 2012", "Articles with unsourced statements from May 2012", "Bayesian statistics", "Nonparametric statistics", "Point processes", "Time series"], "title": "Kernel (statistics)", "method": "Kernel (statistics)", "url": "https://en.wikipedia.org/wiki/Kernel_(statistics)", "summary": "The term kernel is used in statistical analysis to refer to a window function. The term \"kernel\" has several distinct meanings in different branches of statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ca/Kernel_Silverman.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_cosine.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Kernel_epanechnikov.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Kernel_exponential.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0c/Kernel_logistic.svg", "https://upload.wikimedia.org/wikipedia/commons/2/20/Kernel_quartic.svg", "https://upload.wikimedia.org/wikipedia/commons/6/6d/Kernel_triangle.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5c/Kernel_tricube.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e0/Kernel_triweight.svg", "https://upload.wikimedia.org/wikipedia/commons/3/39/Kernel_uniform.svg", "https://upload.wikimedia.org/wikipedia/commons/4/47/Kernels.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayesian analysis", "Bayesian statistics", "Boxcar function", "CiteSeerX", "Cluster analysis", "Conditional expectation", "Conjugate prior", "Density estimation", "Density function", "Digital object identifier", "Integrable", "Integral kernel", "International Standard Book Number", "Kernel (disambiguation)", "Kernel density estimation", "Kernel methods", "Kernel regression", "Kernel smoother", "Logistic distribution", "Machine learning", "Multivariate kernel density estimation", "Naomi Altman", "Non-negative", "Non-parametric", "Nonparametric statistics", "Normal distribution", "Normalization factor", "Normalizing constant", "Parameter", "Periodogram", "Point process", "Probability density function", "Probability distribution", "Probability mass function", "Pseudo-random number sampling", "Random variable", "Real-valued function", "Regression analysis", "Reproducing kernel Hilbert space", "Sigmoid function", "Spectral density", "Statistical classification", "Statistics", "Stochastic kernel", "Support (mathematics)", "Time-series", "Window function", "Window functions"], "references": ["http://staff.ustc.edu.cn/~zwp/teach/Math-Stat/kernel.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.76.8968", "http://doi.org/10.1080/00031305.1992.10475879", "http://doi.org/10.1080/01621459.1988.10478639", "http://doi.org/10.1109/34.1000236", "http://doi.org/10.1137/1114019"]}, "Random permutation statistics": {"categories": ["All articles that may contain original research", "Articles that may contain original research from July 2014", "Articles with French-language external links", "Combinatorics"], "title": "Random permutation statistics", "method": "Random permutation statistics", "url": "https://en.wikipedia.org/wiki/Random_permutation_statistics", "summary": "The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms, especially of sorting algorithms, which operate on random permutations. Suppose, for example, that we are using quickselect (a cousin of quicksort) to select a random element of a random permutation. Quickselect will perform a partial sort on the array, as it partitions the array according to the pivot. Hence a permutation will be less disordered after quickselect has been performed. The amount of disorder that remains may be analysed with generating functions. These generating functions depend in a fundamental way on the generating functions of random permutation statistics. Hence it is of vital importance to compute these generating functions.\nThe article on random permutations contains an introduction to random permutations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["100 prisoners problem", "Analysis of algorithms", "Binomial coefficient", "Binomial theorem", "CiteSeerX", "Derangement", "Determinant", "Divisor function", "Euler\u2013Maclaurin summation", "Even and odd permutations", "Exponential generating function", "Falling factorial", "Flajolet\u2013Sedgewick fundamental theorem", "Formal power series", "Golomb\u2013Dickman constant", "Harmonic number", "Inclusion\u2013exclusion", "Involution (mathematics)", "M\u00f6bius inversion", "On-Line Encyclopedia of Integer Sequences", "Permutation group", "Putnam competition", "Quickselect", "Quicksort", "Random permutation", "Random permutation statistics", "Rencontres numbers", "Stirling numbers of the first kind", "Stirling numbers of the second kind", "Telephone number (mathematics)", "Zero is even"], "references": ["http://math.stackexchange.com/questions/259351/permutations-with-a-cycle-fracn2", "http://math.stackexchange.com/questions/347260/derangements-property", "http://math.stackexchange.com/questions/349118/probability-permutations", "http://math.stackexchange.com/questions/495487/difference-of-number-of-cycles-of-even-and-odd-permutations", "http://math.stackexchange.com/questions/73896/keys-inside-closed-boxes-a-question-on-probability", "http://www.mathematik.uni-stuttgart.de/~riedelmo/papers/qsdis-jalc.pdf", "http://www.daimi.au.dk/~bromille/Papers/succinct.pdf", "http://www.math.dartmouth.edu/~pw/solutions.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.91.1088", "http://www.unl.edu/amc/a-activities/a7-problems/putnamindex.shtml", "http://les-mathematiques.u-strasbg.fr/phorum5/read.php?12,341672", "http://les-mathematiques.net"]}, "Selection bias": {"categories": ["Articles with short description", "Bias", "Causal inference", "Sampling (statistics)", "Scientific method"], "title": "Selection bias", "method": "Selection bias", "url": "https://en.wikipedia.org/wiki/Selection_bias", "summary": "Selection bias is the bias introduced by the selection of individuals, groups or data for analysis in such a way that proper randomization is not achieved, thereby ensuring that the sample obtained is not representative of the population intended to be analyzed. It is sometimes referred to as the selection effect. The phrase \"selection bias\" most often refers to the distortion of a statistical analysis, resulting from the method of collecting samples. If the selection bias is not taken into account, then some conclusions of the study may not be accurate.", "images": ["https://upload.wikimedia.org/wikipedia/en/a/aa/Emblem-question-yellow.svg"], "links": ["Academic bias", "Academic clinical trials", "Acquiescence bias", "Adaptive clinical trial", "Analysis of clinical trials", "Anchoring", "Animal testing", "Animal testing on non-human primates", "Anthropic reasoning", "ArXiv", "Attentional bias", "Attributable fraction among the exposed", "Attributable fraction for the population", "Attribution bias", "Authority bias", "Automation bias", "Availability heuristic", "Belief bias", "Berkson's paradox", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Biased sample", "Bibcode", "Black swan theory", "Blind experiment", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Cherry picking", "Cherry picking (fallacy)", "Choice-supportive bias", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Cohort study", "Combinatorial meta-analysis", "Confirmation bias", "Congruence bias", "Correlation does not imply causation", "Cross-sectional study", "Cultural bias", "Cumulative incidence", "Data dredging", "Debiasing", "Design of experiments", "Digital object identifier", "Distinction bias", "Dunning\u2013Kruger effect", "Ecological study", "Egocentric bias", "Emotional bias", "Endometrial cancer", "Epidemiological methods", "Ethical", "Evidence-based medicine", "Existential risks", "Exogenous", "Experiment", "External validity", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Failure bias", "First-in-man study", "Forecast bias", "Fundamental attribution error", "Funding bias", "Glossary of clinical research", "Halo effect", "Hazard ratio", "Health intervention", "Healthy user bias", "Heckman correction", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "Impact bias", "Impact event", "In-group favoritism", "In vitro", "In vivo", "Incidence (epidemiology)", "Inductive bias", "Infectivity", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "Intention-to-treat analysis", "Internal validity", "International Standard Book Number", "JSTOR", "Lagging (epidemiology)", "Lead time bias", "Length time bias", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "List of cognitive biases", "List of memory biases", "Longitudinal study", "Mean", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "Negativity bias", "Nested case\u2013control study", "Net bias", "Normalcy bias", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Omission bias", "Omitted-variable bias", "Open-label trial", "Optimism bias", "Outcome bias", "Outlier", "Overton window", "Participation bias", "Period prevalence", "Point prevalence", "Population Impact Measures", "Post hoc analysis", "Postmenopausal", "Pre- and post-test probability", "Precision bias", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Pro-innovation bias", "Prospective cohort study", "Protocol (science)", "PubMed Identifier", "Publication bias", "Random sample", "Randomized controlled trial", "Recall bias", "Regression analysis", "Relative risk reduction", "Reporting bias", "Reproducibility", "Response bias", "Response rate (survey)", "Restraint bias", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Sampling bias", "Sampling probability", "Scientific control", "Seeding trial", "Selective exposure theory", "Self-fulfilling prophecy", "Self-selection", "Self-selection bias", "Self-serving bias", "Social comparison bias", "Social desirability bias", "Specificity and sensitivity", "Spectrum bias", "Statistical", "Statistical population", "Statistical sample", "Status quo bias", "Survivorship bias", "Systematic error", "Systematic review", "Systemic bias", "Time-saving bias", "Trait ascription bias", "United States news media and the Vietnam War", "Vaccine trial", "Variance", "Verification bias", "Virulence", "Von Restorff effect", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://www.medilexicon.com/medicaldictionary.php?t=10087", "http://medical-dictionary.thefreedictionary.com/Sample+bias", "http://medical.webends.com/kw/Selection%20Bias", "http://adsabs.harvard.edu/abs/2005Natur.438..754T", "http://www.cs.nyu.edu/~mohri/postscript/bias.pdf", "http://www.cs.nyu.edu/~mohri/pub/nsmooth.pdf", "http://www.tufts.edu/~gdallal/out.htm", "http://www.cancer.gov/dictionary?CdrID=44087", "http://www.ncbi.nlm.nih.gov/pubmed/16341005", "http://www.ncbi.nlm.nih.gov/pubmed/17245804", "http://www.ncbi.nlm.nih.gov/pubmed/20626690", "http://www.ncbi.nlm.nih.gov/pubmed/698947", "http://www.ncbi.nlm.nih.gov/pubmed/9504213", "http://arxiv.org/abs/0805.2775", "http://doi.org/10.1002%2Fpds.1360", "http://doi.org/10.1007%2F978-3-540-87987-9_8", "http://doi.org/10.1016%2FS0145-2134(97)00131-2", "http://doi.org/10.1016%2Fj.tcs.2013.09.027", "http://doi.org/10.1038%2F438754a", "http://doi.org/10.1080%2F00401706.1960.10489875", "http://doi.org/10.1093%2Fije%2Fdyh406", "http://doi.org/10.1111%2Fj.1539-6924.2010.01460.x", "http://doi.org/10.2307%2F1912352", "http://www.jstor.org/stable/1912352", "https://books.google.com/books?id=f0IDHvLiWqUC"]}, "Bayesian experimental design": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from March 2011", "Bayesian statistics", "Design of experiments", "Industrial engineering", "Optimal decisions", "Systems engineering"], "title": "Bayesian experimental design", "method": "Bayesian experimental design", "url": "https://en.wikipedia.org/wiki/Bayesian_experimental_design", "summary": "Bayesian experimental design provides a general probability-theoretical framework from which other theories on experimental design can be derived. It is based on Bayesian inference to interpret the observations/data acquired during the experiment. This allows accounting for both any prior knowledge on the parameters to be determined as well as uncertainties in observations.\nThe theory of Bayesian experimental design is to a certain extent based on the theory for making optimal decisions under uncertainty. The aim when designing an experiment is to maximize the expected utility of the experiment outcome. The utility is most commonly defined in terms of a measure of the accuracy of the information provided by the experiment (e.g. the Shannon information or the negative variance), but may also involve factors such as the financial cost of performing the experiment. What will be the optimal experiment design depends on the particular utility criterion chosen.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Active learning (machine learning)", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian optimization", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calyampudi Radhakrishna Rao", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Differential entropy", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gambling and information theory", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geophysical Journal International", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kelly criterion", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kullback\u2013Leibler divergence", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Mutual information", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior distribution", "Posterior predictive distribution", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shannon information", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.stat.purdue.edu/~dasgupta/publications/tr95-04.pdf", "http://www.stat.uiowa.edu/~gwoodwor/AdvancedDesign/Chaloner%20Verdinelli.pdf", "http://doi.org/10.1046%2Fj.1365-246x.2003.02048.x", "http://doi.org/10.1093%2Fbioinformatics%2Fbts092", "http://doi.org/10.1198%2F1061860032012", "http://doi.org/10.1214%2Faoms%2F1177728069", "http://doi.org/10.1214%2Fss%2F1177009939", "http://doi.org/10.1371%2Fjournal.pcbi.1002888", "http://bioinformatics.oxfordjournals.org/content/28/8/1136.full.pdf", "http://www.ploscompbiol.org/article/info:doi%2F10.1371%2Fjournal.pcbi.1002888", "http://projecteuclid.org/handle/euclid.aoms/1177728069", "http://www.geos.ed.ac.uk/homes/acurtis/Papers/vandenBerg_etal2003.pdf", "https://web.archive.org/web/20110717161649/http://www.geos.ed.ac.uk/homes/acurtis/Papers/vandenBerg_etal2003.pdf"]}, "Evidence under Bayes theorem": {"categories": ["All articles needing additional references", "All articles that may contain original research", "Articles needing additional references from July 2013", "Articles that may contain original research from September 2008", "Bayesian statistics", "Evidence law", "Forensic statistics"], "title": "Evidence under Bayes theorem", "method": "Evidence under Bayes theorem", "url": "https://en.wikipedia.org/wiki/Evidence_under_Bayes_theorem", "summary": "The use of evidence under Bayes' theorem relates to the likelihood of finding evidence in relation to the accused, where Bayes' theorem concerns the probability of an event and its inverse. Specifically, it compares the probability of finding particular evidence if the accused were guilty, versus if they were not guilty. An example would be the probability of finding a person's hair at the scene, if guilty, versus if just passing through the scene. Another issue would be finding a person's DNA where they lived, regardless of committing a crime there.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayes' theorem", "Cancer", "DNA", "Economics", "Empirical", "Evidence (law)", "Expert testimony", "Judicial", "Litigation", "Lotfi Zadeh", "Mamogram", "Probability", "Probability theory", "Psychology", "R v Adams", "Rules of evidence", "Skepticism", "Soft computing", "Statistic", "Trial (law)", "UC Berkeley"], "references": ["http://www.lawyerintl.com/law-articles/2451-Bayes'%20Theorem%20in%20the%20Court%20of%20Appeal", "http://lpr.oxfordjournals.org/"]}, "Log-linear modeling": {"categories": ["All articles lacking sources", "Articles lacking sources from July 2012", "Log-linear models"], "title": "Log-linear model", "method": "Log-linear modeling", "url": "https://en.wikipedia.org/wiki/Log-linear_model", "summary": "A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression. That is, it has the general form\n\n \n \n \n exp\n \u2061\n \n (\n \n c\n +\n \n \u2211\n \n i\n \n \n \n w\n \n i\n \n \n \n f\n \n i\n \n \n (\n X\n )\n \n )\n \n \n \n {\\displaystyle \\exp \\left(c+\\sum _{i}w_{i}f_{i}(X)\\right)}\n ,in which the fi(X) are quantities that are functions of the variables X, in general a vector of values, while c and the wi stand for the model parameters.\nThe term may specifically be used for:\n\nA log-linear plot or graph, which is a type of semi-log plot.\nPoisson regression for contingency tables, a type of generalized linear model.The specific applications of log-linear models are where the output quantity lies in the range 0 to \u221e, for values of the independent variables X, or more immediately, the transformed quantities fi(X) in the range \u2212\u221e to +\u221e. This may be contrasted to logistic models, similar to the logistic function, for which the output quantity lies in the range 0 to 1. Thus the contexts where these models are useful or realistic often depends on the range of the values being modelled.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Boltzmann distribution", "Function (mathematics)", "General linear model", "Generalized linear model", "Linear combination", "Linear regression", "Log-linear analysis", "Logarithm", "Logistic function", "Mathematical model", "Multivariate analysis", "Parameter", "Poisson regression", "Semi-log plot"], "references": []}, "G/G/1 queue": {"categories": ["Single queueing nodes"], "title": "G/G/1 queue", "method": "G/G/1 queue", "url": "https://en.wikipedia.org/wiki/G/G/1_queue", "summary": "In queueing theory, a discipline within the mathematical theory of probability, the G/G/1 queue represents the queue length in a system with a single server where interarrival times have a general (meaning arbitrary) distribution and service times have a (different) general distribution. The evolution of the queue can be described by the Lindley equation.The system is described in Kendall's notation where the G denotes a general distribution for both interarrival times and service times and the 1 that the model has a single server. Different interarrival and service times are considered to be independent, and sometimes the model is denoted GI/GI/1 to emphasise this.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "ArXiv", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bibcode", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "David George Kendall", "Decomposition method (queueing theory)", "Digital object identifier", "Erlang (unit)", "Erlang distribution", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy-tailed distribution", "Heavy traffic approximation", "Information system", "International Standard Book Number", "JSTOR", "Jackson network", "John Kingman", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley's integral equation", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markovian arrival process", "Mathematical Proceedings of the Cambridge Philosophical Society", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Mor Harchol-Balter", "N. U. Prabhu", "Network congestion", "Network scheduler", "Phase type distribution", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Production and Operations Management", "Quality of service", "Quasireversibility", "Queueing Systems", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations", "Wally Smith (mathematician)", "Ward Whitt", "Wiener\u2013Hopf method"], "references": ["http://www.columbia.edu/~ww2040/ApproxGIGm1993.pdf", "http://www.columbia.edu/~ww2040/impact2000.pdf", "http://adsabs.harvard.edu/abs/1953PCPS...49..449S", "http://adsabs.harvard.edu/abs/1961PCPS...57..902K", "http://arxiv.org/abs/1303.4705", "http://doi.org/10.1002%2F9780470400531.eorms0878", "http://doi.org/10.1007%2F978-0-8176-4725-4_9", "http://doi.org/10.1007%2F978-3-642-80838-8_5", "http://doi.org/10.1007%2Fs11134-006-3613-z", "http://doi.org/10.1017%2FCBO9781139226424.031", "http://doi.org/10.1017%2FS0305004100028620", "http://doi.org/10.1017%2FS0305004100036094", "http://doi.org/10.1023%2FA:1019143505968", "http://doi.org/10.1111%2Fj.1937-5956.1993.tb00094.x", "http://doi.org/10.1214%2Faoms%2F1177728975", "http://www.jstor.org/stable/2236285", "http://www.jstor.org/stable/2984229", "http://projecteuclid.org/euclid.aoms/1177728975"]}, "Probability space": {"categories": ["Experiment (probability theory)"], "title": "Probability space", "method": "Probability space", "url": "https://en.wikipedia.org/wiki/Probability_space", "summary": "In probability theory, a probability space or a probability triple \n \n \n \n (\n \u03a9\n ,\n \n \n F\n \n \n ,\n P\n )\n \n \n {\\displaystyle (\\Omega ,{\\mathcal {F}},P)}\n is a mathematical construct that models a real-world process (or \u201cexperiment\u201d) consisting of states that occur randomly. A probability space is constructed with a specific kind of situation or experiment in mind. One proposes that each time a situation of that kind arises, the set of possible outcomes is the same and the probabilities are also the same.\nA probability space consists of three parts:\nA sample space, \n \n \n \n \u03a9\n \n \n {\\displaystyle \\Omega }\n , which is the set of all possible outcomes.\nA set of events \n \n \n \n \n \n F\n \n \n \n \n {\\displaystyle {\\mathcal {F}}}\n , where each event is a set containing zero or more outcomes.\nThe assignment of probabilities to the events; that is, a function \n \n \n \n P\n \n \n {\\displaystyle P}\n from events to probabilities.An outcome is the result of a single execution of the model. Since individual outcomes might be of little practical use, more complex events are used to characterize groups of outcomes. The collection of all such events is a \u03c3-algebra \n \n \n \n \n \n F\n \n \n \n \n {\\displaystyle {\\mathcal {F}}}\n . Finally, there is a need to specify each event's likelihood of happening. This is done using the probability measure function, \n \n \n \n P\n \n \n {\\displaystyle P}\n .\nOnce the probability space is established, it is assumed that \u201cnature\u201d makes its move and selects a single outcome, \n \n \n \n \u03c9\n \n \n {\\displaystyle \\omega }\n , from the sample space \n \n \n \n \u03a9\n \n \n {\\displaystyle \\Omega }\n . All the events in \n \n \n \n \n \n F\n \n \n \n \n {\\displaystyle {\\mathcal {F}}}\n that contain the selected outcome \n \n \n \n \u03c9\n \n \n {\\displaystyle \\omega }\n (recall that each event is a subset of \n \n \n \n \u03a9\n \n \n {\\displaystyle \\Omega }\n ) are said to \u201chave occurred\u201d. The selection performed by nature is done in such a way that if the experiment were to be repeated an infinite number of times, the relative frequencies of occurrence of each of the events would coincide with the probabilities prescribed by the function \n \n \n \n P\n \n \n {\\displaystyle P}\n .\nThe Russian mathematician Andrey Kolmogorov introduced the notion of probability space, together with other axioms of probability, in the 1930s. Nowadays alternative approaches for axiomatization of probability theory exist; see \u201cAlgebra of random variables\u201d, for example.\nThis article is concerned with the mathematics of manipulating probabilities. The article probability interpretations outlines several alternative views of what \u201cprobability\u201d means and how it should be interpreted. In addition, there have been attempts to construct theories for quantities that are notionally similar to probabilities but do not obey all their rules; see, for example, free probability, fuzzy logic, possibility theory, negative probability and quantum probability.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png"], "links": ["Algebra of random variables", "Almost surely", "Andrei Nikolajevich Kolmogorov", "Andrey Kolmogorov", "Arnold Schwarzenegger", "Atom (measure theory)", "Axioms of probability", "Bayes' theorem", "Boole's inequality", "Borel algebra", "Borel set", "Borel \u03c3-algebra", "Carath\u00e9odory's extension theorem", "Comparability", "Complement (set theory)", "Complementary event", "Conditional independence", "Conditional probability", "Countable", "Countable set", "Countably additive", "Cylinder set", "De Morgan\u2019s law", "Disjoint sets", "Disjoint union", "Edward Nelson", "Elementary event", "Empty set", "Encyclopedia of Mathematics", "Eric W. Weisstein", "Event (probability theory)", "Fair coin", "Filtered probability space", "Free probability", "Fuzzy logic", "Fuzzy measure theory", "Harold Jeffreys", "Independence (probability theory)", "International Standard Book Number", "Intersection (set theory)", "Joint probability distribution", "Law of large numbers", "Law of total probability", "Lebesgue measure", "Marginal distribution", "MathWorld", "Mathematical model", "Measurable", "Measurable function", "Measure (mathematics)", "Measure space", "Measure theory", "Michiel Hazewinkel", "Mutually exclusive", "Negative probability", "Non-empty set", "Non-measurable set", "Normal distribution", "One-to-one correspondence", "Outcome (probability)", "Partition of a set", "Patrick Billingsley", "Pierre Simon de Laplace", "Possibility theory", "Power set", "Probability", "Probability Space (novel)", "Probability axioms", "Probability distribution", "Probability interpretations", "Probability mass function", "Probability measure", "Probability theory", "Quantum probability", "Random variable", "Randomness", "Sample space", "Sequence", "Simple random sample", "Space (mathematics)", "Standard probability space", "Statistical independence", "Statistics", "Subset", "Talagrand's concentration inequality", "Tree diagram (probability theory)", "Uncountable", "Uncountable set", "Union (set theory)", "Venn diagram", "\u03a3-algebra"], "references": ["http://mathworld.wolfram.com/ProbabilitySpace.html", "http://www.math.princeton.edu/~nelson/books.html", "http://www.math.uah.edu/stat/", "http://www.math.uah.edu/stat/prob", "http://en.citizendium.org/wiki/Probability_space", "http://www.encyclopediaofmath.org/index.php/Probability_space", "https://www.youtube.com/watch?v=9eaOxgT5ys0", "https://www.encyclopediaofmath.org/index.php?title=P/p074960"]}, "Differential entropy": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from May 2018", "Entropy and information", "Information theory", "Statistical randomness"], "title": "Differential entropy", "method": "Differential entropy", "url": "https://en.wikipedia.org/wiki/Differential_entropy", "summary": "Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Shannon to extend the idea of (Shannon) entropy, a measure of average surprisal of a random variable, to continuous probability distributions. Unfortunately, Shannon did not derive this formula, and rather just assumed it was the correct continuous analogue of discrete entropy, but it is not. The actual continuous version of discrete entropy is the limiting density of discrete points (LDDP). Differential entropy (described here) is commonly encountered in the literature, but it is a limiting case of the LDDP, and one that loses its fundamental association with discrete entropy.", "images": [], "links": ["Almost everywhere", "ArXiv", "Beta distribution", "Beta function", "Bibcode", "Bit", "Cauchy distribution", "Change of variables", "Chi-squared distribution", "Chi distribution", "Conditional entropy", "Covariance", "Digamma function", "Digital object identifier", "Edwin Thompson Jaynes", "Elementary Principles in Statistical Mechanics", "Encyclopedia of Mathematics", "Entropy estimation", "Erlang distribution", "Estimator", "Euler-Mascheroni constant", "Exponential distribution", "F distribution", "Gamma distribution", "Gamma function", "Generalized Gaussian distribution", "Homeomorphisms", "If and only if", "Information entropy", "Information theory", "International Standard Book Number", "Invariant measure", "JSTOR", "Jacobian matrix and determinant", "Joint entropy", "Josiah Willard Gibbs", "Journal of the Royal Statistical Society, Series B", "Kullback\u2013Leibler divergence", "Laplace distribution", "Limiting density of discrete points", "Log-normal distribution", "Logarithm", "Logarithmic units", "Logistic distribution", "Matrix (mathematics)", "Maxwell\u2013Boltzmann distribution", "Michiel Hazewinkel", "Multivariate normal distribution", "Mutual information", "Nat (unit)", "Normal distribution", "Pareto distribution", "Physical Review E", "PlanetMath", "Probability density function", "Probability distribution", "Quantile function", "Quantization (signal processing)", "Random variable", "Rayleigh distribution", "Relative entropy", "Self-information", "Statistical independence", "Student's t-distribution", "Support (mathematics)", "Surprisal", "Triangular distribution", "Uniform distribution (continuous)", "Variational calculus", "Weibull distribution"], "references": ["http://www.wise.xmu.edu.cn/Master/Download/..%5C..%5CUploadFiles%5Cpaper-masterdownload%5C2009519932327055475115776.pdf", "http://adsabs.harvard.edu/abs/2004PhRvE..69f6138K", "http://bayes.wustl.edu/etj/articles/brandeis.pdf", "http://arxiv.org/abs/cond-mat/0305641", "http://doi.org/10.1103%2FPhysRevE.69.066138", "http://doi.org/10.1109%2FTIT.1978.1055832", "http://www.jstor.org/stable/2984828", "http://planetmath.org/?op=getobj&from=objects&id=1915", "https://books.google.com/books?id=RtzpRAiX6OgC&pg=PA8&dq=intitle:%22An+Introduction+to+Information+Theory%22++%22entropy+of+a+simple+source%22&as_brr=0&ei=zP79Ro7UBovqoQK4g_nCCw&sig=j3lPgyYrC3-bvn1Td42TZgTzj0Q", "https://math.stackexchange.com/questions/1745670/proof-of-upper-bound-on-differential-entropy-of-fx", "https://www.encyclopediaofmath.org/index.php?title=p/d031890", "https://pdfs.semanticscholar.org/881c/f0ccc5a9dbb772d5a07671773f3c14b551c2.pdf"]}, "Classification rule": {"categories": ["All articles needing additional references", "All articles needing expert attention", "Articles needing additional references from May 2011", "Articles needing expert attention from May 2011", "Articles needing expert attention with no reason or talk parameter", "Articles needing unspecified expert attention", "Statistical classification"], "title": "Classification rule", "method": "Classification rule", "url": "https://en.wikipedia.org/wiki/Classification_rule", "summary": "Given a population whose members each belong to one of a number of different sets or classes, a classification rule or classifier is a procedure by which the elements of the population set are each predicted to belong to one of the classes. A perfect classification is one for which every element in the population is assigned to the class it really belongs to. An imperfect classification is one in which some errors appear, and then statistical analysis must be applied to analyse the classification.\nA special kind of classification rule is binary classification, for problems in which there are only two classes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Binary-classification-labeled.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayes' theorem", "Bayes classifier", "Bayesian inference", "Binary classification", "Bowel cancer", "Class (set theory)", "Confusion matrix", "Decision rule", "Diagnostic test", "Disease", "Endoscopy", "Fecal occult blood", "Gold standard (test)", "International Standard Book Number", "Likelihood ratios in diagnostic testing", "Logistic regression", "Loss functions for classification", "Matthews correlation coefficient", "Medical test", "Multiclass classification", "Multinomial logit", "Multinomial probit", "Negative predictive value", "Positive predictive value", "Probit regression", "Sariel Har-Peled", "Sensitivity and specificity", "Statistical classification", "Statistical classification (machine learning)", "Statistical power", "Statistics", "Type I and type II errors"], "references": ["http://mathworld.wolfram.com/StatisticalTest.html"]}, "Hierarchical clustering": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2009", "Cluster analysis algorithms", "Network analysis"], "title": "Hierarchical clustering", "method": "Hierarchical clustering", "url": "https://en.wikipedia.org/wiki/Hierarchical_clustering", "summary": "In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types:\nAgglomerative: This is a \"bottom-up\" approach: each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy.\nDivisive: This is a \"top-down\" approach: all observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.In general, the merges and splits are determined in a greedy manner. The results of hierarchical clustering are usually presented in a dendrogram.\nThe standard algorithm for hierarchical agglomerative clustering (HAC) has a time complexity of \n \n \n \n \n \n O\n \n \n (\n \n n\n \n 3\n \n \n )\n \n \n {\\displaystyle {\\mathcal {O}}(n^{3})}\n and requires \n \n \n \n \n \n O\n \n \n (\n \n n\n \n 2\n \n \n )\n \n \n {\\displaystyle {\\mathcal {O}}(n^{2})}\n memory, which makes it too slow for even medium data sets. However, for some special cases, optimal efficient agglomerative methods (of complexity \n \n \n \n \n \n O\n \n \n (\n \n n\n \n 2\n \n \n )\n \n \n {\\displaystyle {\\mathcal {O}}(n^{2})}\n ) are known: SLINK for single-linkage and CLINK for complete-linkage clustering. With a heap the runtime of the general case can be reduced to \n \n \n \n \n \n O\n \n \n (\n \n n\n \n 2\n \n \n log\n \u2061\n n\n )\n \n \n {\\displaystyle {\\mathcal {O}}(n^{2}\\log n)}\n at the cost of further increasing the memory requirements. In many programming languages, the memory overheads of this approach are too large to make it practically usable.\nExcept for the special case of single-linkage, none of the algorithms (except exhaustive search in \n \n \n \n \n \n O\n \n \n (\n \n 2\n \n n\n \n \n )\n \n \n {\\displaystyle {\\mathcal {O}}(2^{n})}\n ) can be guaranteed to find the optimum solution.\nDivisive clustering with an exhaustive search is \n \n \n \n \n \n O\n \n \n (\n \n 2\n \n n\n \n \n )\n \n \n {\\displaystyle {\\mathcal {O}}(2^{n})}\n , but it is common to use faster heuristics to choose splits, such as k-means.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b5/Clusters.svg", "https://upload.wikimedia.org/wikipedia/commons/a/ad/Hierarchical_clustering_simple_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/1/12/Iris_dendrogram.png", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/9/97/Orange-data-mining-hierarchical-clustering.png", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ALGLIB", "Anomaly detection", "ArXiv", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Binary space partitioning", "Boosting (machine learning)", "Bootstrap aggregating", "Bounding volume hierarchy", "Brown clustering", "CURE data clustering algorithm", "Canonical correlation analysis", "Cladistics", "Cluster analysis", "Complete-linkage clustering", "Computational learning theory", "Computational phylogenetics", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "Covariance matrix", "CrimeStat", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Dendrogram", "Determining the number of clusters in a data set", "Digital object identifier", "Dimensionality reduction", "Distance", "Distance matrix", "ELKI", "Empirical risk minimization", "Energy distance", "Ensemble learning", "Euclidean distance", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature engineering", "Feature learning", "GNU", "GNU Octave", "Gated recurrent unit", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Greedy algorithm", "Hamming distance", "Heap (data structure)", "Hidden Markov model", "Hierarchical clustering of networks", "Hierarchy", "Independent component analysis", "International Conference on Machine Learning", "International Standard Book Number", "Iris flower data set", "JSTOR", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Learning to rank", "Levenshtein distance", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Locality-sensitive hashing", "Logistic regression", "Long short-term memory", "MATLAB", "Machine Learning (journal)", "Machine learning", "Mahalanobis distance", "Manhattan distance", "MathWorks", "Mathematica", "Mathematical Reviews", "Mean-shift", "Metric (mathematics)", "Multilayer perceptron", "NCSS (statistical software)", "Naive Bayes classifier", "Nearest-neighbor chain algorithm", "Nearest neighbor search", "Non-negative matrix factorization", "Numerical taxonomy", "OPTICS algorithm", "Occam learning", "Online machine learning", "Orange (software)", "Outline of machine learning", "Perceptron", "Principal component analysis", "Probably approximately correct learning", "Q-learning", "Qlucore", "R (programming language)", "Random forest", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Robert Tibshirani", "SAS Institute", "SAS System", "SCaViS", "SPSS", "SciPy", "Scikit-learn", "Self-organizing map", "Semi-supervised learning", "Single-linkage clustering", "Stata", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical distance", "Statistical learning theory", "Statistics", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Time complexity", "Top-down and bottom-up design", "Trevor Hastie", "U-Net", "UPGMA", "Uniform norm", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory", "Ward's method", "Weka (machine learning)"], "references": ["http://www.springerlink.com/content/c8795u6232184423/", "http://www.cs.gsu.edu/~wkim/index_files/papers/sibson.pdf", "http://www-stat.stanford.edu/~tibs/ElemStatLearn/", "http://www.ams.org/mathscinet-getitem?mr=0148188", "http://arxiv.org/abs/cs/0608049", "http://doi.org/10.1007%2Fs00357-005-0012-9", "http://doi.org/10.1007%2Fs00357-008-9004-x", "http://doi.org/10.1093%2Fcomjnl%2F16.1.30", "http://doi.org/10.1093%2Fcomjnl%2F20.4.364", "http://doi.org/10.2307%2F2282967", "http://www.jstor.org/stable/2282967", "http://comjnl.oxfordjournals.org/content/20/4/364.abstract", "https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/statug_distance_sect016.htm", "https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/statug_cluster_sect012.htm", "https://web.archive.org/web/20091110212529/http://www-stat.stanford.edu/~tibs/ElemStatLearn/", "https://arxiv.org/abs/1208.5092", "https://arxiv.org/list/cs.LG/recent", "https://cran.r-project.org/web/packages/dendextend/vignettes/Cluster_Analysis.html"]}, "Information ratio": {"categories": ["Financial ratios", "Statistical ratios"], "title": "Information ratio", "method": "Information ratio", "url": "https://en.wikipedia.org/wiki/Information_ratio", "summary": "The information ratio, also known as appraisal ratio, is a measure of the risk-adjusted return of a financial security (or asset or portfolio). It is defined as expected active return divided by tracking error, where active return is the difference between the return of the security and the return of a selected benchmark index, and tracking error is the standard deviation of the active return; i.e., the information ratio \n \n \n \n I\n R\n \n \n {\\displaystyle IR}\n is:\n\n \n \n \n I\n R\n =\n \n \n \n E\n [\n \n R\n \n p\n \n \n \u2212\n \n R\n \n b\n \n \n ]\n \n \u03c3\n \n \n =\n \n \n \u03b1\n \u03c9\n \n \n =\n \n \n \n E\n [\n \n R\n \n p\n \n \n \u2212\n \n R\n \n b\n \n \n ]\n \n \n \n v\n a\n r\n \n [\n \n R\n \n p\n \n \n \u2212\n \n R\n \n b\n \n \n ]\n \n \n \n \n \n {\\displaystyle IR={\\frac {E[R_{p}-R_{b}]}{\\sigma }}={\\frac {\\alpha }{\\omega }}={\\frac {E[R_{p}-R_{b}]}{\\sqrt {\\mathrm {var} [R_{p}-R_{b}]}}}}\n ,where \n \n \n \n \n R\n \n p\n \n \n \n \n {\\displaystyle R_{p}}\n is the portfolio return, \n \n \n \n \n R\n \n b\n \n \n \n \n {\\displaystyle R_{b}}\n is the benchmark return, \n \n \n \n \u03b1\n =\n E\n [\n \n R\n \n p\n \n \n \u2212\n \n R\n \n b\n \n \n ]\n \n \n {\\displaystyle \\alpha =E[R_{p}-R_{b}]}\n is the expected value of the active return, and \n \n \n \n \u03c9\n =\n \u03c3\n \n \n {\\displaystyle \\omega =\\sigma }\n is the standard deviation of the active return, which is an alternate definition of the aforementioned tracking error.\nNote in this case, \n \n \n \n \u03b1\n \n \n {\\displaystyle \\alpha }\n is defined as excess return, not the risk-adjusted excess return or Jensen's alpha calculated using regression analysis. Some analysts, however, do use Jensen's alpha for the numerator and a regression-adjusted tracking error for the denominator (this version of the information ratio is often described as the appraisal ratio to differentiate it from the more common definition).The information ratio is often used to gauge the skill of managers of mutual funds, hedge funds, etc. In this case, it measures the active return of the manager's portfolio divided by the amount of risk that the manager takes relative to the benchmark. The higher the information ratio, the higher the active return of the portfolio, given the amount of risk taken, and the better the manager. Top-quartile investment managers typically achieve annualized information ratios of about one-half. There are both ex ante expected and ex post observed information ratios.\nGenerally, the information ratio compares the returns of the manager's portfolio with those of a benchmark such as the yield on three-month Treasury bills or an equity index such as the S&P 500.\nThe information ratio is often annualized. While it is then common for the numerator to be calculated as the arithmetic difference between the annualized portfolio return and the annualized benchmark return, this is an approximation because the annualization of an arithmetic difference between terms is not the arithmetic difference of the annualized terms. Since the denominator is here taken to be the annualized standard deviation of the arithmetic difference of these series, which is a standard measure of annualized risk, and since the ratio of annualized terms is the annualization of their ratio, the annualized information ratio provides the annualized risk-adjusted active return of the portfolio relative to the benchmark.\nThe information ratio is similar to the Sharpe ratio but, whereas the Sharpe ratio is the 'excess' return of an asset over the return of a risk free asset divided by the variability or standard deviation of returns, the information ratio is the 'active' return to the most relevant benchmark index divided by the standard deviation of the 'active' return or tracking error.\nSome hedge funds use Information ratio as a metric for calculating a performance fee.\nOne of the main criticisms of the Information Ratio is that it considers arithmetic returns and ignores leverage. This can lead to the Information Ratio calculated for a manager being negative when the manager produces alpha to the benchmark and vice versa. A better measure of the alpha produced by the manager is the Geometric Information Ratio.", "images": [], "links": ["Active return", "Calmar ratio", "Coefficient of variation", "Expected value", "Hedge fund", "Information coefficient", "International Standard Book Number", "Jensen's alpha", "Modern portfolio theory", "Mutual fund", "Omega ratio", "Performance fee", "S&P 500", "Sharpe ratio", "Sortino ratio", "Standard deviation", "Sterling ratio", "Tracking error", "Treynor ratio", "United States Treasury security", "Upside potential ratio", "V2 ratio"], "references": ["http://www.automated-trading-system.com/geometric-information-ratio/#start", "https://www.evanstoncap.com/docs/news-and-research/evanston-capital-research---appraisal-ratio.pdf"]}, "Recursive Bayesian estimation": {"categories": ["Bayesian estimation", "CS1 maint: Multiple names: authors list", "Linear filters", "Nonlinear filters", "Signal estimation"], "title": "Recursive Bayesian estimation", "method": "Recursive Bayesian estimation", "url": "https://en.wikipedia.org/wiki/Recursive_Bayesian_estimation", "summary": "Recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density function recursively over time using incoming measurements and a mathematical process model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/81/HMM_Kalman_Filter_Derivation.svg"], "links": ["Computer science", "Control theory", "Density estimation", "Digital object identifier", "Hidden Markov model", "Kalman filter", "Markov process", "Multivariate normal distribution", "Naive Bayes spam filtering", "Normal Distribution", "Particle filter", "Probability density function", "Robot", "Robotics", "Smoothing problem"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.1144", "http://becs.aalto.fi/~ssarkka/pub/cup_book_online_20131111.pdf", "http://cogprints.org/3755/1/Diard03a.pdf", "http://doi.org/10.1016%2Fj.sigpro.2014.10.025", "http://doi.org/10.1109%2F78.978374", "https://dx.doi.org/10.1016/j.sigpro.2014.10.025"]}, "Rothamsted Experimental Station": {"categories": ["1843 establishments in England", "Agricultural organisations based in England", "Agricultural soil science", "All articles with dead external links", "Articles with dead external links from April 2018", "Articles with permanently dead external links", "Botanical research institutes", "Buildings and structures in Hertfordshire", "CS1 maint: Archived copy as title", "Charities based in England", "Commons category link is on Wikidata", "Coordinates on Wikidata", "Harpenden", "Organisations based in Hertfordshire", "Organizations established in 1843", "Research institutes in Hertfordshire", "Rothamsted Experimental Station"], "title": "Rothamsted Research", "method": "Rothamsted Experimental Station", "url": "https://en.wikipedia.org/wiki/Rothamsted_Research", "summary": "Rothamsted Research, previously known as the Rothamsted Experimental Station and then the Institute of Arable Crops Research, is one of the oldest agricultural research institutions in the world, having been founded in 1843. It is located at Harpenden in the English county of Hertfordshire and is a registered charity under English law.One of the station's best known and longest running experiments is the Park Grass Experiment, a biological study that started in 1856 and has been continuously monitored ever since.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/56/John_Bennet_Lawes3.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/ad/Makers_of_British_botany%2C_Plate_19_%28Joseph_Henry_Gilbert%29.png", "https://upload.wikimedia.org/wikipedia/commons/4/46/R._A._Fischer.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Rothamsted_-_Centenary_building.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/26/Rothamsted_Research.jpg", "https://upload.wikimedia.org/wikipedia/commons/6/63/Rothamsted_plaque.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["1967 United Kingdom foot-and-mouth outbreak", "2,4-D", "2001 United Kingdom foot-and-mouth outbreak", "2007 United Kingdom foot-and-mouth outbreak", "ADAS (company)", "Agricultural Land Classification", "Agricultural experiment station", "Agriculture", "Agriculture and Horticulture Development Board", "Agriculture in England", "Agriculture in London", "Agriculture in Scotland", "Agriculture in the United Kingdom", "Alfred Daniel Hall", "Animal Health and Veterinary Laboratories Agency", "Arla Foods UK", "Augustus Daniel Imms", "Beekeeping in the United Kingdom", "Bernard Matthews Farms", "Biochemistry", "Biographical Memoirs of Fellows of the Royal Society", "Biotechnology and Biological Sciences Research Council", "Block design", "British Agricultural Revolution", "British Cattle Movement Service", "British Egg Industry Council", "British Poultry Council", "British timber trade", "Broom's Barn Experimental Station", "Bury St Edmunds", "Carrington Bonsor Williams", "Celtic field", "Charitable organization", "Charity Commission for England and Wales", "Colin Butler (entomologist)", "College of Agriculture, Food and Rural Enterprise", "Common land", "Corn Laws", "Cornish cuisine", "Country Land and Business Association", "Countryfile", "Crofting", "Crown Estate", "Cuisine of Devon", "Dairy Crest", "Department for Environment, Food and Rural Affairs", "Department of Agriculture and Rural Development", "Diggers", "Digital object identifier", "Dutch barn", "E. John Russell", "Economy of the United Kingdom", "Eglu", "Enclosure", "Energy crop", "English cuisine", "Eugenics", "Evolutionary biologist", "F. M. L. Sheffield", "Faccenda Group", "Factor (Scotland)", "Farmcare", "Farmers' Union of Wales", "Farmers Weekly", "Farming Today", "Fell farming", "Fishing industry in England", "Fishing industry in Scotland", "Foot-and-mouth disease", "Forestry in the United Kingdom", "Frank Anscombe", "Frank Yates", "Fresh Start Initiative", "Frontier Agriculture", "Genetically modified", "Genetics", "Genstat", "Genus plc", "Geographic coordinate system", "George W. Cooke", "Grazing marsh", "Harpenden", "Haughley Experiment", "Hedgerow removal", "Hertfordshire", "Highland Clearances", "Highland Potato Famine", "Howard Penman", "Hurdles (agricultural)", "Institute for Animal Health", "Institute of Biological, Environmental and Rural Sciences", "James Hutton Institute", "John Bennet Lawes", "John Catt", "John Monteith", "John Nelder", "John Wishart (statistician)", "Joseph Henry Gilbert", "Joseph Oscar Irwin", "Juda Hirsch Quastel", "Judah Hirsch Quastel", "June Gap", "Katherine Warington", "List of domesticated Scottish breeds", "Long-term experiment", "Long Ashton Research Station", "Lowland Clearances", "Mark Lynas", "Mary Dilys Glynne", "Maurice Moloney", "Meat and Livestock Commission", "Museum of English Rural Life", "M\u00fcller Wiseman Dairies", "NFU Mutual", "Napier Commission", "National Farmers' Union of England and Wales", "National Farmers' Union of Scotland", "National Museum of Rural Life", "National Non-Food Crops Centre", "Natural 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"https://apps.charitycommission.gov.uk/Showcharity/RegisterOfCharities/SearchResultHandler.aspx?RegisteredCharityNumber=802038"]}, "Random function": {"categories": ["Statistical data types", "Stochastic models", "Stochastic processes", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from July 2018"], "title": "Stochastic process", "method": "Random function", "url": "https://en.wikipedia.org/wiki/Stochastic_process", "summary": "In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time, such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. They have applications in many disciplines including sciences such as biology, chemistry, ecology, neuroscience, and physics as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries.The term random function is also used to refer to a stochastic or random process, because a stochastic process can also be interpreted as a random element in a function space. The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. But often these two terms are used when the random variables are indexed by the integers or an interval of the real line. If the random variables are indexed by the Cartesian plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects.Based on their mathematical properties, stochastic processes can be divided into various categories, which include random walks, martingales, Markov processes, L\u00e9vy processes, Gaussian processes, random fields, renewal processes, and branching processes. The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis. The theory of stochastic processes is considered to be an important contribution to mathematics and it continues to be an active topic of research for both theoretical reasons and applications.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4e/BMonSphere.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/3f/DriftedWienerProcess1D.svg", "https://upload.wikimedia.org/wikipedia/commons/9/96/Joseph_Doob.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/38/Wiener_Zurich1932.tif", "https://upload.wikimedia.org/wikipedia/commons/f/f8/Wiener_process_3d.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["A.K. Erlang", "A. K. Erlang", "Abraham de Moivre", "Abstract Wiener space", "Abuse of notation", "Actuarial mathematics", "Albert Einstein", "Aleksandr Khinchin", "Alexander A. 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"https://books.google.com/books?id=c_3UBwAAQBAJ", "https://books.google.com/books?id=dBNOHvElXZ4C", "https://books.google.com/books?id=dP2JBAAAQBAJ&pg=PA1", "https://books.google.com/books?id=dQkYMjRK3fYC", "https://books.google.com/books?id=dSDxjX9nmmMC", "https://books.google.com/books?id=ddsrGdsgN9sC&pg=PA269", "https://books.google.com/books?id=e-TbA-dSrzYC", "https://books.google.com/books?id=e9saZ0YSi-AC", "https://books.google.com/books?id=eBeNngEACAAJ", "https://books.google.com/books?id=ePxDAQAAIAAJ", "https://books.google.com/books?id=evbGTPhuvSoC", "https://books.google.com/books?id=fnCQWd0GEZ8C&pg=PA113", "https://books.google.com/books?id=fsgkBAAAQBAJ&pg=PR4", "https://books.google.com/books?id=ftcsQgMp5cUC&pg=PR8", "https://books.google.com/books?id=gqriBQAAQBAJ&pg=PR10", "https://books.google.com/books?id=h3WVqBPHboAC", "https://books.google.com/books?id=hRk_AAAAQBAJ", "https://books.google.com/books?id=hRk_AAAAQBAJ&pg", "https://books.google.com/books?id=iojEts9YAxIC", "https://books.google.com/books?id=jrPVBwAAQBAJ", "https://books.google.com/books?id=kWEwk1UL42AC", "https://books.google.com/books?id=lSz_vQAACAAJ", "https://books.google.com/books?id=n3JNDAAAQBAJ&pg=PR4", "https://books.google.com/books?id=nPENXKw5kwcC", "https://books.google.com/books?id=pOQy6-qnVx8C", "https://books.google.com/books?id=pY5_DkvI-CcC&pg=PR4", "https://books.google.com/books?id=pa20eZJe4LIC", "https://books.google.com/books?id=q0lo91imeD0C", "https://books.google.com/books?id=q7dR3d5nqaUC", "https://books.google.com/books?id=q7eDUjdJxIkC", "https://books.google.com/books?id=r9r6CAAAQBAJ=PA1", "https://books.google.com/books?id=rUbxAAAAMAAJ", "https://books.google.com/books?id=ryejJmJAj28C&pg=PA1", "https://books.google.com/books?id=ryejJmJAj28C&pg=PA263", "https://books.google.com/books?id=tfa5BAAAQBAJ&pg=PR4", "https://books.google.com/books?id=tlWOphOFRgwC", "https://books.google.com/books?id=w0SgBQAAQBAJ&pg=PT5", "https://books.google.com/books?id=wGUECAAAQBAJ", "https://books.google.com/books?id=yJyLzG7N7r8C", "https://books.google.com/books?id=yJyLzG7N7r8C&pg=PR2", "https://books.google.com/books?id=yPvECi_L3bwC", "https://books.google.com/books?id=yWcvT80gQK4C", "https://books.google.co.nz/books?id=321EuQAACAAJ&dq=Stochastic+methods&hl=en&sa=X&ved=0ahUKEwiEz7bPhLHbAhUJNrwKHWdoCXcQ6AEIKTAA"]}, "General linear model": {"categories": ["Regression models"], "title": "General linear model", "method": "General linear model", "url": "https://en.wikipedia.org/wiki/General_linear_model", "summary": "The general linear model or multivariate regression model is a statistical linear model. It may be written as\n\n \n \n \n \n Y\n \n =\n \n X\n \n \n B\n \n +\n \n U\n \n ,\n \n \n {\\displaystyle \\mathbf {Y} =\\mathbf {X} \\mathbf {B} +\\mathbf {U} ,}\n where Y is a matrix with series of multivariate measurements (each column being a set of measurements on one of the dependent variables), X is a matrix of observations on independent variables that might be a design matrix (each column being a set of observations on one of the independent variables), B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors (noise).\nThe errors are usually assumed to be uncorrelated across measurements, and follow a multivariate normal distribution. If the errors do not follow a multivariate normal distribution, generalized linear models may be used to relax assumptions about Y and U.\nThe general linear model incorporates a number of different statistical models: ANOVA, ANCOVA, MANOVA, MANCOVA, ordinary linear regression, t-test and F-test. The general linear model is a generalization of multiple linear regression model to the case of more than one dependent variable. If Y, B, and U were column vectors, the matrix equation above would represent multiple linear regression.\nHypothesis tests with the general linear model can be made in two ways: multivariate or as several independent univariate tests. In multivariate tests the columns of Y are tested together, whereas in univariate tests the columns of Y are tested independently, i.e., as multiple univariate tests with the same design matrix.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANCOVA", "ANOVA", "Academic Press", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Brain scan", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Column vector", "Comparison of general and generalized linear models", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design matrix", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete choice", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fixed effects model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gauss\u2013Markov theorem", "General linear methods", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent variable", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iteratively reweighted least squares", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "K. V. Mardia", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least-angle regression", "Least absolute deviations", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear least squares", "Linear model", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MANCOVA", "MANOVA", "Mann\u2013Whitney U test", "Mathematical Reviews", "Matrix (mathematics)", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multiple linear regression", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares regression", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal component regression", "Prior probability", "Probabilistic design", "Probability distribution", "Probit model", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effects model", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regularized least squares", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Special case", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical parametric mapping", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Univariate", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ams.org/mathscinet-getitem?mr=2283455", "http://doi.org/10.1002%2Fhbm.460020402", "http://doi.org/10.1007%2Fb98890"]}, "Zero\u2013one law (disambiguation)": {"categories": ["All set index articles", "Probability theory", "Set indices on mathematics"], "title": "Zero\u2013one law", "method": "Zero\u2013one law (disambiguation)", "url": "https://en.wikipedia.org/wiki/Zero%E2%80%93one_law", "summary": "In probability theory, a zero\u2013one law is a result that states that an event must have probability 0 or 1 and no intermediate value. Sometimes, the statement is that the limit of certain probabilities must be 0 or 1.\nIt may refer to: \n\nBorel\u2013Cantelli lemma\nBlumenthal's zero\u2013one law for Markov processes,\nEngelbert\u2013Schmidt zero\u2013one law for continuous, nondecreasing additive functionals of Brownian motion,\nHewitt\u2013Savage zero\u2013one law for exchangeable sequences,\nKolmogorov's zero\u2013one law for the tail \u03c3-algebra,\nL\u00e9vy's zero\u2013one law, related to martingale convergence.\ntopological zero\u2013one law related to meager sets", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8c/DAB_list_gray.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg"], "links": ["Blumenthal's zero\u2013one law", "Borel\u2013Cantelli lemma", "Engelbert\u2013Schmidt zero\u2013one law", "Hewitt\u2013Savage zero\u2013one law", "Kolmogorov's zero\u2013one law", "L\u00e9vy's zero\u2013one law", "Markov process", "Meager set", "Probability theory", "Topological zero\u2013one law"], "references": []}, "Nelson rules": {"categories": ["Quality control tools", "Statistical charts and diagrams", "Technical communication"], "title": "Nelson rules", "method": "Nelson rules", "url": "https://en.wikipedia.org/wiki/Nelson_rules", "summary": "Nelson rules are a method in process control of determining if some measured variable is out of control (unpredictable versus consistent). Rules, for detecting \"out-of-control\" or non-random conditions were first postulated by Walter A. Shewhart in the 1920s. The Nelson rules were first published in the October 1984 issue of the Journal of Quality Technology in an article by Lloyd S Nelson.The rules are applied to a control chart on which the magnitude of some variable is plotted against time. The rules are based on the mean value and the standard deviation of the samples.\n\nThe above eight rules apply to a chart of a variable value.\nA second chart, the moving range chart, can also be used but only with rules 1, 2, 3 and 4. Such a chart plots a graph of the maximum value - minimum value of N adjacent points against the time sample of the range.\nAn example moving range: if N = 3 and values are 1, 3, 5, 3, 3, 2, 4, 5 then the sets of adjacent points are (1,3,5) (3,5,3) (5,3,3) (3,3,2) (3,2,4) (2,4,5) resulting in moving range values of (5-1) (5-3) (5-3) (3-2) (4-2) (5-2) = 4, 2, 2, 1, 2, 3.\nApplying these rules indicates when a potential \"out of control\" situation has arisen. However, there will always be some false alerts and the more rules applied the more will occur. For some processes, it may be beneficial to omit one or more rules. Equally there may be some missing alerts where some specific \"out of control\" situation is not detected. Empirically, the detection accuracy is good.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a0/Rule_1_-_Control_Charts_for_Nelson_Rules.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0e/Rule_2_-_Control_Charts_for_Nelson_Rules.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e0/Rule_3_-_Control_Charts_for_Nelson_Rules.svg", "https://upload.wikimedia.org/wikipedia/commons/3/35/Rule_4_-_Control_Charts_for_Nelson_Rules.svg", "https://upload.wikimedia.org/wikipedia/commons/2/20/Rule_5_-_Control_Charts_for_Nelson_Rules.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7b/Rule_6_-_Control_Charts_for_Nelson_Rules.svg", "https://upload.wikimedia.org/wikipedia/commons/a/ae/Rule_7_-_Control_Charts_for_Nelson_Rules.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b7/Rule_8_-_Control_Charts_for_Nelson_Rules.svg"], "links": ["Accuracy", "American Society for Quality", "Common cause and special cause", "Control chart", "Journal of Quality Technology", "Lloyd S Nelson", "Mean", "National Institute of Standards and Technology", "Oscillation (mathematics)", "Process control", "Range (statistics)", "Signal noise", "Standard deviation", "Statistical process control", "Systematic bias", "Trend estimation", "Variable (mathematics)", "Walter A. Shewhart", "Western Electric rules"], "references": ["http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc32.htm", "http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA310869", "http://www.asq.org/learn-about-quality/data-collection-analysis-tools/overview/control-chart.html", "https://doi.org/10.1080/00224065.1984.11978921"]}, "Transferable belief model": {"categories": ["All Wikipedia articles needing context", "All articles lacking in-text citations", "All pages needing cleanup", "Articles lacking in-text citations from June 2010", "Dempster\u2013Shafer theory", "Logic", "Statistical inference", "Wikipedia articles needing context from May 2016", "Wikipedia introduction cleanup from May 2016"], "title": "Transferable belief model", "method": "Transferable belief model", "url": "https://en.wikipedia.org/wiki/Transferable_belief_model", "summary": "The transferable belief model (TBM) is an elaboration on the Dempster\u2013Shafer theory (DST) of evidence developed by Philippe Smets who proposed his approach as a response to Zadeh\u2019s example against Dempster's rule of combination. In contrast to the original DST the TBM propagates the open-world assumption that relaxes the assumption that all possible outcomes are known. Under the open world assumption Dempster's rule of combination is adapted such that there is no normalization. The underlying idea is that the probability mass pertaining to the empty set is taken to indicate an unexpected outcome, e.g. the belief in a hypothesis outside the frame of discernment. This adaptation violates the probabilistic character of the original DST and also Bayesian inference. Therefore, the authors substituted notation such as probability masses and probability update with terms such as degrees of belief and transfer giving rise to the name of the method: The transferable belief model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Bayesian inference", "Belief", "Belief functions", "Beliefs", "Collectively exhaustive events", "Cromwell's rule", "Decision making", "Dempster's rule of combination", "Dempster\u2013Shafer theory", "Digital object identifier", "Empty set", "Frame of discernment", "Hypothesis", "Information fusion", "International Standard Book Number", "Lofti Zadeh", "Normalization (statistics)", "Open-world assumption", "Paradox", "Philip Smets", "Philippe Smets", "Pignistic probability", "Power set", "Principle of insufficient reason", "Principle of maximum entropy", "Probability axioms", "Probability distribution", "Probability functions", "Probability mass", "Probability mass function", "Rudolf Kruse", "Singletons", "Uniform distribution (continuous)", "Zadeh\u2019s example"], "references": ["http://iridia.ulb.ac.be/~psmets/#G", "http://iridia.ulb.ac.be/~psmets/AABPapers.html", "http://iospress.metapress.com/content/FW6KLYTMAB49FNXH", "http://hal.archives-ouvertes.fr/docs/00/34/85/77/PDF/ramasso_rombaut_pellerin_escqaru07_CRHMM.pdf", "http://doi.org/10.1016%2F0004-3702(94)90026-4", "http://doi.org/10.1016%2Fj.ijar.2007.03.004", "https://web.archive.org/web/20060925065210/http://iridia.ulb.ac.be/Projects/trans.html"]}, "Top-coded": {"categories": ["All stub articles", "Econometrics stubs", "Statistical data coding"], "title": "Top-coded", "method": "Top-coded", "url": "https://en.wikipedia.org/wiki/Top-coded", "summary": "In econometrics and statistics, a top-coded data observation is one for which data points whose values are above an upper bound are censored.\nSurvey data are often topcoded before release to the public to preserve the anonymity of respondents. For example, if a survey answer reported a respondent with self-identified wealth of $79 billion, it would not be anonymous because people would know there is a good chance the respondent was Bill Gates. Top-coding may be also applied to prevent possibly-erroneous outliers from being published.\nBottom-coding is analogous, e.g. if amounts below zero are reported as zero. Top-coding occurs for data recorded in groups, e.g. if age ranges are reported in these groups: 0-20, 21-50, 50-99, 100-and-up. Here we only know how many people have ages above 100, not their distribution. Producers of survey data sometimes release the average of the censored amounts to help users impute unbiased estimates of the top group.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170527191524%21Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170519203409%21Emoji_u1f4c8.svg"], "links": ["Bill Gates", "Censoring (statistics)", "Current Population Survey", "Econometrics", "Heckitt model", "International Standard Book Number", "Ordinary least squares", "Statistics", "Tobit model", "Truncated data"], "references": ["http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1431352"]}, "Zipf\u2013Mandelbrot law": {"categories": ["Computational linguistics", "Corpus linguistics", "Discrete distributions", "Power laws", "Quantitative linguistics"], "title": "Zipf\u2013Mandelbrot law", "method": "Zipf\u2013Mandelbrot law", "url": "https://en.wikipedia.org/wiki/Zipf%E2%80%93Mandelbrot_law", "summary": "In probability theory and statistics, the Zipf\u2013Mandelbrot law is a discrete probability distribution. Also known as the Pareto-Zipf law, it is a power-law distribution on ranked data, named after the linguist George Kingsley Zipf who suggested a simpler distribution called Zipf's law, and the mathematician Benoit Mandelbrot, who subsequently generalized it.\nThe probability mass function is given by:\n\n \n \n \n f\n (\n k\n ;\n N\n ,\n q\n ,\n s\n )\n =\n \n \n \n 1\n \n /\n \n (\n k\n +\n q\n \n )\n \n s\n \n \n \n \n H\n \n N\n ,\n q\n ,\n s\n \n \n \n \n \n \n {\\displaystyle f(k;N,q,s)={\\frac {1/(k+q)^{s}}{H_{N,q,s}}}}\n where \n \n \n \n \n H\n \n N\n ,\n q\n ,\n s\n \n \n \n \n {\\displaystyle H_{N,q,s}}\n is given by:\n\n \n \n \n \n H\n \n N\n ,\n q\n ,\n s\n \n \n =\n \n \u2211\n \n i\n =\n 1\n \n \n N\n \n \n \n \n 1\n \n (\n i\n +\n q\n \n )\n \n s\n \n \n \n \n \n \n \n {\\displaystyle H_{N,q,s}=\\sum _{i=1}^{N}{\\frac {1}{(i+q)^{s}}}}\n which may be thought of as a generalization of a harmonic number. In the formula, \n \n \n \n k\n \n \n {\\displaystyle k}\n is the rank of the data, and \n \n \n \n q\n \n \n {\\displaystyle q}\n and \n \n \n \n s\n \n \n {\\displaystyle s}\n are parameters of the distribution. In the limit as \n \n \n \n N\n \n \n {\\displaystyle N}\n approaches infinity, this becomes the Hurwitz zeta function \n \n \n \n \u03b6\n (\n s\n ,\n q\n )\n \n \n {\\displaystyle \\zeta (s,q)}\n . For finite \n \n \n \n N\n \n \n {\\displaystyle N}\n and \n \n \n \n q\n =\n 0\n \n \n {\\displaystyle q=0}\n the Zipf\u2013Mandelbrot law becomes Zipf's law. For infinite \n \n \n \n N\n \n \n {\\displaystyle N}\n and \n \n \n \n q\n =\n 0\n \n \n {\\displaystyle q=0}\n it becomes a Zeta distribution.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Benoit Mandelbrot", "Beno\u00eet Mandelbrot", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponent", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Frequency", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "George Kingsley Zipf", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harmonic number", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hurwitz zeta function", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Integer", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Linguistics", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Power-law", "Probability distribution", "Probability mass function", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Ranking", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relative abundance distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Text corpus", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Vilfredo Pareto", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law"], "references": ["http://www.gelbukh.com/CV/Publications/2001/CICLing-2001-Zipf.htm", "http://shaunwagner.com/writings_computer_evomus.html", "http://cat.inist.fr/?aModele=afficheN&cpsidt=1411186", "http://doi.org/10.1023%2FA:1006297211561", "https://github.com/gkohri/discreteRNG", "https://xlinux.nist.gov/dads/HTML/zipfslaw.html", "https://web.archive.org/web/20060428014625/http://www.nslij-genetics.org/wli/zipf/index.html", "https://arxiv.org/abs/physics/9901035"]}, "Multifactor design of experiments software": {"categories": ["All articles needing additional references", "Articles needing additional references from July 2016", "Design of experiments", "Statistical software", "Use dmy dates from July 2013"], "title": "Multifactor design of experiments software", "method": "Multifactor design of experiments software", "url": "https://en.wikipedia.org/wiki/Multifactor_design_of_experiments_software", "summary": "Software that is used for designing factorial experiments plays an important role in scientific experiments and represents a route to the implementation of design of experiments procedures that derive from statistical and combinatorial theory. In principle, easy-to-use design of experiments (DOE) software should be available to all experimenters to foster use of DOE.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Combinatorics", "Design of experiments", "Design\u2013Expert", "Experimental design", "Factorial experiment", "Fractional factorial design", "George E. P. Box", "Interaction", "International Standard Book Number", "JMP (statistical software)", "Journal of the Royal Statistical Society", "Minitab", "Numerical optimization", "Plackett\u2013Burman design", "Response surface methodology", "Robust statistics", "Sampling (statistics)", "Scientific experiment", "Statistics"], "references": ["http://norvig.com/experiment-design.html", "http://www.wiley.com/WileyCDA/WileyTitle/productCd-1118916018.html", "http://www.wiley.com/WileyCDA/WileyTitle/productCd-EHEP003675.html", "http://www.itl.nist.gov/div898/handbook/pri/pri.htm", "https://www.amazon.com/DOE-Simplified-Practical-Effective-Experimentation/dp/1482218941", "https://www.amazon.com/RSM-Simplified-Optimizing-Processes-Experiments/dp/1498745989"]}, "Lusser's law": {"categories": ["Engineering failures", "Reliability analysis", "Reliability engineering", "Statistics articles needing expert attention", "Survival analysis", "Systems analysis"], "title": "Lusser's law", "method": "Lusser's law", "url": "https://en.wikipedia.org/wiki/Lusser%27s_law", "summary": "Lusser's law in systems engineering is a prediction of reliability. Named after engineer Robert Lusser, and also known as Lusser's product law or the probability product law of series components, it states that the reliability of a series of components is equal to the product of the individual reliabilities of the components, if their failure modes are known to be statistically independent. For a series of n components, this is expressed as:\n\n \n \n \n \n R\n \n s\n \n \n =\n \n \u220f\n \n i\n =\n 1\n \n \n N\n \n \n \n r\n \n i\n \n \n =\n \n r\n \n 1\n \n \n \u00d7\n \n r\n \n 2\n \n \n \u00d7\n \n r\n \n 3\n \n \n \u00d7\n .\n .\n .\n \u00d7\n \n r\n \n n\n \n \n \n \n {\\displaystyle R_{s}=\\prod _{i=1}^{N}r_{i}=r_{1}\\times r_{2}\\times r_{3}\\times ...\\times r_{n}}\n where Rs is the overall reliability of the system, and rn is the reliability of the nth component.\nIf the failure probabilities of all components are equal, then as Lusser's colleague Erich Pieruschka observed, this can be expressed simply as:\n\n \n \n \n \n R\n \n s\n \n \n =\n \n \n 1\n \n r\n \n n\n \n \n \n \n \n \n {\\displaystyle R_{s}={\\frac {1}{r^{n}}}}\n Lusser's law has been described as the idea that a series system is \"weaker than its weakest link\", as the product reliability of a series of components can be less than the lowest-value component.For example, given a series system of two components with different reliabilities \u2014 one of 0.95 and the other of 0.8 \u2014 Lusser's law will predict a reliability of\n\n \n \n \n \n R\n \n s\n \n \n =\n 0.95\n \u00d7\n 0.8\n =\n 0.76\n \n \n {\\displaystyle R_{s}=0.95\\times 0.8=0.76}\n which is lower than either of the individual components.", "images": [], "links": ["Erich Pieruschka", "Failure causes", "International Standard Book Number", "Product (mathematics)", "Reliability (engineering)", "Robert Lusser", "Series circuit", "Statistically independent", "Systems engineering"], "references": ["http://users.ece.cmu.edu/~koopman/des_s99/traditional_reliability/presentation.pdf", "http://www.ausairpower.net/PDF-A/Reliability-PHA.pdf", "https://spectator.org/51313_lussers-law/", "https://books.google.co.uk/books?id=ltAqBgAAQBAJ&pg=PA117&lpg=PA117&dq=Lusser's+law&source=bl&ots=SNPCKYZh-o&sig=NUsUd9m3e45m87gG_bSxWjA7kps&hl=en&sa=X&ved=0CFEQ6AEwB2oVChMI0ZO-5qOfxwIVh4kaCh3oaw9V#v=onepage&q=Lusser's%20law&f=false"]}, "Standardized mortality ratio": {"categories": ["Biostatistics", "Epidemiology", "Medical statistics", "Statistical ratios"], "title": "Standardized mortality ratio", "method": "Standardized mortality ratio", "url": "https://en.wikipedia.org/wiki/Standardized_mortality_ratio", "summary": "In epidemiology, the standardized mortality ratio or SMR, is a quantity, expressed as either a ratio or percentage quantifying the increase or decrease in mortality of a study cohort with respect to the general population.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Age-specific mortality rate", "Analysis of variance", "Arsenic", "Asymptomatic carrier", "Auxology", "Bachelor of Science in Public Health", "Behavior change (public health)", "Behavioural change theories", "Biological hazard", "Biostatistics", "Bladder cancer", "Cancer", "Carl Rogers Darnall", "Case\u2013control study", "Centers for Disease Control and Prevention", "Chief Medical Officer", "Child mortality", "Cohort study", "Community health", "Confidence interval", "Council on Education for Public Health", "Crude death rate", "Cultural competence in health care", "Cumulative exposure", "Deviance (sociology)", "Diffusion of innovations", "Digital object identifier", "Disease surveillance", "Doctor of Public Health", "Drinking water", "Emergency sanitation", "Environmental health", "Epidemic", "Epidemiology", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Family planning", "Fecal\u2013oral route", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Genetically modified food", "Germ theory of disease", "Global health", "Globalization and disease", "Good agricultural practice", "Good manufacturing practice", "HACCP", "Hand washing", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Human factors and ergonomics", "Human nutrition", "Hygiene", "ISO 22000", "Infant mortality", "Infection control", "Injury prevention", "International Standard Book Number", "John Snow (physician)", "Joseph Lister", "Life insurance", "List of epidemics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "Margaret Sanger", "Mary Mallon", "Maternal health", "Medical anthropology", "Medical sociology", "Mental health", "Ministry of Health and Family Welfare", "Mortality rate", "Notifiable disease", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Open defecation", "Oral hygiene", "PRECEDE-PROCEED model", "P value", "Patient safety", "Patient safety organization", "Percentage", "Pharmaceutical policy", "Pharmacovigilance", "Population health", "Positive deviance", "Preventive healthcare", "Preventive nutrition", "Professional degrees of public health", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quarantine", "ROC curve", "Race and health", "Random variable", "Randomized controlled trial", "Ratio", "Regression analysis", "Relative risk", "Reproductive health", "Safe sex", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Sexually transmitted infection", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Sociology of health and illness", "Statistical hypothesis testing", "Statistical significance", "Student's t-test", "Theory of planned behavior", "Transtheoretical model", "Tropical disease", "Uncertainty", "United States Public Health Service", "Vaccination", "Vaccine trial", "Vector control", "Vulnerability index", "Waterborne diseases", "World Health Organization", "World Toilet Organization", "Z-test"], "references": ["http://www.dirk-taeger.de/pamcomp/index.html", "http://doi.org/10.1007%2F978-94-007-5989-3_22"]}, "DeFries\u2013Fulker regression": {"categories": ["All stub articles", "Behavioural genetics", "Regression analysis", "Statistics stubs"], "title": "DeFries\u2013Fulker regression", "method": "DeFries\u2013Fulker regression", "url": "https://en.wikipedia.org/wiki/DeFries%E2%80%93Fulker_regression", "summary": "In behavioural genetics, DeFries\u2013Fulker (DF) regression, also sometimes called DeFries\u2013Fulker extremes analysis, is a type of multiple regression analysis designed for estimating the magnitude of genetic and environmental effects in twin studies. It is named after John C. DeFries and David Fulker, who first proposed it in 1985. It was originally developed to assess heritability of reading disability in twin studies, but it has since been used to assess the heritability of other cognitive traits, and has also been applied to non-twin methodologies.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Behavior Genetics (journal)", "Behavioural genetics", "David Fulker", "Digital object identifier", "Discrete choice", "Dizygotic twins", "Dorothy V. M. Bishop", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Heritability", "International Standard Book Number", "International Standard Serial Number", "Isotonic regression", "Iteratively reweighted least squares", "Jenae Neiderhiser", "John C. DeFries", "John Wiley & Sons, Ltd", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic regression", "Matt McGue", "Mean and predicted response", "Mixed logit", "Mixed model", "Monozygotic twins", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple regression analysis", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Pak Sham", "Partial least squares regression", "Perspectives on Psychological Science", "Poisson regression", "Polynomial regression", "Principal component regression", "Proband", "Probit model", "PubMed Central", "PubMed Identifier", "Quantile regression", "Random effects model", "Reading disability", "Regression analysis", "Regression model validation", "Regression to the mean", "Regularized least squares", "Robert Plomin", "Robust regression", "Segmented regression", "Semiparametric regression", "Shaun Purcell", "Simple linear regression", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Twin studies", "University of Colorado Boulder", "Weighted least squares"], "references": ["http://journals.sagepub.com/doi/10.1177/1745691615617439", "http://doi.wiley.com/10.1002/0470013192.bsa165", "http://psych.colorado.edu/~willcutt/CLDRC/DFanalysis.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3573860", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4739500", "http://www.ncbi.nlm.nih.gov/pubmed/15971028", "http://www.ncbi.nlm.nih.gov/pubmed/23264207", "http://www.ncbi.nlm.nih.gov/pubmed/26817721", "http://doi.org/10.1002%2F0470013192.bsa165", "http://doi.org/10.1007%2Fbf01066239", "http://doi.org/10.1007%2Fbf01067192", "http://doi.org/10.1007%2Fs10519-004-1834-7", "http://doi.org/10.1007%2Fs10519-012-9573-7", "http://doi.org/10.1023%2Fa:1023494408079", "http://doi.org/10.1177%2F1745691615617439", "http://www.worldcat.org/issn/0001-8244", "http://www.worldcat.org/issn/1745-6916", "https://link.springer.com/10.1007/BF01066239", "https://link.springer.com/10.1007/BF01067192", "https://link.springer.com/10.1007/s10519-012-9573-7", "https://link.springer.com/10.1023/A:1023494408079"]}, "Quantile normalization": {"categories": ["Equivalence (mathematics)", "Statistical data transformation"], "title": "Quantile normalization", "method": "Quantile normalization", "url": "https://en.wikipedia.org/wiki/Quantile_normalization", "summary": "In statistics, quantile normalization is a technique for making two distributions identical in statistical properties. To quantile-normalize a test distribution to a reference distribution of the same length, sort the test distribution and sort the reference distribution. The highest entry in the test distribution then takes the value of the highest entry in the reference distribution, the next highest entry in the reference distribution, and so on, until the test distribution is a perturbation of the reference distribution.\nTo quantile normalize two or more distributions to each other, without a reference distribution, sort as before, then set to the average (usually, arithmetic mean) of the distributions. So the highest value in all cases becomes the mean of the highest values, the second highest value becomes the mean of the second highest values, and so on.\nGenerally a reference distribution will be one of the standard statistical distributions such as the Gaussian distribution or the Poisson distribution. The reference distribution can be generated randomly or from taking regular samples from the cumulative distribution function of the distribution. However, any reference distribution can be used.\nQuantile normalization is frequently used in microarray data analysis. It was introduced as quantile standardization and then renamed as quantile normalization.", "images": [], "links": ["Arithmetic mean", "Cumulative distribution function", "Digital object identifier", "Gaussian distribution", "Microarray", "Poisson distribution", "Probability distribution", "PubMed Identifier", "Quantile"], "references": ["http://www.rci.rutgers.edu/~cabrera/DNAMR/", "http://www.ncbi.nlm.nih.gov/pubmed/12538238", "http://doi.org/10.1093%2Fbioinformatics%2F19.2.185", "http://doi.org/10.1198%2F016214501753381814", "http://www.bea.ki.se/staff/reimers/Web.Pages/Affymetrix.Normalization.htm"]}, "Law of the iterated logarithm": {"categories": ["Asymptotic theory (statistics)", "Statistical theorems", "Stochastic processes"], "title": "Law of the iterated logarithm", "method": "Law of the iterated logarithm", "url": "https://en.wikipedia.org/wiki/Law_of_the_iterated_logarithm", "summary": "In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to A. Y. Khinchin (1924). Another statement was given by A. N. Kolmogorov in 1929.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ee/Law_of_large_numbers.gif", "https://upload.wikimedia.org/wikipedia/commons/4/40/LimitTheoremsExhibition.png"], "links": ["Aleksandr Khinchin", "Almost surely", "Andrey Kolmogorov", "Central limit theorem", "Convergence of random variables", "Fundamenta Mathematicae", "Iterated logarithm", "Khinchin", "Kolmogorov", "Kolmogorov's zero\u2013one law", "Law of large numbers", "Leo Breiman", "Limit superior", "Natural logarithm", "Probability theory", "Random variables", "Random walk", "Strong law of large numbers", "Weak law of large numbers", "Wiener process", "Yongge Wang"], "references": ["http://gdz.sub.uni-goettingen.de/en/index.html", "http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN235181684_0101", "http://webpages.uncc.edu/yonwang/liltest/", "http://webpages.uncc.edu/yonwang/papers/CCC96.pdf", "http://webpages.uncc.edu/yonwang/papers/thesis.pdf"]}, "Subcontrary mean": {"categories": ["CS1 maint: Archived copy as title", "Means"], "title": "Harmonic mean", "method": "Subcontrary mean", "url": "https://en.wikipedia.org/wiki/Harmonic_mean", "summary": "In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means. Typically, it is appropriate for situations when the average of rates is desired.\nThe harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is\n\n \n \n \n \n \n (\n \n \n \n \n 1\n \n \u2212\n 1\n \n \n +\n \n 4\n \n \u2212\n 1\n \n \n +\n \n 4\n \n \u2212\n 1\n \n \n \n 3\n \n \n )\n \n \n \u2212\n 1\n \n \n =\n \n \n 3\n \n \n \n 1\n 1\n \n \n +\n \n \n 1\n 4\n \n \n +\n \n \n 1\n 4\n \n \n \n \n \n =\n \n \n 3\n 1.5\n \n \n =\n 2\n \n .\n \n \n {\\displaystyle \\left({\\frac {1^{-1}+4^{-1}+4^{-1}}{3}}\\right)^{-1}={\\frac {3}{{\\frac {1}{1}}+{\\frac {1}{4}}+{\\frac {1}{4}}}}={\\frac {3}{1.5}}=2\\,.}", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c0/%28Mean_-_HarmonicMean%29_for_Beta_distribution_versus_alpha_and_beta_from_0_to_2_-_J._Rodal.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/0d/CrossedLadders.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/0/00/Harmonic_Means_for_Beta_distribution_Purple%3DH%28X%29%2C_Yellow%3DH%281-X%29%2C_larger_values_alpha_and_beta_in_front_-_J._Rodal.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/32/Harmonic_Means_for_Beta_distribution_Purple%3DH%28X%29%2C_Yellow%3DH%281-X%29%2C_smaller_values_alpha_and_beta_in_front_-_J._Rodal.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/8d/Harmonic_mean_for_Beta_distribution_for_alpha_and_beta_ranging_from_0_to_5_-_J._Rodal.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f7/MathematicalMeans.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alloy", "Altitude (triangle)", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arbitrarily large", "Arc (geometry)", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Beta distribution", "Bias", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Capacitor", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemistry", "Chemometrics", "Chi-squared test", "Circumcircle", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computer science", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contraharmonic mean", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossed ladders problem", "Crux Mathematicorum", "Cut-the-knot", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Delta method", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Diagonal", "Dickey\u2013Fuller test", "Dimensional analysis", "Divergence (statistics)", "Dual (mathematics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Ellipse", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental Protection Agency", "Environmental statistics", "Epidemiology", "Equilateral triangle", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "F1 score", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fuel economy in automobiles", "G-test", "Gene pool", "General linear model", "Generalized linear model", "Generalized mean", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic number", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Home run", "Homoscedasticity", "Hydraulic conductivity", "Hydrology", "Hypotenuse", "If and only if", "Inbreeding", "Incircle and excircles of a triangle", "Index (finance)", "Index of dispersion", "Inductor", "Inequality of arithmetic and geometric means", "Infinity", "Information retrieval", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen's inequality", "Johansen test", "Jonckheere's trend test", "Journal of Financial Education", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kepler's laws of planetary motion", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Lognormal distribution", "Loss function", "Lp space", "M-estimator", "Machine learning", "Mann\u2013Whitney U test", "Market capitalization", "MathWorld", "Mathematics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean-preserving spread", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiplicative inverse", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuclear physics", "Observational study", "Official statistics", "Ohm", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parallel (operator)", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population genetics", "Population statistics", "Posterior probability", "Power (statistics)", "Power mean", "Power\u2013speed number", "Precision and recall", "Prediction interval", "Price\u2013earnings ratio", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Pythagorean means", "Quadratic mean", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rate (mathematics)", "Ratio", "Real number", "Regression analysis", "Regression model validation", "Relevance", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Reservoir engineering", "Resistor", "Right triangle", "Robust regression", "Robust statistics", "Run chart", "Sabermetrics", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Schur-concave", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social Science Research Network", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stolen base", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T test", "The Mathematical Gazette", "Time domain", "Time series", "Tolerance interval", "Trapezoid", "Trend estimation", "Triangle", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weight function", "Weighted arithmetic mean", "Weighted geometric mean", "Weighted mean", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.imomath.com/othercomp/Journ/ineq.pdf", "http://ssrn.com/abstract=2621087", "http://mathworld.wolfram.com/HarmonicMean.html", "http://ecee.colorado.edu/~bart/book/effmass.htm", "http://engineering.tufts.edu/cee/people/vogel/publications/estimation-harmonic.pdf", "http://ajmaa.org/RGMIA/papers/v2n1/v2n1-10.pdf", "http://www.cut-the-knot.org/arithmetic/HarmonicMean.shtml", "http://www.jstor.org/stable/41948650", "http://www.dcs.gla.ac.uk/Keith/Preface.html", "https://books.google.com/books?id=C53dCgAAQBAJ&pg=PA172", "https://learningpundits.com/module-view/48-averages/1-tips-on-averages/", "https://web.archive.org/web/20050406090119/http://www.dcs.gla.ac.uk/Keith/Preface.html", "https://web.archive.org/web/20100611205528/http://engineering.tufts.edu/cee/people/vogel/publications/estimation-harmonic.pdf", "https://web.archive.org/web/20141015174828/http://www.imomath.com/othercomp/Journ/ineq.pdf", "https://web.archive.org/web/20171020040802/http://ecee.colorado.edu/~bart/book/effmass.htm", "https://web.archive.org/web/20171229231610/https://learningpundits.com/module-view/48-averages/1-tips-on-averages/"]}, "Collectively exhaustive events": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2017", "CS1 maint: Uses authors parameter", "Probability theory"], "title": "Collectively exhaustive events", "method": "Collectively exhaustive events", "url": "https://en.wikipedia.org/wiki/Collectively_exhaustive_events", "summary": "In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 (each consisting of a single outcome) are collectively exhaustive, because they encompass the entire range of possible outcomes.\nAnother way to describe collectively exhaustive events is that their union must cover all the events within the entire sample space. For example, events A and B are said to be collectively exhaustive if\n\n \n \n \n A\n \u222a\n B\n =\n S\n \n \n {\\displaystyle A\\cup B=S}\n where S is the sample space.\nCompare this to the concept of a set of mutually exclusive events. In such a set no more than one event can occur at a given time. (In some forms of mutual exclusion only one event can ever occur.) The set of all possible die rolls is both mutually exclusive and collectively exhaustive (i.e., \"MECE\"). The events 1 and 6 are mutually exclusive but not collectively exhaustive. The events \"even\" (2,4 or 6) and \"not-6\" (1,2,3,4, or 5) are collectively exhaustive but not mutually exclusive. In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not. For example, tossing a particular biscuit for a group of several dogs cannot be repeated, no matter which dog snaps it up.\nOne example of an event that is both collectively exhaustive and mutually exclusive is tossing a coin. The outcome must be either heads or tails, or p (heads or tails) = 1, so the outcomes are collectively exhaustive. When heads occurs, tails can't occur, or p (heads and tails) = 0, so the outcomes are also mutually exclusive.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Amazon Standard Identification Number", "Cardinal number", "Collectively exhaustive", "Dice", "Event (probability theory)", "Event structure", "International Standard Book Number", "Logic", "MECE principle", "Mutually exclusive events", "Outcome (probability)", "Probability theory", "Sample space", "Set (mathematics)", "Set theory", "Stephen Kleene", "Union (set theory)"], "references": ["http://www.amazon.com/dp/B0006AW17Y"]}, "Matching pursuit": {"categories": ["All articles with dead external links", "Articles with dead external links from January 2018", "Articles with permanently dead external links", "Multivariate statistics", "Signal processing"], "title": "Matching pursuit", "method": "Matching pursuit", "url": "https://en.wikipedia.org/wiki/Matching_pursuit", "summary": "Matching pursuit (MP) is a sparse approximation algorithm which finds the \"best matching\" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary \n \n \n \n D\n \n \n {\\displaystyle D}\n . The basic idea is to approximately represent a signal \n \n \n \n f\n \n \n {\\displaystyle f}\n from Hilbert space \n \n \n \n H\n \n \n {\\displaystyle H}\n as a weighted sum of finitely many functions \n \n \n \n \n g\n \n \n \u03b3\n \n n\n \n \n \n \n \n \n {\\displaystyle g_{\\gamma _{n}}}\n (called atoms) taken from \n \n \n \n D\n \n \n {\\displaystyle D}\n . An approximation with \n \n \n \n N\n \n \n {\\displaystyle N}\n atoms has the form\n\n \n \n \n f\n (\n t\n )\n \u2248\n \n \n \n \n f\n ^\n \n \n \n \n N\n \n \n (\n t\n )\n :=\n \n \u2211\n \n n\n =\n 1\n \n \n N\n \n \n \n a\n \n n\n \n \n \n g\n \n \n \u03b3\n \n n\n \n \n \n \n (\n t\n )\n \n \n {\\displaystyle f(t)\\approx {\\hat {f}}_{N}(t):=\\sum _{n=1}^{N}a_{n}g_{\\gamma _{n}}(t)}\n where \n \n \n \n \n g\n \n \n \u03b3\n \n n\n \n \n \n \n \n \n {\\displaystyle g_{\\gamma _{n}}}\n is the \n \n \n \n \n \u03b3\n \n n\n \n \n \n \n {\\displaystyle \\gamma _{n}}\n th column of the matrix \n \n \n \n D\n \n \n {\\displaystyle D}\n and \n \n \n \n \n a\n \n n\n \n \n \n \n {\\displaystyle a_{n}}\n is the scalar weighting factor (amplitude) for the atom \n \n \n \n \n g\n \n \n \u03b3\n \n n\n \n \n \n \n \n \n {\\displaystyle g_{\\gamma _{n}}}\n . Normally, not every atom in \n \n \n \n D\n \n \n {\\displaystyle D}\n will be used in this sum. Instead, matching pursuit chooses the atoms one at a time in order to maximally (greedily) reduce the approximation error. This is achieved by finding the atom that has the highest inner product with the signal (assuming the atoms are normalized), subtracting from the signal an approximation that uses only that one atom, and repeating the process until the signal is satisfactorily decomposed, i.e., the norm of the residual is small,\nwhere the residual after calculating \n \n \n \n \n \u03b3\n \n N\n \n \n \n \n {\\displaystyle \\gamma _{N}}\n and \n \n \n \n \n a\n \n N\n \n \n \n \n {\\displaystyle a_{N}}\n is denoted by\n\n \n \n \n \n R\n \n N\n +\n 1\n \n \n =\n f\n \u2212\n \n \n \n \n f\n ^\n \n \n \n \n N\n \n \n \n \n {\\displaystyle R_{N+1}=f-{\\hat {f}}_{N}}\n .If \n \n \n \n \n R\n \n n\n \n \n \n \n {\\displaystyle R_{n}}\n converges quickly to zero, then only a few atoms are needed to get a good approximation to \n \n \n \n f\n \n \n {\\displaystyle f}\n . Such sparse representations are desirable for signal coding and compression. More precisely, the sparsity problem that matching pursuit is intended to approximately solve is\n\n \n \n \n \n min\n \n x\n \n \n \u2016\n f\n \u2212\n D\n x\n \n \u2016\n \n 2\n \n \n 2\n \n \n \n \n subject to \n \n \n \u2016\n x\n \n \u2016\n \n 0\n \n \n \u2264\n N\n ,\n \n \n {\\displaystyle \\min _{x}\\|f-Dx\\|_{2}^{2}\\ {\\text{ subject to }}\\ \\|x\\|_{0}\\leq N,}\n where \n \n \n \n \u2016\n x\n \n \u2016\n \n 0\n \n \n \n \n {\\displaystyle \\|x\\|_{0}}\n is the \n \n \n \n \n L\n \n 0\n \n \n \n \n {\\displaystyle L_{0}}\n pseudo-norm (i.e. the number of nonzero elements of \n \n \n \n x\n \n \n {\\displaystyle x}\n ). In the previous notation, the nonzero entries of \n \n \n \n x\n \n \n {\\displaystyle x}\n are \n \n \n \n \n x\n \n \n \u03b3\n \n n\n \n \n \n \n =\n \n a\n \n n\n \n \n \n \n {\\displaystyle x_{\\gamma _{n}}=a_{n}}\n . Solving the sparsity problem exactly is NP-hard, which is why approximation methods like MP are used.\nFor comparison, consider the Fourier transform representation of a signal - this can be described using the terms given above, where the dictionary is built from sinusoidal basis functions (the smallest possible complete dictionary). The main disadvantage of Fourier analysis in signal processing is that it extracts only the global features of the signals and does not adapt to the analysed signals \n \n \n \n f\n \n \n {\\displaystyle f}\n . \nBy taking an extremely redundant dictionary, we can look in it for atoms (functions) that best match a signal \n \n \n \n f\n \n \n {\\displaystyle f}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/21/Matching_pursuit.png"], "links": ["Anna C. Gilbert", "ArXiv", "Assignment (computer science)", "Bibcode", "CLEAN (algorithm)", "Compressed sensing", "Digital object identifier", "Discrete cosine transform", "Fourier transform", "Greedy algorithm", "Heat map", "Hilbert space", "Image processing", "Joel Tropp", "NP-hardness", "Normal distribution", "Principal component analysis", "Projection pursuit", "Signal processing", "Sparse approximation", "Sparse dictionary learning", "St\u00e9phane Mallat"], "references": ["http://www.acm.caltech.edu/~jtropp/papers/TG07-Signal-Recovery.pdf", "http://adsabs.harvard.edu/abs/1993ITSP...41.3397M", "http://adsabs.harvard.edu/abs/1994OptEn..33.2183D", "http://adsabs.harvard.edu/abs/2003JChPh.118.6720W", "http://adsabs.harvard.edu/abs/2006ITSP...54.4311A", "http://adsabs.harvard.edu/abs/2012ITSP...60.6202J", "http://www.incm.cnrs-mrs.fr/LaurentPerrinet/Publications/Perrinet02sparse", "http://arxiv.org/abs/0706.3177", "http://arxiv.org/abs/1111.6664", "http://arxiv.org/abs/1701.06859", "http://doi.org/10.1002%2F9783527680863.ch14", "http://doi.org/10.1002%2Fima.20078", "http://doi.org/10.1016%2Fj.acha.2008.07.002", "http://doi.org/10.1016%2Fj.neucom.2004.01.010", "http://doi.org/10.1016%2Fj.sigpro.2005.05.030", "http://doi.org/10.1063%2F1.1560636", "http://doi.org/10.1109%2F76.554427", "http://doi.org/10.1109%2F78.258082", "http://doi.org/10.1109%2FICIP.1995.529037", "http://doi.org/10.1109%2FTIT.2014.2310482", "http://doi.org/10.1109%2FTSP.2012.2218810", "http://doi.org/10.1109%2Facssc.1993.342465", "http://doi.org/10.1109%2Ftcsvt.2006.883502", "http://doi.org/10.1109%2Ftcsvt.2007.903120", "http://doi.org/10.1109%2Ftit.2007.909108", "http://doi.org/10.1109%2Ftit.2011.2173241", "http://doi.org/10.1109%2Ftsp.2006.881199", "http://doi.org/10.1117%2F12.173207", "http://doi.org/10.1162%2Fneco.2010.05-08-795", "http://doi.org/10.1177%2F1045389X08100044", "https://www.invibe.net/LaurentPerrinet/Publications/Perrinet15bicv"]}, "Odds algorithm": {"categories": ["Optimal decisions", "Optimization algorithms and methods", "Statistical algorithms"], "title": "Odds algorithm", "method": "Odds algorithm", "url": "https://en.wikipedia.org/wiki/Odds_algorithm", "summary": "The odds-algorithm is a mathematical method for computing optimal\nstrategies for a class of problems that belong to the domain of optimal stopping problems. Their solution follows from the odds-strategy, and the importance of the odds-strategy lies in its optimality, as explained below. \nThe odds-algorithm applies to a class of problems called last-success-problems. Formally, the objective in these problems is to maximize the probability of identifying in a \nsequence of sequentially observed independent events the last event satisfying a specific criterion (a \"specific event\"). This identification must be done at the time of observation. No revisiting of preceding observations is permitted. Usually, a specific\nevent is defined by the decision maker as an event that is of true interest in the view of \"stopping\" to take a well-defined action. Such problems are encountered in several situations.", "images": [], "links": ["Annals of Probability", "Clinical trial", "Compassionate use", "European Mathematical Society", "Expanded access", "F. Thomas Bruss", "Independent increments", "Journal of Applied Probability", "Odds", "Optimal stopping", "Parking problem", "Poisson process", "Portfolio (finance)", "Sciences et Technologies de l'automation", "Secretary problem", "Secretary problems", "Sequential estimate"], "references": ["http://www.p-roesler.de/odds.html"]}, "Negentropy": {"categories": ["Entropy and information", "Negative concepts", "Statistical deviation and dispersion", "Thermodynamic entropy"], "title": "Negentropy", "method": "Negentropy", "url": "https://en.wikipedia.org/wiki/Negentropy", "summary": "In information theory and statistics, negentropy is used as a measure of distance to normality. The concept and phrase \"negative entropy\" was introduced by Erwin Schr\u00f6dinger in his 1944 popular-science book What is Life? Later, L\u00e9on Brillouin shortened the phrase to negentropy, to express it in a more \"positive\" way: a living system imports negentropy and stores it. In 1974, Albert Szent-Gy\u00f6rgyi proposed replacing the term negentropy with syntropy. That term may have originated in the 1940s with the Italian mathematician Luigi Fantappi\u00e8, who tried to construct a unified theory of biology and physics. Buckminster Fuller tried to popularize this usage, but negentropy remains common.\nIn a note to What is Life? Schr\u00f6dinger explained his use of this phrase.\n\nIn 2009, Mahulikar & Herwig redefined negentropy of a dynamically ordered sub-system as the specific entropy deficit of the ordered sub-system relative to its surrounding chaos. Thus, negentropy has SI units of (J kg\u22121 K\u22121) when defined based on specific entropy per unit mass, and (K\u22121) when defined based on specific entropy per unit energy. This definition enabled: i) scale-invariant thermodynamic representation of dynamic order existence, ii) formulation of physical principles exclusively for dynamic order existence and evolution, and iii) mathematical interpretation of Schr\u00f6dinger's negentropy debt.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3c/Wykres_Gibbsa.svg"], "links": ["Albert Szent-Gy\u00f6rgyi", "Biology", "Boltzmann constant", "Buckminster Fuller", "Capacity for entropy", "Differential entropy", "Dissipated energy", "Distribution (mathematics)", "Energy", "Entropy", "Entropy and life", "Entropy in thermodynamics and information theory", "Erwin Schr\u00f6dinger", "Exergy", "Extropy", "Fran\u00e7ois Jacques Dominique Massieu", "Free enthalpy", "Free entropy", "Gaussian distribution", "Gibbs energy", "If and only if", "Independent component analysis", "Information entropy", "Information theory", "Internal energy", "Isobaric process", "Isothermal process", "Josiah Willard Gibbs", "Le\u00f3 Szil\u00e1rd", "Luigi Fantappi\u00e8", "L\u00e9on Brillouin", "Max Planck", "Mean", "Partition function (statistical mechanics)", "Physics", "Signal processing", "Statistical mechanics", "Statistics", "Syntropy", "Syntropy (software)", "Thermodynamic free energy", "Thermodynamic potential", "Variance", "Volume", "What is Life?", "What is Life? (Schr\u00f6dinger)", "Willard Gibbs"], "references": ["http://fourier.eng.hmc.edu/e161/lectures/ica/node4.html", "http://www.ecm.ub.es/condensed/eduard/papers/massieu/node2.html", "http://www.cis.hut.fi/aapo/papers/IJCNN99_tutorialweb/node14.html", "http://www.cis.hut.fi/aapo/papers/NCS99web/node32.html", "http://www.biophysj.org/cgi/reprint/73/6/2960.pdf", "http://www.ufn.ru/ufn39/ufn39_4/Russian/r394b.pdf", "http://www.fmrib.ox.ac.uk/analysis/techrep/tr01dl1/tr01dl1/tr01dl1.html", "http://www.i-sis.org.uk/negentr.php", "https://arxiv.org/pdf/chao-dyn/9604008"]}, "Statistical randomness": {"categories": ["Statistical randomness"], "title": "Statistical randomness", "method": "Statistical randomness", "url": "https://en.wikipedia.org/wiki/Statistical_randomness", "summary": "A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal dice roll or the digits of \u03c0 exhibit statistical randomness.Statistical randomness does not necessarily imply \"true\" randomness, i.e., objective unpredictability. Pseudorandomness is sufficient for many uses, such as statistics, hence the name statistical randomness.\nGlobal randomness and local randomness are different. Most philosophical conceptions of randomness are global\u2014because they are based on the idea that \"in the long run\" a sequence looks truly random, even if certain sub-sequences would not look random. In a \"truly\" random sequence of numbers of sufficient length, for example, it is probable there would be long sequences of nothing but repeating numbers, though on the whole the sequence might be random. Local randomness refers to the idea that there can be minimum sequence lengths in which random distributions are approximated. Long stretches of the same numbers, even those generated by \"truly\" random processes, would diminish the \"local randomness\" of a sample (it might only be locally random for sequences of 10,000 numbers; taking sequences of less than 1,000 might not appear random at all, for example).\nA sequence exhibiting a pattern is not thereby proved not statistically random. According to principles of Ramsey theory, sufficiently large objects must necessarily contain a given substructure (\"complete disorder is impossible\"). Chaos theorists disagree with Ramsey Theory.\nLegislation concerning gambling imposes certain standards of statistical randomness to slot machines.", "images": [], "links": ["Algorithmic randomness", "Autocorrelation", "Bernard Babington Smith", "Binomial distribution", "CD-ROM", "C (programming language)", "Check (unit testing framework)", "Complete spatial randomness", "Dice", "Diehard tests", "Digital object identifier", "GNU General Public License", "Gambling", "George Marsaglia", "Information entropy", "International Standard Book Number", "Journal of the Royal Statistical Society", "Kolmogorov\u2013Smirnov test", "M.G. Kendall", "Monobit", "Normal number", "Null hypothesis", "One-time pad", "Pattern", "Pearson's chi-squared test", "Pi", "Poker", "Pseudorandom", "Pseudorandom number generator", "Pseudorandomness", "Purdue University", "Quasi-random", "Ramsey theory", "Randomness", "Randomness tests", "Sequence", "Seven states of randomness", "Slot machine", "Statistical hypothesis testing", "TestU01", "The Art of Computer Programming", "Unpredictability", "W.F.R. Weldon", "Wald\u2013Wolfowitz runs test", "Yongge Wang"], "references": ["http://www.sciencedirect.com/science/article/pii/S0167404815000693", "http://www.sitmo.com/doc/Generating_Normal_Distributed_Random_Numbers", "http://www.phy.duke.edu/~rgb/General/rand_rate.php", "http://news.uns.purdue.edu/UNS/html4ever/2005/050426.Fischbach.pi.html", "http://webpages.uncc.edu/yonwang/liltest/", "http://webpages.uncc.edu/yonwang/papers/liltest.pdf", "http://doi.org/10.1016%2Fj.cose.2015.05.005", "http://doi.org/10.2307%2F2980655"]}, "List of statistics journals": {"categories": ["Lists of academic journals", "Statistics-related lists", "Statistics journals"], "title": "List of statistics journals", "method": "List of statistics journals", "url": "https://en.wikipedia.org/wiki/List_of_statistics_journals", "summary": "This is a list of scientific journals published in the field of statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407084002%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407083328%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407082944%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20110430032449%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20090922000234%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041048%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041018%21Fisher_iris_versicolor_sepalwidth.svg"], "links": ["AStA Wirtschafts- und Sozialstatistisches Archiv", "American Review of Mathematics and Statistics", "Annals of Statistics", "Applied Econometrics and International Development", "Atmospheric Environment", "Australian & New Zealand Journal of Statistics", "Bayesian Analysis (journal)", "Behaviormetrika", "Biometrical Journal", "Biometrics (journal)", "Biometrika", "Biostatistics", "Biostatistics (journal)", "Brazilian Journal of Probability and Statistics", "British journal of mathematical and statistical psychology", "Chemometrics and Intelligent Laboratory Systems", "Chilean Journal of Statistics", "Communications in Biometry and Crop Science", "Communications in Statistics", "Comparison of statistics journals", "Computational Statistics", "Computational Statistics & Data Analysis", "Current Index to Statistics", "Delayed open access journal", "Econometric Reviews", "Econometric Theory", "Econometrica", "Environmental and Ecological Statistics", "Environmetrics", "Glossary of probability and statistics", "International Journal of Forecasting", "International Statistical Review", "Journal of Agricultural, Biological, and Environmental Statistics", "Journal of Applied Econometrics", "Journal of Applied Statistics", "Journal of Business & Economic Statistics", "Journal of Chemometrics", "Journal of Computational and Graphical Statistics", "Journal of Econometrics", "Journal of Economic and Social Measurement", "Journal of Educational and Behavioral Statistics", "Journal of Environmental Statistics", "Journal of Japanese Society of Computational Statistics", "Journal of Machine Learning Research", "Journal of Modern Applied Statistical Methods", "Journal of Multivariate Analysis", "Journal of Official Statistics", "Journal of Probability and Statistical Sciences", "Journal of Statistical Computation and Simulation", "Journal of Statistical Physics", "Journal of Statistical Planning and Inference", "Journal of Statistical Software", "Journal of Statistics Education", "Journal of Time Series Analysis", "Journal of the American Statistical Association", "Journal of the Japanese Statistical Association", "Journal of the Royal Statistical Society", "List of mathematics journals", "List of probability journals", "List of scientific journals", "List of statisticians", "List of statistics articles", "Lists of statistics topics", "Multivariate Behavioral Research", "Notation in probability and statistics", "Open access (publishing)", "Open access journal", "Outline of statistics", "Pharmaceutical Statistics", "Physica A", "Psychological Methods", "Psychometrika", "REVSTAT", "Revista Colombiana de Estadistica", "SORT (journal)", "Sankhya (journal)", "Scandinavian Journal of Statistics", "Scientific journal", "Significance (magazine)", "South African Statistical Journal", "Stat (Wiley)", "Stata", "Statistica Neerlandica", "Statistica Sinica", "Statistical Applications in Genetics and Molecular Biology", "Statistical Methods in Medical Research", "Statistical Modelling", "Statistical Science", "Statistics", "Statistics & Probability Letters", "Statistics Education Research Journal", "Statistics Surveys", "Statistics and Applications", "Statistics and Computing", "Statistics and Risk Modeling", "Statistics and its Interface", "Statistics in Biopharmaceutical Research", "Statistics in Medicine", "Statistics in Medicine (journal)", "Stochastic Environmental Research and Risk Assessment", "Stochastic Processes and their Applications", "Structural Equation Modeling (journal)", "Subscription business model", "Survey Methodology", "Teaching Statistics", "Technology Innovations in Statistics Education", "Technometrics", "The American Statistician", "The Annals of Applied Statistics", "The Canadian Journal of Statistics", "The International Journal of Biostatistics", "The R Journal", "The Review of Economics and Statistics", "Time-series analysis", "Turkiye Klinikleri Journal of Biostatistics"], "references": ["http://www.iospress.nl/html/07479662.php"]}, "Martingale central limit theorem": {"categories": ["Central limit theorem", "Martingale theory"], "title": "Martingale central limit theorem", "method": "Martingale central limit theorem", "url": "https://en.wikipedia.org/wiki/Martingale_central_limit_theorem", "summary": "In probability theory, the central limit theorem says that, under certain conditions, the sum of many independent identically-distributed random variables, when scaled appropriately, converges in distribution to a standard normal distribution. The martingale central limit theorem generalizes this result for random variables to martingales, which are stochastic processes where the change in the value of the process from time t to time t + 1 has expectation zero, even conditioned on previous outcomes.", "images": [], "links": ["Almost surely", "Central limit theorem", "Converges in distribution", "Digital object identifier", "Expected value", "Independent identically-distributed random variables", "International Standard Book Number", "Martingale (probability theory)", "Normal distribution", "Probability theory", "Stochastic process"], "references": ["http://doi.org/10.1007%2FBF01046930"]}, "Statistical significance": {"categories": ["CS1 maint: Explicit use of et al.", "Statistical hypothesis testing"], "title": "Statistical significance", "method": "Statistical significance", "url": "https://en.wikipedia.org/wiki/Statistical_significance", "summary": "In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis. More precisely, a study's defined significance level, \u03b1, is the probability of the study rejecting the null hypothesis, given that it were true; and the p-value of a result, p, is the probability of obtaining a result at least as extreme, given that the null hypothesis were true. The result is statistically significant, by the standards of the study, when p < \u03b1. The significance level for a study is chosen before data collection, and typically set to 5% or much lower, depending on the field of study.In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone. But if the p-value of an observed effect is less than the significance level, an investigator may conclude that the effect reflects the characteristics of the whole population, thereby rejecting the null hypothesis.This technique for testing the statistical significance of results was developed in the early 20th century. The term significance does not imply importance here, and the term statistical significance is not the same as research, theoretical, or practical significance. For example, the term clinical significance refers to the practical importance of a treatment effect.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/b/bf/NormalDist1.96.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["A/B testing", "ABX test", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alternative hypothesis", "American Statistical Association", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bayesian statistics", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical significance", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's d", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional probability", "Confidence interval", "Confidence level", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Data dredging", "Decomposition of time series", "Degrees of freedom (statistics)", "Deirdre McCloskey", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's method", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Genome-wide association study", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Higgs boson", "Histogram", "History of statistics", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human sex ratio", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "John Arbuthnot", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Look-elsewhere effect", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Manufacturing", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiple comparisons problem", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "One-tailed test", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Particle physics", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Philosophical Transactions of the Royal Society A", "Philosophical Transactions of the Royal Society of London", "Pie chart", "Pierre-Simon Laplace", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Reproducibility", "Resampling (statistics)", "Research question", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample (statistics)", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling error", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen Ziliak", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Texas sharpshooter fallacy", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Two-tailed test", "Type I and type II errors", "Type I error", "U-statistic", "Uniformly most powerful test", "University of Michigan Press", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://websites.psychology.uwa.edu.au/labs/cogscience/Publications/Lewandowsky-Mayberry%20(1996)%20-%20Critics%20Rebuttted.pdf", "http://rdcu.be/wbtc", "http://www.nature.com/news/psychology-journal-bans-p-values-1.17001", "http://www.nature.com/nmeth/journal/v10/n11/full/nmeth.2698.html", "http://www.nature.com/nrg/journal/v15/n5/full/nrg3706.html", "http://www.sciencedirect.com/science/article/pii/S104898431730070X", "http://jeff560.tripod.com/s.html", "http://ist-socrates.berkeley.edu/~maccoun/PP279_Cohen1.pdf", "http://blogs.roosevelt.edu/sziliak/cult-of-statistical-significance/", "http://www.press.umich.edu/titleDetailDesc.do?id=186351", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182327", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3154648", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3390399", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3845140", "http://www.ncbi.nlm.nih.gov/pubmed/16060722", "http://www.ncbi.nlm.nih.gov/pubmed/21293453", "http://www.ncbi.nlm.nih.gov/pubmed/22792080", "http://doi.org/10.1007%2F978-0-387-79054-1_9", "http://doi.org/10.1016%2Fj.leaqua.2017.01.006", "http://doi.org/10.1016%2Fj.socec.2004.09.034", "http://doi.org/10.1017%2FS030500410001152X", "http://doi.org/10.1038%2F519009f", "http://doi.org/10.1038%2Fnature.2017.22625", "http://doi.org/10.1038%2Fnmeth.2698", "http://doi.org/10.1038%2Fnprot.2010.182", "http://doi.org/10.1038%2Fnrg3706", "http://doi.org/10.1038%2Fs41562-017-0189-z", "http://doi.org/10.1038%2Fs41562-017-0224-0", "http://doi.org/10.1073%2Fpnas.1313476110", "http://doi.org/10.1080%2F00031305.2016.1154108", "http://doi.org/10.1098%2Frsta.1937.0005", "http://doi.org/10.1098%2Frstl.1710.0011", "http://doi.org/10.1177%2F0013164416668232", "http://doi.org/10.1371%2Fjournal.pgen.1002812", "http://doi.org/10.1371%2Fjournal.pmed.0020124", "http://doi.org/10.3238%2Farztebl.2009.0335", "http://doi.org/10.7717%2Fpeerj.3544", "http://www.ericdigests.org/1995-1/testing.htm", "http://www.jstor.org/stable/91337", "http://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0020124", "http://www.pnas.org/content/early/2013/10/28/1313476110.abstract", "http://www.worldcat.org/issn/0003-1305", "http://www.worldcat.org/issn/0013-1644", "http://www.worldcat.org/title/beyond-significance-testing-reforming-data-analysis-methods-in-behavioral-research/oclc/53288011&referer=brief_results", "http://www.education.leeds.ac.uk/events/2015/cssme-seminar-series-the-argument-over-p-values-and-the-null-hypothesis-significance-testing-nhst-paradigm", "http://www.york.ac.uk/depts/maths/histstat/arbuthnot.pdf", "https://books.google.com/books?id=M7yvkERHIIMC&lpg=PA225&ots=Glm4Zj_E6p&pg=PA225#v=onepage", "https://www.nature.com/articles/s41562-017-0189-z", "https://www.nature.com/news/one-size-fits-all-threshold-for-p-values-under-fire-1.22625", "https://peerj.com/articles/3544", "https://www.cscu.cornell.edu/news/statnews/stnews73.pdf", "https://web.archive.org/web/20120419105227/http://stats.org/faq_significance.htm", "https://web.archive.org/web/20140213062055/http://www.nature.com/news/scientific-method-statistical-errors-1.14700#/b5", "https://www.csicop.org/si/show/moving_sciences_statistical_goal_posts", "https://dx.doi.org/10.1080/00031305.2016.1154108", "https://www.sciencebasedmedicine.org/psychology-journal-bans-significance-testing", "https://www.sciencenews.org/blog/context/p-value-ban-small-step-journal-giant-leap-science"]}, "MANOVA": {"categories": ["Analysis of variance", "Design of experiments"], "title": "Multivariate analysis of variance", "method": "MANOVA", "url": "https://en.wikipedia.org/wiki/Multivariate_analysis_of_variance", "summary": "In statistics, multivariate analysis of variance (MANOVA) is a procedure for comparing multivariate sample means. As a multivariate procedure, it is used when there are two or more dependent variables, and is typically followed by significance tests involving individual dependent variables separately. It helps to answer:\nDo changes in the independent variable(s) have significant effects on the dependent variables?\nWhat are the relationships among the dependent variables?\nWhat are the relationships among the independent variables?", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Approximation", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "C. R. Rao", "Canonical correlation", "Canonical correlation analysis", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension", "Discriminant function analysis", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Eigenvalues", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Harold Hotelling", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hotelling's T-square", "Index of dispersion", "Interaction (statistics)", "Internal validity", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Multivariate Analysis", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "M. S. Bartlett", "Magnitude (mathematics)", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate distribution", "Multivariate normal distribution", "Multivariate random variable", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Positive-definite matrix", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Roy's greatest root", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Stanley Wilks", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular value decomposition", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Trace of a matrix", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Wilks' lambda distribution", "Wishart distribution", "Z-test"], "references": ["http://www.camo.com/multivariate_analysis.html", "http://www.real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/manova-basic-concepts/", "http://ibgwww.colorado.edu/~carey/p7291dir/handouts/manova1.pdf", "http://faculty.chass.ncsu.edu/garson/PA765/manova.htm", "http://online.sfsu.edu/~efc/classes/biol710/manova/manovanewest.htm", "http://www.ats.ucla.edu/stat/stata/output/Stata_MANOVA.htm", "http://pareonline.net/getvn.asp?v=19&n=17", "http://arxiv.org/abs/1401.3987v3", "http://doi.org/10.1080%2F00273171.2014.968836"]}, "Experimental event rate": {"categories": ["All articles with dead external links", "All stub articles", "Articles with dead external links from January 2018", "Articles with permanently dead external links", "Biostatistics", "Epidemiology", "Medical statistics", "Statistical ratios", "Statistics stubs"], "title": "Experimental event rate", "method": "Experimental event rate", "url": "https://en.wikipedia.org/wiki/Experimental_event_rate", "summary": "In epidemiology and biostatistics, the experimental event rate (EER) is a measure of how often a particular statistical event (such as response to a drug, adverse event or death) occurs within the experimental group (non-control group) of an experiment.This value is very useful in determining the therapeutic benefit or risk to patients in experimental groups, in comparison to patients in placebo or traditionally treated control groups.\nThree statistical terms rely on EER for their calculation: absolute risk reduction, relative risk reduction and number needed to treat.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Abbreviation", "Absolute risk reduction", "Adverse event", "Attributable risk", "Attributable risk percent", "Biostatistics", "Control event rate", "Epidemiology", "Number needed to harm", "Number needed to treat", "Odds ratio", "Placebo", "Preventive fraction", "Relative risk", "Relative risk reduction", "Scientific control", "Statistics"], "references": ["http://www.medicine.ox.ac.uk/bandolier/booth/glossary/CER.html", "http://www.medicine.ox.ac.uk/bandolier/booth/glossary/EER.html"]}, "Logit analysis in marketing": {"categories": ["All articles lacking sources", "Articles lacking sources from August 2008", "Logistic regression", "Market research", "Market segmentation", "Marketing performance measurement", "Product management", "Quantitative marketing research"], "title": "Logit analysis in marketing", "method": "Logit analysis in marketing", "url": "https://en.wikipedia.org/wiki/Logit_analysis_in_marketing", "summary": "Logit analysis is a statistical technique used by marketers to assess the scope of customer acceptance of a product, particularly a new product. It attempts to determine the intensity or magnitude of customers' purchase intentions and translates that into a measure of actual buying behaviour. Logit analysis assumes that an unmet need in the marketplace has already been detected, and that the product has been designed to meet that need. The purpose of logit analysis is to quantify the potential sales of that product. It takes survey data on consumers' purchase intentions and converts it into actual purchase probabilities.\nLogit analysis defines the functional relationship between stated purchase intentions and preferences, and the actual probability of purchase. A preference regression is performed on the survey data. This is then modified with actual historical observations of purchase behavior. The resultant functional relationship defines purchase probability.\nThis is the most useful of the purchase intention/rating translations because explicit measures of confidence level and statistical significance can be calculated. Other purchase intention/rating translations include the preference-rank translation and the intent scale translation.\nThe logit function is the reciprocal function to the sigmoid logistic function.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Comparison of statistical packages", "Intent scale translation", "Logistic regression", "Logit", "Marketing", "Marketing research", "New Product Development", "New product development", "Preference-rank translation", "Preference regression (in marketing)", "Product (business)"], "references": []}, "Z-transform": {"categories": ["CS1 Italian-language sources (it)", "Laplace transforms", "Transforms"], "title": "Z-transform", "method": "Z-transform", "url": "https://en.wikipedia.org/wiki/Z-transform", "summary": "In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation.\nIt can be considered as a discrete-time equivalent of the Laplace transform. This similarity is explored in the theory of time-scale calculus.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Region_of_convergence_0.5_0.75_mixed-causal.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a0/Region_of_convergence_0.5_anticausal.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e5/Region_of_convergence_0.5_causal.svg"], "links": ["Abraham de Moivre", "Advanced Z-transform", "Aliasing", "Anti-aliasing filter", "Audio signal processing", "Autoregressive moving average model", "Bilinear transform", "Bluestein's FFT algorithm", "Causal system", "Complex argument", "Complex conjugation", "Complex number", "Constant-Q transform", "Continuous Fourier transform", "Contour integral", "Control theory", "Convolution", "Cross-correlation", "DTFT", "Denominator", "Detection theory", "Difference equation", "Digital image processing", "Digital object identifier", "Digital signal processing", "Dirac delta", "Dirac delta function", "Discrete-time Fourier transform", "Discrete-time signal", "Discrete Fourier transform", "Discrete signal", "Downsampling", "Eliahu I. Jury", "Encyclopedia of Mathematics", "Estimation theory", "Final value theorem", "Finite impulse response", "Fisher transformation", "Formal power series", "Fourier series", "Frequency-domain", "Frequency response", "Fundamental theorem of algebra", "Generating function", "Generating function transformation", "Geometric series", "Geophysics", "Heaviside step function", "Hertz", "Imaginary part", "Imaginary unit", "Impulse invariance", "Impulse response", "Initial value theorem", "Integral transform", "International Standard Book Number", "John R. Ragazzini", "Kronecker delta", "LTI system", "Laplace", "Laplace transform", "Laurent series", "Linearity", "Lotfi A. Zadeh", "Matched Z-transform method", "Mathematics", "Michiel Hazewinkel", "Multiplication", "Normalized frequency (digital signal processing)", "Numerator", "Nyquist frequency", "Nyquist rate", "Nyquist\u2013Shannon sampling theorem", "Oversampling", "Parseval's theorem", "Partial fraction", "Periodic summation", "Pole\u2013zero plot", "Post's inversion formula", "Probability-generating function", "Quantization (signal processing)", "Radian", "Radius of convergence", "Real number", "Real part", "Root of a function", "Sampling (signal processing)", "Sampling rate", "Sequence", "Signal processing", "Speech processing", "Standard score", "Star transform", "Starred transform", "Statistical signal processing", "Time-scale calculus", "Transfer function", "Two-sided Laplace transform", "Undersampling", "Unit circle", "Upsampling", "Witold Hurewicz", "Zak transform", "Zeros and poles", "Zeta function regularization"], "references": ["http://www.dsprelated.com/comp.dsp/keyword/Z_Transform.php", "http://mathworld.wolfram.com/Z-Transform.html", "http://www2.ece.ohio-state.edu/~schniter/ee700/handouts/multirate.pdf", "http://www.swarthmore.edu/NatSci/echeeve1/Ref/LPSA/LaplaceZTable/LaplaceZFuncTable.html", "http://doi.org/10.1049%2Fel.2016.0189", "http://www.ee.ic.ac.uk/hp/staff/dmb/courses/DSPDF/01100_Multirate.pdf", "https://books.google.com/books?id=IH-Pu3PlJgAC&pg=PA375&dq=%22all+the+poles+lie+outside+the+unit+circle%22&hl=en&sa=X&ei=jQDcUo24MM7eoASQ-IHADQ&ved=0CC8Q6AEwAA#v=onepage&q=%22all%20the%20poles%20lie%20outside%20the%20unit%20circle%22&f=false", "https://books.google.com/books?id=aQbk3uidEJoC&pg=PA123", "https://books.google.com/books?id=k8SSLy-FYagC&pg=PA185", "https://books.google.com/books?id=k8SSLy-FYagC&pg=PA249&dq=inauthor:Kanasewich++poles+stability&hl=en&sa=X&ei=igLcUqeXFMmxoQTxzIHoAg&ved=0CC8Q6AEwAA#v=onepage&q=inauthor:Kanasewich%20%20poles%20stability&f=false", "https://www.youtube.com/watch?v=4PV6ikgBShw", "https://arxiv.org/abs/1409.1727", "https://www.encyclopediaofmath.org/index.php?title=p/z130010"]}, "Reproducibility": {"categories": ["All articles with unsourced statements", "All self-contradictory articles", "Articles with unsourced statements from August 2015", "Discovery and invention controversies", "Measurement", "Pages containing links to subscription-only content", "Pages using citations with format and no URL", "Philosophy of science", "Psychometrics", "Scientific method", "Self-contradictory articles from September 2017", "Tests", "Validity (statistics)"], "title": "Reproducibility", "method": "Reproducibility", "url": "https://en.wikipedia.org/wiki/Reproducibility", "summary": "Reproducibility is the closeness of the agreement between the results of measurements of the same measurand carried out with same methodology described in the corresponding scientific evidence (e.g. a publication in a peer-reviewed journal). Reproducibilty can also be applied under changed conditions of measurement for the same measurand to check, that the results are not an artefact of the measurment procedures. A related concept is replicability, meaning the ability to independently achieve non-identical conclusions that are at least similar, when differences in sampling, research procedures and data analysis methods may exist. Reproducibility and replicability together are among the main beliefs of 'the scientific method'\u2014with the concrete expressions of the ideal of such a method varying considerably across research disciplines and fields of study. The reproduced measurement may be based on the raw data and computer programs provided by researchers.\nThe values obtained from distinct experimental trials are said to be commensurate if they are obtained according to the same reproducible experimental description and procedure. The basic idea can be seen in Aristotle's dictum that there is no scientific knowledge of the individual, where the word used for individual in Greek had the connotation of the idiosyncratic, or wholly isolated occurrence. Thus all knowledge, all science, necessarily involves the formation of general concepts and the invocation of their corresponding symbols in language (cf. Turner). Aristotle\u2032s conception about the knowledge of the individual being considered unscientific is due to lack of the field of statistics in his time, so he could not appeal to statistical averaging by the individual.\nA particular experimentally obtained value is said to be reproducible if there is a high degree of agreement between measurements or observations conducted on replicate specimens in different locations by different people\u2014that is, if the experimental value is found to have a high precision. However, in science, a very well reproduced result is one that can be confirmed using as many different experimental setups as possible and as many lines of evidence as possible (consilience).", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2e/Ambox_contradict.svg", "https://upload.wikimedia.org/wikipedia/commons/3/31/Boyle_air_pump.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Open_Access_logo_PLoS_transparent.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg"], "links": ["ANOVA gauge R&R", "Academic clinical trials", "Academic research", "Accuracy", "Accuracy and precision", "Adaptive clinical trial", "Air pump", "Amsterdam", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "ArXiv", "Aristotle", "Arsenic biochemistry", "Attributable fraction among the exposed", "Attributable fraction for the population", "Bibcode", "BioTechniques", "Blind experiment", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Cathode", "Christiaan Huygens", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Cold fusion", "Consilience", "Consolidated Standards of Reporting Trials", "Contingency (philosophy)", "Correlation does not imply causation", "Corroboration", "Cross-sectional study", "Cumulative incidence", "David Donoho", "Design of experiments", "Deterministic compilation", "Deuterium", "Digital object identifier", "Dogma", "EQUATOR Network", "Ecological study", "Electrolysis", "Epidemiological methods", "Evidence-based medicine", "Experiment", "Experimental method", "Falsifiability", "First-in-man study", "GFAJ-1", "Glossary of clinical research", "Hazard ratio", "Heavy water", "Hideyo Noguchi", "History of science", "Hypothesis", "Hypothesis testing", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Intention-to-treat analysis", "International Standard Book Number", "International Union of Pure and Applied Chemistry", "John P. A. Ioannidis", "Jon Claerbout", "Jupyter", "Karl Popper", "Leviathan and the Air-Pump", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "MMR vaccine controversy", "Markdown", "Measurement systems analysis", "Measurement uncertainty", "Measurements", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "Nature (journal)", "Necessity and sufficiency", "Nested case\u2013control study", "Nikola Tesla", "Null result", "Number needed to harm", "Number needed to treat", "OCLC", "Observational study", "Odds ratio", "Open-label trial", "Open access", "Open research computation", "PLOS ONE", "Palladium", "Pathological science", "Period prevalence", "Pharmacology", "Philosophy of science", "Point prevalence", "Population Impact Measures", "Power posing", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Proceedings of the National Academy of Sciences of the United States of America", "Prospective cohort study", "Protocol (science)", "Pseudoscience", "PubMed Central", "PubMed Identifier", "R (programming language)", "Randomized controlled trial", "Relative risk reduction", "Ren\u00e9 Descartes", "Repeatability", "Replication (statistics)", "Replication crisis", "Reproducibility Project", "Retraction", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Robert Boyle", "Robert Hooke", "Ronald Fisher", "Royal Society", "Sch\u00f6n scandal", "Science News", "Science by press conference", "Scientific Data (journal)", "Scientific control", "Scientific method", "Seeding trial", "Selection bias", "Shoreham, New York", "Simon Schaffer", "Singleton (mathematics)", "Social psychology", "Specificity and sensitivity", "Standard deviation", "Stanford University", "Statistical significance", "Statistics", "Steven Shapin", "Stimulus-triggered acquisition of pluripotency", "Survivorship bias", "Syphilis", "Systematic review", "TED talk", "Tautology (logic)", "Testability", "The Design of Experiments", "The Lancet", "The Logic of Scientific Discovery", "Thomas Hobbes", "University of Utah", "Vaccine trial", "Vacuum", "Virulence", "Wardenclyffe Tower", "Wireless energy transfer"], "references": ["http://www.biotechniques.com/BiotechniquesJournal/2014/January/A-Simple-Question-of-Reproducibility/biotechniques-349446.html", "http://www.nature.com/nature/journal/v483/n7391/pdf/483531a.pdf", "http://partners.nytimes.com/library/national/science/050399sci-cold-fusion.html", "http://www.rrplanet.com/", "http://adsabs.harvard.edu/abs/2012Natur.483..531B", "http://adsabs.harvard.edu/abs/2013Natur.497..433B", "http://adsabs.harvard.edu/abs/2013PLoSO...863221M", "http://adsabs.harvard.edu/abs/2015PNAS..112.1645L", "http://adsabs.harvard.edu/abs/2016Natur.533..452B", "http://adsabs.harvard.edu/abs/2017NatSD...470114P", "http://www2.nd.edu/Departments//Maritain/etext/hop.htm", "http://www2.nd.edu/Departments//Maritain/etext/hop11.htm", "http://www.csee.wvu.edu/~xinl/source.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3321166", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3655010", "http://www.ncbi.nlm.nih.gov/pubmed/17032082", "http://www.ncbi.nlm.nih.gov/pubmed/21892149", "http://www.ncbi.nlm.nih.gov/pubmed/22421999", "http://www.ncbi.nlm.nih.gov/pubmed/22460880", "http://www.ncbi.nlm.nih.gov/pubmed/23691000", "http://www.ncbi.nlm.nih.gov/pubmed/23698428", "http://www.ncbi.nlm.nih.gov/pubmed/26315443", "http://physics.nist.gov/Pubs/guidelines/appd.1.html", "http://www.reproducibleresearch.net", "http://researchwaste.net/research-wasteequator-conference/", "http://arxiv.org/abs/1502.03169", "http://www.astm.org/Standards/E177.htm", "http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf", "http://centerforopenscience.org/top/", "http://cTuning.org", "http://cTuning.org/ae", "http://doi.org/10.1007%2Fs10816-015-9272-9", "http://doi.org/10.1016%2Fj.intell.2012.01.004", "http://doi.org/10.1037%2F0003-066X.61.7.726", "http://doi.org/10.1038%2F483531a", "http://doi.org/10.1038%2F497433a", "http://doi.org/10.1038%2F533452a", "http://doi.org/10.1038%2Fembor.2012.36", "http://doi.org/10.1038%2Fnrd3439-c1", "http://doi.org/10.1038%2Fsdata.2017.114", "http://doi.org/10.1073%2Fpnas.1421412111", "http://doi.org/10.1080%2F00031305.2017.1375986", "http://doi.org/10.1109%2FMCSE.2009.14", "http://doi.org/10.1109%2FMCSE.2010.113", "http://doi.org/10.1126%2Fscience.aac4716", "http://doi.org/10.1126%2Fscitranslmed.aaf5027", "http://doi.org/10.1371%2Fjournal.pone.0063221", "http://doi.org/10.1525%2Fcollabra.13", "http://doi.org/10.2481%2Fdsj.8.18", "http://goldbook.iupac.org/R05305.html", "http://www.pnas.org/content/112/6/1645.full", "http://www.worldcat.org/oclc/936687178", "https://arstechnica.com/science/2006/10/5744/", "https://www.nature.com/articles/sdata2017114", "https://www.nytimes.com/2017/10/18/magazine/when-the-revolution-came-for-amy-cuddy.html", "https://link.springer.com/article/10.1007/s10816-015-9272-9", "https://statistics.stanford.edu/sites/default/files/EFS%20NSF%20474.pdf", "https://www.nist.gov/pml/nist-technical-note-1297", "https://osf.io/9f6gx/", "https://ieeexplore.ieee.org/document/4720217", "https://www.sciencenews.org/article/redoing-scientific-research-best-way-find-truth", "https://www.worldcat.org/oclc/936687178", "https://eprints.soton.ac.uk/403913/1/STAL9781614996491-0087.pdf", "https://www.telegraph.co.uk/technology/3342867/Is-the-spirit-of-Piltdown-man-alive-and-well.html"]}, "Log-logistic distribution": {"categories": ["CS1 maint: Extra text: authors list", "CS1 maint: Multiple names: authors list", "Continuous distributions", "Probability distributions with non-finite variance", "Survival analysis"], "title": "Log-logistic distribution", "method": "Log-logistic distribution", "url": "https://en.wikipedia.org/wiki/Log-logistic_distribution", "summary": "In probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for a non-negative random variable. It is used in survival analysis as a parametric model for events whose rate increases initially and decreases later, for example mortality rate from cancer following diagnosis or treatment. It has also been used in hydrology to model stream flow and precipitation, in economics as a simple model of the distribution of wealth or income, and in networking to model the transmission times of data considering both the network and the software.\nThe log-logistic distribution is the probability distribution of a random variable whose logarithm has a logistic distribution.\nIt is similar in shape to the log-normal distribution but has heavier tails. Unlike the log-normal, its cumulative distribution function can be written in closed form.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/98/FitLog-logisticdistr.tif", "https://upload.wikimedia.org/wikipedia/commons/7/75/Loglogisticcdf.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1b/Loglogistichaz.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e1/Loglogisticpdf.svg"], "links": ["ARGUS distribution", "Accelerated failure time model", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr Type XII distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Censoring (statistics)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Closed form expression", "Compound Poisson distribution", "Computer network", "Confidence belt", "Continuous probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Distribution fitting", "Distribution of wealth", "Economics", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gini coefficient", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hazard function", "Heavy-tailed distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hydrology", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Income distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Journal of Hydrology", "Journal of the Royal Statistical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-normal distribution", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment (mathematics)", "Monotonic", "Mortality rate", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Parametric model", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Plotting position", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Precipitation", "Probability", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Quartile", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real-time computing", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Sensor", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singh-Maddala distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical dispersion", "Statistics", "Student's t-distribution", "Support (mathematics)", "Survival analysis", "Survival function", "The Canadian Journal of Statistics", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unimodal", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.waterlog.info/pdf/freqtxt.pdf", "http://www.causascientia.org/math_stat/Dists/Compendium.pdf", "http://doi.org/10.1016%2Fj.jhydrol.2006.01.014", "http://doi.org/10.1093%2Fbiomet%2F69.2.461", "http://doi.org/10.2307%2F1402945", "http://doi.org/10.2307%2F1909287", "http://doi.org/10.2307%2F2347295", "http://doi.org/10.2307%2F3314729", "http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6516944", "http://www.jstor.org/stable/1402945", "http://www.jstor.org/stable/1909287", "http://www.jstor.org/stable/2335422", "http://www.jstor.org/stable/2347295", "http://www.jstor.org/stable/3314729"]}, "Rejection sampling": {"categories": ["Monte Carlo methods", "Non-uniform random numbers"], "title": "Rejection sampling", "method": "Rejection sampling", "url": "https://en.wikipedia.org/wiki/Rejection_sampling", "summary": "In numerical analysis, rejection sampling is a basic technique used to generate observations from a distribution. It is also commonly called the acceptance-rejection method or \"accept-reject algorithm\" and is a type of exact simulation method. The method works for any distribution in \n \n \n \n \n \n R\n \n \n m\n \n \n \n \n {\\displaystyle \\mathbb {R} ^{m}}\n with a density.\nRejection sampling is based on the observation that to sample a random variable one can perform a uniformly random sampling of the 2D cartesian graph, and keep the samples in the region under the graph of its density function. Note that this property can be extended to N-dimension functions.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/66/Circle_sampling.png"], "links": ["Annals of Statistics", "ArXiv", "Bibcode", "Buffon's needle", "CiteSeerX", "Computational statistics", "Curse of dimensionality", "Digital object identifier", "Exponential distribution", "Geometric distribution", "Gibbs sampling", "Handle System", "International Standard Book Number", "International Standard Serial Number", "Inverse transform sampling", "Inversion sampling", "JSTOR", "John von Neumann", "Logarithmically concave function", "Markov chain Monte Carlo", "Mathematical Reviews", "Metropolis algorithm", "Metropolis sampling", "Moment-generating function", "Monte Carlo method", "Natural exponential families", "Natural exponential family", "Normal distribution", "Normalizing constant", "Numerical analysis", "Probability density function", "Probability distribution", "Pseudo-random number sampling", "Pseudorandom number", "Random variable", "Springer Science+Business Media", "Support (mathematics)", "Zentralblatt MATH", "Ziggurat algorithm"], "references": ["http://www.sciencedirect.com/science/article/pii/S0165168410001866", "http://www.sciencedirect.com/science/article/pii/S016794730800008X", "http://adsabs.harvard.edu/abs/2015ITSP...63.3123M", "http://adsabs.harvard.edu/abs/2015arXiv150907985M", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.315.2111", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.9001", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.6055", "http://oa.upm.es/22661/", "http://hdl.handle.net/10016%2F16624", "http://a2rms.sourceforge.net", "http://www.ams.org/mathscinet-getitem?mr=1994729", "http://arxiv.org/abs/0904.1300", "http://arxiv.org/abs/1205.5494", "http://arxiv.org/abs/1710.04948", "http://doi.org/10.1007%2Fs11222-010-9197-9", "http://doi.org/10.1016%2Fj.csda.2008.01.005", "http://doi.org/10.1016%2Fj.sigpro.2010.04.025", "http://doi.org/10.1049%2Fel.2012.0206", "http://doi.org/10.1049%2Fel.2017.1711", "http://doi.org/10.1109%2FTSP.2015.2420537", "http://doi.org/10.1145%2F203082.203089", "http://doi.org/10.1198%2Fjcgs.2011.09058", "http://doi.org/10.1214%2Faos%2F1056562461", "http://doi.org/10.1214%2Flnms%2F1196285403", "http://doi.org/10.2307%2F1390680", "http://doi.org/10.2307%2F2986138", "http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7080917", "http://www.jstor.org/stable/1390680", "http://www.jstor.org/stable/2986138", "http://projecteuclid.org/euclid.lnms/1196285403", "http://www.worldcat.org/issn/0098-3500", "http://www.worldcat.org/issn/0960-3174", "http://www.worldcat.org/issn/1053-587X", "http://www.worldcat.org/issn/1061-8600", "http://zbmath.org/?format=complete&q=an:1051.65007", "http://www.doc.ic.ac.uk/~wl/papers/iee07dt.pdf", "https://stat.duke.edu/~cnk/Links/tangent.method.pdf"]}, "Van Houtum distribution": {"categories": ["All articles needing additional references", "All articles with topics of unclear notability", "Articles needing additional references from March 2010", "Articles with multiple maintenance issues", "Articles with topics of unclear notability from March 2010", "Discrete distributions", "Pages using deprecated image syntax"], "title": "Van Houtum distribution", "method": "Van Houtum distribution", "url": "https://en.wikipedia.org/wiki/Van_Houtum_distribution", "summary": "In probability theory and statistics, the Van Houtum distribution is a discrete probability distribution named after prof. Geert-Jan van Houtum. It can be characterized by saying that all values of a finite set of possible values are equally probable, except for the smallest and largest element of this set. Since the Van Houtum distribution is a generalization of the discrete uniform distribution, i.e. it is uniform except possibly at its boundaries, it is sometimes also referred to as quasi-uniform.\nIt is regularly the case that the only available information concerning some discrete random variable are its first two moments. The Van Houtum distribution can be used to fit a distribution with finite support on these moments.\nA simple example of the Van Houtum distribution arises when throwing a loaded dice which has been tampered with to land on a 6 twice as often as on a 1. The possible values of the sample space are 1, 2, 3, 4, 5 and 6. Each time the die is thrown, the probability of throwing a 2, 3, 4 or 5 is 1/6; the probability of a 1 is 1/9 and the probability of throwing a 6 is 2/9.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/3/39/Van_Houtum_distribution.PNG"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Coefficient of variation", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Loaded dice", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Probability mass function", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://scholar.google.com/scholar?q=%22Van+Houtum+distribution%22", "http://www.google.com/search?&q=%22Van+Houtum+distribution%22+site:news.google.com/newspapers&source=newspapers", "http://www.google.com/search?as_eq=wikipedia&q=%22Van+Houtum+distribution%22&num=50", "http://www.google.com/search?tbm=nws&q=%22Van+Houtum+distribution%22+-wikipedia", "http://www.google.com/search?tbs=bks:1&q=%22Van+Houtum+distribution%22+-wikipedia", "http://alexandria.tue.nl/extra2/afstversl/tm/Arts%202009.pdf", "https://www.jstor.org/action/doBasicSearch?Query=%22Van+Houtum+distribution%22&acc=on&wc=on"]}, "Mediation (statistics)": {"categories": ["Articles with imported dually licensed text", "Independence (probability theory)", "Psychometrics", "Statistical models"], "title": "Mediation (statistics)", "method": "Mediation (statistics)", "url": "https://en.wikipedia.org/wiki/Mediation_(statistics)", "summary": "In statistics, a mediation model is one that seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator variable (also a mediating variable, intermediary variable, or intervening variable). Rather than a direct causal relationship between the independent variable and the dependent variable, a mediation model proposes that the independent variable influences the (non-observable) mediator variable, which in turn influences the dependent variable. Thus, the mediator variable serves to clarify the nature of the relationship between the independent and dependent variables.Mediation analyses are employed to understand a known relationship by exploring the underlying mechanism or process by which one variable influences another variable through a mediator variable. Mediation analysis facilitates a better understanding of the relationship between the independent and dependent variables when the variables appear to not have a definite connection. They are studied by means of operational definitions and have no existence apart.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4d/Mediation.jpg", "https://upload.wikimedia.org/wikipedia/en/d/db/Mediated_moderation_model_1.png", "https://upload.wikimedia.org/wikipedia/en/9/9a/Mediated_moderation_model_2.png", "https://upload.wikimedia.org/wikipedia/en/0/0c/Mediated_moderation_model_3.png", "https://upload.wikimedia.org/wikipedia/en/6/63/Mediated_moderation_model_4.png", "https://upload.wikimedia.org/wikipedia/en/3/37/Mediated_moderation_model_5.png"], "links": ["ArXiv", "Bayesian Networks", "Bibcode", "Bootstrapping (statistics)", "Dependent variable", "Digital object identifier", "Independent variable", "Interaction effect", "JSTOR", "James Robins", "Journal of Personality and Social Psychology", "Judea Pearl", "Moderated mediation", "Moderation (statistics)", "Morgan Kaufmann", "Non-parametric statistics", "Normal distribution", "Operational definition", "Paul E. Meehl", "Prisoner's dilemma", "PubMed Central", "PubMed Identifier", "SPSS", "Sander Greenland", "Sobel test", "Social value orientations", "Statistics", "University of Indiana"], "references": ["http:ftp://ftp.cs.ucla.edu/pub/stat_ser/r389-imai-etal-commentary-r421-reprint.pdf", "http://www2.psych.ubc.ca/~schaller/528Readings/BullockGreenHa2010.pdf", "http://www2.psych.ubc.ca/~schaller/528Readings/SpencerZannaFong2005.pdf", "http://psychclassics.yorku.ca/MacMeehl/hypcon-intvar.htm", "http://www.afhayes.com/", "http://www.afhayes.com/introduction-to-mediation-moderation-and-conditional-process-analysis.html", "http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html", "http://www.informaworld.com/smpp/ftinterface~db=all~content=a917285720~fulltext=713240930", "http://www.psychwiki.com/wiki/Mediation", "http://adsabs.harvard.edu/abs/2013arXiv1302.4929B", "http://adsabs.harvard.edu/abs/2013arXiv1302.6835P", "http://www.indiana.edu/~educy520/sec5982/week_2/variable_types.pdf", "http://www.comm.ohio-state.edu/ahayes/SPSS%20programs/indirect.htm", "http://www.comm.ohio-state.edu/ahayes/sobel.htm", "http://methodology.psu.edu/ra/causal/example", "http://ftp.cs.ucla.edu/pub/stat_ser/R273-U.pdf", "http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf", "http://www.mii.ucla.edu/causality/?p=713", "http://wexler.free.fr/library/files/tolman%20(1938)%20the%20determiners%20of%20behavior%20at%20a%20choice-point.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2819363", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2843515", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3773310", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC526390", "http://www.ncbi.nlm.nih.gov/pubmed/11928892", "http://www.ncbi.nlm.nih.gov/pubmed/12757142", "http://www.ncbi.nlm.nih.gov/pubmed/12940467", "http://www.ncbi.nlm.nih.gov/pubmed/15507130", "http://www.ncbi.nlm.nih.gov/pubmed/1576220", "http://www.ncbi.nlm.nih.gov/pubmed/16393019", "http://www.ncbi.nlm.nih.gov/pubmed/16393020", "http://www.ncbi.nlm.nih.gov/pubmed/18697684", "http://www.ncbi.nlm.nih.gov/pubmed/19234398", "http://www.ncbi.nlm.nih.gov/pubmed/20307128", "http://www.ncbi.nlm.nih.gov/pubmed/20822249", "http://www.ncbi.nlm.nih.gov/pubmed/21500915", "http://www.ncbi.nlm.nih.gov/pubmed/24885338", "http://davidakenny.net/cm/mediate.htm", "http://arxiv.org/abs/1011.1079", "http://arxiv.org/abs/1302.4929", "http://arxiv.org/abs/1302.6835", "http://doi.org/10.1023%2FA:1024649822872", "http://doi.org/10.1037%2F0022-3514.84.5.972", "http://doi.org/10.1037%2F0022-3514.89.6.845", "http://doi.org/10.1037%2F0022-3514.89.6.852", "http://doi.org/10.1037%2F1082-989x.7.1.83", "http://doi.org/10.1037%2F1082-989x.7.4.422", "http://doi.org/10.1037%2Fa0018933", "http://doi.org/10.1037%2Fa0020141", "http://doi.org/10.1037%2Fa0022658", "http://doi.org/10.1037%2Fa0036434", "http://doi.org/10.1037%2Fh0037350", "http://doi.org/10.1037%2Fh0062733", "http://doi.org/10.1080%2F03637750903310360", "http://doi.org/10.1097%2F00001648-199203000-00013", "http://doi.org/10.1097%2Fede.0b013e31818f69ce", "http://doi.org/10.1097%2Fede.0b013e31826c2bb9", "http://doi.org/10.1186%2F1742-5573-1-4", "http://doi.org/10.1214%2F09-ss057", "http://doi.org/10.1214%2F10-sts321", "http://doi.org/10.1515%2F2161-962X.1014", "http://doi.org/10.2307%2F270723", "http://doi.org/10.3758%2FBF03206553", "http://doi.org/10.3758%2FBRM.40.3.879", "http://www.jstor.org/stable/270723"]}, "Seemingly unrelated regressions": {"categories": ["Simultaneous equation methods (econometrics)"], "title": "Seemingly unrelated regressions", "method": "Seemingly unrelated regressions", "url": "https://en.wikipedia.org/wiki/Seemingly_unrelated_regressions", "summary": "In econometrics, the seemingly unrelated regressions (SUR) or seemingly unrelated regression equations (SURE) model, proposed by Arnold Zellner in (1962), is a generalization of a linear regression model that consists of several regression equations, each having its own dependent variable and potentially different sets of exogenous explanatory variables. Each equation is a valid linear regression on its own and can be estimated separately, which is why the system is called seemingly unrelated, although some authors suggest that the term seemingly related would be more appropriate, since the error terms are assumed to be correlated across the equations.\nThe model can be estimated equation-by-equation using standard ordinary least squares (OLS). Such estimates are consistent, however generally not as efficient as the SUR method, which amounts to feasible generalized least squares with a specific form of the variance-covariance matrix. Two important cases when SUR is in fact equivalent to OLS are when the error terms are in fact uncorrelated between the equations (so that they are truly unrelated) and when each equation contains exactly the same set of regressors on the right-hand-side.\nThe SUR model can be viewed as either the simplification of the general linear model where certain coefficients in matrix \n \n \n \n \n B\n \n \n \n {\\displaystyle \\mathrm {B} }\n are restricted to be equal to zero, or as the generalization of the general linear model where the regressors on the right-hand-side are allowed to be different in each equation. The SUR model can be further generalized into the simultaneous equations model, where the right-hand side regressors are allowed to be the endogenous variables as well.", "images": [], "links": ["Arnold Zellner", "Asymptotic distribution", "Bias of an estimator", "Consistency (statistics)", "Consistent estimator", "Digital object identifier", "Econometrics", "Efficiency (statistics)", "Errors and residuals in statistics", "Feasible generalized least squares", "General linear model", "Generalized least squares", "Identity matrix", "International Standard Book Number", "Jan Kmenta", "Kronecker product", "Kruskal's tree theorem", "Limdep", "Linear regression model", "Ordinary least squares", "Python (programming language)", "R (programming language)", "SAS (software)", "Simultaneous equations model", "Simultaneous equations models", "Stata"], "references": ["http://doi.org/10.1016%2Fj.jeconom.2010.04.005", "http://doi.org/10.2307%2F2281644", "http://doi.org/10.2307%2F2285876", "https://books.google.com/books?id=0bzGQE14CwEC&pg=PA197", "https://books.google.com/books?id=86rWI7WzFScC&pg=PA89", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA279", "https://books.google.com/books?id=VL6Gql5MemMC&pg=PA282", "https://books.google.com/books?id=zCym0GtuRE4C&pg=PA238", "https://support.sas.com/documentation/cdl/en/etsug/60372/HTML/default/viewer.htm#etsug_syslin_sect009.htm", "https://www.stata.com/manuals13/rsureg.pdf", "https://books.google.de/books?id=UkKQRAAACAAJ&pg=PA162", "https://people.emich.edu/jthornton/text-files/Econ515_Limdep_Guide.doc", "https://bashtage.github.io/linearmodels/doc/system/models.html#linearmodels.system.model.SUR", "https://cran.r-project.org/web/packages/systemfit/vignettes/systemfit.pdf", "https://cran.r-project.org/web/views/Econometrics.html"]}, "Cophenetic correlation": {"categories": ["Covariance and correlation"], "title": "Cophenetic correlation", "method": "Cophenetic correlation", "url": "https://en.wikipedia.org/wiki/Cophenetic_correlation", "summary": "In statistics, and especially in biostatistics, cophenetic correlation (more precisely, the cophenetic correlation coefficient) is a measure of how faithfully a dendrogram preserves the pairwise distances between the original unmodeled data points. Although it has been most widely applied in the field of biostatistics (typically to assess cluster-based models of DNA sequences, or other taxonomic models), it can also be used in other fields of inquiry where raw data tend to occur in clumps, or clusters. This coefficient has also been proposed for use as a test for nested clusters.", "images": [], "links": ["Biostatistics", "Cophenetic", "DNA", "Dendrogram", "R (programming language)", "Statistics", "Taxonomy (biology)", "United States Department of Energy"], "references": ["http://www.mathworks.com/access/helpdesk/help/toolbox/stats/index.html?/access/helpdesk/help/toolbox/stats/cophenet.html", "http://people.revoledu.com/kardi/tutorial/Clustering/index.html", "http://life.bio.sunysb.edu/ee/rohlf/reprints/RohlfFisher_1968.pdf", "http://www.osti.gov/bridge/servlets/purl/9576-lcvvCD/webviewable/9576.pdf", "https://stackoverflow.com/questions/5639794/in-r-how-can-i-plot-a-similarity-matrix-like-a-block-graph-after-clustering-d", "https://cran.r-project.org/web/packages/dendextend/vignettes/introduction.html#correlation-measures"]}, "Log-linear analysis": {"categories": ["Categorical variable interactions", "Wikipedia articles needing page number citations from June 2012", "Wikipedia articles with GND identifiers"], "title": "Log-linear analysis", "method": "Log-linear analysis", "url": "https://en.wikipedia.org/wiki/Log-linear_analysis", "summary": "Log-linear analysis is a technique used in statistics to examine the relationship between more than two categorical variables. The technique is used for both hypothesis testing and model building. In both these uses, models are tested to find the most parsimonious (i.e., least complex) model that best accounts for the variance in the observed frequencies. (A Pearson's chi-square test could be used instead of log-linear analysis, but that technique only allows for two of the variables to be compared at a time.)\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20161201223606%21Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/7/73/20120912121406%21Blue_pencil.svg"], "links": ["Backward elimination", "Categorical variable", "Cengage Learning", "Chi-square distribution", "Chordal graph", "Contingency table", "Dependent variable", "Deviance (statistics)", "Errors and residuals in statistics", "Independence (probability theory)", "Independent variable", "Integrated Authority File", "Interaction (statistics)", "International Standard Book Number", "JSTOR", "John Wiley & Sons", "Likelihood ratio test", "Log-linear model", "Logistic regression", "Main effect", "Natural logarithm", "Odds ratios", "Pearson's chi-square test", "Poisson regression", "Sage Publications", "Saturated model", "Statistical hypothesis testing", "Statistical model", "Statistical randomness", "Statistics"], "references": ["http://stat.ethz.ch/R-manual/R-devel/library/MASS/html/loglm.html", "http://pic.dhe.ibm.com/infocenter/spssstat/v20r0m0/index.jsp?topic=/com.ibm.spss.statistics.help/syn_genlog.htm", "http://www-01.ibm.com/software/analytics/spss/products/statistics/", "http://onlinelibrary.wiley.com/book/10.1002/0470114754", "http://ww2.coastal.edu/kingw/statistics/R-tutorials/loglin.html", "http://www.tiny-clues.eu/Research/Petitjean2013-ICDM.pdf", "http://www.oxfordjournals.org/tropej/online/ma_chap14.pdf", "http://www.r-project.org/", "https://github.com/fpetitjean/Chordalysis", "https://d-nb.info/gnd/4036197-4", "https://web.archive.org/web/20141112210114/http://www.fico.com/en/resources/predictive-analytics/analytic-technologies/log-linear-models/", "https://www.jstor.org/stable/3033794", "https://cran.r-project.org/package=MASS", "https://www.wikidata.org/wiki/Q259304"]}, "Generalized linear mixed model": {"categories": ["All articles needing additional references", "All articles needing expert attention", "Analysis of variance", "Articles needing additional references from July 2017", "Articles needing expert attention from July 2017", "Articles needing expert attention with no reason or talk parameter", "Generalized linear models", "Statistics articles needing expert attention"], "title": "Generalized linear mixed model", "method": "Generalized linear mixed model", "url": "https://en.wikipedia.org/wiki/Generalized_linear_mixed_model", "summary": "In statistics, a generalized linear mixed model (GLMM) is an extension to the generalized linear model (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects. They also inherit from GLMs the idea of extending linear mixed models to non-normal data.\nGLMMs provide a broad range of models for the analysis of grouped data, since the differences between groups can be modelled as a random effect. These models are useful in the analysis of many kinds of data, including longitudinal data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Akaike information criterion", "Analytic expression", "Approximate Inference", "Boolean value", "CRC Press", "Data set", "David Clayton", "Digital object identifier", "Electronic Journal of Statistics", "Exponential family", "Fixed effects", "Generalized estimating equation", "Generalized linear model", "Hierarchical generalized linear model", "Integral", "International Standard Book Number", "JSTOR", "John Wiley & Sons", "Journal of the American Statistical Association", "Longitudinal study", "Markov chain Monte Carlo", "Maximum likelihood", "Mixed model", "Model selection", "Normal distribution", "Numerical quadrature", "R (programming language)", "Random effects", "SAS (software)", "SPSS", "Springer Publishing", "Springer Science+Business Media", "Statistics"], "references": ["http://doi.org/10.1214%2F14-EJS881", "http://doi.org/10.2307%2F2290687", "http://www.jstor.org/stable/2290687", "https://www.ibm.com/support/knowledgecenter/en/SSLVMB_22.0.0/com.ibm.spss.statistics.help/spss/advanced/idh_idd_genlin_typeofmodel.htm"]}, "Errors and residuals in statistics": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from September 2016", "Articles with unsourced statements from July 2016", "Errors and residuals", "Regression analysis", "Statistical deviation and dispersion"], "title": "Errors and residuals", "method": "Errors and residuals in statistics", "url": "https://en.wikipedia.org/wiki/Errors_and_residuals", "summary": "In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its \"theoretical value\". The error (or disturbance) of an observed value is the deviation of the observed value from the (unobservable) true value of a quantity of interest (for example, a population mean), and the residual of an observed value is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA", "Absolute deviation", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Almost surely", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Approximation theory", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Basu's theorem", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bessel's correction", "Bias (statistics)", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calibration curve", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chapman and Hall", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational statistics", "Confidence interval", "Confounding", "Consensus forecasts", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curve fitting", "Data collection", "David R. Cox", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Deviation (statistics)", "Dickey\u2013Fuller test", "Discrete choice", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Error detection and correction", "Errors-in-variables models", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Explained sum of squares", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fixed effects model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Influence function (statistics)", "Innovation (signal processing)", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the Royal Statistical Society, Series B", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lack-of-fit sum of squares", "Least-angle regression", "Least absolute deviations", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location model (statistics)", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mallows's Cp", "Mann\u2013Whitney U test", "Margin of error", "Mathematical optimization", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean absolute error", "Mean and predicted response", "Mean square error", "Mean squared error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Missing data", "Mixed logit", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observational error", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal polynomials", "Outliers", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial regression", "Population (statistics)", "Population mean", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Principal component regression", "Prior probability", "Probabilistic design", "Probability distribution", "Probable error", "Probit model", "Propagation of error", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random and systematic errors", "Random assignment", "Random effects model", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression coefficient", "Regression dilution", "Regression model validation", "Regularized least squares", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Residual sum of squares", "Response surface methodology", "Ridge regression", "Robust regression", "Robust statistics", "Root mean square deviation", "Run chart", "Sample (statistics)", "Sample mean", "Sample median", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Sampling error", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Squared deviations", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Studentized residual", "Studentized residuals", "Studentizing", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-statistic", "Tikhonov regularization", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Trend estimation", "Type I and type II errors", "U-statistic", "Uniformly most powerful test", "Univariate distribution", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-score", "Z-test"], "references": ["http://www.stat.umn.edu/rir/", "http://www.jstor.org/stable/2984505", "https://books.google.com/books?id=yRrvAAAAMAAJ&dq=editions:UMM1U2yvYVUC", "https://www.encyclopediaofmath.org/index.php?title=p/e036240"]}, "List of statisticians": {"categories": ["Lists of mathematicians", "Lists of scientists", "Statisticians", "Statistics-related lists"], "title": "List of statisticians", "method": "List of statisticians", "url": "https://en.wikipedia.org/wiki/List_of_statisticians", "summary": "This list of statisticians lists people who have made notable contributions to the theories or application of statistics, or to the related fields of probability or machine learning. Also included are actuaries and demographers.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407084002%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407083328%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407082944%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20110430032449%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20090922000234%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041048%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041018%21Fisher_iris_versicolor_sepalwidth.svg"], "links": ["A. Ronald Gallant", "A. Ross Eckler", "A. Ross Eckler, Jr.", "A. W. F. Edwards", "A. William Flux", "Abraham Manie Adelstein", "Abraham Wald", "Abraham de Moivre", "Actuary", "Adolphe Quetelet", "Adrian Raftery", "Adrian Smith (academic)", "Agner Krarup Erlang", "Alain Desrosi\u00e8res", "Alexander Aitken", "Alexander Alexandrovich Chuprov", "Alexander Ivanovich Chuprov", "Alexander Jobson", "Alexey Chervonenkis", "Alfred J. Lotka", "Alfred M. Best", "Allan Birnbaum", "Allyn Abbott Young", "American Statistical Association", "Anders Hald", "Anders Lindstedt", "Anders Nicolai Ki\u00e6r", "Anderson Gray McKendrick", "Andrey Kolmogorov", "Andr\u00e9-Michel Guerry", "Andr\u00e9 Kr\u00fcger", "Anil Kumar Gain", "Ansley J. Coale", "Anthony Ashley-Cooper, 7th Earl of Shaftesbury", "Arif Zaman", "Arnold Weinstock", "Arnold Zellner", "Arnoldo Frigessi", "Arthur Cockfield, Baron Cockfield", "Arthur Lyon Bowley", "Arthur P. Dempster", "Arthur Schuster", "Arthur Young (writer)", "Aryeh Dvoretzky", "August Friedrich Wilhelm Crome", "Austin Bradford Hill", "B. R. Bhat", "B. V. Shah", "Basilio de Bragan\u00e7a Pereira", "Beatrice Aitchison", "Benjamin Gompertz", "Bernard Benjamin", "Bernard Koopman", "Bernard Mallet", "Bernard Silverman", "Bill James", "Bill McLennan", "Bimal Kumar Roy", "Bogoljub Ko\u010dovi\u0107", "Boris Levit", "Bradley Efron", "Brian D. Ripley", "Brian Easton (economist)", "Brian Pink", "Bruno de Finetti", "C.F. Jeff Wu", "C. C. Li", "Calvin Beale", "Calyampudi Radhakrishna Rao", "Carl Charlier", "Carl Morris (statistician)", "Carl O. Nordling", "Carl Snyder", "Carlo Emilio Bonferroni", "Carroll D. Wright", "Cecil J. Nesbitt", "Cedric Smith (statistician)", "Charles Booth (philanthropist)", "Charles Dunnett", "Charles Lawrence (mathematician)", "Charles Lemon", "Charles P. Neill", "Charles Roy Henderson", "Charles Sanders Peirce", "Charles Spearman", "Charles Stein (statistician)", "Charles Wentworth-Fitzwilliam, 5th Earl Fitzwilliam", "Chester Ittner Bliss", "Chris Heyde", "Chris Holmes (mathematician)", "Chris Wallace (computer scientist)", "Christopher Bingham", "Christopher Daykin", "Churchill Eisenhart", "Claude E. Robinson", "Claus Moser, Baron Moser", "Clive Granger", "Col Hutchinson", "Colin Clark (economist)", "Colin McEvedy", "Corrado Gini", "Cyril Goulden", "D. G. Champernowne", "D. J. Finney", "D. Raghavarao", "Dan Krewski", "Daniel Pena", "Darrell Huff", "David A. Freedman (statistician)", "David B. Allison", "David Balding", "David Blackwell", "David Clayton", "David Coleman (academic)", "David Cox (statistician)", "David Donoho", "David E. Bloom", "David F. Duncan", "David Foot (economist)", "David George Kendall", "David Glass (sociologist)", "David Hand (statistician)", "David Salsburg", "David Spiegelhalter", "David V. Hinkley", "David X. Li", "David van Dantzig", "Davis Rich Dewey", "Debabrata Basu", "Demography", "Dennis Lindley", "Dennis Trewin", "Derek Wanless", "Dietrich Stoyan", "Don Berry (statistician)", "Donald Geman", "Donald J. Wheeler", "Donald Marquardt", "Donald Rubin", "Doug Altman", "Dudley Ryder, 2nd Earl of Harrowby", "E. A. Wrigley", "E. C. Rhodes", "E. J. G. Pitman", "E. Morton Jellinek", "Edith Abbott", "Edward C. Molina", "Edward Jones (statistician)", "Edward Rowe Mores", "Edward Stanley, 15th Earl of Derby", "Edward Szturm de Sztrem", "Edward Tufte", "Edward Wakefield (statistician)", "Edward Wegman", "Edwin Bidwell Wilson", "Edwin Thompson Jaynes", "Egon Pearson", "Elena Zarova", "Elizabeth Scott (mathematician)", "Elizur Wright", "El\u017cbieta Pleszczy\u0144ska", "Emanuel Parzen", "Emil Julius Gumbel", "Emmanuel Cand\u00e8s", "Emmanuel Todd", "Emory McClintock", "Enid Charles", "Eric Ghysels", "Erich Leo Lehmann", "Ernest Kurnow", "Ernst Behm", "Ernst Engel", "Esprit Jouffret", "Estate V. Khmaladze", "Ethel M. Elderton", "Eugen Slutsky", "Eugene Grebenik", "Eugene M. Kulischer", "Filip Lundberg", "Florence Nightingale", "Florence Nightingale David", "Founders of statistics", "Francis Amasa Walker", "Francis Anscombe", "Francis Galton", "Francis Ysidro Edgeworth", "Frank Duckworth", "Frank Redington", "Frank W. Notestein", "Frank Wilcoxon", "Frank Yates", "Fran\u00e7ois Simiand", "Frederic J. Mouat", "Frederic M. Lord", "Frederick B. Lindstrom", "Frederick Marquis, 1st Earl of Woolton", "Frederick Mosteller", "Friedrich Robert Helmert", "Gabriel Gabrielsen Holtsmark", "Gareth Roberts (statistician)", "Garrett Hardin", "Gauss Moutinho Cordeiro", "Gene V. Glass", "Genichi Taguchi", "Geoff Bascand", "Geoffrey Grimmett", "Geoffrey Watson", "Georg Rasch", "George A. Milliken", "George Alfred Barnard", "George Chalmers (antiquarian)", "George Dantzig", "George E. P. Box", "George Gallup", "George Goschen, 1st Viscount Goschen", "George Handley Knibbs", "George Henry Wood (statistician)", "George Kingsley Zipf", "George Paine (registrar)", "George P\u00f3lya", "George Shaw-Lefevre, 1st Baron Eversley", "George W. Snedecor", "Gertrude Mary Cox", "Gheorghe Mihoc", "Gilbert Walker", "Gilean McVean", "Giovanni Villani", "Glossary of probability and statistics", "Gottfried Achenwall", "Gottfried E. Noether", "Grace Wahba", "Greg Lawler", "Gregory King", "Griffith Davies", "Gunnar Kulldorff", "Gustav Fechner", "Guy Nason", "Gwilym Jenkins", "Hadley Wickham", "Halbert L. Dunn", "Hans-Rudolf K\u00fcnsch", "Harald Cram\u00e9r", "Harald Ludvig Westergaard", "Harold F. Dodge", "Harold Hotelling", "Harold Jeffreys", "Harold Wilson", "Harry C. Carver", "Harry Campion", "Harry V. Roberts", "Harvey Goldstein", "Henry Daniels", "Henry Fowler, 1st Viscount Wolverhampton", "Henry Heylyn Hayter", "Henry Ludwell Moore", "Henry O. Pollak", "Henry Petty-Fitzmaurice, 3rd Marquess of Lansdowne", "Henry Scheff\u00e9", "Henry Schultz", "Herbert Marshall (statistician)", "Herbert Robbins", "Herbert Samuel, 1st Viscount Samuel", "Herbert Sichel", "Herman Chernoff", "Herman Hollerith", "Herman Otto Hartley", "Herman Wold", "Hilton Young, 1st Baron Kennet", "Hirotsugu Akaike", "Holbrook Working", "Howard Raiffa", "Howell Tong", "Hubert Lilliefors", "Hugh Hedley Scurfield", "I. J. Good", "I. M. Rubinow", "Ian Castles", "Ibrahim Sirkeci", "India", "Ion Ionescu de la Brad", "Irving Fisher", "Ir\u00e9n\u00e9e-Jules Bienaym\u00e9", "Ivan Fellegi", "Ivo Lah", "J. Michael Steele", "J. N. Srivastava", "Jack Hibbert", "Jack Kiefer (mathematician)", "Jacob Cohen (statistician)", "Jacob Marschak", "Jacob Wolfowitz", "Jahar Saha", "Jakob Mohn", "James Berger (statistician)", "James C. Hickman", "James Caird (agricultural writer)", "James Crosby (British businessman)", "James Dodson (mathematician)", "James Durbin", "James Goodnight", "James Joseph Sylvester", "James Jurin", "James Robins", "James Tobin", "James Vaupel", "Jan Czekanowski", "Jan Hoem", "Jan Pieka\u0142kiewicz", "Jan Visman", "Jarl Waldemar Lindeberg", "Jaroslav H\u00e1jek", "Jayanta Kumar Ghosh", "Jean-Marie Robine", "Jean-Paul Benz\u00e9cri", "Jeff Rosenthal", "Jeff Sagarin", "Jerome Cornfield", "Jerzy Neyman", "Jessica Utts", "Jianqing Fan", "Joel E. Cohen", "Johan Frederik Steffensen", "Johann Ernst Fabri", "Johann Peter S\u00fcssmilch", "Johannes Fallati", "John Aitchison", "John Boreham", "John Caldwell (demographer)", "John Chambers (statistician)", "John Darwin (statistician)", "John Erritt", "John F. MacGregor", "John Finlaison (Finlayson)", "John Fox (statistician)", "John Graunt", "John Hajnal", "John Kingman", "John Law (economist)", "John Lubbock, 1st Baron Avebury", "John Mauchly", "John Nelder", "John Pakington, 1st Baron Hampton", "John Panaretos", "John Rickman", "John Russell, 1st Earl Russell", "John Tukey", "John Wingate Thornton", "John Wishart (statistician)", "Joseph Adna Hill", "Joseph Berkson", "Joseph C. G. Kennedy", "Joseph Hilbe", "Joseph J. Spengler", "Joseph Kruskal", "Joseph L. Fleiss", "Joseph Leo Doob", "Joseph M. Juran", "Joseph Oscar Irwin", "Joshua Milne", "Josiah Stamp, 1st Baron Stamp", "Jos\u00e9-Miguel Bernardo", "Jos\u00e9 Enrique Moyal", "Jotun Hein", "Julian C. Stanley Jr.", "Julian Peto", "Julius Bartels", "Jun S. Liu", "J\u00f3zef Buzek", "K. C. Sreedharan Pillai", "Kantilal Mardia", "Kaoru Ishikawa", "Karen Dunnell", "Karl Gustav J\u00f6reskog", "Karl Pearson", "Kenneth Arrow", "Kenneth Massey", "Khandkar Manwar Hossain", "Kingsley Davis", "Ladislaus Bortkiewicz", "Lancelot Hogben", "Larry V. Hedges", "Laurence Baxter", "Lawrence D. Brown", "Lawrence Shepp", "Leland Wilkinson", "Len Cook", "Leo Breiman", "Leon Isserlis", "Leonard Courtney, 1st Baron Courtney of Penwith", "Leonard Henry Caleb Tippett", "Leonard Jimmie Savage", "Leonard Porter Ayres", "Leslie Earl Simon", "Leslie Kish", "Lester Frankel", "Lester G. Telser", "List of actuaries", "List of mathematical probabilists", "List of mathematicians", "List of statistics articles", "List of statistics journals", "List of timelines", "Lists of countries and territories", "Lists of country-related topics", "Lists of people", "Lists of statistics topics", "Lloyd Shapley", "Lord George Hamilton", "Louis Chen Hsiao Yun", "Louis Guttman", "Louis Israel Dublin", "Louis Leon Thurstone", "Luc Anselin", "Lucien Le Cam", "Luigi Bodio", "Lyndhurst Giblin", "L\u00e9on Bottou", "M. C. Chakrabarti", "M. S. Bartlett", "Machine learning", "Major Greenwood", "Mark Kac", "Mark Lathrop", "Martin Wilk", "Mary W. Gray", "Maryse Marpsat", "Matthew Stephens (statistician)", "Maurice Block", "Maurice Kendall", "Maurice Priestley", "Maurice Princet", "Max O. Lorenz", "Mc Sharma, Sharma's Correction to Sample Size Determination", "Michael Healy (statistician)", "Michael I. Jordan", "Michael Teitelbaum", "Michel Gauquelin", "Michel Lo\u00e8ve", "Milton Friedman", "Mir Masoom Ali", "Mollie Orshansky", "Mordecai Ezekiel", "Morris H. DeGroot", "Moses Abramovitz", "Motosaburo Masuyama", "Myles Hollander", "Nan Laird", "Nancy Reid", "Nate Silver", "Nathan Mantel", "Nicholas Polson", "Nicolas-Fran\u00e7ois Dupr\u00e9 de Saint-Maur", "Nils Lid Hjort", "Norman Breslow", "Norman Lloyd Johnson", "Notation in probability and statistics", "Octav Onicescu", "Odd Aalen", "Olav Reiers\u00f8l", "Oscar Kempthorne", "Oscar Phelps Austin", "Oskar Anderson", "Oswald Jacoby", "Otis Dudley Duncan", "Outline of statistics", "P. N. Mari Bhat", "Pafnuty Chebyshev", "Paola Sebastiani", "Partha Niyogi", "Pat Moran (statistician)", "Paul Halmos", "Paul McCrossan", "Paul Meier (statistician)", "Persi Diaconis", "Peter Armitage", "Peter Donnelly", "Peter Gavin Hall", "Peter Green (statistician)", "Peter Laslett", "Peter McCullagh", "Peter Whittle (mathematician)", "Phelim Boyle", "Philip Dawid", "Phillip Good", "Phillip Kott", "Phillip Longman", "Pierre Gy", "Prasanta Chandra Mahalanobis", "Probability", "Pyotr Semyonov-Tyan-Shansky", "Qazi Motahar Hossain", "Quinn McNemar", "R. C. Bose", "R. G. D. Allen", "Raghu Raj Bahadur", "Rattan Chand", "Ravindra Khattree", "Raymond Pearl", "Reginald Hawthorn Hooker", "Reginald Punnett", "Renato Mannheimer", "Rensis Likert", "Reuven Rubinstein", "Riaz Ahsan", "Richard D. Gill", "Richard Doll", "Richard M. Dudley", "Richard Monckton Milnes, 1st Baron Houghton", "Richard Peto", "Richard Price", "Richard Stone", "Richard Threlkeld Cox", "Richard W. B. Clarke", "Robert C. Elston", "Robert F. Engle", "Robert Giffen", "Robert Griffiths (mathematician)", "Robert H. Coats", "Robert L. Thorndike", "Robert Mackenzie Johnston", "Robert P. Abelson", "Robert R. Sokal", "Robert Ren\u00e9 Kuczynski", "Robert Schlaifer", "Robert Tibshirani", "Robert Wedderburn (statistician)", "Robin Plackett", "Roelof Botha", "Ronald Coifman", "Ronald Fisher", "Ronald Freedman", "Ronald L. Iman", "Ross Ihaka", "Roy C. Geary", "Royal Meeker", "S. Jay Olshansky", "S. N. Roy", "S. S. Shrikhande", "Samuel A. Stouffer", "Samuel Goldman", "Samuel H. Preston", "Samuel Jones-Loyd, 1st Baron Overstone", "Samuel S. Wilks", "Sander Greenland", "Sedley Cudmore", "Sewall Wright", "Seymour Geisser", "Shayle R. Searle", "Shlomo Sawilowsky", "Shyamaprasad Mukherjee", "Sidney Siegel", "Simon Kuznets", "Sir Charles Dilke, 2nd Baronet", "Sir Frederick Eden, 2nd Baronet", "Sir John Sinclair, 1st Baronet", "Sir Richard Martin, 1st Baronet, of Overbury Court", "Solomon Kullback", "Stanislaus S. Uyanto", "Stanis\u0142aw Trybu\u0142a", "Statistician", "Statistics", "Stefan Ralescu", "Stefano Franscini", "Stella Cunliffe", "Stephen Fienberg", "Stephen Stigler", "Steve Brooks (statistician)", "Steve Kuzmicich", "Steven Haberman", "Steven Ruggles", "Stuart A. Robertson", "Stuart Pocock", "Subramanian Swamy", "Susan Horn", "Susan Murphy", "Susan P. Holmes", "Sylvia Richardson", "T. Tony Cai", "Takeshi Amemiya", "Ted Harris (mathematician)", "Terry Speed", "Theodore Wilbur Anderson", "Thomas A. Welton", "Thomas Bayes", "Thomas Brassey, 1st Earl Brassey", "Thomas Farrer, 1st Baron Farrer", "Thomas Jaffrey", "Thomas John Bisika", "Thomas M. Cover", "Thomas Robert Malthus", "Thomas Spring Rice, 1st Baron Monteagle of Brandon", "Thorvald N. Thiele", "Tim Holt (statistician)", "Timothy Augustine Coghlan", "Tony Lewis (mathematician)", "Tore Schweder", "Trevor Hastie", "U. Narayan Bhat", "Udny Yule", "University of Southampton", "University of York", "V. S. Huzurbazar", "Victor Zarnowitz", "Vijayan K Pillai", "Vijayan Nair", "Vladimir Vapnik", "W. Allen Wallis", "W. Edwards Deming", "Waloddi Weibull", "Walter A. Shewhart", "Walter Bodmer", "Walter Francis Willcox", "Walter Frank Raphael Weldon", "Walter L. Smith", "Warren Mitofsky", "Warren Randolph Burgess", "Wassily Hoeffding", "Wassily Leontief", "Wendell Milliman", "Wesley Clair Mitchell", "Wesley S. B. Woolhouse", "Wilhelm Lexis", "Willard Thorp", "Willford I. King", "William A. Barnett", "William Beveridge", "William C. Krumbein", "William Farr", "William Feller", "William Fielding Ogburn", "William Fleetwood", "William Fleetwood Sheppard", "William Gemmell Cochran", "William Guy", "William H. Jefferys", "William Henry Sykes", "William Hunter (statistician)", "William Kruskal", "William Morgan (scientist)", "William Newmarch", "William Onslow, 4th Earl of Onslow", "William Palin Elderton", "William Petty", "William Playfair", "William Sanders (statistician)", "William Sealy Gosset", "William Stanley Jevons", "William Wilson Hunter", "Winifred J. Morrison", "Xavier Fernique", "Xiao-Li Meng", "Yuan-Shih Chow", "Yuri Linnik", "Zhang Zhaohuan", "Zvi Griliches", "\u00c9tienne Laspeyres"], "references": ["http://www.amstat.org/about/statisticiansinhistory/index.cfm", "http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm", "http://www.york.ac.uk/depts/maths/histstat/lifework.htm", "https://www.isrt.ac.bd/people/mshkhan"]}, "U test": {"categories": ["All articles with incomplete citations", "All articles with unsourced statements", "Articles with incomplete citations from November 2012", "Articles with unsourced statements from February 2012", "Articles with unsourced statements from November 2009", "Articles with unsourced statements from September 2009", "CS1 maint: Uses authors parameter", "Nonparametric statistics", "Statistical tests", "U-statistics", "Wikipedia articles needing clarification from September 2009"], "title": "Mann\u2013Whitney U test", "method": "U test", "url": "https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test", "summary": "In statistics, the Mann\u2013Whitney U test (also called the Mann\u2013Whitney\u2013Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon\u2013Mann\u2013Whitney test) is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample.\nUnlike the t-test it does not require the assumption of normal distributions. It is nearly as efficient as the t-test on normal distributions.\nThis test can be used to determine whether two independent samples were selected from populations having the same distribution; a similar nonparametric test used on dependent samples is the Wilcoxon signed-rank test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Aesop", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Mathematical Statistics", "Apache Commons", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", 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dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrimination learning", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frank Wilcoxon", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Hare", "Harmonic mean", "Henry Mann", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimate", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JMP (statistical software)", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Java (programming language)", "Johansen test", "Jonckheere's trend test", "Journal of Consulting and Clinical Psychology", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MATLAB", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal measurement", "Ordinary least squares", "Outlier", "Outline of statistics", "PSPP", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Pranab K. Sen", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Project Euclid", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Python (programming language)", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank (set theory)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Receiver operating characteristic", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald L. Iman", "Run chart", "S-Plus", "SAS (software)", "SPSS", "STATISTICA", "SYSTAT (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "SciPy", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "SigmaStat", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard score", "StatXact", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis test", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Statistics Surveys", "StatsDirect", "Stem-and-leaf display", "Stochastic ordering", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "T test", "Test of significance", "The American Statistician", "The Tortoise and the Hare", "Time domain", "Time series", "Tolerance interval", "Tortoise", "Trend estimation", "U-statistic", "UNISTAT", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Welch's t-test", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "Zentralblatt MATH"], "references": ["http://www.inmet.gov.br/documentos/cursoI_INMET_IRI/Climate_Information_Course/References/Mason+Graham_2002.pdf", "http://math.usask.ca/~laverty/S245/Tables/wmw.pdf", "http://stat.ethz.ch/R-manual/R-patched/library/stats/html/wilcox.test.html", "http://journals.sagepub.com/doi/full/10.2466/11.IT.3.1", "http://www.springerlink.com/index/nn141j42838n7u21.pdf", "http://www.statsdirect.com/help/Default.htm#nonparametric_methods/mann_whitney.htm", "http://core.ecu.edu/psyc/wuenschk/docs30/Nonparametric-EffectSize.pdf", "http://faculty.vassar.edu/lowry/utest.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2857732", "http://www.ncbi.nlm.nih.gov/pubmed/17944619", "http://www.ncbi.nlm.nih.gov/pubmed/20414472", "http://www.ncbi.nlm.nih.gov/pubmed/7063747", "http://www.ams.org/mathscinet-getitem?mr=0022058", "http://www.ams.org/mathscinet-getitem?mr=0152070", "http://www.ams.org/mathscinet-getitem?mr=0395032", "http://www.ams.org/mathscinet-getitem?mr=1604954", "http://www.ams.org/mathscinet-getitem?mr=2595125", "http://www.ams.org/mathscinet-getitem?mr=2598854", "http://commons.apache.org/proper/commons-math/javadocs/api-3.3/org/apache/commons/math3/stat/inference/MannWhitneyUTest.html", "http://doi.org/10.1002%2Fejsp.2420020412", "http://doi.org/10.1006%2Fanbe.2001.1691", "http://doi.org/10.1007%2F978-1-4419-0468-3", "http://doi.org/10.1007%2FBF02289138", "http://doi.org/10.1023%2FA:1010920819831", "http://doi.org/10.1037%2F0003-066X.54.8.594", "http://doi.org/10.1037%2F0022-006X.62.2.281", "http://doi.org/10.1037%2F0033-2909.111.2.361", "http://doi.org/10.1037%2F0097-7403.2.4.285", "http://doi.org/10.1080%2F00031305.2000.10474513", "http://doi.org/10.1111%2Fj.1469-185X.2007.00027.x", "http://doi.org/10.1148%2Fradiology.143.1.7063747", "http://doi.org/10.1214%2F09-SS051", "http://doi.org/10.1214%2Faoms%2F1177704172", "http://doi.org/10.1214%2Faoms%2F1177730491", "http://doi.org/10.1256%2F003590002320603584", "http://doi.org/10.2307%2F2280906", "http://doi.org/10.2307%2F2527532", "http://doi.org/10.2307%2F2683975", "http://doi.org/10.2307%2F3001968", "http://www.jstor.org/stable/2238406", "http://www.jstor.org/stable/2280906", "http://www.jstor.org/stable/2527532", "http://www.jstor.org/stable/2683975", "http://www.jstor.org/stable/2685616", "http://www.jstor.org/stable/3001968", "http://projecteuclid.org/euclid.aoms/1177704172", "http://projecteuclid.org/euclid.jdg/euclid.aoms/1177704172", "http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html", "http://zbmath.org/?format=complete&q=an:0041.26103", "http://zbmath.org/?format=complete&q=an:0119.15604", "http://zbmath.org/?format=complete&q=an:0203.21105", "http://www.mathworks.co.uk/help/stats/ranksum.html", "https://www.stata.com/help.cgi?ranksum", "https://doi.org/10.2466%2F11.IT.3.1", "https://www.gnu.org/software/pspp/manual/html_node/WILCOXON.html", "https://www.jstor.org/stable/2283092", "https://onlinepubs.trb.org/onlinepubs/nchrp/cd-22/manual/v2chapter6.pdf"]}, "Function approximation": {"categories": ["All stub articles", "Mathematical analysis stubs", "Regression analysis", "Statistical approximations", "Statistics stubs", "Wikipedia articles needing clarification from October 2017"], "title": "Function approximation", "method": "Function approximation", "url": "https://en.wikipedia.org/wiki/Function_approximation", "summary": "In general, a function approximation problem asks us to select a function among a well-defined class that closely matches (\"approximates\") a target function in a task-specific way. The need for function approximations arises in many branches of applied mathematics, and computer science in particular.\nOne can distinguish two major classes of function approximation problems: \nFirst, for known target functions approximation theory is the branch of numerical analysis that investigates how certain known functions (for example, special functions) can be approximated by a specific class of functions (for example, polynomials or rational functions) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).\nSecond, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. If the codomain (range or target set) of g is a finite set, one is dealing with a classification problem instead.\nTo some extent, the different problems (regression, classification, fitness approximation) have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c9/Lebesgue_Icon.svg"], "links": ["Applied mathematics", "Approximation theory", "Codomain", "Computer science", "Curve fitting", "Domain of a function", "Extrapolation", "Fitness approximation", "Function (mathematics)", "Function fitting", "Interpolation", "Kriging", "Least squares (function approximation)", "Mathematical analysis", "Numerical analysis", "Polynomial", "Radial basis function network", "Rational function", "Real number", "Regression analysis", "Special function", "Statistical classification", "Statistical learning theory", "Statistics", "Supervised learning"], "references": []}, "Binary classification": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2011", "Machine learning", "Statistical classification"], "title": "Binary classification", "method": "Binary classification", "url": "https://en.wikipedia.org/wiki/Binary_classification", "summary": "Binary or binomial classification is the task of classifying the elements of a given set into two groups (predicting which group each one belongs to) on the basis of a classification rule. Contexts requiring a decision as to whether or not an item has some qualitative property, some specified characteristic, or some typical binary classification include:\n\nMedical testing to determine if a patient has certain disease or not \u2013 the classification property is the presence of the disease.\nA \"pass or fail\" test method or quality control in factories, i.e. deciding if a specification has or has not been met \u2013 a Go/no go classification.\nInformation retrieval, namely deciding whether a page or an article should be in the result set of a search or not \u2013 the classification property is the relevance of the article, or the usefulness to the user.Binary classification is dichotomization applied to practical purposes, and in many practical binary classification problems, the two groups are not symmetric \u2013 rather than overall accuracy, the relative proportion of different types of errors is of interest. For example, in medical testing, a false positive (detecting a disease when it is not present) is considered differently from a false negative (not detecting a disease when it is present).", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Binary-classification-labeled.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Accuracy and precision", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Blood values", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Classification rule", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cutoff (reference value)", "Data collection", "Decision tree learning", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Detection theory", "Diagnostic odds ratio", "Dichotomization", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Evaluation of binary classifiers", "Experiment", "Exponential family", "Exponential smoothing", "F-score", "F-test", "F1 score", "Factor analysis", "Factorial experiment", "Failure rate", "False Discovery Rate", "False Negative Rate", "False Omission Rate", "False Positive Rate", "False negative", "False positive", "False positives and false negatives", "Fan chart (statistics)", "Feature vector", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Go/no go", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human chorionic gonadotropin", "Index of dispersion", "Information retrieval", "Informedness", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John Shawe-Taylor", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kernel methods", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratios in diagnostic testing", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Machine learning", "Mann\u2013Whitney U test", "Markedness", "Matthews correlation coefficient", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Medical test", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multi-label classification", "Multiclass classification", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Negative Predictive Value", "Negative predictive value", "Nello Cristianini", "Nelson\u2013Aalen estimator", "Neural network", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Odds ratio", "Official statistics", "One- and two-tailed tests", "One-class classification", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Positive Predictive Value", "Positive or negative test", "Positive predictive value", "Posterior probability", "Power (statistics)", "Precision (information retrieval)", "Precision and recall", "Prediction interval", "Predictive value", "Pregnancy test", "Prevalence", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probit model", "Proportional hazards model", "Prosecutor's fallacy", "Psychometrics", "Qualitative property", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random forests", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recall (information retrieval)", "Receiver operating characteristic", "Regression analysis", "Regression coefficient", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Result set", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sensitivity (tests)", "Sensitivity and specificity", "Set (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Specificity (tests)", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test method", "Thresholding (image processing)", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "True Negative Rate", "True Positive Rate", "True negative", "True positive", "Type I and type II errors", "U-statistic", "Uncertainty coefficient", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Youden's J statistic", "Z-test"], "references": ["http://www.kernel-methods.net", "http://www.learning-with-kernels.org", "https://web.archive.org/web/20180627015707/https://www.support-vector.net/"]}, "Correlation function (quantum field theory)": {"categories": ["All stub articles", "Covariance and correlation", "Quantum field theory", "Quantum physics stubs"], "title": "Correlation function (quantum field theory)", "method": "Correlation function (quantum field theory)", "url": "https://en.wikipedia.org/wiki/Correlation_function_(quantum_field_theory)", "summary": "In quantum field theory, the (real space) n-point correlation function is defined as the functional average (functional expectation value) of a product of \n \n \n \n n\n \n \n {\\displaystyle n}\n field operators at different positions\n\n \n \n \n \n C\n \n n\n \n \n (\n \n x\n \n 1\n \n \n ,\n \n x\n \n 2\n \n \n ,\n \u2026\n ,\n \n x\n \n n\n \n \n )\n :=\n \n \u27e8\n \n \u03d5\n (\n \n x\n \n 1\n \n \n )\n \u03d5\n (\n \n x\n \n 2\n \n \n )\n \u2026\n \u03d5\n (\n \n x\n \n n\n \n \n )\n \n \u27e9\n \n =\n \n \n \n \u222b\n \n \n D\n \n \n \u03d5\n \n \n e\n \n \u2212\n S\n [\n \u03d5\n ]\n \n \n \u03d5\n (\n \n x\n \n 1\n \n \n )\n \u2026\n \u03d5\n (\n \n x\n \n n\n \n \n )\n \n \n \u222b\n \n \n D\n \n \n \u03d5\n \n \n e\n \n \u2212\n S\n [\n \u03d5\n ]\n \n \n \n \n \n \n \n {\\displaystyle C_{n}(x_{1},x_{2},\\ldots ,x_{n}):=\\left\\langle \\phi (x_{1})\\phi (x_{2})\\ldots \\phi (x_{n})\\right\\rangle ={\\frac {\\int {\\mathcal {D}}\\phi \\;e^{-S[\\phi ]}\\phi (x_{1})\\ldots \\phi (x_{n})}{\\int {\\mathcal {D}}\\phi \\;e^{-S[\\phi ]}}}}\n For time-dependent correlation functions, the time-ordering operator \n \n \n \n T\n \n \n {\\displaystyle T}\n is included.\nCorrelation functions are also called simply correlators. Sometimes, the phrase Green's function is used not only for two-point functions, but for any correlators.\nThe correlation function can be interpreted physically as the amplitude for propagation of a particle or excitation between y and x. In the free theory, it is simply the Feynman propagator (for n=2).", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1f/Feynmann_Diagram_Gluon_Radiation.svg", "https://upload.wikimedia.org/wikipedia/commons/a/ad/Hydrogen300.png"], "links": ["Abdus Salam", "Addison-Wesley", "Alexander Markovich Polyakov", "Anomaly (physics)", "Bargmann\u2013Wigner equations", "Bryce DeWitt", "C. R. Hagen", "Cambridge University Press", "Carl D. Anderson", "Charge conjugation", "Chen Ning Yang", "Connected correlation function", "Correlation function (disambiguation)", "Crossing (physics)", "Curtis Callan", "David Gross", "Dirac equation", "Effective field theory", "Electromagnetism", "Electroweak interaction", "Enrico Fermi", "Ettore Majorana", "Expectation value (quantum mechanics)", "Explicit symmetry breaking", "Faddeev\u2013Popov ghost", "Feynman diagram", "Field (physics)", "Field operator", "Frank Wilczek", "Fran\u00e7ois Englert", "Freeman Dyson", "Gauge symmetry (mathematics)", "Gauge theory", "General relativity", "George Sudarshan", "Gerald Guralnik", "Gerard 't Hooft", "Ghosts (physics)", "Giorgio Parisi", "Green's function", "Green's function (many-body theory)", "Hans Bethe", "Henry Way Kendall", "Hermann Weyl", "Hideki Yukawa", "Higgs mechanism", "History of quantum field theory", "James Bjorken", "John Clive Ward", "Julian Schwinger", "J\u00fcrg Fr\u00f6hlich", "Kazuhiko Nishijima", "Kenneth G. Wilson", "Klein\u2013Gordon equation", "LSZ reduction formula", "Lattice gauge theory", "Lev Landau", "Lorentz symmetry", "M-Theory", "Markus Fierz", "Martinus Veltman", "Murray Gell-Mann", "Nikolay Bogolyubov", "Noether charge", "One particle irreducible correlation function", "Parity (physics)", "Partition function (mathematics)", "Partition function (quantum field theory)", "Pascual Jordan", "Paul Dirac", "Peter Higgs", "Philip Warren Anderson", "Poincar\u00e9 symmetry", "Proca action", "Propagator", "Quantization (physics)", "Quantum chromodynamics", "Quantum electrodynamics", "Quantum field theory", "Quantum gravity", "Quantum mechanics", "Real coordinate space", "Regularization (physics)", "Renormalization", "Richard Feynman", "Robert Brout", "Robert Mills (physicist)", "Rotation symmetry", "Rudolf Haag", "Sheldon Glashow", "Shin'ichir\u014d Tomonaga", "Sidney Coleman", "Space translation symmetry", "Special relativity", "Spontaneous symmetry breaking", "Standard Model", "Steven Weinberg", "String theory", "Strong force", "Supergravity", "Superstring theory", "Supersymmetry", "Symmetry (physics)", "Symmetry in quantum mechanics", "T-symmetry", "Technicolor (physics)", "Theory of everything", "Time ordering", "Time translation symmetry", "Tom W. B. Kibble", "Tony Skyrme", "Topological charge", "Topological quantum field theory", "Tsung-Dao Lee", "Vacuum expectation value", "Vacuum state", "Victor Weisskopf", "Vladimir Fock", "Weak force", "Werner Heisenberg", "Wheeler\u2013DeWitt equation", "Wick's theorem", "Wightman axioms", "Willis Lamb", "Yang\u2013Mills theory", "Yoichiro Nambu"], "references": []}, "Dvoretzky\u2013Kiefer\u2013Wolfowitz inequality": {"categories": ["Asymptotic theory (statistics)", "Empirical process", "Statistical inequalities"], "title": "Dvoretzky\u2013Kiefer\u2013Wolfowitz inequality", "method": "Dvoretzky\u2013Kiefer\u2013Wolfowitz inequality", "url": "https://en.wikipedia.org/wiki/Dvoretzky%E2%80%93Kiefer%E2%80%93Wolfowitz_inequality", "summary": "In the theory of probability and statistics, the Dvoretzky\u2013Kiefer\u2013Wolfowitz inequality bounds how close an empirically determined distribution function will be to the distribution function from which the empirical samples are drawn. It is named after Aryeh Dvoretzky, Jack Kiefer, and Jacob Wolfowitz, who in 1956 proved\nthe inequality with an unspecified multiplicative constant C in front of the exponent on the right-hand side. In 1990, Pascal Massart proved the inequality with the sharp constant C = 2, confirming a conjecture due to Birnbaum and McCarty.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/90/DKW_bounds.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/9/90/20180416150152%21DKW_bounds.svg"], "links": ["Allan Birnbaum", "Annals of Mathematical Statistics", "Aryeh Dvoretzky", "CDF-based nonparametric confidence interval", "Concentration inequality", "Confidence and prediction bands", "Cumulative distribution function", "Digital object identifier", "Empirical distribution function", "Glivenko\u2013Cantelli theorem", "Independent and identically distributed", "International Standard Book Number", "Jack Kiefer (mathematician)", "Jacob Wolfowitz", "Kolmogorov\u2013Smirnov test", "Mathematical Reviews", "Probability", "Random function", "Random variable", "Rate of convergence", "Statistics", "Uniform distribution (continuous)", "Zentralblatt MATH"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0083864", "http://www.ams.org/mathscinet-getitem?mr=0093874", "http://www.ams.org/mathscinet-getitem?mr=1062069", "http://doi.org/10.1214/aoms/1177706631", "http://doi.org/10.1214/aoms/1177728174", "http://doi.org/10.1214/aop/1176990746", "http://projecteuclid.org/euclid.aoms/1177706631", "http://projecteuclid.org/euclid.aoms/1177728174", "http://projecteuclid.org/euclid.aop/1176990746", "http://zbmath.org/?format=complete&q=an:0087.34002"]}, "Inductive inference": {"categories": ["All articles covered by WikiProject Wikify", "All articles needing copy edit", "All articles with unsourced statements", "All pages needing cleanup", "Arguments", "Articles containing German-language text", "Articles covered by WikiProject Wikify from September 2018", "Articles with unsourced statements from March 2012", "Causal inference", "Epistemology", "Epistemology of science", "Inductive reasoning", "Philosophy of statistics", "Problem solving skills", "Reasoning", "Use dmy dates from July 2013", "Wikipedia articles needing clarification from April 2018", "Wikipedia articles needing copy edit from October 2018", "Wikipedia introduction cleanup from September 2018"], "title": "Inductive reasoning", "method": "Inductive inference", "url": "https://en.wikipedia.org/wiki/Inductive_reasoning", "summary": "Inductive reasoning is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion (in contrast to deductive reasoning and abductive reasoning). While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given.Many dictionaries define inductive reasoning as the derivation of general principles from specific observations, though some sources find this usage \"outdated\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/52/Acap.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c6/Argument_terminology_used_in_logic.png", "https://upload.wikimedia.org/wikipedia/commons/7/7c/Logic_portal.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Nicolas_P._Rougier%27s_rendering_of_the_human_brain.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["A. J. Ayer", "A General View of Positivism", "A priori and a posteriori", "Abductive reasoning", "Absolute idealism", "Accelerated failure time model", "Accident (fallacy)", "Actuarial science", "Akaike information criterion", "Albert Einstein", "Alchemy", "Alexander Bogdanov", "Alfred North Whitehead", "Algorithmic information theory", "Algorithmic probability", "Altruism", "Analogy", "Analysis of covariance", "Analysis of variance", "Analytic-synthetic distinction", "Analytic philosophy", "Analytic\u2013synthetic distinction", "Anderson\u2013Darling test", "Anti-realism", "Antihumanism", "Antinomy", "Antipositivism", "Applied science", "ArXiv", "Argument form", "Argument from analogy", "Argumentation theory", "Aristotle", "Arithmetic mean", "Artificial Intelligence", "Astronomy", "Asymptotic theory (statistics)", "Auguste Comte", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Availability heuristic", "Averroes", "Avicenna", "Axiology", "Axioms of probability", "Bar chart", "Bas van Fraassen", "Basic belief", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavioralism", "Berlin Circle", "Bertrand Russell", "Bias of an estimator", "Biased sample", "Bibcode", "Binomial regression", "Bioinformatics", "Biology", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brownian motion", "C. D. Broad", "C. S. Peirce", "C S Peirce", "Cambridge University Press", "Canonical correlation", "Carl Gustav Hempel", "Cartography", "Case-based reasoning", "Categorical proposition", "Categorical variable", "Causality", "Census", "Central limit theorem", "Central tendency", "Charles Sanders Peirce", "Chemistry", "Chemometrics", "Chi-squared test", "Chicxulub crater", "Cicero", "Classical conditioning", "Claude Henri de Rouvroy, comte de Saint-Simon", "Clinical study design", "Clinical trial", "Closed world assumption", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Coherentism", "Cointegration", "Commensurability (philosophy of science)", "Common Era", "Common sense", "Complete induction", "Completeness (statistics)", "Conditional probability", "Confidence interval", "Confirmation bias", "Confirmation holism", "Confounding", "Conjectures and Refutations", "Consilience", "Construct (philosophy)", "Constructive empiricism", "Constructive realism", "Constructivist epistemology", "Contextualism", "Contingency (philosophy)", "Contingency table", "Continuous probability distribution", "Control chart", "Conventionalism", "Converse accident", "Correlation and dependence", "Correlogram", "Count data", "Counterfactual", "Counterinduction", "Creative synthesis", "Credible interval", "Crime statistics", "Critical History of Philosophy", "Critical rationalism", "Critical theory", "Critical thinking", "Criticism of science", "Critique of Pure Reason", "Cross-correlation", "Cross-validation (statistics)", "D. Reidel", "Daniel Dennett", "Data collection", "David Hume", "Deccan Traps", "Decomposition of time series", "Deductive-nomological model", "Deductive inference", "Deductive reasoning", "Definition", "Degrees of freedom (statistics)", "Demarcation problem", "Demographic statistics", "Dempster\u2013Shafer theory", "Density estimation", "Description", "Descriptive statistics", "Design of experiments", "Determinism", "Dickey\u2013Fuller test", "Dicto simpliciter", "Digital object identifier", "Divergence (statistics)", "Dominicus Gundissalinus", "Durbin\u2013Watson statistic", "Early modern philosophy", "Econometrics", "Edward N. Zalta", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical evidence", "Empiricism", "Encyclopedia Americana", "Engineering statistics", "Entailment", "Environmental statistics", "Epicureanism", "Epidemiology", "Epistemological anarchism", "Epistemological idealism", "Epistemological nihilism", "Epistemological pluralism", "Epistemological realism", "Epistemology", "Ernst Laas", "Ernst Mach", "Errors and residuals in statistics", "Estimating equations", "Eugen D\u00fchring", "Evidence", "Evolutionism", "Expectation (epistemic)", "Experiment", "Explanation", "Explanatory power", "Exponential family", "Exponential smoothing", "F-test", "Fact", "Factor analysis", "Factorial experiment", "Failure mode and effects analysis", "Failure rate", "Faith and rationality", "Fallibilism", "Falsifiability", "Fan chart (statistics)", "Feminist method", "First-hitting-time model", "Forest plot", "Foundationalism", "Fourier analysis", "Francis Bacon", "French Revolution", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Friedrich Wilhelm Joseph Schelling", "G-test", "Galileo Galilei", "Gambler's fallacy", "Gaston Bachelard", "Geisteswissenschaft", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Georg Friedrich Wilhelm Hegel", "Geostatistics", "German idealism", "Gilbert Harman", "Goodness of fit", "Gottlob Frege", "Grammar induction", "Granger causality", "Graphical model", "Great Debates (international relations)", "Grouped data", "Gy\u00f6rgy Luk\u00e1cs", "Habituation", "Hans-Georg Gadamer", "Hans Reichenbach", "Harmonic mean", "Hasty generalization", "Henri Poincar\u00e9", "Herbert Spencer", "Hermeneutics", "Heteroscedasticity", "Histogram", "Historicism", "Historism", "History and Class Consciousness", "History and philosophy of science", "History of evolutionary thought", "History of logic", "History of science", 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Intuitively, IVs are used when an explanatory variable of interest is correlated with the error term, in which case ordinary least squares and ANOVA give biased results. A valid instrument induces changes in the explanatory variable but has no independent effect on the dependent variable, allowing a researcher to uncover the causal effect of the explanatory variable on the dependent variable.\nInstrumental variable methods allow for consistent estimation when the explanatory variables (covariates) are correlated with the error terms in a regression model. Such correlation may occur 1) when changes in the dependent variable change the value of at least one of the covariates (\"reverse\" causation), 2) when there are omitted variables that affect both the dependent and independent variables, or 3) when the covariates are subject to non-random measurement error. Explanatory variables which suffer from one or more of these issues in the context of a regression are sometimes referred to as endogenous. In this situation, ordinary least squares produces biased and inconsistent estimates. However, if an instrument is available, consistent estimates may still be obtained. An instrument is a variable that does not itself belong in the explanatory equation but is correlated with the endogenous explanatory variables, conditional on the value of other covariates. \nIn linear models, there are two main requirements for using IVs:\n\nThe instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the instrument is said to have a strong first stage. A weak correlation may provide misleading inferences about parameter estimates and standard errors.\nThe instrument cannot be correlated with the error term in the explanatory equation, conditionally on the other covariates. In other words, the instrument cannot suffer from the same problem as the original predicting variable. If this condition is met, then the instrument is said to satisfy the exclusion restriction.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a6/Instrumental_Variable_Example_Effect_of_Tutoring_%28Edge_Deleted%29_2.png", "https://upload.wikimedia.org/wikipedia/commons/f/fc/Instrumental_Variable_Example_Effect_of_Tutoring_1.png", "https://upload.wikimedia.org/wikipedia/commons/4/4a/Instrumental_Variable_Example_Effect_of_Tutoring_2.png", "https://upload.wikimedia.org/wikipedia/commons/5/51/Instrumental_Variable_Example_Effect_of_Tutoring_3.png"], "links": ["ANOVA", "Alan Krueger", "Average treatment effects", "Bayesian network", "Bias (statistics)", "Cambridge University Press", "Causal graphs", "Causal inference", "CiteSeerX", "Coefficient of determination", "Consistent estimator", "Controlled experiment", "Correlation", "Covariate", "Damodar N. Gujarati", "Daniel McFadden", "David A. Jaeger", "Dependent and independent variables", "Digital object identifier", "Econometrica", "Econometrics", "Endogeneity (econometrics)", "Epidemiology", "Errors-in-variables models", "Errors and residuals in statistics", "Estimator bias", "F-test", "Fixed effects model", "Frisch\u2013Waugh\u2013Lovell theorem", "Generalized method of moments", "Grading in education", "Homoskedastic", "Idempotence", "Identifiability", "International Standard Book Number", "Invertible matrix", "JSTOR", "Jeffrey Wooldridge", "Joshua Angrist", "Journal of Clinical Epidemiology", "Journal of Economic Perspectives", "Journal of Human Resources", "Journal of Personality and Social Psychology", "Journal of the American Statistical Association", "Least squares", "Mark Thoma", "Null hypothesis", "OCLC", "Olav Reiers\u00f8l", "Omitted-variable bias", "Ordinary least squares", "Parameter identification problem", "Projection (linear algebra)", "PubMed Identifier", "Random effects model", "Regression analysis", "Sargan\u2013Hansen test", "Sewall Wright", "Simultaneous equations", "Statistics", "Variance", "William Greene (economist)", "YouTube"], "references": ["http://emlab.berkeley.edu/users/mcfadden/e240b_f01/ch4.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.169.5465", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.3952", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.319.2477", "http://www.ncbi.nlm.nih.gov/pubmed/15066689", "http://www.ncbi.nlm.nih.gov/pubmed/20307128", "http://doi.org/10.1016%2Fj.jclinepi.2003.08.006", "http://doi.org/10.1037%2Fa0018933", "http://doi.org/10.1080%2F01621459.1995.10476536", "http://doi.org/10.1080%2F01621459.1997.10474074", "http://doi.org/10.1198%2F073500102288618658", "http://doi.org/10.1257%2F089533003769204416", "http://doi.org/10.1257%2Fjep.15.4.69", "http://doi.org/10.2307%2F2663184", "http://www.jstor.org/stable/146178", "http://www.jstor.org/stable/2663184", "http://www.jstor.org/stable/2938359", "http://www.jstor.org/stable/2951620", "http://www.worldcat.org/oclc/793451601", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA217", "https://www.quora.com/What-is-this-formula-in-the-simple-linear-model-environment-b-Cov-X-Y-Var-X", "https://www.stata.com/meeting/5nasug/wiv.pdf", "https://www.youtube.com/watch?v=D5lt9bhOshc&list=PLD15D38DC7AA3B737&index=15#t=54m09s", "https://www.youtube.com/watch?v=Kb4LvSguwjg&list=PLD15D38DC7AA3B737&index=12"]}, "Logarithmic distribution": {"categories": ["Discrete distributions", "Logarithms", "Pages using deprecated image syntax"], "title": "Logarithmic distribution", "method": "Logarithmic distribution", "url": "https://en.wikipedia.org/wiki/Logarithmic_distribution", "summary": "In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion\n\n \n \n \n \u2212\n ln\n \u2061\n (\n 1\n \u2212\n p\n )\n =\n p\n +\n \n \n \n p\n \n 2\n \n \n 2\n \n \n +\n \n \n \n p\n \n 3\n \n \n 3\n \n \n +\n \u22ef\n .\n \n \n {\\displaystyle -\\ln(1-p)=p+{\\frac {p^{2}}{2}}+{\\frac {p^{3}}{3}}+\\cdots .}\n From this we obtain the identity\n\n \n \n \n \n \u2211\n \n k\n =\n 1\n \n \n \u221e\n \n \n \n \n \n \u2212\n 1\n \n \n ln\n \u2061\n (\n 1\n \u2212\n p\n )\n \n \n \n \n \n \n \n p\n \n k\n \n \n k\n \n \n =\n 1.\n \n \n {\\displaystyle \\sum _{k=1}^{\\infty }{\\frac {-1}{\\ln(1-p)}}\\;{\\frac {p^{k}}{k}}=1.}\n This leads directly to the probability mass function of a Log(p)-distributed random variable:\n\n \n \n \n f\n (\n k\n )\n =\n \n \n \n \u2212\n 1\n \n \n ln\n \u2061\n (\n 1\n \u2212\n p\n )\n \n \n \n \n \n \n \n p\n \n k\n \n \n k\n \n \n \n \n {\\displaystyle f(k)={\\frac {-1}{\\ln(1-p)}}\\;{\\frac {p^{k}}{k}}}\n for k \u2265 1, and where 0 < p < 1. Because of the identity above, the distribution is properly normalized.\nThe cumulative distribution function is\n\n \n \n \n F\n (\n k\n )\n =\n 1\n +\n \n \n \n \n B\n \n (\n p\n ;\n k\n +\n 1\n ,\n 0\n )\n \n \n ln\n \u2061\n (\n 1\n \u2212\n p\n )\n \n \n \n \n \n {\\displaystyle F(k)=1+{\\frac {\\mathrm {B} (p;k+1,0)}{\\ln(1-p)}}}\n where B is the incomplete beta function.\nA Poisson compounded with Log(p)-distributed random variables has a negative binomial distribution. In other words, if N is a random variable with a Poisson distribution, and Xi, i = 1, 2, 3, ... is an infinite sequence of independent identically distributed random variables each having a Log(p) distribution, then\n\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n N\n \n \n \n X\n \n i\n \n \n \n \n {\\displaystyle \\sum _{i=1}^{N}X_{i}}\n has a negative binomial distribution. In this way, the negative binomial distribution is seen to be a compound Poisson distribution.\nR. A. Fisher described the logarithmic distribution in a paper that used it to model relative species abundance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6a/Logarithmiccdf.svg", "https://upload.wikimedia.org/wikipedia/commons/2/20/Logarithmicpmf.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Eric W. Weisstein", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Incomplete beta function", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Maclaurin series", "Marchenko\u2013Pastur distribution", "MathWorld", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability-generating function", "Probability distribution", "Probability mass function", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relative species abundance", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Ronald Fisher", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.math.mcgill.ca/~dstephens/556/Papers/Fisher1943.pdf", "http://mathworld.wolfram.com/Log-SeriesDistribution.html", "http://doi.org/10.2307%2F1411", "http://www.jstor.org/stable/1411", "https://web.archive.org/web/20110726144520/http://www.math.mcgill.ca/~dstephens/556/Papers/Fisher1943.pdf"]}, "Gordon\u2013Newell theorem": {"categories": ["Probability theorems", "Queueing theory"], "title": "Gordon\u2013Newell theorem", "method": "Gordon\u2013Newell theorem", "url": "https://en.wikipedia.org/wiki/Gordon%E2%80%93Newell_theorem", "summary": "In queueing theory, a discipline within the mathematical theory of probability, the Gordon\u2013Newell theorem is an extension of Jackson's theorem from open queueing networks to closed queueing networks of exponential servers where customers cannot leave the network. Jackson's theorem cannot be applied to closed networks because the queue length at a node in the closed network is limited by the population of the network. The Gordon\u2013Newell theorem calculates the open network solution and then eliminates the infeasible states by renormalizing the probabilities. Calculation of the normalizing constant makes the treatment more awkward as the whole state space must be enumerated. Buzen's algorithm or mean value analysis can be used to calculate the normalizing constant more efficiently.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Erlang (unit)", "Erlang distribution", "FCFS", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon F. Newell", "Heavy traffic approximation", "Information system", "JSTOR", "Jackson's theorem (queueing theory)", "Jackson network", "Jeffrey P. Buzen", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Normalizing constant", "Operations Research (journal)", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations"], "references": ["http://www-unix.ecs.umass.edu/~krishna/ece673/buzen.pdf", "http://doi.org/10.1016/j.ijpe.2007.10.013", "http://doi.org/10.1145/362342.362345", "http://doi.org/10.1287/opre.15.2.254", "http://doi.org/10.2307/1426680", "http://www.jstor.org/stable/168557"]}, "Pre- and post-test probability": {"categories": ["Evidence-based medicine", "Medical statistics", "Summary statistics for contingency tables", "Use dmy dates from August 2013", "Webarchive template wayback links"], "title": "Pre- and post-test probability", "method": "Pre- and post-test probability", "url": "https://en.wikipedia.org/wiki/Pre-_and_post-test_probability", "summary": "Pre-test probability and post-test probability (alternatively spelled pretest and posttest probability) are the probabilities of the presence of a condition (such as a disease) before and after a diagnostic test, respectively. Post-test probability, in turn, can be positive or negative, depending on whether the test falls out as a positive test or a negative test, respectively. In some cases, it is used for the probability of developing the condition of interest in the future.\nTest, in this sense, can refer to any medical test (but usually in the sense of diagnostic tests), and in a broad sense also including questions and even assumptions (such as assuming that the target individual is a female or male). The ability to make a difference between pre- and post-test probabilities of various conditions is a major factor in the indication of medical tests.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Absolute_changes_by_various_pre-test_probabilities.svg", "https://upload.wikimedia.org/wikipedia/commons/6/66/Fagan_nomogram.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e2/Pre-_and_post-test_probabilities_for_various_likelihood_ratios.png"], "links": ["Abdominal auscultation", "Abdominal palpation", "Abdominal ultrasonography", "Absolute value", "Academic clinical trials", "Adaptive clinical trial", "American Cancer Society", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Ashkenazi Jews", "Attributable fraction among the exposed", "Attributable fraction for the population", "BRCA1", "BRCA2", "Barium contrast", "Binary classification", "Biopsy", "Blind experiment", "Bowel cancer", "Breast cancer", "Case-control study", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical prediction rule", "Clinical prediction rules", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Continuity (mathematics)", "Correlation does not imply causation", "Cross-sectional study", "Cumulative incidence", "Design of experiments", "Diagnostic criteria", "Diagnostic test", "Diagnostic test interpretation", "Diagnostics", "Differential diagnosis", "Digital object identifier", "Disease", "Ecological study", "Endoscopy", "Epidemiological methods", "Evidence-based medicine", "Experiment", "Fecal occult blood", "First-in-man study", "Framingham Heart Study", "Glossary of clinical research", "Gold standard (test)", "Hazard ratio", "In vitro", "In vivo", "Incidence (epidemiology)", "Infectivity", "Intention-to-treat analysis", "International Standard Book Number", "Ionizing radiation", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Medical history", "Medical test", "Meta-analysis", "Metabolic pathway", "Monitoring (medicine)", "Morbidity", "Mortality rate", "Multicenter trial", "Multivariate regression analysis", "Negative predictive value", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "Obesity", "Observational study", "Odds ratio", "Open-label trial", "Pathognomonic", "Period prevalence", "Physical examination", "Point prevalence", "Population Impact Measures", "Positive or negative test", "Positive predictive value", "Positive test", "Predictive value", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Probabilities", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Radiography", "Randomized controlled trial", "Rare disease", "Reference group", "Relative risk", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Sampling bias", "Scientific control", "Seeding trial", "Selection bias", "Sensitivity and specificity", "Side effects", "Sine qua non", "Specificity and sensitivity", "Subjectivity", "Survivorship bias", "Synergy", "Systematic review", "Systemic lupus erythematosus", "Tobacco smoking", "Type I and type II errors", "Vaccine trial", "Value (personal and cultural)", "Virulence", "Wayback Machine", "Weighing scale"], "references": ["http://ard.bmj.com/content/65/10/1301.abstract", "http://ard.bmj.com/content/65/10/1301/F4.large.jpg", "http://ebp.uga.edu/ebp-modules/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1798330", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3055966", "http://www.ncbi.nlm.nih.gov/pubmed/11352856", "http://www.ncbi.nlm.nih.gov/pubmed/12883521", "http://www.ncbi.nlm.nih.gov/pubmed/16707533", "http://www.ncbi.nlm.nih.gov/pubmed/21053091", "http://www.cebm.net/index.aspx?o=1043", "http://www.cancer.org/downloads/STT/CAFF2005BrFacspdf2005.pdf", "http://info.cancerresearchuk.org/cancerstats/types/breast/incidence/", "http://info.cancerresearchuk.org/prod_consump/groups/cr_common/@nre/@sta/documents/generalcontent/cases_crude_breast1_xls.xls", "http://doi.org/10.1007%2Fs11606-010-1540-5", "http://doi.org/10.1067%2Fmem.2003.274", "http://doi.org/10.1136%2Fard.2006.055251", "https://books.google.com/books?id=CQuBkXDspBkC&pg=PA750", "https://web.archive.org/web/20060511202743/http://hp2010.nhlbihin.net/atpiii/calculator.asp?usertype=prof", "https://web.archive.org/web/20070613192148/http://www.cancer.org/downloads/STT/CAFF2005BrFacspdf2005.pdf", "https://web.archive.org/web/20101222032115/http://www.cebm.net/index.aspx?o=1043", "https://web.archive.org/web/20120514135436/http://info.cancerresearchuk.org/cancerstats/types/breast/incidence/"]}, "Bean machine": {"categories": ["All articles needing additional references", "Articles lacking ISBNs", "Articles needing additional references from March 2018", "Central limit theorem", "Commons category link is locally defined"], "title": "Bean machine", "method": "Bean machine", "url": "https://en.wikipedia.org/wiki/Bean_machine", "summary": "The bean machine, also known as the Galton Board or quincunx, is a device invented by Sir Francis Galton to demonstrate the central limit theorem, in particular that the normal distribution is approximate to the binomial distribution. Among its applications, it afforded insight into regression to the mean or \"regression to mediocrity\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d2/GaltonBoard.png", "https://upload.wikimedia.org/wikipedia/commons/c/c1/Galton_box.jpg", "https://upload.wikimedia.org/wikipedia/commons/d/dc/Galton_box.webm", "https://upload.wikimedia.org/wikipedia/commons/1/18/Nuvola_kdict_glass.svg", "https://upload.wikimedia.org/wikipedia/commons/2/21/Planche_de_Galton.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/7a/Tabuleiros_de_Galton_%28antes_e_depois%29.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7f/Quincunx_%28Galton_Box%29_-_Galton_1889_diagram.png"], "links": ["Binomial coefficient", "Binomial distribution", "Boston Museum of Science", "Central limit theorem", "Charles and Ray Eames", "De Moivre\u2013Laplace theorem", "Francis Galton", "Henry Ford Museum", "Index Fund Advisors", "International Standard Book Number", "John Carroll University", "Math Is Fun", "Mathematica: A World of Numbers... and Beyond", "New York Hall of Science", "Normal distribution", "Pachinko", "Pascal's triangle", "Payazzo", "Peggle", "Pinball", "Plinko", "Quincunx (disambiguation)", "R (programming language)", "Regression toward the mean", "Sir Francis Galton", "Standard deviations", "The Wall (game show)"], "references": ["http://www.galtonboard.com", "http://www.ifa.com", "http://www.karlsims.com/marbles/", "http://www.mathsisfun.com/probability/quincunx-explained.html", "http://vis.supstat.com/2013/04/bean-machine/", "http://www.althofer.de/galton-game.html", "http://www.jcu.edu/math/isep/Quincunx/Quincunx.html", "http://ccl.northwestern.edu/netlogo/models/community/Marble-Fall-Icosystem-4", "http://www.math.psu.edu/dlittle/java/probability/plinko/index.html", "http://www.ms.uky.edu/~mai/java/stat/GaltonMachine.html", "http://www.quantware.ups-tlse.fr/dima/galton/", "http://tools.wmflabs.org/citations/process_page.php?edit=template&slow=1&user=Biblio+template+user&page=Bean_machine", "https://www.amazon.com/The-Random-Walker/dp/B06XDWZY9C", "https://www.liveauctioneers.com/news/top-news/museums/henry-ford-museum-acquires-eames-mathematica-exhibit/", "https://www.youtube.com/watch?v=9xUBhhM4vbM&t=10s", "https://www.youtube.com/watch?v=AUSKTk9ENzg", "https://cran.r-project.org/package=animation"]}, "P-rep": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from October 2011", "Articles with unsourced statements from January 2011", "Statistical hypothesis testing", "Statistical tests"], "title": "P-rep", "method": "P-rep", "url": "https://en.wikipedia.org/wiki/P-rep", "summary": "In statistical hypothesis testing, p-rep or prep has been proposed as a statistical alternative to the classic p-value. Whereas a p-value is the probability of obtaining a result under the null hypothesis, p-rep computes the probability of replicating an effect. Whether it does so is heavily disputed \u2013 some have argued that the concept rests on a mathematical falsehood.\nFor a while, the Association for Psychological Science recommended that articles submitted to Psychological Science and their other journals report p-rep rather than the classic p-value, but this is no longer the case.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/7/74/Prep_log.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Association for Psychological Science", "Bijection", "Digital object identifier", "Effect size", "Experimenter's bias", "Folk science", "Hypothesis testing", "Meta-analysis", "P-value", "Parameter", "Probability distribution", "Psychological Science", "PubMed Central", "PubMed Identifier", "Random variable", "Statistical hypothesis testing", "Statistical independence", "Statistics"], "references": ["http://sciencewatch.com/dr/erf/2010/10octerf/10octerfKill/", "http://www3.interscience.wiley.com/journal/118661704/abstract/", "http://www.wiley.com/bw/submit.asp?ref=0956-7976", "http://probonostats.wordpress.com/2007/09/14/p-rep/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1473027", "http://www.ncbi.nlm.nih.gov/pubmed/15869691", "http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1440522", "http://doi.org/10.1111%2Fj.0956-7976.2005.01538.x", "https://web.archive.org/web/20060525043648/http://www.blackwellpublishing.com/submit.asp?ref=0956-7976"]}, "Weibull chart": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from June 2010", "Articles with unsourced statements from December 2017", "Articles with unsourced statements from June 2010", "Articles with unsourced statements from May 2011", "Continuous distributions", "Exponential family distributions", "Extreme value data", "Pages using deprecated image syntax", "Survival analysis"], "title": "Weibull distribution", "method": "Weibull chart", "url": "https://en.wikipedia.org/wiki/Weibull_distribution", "summary": "In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1951, although it was first identified by Fr\u00e9chet (1927) and first applied by Rosin & Rammler (1933) to describe a particle size distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/29/FitWeibullDistr.tif", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7e/Weibull_CDF.svg", "https://upload.wikimedia.org/wikipedia/commons/5/58/Weibull_PDF.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asbestosis", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bathtub curve", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Channel (communications)", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Comminution", "Compound Poisson distribution", "Confidence belt", "Conway\u2013Maxwell\u2013Poisson distribution", "Crusher", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Delivery (commerce)", "Diffusion of innovations", "Digital object identifier", "Dirac delta distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Distribution fitting", "Electrical engineering", "Elliptical distribution", "Empirical cumulative distribution function", "Encyclopedia of Mathematics", "Entropy (information theory)", "Erlang distribution", "Euler\u2013Mascheroni constant", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponentiated Weibull distribution", "Extended negative binomial distribution", "Extreme value theory", "F-distribution", "Fading channel", "Failure analysis", "Failure rate", "Fisher's z-distribution", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General insurance", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Granular material", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hydrology", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Industrial engineering", "Information entropy", "Information retrieval", "International Standard Book Number", "Interpolation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "John Wiley & Sons", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "Lindy effect", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Manufacturing", "Marchenko\u2013Pastur distribution", "Mass fraction (chemistry)", "Materials science", "Mathematical Reviews", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maurice Fr\u00e9chet", "Maximum entropy distribution", "Maximum entropy probability distribution", "Maximum likelihood estimation", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Meijer G-function", "Michiel Hazewinkel", "Mill (grinding)", "Mineral processing", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Moment generating function", "Monotonic function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "National Institute of Standards and Technology", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Particle-size distribution", "Particle size distribution", "Pearson distribution", "Phase-type distribution", "Plotting position", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Power series", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Q plot", "Q-Weibull distribution", "Q-exponential distribution", "Radar", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Raw moment", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Reinsurance", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Spreadsheet", "Stable distribution", "Statistics", "Stretched exponential function", "Student's t-distribution", "Support (mathematics)", "Survival analysis", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unimodal function", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Waloddi Weibull", "Weather forecasting", "Weibull fading", "Weibull modulus", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wind power", "Wireless", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.mathworks.com.au/help/stats/rayleigh-distribution.html", "http://www.barringer1.com/wa_files/Weibull-ASME-Paper-1951.pdf", "http://www.crgraph.com/Weibull.pdf", "http://www.mathpages.com/home/kmath122/kmath122.htm", "http://www.reliafy.com/", "http://www.statsoft.com/textbook/survival-failure-time-analysis/#distribution", "http://www.sys-ev.com/reliability01.htm", "http://www.math.wm.edu/~leemis/chart/UDR/UDR.html", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm", "http://www.itl.nist.gov/div898/handbook/eda/section3/weibplot.htm", "http://dl.acm.org/citation.cfm?id=1835449.1835513", "http://www.ams.org/mathscinet-getitem?mr=1299979", "http://www.ams.org/mathscinet-getitem?mr=2237527", "http://doi.org/10.1016%2F0040-1625(80)90026-8", "http://doi.org/10.1016%2Fj.coastaleng.2007.05.001", "http://doi.org/10.1016%2Fj.ress.2011.09.003", "http://doi.org/10.1080%2F01621459.1973.10481432", "http://doi.org/10.1109%2FTIT.2005.855598", "http://doi.org/10.1145%2F1835449.1835513", "http://www.erpt.org/014Q/nelsa-06.htm", "http://reliawiki.org/index.php/The_Weibull_Distribution", "http://www.reuk.co.uk/Wind-Speed-Distribution-Weibull.htm", "https://www.waterlog.info/cumfreq.htm", "https://www.encyclopediaofmath.org/index.php?title=p/w097370"]}, "Autoregressive\u2013moving-average model": {"categories": ["All articles lacking in-text citations", "All articles to be expanded", "All articles with unsourced statements", "Articles lacking in-text citations from August 2010", "Articles to be expanded from March 2017", "Articles using small message boxes", "Articles with unsourced statements from November 2018", "Autocorrelation", "Webarchive template wayback links"], "title": "Autoregressive\u2013moving-average model", "method": "Autoregressive\u2013moving-average model", "url": "https://en.wikipedia.org/wiki/Autoregressive%E2%80%93moving-average_model", "summary": "In the statistical analysis of time series, autoregressive\u2013moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression (AR) and the second for the moving average (MA). The general ARMA model was described in the 1951 thesis of Peter Whittle, Hypothesis testing in time series analysis, and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins.\nGiven a time series of data Xt , the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The AR part involves regressing the variable on its own lagged (i.e., past) values. The MA part involves modeling the error term as a linear combination of error terms occurring contemporaneously and at various times in the past.\nThe model is usually referred to as the ARMA(p,q) model where p is the order of the AR part and q is the order of the MA part (as defined below).\nARMA models can be estimated by using the Box\u2013Jenkins method.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARMA (disambiguation)", "AR model", "Abstract Wiener space", "Accelerated failure time model", "Actuarial mathematics", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autocorrelation function", "Autoregressive conditional heteroskedasticity", "Autoregressive fractionally integrated moving average", "Autoregressive integrated moving average", "Autoregressive model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli process", "Bessel process", "Bias of an estimator", "Biased random walk on a graph", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Blocking (statistics)", "Boolean network", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins", "Box\u2013Jenkins method", "Branching process", "Breusch\u2013Godfrey test", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Canonical correlation", "Cartography", "Categorical variable", "Cauchy process", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chen model", "Chi-squared test", "Chinese restaurant process", "Classical Wiener space", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson process", "Confidence interval", "Confounding", "Constant elasticity of variance model", "Contact process (mathematics)", "Contingency table", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous probability distribution", "Continuous stochastic process", "Control chart", "Convergence of random variables", "Correlation and dependence", "Correlogram", "Count data", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "C\u00e0dl\u00e0g", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Divergence (statistics)", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Durbin\u2013Watson statistic", "Dynkin's formula", "Econometrics", "Edward James Hannan", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical process", "Engineering statistics", "Environmental statistics", "Epidemiology", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Errors and residuals in statistics", "Estimating equations", "Exchangeable random variables", "Experiment", "Exponential family", "Exponential smoothing", "Extreme value theory", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "First-hitting-time model", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Forest plot", "Fourier analysis", "Fractional Brownian motion", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-network", "G-test", "GNU Octave", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "General linear model", "Generalized linear model", "Geographic information system", "Geometric Brownian motion", "Geometric mean", "George Box", "George E. P. Box", "Geostatistics", "Gibbs measure", "Girsanov theorem", "Goodness of fit", "Granger causality", "Graphical model", "Gretl", "Grouped data", "Gwilym Jenkins", "Gwilym M. Jenkins", "Harmonic mean", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Heteroscedasticity", "Hidden Markov model", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "IMSL Numerical Libraries", "Independent and identically distributed random variables", "Independent identically distributed random variables", "Index of dispersion", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Ising model", "Isotonic regression", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Jump diffusion", "Jump process", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kunita\u2013Watanabe inequality", "Kurtosis", "L-moment", "LIBOR market model", "Lag operator", "Large deviation principle", "Large deviations theory", "Laurent series", "Law of large numbers", "Law of the iterated logarithm", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear predictive coding", "Linear regression", "List of fields of application of statistics", "List of inequalities", "List of statistics articles", "List of stochastic processes topics", "Ljung\u2013Box test", "Local martingale", "Local time (mathematics)", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loop-erased random walk", "Loss function", "Lp space", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M-estimator", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "MATLAB", "MA model", "Machine learning", "Malliavin calculus", "Mann\u2013Whitney U test", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematica", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "Maximum a posteriori estimation", "Maximum likelihood", "McKean\u2013Vlasov process", "McNemar's test", "Mean", "Mean reversion (finance)", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mixing (mathematics)", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moran process", "Moving-average model", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-homogeneous Poisson process", "Nonlinear autoregressive exogenous model", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Optional stopping theorem", "Order statistic", "Ordinary least squares", "Ornstein\u2013Uhlenbeck process", "Outline of statistics", "Pandas (software)", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Percolation theory", "Permutation test", "Peter Whittle (mathematician)", "Pie chart", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Pivotal quantity", "Plug-in principle", "Point estimation", "Point process", "Poisson point process", "Poisson process", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Potts model", "Power (statistics)", "Predictable process", "Prediction interval", "Predictive analytics", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Proportional hazards model", "Psychometrics", "PyFlux", "Quadratic variation", "Quality control", "Quasi-experiment", "Questionnaire", "Queueing model", "Queueing theory", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Random dynamical system", "Random field", "Random graph", "Random walk", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Reflection principle (Wiener process)", "Regenerative process", "Regression analysis", "Regression model validation", "Reliability engineering", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Replication (statistics)", "Resampling (statistics)", "Risk process", "Robust regression", "Robust statistics", "Ruin theory", "Run chart", "SABR volatility model", "SAS (software)", "Sample-continuous process", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sanov's theorem", "Scale parameter", "Scatter plot", "Schramm\u2013Loewner evolution", "Scientific control", "Scikit-learn", "Score test", "Seasonal adjustment", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sigma-martingale", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Social statistics", "Sparre\u2013Anderson model", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable process", "Standard deviation", "Standard error", "Stata", "Stationary process", "Stationary stochastic process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Statsmodels", "Stem-and-leaf display", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratified sampling", "Stratonovich integral", "Structural break", "Structural equation modeling", "Student's t-test", "SuanShu", "Submartingale", "Sufficient statistic", "Supermartingale", "Superprocess", "Survey methodology", "Survival analysis", "Survival function", "System identification", "System on a chip", "Tanaka equation", "Telegraph process", "Time domain", "Time reversibility", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniform integrability", "Uniformly most powerful test", "Usual hypotheses", "V-statistic", "Variance", "Variance gamma process", "Vasicek model", "Vector autoregression", "Wald test", "Wavelet", "Wayback Machine", "White noise", "Whittle likelihood", "Wiener process", "Wiener sausage", "Wiener space", "Wilcoxon signed-rank test", "Wilkie investment model", "Z-test"], "references": ["http://www.mathworks.com/help/econ/arima.estimate.html", "http://www.mathworks.com/help/econ/arma-model.html", "http://www.mathworks.com/help/ident/ref/ar.html", "http://www.mathworks.com/help/ident/ug/estimating-ar-and-arma-models.html", "http://www.numericalmethod.com/javadoc/suanshu/", "http://www.wolfram.com/products/applications/timeseries/features.html", "http://constantdream.wordpress.com/2008/03/16/gnu-regression-econometrics-and-time-series-library-gretl/", "http://finzi.psych.upenn.edu/R/library/tseries/html/arma.html", "http://octave.sourceforge.net/", "http://statsmodels.sourceforge.net/", "http://search.r-project.org/R/library/stats/html/arima.html", "https://www.stata.com/help.cgi?arima.", "https://web.archive.org/web/20110930032431/http://support.sas.com/rnd/app/ets/proc/ets_arima.html", "https://web.archive.org/web/20111124032002/http://www.wolfram.com/products/applications/timeseries/features.html", "https://cran.r-project.org/web/packages/fracdiff", "https://cran.r-project.org/web/views/TimeSeries.html"]}, "Response rate (survey)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from March 2016", "Pages with citations having bare URLs", "Pages with citations lacking titles", "Rates", "Survey methodology"], "title": "Response rate (survey)", "method": "Response rate (survey)", "url": "https://en.wikipedia.org/wiki/Response_rate_(survey)", "summary": "In survey research, response rate, also known as completion rate or return rate, is the number of people who answered the survey divided by the number of people in the sample. It is usually expressed in the form of a percentage. The term is also used in direct marketing to refer to the number of people who responded to an offer.\nThe general consensus in academic surveys is to choose one of the six definitions summarized by the American Association for Public Opinion Research (AAPOR). These definitions are endorsed by the National Research Council and the Journal of the American Medical Association, among other well recognized institutions. They are:\n\nResponse Rate 1 (RR1) \u2013 or the minimum response rate, is the number of complete interviews divided by the number of interviews (complete plus partial) plus the number of non-interviews (refusal and break-off plus non-contacts plus others) plus all cases of unknown eligibility (unknown if housing unit, plus unknown, other).\nResponse Rate 2 (RR2) \u2013 RR1 + counting partial interviews as respondents.\nResponse Rate 3 (RR3) \u2013 estimates what proportion of cases of unknown eligibility is actually eligible. Those respondents estimated to be ineligible are excluded from the denominator. The method of estimation *must* be explicitly stated with RR3.\nResponse Rate 4 (RR4) \u2013 allocates cases of unknown eligibility as in RR3, but also includes partial interviews as respondents as in RR2.\nResponse Rate 5 (RR5) \u2013 is either a special case of RR3 in that it assumes that there are no eligible cases among the cases of unknown eligibility or the rare case in which there are no cases of unknown eligibility. RR5 is only appropriate when it is valid to assume that none of the unknown cases are eligible ones, or when there are no unknown cases.\nResponse Rate 6 (RR6) \u2013 makes that same assumption as RR5 and also includes partial interviews as respondents. RR6 represents the maximum response rate.The six AAPOR definitions vary with respect to whether or not the surveys are partially or entirely completed and how researchers deal with unknown nonrespondents. Definition #1, for example, does NOT include partially completed surveys in the numerator, while definition #2 does. Definitions 3\u20136 deal with the unknown eligibility of potential respondents who could not be contacted. For example, there is no answer at the doors of 10 houses you attempted to survey. Maybe 5 of those you already know house people who qualify for your survey based on neighbors telling you whom lived there, but the other 5 are completely unknown. Maybe the dwellers fit your target population, maybe they don't. This may or may not be considered in your response rate, depending on which definition you use.\nExample: if 1,000 surveys were sent by mail, and 257 were successfully completed (entirely) and returned, then the response rate would be 25.7%.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/db/20170810-OSEC-LSC-0151_%2836510226215%29.jpg"], "links": ["Biased sample", "Conversion rate", "Digital object identifier", "Direct marketing", "Edith D. De Leeuw", "International Standard Serial Number", "Landing page", "National Agricultural Statistics Service", "Nonresponse bias", "Percentage", "PubMed Central", "PubMed Identifier", "Response rate ratio", "Sample (statistics)", "Statistical survey"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1669002", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1804157", "http://www.ncbi.nlm.nih.gov/pubmed/17322261", "http://www.ncbi.nlm.nih.gov/pubmed/2001503", "http://www.aapor.org/AAPOR_Main/media/publications/Standard-Definitions2015_8theditionwithchanges_April2015_logo.pdf", "http://www.aapor.org/Education-Resources/For-Researchers/Poll-Survey-FAQ/Response-Rates-An-Overview.aspx", "http://www.aapor.org/Standards-Ethics/Standard-Definitions-(1).aspx", "http://doi.org/10.1007%2Fs10389-012-0513-z", "http://doi.org/10.1086%2F297748", "http://doi.org/10.1086%2F318638", "http://doi.org/10.1136%2Fbmj.302.6772.302", "http://doi.org/10.1136%2Fbmj.38977.682025.2C", "http://doi.org/10.28945%2F4015", "http://www.worldcat.org/issn/1547-9684", "https://pprg.stanford.edu/wp-content/uploads/2007-TSMII-chapter-proof.pdf", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1669002/pdf/bmj00112-0008.pdf", "https://doi.org/10.28945/4015"]}, "Cohort study": {"categories": ["All articles with unsourced statements", "All pages needing cleanup", "Articles needing cleanup from July 2011", "Articles with unsourced statements from August 2014", "Cleanup tagged articles without a reason field from July 2011", "Cohort studies", "Cohort study methods", "Nursing research", "Research", "Use dmy dates from July 2011", "Wikipedia pages needing cleanup from July 2011"], "title": "Cohort study", "method": "Cohort study", "url": "https://en.wikipedia.org/wiki/Cohort_study", "summary": "A cohort study is a particular form of longitudinal study that sample a cohort (a group of people who share a defining characteristic, typically those who experienced a common event in a selected period, such as birth or graduation), performing a cross-section at intervals through time. While a cohort study is a panel study, a panel study is not always a cohort study as individuals in a panel study do not always share a common characteristic.Cohort studies represent one of the fundamental designs of epidemiology which are used in research in the fields of medicine, nursing, psychology, social science, and in any field reliant on 'difficult to reach' answers that are based on evidence (statistics). In medicine for instance, while clinical trials are used primarily for assessing the safety of newly developed pharmaceuticals before they are approved for sale, epidemiological analysis on how risk factors affect the incidence of diseases is often used to identify the causes of diseases in the first place, and to help provide pre-clinical justification for the plausibility of protective factors (treatments). Cohort studies differ from clinical trials in that no intervention, treatment, or exposure is administered to participants in a cohort design; and no control group is defined. Rather, cohort studies are largely about the life histories of segments of populations, and the individual people who constitute these segments. Exposures or protective factors are identified as preexisting characteristics of participants. The study is controlled by including other common characteristics of the cohort in the statistical analysis. Both exposure/treatment and control variables are measured at baseline. Participants are then followed over time to observe the incidence rate of the disease or outcome in question. Regression analysis can then be used to evaluate the extent to which the exposure or treatment variable contributes to the incidence of the disease, while accounting for other variables that may be at play.\nDouble-blind randomized controlled trials (RCTs) are generally considered superior methodology in the hierarchy of evidence in treatment, because they allow for the most control over other variables that could affect the outcome, and the randomization and blinding processes reduce bias in the study design. This minimizes the chance that results will be influenced by confounding variables, particularly ones that are unknown. However, educated hypotheses based on prior research and background knowledge are used to select variables to be included in the regression model for cohort studies, and statistical methods can be used to identify and account potential confounders from these variables. Bias can also be mitigated in a cohort study when selecting participants for the cohort. It is also important to note that RCTs may not be suitable in all cases; such as when the outcome is a negative health effect and the exposure is hypothesized to be a risk factor for the outcome. Ethical standards, and morality, would prevent the use of risk factors in RCTs. The natural or incidental exposure to these risk factors (e.g. time spent in the sun), or self-administered exposure (e.g. smoking), can be measured without subjecting participants to risk factors outside of their individual lifestyles, habits, and choices.\nCohort studies can be retrospective (looking back in time, thus using existing data such as medical records or claims database) or prospective (requiring the collection of new data). Retrospectives cohort studies restrict the investigators ability to reduce confounding and bias because collected information is restricted to data that already exists. There are advantages to this design however, as retrospective studies are much cheaper and faster because the data has already been collected and stored.\nA cohort is a group of people who share a common characteristic or experience within a defined period (e.g., are currently living, are exposed to a drug or vaccine or pollutant, or undergo a certain medical procedure). Thus a group of people who were born on a day or in a particular period, say 1948, form a birth cohort. The comparison group may be the general population from which the cohort is drawn, or it may be another cohort of persons thought to have had little or no exposure to the substance under investigation, but otherwise similar. Alternatively, subgroups within the cohort may be compared with each other.\nIndicators of cohort study: \n\nWhen there is a strong association between cause and effect, established by any observational study\nWhen the exposure is rare, but incidence of disease among exposed is high\nWhen people's attrition can be minimized\nWhen resources are ample", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b5/ExplainingCaseControlSJW.jpg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Academic clinical trials", "Adaptive clinical trial", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Attrition (medicine, epidemiology)", "Birth to Twenty", "Blind experiment", "British Doctors Study", "British Household Panel Survey", "British birth cohort studies", "Caerphilly Heart Disease Study", "Case-control", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort (disambiguation)", "Cohort (statistics)", "Cohort analysis", "Confounding", "Correlation does not imply causation", "Cross-sectional data", "Cross-sectional study", "Cumulative incidence", "Dependent variable", "Design of experiments", "Digital object identifier", "Dunedin", "Dunedin Longitudinal Study", "Ecological study", "Epidemiological methods", "Epidemiology", "European Community Household Panel", "Evidence-based medicine", "Experiment", "First-in-man study", "Framingham Heart Study", "Glossary of clinical research", "Grant Study", "Hazard ratio", "Hierarchy of evidence", "Household, Income and Labour Dynamics in Australia Survey", "In vitro", "In vivo", "Incidence (epidemiology)", "Independent variable", "Infectivity", "Intention-to-treat analysis", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Medicine", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "National Child Development Study", "Nelson Mandela", "Nested case-control study", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "Nurses' Health Study", "Nursing", "Observational study", "Odds ratio", "Open-label trial", "Panel Study of Income Dynamics", "Panel analysis", "Panel data", "Period prevalence", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort", "Prospective cohort study", "Protocol (science)", "Psychological research", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Relative risk reduction", "Reproducibility", "Retrospective cohort", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Scientific control", "Seeding trial", "Selection bias", "Social science", "Socio-Economic Panel", "Specificity and sensitivity", "Statistical significance", "Statistics", "Survivorship bias", "Systematic review", "The Lothian Birth Cohort Studies", "Vaccine trial", "Virulence", "Whitehall Study"], "references": ["http://www.gfmer.ch/Books/Reproductive_health/Cohort_and_case_control_studies.html", "http://www.oup.com/us/catalog/general/subject/Medicine/EpidemiologyBiostatistics/?view=usa&ci=9780195314502", "http://academia.stackexchange.com/questions/54017/what-is-the-difference-between-a-panel-study-and-a-cohort-study", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1052363", "http://www.ncbi.nlm.nih.gov/pubmed/15602020", "http://www.ncbi.nlm.nih.gov/pubmed/16155052", "http://www.ncbi.nlm.nih.gov/pubmed/17715409", "http://www.ncbi.nlm.nih.gov/pubmed/6332166", "http://www.who.int/water_sanitation_health/dwq/iwachap7.pdf", "http://www.socialresearchmethods.net/tutorial/Cho2/cohort.html", "http://doi.org/10.1056%2FNEJMoa040967", "http://doi.org/10.1056%2FNEJMoa066603", "http://doi.org/10.1093%2Fije%2Fdyi183", "http://doi.org/10.1136%2Fjech.38.3.259", "http://www.ehib.org/faq.jsp?faq_key=37", "http://www.psy.ed.ac.uk/research/lbc/LBC.html", "http://www.cls.ioe.ac.uk", "https://web.archive.org/web/20060310202137/http://clio.stanford.edu:7080/cocoon/cliomods/trailmaps/design/design/prospectiveCohort/index.html", "https://web.archive.org/web/20060310202147/http://clio.stanford.edu:7080/cocoon/cliomods/trailmaps/design/design/retrospectiveCohort/index.html", "https://web.archive.org/web/20091022052040/http://www.psy.ed.ac.uk/research/lbc/LBC.html", "https://web.archive.org/web/20100414204016/http://www.esds.ac.uk/longitudinal/resources/international.asp", "https://web.archive.org/web/20110726020518/http://www.ehib.org/faq.jsp?faq_key=37", "https://web.archive.org/web/20110809135039/http://www.vet.cornell.edu/hospital/imaging/tutorial/index.html", "https://web.archive.org/web/20110909043451/http://www.socialresearchmethods.net/tutorial/Cho2/cohort.html"]}, "Stationary sequence": {"categories": ["All stub articles", "Probability stubs", "Sequences and series", "Time series"], "title": "Stationary sequence", "method": "Stationary sequence", "url": "https://en.wikipedia.org/wiki/Stationary_sequence", "summary": "In probability theory \u2013 specifically in the theory of stochastic processes, a stationary sequence is a random sequence whose joint probability distribution is invariant over time. If a random sequence X j is stationary then the following holds:\n\n \n \n \n \n \n \n \n \n \n\n \n \n \n F\n \n \n X\n \n n\n \n \n ,\n \n X\n \n n\n +\n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n +\n N\n \u2212\n 1\n \n \n \n \n (\n \n x\n \n n\n \n \n ,\n \n x\n \n n\n +\n 1\n \n \n ,\n \u2026\n ,\n \n x\n \n n\n +\n N\n \u2212\n 1\n \n \n )\n \n \n \n \n \n \n =\n \n F\n \n \n X\n \n n\n +\n k\n \n \n ,\n \n X\n \n n\n +\n k\n +\n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n +\n k\n +\n N\n \u2212\n 1\n \n \n \n \n (\n \n x\n \n n\n \n \n ,\n \n x\n \n n\n +\n 1\n \n \n ,\n \u2026\n ,\n \n x\n \n n\n +\n N\n \u2212\n 1\n \n \n )\n ,\n \n \n \n \n \n \n {\\displaystyle {\\begin{aligned}&{}\\quad F_{X_{n},X_{n+1},\\dots ,X_{n+N-1}}(x_{n},x_{n+1},\\dots ,x_{n+N-1})\\\\&=F_{X_{n+k},X_{n+k+1},\\dots ,X_{n+k+N-1}}(x_{n},x_{n+1},\\dots ,x_{n+N-1}),\\end{aligned}}}\n where F is the joint cumulative distribution function of the random variables in the subscript.\nIf a sequence is stationary then it is wide-sense stationary.\nIf a sequence is stationary then it has a constant mean (which may not be finite):\n\n \n \n \n E\n (\n X\n [\n n\n ]\n )\n =\n \u03bc\n \n \n for all \n \n n\n .\n \n \n {\\displaystyle E(X[n])=\\mu \\quad {\\text{for all }}n.}", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["Cumulative distribution function", "Invariant (mathematics)", "Joint probability distribution", "Mean (mathematics)", "Probability", "Probability theory", "Random sequence", "Random variable", "Stationary process", "Stochastic process", "Wide-sense stationary"], "references": []}, "Barber\u2013Johnson diagram": {"categories": ["Medical statistics", "Statistical charts and diagrams"], "title": "Barber\u2013Johnson diagram", "method": "Barber\u2013Johnson diagram", "url": "https://en.wikipedia.org/wiki/Barber%E2%80%93Johnson_diagram", "summary": "A Barber\u2013Johnson diagram is a method of presenting hospital statistics combining four different variables in a unique graph, introduced in 1973. The method constructs a scattergram where length of stay, turnover interval, discharges, and deaths per available bed are combined. These four variables have a common relationship between them and their combination in the diagram permitted a new improved way for analyzing efficiency and performance of the hospital sector. The most complete reference about how to construct the diagram could be found in Yates. In this book, the appendix explains in detail the way for elaborating this kind of diagram.", "images": [], "links": ["Business efficiency", "Dependent and independent variables", "Information graphics", "International Standard Book Number", "Length of stay", "Scatter plot"], "references": ["http://eurpub.oxfordjournals.org/cgi/reprint/9/2/103.pdf", "https://web.archive.org/web/20060908085540/http://www.publichealth.pitt.edu/supercourse/SupercoursePPT/7011-8001/7891.ppt"]}, "Blind deconvolution": {"categories": ["Signal processing"], "title": "Blind deconvolution", "method": "Blind deconvolution", "url": "https://en.wikipedia.org/wiki/Blind_deconvolution", "summary": "In electrical engineering and applied mathematics, blind deconvolution is deconvolution without explicit knowledge of the impulse response function used in the convolution. This is usually achieved by making appropriate assumptions of the input to estimate the impulse response by analyzing the output. Blind deconvolution is not solvable without making assumptions on input and impulse response. Most of the algorithms to solve this problem are based on assumption that both input and impulse response live in respective known subspaces. However, blind deconvolution remains a very challenging non-convex optimization problem even with this assumption.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/74/Blind_deconvolution_illustration.png", "https://upload.wikimedia.org/wikipedia/commons/9/9b/Blur_img.png", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Blurred_img.png", "https://upload.wikimedia.org/wikipedia/commons/a/ab/Original_img.png", "https://upload.wikimedia.org/wikipedia/commons/5/5e/Rcvrd_img.png", "https://upload.wikimedia.org/wikipedia/commons/9/94/Recovered_img.png"], "links": ["Applied mathematics", "ArXiv", "Auto correlation", "Bibcode", "Blind equalization", "Cepstrum", "Channel model", "Cocktail party effect", "Convolution", "Deconvolution", "Digital object identifier", "Equalization (communications)", "Expectation-maximization algorithm", "High-order statistics", "Hubble Space Telescope", "Image processing", "Impulse response function", "Independent component analysis", "Inverse problem", "Journal of the Optical Society of America A", "LTI system theory", "Maximum a posteriori estimation", "Maximum likelihood", "Phase (waves)", "Point spread function", "Regularization (mathematics)", "Reverberation", "Sparsity", "Spectral power density", "The Astronomical Journal", "Whitening transform", "Wiener filter"], "references": ["http://bigwww.epfl.ch/algorithms/deconvolutionlab/", "http://www.inf.fu-berlin.de/lehre/WS05/Mustererkennung/infomax/infomax.pdf", "http://adsabs.harvard.edu/abs/2000JOSAA..17.1177L", "http://adsabs.harvard.edu/abs/2002ApOpt..41.6884C", "http://adsabs.harvard.edu/abs/2007AJ....133.2764B", "http://adsabs.harvard.edu/abs/2015ISPL...22..539R", "http://sepwww.stanford.edu/oldreports/sep14/14_19.pdf", "http://arxiv.org/abs/0704.2057", "http://arxiv.org/abs/1407.5465", "http://doi.org/10.1086%2F516777", "http://doi.org/10.1109%2FLSP.2014.2362861", "http://doi.org/10.1364%2FAO.41.006884", "http://doi.org/10.1364%2FJOSAA.17.001177", "http://ieeexplore.ieee.org/document/150113/", "http://www.opticsinfobase.org/abstract.cfm?uri=josaa-17-7-1177", "https://web.archive.org/web/20150409220356/http://sepwww.stanford.edu/oldreports/sep14/14_19.pdf", "https://www.osapublishing.org/ao/abstract.cfm?uri=ao-41-32-6884"]}, "Mixture distribution": {"categories": ["All articles to be expanded", "All articles with unsourced statements", "Articles to be expanded from March 2009", "Articles using small message boxes", "Articles with unsourced statements from December 2010", "Systems of probability distributions"], "title": "Mixture distribution", "method": "Mixture distribution", "url": "https://en.wikipedia.org/wiki/Mixture_distribution", "summary": "In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized. The underlying random variables may be random real numbers, or they may be random vectors (each having the same dimension), in which case the mixture distribution is a multivariate distribution.\nIn cases where each of the underlying random variables is continuous, the outcome variable will also be continuous and its probability density function is sometimes referred to as a mixture density. The cumulative distribution function (and the probability density function if it exists) can be expressed as a convex combination (i.e. a weighted sum, with non-negative weights that sum to 1) of other distribution functions and density functions. The individual distributions that are combined to form the mixture distribution are called the mixture components, and the probabilities (or weights) associated with each component are called the mixture weights. The number of components in mixture distribution is often restricted to being finite, although in some cases the components may be countably infinite. More general cases (i.e. an uncountable set of component distributions), as well as the countable case, are treated under the title of compound distributions.\nA distinction needs to be made between a random variable whose distribution function or density is the sum of a set of components (i.e. a mixture distribution) and a random variable whose value is the sum of the values of two or more underlying random variables, in which case the distribution is given by the convolution operator. As an example, the sum of two jointly normally distributed random variables, each with different means, will still have a normal distribution. On the other hand, a mixture density created as a mixture of two normal distributions with different means will have two peaks provided that the two means are far enough apart, showing that this distribution is radically different from a normal distribution.\nMixture distributions arise in many contexts in the literature and arise naturally where a statistical population contains two or more subpopulations. They are also sometimes used as a means of representing non-normal distributions. Data analysis concerning statistical models involving mixture distributions is discussed under the title of mixture models, while the present article concentrates on simple probabilistic and statistical properties of mixture distributions and how these relate to properties of the underlying distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/12/Bimodal-bivariate-small.png", "https://upload.wikimedia.org/wikipedia/commons/e/e2/Bimodal.png", "https://upload.wikimedia.org/wikipedia/commons/7/71/Gaussian-mixture-example.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg"], "links": ["Ann E. Watkins", "ArXiv", "Bimodal distribution", "Compound distribution", "Compound probability distribution", "Continuous random variable", "Convex combination", "Convolution", "Countable", "Cumulative distribution function", "Digital object identifier", "Discrete distribution", "Expectation-maximization algorithm", "Experimental error", "Exponential distribution", "Fat tail", "Generalized function", "Graphical model", "Hierarchical Bayes model", "Homoscedastic", "International Standard Book Number", "JSTOR", "Kurtosis", "Linear combination", "List of convolutions of probability distributions", "Mahalanobis distance", "Manifold", "Margin of error", "Meta-analysis", "Mixture (probability)", "Mixture model", "Multimodal distribution", "Multivariate distribution", "Multivariate normal distribution", "Normal distribution", "Outliers", "Overdispersion", "Parametric family", "Probability", "Probability density function", "Probability distribution", "Product distribution", "Random variable", "Random vector", "Robust statistics", "Sampling bias", "Sampling error", "Skewness", "Statistical model", "Statistical population", "Statistical survey", "Statistics", "Study heterogeneity", "Subpopulation", "The American Statistician", "The Annals of Statistics", "Uncountable", "Unimodality"], "references": ["http://faculty2.ucmerced.edu/mcarreira-perpinan/papers/EDI-INF-RR-0159.pdf", "http://arxiv.org/abs/math/0602238", "http://doi.org/10.1007%2F978-3-642-04898-2", "http://doi.org/10.1198%2F00031300265", "http://doi.org/10.1214%2F009053605000000417", "http://doi.org/10.1214%2Faos%2F1176348653", "http://doi.org/10.2307%2F1267357", "http://www.jstor.org/stable/1267357", "http://www.jstor.org/stable/4153184", "http://projecteuclid.org/euclid.aos/1176348653"]}, "Hausman test": {"categories": ["Econometric modeling", "Statistical tests"], "title": "Durbin\u2013Wu\u2013Hausman test", "method": "Hausman test", "url": "https://en.wikipedia.org/wiki/Durbin%E2%80%93Wu%E2%80%93Hausman_test", "summary": "The Durbin\u2013Wu\u2013Hausman test (also called Hausman specification test) is a statistical hypothesis test in econometrics named after James Durbin, De-Min Wu, and Jerry A. Hausman. The test evaluates the consistency of an estimator when compared to an alternative, less efficient estimator which is already known to be consistent. It helps one evaluate if a statistical model corresponds to the data.", "images": [], "links": ["Alternative hypothesis", "Chi-squared distribution", "Consistent estimator", "De-Min Wu", "Delta method", "Digital object identifier", "Econometrica", "Econometrics", "Efficiency (statistics)", "Efficient estimator", "Endogeneity (economics)", "Error term", "Fixed effects model", "Instrumental variable", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "James Durbin", "Jerry A. Hausman", "Moore\u2013Penrose pseudoinverse", "Null hypothesis", "Ordinary least squares", "Random effects model", "Regression model validation", "Regressor", "Review of the International Statistical Institute", "Statistic", "Statistical consistency", "Statistical hypothesis test"], "references": ["http://doi.org/10.2307%2F1401917", "http://www.jstor.org/stable/1911420", "http://www.jstor.org/stable/1913827", "http://www.jstor.org/stable/1914093", "http://www.worldcat.org/issn/0012-9682", "https://books.google.com/books?id=MrkUeviIvYkC&pg=PA78", "https://books.google.com/books?id=Ot6DByCF6osC&pg=PA237"]}, "Basu's theorem": {"categories": ["All articles lacking in-text citations", "Articles containing proofs", "Articles lacking in-text citations from December 2009", "Independence (probability theory)", "Statistical theorems"], "title": "Basu's theorem", "method": "Basu's theorem", "url": "https://en.wikipedia.org/wiki/Basu%27s_theorem", "summary": "In statistics, Basu's theorem states that any boundedly complete sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu.It is often used in statistics as a tool to prove independence of two statistics, by first demonstrating one is complete sufficient and the other is ancillary, then appealing to the theorem. An example of this is to show that the sample mean and sample variance of a normal distribution are independent statistics, which is done in the Example section below. This property (independence of sample mean and sample variance) characterizes normal distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "American Statistical Association", "Analysis of covariance", "Analysis of variance", "Ancillary statistic", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Characterization (mathematics)", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Debabrata Basu", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent and identically-distributed random variables", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jahrbuch \u00fcber die Fortschritte der Mathematik", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Malay Ghosh", "Mann\u2013Whitney U test", "Marginal distribution", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurable space", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Preimage", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Roy C. Geary", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sankhya (journal)", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The American Statistician", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test", "Zentralblatt MATH"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0074745", "http://www.ams.org/mathscinet-getitem?mr=1650407", "http://www.ams.org/mathscinet-getitem?mr=1985397", "http://doi.org/10.2307%2F2685927", "http://doi.org/10.2307%2F2983669", "http://www.jstor.org/stable/25048259", "http://www.jstor.org/stable/25051412", "http://www.jstor.org/stable/2685927", "http://www.jstor.org/stable/2983669", "http://zbmath.org/?format=complete&q=an:0068.13401", "http://zbmath.org/?format=complete&q=an:63.1090.03", "https://books.google.com/books?id=_5Xqo02nzO0C&pg=PA80"]}, "Fair coin": {"categories": ["CS1 maint: BOT: original-url status unknown", "Experiment (probability theory)", "Gambling mathematics"], "title": "Fair coin", "method": "Fair coin", "url": "https://en.wikipedia.org/wiki/Fair_coin", "summary": "In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin. In theoretical studies, the assumption that a coin is fair is often made by referring to an ideal coin.\nJohn Edmund Kerrich performed experiments in coin flipping and found that a coin made from a wooden disk about the size of a crown and coated on one side with lead landed heads (wooden side up) 679 times out of 1000. In this experiment the coin was tossed by balancing it on the forefinger, flipping it using the thumb so that it spun through the air for about a foot before landing on a flat cloth spread over a table. Edwin Thompson Jaynes claimed that when a coin is caught in the hand, instead of being allowed to bounce, the physical bias in the coin is insignificant compared to the method of the toss, where with sufficient practice a coin can be made to land heads 100% of the time. Exploring the problem of checking whether a coin is fair is a well-established pedagogical tool in teaching statistics.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/15/Coin_Toss_%283635981474%29.jpg"], "links": ["Andrew Gelman", "Bernoulli process", "Bernoulli trial", "Checking whether a coin is fair", "Coin flipping", "Crown (British coin)", "Digital object identifier", "Edwin Thompson Jaynes", "Feller's coin-tossing constants", "Homogeneity (statistics)", "International Standard Book Number", "John Edmund Kerrich", "John von Neumann", "Lead", "Malleable", "Pedagogy", "Polya urn", "Probability of zero", "Probability theory", "Random walk", "Statistical independence", "Statistics", "Time-series", "Wald\u2013Wolfowitz runs test"], "references": ["http://www.stat.columbia.edu/~gelman/research/published/diceRev2.pdf", "http://news-service.stanford.edu/news/2004/june9/diaconis-69.html", "http://doi.org/10.1198/000313002605", "https://web.archive.org/web/20020205134720/http://bayes.wustl.edu/etj/prob.html"]}, "Cochran\u2013Armitage test for trend": {"categories": ["Statistical tests for contingency tables", "Use dmy dates from August 2012"], "title": "Cochran\u2013Armitage test for trend", "method": "Cochran\u2013Armitage test for trend", "url": "https://en.wikipedia.org/wiki/Cochran%E2%80%93Armitage_test_for_trend", "summary": "The Cochran\u2013Armitage test for trend, named for William Cochran and Peter Armitage, is used in categorical data analysis when the aim is to assess for the presence of an association between a variable with two categories and an ordinal variable with k categories. It modifies the Pearson chi-squared test to incorporate a suspected ordering in the effects of the k categories of the second variable. For example, doses of a treatment can be ordered as 'low', 'medium', and 'high', and we may suspect that the treatment benefit cannot become smaller as the dose increases. The trend test is often used as a genotype-based test for case-control genetic association studies.", "images": [], "links": ["Allele", "Alternative hypothesis", "Association (statistics)", "Case-control study", "Codominant", "Complex disease", "Contingency table", "Digital object identifier", "Dominance relationship", "Expected value", "Genetic association", "Genetics", "Genome-wide association study", "Genotype", "Heredity", "International Standard Book Number", "JSTOR", "List of analyses of categorical data", "Locus (genetics)", "Null hypothesis", "P-value", "Pearson chi-squared test", "Peter Armitage", "PubMed Central", "PubMed Identifier", "Recessive (genetics)", "Statistical power", "Test statistic", "Variance", "William Gemmell Cochran"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1950838", "http://www.ncbi.nlm.nih.gov/pubmed/17701901", "http://www.ncbi.nlm.nih.gov/pubmed/9423247", "http://doi.org/10.1086%2F519795", "http://doi.org/10.2307%2F2533494", "http://doi.org/10.2307%2F3001616", "http://doi.org/10.2307%2F3001775", "http://www.jstor.org/stable/2533494", "http://www.jstor.org/stable/3001616", "http://www.jstor.org/stable/3001775", "http://statgen.org/wp-content/uploads/2012/08/armitage.pdf"]}, "Exponentiated Weibull distribution": {"categories": ["Continuous distributions", "Survival analysis"], "title": "Exponentiated Weibull distribution", "method": "Exponentiated Weibull distribution", "url": "https://en.wikipedia.org/wiki/Exponentiated_Weibull_distribution", "summary": "In statistics, the exponentiated Weibull family of probability distributions was introduced by Mudholkar and Srivastava (1993) as an extension of the Weibull family obtained by adding a second shape parameter.\nThe cumulative distribution function for the exponentiated Weibull distribution is\n\n \n \n \n F\n (\n x\n ;\n k\n ,\n \u03bb\n ;\n \u03b1\n )\n =\n \n \n [\n \n 1\n \u2212\n \n e\n \n \u2212\n (\n x\n \n /\n \n \u03bb\n \n )\n \n k\n \n \n \n \n \n ]\n \n \n \u03b1\n \n \n \n \n \n {\\displaystyle F(x;k,\\lambda ;\\alpha )=\\left[1-e^{-(x/\\lambda )^{k}}\\right]^{\\alpha }\\,}\n for x > 0, and F(x; k; \u03bb; \u03b1) = 0 for x < 0. Here k > 0 is the first shape parameter, \u03b1 > 0 is the second shape parameter and \u03bb > 0 is the scale parameter of the distribution.\nThe density is\n\n \n \n \n f\n (\n x\n ;\n k\n ,\n \u03bb\n ;\n \u03b1\n )\n =\n \u03b1\n \n \n k\n \u03bb\n \n \n \n \n [\n \n \n x\n \u03bb\n \n \n ]\n \n \n k\n \u2212\n 1\n \n \n \n \n [\n \n 1\n \u2212\n \n e\n \n \u2212\n (\n x\n \n /\n \n \u03bb\n \n )\n \n k\n \n \n \n \n \n ]\n \n \n \u03b1\n \u2212\n 1\n \n \n \n e\n \n \u2212\n (\n x\n \n /\n \n \u03bb\n \n )\n \n k\n \n \n \n \n \n \n \n {\\displaystyle f(x;k,\\lambda ;\\alpha )=\\alpha {\\frac {k}{\\lambda }}\\left[{\\frac {x}{\\lambda }}\\right]^{k-1}\\left[1-e^{-(x/\\lambda )^{k}}\\right]^{\\alpha -1}e^{-(x/\\lambda )^{k}}\\,}\n There are two important special cases:\n\n\u03b1 = 1 gives the Weibull distribution;\nk = 1 gives the exponentiated exponential distribution.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bathtub curve", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "Extreme value", "F-distribution", "Failure rate", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hazard function", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Monotonic function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistica (journal)", "Statistics", "Student's t-distribution", "Technometrics", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unimodal function", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.sys-ev.com/reliability01.htm", "http://doi.org/10.1007%2Fs001840400351", "http://doi.org/10.1016%2Fj.csda.2012.08.002", "http://doi.org/10.1080%2F03610929608831886", "http://doi.org/10.1081%2FSTA-120021561", "http://doi.org/10.1081%2FSTA-200047460", "http://doi.org/10.1109%2F24.210287", "http://doi.org/10.1109%2F24.229504", "http://doi.org/10.1287%2Fopre.32.3.741", "http://doi.org/10.2307%2F1269735", "http://www.jstor.org/stable/1269735"]}, "Mean reciprocal rank": {"categories": ["All articles needing additional references", "Articles needing additional references from June 2007", "Information retrieval evaluation", "Summary statistics"], "title": "Mean reciprocal rank", "method": "Mean reciprocal rank", "url": "https://en.wikipedia.org/wiki/Mean_reciprocal_rank", "summary": "The mean reciprocal rank is a statistic measure for evaluating any process that produces a list of possible responses to a sample of queries, ordered by probability of correctness. The reciprocal rank of a query response is the multiplicative inverse of the rank of the first correct answer: 1 for first place, \u200b1\u20442 for second place, \u200b1\u20443 for third place and so on. The mean reciprocal rank is the average of the reciprocal ranks of results for a sample of queries Q:\n\n \n \n \n \n MRR\n \n =\n \n \n 1\n \n \n |\n \n Q\n \n |\n \n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n \n |\n \n Q\n \n |\n \n \n \n \n \n 1\n \n \n rank\n \n \n i\n \n \n \n \n .\n \n \n \n {\\displaystyle {\\text{MRR}}={\\frac {1}{|Q|}}\\sum _{i=1}^{|Q|}{\\frac {1}{{\\text{rank}}_{i}}}.\\!}\n where \n \n \n \n \n \n rank\n \n \n i\n \n \n \n \n {\\displaystyle {\\text{rank}}_{i}}\n refers to the rank position of the first relevant document for the i-th query.\nThe reciprocal value of the mean reciprocal rank corresponds to the harmonic mean of the ranks.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Evaluation measures (information retrieval)", "Harmonic mean", "Information retrieval", "Multiplicative inverse", "Question answering", "Statistic"], "references": []}, "Control variate": {"categories": ["All articles needing additional references", "Articles needing additional references from August 2011", "Computational statistics", "Monte Carlo methods", "Statistical randomness", "Variance reduction"], "title": "Control variates", "method": "Control variate", "url": "https://en.wikipedia.org/wiki/Control_variates", "summary": "The control variates method is a variance reduction technique used in Monte Carlo methods. It exploits information about the errors in estimates of known quantities to reduce the error of an estimate of an unknown quantity.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Antithetic variates", "Bias of an estimator", "Digital object identifier", "Expected value", "Importance sampling", "International Standard Book Number", "Least squares", "Monte Carlo integration", "Monte Carlo methods", "Parameter", "Pearson product-moment correlation coefficient", "Statistic", "Uniform distribution (continuous)", "Variance", "Variance reduction"], "references": ["http://doi.org/10.1002%2F9781118445112.stat07947", "http://doi.org/10.1002%2F9781118445112.stat07975", "https://web.archive.org/web/20100619011046/https://netfiles.uiuc.edu/meyn/www/spm_files/CTCN/CTCN.html"]}, "Age stratification": {"categories": ["Actuarial science", "All articles needing additional references", "Articles needing additional references from October 2008", "CS1 maint: Explicit use of et al.", "Population"], "title": "Age stratification", "method": "Age stratification", "url": "https://en.wikipedia.org/wiki/Age_stratification", "summary": "In sociology, age stratification refers to the hierarchical ranking of people into age groups within a society. Age stratification could also be defined as a system of inequalities linked to age. In Western societies, for example, both the old and the young are perceived and treated as relatively incompetent and excluded from much social life. Age stratification based on an ascribed status is a major source inequality, and thus may lead to ageism. Ageism is a social inequality resulting from age stratification. This is a sociological concept that comes with studying aging population. Age stratification within a population can have major implications, affecting things such as workforce trends, social norms, family structures, government policies, and even health outcomes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6e/Argentina_population_pyramid_2009.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Age group", "Ageism", "Alair Maclean", "Ascribed status", "CiteSeerX", "Dependency ratio", "Digital object identifier", "Discrimination", "Equal Employment Opportunity Commission", "Gerontology", "Health equity", "Hierarchy", "International Standard Book Number", "John A. Clauson", "Life expectancy", "Major depressive disorder", "OCLC", "Population pyramid", "Robert A. Keel", "Society", "Sociology", "University of Wisconsin-Madison"], "references": ["http://www.encyclopedia.com/social-sciences/dictionaries-thesauruses-pictures-and-press-releases/age-stratification", "http://www.philforhumanity.com/Age_Stratification_in_the_USA.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.152", "http://www.umsl.edu/~keelr/010/age.html", "http://eric.ed.gov/ERICWebPortal/contentdelivery/servlet/ERICServlet?accno=ED054484", "http://doi.org/10.1016%2Fj.rssm.2005.08.001", "http://www.worldcat.org/oclc/50073658", "https://opentextbc.ca/introductiontosociology/chapter/chapter13-aging-and-the-elderly/", "https://books.google.com/books?id=X7s9hvROWjoC&pg=PA87", "https://www.wsj.com/articles/graying-japan-tries-to-embrace-the-go", "https://www.dol.gov/general/topic/discrimination/agedisc", "https://www.eeoc.gov/laws/types/age.cfm", "https://web.archive.org/web/20090130025744/http://uic.edu/classes/socw/socw550/AGING/sld033.htm", "https://web.archive.org/web/20090208213358/http://media.pfeiffer.edu/lridener/DSS/age.html", "https://doi-org.aurarialibrary.idm.oclc.org/10.1016/j.rssm.2005.08.001", "https://www.jstor.org.aurarialibrary.idm.oclc.org/stable/41290130"]}, "Experimenter's bias": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from December 2013", "Articles with unsourced statements from June 2015", "CS1 maint: Multiple names: authors list", "Cognitive inertia", "Design of experiments", "Webarchive template wayback links"], "title": "Observer-expectancy effect", "method": "Experimenter's bias", "url": "https://en.wikipedia.org/wiki/Observer-expectancy_effect", "summary": "The observer-expectancy effect (also called the experimenter-expectancy effect, expectancy bias, observer effect, or experimenter effect) is a form of reactivity in which a researcher's cognitive bias causes them to subconsciously influence the participants of an experiment. Confirmation bias can lead to the experimenter interpreting results incorrectly because of the tendency to look for information that conforms to their hypothesis, and overlook information that argues against it. It is a significant threat to a study's internal validity, and is therefore typically controlled using a double-blind experimental design.\nAn example of the observer-expectancy effect is demonstrated in music backmasking, in which hidden verbal messages are said to be audible when a recording is played backwards. Some people expect to hear hidden messages when reversing songs, and therefore hear the messages, but to others it sounds like nothing more than random sounds. Often when a song is played backwards, a listener will fail to notice the \"hidden\" lyrics until they are explicitly pointed out, after which they are obvious. Other prominent examples include facilitated communication and dowsing.\nIn research, experimenter bias occurs when experimenter expectancies regarding study results bias the research outcome. Examples of experimenter bias include conscious or unconscious influences on subject behavior including creation of demand characteristics that influence subjects, and altered or selective recording of experimental results themselves.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a6/Logo_sociology.svg", "https://upload.wikimedia.org/wikipedia/commons/6/6c/Psi2.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cd/Socrates.png", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["Abnormal psychology", "Academic bias", "Accident (fallacy)", "Acquiescence bias", "Ad hominem", "Ad nauseam", "Affirmative conclusion from a negative premise", "Affirming a disjunct", "Affirming the consequent", "Allegiance bias", "Ambiguity", "Anagram", "Anchoring", "Anecdotal evidence", "Animistic fallacy", "Apophenia", "Appeal to accomplishment", "Appeal to consequences", "Appeal to emotion", "Appeal to fear", "Appeal to flattery", "Appeal to motive", "Appeal to nature", "Appeal to novelty", "Appeal to pity", "Appeal to ridicule", "Appeal to spite", "Appeal to the stone", "Appeal to tradition", "Applied behavior analysis", "Applied psychology", "Argument from analogy", "Argument from authority", "Argument from fallacy", "Argument from ignorance", "Argument from silence", "Argument to moderation", "Argumentum ad baculum", "Argumentum ad crumenam", "Argumentum ad lazarum", "Argumentum ad populum", "Asch conformity experiments", "Asemic writing", "Association fallacy", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "Backmasking", "Base rate fallacy", "Basic science (psychology)", "Begging the question", "Behavioral neuroscience", "Behavioural genetics", "Belief bias", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Bible code", "Big Five personality traits", "Bulverism", "California Law Review", "Carl Stumpf", "Causality", "Central limit theorem", "Cherry picking", "Choice-supportive bias", "Chronological snobbery", "Circular reasoning", "Clever Hans", "Clich\u00e9", "Clinical psychology", "Clinical trials", "Clustering illusion", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Cognitive psychology", "Cognitivism (psychology)", "Community psychology", "Comparative psychology", "Complex question", "Confirmation bias", "Confounding factor", "Congruence bias", "Conjunction fallacy", "Consumer behaviour", "Continuum fallacy", "Converse accident", "Correlation does not imply causation", "Correlative-based fallacies", "Counseling psychology", "Critical psychology", "Cross-cultural psychology", "Cryptography", "Cultural bias", "Cultural psychology", "Debiasing", "Demand characteristics", "Denying the antecedent", "Denying the correlative", "Developmental psychology", "Differential psychology", "Digital object identifier", "Distinction bias", "Double-barreled question", "Double-blind experiment", "Double blind", "Double counting (fallacy)", "Dowsing", "Dunning\u2013Kruger effect", "Easter egg (media)", "Ecological fallacy", "Educational psychology", "Egocentric bias", "Elementary arithmetic", "Emotional bias", "Environmental psychology", "Epidemiology", "Epistemic feedback", "Equivocation", "Ethical", "Etymological fallacy", "Evolutionary psychology", "Existential fallacy", "Expectation (epistemic)", "Experiment", "Experimental control", "Experimental psychology", "Extrinsic incentives bias", "FUTON bias", "Facilitated communication", "Fading affect bias", "Fallacies of illicit transference", "Fallacy", "Fallacy of accent", "Fallacy of composition", "Fallacy of division", "Fallacy of exclusive premises", "Fallacy of four terms", "Fallacy of the single cause", "Fallacy of the undistributed middle", "False attribution", "False dilemma", "False equivalence", "False precision", "Faulty generalization", "Fnord", "Forecast bias", "Forensic psychology", "Formal fallacy", "Fundamental attribution error", "Funding bias", "Furtive fallacy", "Gambler's fallacy", "Garden cress", "Genetic fallacy", "German (language)", "Godwin's law", "Halo effect", "Hawthorne effect", "Health psychology", "Healthy user bias", "Heuristics in judgment and decision-making", "Hidden message", "Hindsight bias", "History of psychology", "Horn effect", "Horse", "Hostile attribution bias", "Human factors and ergonomics", "Human position", "Humanistic psychology", "I'm entitled to my opinion", "Illicit major", "Illicit minor", "Impact bias", "In-group favoritism", "Independent variable", "Index of psychology articles", "Inductive bias", "Industrial and organizational psychology", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "Internal validity", "International Standard Book Number", "Invented here", "Inverse gambler's fallacy", "Invincible ignorance fallacy", "Ipse dixit", "Irrelevant conclusion", "Island mentality", "JSTOR", "Journal of Forensic Sciences", "Lead time bias", "Leading question", "Legal psychology", "Length time bias", "List of cognitive biases", "List of fallacies", "List of important publications in psychology", "List of memory biases", "List of psychological research methods", "List of psychological schools", "List of psychologists", "List of psychology disciplines", "List of psychology organizations", "List of psychotherapies", "Loaded language", "Loaded question", "Loki's Wager", "Masked man fallacy", "Mathematical fallacy", "Mathematical psychology", "McNamara fallacy", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Medical psychology", "Mere-exposure effect", "Military psychology", "Modal scope fallacy", "Moralistic fallacy", "Moving the goalposts", "Music psychology", "N ray", "Naturalistic fallacy", "Naturalistic observation", "Negative conclusion from affirmative premises", "Negativity bias", "Net bias", "Neuropsychology", "Nirvana fallacy", "No true Scotsman", "Nocebo", "Normalcy bias", "Not invented here", "Numerology", "Objectivity (philosophy)", "Occupational health psychology", "Omission bias", "Omitted-variable bias", "Optimism bias", "Orlov Trotter", "Oskar Pfungst", "Outcome bias", "Outline of psychology", "Overton window", "Overwhelming exception", "Palindrome", "Parade of horribles", "Paranoiac-critical method", "Pareidolia", "Participant observer", "Participation bias", "Pattern recognition (psychology)", "Personality psychology", "Philosopher", "Placebo", "Poisoning the well", "Political psychology", "Positive psychology", "Post hoc ergo propter hoc", "Precision bias", "Pro-innovation bias", "Proof by assertion", "Proof by example", "Propositional calculus", "Psychologist", "Psychology", "Psychology of religion", "PubMed Central", "PubMed Identifier", "Publication bias", "Pygmalion effect", "Quantifier (logic)", "Quantifier shift", "Quantitative psychology", "Questionable cause", "Quoting out of context", "Rationalization (psychology)", "Reactivity (psychology)", "Reality tunnel", "Recall bias", "Red-baiting", "Red herring", "Reductio ad Hitlerum", "Reflexivity (social theory)", "Regression fallacy", "Reification (fallacy)", "Reinforcement learning", "Reporting bias", "Researcher", "Response bias", "Restraint bias", "Reverse speech", "Rounding", "Sacred geometry", "Sampling bias", "School psychology", "Secundum quid", "Selection bias", "Self-selection bias", "Self-serving bias", "Sidereal time", "Slippery slope", "Slothful induction", "Social comparison bias", "Social desirability bias", "Social psychology", "Sorites paradox", "Special pleading", "Spectrum bias", "Sport psychology", "Status quo bias", "Steganography", "Straw man", "Subfields of psychology", "Subject-expectancy effect", "Subliminal stimuli", "Suppressed correlative", "Survivorship bias", "Syllogistic fallacy", "Synchronicity", "Syntactic ambiguity", "Systematic bias", "Systematic error", "Systemic bias", "Texas sharpshooter fallacy", "Theomatics", "Think of the children", "Time-saving bias", "Timeline of psychology", "Tone policing", "Traffic psychology", "Trait ascription bias", "Tu quoque", "Two wrongs make a right", "Unconscious mind", "United States news media and the Vietnam War", "Vagueness", "Verification bias", "Visual cryptography", "Von Restorff effect", "Wayback Machine", "Wet bias", "Whataboutism", "White hat bias", "Wisdom of repugnance", "Wishful thinking", "Zero-risk bias"], "references": ["http://www.bioforensics.com/articles/sequential_unmasking.html", "http://skepdic.com/experimentereffect.html", "http://www.williamjames.com/Science/ESP.htm", "http://gking.harvard.edu/gking/talks/bigprobP.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1295164", "http://www.ncbi.nlm.nih.gov/pubmed/11240080", "http://www.ncbi.nlm.nih.gov/pubmed/18638252", "http://www.ncbi.nlm.nih.gov/pubmed/447779", "http://www.ncbi.nlm.nih.gov/pubmed/7745566", "http://doi.org/10.1016%2F0021-9681(79)90012-2", "http://doi.org/10.1016%2FS0304-3959(00)00421-8", "http://doi.org/10.1111%2Fj.1556-4029.2008.00787.x", "http://doi.org/10.2307%2F3481305", "http://www.jstor.org/stable/3481305", "https://books.google.com/books?id=2-5VL8PHLsIC&pg=PA371", "https://web.archive.org/web/20040618030759/http://www.sheldrake.org/experiments/expectations/", "https://web.archive.org/web/20120318052318/http://gking.harvard.edu/gking/talks/bigprobP.pdf", "https://web.archive.org/web/20130609095907/http://www.bioforensics.com/articles/sequential_unmasking.html"]}, "Timeline of probability and statistics": {"categories": ["All articles needing additional references", "Articles needing additional references from October 2008", "History of probability and statistics", "Mathematics timelines", "Statistics-related lists", "Use dmy dates from October 2010"], "title": "Timeline of probability and statistics", "method": "Timeline of probability and statistics", "url": "https://en.wikipedia.org/wiki/Timeline_of_probability_and_statistics", "summary": "A timeline of probability and statistics\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abraham de Moivre", "Accelerated failure time model", "Actuarial science", "Adolphe Quetelet", "Adrien-Marie Legendre", "Akaike information criterion", "Al-Kindi", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrey Nikolaevich Kolmogorov", "Annuities", "Arithmetic mean", "Ars Conjectandi", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bartolom\u00e9 de Medina", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernstein\u2013von Mises theorem", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blaise Pascal", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brownian motion", "Canonical correlation", "Cardano", "Cartography", "Categorical variable", "Catholic probabilism", "Census", "Central limit theorem", "Central tendency", "Ceres (dwarf planet)", "Charles Sanders Peirce", "Chemometrics", "Chi-squared test", "Christiaan Huygens", "Claude Shannon", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Conjugate prior", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Cox's theorem", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Data collection", "David Hume", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Edmund Halley", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential families", "Exponential family", "Exponential smoothing", "Extreme value theory", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher information", "Forest plot", "Founders of statistics", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist", "Frequentist inference", "Frequentist statistics", "Friedman test", "G-test", "Galton", "Gauss", "General linear model", "Generalized linear model", "Generating function", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "History of probability", "History of statistics", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human sex ratio", "Index of dispersion", "Inductive reasoning", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jacob Bernoulli", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "John Arbuthnot", "John Graunt", "John Venn", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Keynes", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laplace", "Laplace transform", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Leonard Henry Caleb Tippett", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Line chart", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of important publications in statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Louis Bachelier", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Theory of Communication", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measure theory", "Median", "Median-unbiased estimator", "Medical statistics", "Method of least squares", "Method of moments (statistics)", "Methods engineering", "Michael Friendly", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Mortality table", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nicholas Metropolis", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Odds", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Path analysis (statistics)", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pierre de Fermat", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability axiom", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sewall Wright", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simon Singh", "Simple linear regression", "Simulated annealing", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic process", "Stock price", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The code book : the science of secrecy from ancient Egypt to quantum cryptography", "Thomas Bayes", "Thorvald N. Thiele", "Time domain", "Time series", "Timeline", "Tolerance interval", "Treatise of Human Nature", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Playfair", "Z-test"], "references": ["http://euclid.psych.yorku.ca/SCS/Gallery/milestone/", "http://www.columbia.edu/~pg2113/index_files/Gorroochurn-Some%20Laws.pdf", "http://www.leidenuniv.nl/fsw/verduin/stathist/stathist.htm", "http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm", "http://www.economics.soton.ac.uk/staff/aldrich/Probability%20Earliest%20Uses.htm"]}, "Multivariate distribution": {"categories": ["Theory of probability distributions", "Types of probability distributions", "Use dmy dates from December 2010"], "title": "Joint probability distribution", "method": "Multivariate distribution", "url": "https://en.wikipedia.org/wiki/Joint_probability_distribution", "summary": "Given random variables X, Y, ..., that are defined on a probability space, the joint probability distribution for X, Y, ... is a probability distribution that gives the probability that each of X, Y, ... falls in any particular range or discrete set of values specified for that variable. In the case of only two random variables, this is called a bivariate distribution, but the concept generalizes to any number of random variables, giving a multivariate distribution.\nThe joint probability distribution can be expressed either in terms of a joint cumulative distribution function or in terms of a joint probability density function (in the case of continuous variables) or joint probability mass function (in the case of discrete variables). These in turn can be used to find two other types of distributions: the marginal distribution giving the probabilities for any one of the variables with no reference to any specific ranges of values for the other variables, and the conditional probability distribution giving the probabilities for any subset of the variables conditional on particular values of the remaining variables.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/57/Multivariate_Gaussian.png", "https://upload.wikimedia.org/wikipedia/commons/9/95/Multivariate_normal_sample.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayes' theorem", "Bayesian network", "Bayesian programming", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli trial", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Boole's inequality", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chain rule (probability)", "Chi-squared distribution", "Chi distribution", "Chow\u2013Liu tree", "Circular distribution", "Circular uniform distribution", "Complementary event", "Compound Poisson distribution", "Conditional dependence", "Conditional distribution", "Conditional independence", "Conditional probability", "Conditional probability distribution", "Continuous random variable", "Continuous variable", "Conway\u2013Maxwell\u2013Poisson distribution", "Copula (probability theory)", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete random variable", "Discrete uniform distribution", "Disintegration theorem", "Elementary event", "Elliptical distribution", "Encyclopedia of Mathematics", "Erlang distribution", "Event (probability theory)", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fair coin", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independence (probability theory)", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Law of large numbers", "Law of total probability", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Marginal density", "Marginal distribution", "Marginal probability distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Michiel Hazewinkel", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate hypergeometric distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "PlanetMath", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability axioms", "Probability density function", "Probability distribution", "Probability mass function", "Probability measure", "Probability space", "Probability theory", "Product measure", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Sample space", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Statistical independence", "Statistical interference", "Statistics", "Student's t-distribution", "Support (measure theory)", "Tracy\u2013Widom distribution", "Tree diagram (probability theory)", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Venn diagram", "Voigt profile", "Volume", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://mathworld.wolfram.com/JointDistributionFunction.html", "http://planetmath.org/?op=getobj&from=objects&id=576", "https://www.encyclopediaofmath.org/index.php?title=p/j054260", "https://www.encyclopediaofmath.org/index.php?title=p/m065120"]}, "Box\u2013Jenkins method": {"categories": ["Time series models", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Box\u2013Jenkins method", "method": "Box\u2013Jenkins method", "url": "https://en.wikipedia.org/wiki/Box%E2%80%93Jenkins_method", "summary": "In time series analysis, the Box\u2013Jenkins method, named after the statisticians George Box and Gwilym Jenkins, applies autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) models to find the best fit of a time-series model to past values of a time series.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["AR(1)", "ARIMA", "Akaike information criterion", "Autocorrelation", "Autocorrelation function", "Autocorrelation plot", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive moving average", "Autoregressive moving average model", "Confidence interval", "Copyright status of work by the U.S. government", "Curve fitting", "George Box", "Gwilym Jenkins", "Ljung\u2013Box test", "Maximum likelihood estimation", "Model identification", "Model selection", "Moving average model", "NIST", "National Institute of Standards and Technology", "Non-linear least-squares estimation", "Oxford University Press", "Parameter estimation", "Partial autocorrelation", "Random variable", "Run sequence plot", "Scale (ratio)", "Seasonal subseries plot", "Seasonality", "Spectral plot", "Stationary process", "Statistical graphics", "Statistical model validation", "Statistician", "Time series", "Time series analysis", "White noise"], "references": ["http://robjhyndman.com/papers/BoxJenkins.pdf", "http://support.sas.com/resources/papers/proceedings13/454-2013.pdf", "http://statistik.mathematik.uni-wuerzburg.de/timeseries/", "http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc445.htm", "http://www.nist.gov", "https://www.otexts.org/fpp/8/5"]}, "Adapted process": {"categories": ["Stochastic processes"], "title": "Adapted process", "method": "Adapted process", "url": "https://en.wikipedia.org/wiki/Adapted_process", "summary": "In the study of stochastic processes, an adapted process (also referred to as a non-anticipating or non-anticipative process) is one that cannot \"see into the future\". An informal interpretation is that X is adapted if and only if, for every realisation and every n, Xn is known at time n. The concept of an adapted process is essential, for instance, in the definition of the It\u014d integral, which only makes sense if the integrand is an adapted process.", "images": [], "links": ["Borel sigma algebra", "Filtration (probability theory)", "Integrand", "International Standard Book Number", "It\u014d integral", "Measurable function", "Measurable space", "Natural filtration", "Open sets", "Predictable process", "Probability space", "Progressively measurable process", "Random variable", "Real line", "Sigma algebra", "Stochastic process", "Stochastic processes"], "references": []}, "Maximum likelihood sequence estimation": {"categories": ["All Wikipedia articles needing context", "All articles lacking in-text citations", "All pages needing cleanup", "Articles lacking in-text citations from September 2010", "Error detection and correction", "Signal estimation", "Telecommunications techniques", "Wikipedia articles needing context from December 2010", "Wikipedia introduction cleanup from December 2010"], "title": "Maximum likelihood sequence estimation", "method": "Maximum likelihood sequence estimation", "url": "https://en.wikipedia.org/wiki/Maximum_likelihood_sequence_estimation", "summary": "Maximum likelihood sequence estimation (MLSE) is a mathematical algorithm to extract useful data out of a noisy data stream.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Bayes' theorem", "Bayesian inference", "Digital object identifier", "International Standard Book Number", "Least squares", "Maximum-likelihood estimation", "Maximum a posteriori", "Maximum likelihood", "Multivariate normal distribution", "Partial response maximum likelihood", "Prior distribution", "Random noise", "Root mean square deviation", "Statistical parameter"], "references": ["http://www.scielo.org.ar/pdf/laar/v35n2/v35n2a04.pdf", "http://wwwold.ftw.at/ftw/events/telekommunikationsforum/SS2001/ss01docs/010406a.pdf", "https://doi.org/10.1117%2F1.2904827"]}, "Time domain": {"categories": ["All articles needing additional references", "Articles needing additional references from August 2012", "Time domain analysis"], "title": "Time domain", "method": "Time domain", "url": "https://en.wikipedia.org/wiki/Time_domain", "summary": "Time domain is the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various separate instants in the case of discrete time. An oscilloscope is a tool commonly used to visualize real-world signals in the time domain. A time-domain graph shows how a signal changes with time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/72/Fourier_transform_time_and_frequency_domains_%28small%29.gif", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Communication engineering", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous time", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete time", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fourier transform", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Function (mathematics)", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hertz", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Oscilloscope", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real number", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Second", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal (information theory)", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Unit of measurement", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1109%2FJRPROC.1950.233423"]}, "Quasireversibility": {"categories": ["Queueing theory"], "title": "Quasireversibility", "method": "Quasireversibility", "url": "https://en.wikipedia.org/wiki/Quasireversibility", "summary": "In queueing theory, a discipline within the mathematical theory of probability, quasireversibility (sometimes QR) is a property of some queues. The concept was first identified by Richard R. Muntz and further developed by Frank Kelly. Quasireversibility differs from reversibility in that a stronger condition is imposed on arrival rates and a weaker condition is applied on probability fluxes. For example, an M/M/1 queue with state-dependent arrival rates and state-dependent service times is reversible, but not quasireversible.A network of queues, such that each individual queue when considered in isolation is quasireversible, always has a product form stationary distribution. Quasireversibility had been conjectured to be a necessary condition for a product form solution in a queueing network, but this was shown not to be the case. Chao et al. exhibited a product form network where quasireversibility was not satisfied.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Erlang (unit)", "Erlang distribution", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "Frank Kelly (mathematician)", "Frank Kelly (professor)", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "International Standard Book Number", "JSTOR", "Jackson network", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/m", "M/M/\u221e queue", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Partial balance equations", "Peter G. Harrison", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Product form solution", "Quality of service", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Richard R. Muntz", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Time reversibility", "Traffic equations"], "references": ["http://domino.research.ibm.com/library/cyberdig.nsf/1e4115aea78b6e7c85256b360066f0d4/20b9b17a2db64886852574ef005775ce", "http://doi.org/10.1007/11549970_6", "http://doi.org/10.1016/S0304-4149(01)00119-3", "http://doi.org/10.1023/A:1019115626557", "http://doi.org/10.1214/aoms/1177698238", "http://doi.org/10.1287/opre.4.6.699", "http://doi.org/10.2307/1425912", "http://doi.org/10.2307/3212869", "http://www.jstor.org/stable/1425912", "http://www.jstor.org/stable/3212869", "http://www.statslab.cam.ac.uk/~frank/BOOKS/kelly_book.html", "http://www.statslab.cam.ac.uk/~frank/PAPERS/nqrn.pdf", "http://www.statslab.cam.ac.uk/~frank/rsn.html"]}, "Descriptive research": {"categories": ["All articles with specifically marked weasel-worded phrases", "Articles with specifically marked weasel-worded phrases from November 2014", "Descriptive statistics", "Philosophy of science"], "title": "Descriptive research", "method": "Descriptive research", "url": "https://en.wikipedia.org/wiki/Descriptive_research", "summary": "Descriptive research is used to describe characteristics of a population or phenomenon being studied. It does not answer questions about how/when/why the characteristics occurred. Rather it addresses the \"what\" question (what are the characteristics of the population or situation being studied?) The characteristics used to describe the situation or population are usually some kind of categorical scheme also known as descriptive categories. For example, the periodic table categorizes the elements. Scientists use knowledge about the nature of electrons, protons and neutrons to devise this categorical scheme. We now take for granted the periodic table, yet it took descriptive research to devise it. Descriptive research generally precedes explanatory research. For example, over time the periodic table\u2019s description of the elements allowed scientists to explain chemical reaction and make sound prediction when elements were combined.\nHence, descriptive research cannot describe what caused a situation. Thus, descriptive research cannot be used as the basis of a causal relationship, where one variable affects another. In other words, descriptive research can be said to have a low requirement for internal validity.\nThe description is used for frequencies, averages and other statistical calculations. Often the best approach, prior to writing descriptive research, is to conduct a survey investigation. Qualitative research often has the aim of description and researchers may follow-up with examinations of why the observations exist and what the implications of the findings are.\n\n", "images": [], "links": ["Applied science", "Arturo Casadevall", "Astronomy", "Average", "Basic research", "Causality", "Conceptual framework", "David Grimaldi (entomologist)", "Digital object identifier", "Ernest Rutherford", "Ernest rutherford", "Experimentation", "Exploratory research", "Frequency (disambiguation)", "Hypothesis", "Hypothesis testing", "Ilkka Niiniluoto", "Infection and Immunity", "Internal validity", "Michael S. Engel", "Normative science", "Patricia M. Shields", "Periodic table", "Phenomena", "Philosophy of physics", "Physical law", "Procedural knowledge", "PubMed Central", "Qualitative research", "Science", "Statistical population"], "references": ["http://linguistics.byu.edu/faculty/henrichsenl/ResearchMethods/RM_2_05.html", "http://ecommons.txstate.edu/polsfacp/39/", "http://www.mv.helsinki.fi/home/praatika/Valuefreedom%20of%20science.DOC", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2519409", "http://www.bioone.org/perlserv/?request=get-document&doi=10.1641/B570802", "http://doi.org/10.1128%2FIAI.00743-08", "https://books.google.com/books?id=tVYbAgAAQBAJ&printsec=frontcover&dq=inauthor:%22Patricia+M.+Shields%22&hl=en&sa=X&ei=c3iIU6X7HdOYyASjlIDwBw&ved=0CC4Q6wEwAA#v=onepage&q&f=false"]}, "Linear prediction": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from November 2010", "Articles with unsourced statements from October 2010", "Signal estimation", "Statistical forecasting"], "title": "Linear prediction", "method": "Linear prediction", "url": "https://en.wikipedia.org/wiki/Linear_prediction", "summary": "Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples.\nIn digital signal processing, linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of filter theory. In system analysis (a subfield of mathematics), linear prediction can be viewed as a part of mathematical modelling or optimization.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Autocorrelation", "Autoregressive model", "Digital object identifier", "Digital signal processing", "Discrete time and continuous time", "Expectation\u2013maximization algorithm", "Expected value", "Filter theory", "Gaussian elimination", "Global System for Mobile Communications", "International Standard Book Number", "JSTOR", "Journal of Mathematics and Physics", "Kalman filter", "Levinson recursion", "Linear predictive coding", "Linear transformation", "Lp space", "Mathematical model", "Mathematics", "Maximum likelihood estimation", "Minimum mean square error", "Monson H. Hayes", "Norm (mathematics)", "Normal equations", "Norman Levinson", "Optimization (mathematics)", "Pascal's triangle", "Philosophical Transactions of the Royal Society A", "Polynomial interpolation", "Prediction interval", "Rasta filtering", "Root mean square", "Signal processing", "Speech coding", "System analysis", "Toeplitz matrix"], "references": ["http://www.producao.usp.br/bitstream/handle/BDPI/18665/lts2r1f.pdf", "http://www.intechopen.com/books/smoothing-filtering-and-prediction-estimating-the-past-present-and-future", "http://labrosa.ee.columbia.edu/matlab/rastamat/", "http://doi.org/10.1098%2Frsta.1927.0007", "http://doi.org/10.1109%2FLSP.2007.910319", "http://doi.org/10.1109%2FPROC.1975.9792", "http://www.jstor.org/stable/91170"]}, "Direct relationship": {"categories": ["Mathematical terminology", "Ratios"], "title": "Proportionality (mathematics)", "method": "Direct relationship", "url": "https://en.wikipedia.org/wiki/Proportionality_(mathematics)", "summary": "In mathematics, two variables are proportional if there is always a constant ratio between them. The constant is called the coefficient of proportionality or proportionality constant.\n\nIf one variable is always the product of the other variable and a constant, the two are said to be directly proportional. x and y are directly proportional if the ratio y/x is constant.\nIf the product of the two variables is always a constant, the two are said to be inversely proportional. x and y are inversely proportional if the product xy is constant.The statement \"y is directly proportional to x\" is written mathematically as \"y = cx,\" or \"y \u221d x,\" where c is the proportionality constant.\nThe statement \"y is inversely proportional to x\" is written mathematically as \"y = c/x.\" This is equivalent to \"y is directly proportional to 1/x.\"", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/84/Inverse_proportionality_function_plot.gif", "https://upload.wikimedia.org/wikipedia/commons/0/03/Proportional_variables.svg"], "links": ["Basic proportionality theorem", "Cartesian coordinate", "Ceteris paribus", "Circle", "Circumference", "Coefficient", "Correlation", "Diameter", "Distance", "Equals sign", "Eudoxus of Cnidus", "Force (physics)", "Function (mathematics)", "Golden ratio", "Gravitational acceleration", "Gravity", "Hyperbolic coordinates", "Hyperbolic growth", "International Standard Book Number", "Isaak Yaglom", "Line (mathematics)", "Linear equation", "Linear growth", "Map", "Mass", "Mathematics", "Multiplicative inverse", "Newton's Second Law", "Origin (mathematics)", "Pi", "Product (mathematics)", "Proportional font", "Proportionality (disambiguation)", "Ratio", "Rectangular hyperbola", "Rule of three (mathematics)", "Sample size", "Scale (map)", "Similarity (geometry)", "Slope", "Speed", "Time", "Unicode", "Variable (math)", "Y-intercept"], "references": ["http://mathworld.wolfram.com/DirectlyProportional.html", "http://mathworld.wolfram.com/InverselyProportional.html", "https://books.google.de/books?id=XeaorGgYAXsC&pg=PA85", "https://books.google.de/books?id=dUB8BwAAQBAJ&pg=PA35", "https://www.jstor.org/stable/40539331", "https://www.jstor.org/stable/41181344", "https://www.jstor.org/stable/41182513"]}, "Lexis ratio": {"categories": ["All articles lacking sources", "All stub articles", "Articles lacking sources from December 2006", "Statistical ratios", "Statistical tests", "Statistics stubs", "Summary statistics"], "title": "Lexis ratio", "method": "Lexis ratio", "url": "https://en.wikipedia.org/wiki/Lexis_ratio", "summary": "The Lexis ratio is used in statistics as a measure which seeks to evaluate differences between the statistical properties of random mechanisms where the outcome is two-valued \u2014 for example \"success\" or \"failure\", \"win\" or \"lose\". The idea is that the probability of success might vary between different sets of trials in different situations. \nThe measure compares the between-set variance of the sample proportions (evaluated for each set) with what the variance should be if there were no difference between in the true proportions of success across the different sets. Thus the measure is used to evaluate how data compares to a fixed-probability-of-success Bernoulli distribution. The term \"Lexis ratio\" is sometimes referred to as L or Q, where\n\n \n \n \n \n L\n \n 2\n \n \n =\n \n Q\n \n 2\n \n \n =\n \n \n \n s\n \n 2\n \n \n \n \u03c3\n \n 0\n \n \n 2\n \n \n \n \n .\n \n \n {\\displaystyle L^{2}=Q^{2}={\\frac {s^{2}}{\\sigma _{0}^{2}}}.}\n Where \n \n \n \n \n s\n \n 2\n \n \n \n \n {\\displaystyle s^{2}}\n is the (weighted) sample variance derived from the observed proportions of success in sets in \"Lexis trials\" and \n \n \n \n \n \u03c3\n \n 0\n \n \n 2\n \n \n \n \n {\\displaystyle \\sigma _{0}^{2}}\n is the variance computed from the expected Bernoulli distribution on the basis of the overall average proportion of success. Trials where L falls significantly above or below 1 are known as supernormal and subnormal, respectively.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bernoulli distribution", "Overdispersion", "Sample variance", "Statistics"], "references": []}, "Gaussian q-distribution": {"categories": ["Continuous distributions", "Q-analogs", "Wikipedia articles needing clarification from August 2011"], "title": "Gaussian q-distribution", "method": "Gaussian q-distribution", "url": "https://en.wikipedia.org/wiki/Gaussian_q-distribution", "summary": "In mathematical physics and probability and statistics, the Gaussian q-distribution is a family of probability distributions that includes, as limiting cases, the uniform distribution and the normal (Gaussian) distribution. It was introduced by Diaz and Teruel, is a q-analogue of the Gaussian or normal distribution.\nThe distribution is symmetric about zero and is bounded, except for the limiting case of the normal distribution. The limiting uniform distribution is on the range -1 to +1.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/68/CumulativeGaussianq-distribution2.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f5/Gaussianq-density2.jpg"], "links": ["ARGUS distribution", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "CiteSeerX", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Double factorial", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential function", "Extended negative binomial distribution", "F-distribution", "Factorial", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Integral", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Jackson integral", "Johnson's SU-distribution", "Joint probability distribution", "Journal of Mathematical Analysis and Applications", "Journal of Mathematical Physics", "Journal of Nonlinear Mathematical Physics", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Limiting case (mathematics)", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mathematical physics", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability density function", "Probability distribution", "Q-Gaussian", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-analogue", "Q-exponential", "Q-exponential distribution", "Q-factorial", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://adsabs.harvard.edu/abs/1995JMP....36.4743V", "http://adsabs.harvard.edu/abs/2005JNMP...12..118D", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.6957", "http://www.math.ru.nl/~maassen/preps/qGauss.pdf", "http://arxiv.org/abs/math/0405402", "http://doi.org/10.1016%2Fj.jmaa.2009.04.046", "http://doi.org/10.1063%2F1.530917", "http://doi.org/10.2991%2Fjnmp.2005.12.1.10", "http://staff.www.ltu.se/~norbert/home_journal/electronic/121art6.pdf"]}, "FWL theorem": {"categories": ["Economics theorems", "Regression analysis", "Statistical theorems"], "title": "Frisch\u2013Waugh\u2013Lovell theorem", "method": "FWL theorem", "url": "https://en.wikipedia.org/wiki/Frisch%E2%80%93Waugh%E2%80%93Lovell_theorem", "summary": "In econometrics, the Frisch\u2013Waugh\u2013Lovell (FWL) theorem is named after the econometricians Ragnar Frisch, Frederick V. Waugh, and Michael C. Lovell.The Frisch\u2013Waugh\u2013Lovell theorem states that if the regression we are concerned with is:\n\n \n \n \n Y\n =\n \n X\n \n 1\n \n \n \n \u03b2\n \n 1\n \n \n +\n \n X\n \n 2\n \n \n \n \u03b2\n \n 2\n \n \n +\n u\n \n \n {\\displaystyle Y=X_{1}\\beta _{1}+X_{2}\\beta _{2}+u}\n where \n \n \n \n \n X\n \n 1\n \n \n \n \n {\\displaystyle X_{1}}\n and \n \n \n \n \n X\n \n 2\n \n \n \n \n {\\displaystyle X_{2}}\n are \n \n \n \n n\n \u00d7\n \n k\n \n 1\n \n \n \n \n {\\displaystyle n\\times k_{1}}\n and \n \n \n \n n\n \u00d7\n \n k\n \n 2\n \n \n \n \n {\\displaystyle n\\times k_{2}}\n matrices respectively and where \n \n \n \n \n \u03b2\n \n 1\n \n \n \n \n {\\displaystyle \\beta _{1}}\n and \n \n \n \n \n \u03b2\n \n 2\n \n \n \n \n {\\displaystyle \\beta _{2}}\n are conformable, then the estimate of \n \n \n \n \n \u03b2\n \n 2\n \n \n \n \n {\\displaystyle \\beta _{2}}\n will be the same as the estimate of it from a modified regression of the form:\n\n \n \n \n \n M\n \n \n X\n \n 1\n \n \n \n \n Y\n =\n \n M\n \n \n X\n \n 1\n \n \n \n \n \n X\n \n 2\n \n \n \n \u03b2\n \n 2\n \n \n +\n \n M\n \n \n X\n \n 1\n \n \n \n \n u\n \n ,\n \n \n {\\displaystyle M_{X_{1}}Y=M_{X_{1}}X_{2}\\beta _{2}+M_{X_{1}}u\\!,}\n where \n \n \n \n \n M\n \n \n X\n \n 1\n \n \n \n \n \n \n {\\displaystyle M_{X_{1}}}\n projects onto the orthogonal complement of the image of the projection matrix \n \n \n \n \n X\n \n 1\n \n \n (\n \n X\n \n 1\n \n \n \n T\n \n \n \n \n X\n \n 1\n \n \n \n )\n \n \u2212\n 1\n \n \n \n X\n \n 1\n \n \n \n T\n \n \n \n \n \n {\\displaystyle X_{1}(X_{1}^{\\mathsf {T}}X_{1})^{-1}X_{1}^{\\mathsf {T}}}\n . Equivalently, MX1 projects onto the orthogonal complement of the column space of X1. Specifically,\n\n \n \n \n \n M\n \n \n X\n \n 1\n \n \n \n \n =\n I\n \u2212\n \n X\n \n 1\n \n \n (\n \n X\n \n 1\n \n \n \n T\n \n \n \n \n X\n \n 1\n \n \n \n )\n \n \u2212\n 1\n \n \n \n X\n \n 1\n \n \n \n T\n \n \n \n ,\n \n \n {\\displaystyle M_{X_{1}}=I-X_{1}(X_{1}^{\\mathsf {T}}X_{1})^{-1}X_{1}^{\\mathsf {T}},}\n and this is known as the annihilator matrix or orthogonal projection matrix. This result implies that the secondary regression used for obtaining \n \n \n \n \n M\n \n \n X\n \n 1\n \n \n \n \n \n \n {\\displaystyle M_{X_{1}}}\n is unnecessary: using projection matrices to make the explanatory variables orthogonal to each other will lead to the same results as running the regression with all non-orthogonal explanators included.", "images": [], "links": ["Conformable matrix", "Digital object identifier", "Econometrica", "Econometrics", "Frederick V. Waugh", "Fumio Hayashi", "Image (mathematics)", "International Standard Book Number", "JSTOR", "Journal of Economic Education", "Journal of the American Statistical Association", "Linear regression", "Matrix (mathematics)", "Michael C. Lovell", "Orthogonal complement", "Projection matrix", "Ragnar Frisch"], "references": ["http://doi.org/10.1080%2F01621459.1963.10480682", "http://doi.org/10.3200%2FJECE.39.1.88-91", "http://www.jstor.org/stable/1907330", "https://books.google.com/books?id=DrbrDAAAQBAJ&pg=PA311", "https://books.google.com/books?id=Ot6DByCF6osC&pg=PA19", "https://books.google.com/books?id=PnVCEZOOFr0C&pg=PA54", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA18", "https://books.google.com/books?id=shWtvsFbxlkC&pg=PA7"]}, "Most probable number": {"categories": ["All articles needing expert attention", "Articles needing expert attention from February 2009", "Articles needing expert attention with no reason or talk parameter", "Biostatistics", "Laboratory techniques", "Quantitative research", "Statistics articles needing expert attention"], "title": "Most probable number", "method": "Most probable number", "url": "https://en.wikipedia.org/wiki/Most_probable_number", "summary": "The most probable number method, otherwise known as the method of Poisson zeroes, is a method of getting quantitative data on concentrations of discrete items from positive/negative (incidence) data.\nThere are many discrete entities that are easily detected but difficult to count. Any sort of amplification reaction or catalysis reaction obliterates easy quantification but allows presence to be detected very sensitively. Common examples include microorganism growth, enzyme action, or catalytic chemistry. The MPN method involves taking the original solution or sample, and subdividing it by orders of magnitude (frequently 10\u00d7 or 2\u00d7), and assessing presence/absence in multiple subdivisions. \nThe degree of dilution at which absence begins to appear indicates that the items have been diluted so much that there are many subsamples in which none appear. A suite of replicates at any given concentration allow finer resolution, to use the number of positive and negative samples to estimate the original concentration within the appropriate order of magnitude.\nIn microbiology, the cultures are incubated and assessed by eye, bypassing tedious colony counting or expensive and tedious microscopic counts. Presumptive, Confirmative and Completed tests are a part of MPN\nIn molecular biology, a common application involves DNA templates diluted into polymerase chain reactions (PCR). Reactions only proceed when a template is present, allowing for a form of quantitative PCR, to assess the original concentration of template molecules. Another application involves diluting enzyme stocks into solution containing a chromogenic substrate, or diluting antigens into solutions for ELISA (Enzyme-Linked ImmunoSorbent Assay) or some other antibody cascade detection reaction, to measure the original concentration of the enzyme or antigen.\nThe major weakness of MPN methods is the need for large numbers of replicates at the appropriate dilution to narrow the confidence intervals. However, it is a very important method for counts when the appropriate order of magnitude is unknown a priori and sampling is necessarily destructive.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["Bacterial growth", "Catalyst", "DNA", "Dilution assay", "ELISA", "Enzyme", "Poisson process", "Polymerase chain reaction"], "references": ["http://www.mpnballastwaterfacts.com", "http://www.wiwiss.fu-berlin.de/fachbereich/vwl/iso/ehemalige/professoren/wilrich/index.html", "http://www.fda.gov/Food/FoodScienceResearch/LaboratoryMethods/ucm109656.htm", "http://www.jlindquist.net/generalmicro/102dil3.html", "http://www.jlindquist.net/generalmicro/102dil3a.html"]}, "Dirichlet-multinomial distribution": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from June 2012", "Compound probability distributions", "Discrete distributions", "Multivariate discrete distributions"], "title": "Dirichlet-multinomial distribution", "method": "Dirichlet-multinomial distribution", "url": "https://en.wikipedia.org/wiki/Dirichlet-multinomial_distribution", "summary": "In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate P\u00f3lya distribution (after George P\u00f3lya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector \n \n \n \n \n \u03b1\n \n \n \n {\\displaystyle {\\boldsymbol {\\alpha }}}\n , and an observation drawn from a multinomial distribution with probability vector p and number of trials n. The compounding corresponds to a Polya urn scheme. It is frequently encountered in Bayesian statistics, empirical Bayes methods and classical statistics as an overdispersed multinomial distribution.\nIt reduces to the categorical distribution as a special case when n = 1. It also approximates the multinomial distribution arbitrarily well for large \u03b1. The Dirichlet-multinomial is a multivariate extension of the beta-binomial distribution, as the multinomial and Dirichlet distributions are multivariate versions of the binomial distribution and beta distributions, respectively.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["ARGUS distribution", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian network", "Bayesian statistics", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Burstiness", "Cantor distribution", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Chinese restaurant process", "Circular distribution", "Circular uniform distribution", "Classical statistics", "Compound Poisson distribution", "Compound distribution", "Compound probability distribution", "Conditional distribution", "Conjugate distribution", "Conjugate prior distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlated", "Correlation matrix", "Covariance", "Covariance matrix", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet distribution", "Dirichlet process", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Document classification", "Document clustering", "Economy", "Elliptical distribution", "Empirical Bayes methods", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Genetics", "Geometric distribution", "Geometric stable distribution", "George P\u00f3lya", "Gibbs sampling", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Integer", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Krichevsky\u2013Trofimov estimator", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Latent Dirichlet allocation", "Latent variable", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Machine translation", "Marchenko\u2013Pastur distribution", "Marginal distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mixture model", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate hypergeometric distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Naive Bayes", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normalizing constant", "Overdispersion", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Polya urn model", "Polya urn scheme", "Positive-definite matrix", "Posterior distribution", "Probability-generating function", "Probability distribution", "Probability mass function", "Probability theory", "Pseudo-random number sampling", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random vector", "Rank (linear algebra)", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Semi-supervised learning", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Spam (electronic)", "Sparse Matrix", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Topic model", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unsupervised learning", "Urn model", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://research.microsoft.com/~minka/papers/dirichlet/", "http://www.cse.ucsd.edu/~dkauchak/kauchak05modeling.pdf", "http://www-cse.ucsd.edu/users/elkan/edcm.pdf", "http://arxiv.org/abs/1712.01293", "http://doi.org/10.1140%2Fepjp%2Fi2018-12042-x", "https://www.jstor.org/stable/2333468"]}, "Fork-join queue": {"categories": ["Single queueing nodes", "Use dmy dates from August 2012"], "title": "Fork\u2013join queue", "method": "Fork-join queue", "url": "https://en.wikipedia.org/wiki/Fork%E2%80%93join_queue", "summary": "In queueing theory, a discipline within the mathematical theory of probability, a fork\u2013join queue is a queue where incoming jobs are split on arrival for service by numerous servers and joined before departure. The model is often used for parallel computations or systems where products need to be obtained simultaneously from different suppliers (in a warehouse or manufacturing setting). The key quantity of interest in this model is usually the time taken to service a complete job. The model has been described as a \"key model for the performance analysis of parallel and distributed systems.\" Few analytical results exist for fork\u2013join queues, but various approximations are known.\nThe situation where jobs arrive according to a Poisson process and service times are exponentially distributed is sometimes referred to as a Flatto\u2013Hahn\u2013Wright model or FHW model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fb/Fork-join-queue.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "ArXiv", "Arrival theorem", "Asymptotic analysis", "BCMP network", "Balance equation", "Bene\u0161 method", "Bibcode", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Centrum Wiskunde & Informatica", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Deterministic system", "Digital object identifier", "Distributed computing", "Erlang (unit)", "Erlang distribution", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "International Standard Book Number", "JSTOR", "Jackson network", "Jean Walrand", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markov chain", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Moment (mathematics)", "Network congestion", "Network scheduler", "Onno J. Boxma", "Parallel computing", "Performance Evaluation", "Peter G. Harrison", "Phase-type distribution", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Product form solution", "Quality of service", "Quasireversibility", "Queueing theory", "RAID", "Range (statistics)", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering", "Traffic equations", "Uniformization (probability theory)", "Utilization"], "references": ["http://adsabs.harvard.edu/abs/2012arXiv1210.3012J", "http://adsabs.harvard.edu/abs/2013arXiv1305.3945J", "http://drum.lib.umd.edu/bitstream/1903/5028/1/PhD_90-2.pdf", "http://www.cs.unh.edu/~varki/publication/open.pdf", "http://hal.inria.fr/docs/00/07/61/62/PDF/RR-0394.pdf", "http://webee.technion.ac.il/people/atar/FJN.pdf", "http://oai.cwi.nl/oai/asset/5133/05133D.pdf", "http://dl.acm.org/citation.cfm?id=2825257&dl=ACM&coll=DL&CFID=580850231&CFTOKEN=70523472", "http://arxiv.org/abs/1210.3012", "http://arxiv.org/abs/1305.3945", "http://doi.org/10.1002%2Fnav.20294", "http://doi.org/10.1007%2F978-3-540-45232-4_10", "http://doi.org/10.1007%2F978-3-540-74472-6_62", "http://doi.org/10.1007%2F978-3-540-89332-5_1", "http://doi.org/10.1007%2F978-3-642-02924-0_2", "http://doi.org/10.1007%2F978-3-642-40725-3_25", "http://doi.org/10.1007%2FBF01149176", "http://doi.org/10.1007%2Fs00291-010-0235-y", "http://doi.org/10.1016%2Fj.orl.2004.12.005", "http://doi.org/10.1016%2Fj.peva.2015.06.007", "http://doi.org/10.1017%2FS0269964810000112", "http://doi.org/10.1109%2F12.16501", "http://doi.org/10.1109%2F12.2213", "http://doi.org/10.1109%2FAllerton.2012.6483303", "http://doi.org/10.1109%2FTPDS.2013.70", "http://doi.org/10.1137%2F0144074", "http://doi.org/10.1239%2Faap%2F1093962238", "http://doi.org/10.2307%2F3214417", "http://www.jstor.org/stable/1427722", "http://www.jstor.org/stable/3214417", "http://www2.math.uu.se/~takis/public_html/PAPERS/forkjoin.pdf", "http://pubs.doc.ic.ac.uk/forkjoin/forkjoin.pdf", "http://www.doc.ic.ac.uk/~wjk/publications/tsimashenka-knottenbelt-epew-2013.pdf"]}, "Cumulative incidence": {"categories": ["Epidemiology"], "title": "Cumulative incidence", "method": "Cumulative incidence", "url": "https://en.wikipedia.org/wiki/Cumulative_incidence", "summary": "Cumulative incidence or incidence proportion is a measure of frequency, as in epidemiology, where it is a measure of disease frequency during a period of time. Where the period of time considered is an entire lifetime, the incidence proportion is called lifetime risk.Cumulative incidence is defined as the probability that a particular event, such as occurrence of a particular disease, has occurred before a given time. It is equivalent to the incidence, calculated using a period of time during which all of the individuals in the population are considered to be at risk for the outcome. It is sometimes also referred to as the incidence proportion.\nCumulative incidence is calculated by the number of new cases during a period divided by the number of subjects at risk in the population at the beginning of the study.\nIt may also be calculated by the incidence rate multiplied by duration:\n\n \n \n \n C\n I\n (\n t\n )\n =\n 1\n \u2212\n \n e\n \n \u2212\n I\n R\n (\n t\n )\n \u22c5\n D\n \n \n \n .\n \n \n {\\displaystyle CI(t)=1-e^{-IR(t)\\cdot D}\\,.}\n \n\n", "images": [], "links": ["Academic clinical trials", "Adaptive clinical trial", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attack rate", "Attributable fraction among the exposed", "Attributable fraction for the population", "Blind experiment", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Correlation does not imply causation", "Cross-sectional study", "Design of experiments", "Digital object identifier", "Ecological study", "Epidemiological methods", "Epidemiology", "Evidence-based medicine", "Experiment", "First-in-man study", "Glossary of clinical research", "Hazard ratio", "In vitro", "In vivo", "Incidence (epidemiology)", "Incidence rate", "Infectivity", "Intention-to-treat analysis", "International Standard Book Number", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Meta-analysis", "Morbidity", "Mortality rate", "Multicenter trial", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "Period prevalence", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Scientific control", "Seeding trial", "Selection bias", "Specificity and sensitivity", "Survivorship bias", "Systematic review", "Vaccine trial", "Virulence"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1732833", "http://www.ncbi.nlm.nih.gov/pubmed/15194712", "http://doi.org/10.1136%2Fjech.2003.011585"]}, "Non-linear least squares": {"categories": ["Least squares"], "title": "Non-linear least squares", "method": "Non-linear least squares", "url": "https://en.wikipedia.org/wiki/Non-linear_least_squares", "summary": "Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m > n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Analysis of covariance", "Analysis of variance", "Approximation theory", "Bayesian experimental design", "Bayesian linear regression", "Bayesian multivariate linear regression", "Binomial regression", "Block matrix", "Calibration curve", "Cauchy distribution", "Chebyshev nodes", "Chebyshev polynomials", "Cholesky decomposition", "Computational statistics", "Computer simulation", "Confounding", "Conjugate gradient method", "Correlated", "Correlation and dependence", "Curve fitting", "Davidon\u2013Fletcher\u2013Powell formula", "Design of experiments", "Diagonal matrix", "Discrete choice", "Ellipse", "Errors-in-variables models", "Errors and residuals in statistics", "Fixed effects model", "Gaussian quadrature", "Gauss\u2013Markov theorem", "Gauss\u2013Newton algorithm", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Gradient", "Grey box model", "Growth curve (statistics)", "Hessian matrix", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Jacobian matrix and determinant", "Kendall tau rank correlation coefficient", "Least-angle regression", "Least absolute deviations", "Least squares", "Least squares support vector machine", "Levenberg\u2013Marquardt algorithm", "Line search", "Linear least squares", "Linear least squares (mathematics)", "Linear regression", "Lineweaver\u2013Burk plot", "List of statistics articles", "Local regression", "Log normal distribution", "Logistic regression", "Mallows's Cp", "Maxima and minima", "Mean and predicted response", "Michaelis\u2013Menten kinetics", "Minimum mean-square error", "Mixed logit", "Mixed model", "Model selection", "Moving least squares", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate analysis of variance", "Nelder\u2013Mead method", "Newton's method in optimization", "Non-negative least squares", "Nonlinear programming", "Nonlinear regression", "Nonparametric regression", "Numerical Recipes", "Numerical analysis", "Numerical differentiation", "Numerical integration", "Numerical smoothing and differentiation", "Optimal design", "Optimization (mathematics)", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal", "Orthogonal matrix", "Orthogonal polynomials", "Outline of statistics", "Parabola", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson product-moment correlation coefficient", "Poisson regression", "Polynomial regression", "Polytope", "Positive-definite matrix", "Principal component regression", "Probit model", "QR decomposition", "Quadratic function", "Quantile regression", "Random effects model", "Rank correlation", "Regression analysis", "Regression model validation", "Regularized least squares", "Response surface methodology", "Ridge regression", "Robust regression", "Round-off", "Round-off error", "Segmented regression", "Semi-log plot", "Semiparametric regression", "Simple linear regression", "Simplex", "Singular value decomposition", "Spearman's rank correlation coefficient", "Statistical model", "Statistics", "Steepest descent", "Stepwise regression", "Studentized residual", "System identification", "Taylor series", "Tikhonov regularization", "Total least squares", "Variance", "Variance-covariance matrix", "Weighted least squares"], "references": ["http://www.siam.org/books/textbooks/fr18_book.pdf"]}, "De Moivre's law": {"categories": ["Actuarial science", "Survival analysis"], "title": "De Moivre's law", "method": "De Moivre's law", "url": "https://en.wikipedia.org/wiki/De_Moivre%27s_law", "summary": "De Moivre's Law is a survival model applied in actuarial science, named for Abraham de Moivre. It is a simple law of mortality based on a linear survival function.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/71/De_Moivre_1725_page_25.jpg"], "links": ["Abraham de Moivre", "Actuarial notation", "Actuarial science", "Benjamin Gompertz", "Continuous probability distribution", "De Moivre's formula", "Failure rate", "Force of mortality", "Hazard rate", "International Standard Book Number", "Life table", "Survival function", "Survival model", "Uniform distribution (continuous)"], "references": ["https://books.google.com/books?id=ed5bAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false"]}, "Learning theory (statistics)": {"categories": ["Estimation theory", "Machine learning"], "title": "Statistical learning theory", "method": "Learning theory (statistics)", "url": "https://en.wikipedia.org/wiki/Statistical_learning_theory", "summary": "Statistical learning theory is a framework for machine learning\ndrawing from the fields of statistics and functional analysis. Statistical learning theory deals with the problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields such as computer vision, speech recognition, bioinformatics and baseball.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f4/Overfitting_on_Training_Set_Data.pdf", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Baseball", "Bayesian network", "Bias-variance dilemma", "Bioinformatics", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Cluster analysis", "Computational learning theory", "Computer vision", "Conditional random field", "Conference on Neural Information Processing Systems", "Convolutional neural network", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Dimensionality reduction", "Empirical risk", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Expected risk", "Facial recognition system", "Factor analysis", "Feature engineering", "Feature learning", "Functional analysis", "Gated recurrent unit", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Heaviside step function", "Hidden Markov model", "Hierarchical clustering", "Independent component analysis", "Indicator function", "International Conference on Machine Learning", "International Standard Book Number", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "L1-norm", "L2-norm", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Loss function", "Lp space", "Machine Learning (journal)", "Machine learning", "Mean-shift", "Mehryar Mohri", "Multilayer perceptron", "Naive Bayes classifier", "Non-negative matrix factorization", "OPTICS algorithm", "Occam learning", "Ohm's Law", "Online machine learning", "Ordinary least squares regression", "Outline of machine learning", "Overfitting", "Perceptron", "Principal component analysis", "Probably approximately correct learning", "Proximal gradient methods for learning", "Q-learning", "Random forest", "Recurrent neural network", "Regression analysis", "Regularization (mathematics)", "Reinforcement learning", "Relevance vector machine", "Reproducing kernel Hilbert spaces", "Restricted Boltzmann machine", "Self-organizing map", "Semi-supervised learning", "Speech recognition", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning in language acquisition", "Statistics", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "Tikhonov regularization", "Training set", "Trevor Hastie", "U-Net", "Unsupervised learning", "Vapnik\u2013Chervonenkis theory"], "references": ["http://ai2-s2-pdfs.s3.amazonaws.com/a36b/028d024bf358c4af1a5e1dc3ca0aed23b553.pdf", "http://www.mit.edu/~9.520/spring12/slides/class01/class01.pdf", "http://www.mit.edu/~9.520/spring12/slides/class02/class02.pdf", "https://arxiv.org/list/cs.LG/recent"]}, "Bias (statistics)": {"categories": ["Accuracy and precision", "All articles covered by WikiProject Wikify", "All articles needing additional references", "All articles needing expert attention", "All pages needing cleanup", "Articles covered by WikiProject Wikify from October 2017", "Articles needing additional references from June 2012", "Articles needing expert attention from October 2017", "Articles needing expert attention with no reason or talk parameter", "Articles needing more viewpoints from October 2017", "Articles with multiple maintenance issues", "Bias", "Statistics articles needing expert attention", "Webarchive template wayback links", "Wikipedia introduction cleanup from October 2017"], "title": "Bias (statistics)", "method": "Bias (statistics)", "url": "https://en.wikipedia.org/wiki/Bias_(statistics)", "summary": "Statistical bias is a feature of a statistical technique or of its results whereby the expected value of the results differs from the true underlying quantitative parameter being estimated.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/6/6c/Wiki_letter_w.svg"], "links": ["Academic bias", "Acquiescence bias", "Analytical bias", "Anchoring", "Attentional bias", "Attribution bias", "Attrition bias", "Authority bias", "Automation bias", "Belief bias", "Bias", "Bias blind spot", "Bias in education", "Bias of an estimator", "Choice-supportive bias", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Confirmation bias", "Congruence bias", "Cultural bias", "Debiasing", "Diabetes mellitus", "Distinction bias", "Dunning\u2013Kruger effect", "Educational measurement", "Egocentric bias", "Emotional bias", "Estimation theory", "Exclusion bias", "Expected value", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Forecast bias", "Fundamental attribution error", "Funding bias", "Halo effect", "Healthy user bias", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "Impact bias", "In-group favoritism", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "Lead time bias", "Length time bias", "Lippincott Williams & Wilkins", "List of cognitive biases", "List of memory biases", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Negativity bias", "Net bias", "Normalcy bias", "Obesity", "Observer bias", "Omission bias", "Omitted-variable bias", "Optimism bias", "Outcome bias", "Overton window", "Parameter", "Participation bias", "Precision bias", "Pro-innovation bias", "Publication bias", "Recall bias", "Reporting bias", "Response bias", "Restraint bias", "Sampling bias", "Selection bias", "Self-selection bias", "Self-serving bias", "Sensitivity and specificity", "Social comparison bias", "Social desirability bias", "Spectrum bias", "Statistic", "Statistical hypothesis testing", "Statistical parameter", "Statistics", "Status quo bias", "Survivorship bias", "Syndemic", "Systematic error", "Systemic bias", "Time-saving bias", "Trait ascription bias", "Trueness", "United States news media and the Vietnam War", "Verification bias", "Von Restorff effect", "Wayback Machine", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://handbook.cochrane.org/chapter_8/8_4_introduction_to_sources_of_bias_in_clinical_trials.htm", "http://www.ncme.org/ncme/NCME/Resource_Center/Glossary/NCME/Resource_Center/Glossary1.aspx?hkey=4bb87415-44dc-4088-9ed9-e8515326a061#anchorB", "https://web.archive.org/web/20170722194028/http://www.ncme.org/ncme/NCME/Resource_Center/Glossary/NCME/Resource_Center/Glossary1.aspx?hkey=4bb87415-44dc-4088-9ed9-e8515326a061#anchorB"]}, "Gillespie algorithm": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2012", "Articles with unsourced statements from June 2016", "CS1 maint: Multiple names: authors list", "Chemical kinetics", "Computational chemistry", "Monte Carlo methods", "Stochastic simulation"], "title": "Gillespie algorithm", "method": "Gillespie algorithm", "url": "https://en.wikipedia.org/wiki/Gillespie_algorithm", "summary": "In probability theory, the Gillespie algorithm (or occasionally the Doob-Gillespie algorithm) generates a statistically correct trajectory (possible solution) of a stochastic equation. It was created by Joseph L. Doob and others (circa 1945), presented by Dan Gillespie in 1976, and popularized in 1977 in a paper where he uses it to simulate chemical or biochemical systems of reactions efficiently and accurately using limited computational power (see stochastic simulation). As computers have become faster, the algorithm has been used to simulate increasingly complex systems. The algorithm is particularly useful for simulating reactions within cells, where the number of reagents is low and keeping track of the position and behaviour of individual molecules is computationally feasible. Mathematically, it is a variant of a dynamic Monte Carlo method and similar to the kinetic Monte Carlo methods. It is used heavily in computational systems biology.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e2/Example_calculation_illustrating_the_Gillespie_algorithm_for_reversible_dimerising_molecules.png", "https://upload.wikimedia.org/wikipedia/commons/f/f7/SIR_graph.png", "https://upload.wikimedia.org/wikipedia/commons/a/ac/SIR_trajectory.png"], "links": ["Andrei Kolmogorov", "ArXiv", "Bibcode", "Computational systems biology", "Dan Gillespie", "David George Kendall", "Digital object identifier", "Dynamic Monte Carlo method", "International Standard Book Number", "JSTOR", "Joseph L. Doob", "Kinetic Monte Carlo", "Kolmogorov equations (Markov jump process)", "Linda Petzold", "Manchester Mark 1", "Master equation", "Maurice S. Bartlett", "Probability theory", "PubMed Central", "PubMed Identifier", "Reagent", "SIR model", "Stochastic", "Stochastic process", "Stochastic simulation", "Tau-leaping", "William Feller"], "references": ["http://www.menem.com/~ilya/wiki/images/1/18/Sinitsyn-etal-09.pdf", "http://apps.nrbook.com/empanel/index.html#pg=946", "http://www.springerlink.com/content/v724507673277262/fulltext.pdf", "http://demonstrations.wolfram.com/DeterministicVersusStochasticChemicalKinetics/", "http://mosaic.mpi-cbg.de/?q=downloads/stochastic_chemical_net", "http://adsabs.harvard.edu/abs/1976JCoPh..22..403G", "http://adsabs.harvard.edu/abs/2000JPCA..104.1876G", "http://adsabs.harvard.edu/abs/2003JChPh.11912784R", "http://adsabs.harvard.edu/abs/2005JChPh.122e4103S", "http://adsabs.harvard.edu/abs/2005PNAS..10214593B", "http://adsabs.harvard.edu/abs/2006PLSCB...2..117B", "http://adsabs.harvard.edu/abs/2007JChPh.126l4108C", "http://adsabs.harvard.edu/abs/2008JChPh.128t5101S", "http://adsabs.harvard.edu/abs/2009JChPh.130x4104R", "http://adsabs.harvard.edu/abs/2009PNAS..10610546S", "http://adsabs.harvard.edu/abs/2010JChPh.132d4102R", "http://adsabs.harvard.edu/abs/2010PLoSO...5.8125I", "http://adsabs.harvard.edu/abs/2011JChPh.134a4106R", "http://adsabs.harvard.edu/abs/2013JChPh.138i4103Y", "http://www.engineering.ucsb.edu/~cse/StochKit/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1253555", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1560403", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2705573", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2798956", "http://www.ncbi.nlm.nih.gov/pubmed/15740306", "http://www.ncbi.nlm.nih.gov/pubmed/16199522", "http://www.ncbi.nlm.nih.gov/pubmed/16965175", "http://www.ncbi.nlm.nih.gov/pubmed/17411109", "http://www.ncbi.nlm.nih.gov/pubmed/18513044", "http://www.ncbi.nlm.nih.gov/pubmed/19525397", "http://www.ncbi.nlm.nih.gov/pubmed/19566139", "http://www.ncbi.nlm.nih.gov/pubmed/20066048", "http://www.ncbi.nlm.nih.gov/pubmed/20113014", "http://www.ncbi.nlm.nih.gov/pubmed/21218996", "http://www.ncbi.nlm.nih.gov/pubmed/23485273", "http://cain.sourceforge.net/", "http://stochpy.sourceforge.net/", "http://synbioss.sourceforge.net/", "http://arxiv.org/abs/0906.1992", "http://doi.org/10.1007%2FBF01457949", "http://doi.org/10.1016%2F0021-9991(76)90041-3", "http://doi.org/10.1021%2Fj100540a008", "http://doi.org/10.1021%2Fjp993732q", "http://doi.org/10.1063%2F1.1627296", "http://doi.org/10.1063%2F1.1835951", "http://doi.org/10.1063%2F1.2710253", "http://doi.org/10.1063%2F1.2919546", "http://doi.org/10.1063%2F1.3154624", "http://doi.org/10.1063%2F1.3297948", "http://doi.org/10.1063%2F1.3521496", "http://doi.org/10.1063%2F1.4792207", "http://doi.org/10.1073%2Fpnas.0503858102", "http://doi.org/10.1073%2Fpnas.0809340106", "http://doi.org/10.1090%2FS0002-9947-1942-0006633-7", "http://doi.org/10.1371%2Fjournal.pcbi.0020117", "http://doi.org/10.1371%2Fjournal.pone.0008125", "http://doi.org/10.2307%2F1990095", "http://doi.org/10.2307%2F1990339", "http://www.jstor.org/stable/1970064", "http://www.jstor.org/stable/1990152", "http://www.jstor.org/stable/1990339", "http://www.jstor.org/stable/2983837", "http://www.jstor.org/stable/2985327", "http://www.stochss.org/", "https://github.com/sdwfrost/Gillespie.jl", "https://web.archive.org/web/20110714072216/http://www.menem.com/~ilya/wiki/images/1/18/Sinitsyn-etal-09.pdf", "https://cran.r-project.org/web/packages/GillespieSSA/index.html"]}, "Risk perception": {"categories": ["Perception", "Probability assessment", "Risk"], "title": "Risk perception", "method": "Risk perception", "url": "https://en.wikipedia.org/wiki/Risk_perception", "summary": "Risk perception is the subjective judgement that people make about the characteristics and severity of a risk. The phrase is most commonly used in reference to natural hazards and threats to the environment or health, such as nuclear power. Several theories have been proposed to explain why different people make different estimates of the dangerousness of risks. Three major families of theory have been developed: psychology approaches (heuristics and cognitive), anthropology/sociology approaches (cultural theory) and interdisciplinary approaches (social amplification of risk framework).\n\n", "images": [], "links": ["Aaron Wildavsky", "Amos Tversky", "Anchoring and Adjustment", "Availability heuristic", "Base rate neglect", "Chauncey Starr", "Cognitive bias", "Conjunction fallacy", "Cultural Theory of risk", "Cultural cognition", "Daniel Kahneman", "Digital object identifier", "Environment (biophysical)", "Expected utility", "Fuzzy-trace theory", "Gambler's fallacy", "Health", "Heuristics in judgment and decision making", "Illusion of validity", "Illusory correlation", "Insensitivity to predictability", "Insensitivity to sample size", "Insurance", "Mary Douglas", "Melissa Finucane", "Natural hazards", "Nuclear power", "Paul James (academic)", "Paul Slovic", "Preference", "PubMed Identifier", "Regression fallacy", "Representativeness", "Revealed preference", "Risk", "Roger Kasperson", "Subjectivity"], "references": ["http://oxfordbibliographiesonline.com/display/id/obo-9780195396607-0051", "http://cdp.sagepub.com/content/15/6/322.full", "http://elib.uni-stuttgart.de/opus/volltexte/2010/5307/pdf/ren27.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/17835457", "http://www.culturalcognition.net/projects/first-national-risk-culture-study.html", "http://www.apa.org/science/about/publications/climate-change-booklet.pdf", "http://doi.org/10.1080%2F026999300402763", "http://doi.org/10.1093%2Fsf%2F71.4.909", "http://doi.org/10.1111%2Fj.1467-8721.2006.00461.x", "http://doi.org/10.1111%2Fj.1539-6924.1982.tb01369.x", "http://doi.org/10.1111%2Fj.1539-6924.1988.tb01168.x", "http://doi.org/10.1111%2Fj.1539-6924.1993.tb01077.x", "http://doi.org/10.1126%2Fscience.165.3899.1232", "http://doi.org/10.1126%2Fscience.185.4157.1124", "https://www.academia.edu/3791859/Trust_Us_and_Be_Scared_The_Changing_Nature_of_Contemporary_Risk"]}, "Negative multinomial distribution": {"categories": ["All pages needing cleanup", "Articles needing cleanup from December 2010", "Cleanup tagged articles without a reason field from December 2010", "Factorial and binomial topics", "Multivariate discrete distributions", "Use dmy dates from September 2010", "Wikipedia pages needing cleanup from December 2010"], "title": "Negative multinomial distribution", "method": "Negative multinomial distribution", "url": "https://en.wikipedia.org/wiki/Negative_multinomial_distribution", "summary": "In probability theory and statistics, the negative multinomial distribution is a generalization of the negative binomial distribution (NB(r,\u2009p)) to more than two outcomes.Suppose we have an experiment that generates m+1\u22652 possible outcomes, {X0,\u2026,Xm}, each occurring with non-negative probabilities {p0,\u2026,pm} respectively. If sampling proceeded until n observations were made, then {X0,\u2026,Xm} would have been multinomially distributed. However, if the experiment is stopped once X0 reaches the predetermined value k0, then the distribution of the m-tuple {X1,\u2026,Xm} is negative multinomial. These variables are not multinomially distributed because their sum X1+\u2026+Xm is not fixed, being a draw from a negative binomial distribution.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Chi square distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conjugate prior", "Conway\u2013Maxwell\u2013Poisson distribution", "Covariance matrix", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverted Dirichlet distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Marginal distribution", "Mathematica", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood estimation", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Melanoma", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial", "Negative binomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.sciencedirect.com/science/article/B6V1D-4H7T8P0-1/2/54b376fc96fdd6ad4331325a822df997"]}, "Parzen window": {"categories": ["Articles with example MATLAB/Octave code", "Commons category link is on Wikidata", "Estimation of densities", "Machine learning", "Nonparametric statistics"], "title": "Kernel density estimation", "method": "Parzen window", "url": "https://en.wikipedia.org/wiki/Kernel_density_estimation", "summary": "In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable. Kernel density estimation is a fundamental data smoothing problem where inferences about the population are made, based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen\u2013Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e5/Comparison_of_1D_bandwidth_selectors.png", "https://upload.wikimedia.org/wikipedia/commons/4/41/Comparison_of_1D_histogram_and_KDE.png", "https://upload.wikimedia.org/wikipedia/commons/2/2a/Kernel_density.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b2/Kernel_density_estimation%2C_comparison_between_rule_of_thumb_and_solve-the-equation_bandwidth.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Analytica (software)", "Annals of Statistics", "Apache Spark", "ArXiv", "Bernard Silverman", "Big o notation", "C++", "C (programming language)", "Characteristic function (probability theory)", "CrimeStat", "Cross-validation (statistics)", "D3js", "Density estimation", "Digital object identifier", "Discrete Laplace operator", "ELKI", "Econometrics", "Emanuel Parzen", "Environmental Systems Research Institute", "Fourier transform", "Free parameter", "GNU Octave", "Gaussian function", "Gnuplot", "Haskell (programming language)", "Head/tail Breaks", "Heat equation", "Heat kernel", "Histograms", "IGOR Pro", "Independent and identically distributed random variables", "International Standard Book Number", "JMP (statistical software)", "JSTOR", "JavaScript", "Java (programming language)", "Julia (programming language)", "Kernel (statistics)", "Kernel regression", "Kernel smoothing", "Little o notation", "MATLAB", "Manifold learning", "Mathematica", "Mean-shift", "Mean integrated squared error", "Microsoft Excel", "Minitab", "Multivariate kernel density estimation", "Murray Rosenblatt", "NAG Numerical Library", "Non-parametric statistics", "Normal distribution", "Origin (data analysis software)", "PHP", "Perl", "Probability density function", "Python (programming language)", "R (programming language)", "Random number generator", "Random variable", "Risk function", "Rug plot", "SAS (software)", "Scale space", "Signal processing", "Smoothing", "Standard deviation", "Standard normal", "Stata", "Statistical population", "Statistical sample", "Statistics", "The Annals of Mathematical Statistics", "Thermodynamics", "Univariate", "Variable kernel density estimation", "Weka (machine learning)"], "references": ["http://web.maths.unsw.edu.au/~zdravkobotev/kde.R", "http://www.mathworks.com/matlabcentral/fileexchange/14034", "http://www.mathworks.com/matlabcentral/fileexchange/14034-kernel-density-estimator", "http://www.mathworks.com/matlabcentral/fileexchange/17204-kernel-density-estimation", "http://www.mathworks.com/matlabcentral/fileexchange/58312-kernel-density-estimator-for-high-dimensions", "http://wiki.originlab.com/~originla/ltwiki/index.php?title=Category:LabTalk_Programming", "http://pcarvalho.com/things/kerneldensityestimation/index.html", "http://reference.wolfram.com/mathematica/ref/KernelMixtureDistribution.html", "http://reference.wolfram.com/mathematica/ref/SmoothKernelDistribution.html", "http://www.math.muni.cz/english/science-and-research/developed-software/232-matlab-toolbox.html", "http://www.umiacs.umd.edu/~morariu/figtree/", "http://2000.jukuin.keio.ac.jp/shimazaki/res/kernel.html", "http://www.mvstat.net/tduong/research/seminars/seminar-2001-05", "http://libagf.sf.net", "http://nuklei.sourceforge.net/", "http://weka.sourceforge.net/doc.stable/weka/estimators/KernelEstimator.html", "http://www.wessa.net/rwasp_density.wasp", "http://spark.apache.org/docs/latest/mllib-statistics.html#kernel-density-estimation", "http://arxiv.org/abs/1011.2602", "http://search.cpan.org/~janert/Statistics-KernelEstimation-0.05", "http://doi.org/10.1007%2FBF01205233", "http://doi.org/10.1016%2F0167-9473(92)00066-Z", "http://doi.org/10.1080%2F01621459.1990.10475307", "http://doi.org/10.1080%2F02331880500439782", "http://doi.org/10.1093%2Fbiomet%2F66.3.605", "http://doi.org/10.1093%2Fbiomet%2F71.2.353", "http://doi.org/10.1137%2F1114019", "http://doi.org/10.1214%2F10-AOS799", "http://doi.org/10.1214%2Faoms%2F1177704472", "http://doi.org/10.1214%2Faoms%2F1177728190", "http://doi.org/10.1214%2Faos%2F1176342997", "http://doi.org/10.2307%2F2291420", "http://hackage.haskell.org/package/statistics", "http://www.jstor.org/stable/2237880", "http://www.jstor.org/stable/2289526", "http://www.jstor.org/stable/2291420", "http://www.jstor.org/stable/2345597", "http://www.jstor.org/stable/4615859", "http://projecteuclid.org/euclid.aos/1176342997", "http://pythonhosted.org/PyQt-Fit/mod_kde.html", "http://www.rsc.org/Membership/Networking/InterestGroups/Analytical/AMC/Software/kerneldensities.asp", "http://www.nag.co.uk/numeric/CL/nagdoc_cl09/pdf/G10/g10bac.pdf", "http://www.nag.co.uk/numeric/fl/nagdoc_fl23/pdf/G10/g10baf.pdf", "https://github.com/JuliaStats/KernelDensity.jl", "https://github.com/markrogoyski/math-php", "https://www.mathworks.com/help/stats/ksdensity.html", "https://www.sciencedirect.com/science/article/pii/S0378779614004374", "https://www.stata.com/manuals13/rkdensity.pdf", "https://webhost.engr.illinois.edu/~aluru/Journals/IJNME10.pdf", "https://jakevdp.github.io/blog/2013/12/01/kernel-density-estimation/", "https://kdepy.readthedocs.io/en/latest/", "https://pypi.python.org/packages/source/P/PyQt-Fit/PyQt-Fit-1.3.4.tar.gz", "https://cran.r-project.org/web/packages/AdaptGauss/index.html", "https://cran.r-project.org/web/packages/KernSmooth/index.html", "https://cran.r-project.org/web/packages/btb/index.html", "https://cran.r-project.org/web/packages/evmix/index.html", "https://cran.r-project.org/web/packages/ks/index.html", "https://cran.r-project.org/web/packages/np/index.html", "https://cran.r-project.org/web/packages/sm/index.html", "https://ideas.repec.org/c/boc/bocode/s456410.html", "https://ideas.repec.org/p/cor/louvco/1992005.html"]}, "Pairwise independence": {"categories": ["CS1 maint: Multiple names: authors list", "Independence (probability theory)", "Theory of probability distributions"], "title": "Pairwise independence", "method": "Pairwise independence", "url": "https://en.wikipedia.org/wiki/Pairwise_independence", "summary": "In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. Pairwise independent random variables with finite variance are uncorrelated.\nA pair of random variables X and Y are independent if and only if the random vector (X, Y) with joint cumulative distribution function (CDF) \n \n \n \n \n F\n \n X\n ,\n Y\n \n \n (\n x\n ,\n y\n )\n \n \n {\\displaystyle F_{X,Y}(x,y)}\n satisfies\n\n \n \n \n \n F\n \n X\n ,\n Y\n \n \n (\n x\n ,\n y\n )\n =\n \n F\n \n X\n \n \n (\n x\n )\n \n F\n \n Y\n \n \n (\n y\n )\n ,\n \n \n {\\displaystyle F_{X,Y}(x,y)=F_{X}(x)F_{Y}(y),}\n or equivalently, their joint density \n \n \n \n \n f\n \n X\n ,\n Y\n \n \n (\n x\n ,\n y\n )\n \n \n {\\displaystyle f_{X,Y}(x,y)}\n satisfies\n\n \n \n \n \n f\n \n X\n ,\n Y\n \n \n (\n x\n ,\n y\n )\n =\n \n f\n \n X\n \n \n (\n x\n )\n \n f\n \n Y\n \n \n (\n y\n )\n .\n \n \n {\\displaystyle f_{X,Y}(x,y)=f_{X}(x)f_{Y}(y).}\n That is, the joint distribution is equal to the product of the marginal distributions.Unless it is not clear in context, in practice the modifier \"mutual\" is usually dropped so that independence means mutual independence. A statement such as \" X, Y, Z are independent random variables\" means that X, Y, Z are mutually independent.", "images": [], "links": ["International Standard Book Number", "Joint distribution", "Joint probability distribution", "K-independent hashing", "MAXEkSAT", "Message authentication code", "Modular arithmetic", "Mutual independence", "Mutually independent", "Pairwise disjoint", "Probability theory", "Random variable", "Statistical independence", "Uncorrelated", "Variance"], "references": []}, "Confidence band": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "CS1 maint: Archived copy as title", "Estimation theory"], "title": "Confidence and prediction bands", "method": "Confidence band", "url": "https://en.wikipedia.org/wiki/Confidence_and_prediction_bands", "summary": "A confidence band is used in statistical analysis to represent the uncertainty in an estimate of a curve or function based on limited or noisy data. Similarly, a prediction band is used to represent the uncertainty about the value of a new data-point on the curve, but subject to noise. Confidence and prediction bands are often used as part of the graphical presentation of results of a regression analysis.\nConfidence bands are closely related to confidence intervals, which represent the uncertainty in an estimate of a single numerical value. \"As confidence intervals, by construction, only refer to a single point, they are narrower (at this point) than a confidence band which is supposed to hold simultaneously at many points.\"", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b6/Binomial_confidence_band.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/0/01/Regression_confidence_band.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bonferroni correction", "Bonferroni method", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "CDF-based nonparametric confidence interval", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Characteristic function (probability theory)", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Familywise error rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov-Smirnov test", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scheff\u00e9's method", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Smoothing", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode17.html", "http://doi.org/10.1093%2Fbiomet%2Fasn005", "http://doi.org/10.1111%2Fj.1751-5823.2007.00027.x", "http://doi.org/10.2307%2F2291062", "http://www.jstor.org/stable/2291062", "https://books.google.com/books?id=qPCmAOS-CoMC&lpg=PA65&vq=As%20confidence%20intervals,%20by%20construction,%20only%20refer%20to%20a%20single%20point,%20they%20are%20narrower%20(at%20this%20point)%20than%20a%20confidence%20band%20which%20is%20supposed%20to%20hold%20simultaneously%20at%20many%20points&pg=PA65#v=snippet&q=As%20confidence%20intervals,%20by%20construction,%20only%20refer%20to%20a%20single%20point,%20they%20are%20narrower%20(at%20this%20point)%20than%20a%20confidence%20band%20which%20is%20supposed%20to%20hold%20simultaneously%20at%20many%20points&f=false", "https://archive.is/20130412073504/http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode17.html"]}, "Benford's law": {"categories": ["Commons category link from Wikidata", "Statistical laws", "Theory of probability distributions", "Use dmy dates from June 2013", "Webarchive template wayback links"], "title": "Benford's law", "method": "Benford's law", "url": "https://en.wikipedia.org/wiki/Benford%27s_law", "summary": "Benford's law, also called Newcomb-Benford's law, law of anomalous numbers, and first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small. For example, in sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. If the digits were distributed uniformly, they would each occur about 11.1% of the time. Benford's law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.\nThe graph to the right shows Benford's law for base 10. There is a generalization of the law to numbers expressed in other bases (for example, base 16), and also a generalization from leading 1 digit to leading n digits.\nIt has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, house prices, population numbers, death rates, lengths of rivers, physical and mathematical constants. Like other general principles about natural data \u2014 for example the fact that many data sets are well approximated by a normal distribution \u2014 there are illustrative examples and explanations that cover many of the cases where Benford's law applies, though there are many other cases where Benford's law applies that resist a simple explanation. It tends to be most accurate when values are distributed across multiple orders of magnitude, especially if the process generating the numbers is described by a power law (which are common in nature).\nIt is named after physicist Frank Benford, who stated it in 1938 in a paper titled \"The Law of Anomalous Numbers\", although it had been previously stated by Simon Newcomb in 1881.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/82/Benford-physical.svg", "https://upload.wikimedia.org/wikipedia/commons/d/de/BenfordBroad.png", "https://upload.wikimedia.org/wikipedia/commons/d/de/BenfordBroad.png", "https://upload.wikimedia.org/wikipedia/commons/c/c8/BenfordNarrow.gif", "https://upload.wikimedia.org/wikipedia/commons/1/14/Benford_law_bases.svg", "https://upload.wikimedia.org/wikipedia/commons/1/14/Benford_law_log_log_graph.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0b/Benfords_law_illustrated_by_world%27s_countries_population.png", "https://upload.wikimedia.org/wikipedia/commons/8/8a/Logarithmic_scale.png", "https://upload.wikimedia.org/wikipedia/commons/4/46/Rozklad_benforda.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["112 (emergency telephone number)", "ARGUS distribution", "American Journal of Mathematics", "American Mathematical Monthly", "American Scientist", "Anton Formann", "ArXiv", "Arcsine distribution", "Asymmetric Laplace distribution", "Asymptotic limit", "Audit", "BBC", "Balding\u2013Nichols model", "Bates distribution", "Benford's law of controversy", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bibcode", "Binary numeral system", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Brady Haran", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Chi-squared distribution", "Chi distribution", "Chi square", "Chi square distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Data", "Davis distribution", "Decimal", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Dependent variable", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Equidistribution theorem", "Equivalence test", "Eric W. Weisstein", "Erich Kirchler", "Erlang distribution", "Eukaryote", "Eurozone", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential decay", "Exponential distribution", "Exponential family", "Exponential growth", "Exponential power distribution", "Extended negative binomial distribution", "F-distribution", "F distribution", "Factorial", "Fibonacci number", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forbes", "Forensic accounting", "Fractional part", "Frank Benford", "Fraud", "Fraud detection", "Frequency distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "German Economic Review", "Gompertz distribution", "Goodness-of-fit test", "Gumbel distribution", "Hal Varian", "Half-logistic distribution", "Half-normal distribution", "Hexadecimal", "Hilda Geiringer", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Integer sequence", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Iranian presidential election, 2009", "Irrational number", "Irwin\u2013Hall distribution", "J. Clin. Pathol.", "JSTOR", "Jean-Paul Delahaye", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the Royal Statistical Society, Series B", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kuiper test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "List of countries by population", "List of probability distributions", "List of tallest buildings and structures in the world", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log normal", "Log normal distribution", "Log scale", "Logarithm", "Logarithmic distribution", "Logarithmic scale", "Logistic distribution", "Logit-normal distribution", "Lognormal", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Mark Nigrini", "MathWorld", "Mathematical Reviews", "Mathematical constant", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mittag-Leffler distribution", "Mixture distribution", "Molecular weight", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Muth distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Normal probability distribution", "North American Numbering Plan", "On-Line Encyclopedia of Integer Sequences", "Open reading frame", "Order of magnitude", "Orders of magnitude", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Physical constant", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Power law", "Predictive analytics", "Probability", "Probability density", "Probability distribution", "Proc. Am. Philos. Soc.", "Prokaryote", "Psychological pricing", "PubMed Central", "PubMed Identifier", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Radio Lab", "Radiolab", "Radix", "Raised cosine distribution", "Random matrix", "Random variable", "Random walk", "Ratio distribution", "Rayleigh distribution", "Reader's Digest", "Real versus nominal value (economics)", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Sankhya", "Scale invariant", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Significance level", "Significand", "Significant digit", "Simon Newcomb", "Simon Singh", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Social Science Research Network", "Soliton distribution", "Stable distribution", "Stigler's Law", "Student's t-distribution", "Tally marks", "Ted Hill (mathematician)", "Terence Tao", "The American Statistician", "The Fibonacci Quarterly", "The New York Times", "Theodore P. Hill", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Unary numeral system", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wayback Machine", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wolfram Demonstrations Project", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z statistic", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.dspguide.com/CH34.PDF", "http://www.dspguide.com/ch34.htm", "http://www.dspguide.com/ch34/10.htm", "http://www.dspguide.com/ch34/4.htm", "http://www.journalofaccountancy.com/Issues/1999/May/nigrini", "http://www.kirix.com/blog/2008/07/22/fun-and-fraud-detection-with-benfords-law/", "http://www.nigrini.com/benfordslaw.htm", "http://www.numberphile.com/videos/benfords_law.html", "http://www.rexswain.com/benford.html", "http://www.sciencedirect.com/science/article/pii/S0167811605000522", "http://ssrn.com/abstract=2907258", "http://testingbenfordslaw.com/", "http://demonstrations.wolfram.com/BenfordsLawFromRatiosOfRandomNumbers/", "http://demonstrations.wolfram.com/CountryDataAndBenfordsLaw/", "http://mathworld.wolfram.com/BenfordsLaw.html", "http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-the-pareto-distribution/", "http://www.worldscientific.com/worldscibooks/10.1142/9089", "http://www.metrica-bi.de/fraud-analysis-with-ssas-benfords-law-test-in-olap-cubes/", "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1042&context=rgp_rsr", "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1074&context=rgp_rsr", "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1041&context=rgp_rsr", "http://vote.caltech.edu/sites/default/files/benford_pdf_4b97cc5b5b.pdf", "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf", "http://adsabs.harvard.edu/abs/1998AmSci..86..358H", "http://adsabs.harvard.edu/abs/2001PhyA..293..297P", "http://adsabs.harvard.edu/abs/2009arXiv0910.1359G", "http://adsabs.harvard.edu/abs/2010PLoSO...510541F", "http://adsabs.harvard.edu/abs/2012PLoSO...736624F", "http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/Articles/Abstracts/abs_2010v2n2a7.pdf", "http://www.math.wm.edu/~leemis/chart/UDR/UDR.html", "http://lmrs.univ-rouen.fr/Persopage/Delarue/Publis/PDF/uniform_distribution_to_Benford_law.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2866333", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3356352", "http://www.ncbi.nlm.nih.gov/pubmed/20479878", "http://www.ncbi.nlm.nih.gov/pubmed/22629319", "http://www.johnmorrow.info/projects/benford/benfordMain.pdf", "http://www.benfordonline.net/", "http://blog.iharder.net/2010/11/10/benford-how-to-generate-your-own-benfords-law-numbers/", "http://www.ams.org/mathscinet-getitem?mr=1421567", "http://www.ams.org/publications/journals/notices/201702/rnoti-p132.pdf", "http://arxiv.org/abs/0705.4488", "http://arxiv.org/abs/0910.1359", "http://arxiv.org/abs/1205.6512", "http://arxiv.org/abs/cond-mat/9808305", "http://doi.org/10.1016%2FS0378-4371(00)00633-6", "http://doi.org/10.1016%2Fj.exmath.2012.03.001", "http://doi.org/10.1016%2Fj.ijresmar.2005.09.002", "http://doi.org/10.1016%2Fj.spl.2017.01.004", "http://doi.org/10.1080%2F00031305.1972.10478934", "http://doi.org/10.1080%2F00031305.2000.10474554", "http://doi.org/10.1090%2Fnoti1477", "http://doi.org/10.1111%2Fj.1468-0475.2011.00542.x", "http://doi.org/10.1136%2Fjcp.2008.061721", "http://doi.org/10.1142%2F9789814327756_0004", "http://doi.org/10.1198%2F000313007X223496", "http://doi.org/10.1198%2Ftast.2009.0005", "http://doi.org/10.1214%2FECP.v13-1358", "http://doi.org/10.1214%2Fss%2F1177009869", "http://doi.org/10.1371%2Fjournal.pone.0010541", "http://doi.org/10.1371%2Fjournal.pone.0036624", "http://doi.org/10.1511%2F1998.4.358", "http://doi.org/10.2307%2F2280379", "http://doi.org/10.2307%2F2319349", "http://doi.org/10.2307%2F2369148", "http://www.jstor.org/stable/2280379", "http://www.jstor.org/stable/2369148", "http://www.jstor.org/stable/984802", "http://plus.maths.org/issue9/features/benford/index-gifd.html", "http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoms/1177704862", "http://upload.wikimedia.org/wikipedia/commons/1/14/Benford_law_bases.svg", "http://upload.wikimedia.org/wikipedia/commons/1/14/Benford_law_log_log_graph.svg", "http://www.wnyc.org/shows/radiolab/episodes/2009/10/09/segments/137643", "http://dces.essex.ac.uk/technical-reports/2001/CSM-349.pdf", "https://www.forbes.com/sites/timworstall/2011/09/12/greece-was-lying-about-its-budget-numbers/", "https://www.newscientist.com/article/mg20227144.000-statistics-hint-at-fraud-in-iranian-election.html", "https://www.scribd.com/document/209534421/The-Law-of-Anomalous-Numbers", "https://www.youtube.com/watch?v=4iz4EHriYz0", "https://www.stat.auckland.ac.nz/~fewster/RFewster_Benford.pdf", "https://mathscinet.ams.org/mathscinet-getitem?mr=2122815", "https://web.archive.org/web/20110514041058/https://mpi-inf.mpg.de/~fietzke/benford.html", "https://web.archive.org/web/20121112200403/http://www.bbc.co.uk/radio4/science/further5.shtml", "https://web.archive.org/web/20140517120934/http://vote.caltech.edu/sites/default/files/benford_pdf_4b97cc5b5b.pdf", "https://arxiv.org/pdf/cond-mat/9808305v2.pdf", "https://doi.org/10.1063%2F1.166498", "https://doi.org/10.1080%2F02664760601004940", "https://doi.org/10.1239%2Fjap%2F1101840566", "https://www.jstor.org/stable/2974952", "https://www.independent.co.uk/property/property-news-roundup-a-third-of-property-values-begin-with-a-1-9154071.html"]}, "Hedonic regression": {"categories": ["All articles with specifically marked weasel-worded phrases", "Articles with specifically marked weasel-worded phrases from April 2014", "Economic data", "Real estate", "Real estate valuation", "Regression models", "Single-equation methods (econometrics)", "Urban economics", "Webarchive template wayback links"], "title": "Hedonic regression", "method": "Hedonic regression", "url": "https://en.wikipedia.org/wiki/Hedonic_regression", "summary": "In real estate and property studies, the hedonic regression (P = f1, f2, f3, ..., fn) is often used to study the impact of a number of factors that affect housing prices \nIn economics, hedonic regression or hedonic demand theory is a revealed preference method of estimating demand or value. It breaks down the item being researched into its constituent characteristics, and obtains estimates of the contributory value of each characteristic. This requires that the composite good being valued can be reduced to its constituent parts and that the market values those constituent parts. Hedonic models are most commonly estimated using regression analysis, although more generalized models, such as sales adjustment grids, are special cases of hedonic models.\nAn attribute vector, which may be a dummy or panel variable, is assigned to each characteristic or group of characteristics. Hedonic models can accommodate non-linearity, variable interaction, or other complex valuation situations.\nHedonic models are commonly used in real estate appraisal, real estate economics, and consumer price index (CPI) calculations. In CPI calculations, hedonic regression is used to control the effect of changes in product quality. Price changes that are due to substitution effects are subject to hedonic quality adjustments.", "images": [], "links": ["Air pollution", "Amenity", "Austrian economists", "CiteSeerX", "Compensating differential", "Consumer price index", "Correlated", "Demand", "Dependent and independent variables", "Digital object identifier", "Dynamic pricing", "Economics", "Environmental good", "Externalities", "Hedonic index", "Heterogeneous", "Interest rates", "JSTOR", "Journal of Political Economy", "Kelvin Lancaster", "Linear", "Market price", "Market prices", "Multicollinearity", "Non-linear", "Pollution", "Real estate", "Real estate appraisal", "Real estate economics", "Regression analysis", "Research papers in economics", "Revealed preference", "Sales comparison approach", "Social Security (United States)", "Taxation", "Treasury Inflation-Protected Securities", "Uniform Standards of Professional Appraisal Practice", "Value (economics)", "Water pollution", "Wayback Machine", "Willingness to pay"], "references": ["http://www.greenfieldadvisors.com/publications/classcert.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.517.5639", "http://www.bls.gov/cpi/cpidryer.htm", "http://coe.mse.ac.in/dp/hedonic%20price.pdf", "http://www.ivm.vu.nl/en/Images/CBA3_tcm53-161539.pdf", "http://doi.org/10.1016%2F0094-1190(78)90016-5", "http://doi.org/10.1016%2Fj.econmod.2006.04.003", "http://doi.org/10.1086%2F260169", "http://www.ecosystemvaluation.org/hedonic_pricing.htm", "http://www.jstor.org/stable/1830899", "http://biblio.repec.org/entry/tbbb.html", "http://www.von-der-lippe.org/dokumente/hedon-vdl.pdf", "http://www.cbabuilder.co.uk/Quant5.html", "https://www.researchgate.net/publication/322759961_Have_Housing_Prices_Gone_with_the_Smelly_Wind_Big_Data_Analysis_on_Landfill_in_Hong_Kong", "https://web.archive.org/web/20071010090625/http://www.greenfieldadvisors.com/publications/classcert.pdf", "https://web.archive.org/web/20111027084754/http://coe.mse.ac.in/dp/hedonic%20price.pdf", "https://web.archive.org/web/20120425063715/http://www.ivm.vu.nl/en/Images/CBA3_tcm53-161539.pdf"]}, "Rescaled range": {"categories": ["Autocorrelation", "Independence (probability theory)", "Statistical deviation and dispersion", "Statistical ratios"], "title": "Rescaled range", "method": "Rescaled range", "url": "https://en.wikipedia.org/wiki/Rescaled_range", "summary": "The rescaled range is a statistical measure of the variability of a time series introduced by the British hydrologist Harold Edwin Hurst (1880\u20131978). Its purpose is to provide an assessment of how the apparent variability of a series changes with the length of the time-period being considered.\nThe rescaled range is calculated from dividing the range of the values exhibited in a portion of the time series by the standard deviation of the values over the same portion of the time series. For example, consider a time series {2, 5, 3, 7, 8, 12, 4, 2} which has a range, R, of 12 - 2 = 10. Its standard deviation, s, is 3.46, so the rescaled range is R/s = 2.89.\nIf we consider the same time series, but increase the number of observations of it, the rescaled range will generally also increase. The increase of the rescaled range can be characterized by making a plot of the logarithm of R/s vs. the logarithm of n. The slope of this line gives the Hurst exponent, H. If the time series is generated by a random walk (or a Brownian motion process) it has the value of H =1/2. Many physical phenomena that have a long time series suitable for analysis exhibit a Hurst exponent greater than 1/2. For example, observations of the height of the Nile River measured annually over many years gives a value of H = 0.77.\nSeveral researchers (including Peters, 1991) have found that the prices of many financial instruments (such as currency exchange rates, stock values, etc.) also have H > 1/2. This means that they have a behavior that is distinct from a random walk, and therefore the time series is not generated by a stochastic process that has the nth value independent of all of the values before this. According to model of Fractional Brownian motion this is referred to as long memory of positive linear autocorrelation. However it has been shown that this measure is correct only for linear evaluation: complex nonlinear processes with memory need additional descriptive parameters. Several studies using Lo's modified rescaled range statistic have contradicted Peters' results as well.", "images": [], "links": ["Andrew Lo", "Autocorrelation", "Autocovariance", "Brownian motion", "CiteSeerX", "Digital object identifier", "Edgar E. Peters", "Fat tail", "Financial instruments", "Fractal", "Fractional Brownian motion", "Harold Edwin Hurst", "Hurst exponent", "International Standard Book Number", "Long memory", "Mean", "Nile River", "Random walk", "Range (statistics)", "Slope", "Standard deviation", "Statistical", "Stochastic process", "Time series"], "references": ["http://dspace.mit.edu/bitstream/1721.1/2245/1/SWP-3014-20126283.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.207", "http://doi.org/10.1137%2F1010093", "http://doi.org/10.1155%2F2014%2F346743", "http://doi.org/10.2307%2F2938368", "https://github.com/Mottl/hurst", "https://dx.doi.org/10.1142/S0219091514500234", "https://ideas.repec.org/s/wuu/hscode.html"]}, "Endogeneity (economics)": {"categories": ["Causality", "Econometric models", "Estimation theory"], "title": "Endogeneity (econometrics)", "method": "Endogeneity (economics)", "url": "https://en.wikipedia.org/wiki/Endogeneity_(econometrics)", "summary": "In econometrics, endogeneity broadly refers to situations in which an explanatory variable is correlated with the error term. The distinction between endogenous and exogenous variables originated in simultaneous equations models, where one separates variables whose values are determined by the model from variables which are predetermined; ignoring simultaneity in the estimation leads to biased estimates as it violates the exogeneity assumption of the Gauss\u2013Markov theorem. The problem of endogeneity, is, unfortunately, oftentimes ignored by researchers conducting non-experimental research and doing so precludes making policy recommendations. Instrumental variable techniques are commonly used to address this problem.\nBesides simultaneity, correlation between explanatory variables and the error term can arise when an unobserved or omitted variable is confounding both independent and dependent variables, or when dependent variables are measured with error.", "images": [], "links": ["Bias of an estimator", "Causal", "Confounding", "Confounding variable", "Consistent estimator", "Consumer", "Correlation", "Demand curve", "Dependent and independent variables", "Digital object identifier", "Econometrics", "Economic model", "Endogenous", "Endogeny", "Error term", "Errors-in-variables models", "Errors and residuals", "Exogenous", "Explanatory variable", "Gauss\u2013Markov theorem", "Granger causality", "Heckman correction", "Heterogeneity", "Independent variable", "Instrumental variable", "International Standard Book Number", "International Standard Serial Number", "Jan Kmenta", "John Johnston (econometrician)", "Mark Thoma", "Omitted-variable bias", "Ordinary least squares", "Preference", "Regression analysis", "Simultaneity", "Simultaneous equations model", "Stochastic model", "Supply and demand", "Time series", "Variable (mathematics)", "Virtuous circle and vicious circle", "YouTube"], "references": ["http://sethgodin.typepad.com/seths_blog/2017/05/what-about-endogeneity.html", "http://doi.org/10.1016%2Fj.leaqua.2010.10.010", "http://www.worldcat.org/issn/1048-9843", "https://www.youtube.com/watch?v=WlOtUA8Rqw8&list=PLD15D38DC7AA3B737&index=14#t=7m42s", "https://www.youtube.com/watch?v=dLuTjoYmfXs", "https://doi.org/10.1016/j.leaqua.2010.10.010"]}, "Inverse Mills ratio": {"categories": ["Statistical ratios", "Theory of probability distributions"], "title": "Mills ratio", "method": "Inverse Mills ratio", "url": "https://en.wikipedia.org/wiki/Mills_ratio", "summary": "In probability theory, the Mills ratio (or Mills's ratio) of a continuous random variable \n \n \n \n X\n \n \n {\\displaystyle X}\n is the function\n\n \n \n \n m\n (\n x\n )\n :=\n \n \n \n \n \n \n F\n \u00af\n \n \n \n (\n x\n )\n \n \n f\n (\n x\n )\n \n \n \n ,\n \n \n {\\displaystyle m(x):={\\frac {{\\bar {F}}(x)}{f(x)}},}\n where \n \n \n \n f\n (\n x\n )\n \n \n {\\displaystyle f(x)}\n is the probability density function, and\n\n \n \n \n \n \n \n F\n \u00af\n \n \n \n (\n x\n )\n :=\n Pr\n [\n X\n >\n x\n ]\n =\n \n \u222b\n \n x\n \n \n +\n \u221e\n \n \n f\n (\n u\n )\n \n d\n u\n \n \n {\\displaystyle {\\bar {F}}(x):=\\Pr[X>x]=\\int _{x}^{+\\infty }f(u)\\,du}\n is the complementary cumulative distribution function (also called survival function). The concept is named after John P. Mills. The Mills ratio is related to the hazard rate h(x) which is defined as\n\n \n \n \n h\n (\n x\n )\n :=\n \n lim\n \n \u03b4\n \u2192\n 0\n \n \n \n \n 1\n \u03b4\n \n \n Pr\n [\n x\n <\n X\n \u2264\n x\n +\n \u03b4\n \n |\n \n X\n >\n x\n ]\n \n \n {\\displaystyle h(x):=\\lim _{\\delta \\to 0}{\\frac {1}{\\delta }}\\Pr[x<X\\leq x+\\delta |X>x]}\n by\n\n \n \n \n m\n (\n x\n )\n =\n \n \n 1\n \n h\n (\n x\n )\n \n \n \n .\n \n \n {\\displaystyle m(x)={\\frac {1}{h(x)}}.}", "images": [], "links": ["Bias (statistics)", "Biometrika", "Censoring (statistics)", "Continuous random variable", "Correlation", "Cumulative distribution function", "Digital object identifier", "Econometrica", "Eric W. Weisstein", "Errors and residuals in statistics", "Gauss\u2013Markov theorem", "Hazard rate", "Heckman correction", "International Standard Book Number", "JSTOR", "James Heckman", "John P. Mills", "Logit", "MathWorld", "Normal distribution", "Ordinary least squares", "Probability density function", "Probability theory", "Probit", "Probit model", "Random variable", "Ratio", "Regression analysis", "Selection bias", "Standard normal distribution", "Survival function", "Takeshi Amemiya", "Truncation (statistics)"], "references": ["http://mathworld.wolfram.com/MillsRatio.html", "http://doi.org/10.1093%2Fbiomet%2F18.3-4.395", "http://doi.org/10.2307%2F1907382", "http://doi.org/10.2307%2F1912352", "http://www.jstor.org/stable/1907382", "http://www.jstor.org/stable/1912352", "http://www.jstor.org/stable/2331957", "https://books.google.com/books?id=0bzGQE14CwEC&pg=PA366", "https://books.google.com/books?id=0bzGQE14CwEC&pg=PA368", "https://books.google.com/books?id=G3ig-0M4wSIC&pg=PA98", "https://books.google.com/books?id=aO7xBwAAQBAJ&pg=PA27", "https://books.google.com/books?id=uXexXLoZnZAC&pg=PA48"]}, "Official statistics": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2015", "Mathematical and quantitative methods (economics)", "Official statistics", "Political communication", "Survey methodology"], "title": "Official statistics", "method": "Official statistics", "url": "https://en.wikipedia.org/wiki/Official_statistics", "summary": "Official statistics are statistics published by government agencies or other public bodies such as international organizations as a public good. They provide quantitative or qualitative information on all major areas of citizens' lives, such as economic and social development, living conditions, health, education, and the environment.During the 16th and 17th centuries, statistics were a method for counting and listing populations and State resources. The term statistics comes from the New Latin statisticum collegium (council of state) and refers to science of the state. According to the Organisation for Economic Co-operation and Development, official statistics are statistics disseminated by the national statistical system, excepting those that are explicitly not to be official\".Governmental agencies at all levels, including municipal, county, and state administrations, may generate and disseminate official statistics. This broader possibility is accommodated by later definitions. For example:\n\nAlmost every country in the world has one or more government agencies (usually national institutes) that supply decision-makers and other users including the general public and the research community with a continuing flow of information (...). This bulk of data is usually called official statistics. Official statistics should be objective and easily accessible and produced on a continuing basis so that measurement of change is possible.\nOfficial statistics result from the collection and processing of data into statistical information by a government institution or international organisation. They are then disseminated to help users develop their knowledge about a particular topic or geographical area, make comparisons between countries or understand changes over time. Official statistics make information on economic and social development accessible to the public, allowing the impact of government policies to be assessed, thus improving accountability.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ca/ECE_weekly_235.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e0/UNECE_Germany_2010.gif", "https://upload.wikimedia.org/wikipedia/commons/e/e9/User_Types.JPG", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balance of payments", "Bar chart", "Bar graph", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chart", "Charts", "Chemometrics", "Chi-squared test", "Choropleth map", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Consumer price index", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "County", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decision making", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Economic", "Economic activity rate", "Education", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Employment rate", "Engineering statistics", "Environmental protection expenditure accounts", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Exchange rate", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Federal Reserve Bank of Philadelphia", "First-hitting-time model", "Foreign born", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gender pay gap", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Government", "Government agencies", "Granger causality", "Graphical model", "Gross Domestic Product", "Grouped data", "Harmonic mean", "Health", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holland Codes", "Homoscedasticity", "Index of dispersion", "Infant mortality", "Interaction (statistics)", "International Monetary Fund", "International Standard Book Number", "International standards", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", 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"Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sample survey", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stacked bar chart", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical survey", "Statistical theory", "Statistics", "Stem-and-leaf display", 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"http://ec.europa.eu/eurostat/ramon/nomenclatures/index.cfm?TargetUrl=DSP_GLOSSARY_NOM_DTL_VIEW&StrNom=CODED2&StrLanguageCode=EN&IntKey=16635185&RdoSearch=BEGIN&TxtSearch=transparency&CboTheme=&IntCurrentPage=1", "http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/Main_Page", "http://www.eurofound.europa.eu/pubdocs/2006/101/en/1/ef06101en.pdf", "http://www.stat.fi/eusilc/index_en.html", "http://www.who.int/whosis/whostat/2008/en/index.html", "http://isi.cbs.nl/iaos/", "http://www.eabcn.org/eabcn-real-time-database", "http://www.ilo.org/public/english/bureau/stat/guides/cpi/index.htm", "http://imf.org/external/np/sta/bop/BOPman.pdf", "http://stats.oecd.org/glossary/detail.asp?ID=3029", "http://stats.oecd.org/glossary/index.htm", "http://www.oecd.org/dataoecd/46/17/37671574.pdf", "http://www.oecd.org/statistics/understandingeconomicstatistics", "http://www.philadelphiafed.org/research-and-data/real-time-center/real-time-data/", "http://sdmx.org/wp-content/uploads/2008/02/sdmx_annex4_metadata_common_vocabulary_draft_february_2008.doc", "http://data.un.org/Glossary.aspx?q=data+security", "http://data.un.org/Glossary.aspx?q=questionnaire", "http://data.un.org/Glossary.aspx?q=relevance", "http://unstats.un.org/unsd/censuskb/attachments/2001NLD_Registers-", "http://unstats.un.org/unsd/demographic/sources/census/2010_PHC/docs/resolution_A_2005_13.pdf", "http://unstats.un.org/unsd/dnss/gp/fundprinciples.aspx", "http://unstats.un.org/unsd/statcom/stacom_archive/brochures/for%20web/Brochure%20-%20Environment.pdf", "http://www.un.org/esa/progareas/stats.html", "http://www.unece.org/stats/archive/docs.fp.e.html", "http://www.unece.org/stats/census/", "http://www.unece.org/stats/documents/2000/11/metis/crp.2.e.pdf", "http://www.unece.org/stats/publications/editingglossary.pdf", "http://www1.unece.org/stat/platform/display/disaarchive/Classification+of+Statistical+Activities", "http://www1.unece.org/stat/platform/display/metis/The+Generic+Statistical+Business+Process+Model", "http://www.uis.unesco.org/ev.php?ID=7167_201&ID2=DO_TOPIC", "http://web.worldbank.org/WBSITE/EXTERNAL/DATASTATISTICS/ICPEXT/0,,menuPK:1973757~pagePK:62002243~piPK:62002387~theSitePK:270065,00.html", "https://www.un.org/ecosoc/"]}, "Berlin procedure": {"categories": ["Time series"], "title": "Berlin procedure", "method": "Berlin procedure", "url": "https://en.wikipedia.org/wiki/Berlin_procedure", "summary": "The Berlin procedure (BV) is a mathematical procedure for time series decomposition and seasonal adjustment of monthly and quarterly economic time series. The mathematical foundations of the procedure were developed in 1960's at the Technical University of Berlin and the German Institute for Economic Research (DIW). The most important user of the procedure is the Federal Statistical Office of Germany. \nFor the latest version 4.1 of BV a BV4.1 software is available as freeware for non-commercial purposes.", "images": [], "links": ["BV4.1 (software)", "Federal Statistical Office of Germany", "Freeware", "German Institute for Economic Research", "Linear regression", "Seasonal adjustment", "Technical University of Berlin", "Time series", "X-12-ARIMA"], "references": ["http://www.destatis.de/DE/Publikationen/WirtschaftStatistik/AllgemeinesMethoden/UmstellungZeitreihenanalyse111983.pdf?__blob=publicationFile", "http://www.destatis.de/EN/Methods/TimeSeries/DecompositionBV41.pdf?__blob=publicationFile", "http://www.destatis.de/EN/Methods/TimeSeries/SeasonalAdjustment.pdf?__blob=publicationFile", "http://www.destatis.de/EN/Methods/TimeSeries/TimeSeriesAnalysis.html"]}, "Chain rule for Kolmogorov complexity": {"categories": ["Algorithmic information theory", "All articles lacking in-text citations", "All articles with unsourced statements", "Articles containing proofs", "Articles lacking in-text citations from July 2014", "Articles with unsourced statements from July 2014", "Computability theory", "Information theory", "Theory of computation"], "title": "Chain rule for Kolmogorov complexity", "method": "Chain rule for Kolmogorov complexity", "url": "https://en.wikipedia.org/wiki/Chain_rule_for_Kolmogorov_complexity", "summary": "The chain rule for Kolmogorov complexity is an analogue of the chain rule for information entropy, which states:\n\n \n \n \n H\n (\n X\n ,\n Y\n )\n =\n H\n (\n X\n )\n +\n H\n (\n Y\n \n |\n \n X\n )\n \n \n {\\displaystyle H(X,Y)=H(X)+H(Y|X)}\n That is, the combined randomness of two sequences X and Y is the sum of the randomness of X plus whatever randomness is left in Y once we know X.\nThis follows immediately from the definitions of conditional and joint entropy, and the fact from probability theory that the joint probability is the product of the marginal and conditional probability:\n\n \n \n \n P\n (\n X\n ,\n Y\n )\n =\n P\n (\n X\n )\n P\n (\n Y\n \n |\n \n X\n )\n \n \n {\\displaystyle P(X,Y)=P(X)P(Y|X)}\n \n\n \n \n \n \u21d2\n log\n \u2061\n P\n (\n X\n ,\n Y\n )\n =\n log\n \u2061\n P\n (\n X\n )\n +\n log\n \u2061\n P\n (\n Y\n \n |\n \n X\n )\n \n \n {\\displaystyle \\Rightarrow \\log P(X,Y)=\\log P(X)+\\log P(Y|X)}\n The equivalent statement for Kolmogorov complexity does not hold exactly; it is true only up to a logarithmic term:\n\n \n \n \n K\n (\n x\n ,\n y\n )\n =\n K\n (\n x\n )\n +\n K\n (\n y\n \n |\n \n x\n )\n +\n O\n (\n log\n \u2061\n (\n K\n (\n x\n ,\n y\n )\n )\n )\n \n \n {\\displaystyle K(x,y)=K(x)+K(y|x)+O(\\log(K(x,y)))}\n (An exact version, KP(x, y) = KP(x) + KP(y|x*) + O(1),\nholds for the prefix complexity KP, where x* is a shortest program for x.)\nIt states that the shortest program printing X and Y is obtained by concatenating a shortest program printing X with a program printing Y given X, plus at most a logarithmic factor. The results implies that algorithmic mutual information, an analogue of mutual information for Kolmogorov complexity is symmetric: I(x:y) = I(y:x) + O(log K(x,y)) for all x,y.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Big-O notation", "Conditional entropy", "Conditional probability", "Information entropy", "International Standard Book Number", "Joint entropy", "Joint probability", "Kolmogorov complexity", "Logarithm", "Marginal probability", "Mutual information", "Probability theory", "Randomness", "Recursively enumerable", "Springer-Verlag"], "references": []}, "Fuzzy logic": {"categories": ["All Wikipedia articles needing clarification", "All articles with specifically marked weasel-worded phrases", "All articles with unsourced statements", "Articles with specifically marked weasel-worded phrases from July 2015", "Articles with unsourced statements from May 2018", "Articles with unsourced statements from September 2017", "Artificial intelligence", "CS1 maint: Archived copy as title", "CS1 maint: Explicit use of et al.", "Fuzzy logic", "Logic in computer science", "Non-classical logic", "Probability interpretations", "Wikipedia articles needing clarification from July 2015", "Wikipedia articles needing clarification from May 2018"], "title": "Fuzzy logic", "method": "Fuzzy logic", "url": "https://en.wikipedia.org/wiki/Fuzzy_logic", "summary": "Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1.\nThe term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Lotfi Zadeh. Fuzzy logic had however been studied since the 1920s, as infinite-valued logic\u2014notably by \u0141ukasiewicz and Tarski.It is based on the observation that people make decisions based on imprecise and non-numerical information, fuzzy models or sets are mathematical means of representing vagueness and imprecise information, hence the term fuzzy. These models have the capability of recognising, representing, manipulating, interpreting, and utilising data and information that are vague and lack certainty.Fuzzy logic has been applied to many fields, from control theory to artificial intelligence.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/61/Fuzzy_logic_temperature_en.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7c/Logic_portal.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Nicolas_P._Rougier%27s_rendering_of_the_human_brain.png", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Actor\u2013network theory", "Adaptive neuro fuzzy inference system", "Addison-Wesley", "Adjectives", "Adverbs", "Alfred Tarski", "Anti-lock braking system", "Antipositivism", "Antiscience", "Artificial intelligence", "Artificial neural network", "Axiomatic system", "BL (logic)", "Bart Kosko", "Bayes' theorem", "Bibliometrics", "Boolean algebra", "Boolean logic", "Boundary-work", "CiteSeerX", "Citizen science", "Citizendium", "Classical logic", "Classical mathematics", "Co-production (society)", "Consilience", "Constructive analysis", "Constructive set theory", "Control theory", "Criticism of technology", "Cybernetics and Systems Analysis", "Cyborg anthropology", "Defuzzification", "Degree of truth", "Demarcation problem", "Dematerialization (products)", "Dempster-Shafer theory", "Deontic logic", "Description logic", "Dialetheism", "Diffusion of innovations", "Digital anthropology", "Digital divide", "Digital object identifier", "Disruptive innovation", "Double hermeneutic", "Doxastic logic", "Early adopter", "Economics", "Economics of science", "Economics of scientific knowledge", "Empiricism", "Engineering studies", "Epistemic modal logic", "Evidence-based policy", "Existential quantifier", "Expert system", "FSQL", "Factor 10", "False dilemma", "Feed forward (control)", "Feminist technoscience", "Formal system", "Four-valued logic", "FuzzyCLIPS", "Fuzzy Control Language", "Fuzzy architectural spatial analysis", "Fuzzy classification", "Fuzzy concept", "Fuzzy control system", "Fuzzy electronics", "Fuzzy finite element", "Fuzzy logic (disambiguation)", "Fuzzy markup language", "Fuzzy mathematics", "Fuzzy rule", "Fuzzy set", "Fuzzy set operations", "Fuzzy set theory", "Fuzzy subalgebra", "George Ji\u0159\u00ed Klir", "G\u00f6del", "Hedge (linguistics)", "Heyting arithmetic", "High Performance Fuzzy Computing", "History", "History and philosophy of science", "History of science", "History of science and technology", "History of science policy", "History of technology", "Hype cycle", "IEC 61131", "IEEE 1164", "IEEE 1855", "IEEE Computational Intelligence Society", "IEEE Standards Association", "Infimum", "Innovation", "International Standard Book Number", "International Standard Serial Number", "Interval finite element", "Intuitionism", "Intuitionistic logic", "Intuitionistic type theory", "JSTOR", "Jan \u0141ukasiewicz", "Kluwer Academic Publishers", "Leapfrogging", "Learning algorithms", "Leslie Valiant", "Linear logic", "Linear model of innovation", "Logic synthesis", "Logical conjunction", "Logistic function", "Lotfi A. Zadeh", "Lukasiewicz fuzzy logic", "MIT Press", "MTL (logic)", "Machine learning", "Many-valued logic", "Mapping controversies", "Maria Zemankova", "Mathematical formula", "Mathematical logic", "Mathematical model", "Modal logic", "Modal operator", "Neuro-fuzzy", "Noise-based logic", "Non-classical logic", "Normal science", "Normalization process theory", "Ontology", "Ontology language", "Operator (computer programming)", "P. M. Pu", "Paraconsistent logic", "Paradigm shift", "Petr H\u00e1jek", "Philosophy", "Philosophy of science", "Philosophy of social science", "Philosophy of technology", "Policy", "Politicization of science", "Positivism", "Possibility theory", "Post-normal science", "Postpositivism", "Predicate logic", "Prentice Hall", "Prentice Hall PTR", "Probability", "Propositional logic", "Pseudoscience", "Recursively enumerable", "Regulation of science", "Relational database", "Relevance logic", "Research ethics", "Residuated lattice", "Reverse salient", "Rhetoric of science", "Richard Onses", "Rough set", "Rudolf Kruse", "SQLf", "Scholarpedia", "Science and technology studies", "Science communication", "Science education", "Science of science policy", "Science of team science", "Science policy", "Science studies", "Science wars", "Scientific consensus", "Scientific controversy", "Scientific enterprise", "Scientific method", "Scientific misconduct", "Scientometrics", "Sendai", "Sigmoid function", "Skunkworks project", "Social construction of technology", "Social constructivism", "Social epistemology", "Social shaping of technology", "Socio-scientific issues", "Sociology", "Sociology of knowledge", "Sociology of scientific ignorance", "Sociology of scientific knowledge", "Sociology of the history of science", "Sociotechnical system", "Sociotechnology", "Sorites paradox", "Stanford Encyclopedia of Philosophy", "Strong programme", "Structural rule", "Structure (mathematical logic)", "Subjective probability", "Substructural logic", "Supremum", "T-norm", "T-norm fuzzy logics", "Technical change", "Technological change", "Technological convergence", "Technological determinism", "Technological innovation system", "Technological revolution", "Technological transitions", "Technology", "Technology and society", "Technology assessment", "Technology dynamics", "Technology policy", "Technology transfer", "Technoscience", "Temporal logic", "Theories of technology", "Three-state logic", "Three-valued logic", "Traditional ecological knowledge", "Traditional knowledge", "Transition management (governance)", "Tri-state buffer", "Truth value", "Turing machine", "Type-2 fuzzy sets and systems", "Unity of science", "Universal quantifier", "User innovation", "VHDL", "Vagueness", "Variable (mathematics)", "Vector logic", "Verilog", "W3C", "Wiley-Interscience", "Women in STEM fields", "Women in engineering", "Women in science", "XML", "XML Schema", "\u0141ukasiewicz logic"], "references": ["http://www.beyondwilber.ca/books/mandala/holism_mysticism/fuzziness-exactness.html", "http://www.cirvirlab.com/simulation/fuzzy_logic_calculator.php", "http://www.fuzzylite.com/", "http://www.fuzzytech.com/binaries/ieccd1.pdf", "http://www.sciencedirect.com/science/article/pii/S1568494609002014", "http://news.mit.edu/2015/more-flexible-machine-learning-1001", "http://web.mit.edu/6.863/www/fall2012/projects/writeups/semantic-similarity-betweenverbs.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.8029", "http://plato.stanford.edu/entries/logic-fuzzy/", "http://sipi.usc.edu/~kosko/Fuzziness_Vs_Probability.pdf", "http://en.citizendium.org/wiki/Formal_fuzzy_logic", "http://doi.org/10.1002%2Fhyp.7831", "http://doi.org/10.1007%2F978-3-642-35488-5", "http://doi.org/10.1007%2F978-3-642-35488-5_1", "http://doi.org/10.1007%2FBF02742068", "http://doi.org/10.1007%2Fs001530100128", "http://doi.org/10.1007%2Fs10958-005-0281-1", "http://doi.org/10.1007%2Fs11269-005-9015-x", "http://doi.org/10.1016%2F0022-247X(80)90048-7", "http://doi.org/10.1016%2F0165-0114(94)00299-M", "http://doi.org/10.1016%2FS0019-9958(65)90241-X", "http://doi.org/10.1016%2FS0019-9958(68)90211-8", "http://doi.org/10.1016%2FS0019-9958(70)80032-8", "http://doi.org/10.1016%2Fj.asoc.2009.10.011", "http://doi.org/10.1016%2Fj.asoc.2014.10.035", "http://doi.org/10.1016%2Fj.fss.2004.03.027", "http://doi.org/10.1016%2Fj.fss.2005.05.029", "http://doi.org/10.1016%2Fj.jhydrol.2006.05.007", "http://doi.org/10.1016%2Fj.jhydrol.2012.03.031", "http://doi.org/10.1016%2Fj.tcs.2003.12.004", "http://doi.org/10.1016%2Fs0019-9958(65)90241-x", "http://doi.org/10.1023%2FA:1011958407631", "http://doi.org/10.1038%2Fscientificamerican0793-76", "http://doi.org/10.1080%2F03081079.2015.1076403", "http://doi.org/10.1109%2FPGEC.1963.263419", "http://doi.org/10.1177%2F0049124117729693", "http://doi.org/10.1623%2Fhysj.52.4.793", "http://doi.org/10.2178%2Fjsl%2F1140641166", "http://doi.org/10.2307%2F2964111", "http://doi.org/10.2307%2F421060", "http://doi.org/10.4249%2Fscholarpedia.2031", "http://www.jstor.org/stable/2964111", "http://www.jstor.org/stable/421060", "http://www.scholarpedia.org/article/Fuzzy_Logic", "http://www.scholarpedia.org/article/Fuzzy_sets", "http://www.scholarpedia.org/article/Modeling_with_words", "http://www.worldcat.org/issn/0019-9958", "http://www.worldcat.org/issn/0022-247X", "http://www.worldcat.org/issn/0022-4812", "http://www.worldcat.org/issn/0039-3215", "http://www.worldcat.org/issn/0165-0114", "http://www.worldcat.org/issn/0933-5846", "http://www.worldcat.org/issn/1072-3374", "http://www.worldcat.org/issn/1434-9922", "http://www.worldcat.org/issn/1568-4946", "http://www.worldcat.org/issn/1815-5936", "https://www.sfu.ca/~jeffpell/papers/ReviewHajek.pdf", "https://books.google.com/?id=-ZXJDQAAQBAJ&pg=PA47&dq=For+instance,+a+temperature+measurement+for+anti-lock+brakes+might+have+several+separate+membership+functions+defining+particular+temperature+ranges+needed+to+control+the+brakes+properly.+Each+function+maps+the+same+temperature+value+to+a+truth+value+in+the+0+to+1+range.+These+truth+values+can+then+be+used+to+determine+how+the+brakes+should+be+controlled#v=onepage&q=For%20instance,%20a%20temperature%20measurement%20for%20anti-lock%20brakes%20might%20have%20several%20separate%20membership%20functions%20defining%20particular%20temperature%20ranges%20needed%20to%20control%20the%20brakes%20properly.%20Each%20function%20maps%20the%20same%20temperature%20value%20to%20a%20truth%20value%20in%20the%200%20to%201%20range.%20These%20truth%20values%20can%20then%20be%20used%20to%20determine%20how%20the%20brakes%20should%20be%20controlled&f=false", "https://books.google.com/?id=QBBADwAAQBAJ&pg=SA4-PA13&lpg=SA4-PA13&dq=Both+degrees+of+truth+and+probabilities+range+between+0+and+1+and+hence+may+seem+similar+at+first,+but+fuzzy+logic+uses+degrees+of+truth+as+a+mathematical+model+of+vagueness,+while+probability+is+a+mathematical+model+of+ignorance#v=onepage&q=Both%20degrees%20of%20truth%20and%20probabilities%20range%20between%200%20and%201%20and%20hence%20may%20seem%20similar%20at%20first,%20but%20fuzzy%20logic%20uses%20degrees%20of%20truth%20as%20a%20mathematical%20model%20of%20vagueness,%20while%20probability%20is%20a%20mathematical%20model%20of%20ignorance&f=false", "https://books.google.com/books?hl=fr&lr=&id=IkajJC9iGxMC&oi=fnd&pg=PA73&ots=wCguK3mg5U&sig=s0AeSESut1p9dXQriXJG01oJ3ac", "https://mechanicalsite.com/157/what-is-fuzzy-logic", "https://www.sciencedirect.com/science/article/pii/S156849461400547X", "https://www2.eecs.berkeley.edu/Faculty/Homepages/zadeh.html", "https://www.creighton.edu/fileadmin/user/CCAS/programs/fuzzy_math/docs/MOU.pdf", "https://web.archive.org/web/20061205114153/http://blog.peltarion.com/2006/10/25/fuzzy-math-part-1-the-theory", "https://web.archive.org/web/20090413125658/http://www.scholarpedia.org/article/Fuzzy_sets", "https://web.archive.org/web/20120730155249/https://www.creighton.edu/fileadmin/user/CCAS/programs/fuzzy_math/docs/MOU.pdf", "https://web.archive.org/web/20151004060002/http://web.mit.edu/6.863/www/fall2012/projects/writeups/semantic-similarity-betweenverbs.pdf", "https://web.archive.org/web/20160303172812/http://www.sfu.ca/~jeffpell/papers/ReviewHajek.pdf", "https://web.archive.org/web/20170211080227/https://www2.eecs.berkeley.edu/Faculty/Homepages/zadeh.html", "https://ieeexplore.ieee.org/iel7/10207/7587461/07587505.pdf"]}, "Hubbert curve": {"categories": ["Continuous distributions", "Economics curves", "Equations", "Peak oil"], "title": "Hubbert curve", "method": "Hubbert curve", "url": "https://en.wikipedia.org/wiki/Hubbert_curve", "summary": "The Hubbert curve is an approximation of the production rate of a resource over time. It is a symmetric logistic distribution curve, often confused with the \"normal\" gaussian function. It first appeared in \"Nuclear Energy and the Fossil Fuels,\" geologist M. King Hubbert's 1956 presentation to the American Petroleum Institute, as an idealized symmetric curve, during his tenure at the Shell Oil Company. It has gained a high degree of popularity in the scientific community for predicting the depletion of various natural resources. The curve is the main component of Hubbert peak theory, which has led to the rise of peak oil concerns. Basing his calculations on the peak of oil well discovery in 1948, Hubbert used his model in 1956 to create a curve which predicted that oil production in the contiguous United States would peak around 1970.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/03/Hubbert_curve.svg"], "links": ["Association for the Study of Peak Oil and Gas", "Bioeconomics (biophysical)", "Cod", "Energy Accounting", "Gaussian function", "Hubbert peak theory", "Jean Laherr\u00e8re", "Logistic distribution", "M. King Hubbert", "Normal distribution", "Peak coal", "Peak copper", "Peak gas", "Peak helium", "Peak oil", "Peak uranium", "Peak water", "Probability density function", "Shell Oil Company", "Thermoeconomics", "Whaling"], "references": ["http://www.hubbertpeak.com/hubbert/1956/1956.pdf", "http://www.hubbertpeak.com/hubbert/Bibliography.htm", "http://www.hubbertpeak.com/laherrere/multihub.htm", "http://sepwww.stanford.edu/sep/jon/hubbert.pdf", "http://www.aspoitalia.net/index.php?option=com_content&task=view&id=34&Itemid=39", "http://dieoff.org/page191.htm", "https://www.researchgate.net/publication/228663031_Exponential_growth_energetic_Hubbert_cycles_and_the_advancement_of_technology", "https://web.archive.org/web/20080527233843/http://www.hubbertpeak.com/hubbert/1956/1956.pdf"]}, "Law (stochastic processes)": {"categories": ["All articles lacking sources", "All stub articles", "Articles lacking sources from November 2009", "Probability stubs", "Stochastic processes"], "title": "Law (stochastic processes)", "method": "Law (stochastic processes)", "url": "https://en.wikipedia.org/wiki/Law_(stochastic_processes)", "summary": "In mathematics, the law of a stochastic process is the measure that the process induces on the collection of functions from the index set into the state space. The law encodes a lot of information about the process; in the case of a random walk, for example, the law is the probability distribution of the possible trajectories of the walk.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Brownian motion", "Classical Wiener measure", "Currying", "Finite-dimensional distribution", "Function (mathematics)", "Index set", "Mathematics", "Measurable function", "Measurable space", "Measure (mathematics)", "Probability", "Probability measure", "Probability space", "Pushforward measure", "Random walk", "Sample continuous process", "Stochastic process"], "references": []}, "Omitted-variable bias": {"categories": ["All articles lacking in-text citations", "All articles needing expert attention", "Articles lacking in-text citations from July 2010", "Articles needing expert attention from February 2018", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Bias", "Regression analysis", "Statistics articles needing expert attention"], "title": "Omitted-variable bias", "method": "Omitted-variable bias", "url": "https://en.wikipedia.org/wiki/Omitted-variable_bias", "summary": "In statistics, omitted-variable bias (OVB) occurs when a statistical model leaves out one or more relevant variables. The bias results in the model attributing the effect of the missing variables to the estimated effects of the included variables.\nMore specifically, OVB is the bias that appears in the estimates of parameters in a regression analysis, when the assumed specification is incorrect in that it omits an independent variable that is correlated with both the dependent variable and one or more of the included independent variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Academic bias", "Acquiescence bias", "Anchoring", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "Belief bias", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Choice-supportive bias", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Confirmation bias", "Confounding variable", "Congruence bias", "Consistency (statistics)", "Covariance", "Cultural bias", "Debiasing", "Dependent variable", "Digital object identifier", "Distinction bias", "Dunning\u2013Kruger effect", "Efficiency (statistics)", "Egocentric bias", "Emotional bias", "Errors and residuals in statistics", "Estimator bias", "Expected value", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Forecast bias", "Fundamental attribution error", "Funding bias", "Gauss\u2013Markov theorem", "Halo effect", "Healthy user bias", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "Impact bias", "In-group favoritism", "Independent variable", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "International Standard Book Number", "Lead time bias", "Least squares", "Length time bias", "Linear model", "Linear regression", "List of cognitive biases", "List of memory biases", "Matrix (mathematics)", "Matrix inversion", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Negativity bias", "Net bias", "Normalcy bias", "Omission bias", "Optimism bias", "Ordinary least squares", "Outcome bias", "Overton window", "Parameter", "Partial derivative", "Participation bias", "Precision bias", "Pro-innovation bias", "Publication bias", "Random variable", "Recall bias", "Regression analysis", "Reporting bias", "Response bias", "Restraint bias", "Sampling bias", "Selection bias", "Self-selection bias", "Self-serving bias", "Social comparison bias", "Social desirability bias", "Specification (regression)", "Spectrum bias", "Statistics", "Status quo bias", "Survivorship bias", "Systematic error", "Systemic bias", "Time-saving bias", "Total derivative", "Trait ascription bias", "Transpose", "United States news media and the Vietnam War", "Vector (mathematics)", "Verification bias", "Von Restorff effect", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://www3.wabash.edu/econometrics/EconometricsBook/chap18.htm", "http://doi.org/10.1080%2F07388940500339183"]}, "Epidemiological methods": {"categories": ["Epidemiology"], "title": "Epidemiological method", "method": "Epidemiological methods", "url": "https://en.wikipedia.org/wiki/Epidemiological_method", "summary": "The science of epidemiology has matured significantly from the times of Hippocrates, Semmelweis and John Snow. The techniques for gathering and analyzing epidemiological data vary depending on the type of disease being monitored but each study will have overarching similarities.", "images": [], "links": ["Absolute risk reduction", "Academic clinical trials", "Adaptive clinical trial", "Analysis of clinical trials", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Attributable risk", "Attributable risk in exposed", "Blind experiment", "Case definition", "Case fatality", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Cohort study", "Correlation does not imply causation", "Cross-sectional study", "Cumulative incidence", "Design of experiments", "Digital object identifier", "Ecological study", "Epi Info", "Epidemiological methods", "Epidemiology", "Evidence-based medicine", "Experiment", "First-in-man study", "Glossary of clinical research", "Hazard rate", "Hazard ratio", "Hippocrates", "Homogeneity and heterogeneity", "Ignaz Semmelweis", "In vitro", "In vivo", "Incidence (epidemiology)", "Incidence rate", "Infectivity", "Intention-to-treat analysis", "International Standard Book Number", "John Snow (physician)", "Koch's postulates", "Levin's attributable risk", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Meta-analysis", "Miquel Porta", "Molecular pathological epidemiology", "Morbidity", "Morbidity rate", "Mortality rate", "Multicenter trial", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "OpenEpi", "Outbreak", "Percent attributable risk", "Period prevalence", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Rate ratio", "Relative risk reduction", "Reproducibility", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Sanitary epidemiological reconnaissance", "Scientific control", "Seeding trial", "Selection bias", "Sensitivity (tests)", "Specificity (tests)", "Specificity and sensitivity", "Study design", "Survivorship bias", "Systematic review", "Vaccine trial", "Virulence"], "references": ["http://www.bmj.com/about-bmj/resources-readers/publications/epidemiology-uninitiated", "http://global.oup.com/academic/product/a-dictionary-of-epidemiology-9780199976737?cc=us&lang=en", "http://sphweb.bumc.bu.edu/otlt/MPH-Modules/EP/EP713_Causality/EP713_Causality_print.html", "http://www.sph.unc.edu/nccphp/training/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2841039", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3040598", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3043163", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3637979", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4589117", "http://www.ncbi.nlm.nih.gov/pubmed/20208016", "http://www.ncbi.nlm.nih.gov/pubmed/20949563", "http://www.ncbi.nlm.nih.gov/pubmed/21036793", "http://www.ncbi.nlm.nih.gov/pubmed/23307060", "http://www.ncbi.nlm.nih.gov/pubmed/26425136", "http://www.epimonitor.net/index.htm", "http://doi.org/10.1002%2Fijc.25714", "http://doi.org/10.1038%2Fmodpathol.2012.214", "http://doi.org/10.1093%2Fjnci%2Fdjq031", "http://doi.org/10.1136%2Fgut.2010.217182", "http://doi.org/10.1186%2Fs12982-015-0037-4", "https://web.archive.org/web/20030623032830/http://cebm.net/toolbox.asp", "https://web.archive.org/web/20061217105946/http://www.epidemiologic.org/", "https://web.archive.org/web/20070228224146/http://www.epidemiologic.org/forum/", "https://web.archive.org/web/20120323082628/http://www.epidemiology.ch/history/betaversion.htm"]}, "Gompertz\u2013Makeham law of mortality": {"categories": ["Actuarial science", "Applied probability", "CS1 Czech-language sources (cs)", "Medical aspects of death", "Population", "Senescence", "Statistical laws"], "title": "Gompertz\u2013Makeham law of mortality", "method": "Gompertz\u2013Makeham law of mortality", "url": "https://en.wikipedia.org/wiki/Gompertz%E2%80%93Makeham_law_of_mortality", "summary": "The Gompertz\u2013Makeham law\nstates that the human death rate is the sum of an age-independent component (the Makeham term, named after William Makeham) and an age-dependent component (the Gompertz function, named after Benjamin Gompertz), which increases exponentially with age. In a protected environment where external causes of death are rare (laboratory conditions, low mortality countries, etc.), the age-independent mortality component is often negligible. In this case the formula simplifies to a Gompertz law of mortality. In 1825, Benjamin Gompertz proposed an exponential increase in death rates with age.\nThe Gompertz\u2013Makeham law of mortality describes the age dynamics of human mortality rather accurately in the age window from about 30 to 80 years of age. At more advanced ages, some studies have found that death rates increase more slowly \u2013 a phenomenon known as the late-life mortality deceleration \u2013 but more recent studies disagree.\n\nThe decline in the human mortality rate before the 1950s was mostly due to a decrease in the age-independent (Makeham) mortality component, while the age-dependent (Gompertz) mortality component was surprisingly stable. Since the 1950s, a new mortality trend has started in the form of an unexpected decline in mortality rates at advanced ages and \"rectangularization\" of the survival curve.The hazard function for the Gompertz-Makeham distribution is most often characterised as \n \n \n \n h\n (\n x\n )\n =\n \u03b1\n \n e\n \n \u03b2\n x\n \n \n +\n \u03bb\n \n \n {\\displaystyle h(x)=\\alpha e^{\\beta x}+\\lambda }\n . The empirical magnitude of the beta-parameter is about .085, implying a doubling of mortality every .69/.085 = 8 years (Denmark, 2006).\nThe quantile function can be expressed in a closed-form expressions using the Lambert W function:\n\n \n \n \n Q\n (\n u\n )\n =\n \n \n \u03b1\n \n \u03b2\n \u03bb\n \n \n \n \u2212\n \n \n 1\n \u03bb\n \n \n ln\n \u2061\n (\n 1\n \u2212\n u\n )\n \u2212\n \n \n 1\n \u03b2\n \n \n \n W\n \n 0\n \n \n \n (\n \n \n \n \u03b1\n \n e\n \n \u03b1\n \n /\n \n \u03bb\n \n \n (\n 1\n \u2212\n u\n \n )\n \n \u2212\n (\n \u03b2\n \n /\n \n \u03bb\n )\n \n \n \n \u03bb\n \n \n )\n \n \n \n {\\displaystyle Q(u)={\\frac {\\alpha }{\\beta \\lambda }}-{\\frac {1}{\\lambda }}\\ln(1-u)-{\\frac {1}{\\beta }}W_{0}\\left({\\frac {\\alpha e^{\\alpha /\\lambda }(1-u)^{-(\\beta /\\lambda )}}{\\lambda }}\\right)}\n The Gompertz law is the same as a Fisher\u2013Tippett distribution for the negative of age, restricted to negative values for the random variable (positive values for age).", "images": ["https://upload.wikimedia.org/wikipedia/en/4/4d/USGompertzCurve.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benjamin Gompertz", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biodemography", "Biodemography of human longevity", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Demography", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential growth", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Fisher\u2013Tippett distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gerontology", "Gerontology (journal)", "Gompertz distribution", "Gompertz function", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hazard function", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Lambert W function", "Landau distribution", "Laplace distribution", "Late-life mortality deceleration", "Life table", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum life span", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Mortality rate", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Reliability theory of aging and longevity", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "William Makeham", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-55920", "http://doi.org/10.1016%2Fj.matcom.2009.02.002", "http://doi.org/10.1098%2Frstl.1825.0026", "http://doi.org/10.1159%2F000213111", "http://longevity-science.org/pdf/Mortality-NAAJ-2011.pdf", "https://www.cdc.gov/nchs/data/nvsr/nvsr54/nvsr54_14.pdf", "https://archive.org/details/jstor-41134925"]}, "Training set": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from December 2012", "Articles with unsourced statements from October 2017", "Datasets in machine learning", "Machine learning", "Validity (statistics)"], "title": "Training, validation, and test sets", "method": "Training set", "url": "https://en.wikipedia.org/wiki/Training,_validation,_and_test_sets", "summary": "In machine learning, the study and construction of algorithms that can learn from and make predictions on data is a common task. Such algorithms work by making data-driven predictions or decisions, through building a mathematical model from input data.\nThe data used to build the final model usually comes from multiple datasets. In particular, three data sets are commonly used in different stages of the creation of the model.\nThe model is initially fit on a training dataset, that is a set of examples used to fit the parameters (e.g. weights of connections between neurons in artificial neural networks) of the model. The model (e.g. a neural net or a naive Bayes classifier) is trained on the training dataset using a supervised learning method (e.g. gradient descent or stochastic gradient descent). In practice, the training dataset often consist of pairs of an input vector (or scalar) and the corresponding output vector (or scalar), which is commonly denoted as the target (or label). The current model is run with the training dataset and produces a result, which is then compared with the target, for each input vector in the training dataset. Based on the result of the comparison and the specific learning algorithm being used, the parameters of the model are adjusted. The model fitting can include both variable selection and parameter estimation.\nSuccessively, the fitted model is used to predict the responses for the observations in a second dataset called the validation dataset. The validation dataset provides an unbiased evaluation of a model fit on the training dataset while tuning the model's hyperparameters (e.g. the number of hidden units in a neural network). Validation datasets can be used for regularization by early stopping: stop training when the error on the validation dataset increases, as this is a sign of overfitting to the training dataset.\nThis simple procedure is complicated in practice by the fact that the validation dataset's error may fluctuate during training, producing multiple local minima. This complication has led to the creation of many ad-hoc rules for deciding when overfitting has truly begun.Finally, the test dataset is a dataset used to provide an unbiased evaluation of a final model fit on the training dataset.. When the data in the test dataset has never been used in training (for example in cross-validation), the test dataset is also called a holdout dataset.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0e/Traintest.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accuracy", "Array data structure", "Artificial neural networks", "Classifier (machine learning)", "Cross-validation (statistics)", "Data", "Dataset", "Early stopping", "Estimation theory", "Feature selection", "Gradient descent", "Hyperparameter (machine learning)", "Independence (probability theory)", "International Standard Book Number", "Klaus-Robert M\u00fcller", "List of datasets for machine learning research", "Machine Learning (journal)", "Machine learning", "Mathematical model", "Mean squared error", "Naive Bayes classifier", "Neural net", "Overfit", "Overfitting", "Precision and recall", "Probability distribution", "Regularization (mathematics)", "Sensitivity and specificity", "Statistical classification", "Stochastic gradient descent", "Supervised learning"], "references": ["http:ftp://ftp.sas.com/pub/neural/FAQ.html", "http:ftp://ftp.sas.com/pub/neural/FAQ.html#A_data", "http:ftp://ftp.sas.com/pub/neural/FAQ1.txt", "http://ai.stanford.edu/~ronnyk/glossary.html", "http://www-bcf.usc.edu/~gareth/ISL/", "https://www.amazon.com/Pattern-Recognition-Neural-Networks-Ripley/dp/0521717701", "https://machinelearningmastery.com/difference-test-validation-datasets/", "https://www.quora.com/What-is-training-validation-and-testing-data-sets-scenario-in-machine-learning", "https://link.springer.com/chapter/10.1007/978-3-642-35289-8_5", "https://stackoverflow.com/q/13610074/3924118", "https://www.researchgate.net/profile/Ron_Kohavi/publication/2352264_A_Study_of_Cross-Validation_and_Bootstrap_for_Accuracy_Estimation_and_Model_Selection/links/02e7e51bcc14c5e91c000000.pdf"]}, "Studentized range": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "Multiple comparisons", "Statistical ratios", "Summary statistics"], "title": "Studentized range", "method": "Studentized range", "url": "https://en.wikipedia.org/wiki/Studentized_range", "summary": "In statistics, the studentized range is the difference between the largest and smallest data in a sample measured in units of sample standard deviations, so long as the standard deviation used is independent of the data.\nThe studentized range, q, is named for William Sealy Gosset (who wrote under the pseudonym \"Student\"), and was introduced by him (1927). The concept was later presented by a number of actual students, Newman (1939) and Keuls (1952) and John Tukey in some unpublished notes. q is the basic statistic for the studentized range distribution, which is used for multiple comparison procedures, such as the single step procedure Tukey's range test , the Newman\u2013Keuls method, and the Duncan's step down procedure, and establishing confidence intervals that are still valid after data snooping has occurred.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Analysis of variance", "CiteSeerX", "Confidence interval", "Data snooping", "Digital object identifier", "Duncan's new multiple range test", "Estimation theory", "Expected value", "Hypothesis testing", "Independence (probability theory)", "Independent identically distributed", "International Standard Book Number", "John Tukey", "Multiple comparisons", "Multiple comparisons problem", "Newman\u2013Keuls method", "Normal distribution", "Null hypothesis", "Pooled variance", "Post-hoc analysis", "Random variable", "Sample (statistics)", "Sample mean", "Sample variance", "Standard deviation", "Statistics", "Student", "Student's t distribution", "Studentization", "Studentized range distribution", "Studentized residual", "Tukey's range test", "William Sealy Gosset"], "references": ["http://www.watpon.com/table/studen_range.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.2976", "http://doi.org/10.1007%2Fbf01908269", "http://doi.org/10.1093%2Fbiomet%2F31.1-2.20", "http://doi.org/10.1137%2Fs0036144501357233", "http://doi.org/10.2307%2F2332181"]}, "Wrapped Cauchy distribution": {"categories": ["Continuous distributions", "Directional statistics", "Pages using deprecated image syntax", "Wikipedia articles needing page number citations from November 2010"], "title": "Wrapped Cauchy distribution", "method": "Wrapped Cauchy distribution", "url": "https://en.wikipedia.org/wiki/Wrapped_Cauchy_distribution", "summary": "In probability theory and directional statistics, a wrapped Cauchy distribution is a wrapped probability distribution that results from the \"wrapping\" of the Cauchy distribution around the unit circle. The Cauchy distribution is sometimes known as a Lorentzian distribution, and the wrapped Cauchy distribution may sometimes be referred to as a wrapped Lorentzian distribution.\nThe wrapped Cauchy distribution is often found in the field of spectroscopy where it is used to analyze diffraction patterns (e.g. see Fabry\u2013P\u00e9rot interferometer)", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/15/WrappedCauchyCDF.png", "https://upload.wikimedia.org/wikipedia/commons/7/7e/WrappedCauchyPDF.png"], "links": ["ARGUS distribution", "Academic Press", "Academic Press, Inc.", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Closed form expression", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac comb", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Entropy (information theory)", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fabry\u2013P\u00e9rot interferometer", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fourier series", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gradshteyn and Ryzhik", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holomorphic function", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Iosif Moiseevich Ryzhik", "Irwin\u2013Hall distribution", "Izrail Solomonovich Gradshteyn", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kantilal Mardia", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Library of Congress Control Number", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McCullagh's parametrization of the Cauchy distributions", "Michail Yulyevich Tseytlin", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poisson kernel", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Taylor expansion", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unit circle", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Yuri Veniaminovich Geronimus", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.stat.uchicago.edu/~pmcc/pubs/paper18.pdf", "http://lccn.loc.gov/2010481177", "http://doi.org/10.1080%2F01621459.1978.10480031", "http://doi.org/10.1093%2Fbiomet%2F62.3.701", "http://doi.org/10.1093%2Fbiomet%2F79.2.247", "http://www.jstor.org/stable/2242674", "http://www.jstor.org/stable/2286549", "https://www.amazon.com/Directional-Statistics-Kanti-V-Mardia/dp/0471953334/ref=sr_1_1?s=books&ie=UTF8&qid=1311003484&sr=1-1#reader_0471953334", "https://books.google.com/books?id=IIpeevaNH88C&dq=%22circular+variance%22+fisher&source=gbs_navlinks_s", "https://books.google.com/books?id=R3GpDglVOSEC&printsec=frontcover&source=gbs_navlinks_s#v=onepage&q=&f=false"]}, "Jaccard index": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from March 2011", "Clustering criteria", "Index numbers", "Measure theory", "Similarity and distance measures", "String similarity measures"], "title": "Jaccard index", "method": "Jaccard index", "url": "https://en.wikipedia.org/wiki/Jaccard_index", "summary": "The Jaccard index, also known as Intersection over Union and the Jaccard similarity coefficient (originally coined coefficient de communaut\u00e9 by Paul Jaccard), is a statistic used for comparing the similarity and diversity of sample sets. The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the intersection divided by the size of the union of the sample sets:\n\n \n \n \n J\n (\n A\n ,\n B\n )\n =\n \n \n \n \n |\n \n A\n \u2229\n B\n \n |\n \n \n \n \n |\n \n A\n \u222a\n B\n \n |\n \n \n \n \n =\n \n \n \n \n |\n \n A\n \u2229\n B\n \n |\n \n \n \n \n |\n \n A\n \n |\n \n +\n \n |\n \n B\n \n |\n \n \u2212\n \n |\n \n A\n \u2229\n B\n \n |\n \n \n \n \n .\n \n \n {\\displaystyle J(A,B)={{|A\\cap B|} \\over {|A\\cup B|}}={{|A\\cap B|} \\over {|A|+|B|-|A\\cap B|}}.}\n (If A and B are both empty, we define J(A,B) = 1.) \n\n \n \n \n 0\n \u2264\n J\n (\n A\n ,\n B\n )\n \u2264\n 1.\n \n \n {\\displaystyle 0\\leq J(A,B)\\leq 1.}\n The Jaccard distance, which measures dissimilarity between sample sets, is complementary to the Jaccard coefficient and is obtained by subtracting the Jaccard coefficient from 1, or, equivalently, by dividing the difference of the sizes of the union and the intersection of two sets by the size of the union:\n\n \n \n \n \n d\n \n J\n \n \n (\n A\n ,\n B\n )\n =\n 1\n \u2212\n J\n (\n A\n ,\n B\n )\n =\n \n \n \n \n |\n \n A\n \u222a\n B\n \n |\n \n \u2212\n \n |\n \n A\n \u2229\n B\n \n |\n \n \n \n \n |\n \n A\n \u222a\n B\n \n |\n \n \n \n \n .\n \n \n {\\displaystyle d_{J}(A,B)=1-J(A,B)={{|A\\cup B|-|A\\cap B|} \\over |A\\cup B|}.}\n An alternate interpretation of the Jaccard distance is as the ratio of the size of the symmetric difference \n \n \n \n A\n \u25b3\n B\n =\n (\n A\n \u222a\n B\n )\n \u2212\n (\n A\n \u2229\n B\n )\n \n \n {\\displaystyle A\\triangle B=(A\\cup B)-(A\\cap B)}\n to the union. \nThis distance is a metric on the collection of all finite sets.There is also a version of the Jaccard distance for measures, including probability measures. If \n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n is a measure on a measurable space \n \n \n \n X\n \n \n {\\displaystyle X}\n , then we define the Jaccard coefficient by \n \n \n \n \n J\n \n \u03bc\n \n \n (\n A\n ,\n B\n )\n =\n \n \n \n \u03bc\n (\n A\n \u2229\n B\n )\n \n \n \u03bc\n (\n A\n \u222a\n B\n )\n \n \n \n \n \n {\\displaystyle J_{\\mu }(A,B)={{\\mu (A\\cap B)} \\over {\\mu (A\\cup B)}}}\n , and the Jaccard distance by \n \n \n \n \n d\n \n \u03bc\n \n \n (\n A\n ,\n B\n )\n =\n 1\n \u2212\n \n J\n \n \u03bc\n \n \n (\n A\n ,\n B\n )\n =\n \n \n \n \u03bc\n (\n A\n \u25b3\n B\n )\n \n \n \u03bc\n (\n A\n \u222a\n B\n )\n \n \n \n \n \n {\\displaystyle d_{\\mu }(A,B)=1-J_{\\mu }(A,B)={{\\mu (A\\triangle B)} \\over {\\mu (A\\cup B)}}}\n . Care must be taken if \n \n \n \n \u03bc\n (\n A\n \u222a\n B\n )\n =\n 0\n \n \n {\\displaystyle \\mu (A\\cup B)=0}\n or \n \n \n \n \u221e\n \n \n {\\displaystyle \\infty }\n , since these formulas are not well defined in these cases.\nThe MinHash min-wise independent permutations locality sensitive hashing scheme may be used to efficiently compute an accurate estimate of the Jaccard similarity coefficient of pairs of sets, where each set is represented by a constant-sized signature derived from the minimum values of a hash function.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1f/Intersection_of_sets_A_and_B.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2d/Intersection_over_Union_-_object_detection_bounding_boxes.jpg", "https://upload.wikimedia.org/wikipedia/commons/e/e6/Intersection_over_Union_-_poor%2C_good_and_excellent_score.png", "https://upload.wikimedia.org/wikipedia/commons/c/c7/Intersection_over_Union_-_visual_equation.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ee/Union_of_sets_A_and_B.svg"], "links": ["Binary numeral system", "Bit array", "Bitwise operation", "Computer vision", "Correlation", "Digital object identifier", "Distance function", "Diversity index", "Dummy variable (statistics)", "Hamming distance", "Hash function", "International Standard Book Number", "Intersection (set theory)", "Locality sensitive hashing", "Logical conjunction", "Logical disjunction", "Measurable space", "Measure (mathematics)", "MinHash", "Most frequent k characters", "Mutual information", "Object detection", "Paul Jaccard", "Probability measure", "Sample (statistics)", "Science (journal)", "Similarity measure", "Simple matching coefficient", "Statistic", "Symmetric difference", "S\u00f8rensen\u2013Dice coefficient", "Triangle inequality", "Tversky index", "Union (set theory)"], "references": ["http://www.gettingcirrius.com/2011/01/calculating-similarity-part-2-jaccard.html", "http://www.planetcalc.com/1664/", "http://www.pyimagesearch.com/2016/11/07/intersection-over-union-iou-for-object-detection/", "http://www-users.cs.umn.edu/~kumar/dmbook/dmslides/chap2_data.pdf", "http://sourceforge.net/projects/simmetrics/", "http://doi.org/10.1038%2F234034a0", "http://doi.org/10.1111%2Fj.1469-8137.1912.tb05611.x", "http://doi.org/10.1126%2Fscience.132.3434.1115", "http://www.worldcat.org/title/elementary-mathematical-theory-of-classification-and-prediction/oclc/10917698&referer=brief_results", "https://www.kaggle.com/c/dstl-satellite-imagery-feature-detection#evaluation", "https://arxiv.org/pdf/1612.02696.pdf"]}, "Focused information criterion": {"categories": ["All articles lacking in-text citations", "All articles lacking reliable references", "Articles lacking in-text citations from May 2015", "Articles lacking reliable references from March 2012", "Model selection", "Regression variable selection"], "title": "Focused information criterion", "method": "Focused information criterion", "url": "https://en.wikipedia.org/wiki/Focused_information_criterion", "summary": "In statistics, the focused information criterion (FIC) is a method for selecting the most appropriate model among a set of competitors for a given data set. Unlike most other model selection strategies, like the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the deviance information criterion (DIC), the FIC does not attempt to assess the overall fit of candidate models but focuses attention directly on the parameter of primary interest with the statistical analysis, say \n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n , for which competing models lead to different estimates, say \n \n \n \n \n \n \n \n \u03bc\n ^\n \n \n \n \n j\n \n \n \n \n {\\displaystyle {\\hat {\\mu }}_{j}}\n for model \n \n \n \n j\n \n \n {\\displaystyle j}\n . The FIC method consists in first developing an exact or approximate expression for the precision or quality of each estimator, say \n \n \n \n \n r\n \n j\n \n \n \n \n {\\displaystyle r_{j}}\n for \n \n \n \n \n \n \n \n \u03bc\n ^\n \n \n \n \n j\n \n \n \n \n {\\displaystyle {\\hat {\\mu }}_{j}}\n , and then use data to estimate these precision measures, say \n \n \n \n \n \n \n \n r\n ^\n \n \n \n \n j\n \n \n \n \n {\\displaystyle {\\hat {r}}_{j}}\n . In the end the model with best estimated precision is selected. The FIC methodology was developed by Gerda Claeskens and Nils Lid Hjort, first in two 2003 discussion articles in Journal of the American Statistical Association and later on in other papers and in their 2008 book.\nThe concrete formulae and implementation for FIC depend firstly on the particular parameter of interest, the choice of which does not depend on mathematics but on the scientific and statistical context. Thus the FIC apparatus may be selecting one model as most appropriate for estimating a quantile of a distribution but preferring another model as best for estimating the mean value. Secondly, the FIC formulae depend on the specifics of the models used for the observed data and also on how precision is to be measured. The clearest case is where precision is taken to be mean squared error, say \n \n \n \n \n r\n \n j\n \n \n =\n \n b\n \n j\n \n \n 2\n \n \n +\n \n \u03c4\n \n j\n \n \n 2\n \n \n \n \n {\\displaystyle r_{j}=b_{j}^{2}+\\tau _{j}^{2}}\n in terms of squared bias and variance for the estimator associated with model \n \n \n \n j\n \n \n {\\displaystyle j}\n . FIC formulae are then available in a variety of situations, both for handling parametric, semiparametric and nonparametric situations, involving separate estimation of squared bias and variance, leading to estimated precision \n \n \n \n \n \n \n \n r\n ^\n \n \n \n \n j\n \n \n \n \n {\\displaystyle {\\hat {r}}_{j}}\n . In the end the FIC selects the model with smallest estimated mean squared error.\nAssociated with the use of the FIC for selecting a good model is the FIC plot, designed to give a clear and informative picture of all estimates, across all candidate models, and their merit. It displays estimates on the \n \n \n \n y\n \n \n {\\displaystyle y}\n axis along with FIC scores on the \n \n \n \n x\n \n \n {\\displaystyle x}\n axis; thus estimates found to the left in the plot are associated with the better models and those found in the middle and to the right stem from models less or not adequate for the purpose of estimating the focus parameter in question.\nGenerally speaking, complex models (with many parameters relative to sample size) tend to lead to estimators with small bias but high variance; more parsimonious models (with fewer parameters) typically yield estimators with larger bias but smaller variance. The FIC method balances the two desired data of having small bias and small variance in an optimal fashion. The main difficulty lies with the bias \n \n \n \n \n b\n \n j\n \n \n \n \n {\\displaystyle b_{j}}\n , as it involves the distance from the expected value of the estimator to the true underlying quantity to be estimated, and the true data generating mechanism may lie outside each of the candidate models. \nIn situations where there is not a unique focus parameter, but rather a family of such, there are versions of average FIC (AFIC or wFIC) that find the best model in terms of suitably weighted performance measures, e.g. when searching for a regression model to perform particularly well in a portion of the covariate space. \nIt is also possible to keep several of the best models on board, ending the statistical analysis with a data-dicated weighted average of the estimators of the best FIC scores, typically giving highest weight to estimators associated with the best FIC scores. Such schemes of model averaging extend the direct FIC selection method.\nThe FIC methodology applies in particular to selection of variables in different forms of regression analysis, including the framework of generalised linear models and the semiparametric proportional hazards models (i.e. Cox regression).", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Akaike information criterion", "Bayesian information criterion", "Bias of an estimator", "Cambridge University Press", "Covariate", "Deviance information criterion", "Digital object identifier", "Estimator", "Generalized linear model", "Gerda Claeskens", "Hannan-Quinn information criterion", "Journal of the American Statistical Association", "Mean squared error", "Model selection", "Nils Lid Hjort", "Non-parametric statistics", "Parametric model", "Proportional hazards models", "Regression analysis", "Sample size", "Semiparametric model", "Statistics", "Variance"], "references": ["http://www.econ.kuleuven.ac.be/public/ndbaf45/modelselection/", "http://www.esi-topics.com/fbp/2005/august05-Hjort_Claeskens.html", "https://doi.org/10.1198%2F016214503000000819", "https://doi.org/10.1198%2F016214503000000828", "https://doi.org/10.1198%2F016214506000000069"]}, "Signal-to-noise ratio": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2015", "Audio amplifier specifications", "Electrical parameters", "Engineering ratios", "Error measures", "Measurement", "Noise (electronics)", "Statistical ratios", "Wikipedia articles needing clarification from April 2015"], "title": "Signal-to-noise ratio", "method": "Signal-to-noise ratio", "url": "https://en.wikipedia.org/wiki/Signal-to-noise_ratio", "summary": "Signal-to-noise ratio (abbreviated SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise.\nWhile SNR is commonly quoted for electrical signals, it can be applied to any form of signal, for example isotope levels in an ice core, biochemical signaling between cells, or financial trading signals. Signal-to-noise ratio is sometimes used metaphorically to refer to the ratio of useful information to false or irrelevant data in a conversation or exchange. For example, in online discussion forums and other online communities, off-topic posts and spam are regarded as \"noise\" that interferes with the \"signal\" of appropriate discussion.The signal-to-noise ratio, the bandwidth, and the channel capacity of a communication channel are connected by the Shannon\u2013Hartley theorem.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8e/Analyse_thermo_gravimetrique_bruit.png", "https://upload.wikimedia.org/wikipedia/commons/archive/8/8e/20110528170844%21Analyse_thermo_gravimetrique_bruit.png", "https://upload.wikimedia.org/wikipedia/commons/archive/8/8e/20100405225638%21Analyse_thermo_gravimetrique_bruit.png"], "links": ["16-bit", "20 log rule", "Acoustic quieting", "Acoustics", "Active noise control", "Additive white Gaussian noise", "Albert Rose (physicist)", "Alignment level", "Amplitude", "Analog-to-digital converter", "Analog Devices", "Anisotropic diffusion", "Architectural acoustics", "Atmospheric noise", "Audio engineering", "Audio system measurements", "Background noise", "Bandwidth (signal processing)", "Bilateral filter", "Biochemical signaling", "Block-matching and 3D filtering", "Brownian noise", "Burst noise", "Carrier-to-noise ratio", "Carrier-to-receiver noise density", "Carrier frequency", "Channel capacity", "Channel noise level", "Circuit noise level", "Coefficient of variation", "Colors of noise", "Comb filter", "Communication channel", "Contrast-to-noise ratio", "Contrast ratio", "Cosmic noise", "DBrnC", "DBu", "DPSK", "Decibel", "Distortion", "Dither", "Dynamic range", "Eb/N0", "Effect size", "Effective input noise temperature", "Electrical impedance", "Electronic noise", "Equivalent noise resistance", "Equivalent pulse code modulation noise", "Error", "Expected value", "Exponent", "Film speed", "Filter (signal processing)", "Financial signal processing", "Fixed point arithmetic", "Flicker noise", "Floating point", "Full-scale", "Gaussian blur", "Gaussian noise", "Generation loss", "Gradient noise", "Grey noise", "Health effects from noise", "Ice core", "Image", "Image noise", "Image processing", "Impulse noise (audio)", "Information", "Interference (communication)", "Interferometer", "International Standard Book Number", "Internet forum", "Isotope", "Jitter", "Johnson\u2013Nyquist noise", "List of noise topics", "Lock-in amplifier", "Logarithm", "Low-noise amplifier", "Low-pass filter", "Luminance", "Matched filter", "Maxim Integrated Products", "Mean", "Median filter", "Modulation error ratio", "Near-far problem", "Noise", "Noise, vibration, and harshness", "Noise (audio)", "Noise (electronic)", "Noise (electronics)", "Noise (radio)", "Noise (signal processing)", "Noise (video)", "Noise and vibration on maritime vessels", "Noise barrier", "Noise control", "Noise figure", "Noise floor", "Noise generator", "Noise margin", "Noise measurement", "Noise pollution", "Noise power", "Noise reduction", "Noise regulation", "Noise shaping", "Noise spectral density", "Noise temperature", "Nominal level", "Non-local means", "Off-topic", "Omega ratio", "Optical power", "Optical spectrum analyzer", "Peak signal-to-noise ratio", "Phase distortion", "Phase noise", "Pink noise", "Power (physics)", "Pseudorandom noise", "Quantization (signal processing)", "Quantization error", "Quantization noise", "Radio noise source", "Rane Corporation", "Reactance (electronics)", "Resistive", "Root mean square", "Root mean square (RMS) amplitude", "SINAD", "SINR", "Sawtooth wave", "Science and engineering", "Shannon\u2013Hartley theorem", "Shot noise", "Shrinkage Fields (image restoration)", "Signal-to-interference ratio", "Signal-to-noise ratio (imaging)", "Signal-to-noise statistic", "Signal-to-quantization-noise ratio", "Signal (electrical engineering)", "Signal (information theory)", "Signal to Noise (disambiguation)", "Signal to noise plus interference", "Signal to noise ratio (imaging)", "Sine wave", "Sound masking", "Soundproofing", "Spamming", "Spectrum analyzer", "Standard deviation", "Statistical noise", "Subjective video quality", "Thermal radiation", "Thermogravimetric analysis", "Total harmonic distortion", "Total variation denoising", "Value noise", "Variance", "Video quality", "Voltage", "Wavelet", "White noise", "Worley noise"], "references": ["http://www.analog.com/static/imported-files/tutorials/MT-003.pdf", "http://www.analog.com/static/imported-files/tutorials/MT-001.pdf", "http://www.maxim-ic.com/appnotes.cfm/appnote_number/641", "http://www.maxim-ic.com/appnotes.cfm/appnote_number/728", "http://www.sengpielaudio.com/calculator-noise.htm", "http://focus.ti.com/lit/an/sbaa055/sbaa055.pdf", "http://webdemo.inue.uni-stuttgart.de/webdemos/02_lectures/uebertragungstechnik_1/qam_constellation_diagram_from_snr", "http://www.circuitdesign.info/blog/2008/11/fundamentals-of-analogrf-design-noise-signal-power/", "http://www.scholarpedia.org/article/Signal-to-noise_ratio", "http://www.vias.org/simulations/simusoft_spectaccu.html", "https://books.google.com/books?id=7s8xpR-5rOUC&lpg=PA471", "https://books.google.com/books?id=8uGOnjRGEzoC&lpg=PA354", "https://books.google.com/books?id=VZvqqaQ5DvoC&lpg=PA280", "https://books.google.com/books?id=VmvY4MTMFTwC&lpg=PA471", "https://books.google.com/books?id=Vs2AM2cWl1AC&lpg=PA26", "https://books.google.com/books?id=W5bAcxc2TcgC&pg=PA128", "https://books.google.com/books?id=s0GjM_rY95kC", "https://books.google.com/books?id=v7E25646wz0C&pg=PA433", "https://web.archive.org/web/20060515074349/http://www.rane.com/note153.html", "https://web.archive.org/web/20060522134626/http://www.techonline.com/community/related_content/20771"]}, "Principle of maximum entropy": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2008", "Bayesian statistics", "CS1 maint: Extra text: editors list", "Entropy and information", "Mathematical principles", "Probability assessment", "Statistical principles"], "title": "Principle of maximum entropy", "method": "Principle of maximum entropy", "url": "https://en.wikipedia.org/wiki/Principle_of_maximum_entropy", "summary": "The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge is the one with largest entropy, in the context of precisely stated prior data (such as a proposition that expresses testable information).\nAnother way of stating this: Take precisely stated prior data or testable information about a probability distribution function. Consider the set of all trial probability distributions that would encode the prior data. According to this principle, the distribution with maximal information entropy is the best choice.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Admissible decision rule", "Akaike information criterion", "Approximate Bayesian computation", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernstein\u2013von Mises theorem", "Bibcode", "Bounded interval", "Brian Skyrms", "Channel coding", "Closed form solution", "Conjugate prior", "Conserved quantities", "Continuous distribution", "Convex optimization", "Credible interval", "Cromwell's rule", "Cross entropy", "Differential entropy", "Digital object identifier", "Dissipation", "E. T. Jaynes", "Edwin Thompson Jaynes", "Empirical Bayes method", "Empirical likelihood", "Entropy", "Entropy (information theory)", "Entropy maximization", "Ergodic", "Expected value", "Exponentially tilted empirical likelihood", "Gibbs distribution", "Gibbs measure", "Graham Wallis", "H. K. Kesavan", "Hyperparameter", "Hyperprior", "Inference", "Info-metrics", "Information entropy", "Information theory", "International Standard Book Number", "Interval (mathematics)", "JSTOR", "Journal of Econometrics", "Journal of the American Statistical Association", "Kinetic theory of gases", "Kullback\u2013Leibler divergence", "Lagrange multiplier", "Likelihood function", "Limiting density of discrete points", "Logical inference", "Logistic regression", "Machine learning", "Marginalization (probability)", "Markov chain Monte Carlo", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum entropy (disambiguation)", "Maximum entropy classifier", "Maximum entropy probability distribution", "Maximum entropy spectral estimation", "Maximum entropy thermodynamics", "Maxwell\u2013Boltzmann statistics", "Molecular chaos", "Multinomial distribution", "Mutually exclusive", "Natural language processing", "Numerical analysis", "Partition function (mathematics)", "Pitman\u2013Koopman theorem", "Posterior predictive distribution", "Posterior probability", "Principle of indifference", "Principle of maximum caliber", "Principle of transformation groups", "Prior information", "Prior probability", "Probability distribution", "Probability interpretations", "Probability kinematics", "Proposition", "PubMed Identifier", "Quadratic programming", "Radical probabilism", "Real numbers", "Relative entropy", "Richard Jeffrey", "Schwarz criterion", "Statistical ensemble", "Statistical mechanics", "Statistical thermodynamics", "Statistics", "Stirling's approximation", "Sufficiency (statistics)", "Support vector machine", "Symmetries", "Symmetry groups", "Thermodynamic equilibrium", "Uniform distribution (discrete)"], "references": ["http://www.sciencedirect.com/science/article/pii/S1566253512000139", "http://www.cs.cmu.edu/~./aberger/maxent.html", "http://adsabs.harvard.edu/abs/1957PhRv..106..620J", "http://adsabs.harvard.edu/abs/1957PhRv..108..171J", "http://adsabs.harvard.edu/abs/2001Entrp...3..191H", "http://adsabs.harvard.edu/abs/2017Entrp..19..381C", "http://repository.upenn.edu/cgi/viewcontent.cgi?article=1083&context=ircs_reports", "http://bayes.wustl.edu/etj/articles/brandeis.pdf", "http://bayes.wustl.edu/etj/articles/brandeis.ps.gz", "http://bayes.wustl.edu/etj/articles/cmonkeys.pdf", "http://bayes.wustl.edu/etj/articles/relationship.pdf", "http://bayes.wustl.edu/etj/articles/theory.1.pdf", "http://bayes.wustl.edu/etj/articles/theory.2.pdf", "http://bayes.wustl.edu/etj/node1.html", "http://cowles.econ.yale.edu/P/cd/d15b/d1569.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/18184793", "http://www.ams.org/mathscinet-getitem?mr=0087305", "http://www.ams.org/mathscinet-getitem?mr=0096414", "http://www.ams.org/mathscinet-getitem?mr=1825292", "http://doi.org/10.1007%2Fbf03023004", "http://doi.org/10.1007%2Fs00362-008-0149-9", "http://doi.org/10.1007%2Fs11009-007-9057-z", "http://doi.org/10.1007%2Fs11009-009-9133-7", "http://doi.org/10.1016%2Fj.inffus.2012.01.012", "http://doi.org/10.1016%2Fj.jeconom.2006.05.003", "http://doi.org/10.1080%2F10556799208230532", "http://doi.org/10.1093%2Fbiomet%2F90.2.319", "http://doi.org/10.1093%2Fbiomet%2F92.1.31", "http://doi.org/10.1103%2FPhysRev.106.620", "http://doi.org/10.1103%2FPhysRev.108.171", "http://doi.org/10.1109%2FTSSC.1968.300117", "http://doi.org/10.1523%2FJNEUROSCI.3359-07.2008", "http://doi.org/10.2307%2F2669786", "http://doi.org/10.3390%2Fe19080381", "http://doi.org/10.3390%2Fe3030191", "http://www.jstor.org/stable/2669786", "http://przyrbwn.icm.edu.pl/APP/PDF/117/a117z602.pdf", "http://homepages.inf.ed.ac.uk/s0450736/maxent.html", "https://link.springer.com/article/10.1007/s11009-007-9057-z", "https://link.springer.com/article/10.1007/s11009-009-9133-7", "https://web.archive.org/web/20060603144738/http://www.phys.uu.nl/~wwwgrnsl/jos/mepabst/mep.pdf", "https://arxiv.org/abs/0708.1593"]}, "SHAZAM (software)": {"categories": ["C++ software", "Econometrics software", "Regression and curve fitting software", "Simulation programming languages", "Statistical programming languages", "Time series software", "Windows-only software"], "title": "SHAZAM (software)", "method": "SHAZAM (software)", "url": "https://en.wikipedia.org/wiki/SHAZAM_(software)", "summary": "SHAZAM is a comprehensive econometrics and statistics package for estimating, testing, simulating and forecasting many types of econometrics and statistical models. SHAZAM was originally created in 1977 by Kenneth White.", "images": ["https://upload.wikimedia.org/wikipedia/en/0/0e/SHAZAM_Software_Logo.png"], "links": [".NET Framework", "ADMB", "Analyse-it", "BMDP", "BV4.1 (software)", "C++", "CSPro", "C Sharp (programming language)", "Comma-separated values", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "DBMS", "Data Desk", "Dataplot", "Desktop computer", "EViews", "Econometric software", "Econometrica", "Econometrics", "Epi Info", "FORTRAN", "Forecasting", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "International Standard Book Number", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Access", "Microsoft Excel", "Microsoft Windows", "Minitab", "Multiple document interface", "NCSS (statistical software)", "Open-source software", "OpenBUGS", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Programming language", "Proprietary software", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "Server computer", "Shazam (disambiguation)", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "Statistical analysis", "Statistical hypothesis testing", "Statistics", "StatsDirect", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "WinBUGS", "Windows", "Workstation", "World Programming System", "X-12-ARIMA", "XLSX", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://shazam.econ.ubc.ca/intro/", "http://shazam.econ.ubc.ca/intro/ref.htm", "http://shazam.econ.ubc.ca/intro/review.htm", "http://www.econometrics.com/", "http://www.econometrics.com/ref/", "http://ideas.repec.org/s/shz/shazam.html", "https://www.jstor.org/pss/1913664"]}, "Principal component regression": {"categories": ["Factor analysis", "Regression analysis"], "title": "Principal component regression", "method": "Principal component regression", "url": "https://en.wikipedia.org/wiki/Principal_component_regression", "summary": "In statistics, principal component regression (PCR) is a regression analysis technique that is based on principal component analysis (PCA). Typically, it considers regressing the outcome (also known as the response or the dependent variable) on a set of covariates (also known as predictors, or explanatory variables, or independent variables) based on a standard linear regression model, but uses PCA for estimating the unknown regression coefficients in the model.\nIn PCR, instead of regressing the dependent variable on the explanatory variables directly, the principal components of the explanatory variables are used as regressors. One typically uses only a subset of all the principal components for regression, thus making PCR some kind of a regularized procedure. Often the principal components with higher variances (the ones based on eigenvectors corresponding to the higher eigenvalues of the sample variance-covariance matrix of the explanatory variables) are selected as regressors. However, for the purpose of predicting the outcome, the principal components with low variances may also be important, in some cases even more important.One major use of PCR lies in overcoming the multicollinearity problem which arises when two or more of the explanatory variables are close to being collinear. PCR can aptly deal with such situations by excluding some of the low-variance principal components in the regression step. In addition, by usually regressing on only a subset of all the principal components, PCR can result in dimension reduction through substantially lowering the effective number of parameters characterizing the underlying model. This can be particularly useful in settings with high-dimensional covariates. Also, through appropriate selection of the principal components to be used for regression, PCR can lead to efficient prediction of the outcome based on the assumed model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Approximate", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bias of an estimator", "Canonical correlation", "Centering matrix", "Collinear", "Column space", "Column vector", "Constrained optimization", "Coordinate system", "Correlation and dependence", "Covariance matrix", "Cross-validation (statistics)", "Data matrix (multivariate statistics)", "Data transformation", "Deming regression", "Dependent and independent variables", "Digital object identifier", "Dimension (vector space)", "Dimension reduction", "Dimensionality reduction", "Discrete choice", "Efficient estimator", "Eigendecomposition of a matrix", "Eigenvalues", "Eigenvalues and eigenvectors", "Eigenvectors", "Errors-in-variables models", "Errors and residuals in statistics", "Estimation", "Estimator", "Feature space", "Fixed effects model", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Henri Theil", "High-dimensional statistics", "Inner product", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society, Series C", "Kernel PCA", "Kernel machine", "Kernel methods", "Kernel trick", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear approximation", "Linear combination", "Linear form", "Linear independence", "Linear least squares", "Linear regression", "Linear transformation", "Linearity", "Local regression", "Logistic regression", "Machine learning", "Mallows's Cp", "Map (mathematics)", "Mean and predicted response", "Mean squared error", "Mixed logit", "Mixed model", "Multicollinearity", "Multilevel model", "Multilinear subspace learning", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Ordered logit", "Ordered probit", "Ordinary least squares", "Orthogonal matrix", "Orthonormality", "Partial least squares", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Positive-definite kernel", "Positive-definite matrix", "Prediction", "Principal component analysis", "Probit model", "Quantile regression", "Random effects model", "Rank (linear algebra)", "Regression analysis", "Regression model validation", "Regularization (mathematics)", "Regularized least squares", "Reproducing kernel Hilbert space", "Ridge regression", "Robust regression", "Sample (statistics)", "Sample mean and sample covariance", "Segmented regression", "Semiparametric regression", "Shrinkage estimator", "Simple linear regression", "Singular value decomposition", "Statistics", "Studentized residual", "Symmetric function", "Takeshi Amemiya", "Technometrics", "Tikhonov regularization", "Total least squares", "Total sum of squares", "Transformation matrix", "Variance", "Variance inflation factor", "Weighted least squares"], "references": ["http://doi.org/10.1080%2F00401706.1981.10487652", "http://doi.org/10.1080%2F00401706.1993.10485033", "http://doi.org/10.1198%2F016214505000000628", "http://doi.org/10.2307%2F2348005", "http://www.jstor.org/stable/2348005"]}, "Multidimensional Chebyshev's inequality": {"categories": ["All articles lacking sources", "Articles lacking sources from August 2008", "Probabilistic inequalities", "Statistical inequalities"], "title": "Multidimensional Chebyshev's inequality", "method": "Multidimensional Chebyshev's inequality", "url": "https://en.wikipedia.org/wiki/Multidimensional_Chebyshev%27s_inequality", "summary": "In probability theory, the multidimensional Chebyshev's inequality is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount.\nLet X be an N-dimensional random vector with expected value \n \n \n \n \u03bc\n =\n E\n \u2061\n [\n X\n ]\n \n \n {\\displaystyle \\mu =\\operatorname {E} [X]}\n and covariance matrix\n\n \n \n \n V\n =\n E\n \u2061\n [\n (\n X\n \u2212\n \u03bc\n )\n (\n X\n \u2212\n \u03bc\n \n )\n \n T\n \n \n ]\n .\n \n \n \n {\\displaystyle V=\\operatorname {E} [(X-\\mu )(X-\\mu )^{T}].\\,}\n If \n \n \n \n V\n \n \n {\\displaystyle V}\n is a positive-definite matrix, for any real number \n \n \n \n t\n >\n 0\n \n \n {\\displaystyle t>0}\n :\n\n \n \n \n Pr\n \n (\n \n \n \n (\n X\n \u2212\n \u03bc\n \n )\n \n T\n \n \n \n V\n \n \u2212\n 1\n \n \n (\n X\n \u2212\n \u03bc\n )\n \n \n >\n t\n \n )\n \n \u2264\n \n \n N\n \n t\n \n 2\n \n \n \n \n \n \n {\\displaystyle \\Pr \\left({\\sqrt {(X-\\mu )^{T}V^{-1}(X-\\mu )}}>t\\right)\\leq {\\frac {N}{t^{2}}}}", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Chebyshev's inequality", "Covariance matrix", "Expected value", "Markov's inequality", "Positive-definite matrix", "Probability theory", "Random variable", "Random vector", "Real number"], "references": []}, "Five-number summary": {"categories": ["All articles needing additional references", "Articles needing additional references from January 2013", "Summary statistics"], "title": "Five-number summary", "method": "Five-number summary", "url": "https://en.wikipedia.org/wiki/Five-number_summary", "summary": "The five-number summary is a set of descriptive statistics that provide information about a dataset. It consists of the five most important sample percentiles:\n\nthe sample minimum (smallest observation)\nthe lower quartile or first quartile\nthe median (the middle value)\nthe upper quartile or third quartile\nthe sample maximum (largest observation)In addition to the median of a single set of data there are two related statistics called the upper and lower quartiles. If data are placed in order, then the lower quartile is central to the lower half of the data and the upper quartile is central to the upper half of the data. These quartiles are used to calculate the interquartile range, which helps to describe the spread of the data, and determine whether or not any data points are outliers.\nIn order for these statistics to exist the observations must be from a univariate variable that can be measured on an ordinal, interval or ratio scale.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4f/Five_number_summary.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Box plot", "Boxplot", "Descriptive statistics", "International Standard Book Number", "Interquartile range", "John W. Tukey", "L-estimator", "Level of measurement", "Median", "Mid-range", "Midhinge", "Order statistic", "Percentile", "Probability distribution", "Quartile", "R programming language", "Range (statistics)", "SAS (software)", "Sample maximum", "Sample minimum", "Seven-number summary", "Solar System", "Three-point estimation", "Trimean", "Univariate"], "references": ["http://cambridge.edu.au/go/resource/?pid=1145"]}, "Order of integration": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from December 2009", "Time series"], "title": "Order of integration", "method": "Order of integration", "url": "https://en.wikipedia.org/wiki/Order_of_integration", "summary": "In statistics, the order of integration, denoted I(d), of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["ARIMA", "Autocovariance", "Autoregressive\u2013moving-average model", "International Standard Book Number", "Lag operator", "Moving average representation", "Order of integration (calculus)", "Random walk", "Stationary process", "Statistics", "Summary statistics", "Time series"], "references": []}, "Variance-stabilizing transformation": {"categories": ["All articles needing expert attention", "Articles needing expert attention from May 2014", "Articles needing expert attention with no reason or talk parameter", "Articles needing unspecified expert attention", "Statistical data transformation"], "title": "Variance-stabilizing transformation", "method": "Variance-stabilizing transformation", "url": "https://en.wikipedia.org/wiki/Variance-stabilizing_transformation", "summary": "In applied statistics, a variance-stabilizing transformation is a data transformation that is specifically chosen either to simplify considerations in graphical exploratory data analysis or to allow the application of simple regression-based or analysis of variance techniques.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["Analysis of variance", "Anscombe transform", "Binomial distribution", "Data transformation (statistics)", "Delta method", "Digital object identifier", "Heteroscedasticity", "International Standard Book Number", "Inverse hyperbolic sine", "M. S. Bartlett", "Poisson distribution", "Power transform", "Relative error", "Statistics"], "references": ["http://doi.org/10.2307%2F3001536"]}, "Linear model": {"categories": ["Regression models"], "title": "Linear model", "method": "Linear model", "url": "https://en.wikipedia.org/wiki/Linear_model", "summary": "In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning. In each case, the designation \"linear\" is used to identify a subclass of models for which substantial reduction in the complexity of the related statistical theory is possible.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive moving average model", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent variables", "Index of dispersion", "Innovation (signal processing)", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear model of innovation", "Linear predictor function", "Linear regression", "Linear system", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear dimensionality reduction", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression coefficient", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Q-statistic": {"categories": ["All articles lacking sources", "All stub articles", "Articles lacking sources from July 2010", "Statistical tests", "Statistics stubs"], "title": "Q-statistic", "method": "Q-statistic", "url": "https://en.wikipedia.org/wiki/Q-statistic", "summary": "The Q-statistic is a test statistic output by either the Box-Pierce test or, in a modified version which provides better small sample properties, by the Ljung-Box test. It follows the chi-squared distribution. See also Portmanteau test.\nThe q statistic or studentized range statistic is a statistic used for multiple significance testing across a number of means: see Tukey\u2013Kramer method.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Box-Pierce test", "Chi-squared distribution", "Ljung-Box test", "Portmanteau test", "Statistics", "Studentized range", "Test statistic", "Tsallis statistics", "Tukey\u2013Kramer method"], "references": []}, "Autoregressive conditional heteroskedasticity": {"categories": ["All articles to be expanded", "Articles to be expanded from October 2017", "Articles using small message boxes", "Autocorrelation", "Nonlinear time series analysis", "Use dmy dates from October 2017"], "title": "Autoregressive conditional heteroskedasticity", "method": "Autoregressive conditional heteroskedasticity", "url": "https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity", "summary": "In econometrics, the autoregressive conditional heteroskedasticity (ARCH) model is a statistical model for time series data that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the variance is related to the squares of the previous innovations. The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average model (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model. For forecasting, combining ARIMA and ARCH models could be considered. For instance, a hybrid ARIMA-ARCH model was examined for shipping freight rate forecast.ARCH models are commonly employed in modeling financial time series that exhibit time-varying volatility and volatility clustering, i.e. periods of swings interspersed with periods of relative calm. ARCH-type models are sometimes considered to be in the family of stochastic volatility models, although this is strictly incorrect since at time t the volatility is completely pre-determined (deterministic) given previous values.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARCH", "Abstract Wiener space", "Accelerated failure time model", "Actuarial mathematics", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arch (disambiguation)", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive moving average model", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli process", "Bessel process", "Bias of an estimator", "Biased random walk on a graph", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Blocking (statistics)", "Boolean network", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Branching process", "Breusch\u2013Godfrey test", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Canonical correlation", "Cartography", "Categorical variable", "Cauchy process", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chen model", "Chi-squared test", "Chinese restaurant process", "Chris Brooks (academic)", "Classical Wiener space", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson process", "Conditional variance", "Confidence interval", "Confounding", "Constant elasticity of variance model", "Contact process (mathematics)", "Contingency table", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous probability distribution", "Continuous stochastic process", "Control chart", "Convergence of random variables", "Correlation and dependence", "Correlogram", "Count data", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "C\u00e0dl\u00e0g", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Divergence (statistics)", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Durbin\u2013Watson statistic", "Dynkin's formula", "Econometrica", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical process", "Engineering statistics", "Environmental statistics", "Epidemiology", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Errors and residuals in statistics", "Estimating equations", "Exchangeable random variables", "Experiment", "Exponential family", "Exponential smoothing", "Exponentially weighted moving average", "Extreme value theory", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "First-hitting-time model", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Forest plot", "Fourier analysis", "Fractional Brownian motion", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-network", "G-test", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "General linear model", "Generalized error distribution", "Generalized linear model", "Geographic information system", "Geometric Brownian motion", "Geometric mean", "Geostatistics", "Gibbs measure", "Girsanov theorem", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Heteroscedasticity", "Hidden Markov model", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "IVX", "Implied volatility", "Independent and identically distributed random variables", "Index of dispersion", "Infinitesimal generator (stochastic processes)", "Innovation (signal processing)", "Interacting particle system", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Ising model", "Isotonic regression", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Econometrics", "Journal of Economic Perspectives", "Jump-diffusion models", "Jump diffusion", "Jump process", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kunita\u2013Watanabe inequality", "Kurtosis", "L-moment", "LIBOR market model", "Lagrange multiplier test", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of inequalities", "List of statistics articles", "List of stochastic processes topics", "Ljung-Box test", "Ljung\u2013Box test", "Local martingale", "Local time (mathematics)", "Local volatility", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loop-erased random walk", "Loss function", "Lp space", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M-estimator", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Mann\u2013Whitney U test", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "Maximum a posteriori estimation", "Maximum likelihood", "McKean\u2013Vlasov process", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mixing (mathematics)", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moran process", "Moving-average model", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-homogeneous Poisson process", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Optional stopping theorem", "Order statistic", "Ordinary least squares", "Ornstein\u2013Uhlenbeck process", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Percolation theory", "Permutation test", "Pie chart", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Pivotal quantity", "Plug-in principle", "Point estimation", "Point process", "Poisson point process", "Poisson process", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Potts model", "Power (statistics)", "Predictable process", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Proportional hazards model", "Psychometrics", "Q-statistic", "QMLE", "Quadratic variation", "Quality control", "Quasi-experiment", "Questionnaire", "Queueing model", "Queueing theory", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random dynamical system", "Random field", "Random graph", "Random walk", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Reflection principle (Wiener process)", "Regenerative process", "Regression analysis", "Regression model validation", "Reliability engineering", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Replication (statistics)", "Resampling (statistics)", "RiskMetrics", "Risk process", "Robert F. Engle", "Robust regression", "Robust statistics", "Ruin theory", "Run chart", "SABR volatility model", "Sample-continuous process", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sanov's theorem", "Scale parameter", "Scatter plot", "Schramm\u2013Loewner evolution", "Scientific control", "Score test", "Seasonal adjustment", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sigma-martingale", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Social Science Research Network", "Social statistics", "Sparre\u2013Anderson model", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable process", "Standard deviation", "Standard error", "Standard normal variable", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic differential equations", "Stochastic process", "Stochastic volatility", "Stopping time", "Straddle", "Stratified sampling", "Stratonovich integral", "Structural break", "Structural equation modeling", "Student's t-test", "Submartingale", "Sufficient statistic", "Supermartingale", "Superprocess", "Survey methodology", "Survival analysis", "Survival function", "System identification", "System on a chip", "Tanaka equation", "Telegraph process", "Tim Bollerslev", "Time domain", "Time reversibility", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniform integrability", "Uniformly most powerful test", "Unit root", "Usual hypotheses", "V-statistic", "VIX", "Variance", "Variance gamma process", "Vasicek model", "Vector autoregression", "Volatility (finance)", "Volatility arbitrage", "Volatility clustering", "Volatility smile", "Volatility swap", "Wald test", "Wavelet", "White noise", "White test", "Whittle likelihood", "Wiener process", "Wiener sausage", "Wiener space", "Wilcoxon signed-rank test", "Wilkie investment model", "Z-test"], "references": ["http://www.finance.martinsewell.com/stylized-facts/volatility/EngleNg1993.pdf", "http://ssrn.com/abstract=262096", "http://public.econ.duke.edu/~boller/Published_Papers/glossary_10.pdf", "http://www.ijf.hr/eng/FTP/2006/4/posedel.pdf", "http://doi.org/10.1016%2F0304-405X(94)00821-H", "http://doi.org/10.1016%2F0304-4076(86)90063-1", "http://doi.org/10.1016%2FS1062-9769(99)80110-0", "http://doi.org/10.1016%2Fj.jeconom.2017.09.003", "http://doi.org/10.1057%2Fs41278-016-0051-7", "http://doi.org/10.1080%2F13504850500092129", "http://doi.org/10.1111%2Fj.1368-423X.2005.00163.x", "http://doi.org/10.1111%2Fj.1540-6261.1993.tb05127.x", "http://doi.org/10.1142%2FS2010495216500081", "http://doi.org/10.1239%2Fjap%2F1091543413", "http://doi.org/10.1257%2Fjep.15.4.157", "http://www.jstor.org/stable/1912773", "http://www.jstor.org/stable/23113641", "http://www.jstor.org/stable/2526988", "http://www.jstor.org/stable/2696523", "http://www.jstor.org/stable/2938260", "https://link.springer.com/article/10.1057/s41278-016-0051-7", "https://ideas.repec.org/a/taf/apeclt/v12y2005i7p411-417.html"]}, "Student's t-statistic": {"categories": ["All articles lacking sources", "All articles with unsourced statements", "Articles lacking sources from February 2011", "Articles with unsourced statements from February 2011", "Normal distribution", "Parametric statistics", "Statistical ratios", "Use dmy dates from November 2010"], "title": "T-statistic", "method": "Student's t-statistic", "url": "https://en.wikipedia.org/wiki/T-statistic", "summary": "In statistics, the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is used in hypothesis testing via Student's t-test. For example, it is used in estimating the population mean from a sampling distribution of sample means if the population standard deviation is unknown.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Ancillary statistic", "Asymptotic normality", "Augmented Dickey\u2013Fuller test", "Brewery", "Confidence interval", "Consistent estimator", "Dublin, Ireland", "Errors and residuals in statistics", "Estimator", "F-test", "Guinness", "Homoscedasticity", "Hotelling's t-squared statistic", "Linear regression model", "Normal distribution", "Ordinary least squares", "Pen name", "Pivotal quantity", "Population mean", "Prediction interval", "Regression analysis", "Sample mean", "Sampling distribution", "Simple linear regression", "Standard deviation", "Standard error (statistics)", "Standard normal", "Standardized testing (statistics)", "Statistical hypothesis testing", "Statistical model", "Statistics", "Student's t-distribution", "Student's t-test", "Student's t test", "Studentized residual", "T-test", "Time series", "Unit root", "William Sealy Gosset", "Z-score", "Z-test"], "references": []}, "Pensim2": {"categories": ["All stub articles", "Econometric models", "Econometrics stubs"], "title": "Pensim2", "method": "Pensim2", "url": "https://en.wikipedia.org/wiki/Pensim2", "summary": "Pensim2 is a dynamic microsimulation model to simulate the income of pensioners, owned by the British Department for Work and Pensions. \nPensim2 is the second version of Pensim which was developed in the 1990s. The time horizon of the model is 100 years, by which time today's school leavers will retire. Pensim2 uses a lot of external alignment figures. Pensim2 uses data from different data sources, e.g. BHPS, LLMDB and the Family Resources Survey.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1a/Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170527191524%21Emoji_u1f4c8.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1a/20170519203409%21Emoji_u1f4c8.svg"], "links": ["BHPS", "Department for Work and Pensions", "Econometrics", "Family Resources Survey", "Income", "LLMDB", "Microsimulation", "Model (abstract)", "Pensioner", "Policy Simulation Model", "Time horizon", "United Kingdom"], "references": ["http://www.dwp.gov.uk"]}, "Bennett's inequality": {"categories": ["All articles with unsourced statements", "All stub articles", "Articles with unsourced statements from September 2016", "Probabilistic inequalities", "Probability stubs"], "title": "Bennett's inequality", "method": "Bennett's inequality", "url": "https://en.wikipedia.org/wiki/Bennett%27s_inequality", "summary": "In probability theory, Bennett's inequality provides an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount. Bennett's inequality was proved by George Bennett of the University of New South Wales in 1962.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg"], "links": ["Almost surely", "ArXiv", "Concentration inequality", "David A. Freedman", "Digital object identifier", "Expected value", "Hoeffding's inequality", "Independent random variables", "Inequality (mathematics)", "International Standard Book Number", "JSTOR", "Journal of the American Statistical Association", "Luc Devroye", "Martingale (probability theory)", "Probability", "Probability theory", "Springer (publisher)", "Stochastic Processes and their Applications", "The Annals of Probability", "University of New South Wales", "Upper bound", "Without loss of generality"], "references": ["http://www.sciencedirect.com/science/article/pii/S0304414912001378", "http://arxiv.org/abs/1109.4359", "http://doi.org/10.1016/j.spa.2012.06.009", "http://doi.org/10.2307/2282438", "http://www.jstor.org/stable/2282438", "https://books.google.com/books?id=jvT-sUt1HZYC&pg=PA11", "https://www.jstor.org/discover/10.2307/2959268?uid=3738016&uid=2&uid=4&sid=21104036220407"]}, "Resampling (statistics)": {"categories": ["All articles to be merged", "All articles with incomplete citations", "Articles to be merged from August 2018", "Articles with incomplete citations from November 2012", "Monte Carlo methods", "Nonparametric statistics", "Resampling (statistics)", "Statistical inference", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from June 2016"], "title": "Resampling (statistics)", "method": "Resampling (statistics)", "url": "https://en.wikipedia.org/wiki/Resampling_(statistics)", "summary": "In statistics, resampling is any of a variety of methods for doing one of the following:\n\nEstimating the precision of sample statistics (medians, variances, percentiles) by using subsets of available data (jackknifing) or drawing randomly with replacement from a set of data points (bootstrapping)\nExchanging labels on data points when performing significance tests (permutation tests, also called exact tests, randomization tests, or re-randomization tests)\nValidating models by using random subsets (bootstrapping, cross validation)Common resampling techniques include bootstrapping, jackknifing and permutation tests.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute difference", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrew P. Holmes", "Annals of Mathematical Statistics", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balanced repeated replication", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behrens\u2013Fisher problem", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrap (statistics)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Bradley Efron", "Breusch\u2013Godfrey test", "C.F. Jeff Wu", "Canadian Journal of Forest Research", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chapman & Hall", "Chemometrics", "Chi-squared test", "Classical statistics", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational physics", "Confidence interval", "Confidence intervals", "Confounding", "Consistency (statistics)", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "E. 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A. Fisher", "Radar chart", "Random", "Random assignment", "Random permutation", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression coefficient", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (disambiguation)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "SAGE Publications", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific American", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shlomo Sawilowsky", "Sign test", "Significance test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Springer Science+Business Media", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Subsampling (statistics)", "Sufficient statistic", "Survey Methodology", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "Test statistic", "The Annals of Mathematical Statistics", "The Annals of Statistics", "The Design of Experiments", "Thomas E. Nichols", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.mansci.uwaterloo.ca/~msmucker/software.html", "http://statwww.epfl.ch/davison/BMA/library.html", "http://www.crcpress.com/product/isbn/9781466504059", "http://people.revoledu.com/kardi/tutorial/Bootstrap/index.html", "http://bcs.whfreeman.com/pbs/cat_140/chap18.pdf", "http://zanybooks.com/statist.htm", "http://adsabs.harvard.edu/abs/1989EnMan..13..783V", "http://tbf.coe.wayne.edu/jmasm/vol1_no2.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/11747097", "http://rosetta.ahmedmoustafa.io/bootstrap/", "http://rosetta.ahmedmoustafa.io/permutation/", "http://PAREonline.net/getvn.asp?v=8&n=19", "http://www.statistics101.net", "http://arxiv.org/abs/math/0612488", "http://www.bioconductor.org/packages/release/bioc/html/multtest.html", "http://doi.org/10.1002%2Fhbm.1058", "http://doi.org/10.1007%2Fbf01868317", "http://doi.org/10.1016%2Fj.jeconom.2004.08.004", "http://doi.org/10.1016%2Fs0165-1765(01)00494-3", "http://doi.org/10.1016%2Fs0304-4076(97)86569-4", "http://doi.org/10.1080%2F01621459.1983.10477989", "http://doi.org/10.1080%2F01621459.1988.10478691", "http://doi.org/10.1080%2F01621459.1990.10474929", "http://doi.org/10.1080%2F10629360500108053", "http://doi.org/10.1093%2Fbiomet%2F29.3-4.322", "http://doi.org/10.1093%2Fbiomet%2F43.3-4.353", "http://doi.org/10.1093%2Fbiomet%2F79.4.811", "http://doi.org/10.1093%2Fbiomet%2Fasm072", "http://doi.org/10.1111%2F1468-0262.00242", "http://doi.org/10.1111%2Fj.1467-9868.2005.00489.x", "http://doi.org/10.1111%2Fj.1467-9868.2006.00555.x", "http://doi.org/10.1139%2Fx86-222", "http://doi.org/10.1177%2F1558689812454457", "http://doi.org/10.1198%2Fjasa.2009.tm08368", "http://doi.org/10.1214%2Faoms%2F1177707045", "http://doi.org/10.1214%2Faos%2F1043351257", "http://doi.org/10.1214%2Faos%2F1176325770", "http://doi.org/10.1214%2Faos%2F1176344552", "http://doi.org/10.1214%2Faos%2F1176345580", "http://doi.org/10.1214%2Faos%2F1176350142", "http://doi.org/10.22237%2Fjmasm%2F1036110240", "http://doi.org/10.2307%2F2334363", "http://doi.org/10.2307%2F2335441", "http://www.ericdigests.org/1993/marriage.htm", "http://www.jstor.org/stable/2237031", "http://www.jstor.org/stable/2237363", "http://www.jstor.org/stable/2334363", "http://www.jstor.org/stable/2335441", "http://www.jstor.org/stable/2981330", "http://www.jstor.org/stable/2983696", "http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.aos/1176344552", "http://cran.at.r-project.org/web/packages/boot/index.html", "http://www.fil.ion.ucl.ac.uk/spm/doc/papers/NicholsHolmes.pdf", "https://github.com/searchivarius/PermTest", "https://www.springer.com/mathematics/probability/book/978-0-387-20268-6", "https://archive.is/20120712124533/http://lib.stat.cmu.edu/S/bootstrap.funs", "https://web.archive.org/web/20030505044125/http://tbf.coe.wayne.edu/jmasm/vol1_no2.pdf", "https://web.archive.org/web/20051223034539/http://www.resample.com/content/text/index.shtml", "https://web.archive.org/web/20060110182635/http://www.insightful.com/Hesterberg/bootstrap/", "https://web.archive.org/web/20060215221403/http://bcs.whfreeman.com/ips5e/content/cat_080/pdf/moore14.pdf", "https://www.jstor.org/stable/2983647", "https://www.jstor.org/stable/2984124", "https://cran.r-project.org/web/packages/permtest/index.html", "https://cran.r-project.org/web/packages/samplingVarEst"]}, "Generalized Dirichlet distribution": {"categories": ["Conjugate prior distributions", "Continuous distributions", "Exponential family distributions", "Multivariate continuous distributions"], "title": "Generalized Dirichlet distribution", "method": "Generalized Dirichlet distribution", "url": "https://en.wikipedia.org/wiki/Generalized_Dirichlet_distribution", "summary": "In statistics, the generalized Dirichlet distribution (GD) is a generalization of the Dirichlet distribution with a more general covariance structure and almost twice the number of parameters. Random variables with a GD distribution are not completely neutral .The density function of \n \n \n \n \n p\n \n 1\n \n \n ,\n \u2026\n ,\n \n p\n \n k\n \u2212\n 1\n \n \n \n \n {\\displaystyle p_{1},\\ldots ,p_{k-1}}\n is\n\n \n \n \n \n \n [\n \n \n \u220f\n \n i\n =\n 1\n \n \n k\n \u2212\n 1\n \n \n B\n (\n \n a\n \n i\n \n \n ,\n \n b\n \n i\n \n \n )\n \n ]\n \n \n \u2212\n 1\n \n \n \n p\n \n k\n \n \n \n b\n \n k\n \u2212\n 1\n \n \n \u2212\n 1\n \n \n \n \u220f\n \n i\n =\n 1\n \n \n k\n \u2212\n 1\n \n \n \n [\n \n \n p\n \n i\n \n \n \n a\n \n i\n \n \n \u2212\n 1\n \n \n \n \n (\n \n \n \u2211\n \n j\n =\n i\n \n \n k\n \n \n \n p\n \n j\n \n \n \n )\n \n \n \n b\n \n i\n \u2212\n 1\n \n \n \u2212\n (\n \n a\n \n i\n \n \n +\n \n b\n \n i\n \n \n )\n \n \n \n ]\n \n \n \n {\\displaystyle \\left[\\prod _{i=1}^{k-1}B(a_{i},b_{i})\\right]^{-1}p_{k}^{b_{k-1}-1}\\prod _{i=1}^{k-1}\\left[p_{i}^{a_{i}-1}\\left(\\sum _{j=i}^{k}p_{j}\\right)^{b_{i-1}-(a_{i}+b_{i})}\\right]}\n where we define \n \n \n \n \n p\n \n k\n \n \n =\n 1\n \u2212\n \n \u2211\n \n i\n =\n 1\n \n \n k\n \u2212\n 1\n \n \n \n p\n \n i\n \n \n \n \n {\\displaystyle p_{k}=1-\\sum _{i=1}^{k-1}p_{i}}\n . Here \n \n \n \n B\n (\n x\n ,\n y\n )\n \n \n {\\displaystyle B(x,y)}\n denotes the Beta function. This reduces to the standard Dirichlet distribution if \n \n \n \n \n b\n \n i\n \u2212\n 1\n \n \n =\n \n a\n \n i\n \n \n +\n \n b\n \n i\n \n \n \n \n {\\displaystyle b_{i-1}=a_{i}+b_{i}}\n for \n \n \n \n 2\n \u2a7d\n i\n \u2a7d\n k\n \u2212\n 1\n \n \n {\\displaystyle 2\\leqslant i\\leqslant k-1}\n (\n \n \n \n \n b\n \n 0\n \n \n \n \n {\\displaystyle b_{0}}\n is arbitrary).\nFor example, if k=4, then the density function of \n \n \n \n \n p\n \n 1\n \n \n ,\n \n p\n \n 2\n \n \n ,\n \n p\n \n 3\n \n \n \n \n {\\displaystyle p_{1},p_{2},p_{3}}\n is\n\n \n \n \n \n \n [\n \n \n \u220f\n \n i\n =\n 1\n \n \n 3\n \n \n B\n (\n \n a\n \n i\n \n \n ,\n \n b\n \n i\n \n \n )\n \n ]\n \n \n \u2212\n 1\n \n \n \n p\n \n 1\n \n \n \n a\n \n 1\n \n \n \u2212\n 1\n \n \n \n p\n \n 2\n \n \n \n a\n \n 2\n \n \n \u2212\n 1\n \n \n \n p\n \n 3\n \n \n \n a\n \n 3\n \n \n \u2212\n 1\n \n \n \n p\n \n 4\n \n \n \n b\n \n 3\n \n \n \u2212\n 1\n \n \n \n \n (\n \n \n p\n \n 2\n \n \n +\n \n p\n \n 3\n \n \n +\n \n p\n \n 4\n \n \n \n )\n \n \n \n b\n \n 1\n \n \n \u2212\n \n (\n \n \n a\n \n 2\n \n \n +\n \n b\n \n 2\n \n \n \n )\n \n \n \n \n \n (\n \n \n p\n \n 3\n \n \n +\n \n p\n \n 4\n \n \n \n )\n \n \n \n b\n \n 2\n \n \n \u2212\n \n (\n \n \n a\n \n 3\n \n \n +\n \n b\n \n 3\n \n \n \n )\n \n \n \n \n \n {\\displaystyle \\left[\\prod _{i=1}^{3}B(a_{i},b_{i})\\right]^{-1}p_{1}^{a_{1}-1}p_{2}^{a_{2}-1}p_{3}^{a_{3}-1}p_{4}^{b_{3}-1}\\left(p_{2}+p_{3}+p_{4}\\right)^{b_{1}-\\left(a_{2}+b_{2}\\right)}\\left(p_{3}+p_{4}\\right)^{b_{2}-\\left(a_{3}+b_{3}\\right)}}\n where \n \n \n \n \n p\n \n 1\n \n \n +\n \n p\n \n 2\n \n \n +\n \n p\n \n 3\n \n \n <\n 1\n \n \n {\\displaystyle p_{1}+p_{2}+p_{3}<1}\n and \n \n \n \n \n p\n \n 4\n \n \n =\n 1\n \u2212\n \n p\n \n 1\n \n \n \u2212\n \n p\n \n 2\n \n \n \u2212\n \n p\n \n 3\n \n \n \n \n {\\displaystyle p_{4}=1-p_{1}-p_{2}-p_{3}}\n .\nConnor and Mosimann define the PDF as they did for the following reason. Define random variables \n \n \n \n \n z\n \n 1\n \n \n ,\n \u2026\n ,\n \n z\n \n k\n \u2212\n 1\n \n \n \n \n {\\displaystyle z_{1},\\ldots ,z_{k-1}}\n with \n \n \n \n \n z\n \n 1\n \n \n =\n \n p\n \n 1\n \n \n ,\n \n z\n \n 2\n \n \n =\n \n p\n \n 2\n \n \n \n /\n \n \n (\n \n 1\n \u2212\n \n p\n \n 1\n \n \n \n )\n \n ,\n \n z\n \n 3\n \n \n =\n \n p\n \n 3\n \n \n \n /\n \n \n (\n \n 1\n \u2212\n (\n \n p\n \n 1\n \n \n +\n \n p\n \n 2\n \n \n )\n \n )\n \n ,\n \u2026\n ,\n \n z\n \n i\n \n \n =\n \n p\n \n i\n \n \n \n /\n \n \n (\n \n 1\n \u2212\n \n (\n \n \n p\n \n 1\n \n \n +\n \u22ef\n +\n \n p\n \n i\n \u2212\n 1\n \n \n \n )\n \n \n )\n \n \n \n {\\displaystyle z_{1}=p_{1},z_{2}=p_{2}/\\left(1-p_{1}\\right),z_{3}=p_{3}/\\left(1-(p_{1}+p_{2})\\right),\\ldots ,z_{i}=p_{i}/\\left(1-\\left(p_{1}+\\cdots +p_{i-1}\\right)\\right)}\n . Then \n \n \n \n \n p\n \n 1\n \n \n ,\n \u2026\n ,\n \n p\n \n k\n \n \n \n \n {\\displaystyle p_{1},\\ldots ,p_{k}}\n have the generalized Dirichlet distribution as parametrized above, if the \n \n \n \n \n z\n \n i\n \n \n \n \n {\\displaystyle z_{i}}\n are independent beta with parameters \n \n \n \n \n a\n \n i\n \n \n ,\n \n b\n \n i\n \n \n \n \n {\\displaystyle a_{i},b_{i}}\n , \n \n \n \n i\n =\n 1\n ,\n \u2026\n ,\n k\n \u2212\n 1\n \n \n {\\displaystyle i=1,\\ldots ,k-1}\n .\n\n", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta function", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Lukacs's proportion-sum independence theorem", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Neutral vector", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": []}, "Statistical conclusion validity": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from May 2012", "Validity (statistics)"], "title": "Statistical conclusion validity", "method": "Statistical conclusion validity", "url": "https://en.wikipedia.org/wiki/Statistical_conclusion_validity", "summary": "Statistical conclusion validity is the degree to which conclusions about the relationship among variables based on the data are correct or \u2018reasonable\u2019. This began as being solely about whether the statistical conclusion about the relationship of the variables was correct, but now there is a movement towards moving to \u2018reasonable\u2019 conclusions that use: quantitative, statistical, and qualitative data.\nFundamentally, two types of errors can occur: type I (finding a difference or correlation when none exists) and type II (finding no difference when one exists). Statistical conclusion validity concerns the qualities of the study that make these types of errors more likely.\nStatistical conclusion validity involves ensuring the use of adequate sampling procedures, appropriate statistical tests, and reliable measurement procedures. \n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Ceiling effect (statistics)", "Correlation", "Digital object identifier", "Effect sizes", "Extraneous variables", "Inferential statistics", "Internal Validity", "Internal validity", "Measurement error", "Pearson product-moment correlation coefficient", "PubMed Identifier", "Reliability (psychometrics)", "Robust statistics", "Sampling error", "Selection effects", "Standardization", "Statistical power", "Test Validity", "Type I and type II errors", "Validity (statistics)", "Variable (research)"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/17371098", "http://doi.org/10.1037%2F0021-9010.92.2.538", "https://www.researchgate.net/publication/6436643_A_cautionary_note_on_the_effects_of_range_restriction_on_predictor_intercorrelations/file/d912f50dd667aa5857.pdf"]}, "Linear regression": {"categories": ["All articles to be expanded", "All articles with unsourced statements", "Articles to be expanded from January 2010", "Articles using small message boxes", "Articles with inconsistent citation formats", "Articles with unsourced statements from June 2018", "Estimation theory", "Parametric statistics", "Single-equation methods (econometrics)", "Webarchive template wayback links", "Wikipedia articles needing clarification from March 2012", "Wikipedia articles needing clarification from May 2018"], "title": "Linear regression", "method": "Linear regression", "url": "https://en.wikipedia.org/wiki/Linear_regression", "summary": "In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables). The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis.\nLinear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications. This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.\nLinear regression has many practical uses. Most applications fall into one of the following two broad categories:\n\nIf the goal is prediction, or forecasting, or error reduction, linear regression can be used to fit a predictive model to an observed data set of values of the response and explanatory variables. After developing such a model, if additional values of the explanatory variables are collected without an accompanying response value, the fitted model can be used to make a prediction of the response.\nIf the goal is to explain variation in the response variable that can be attributed to variation in the explanatory variables, linear regression analysis can be applied to quantify the strength of the relationship between the response and the explanatory variables, and in particular to determine whether some explanatory variables may have no linear relationship with the response at all, or to identify which subsets of explanatory variables may contain redundant information about the response.Linear regression models are often fitted using the least squares approach, but they may also be fitted in other ways, such as by minimizing the \"lack of fit\" in some other norm (as with least absolute deviations regression), or by minimizing a penalized version of the least squares cost function as in ridge regression (L2-norm penalty) and lasso (L1-norm penalty). Conversely, the least squares approach can be used to fit models that are not linear models. Thus, although the terms \"least squares\" and \"linear model\" are closely linked, they are not synonymous.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b2/Galton%27s_correlation_diagram_1875.jpg", "https://upload.wikimedia.org/wikipedia/commons/5/53/Linear_least_squares_example2.png", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8b/Polyreg_scheffe.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e9/Thiel-Sen_estimator.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ec/Anscombe%27s_quartet_3.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Affine transformation", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anscombe's quartet", "Approximation theory", "ArXiv", "Arithmetic mean", "Artificial intelligence", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bayesian probability", "Bayesian statistics", "Benthic zone", "Bernoulli distribution", "Beta (finance)", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate normal distribution", "Blinder\u2013Oaxaca decomposition", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calibration curve", "Cambridge University Press", "Canonical correlation", "Capital asset pricing model", "Cartography", "Categorical data", "Categorical distribution", "Categorical variable", "Censored regression model", "Census", "Central limit theorem", "Central tendency", "Charles Darwin", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Column rank", "Completeness (statistics)", "Computational statistics", "Conditional expectation", "Conditional probability distribution", "Confidence interval", "Confounding", "Consistent estimator", "Consumption (economics)", "Contingency table", "Continuous probability distribution", "Control chart", "Coordinate vector", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-sectional regression", "Cross-validation (statistics)", "Curve fitting", "Data", "Data collection", "Data set", "David A. 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"Poisson distribution", "Poisson regression", "Polynomial", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior distribution", "Posterior probability", "Power (statistics)", "Pranab K. Sen", "Prediction interval", "Principal component analysis", "Principal component regression", "Prior distribution", "Prior probability", "Probabilistic design", "Probability distribution", "Probit model", "Probit regression", "Projection pursuit regression", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effects model", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regression toward the mean", "Regularization (mathematics)", "Regularized least squares", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Ridge regression", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scalar (mathematics)", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewed distribution", "Skewness", "Social statistics", "Socioeconomic status", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spurious correlation", "Standard deviation", "Standard error", "Standard gravity", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistical unit", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Theil\u2013Sen estimator", "Tikhonov regularization", "Time domain", "Time series", "Tobacco smoking", "Tolerance interval", "Total derivative", "Total least squares", "Transpose", "Trend estimation", "Truncated regression model", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wayback Machine", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Y-intercept", "Z-test"], "references": ["http://www.ec.gc.ca/esee-eem/default.asp?lang=En&n=453D78FC-1", "http://www.mugu.com/galton/essays/1880-1889/galton-1886-jaigi-regression-stature.pdf", "http://www.incertitudes.fr/book.pdf", "http://www.ams.org/mathscinet-getitem?mr=0036489", "http://www.ams.org/mathscinet-getitem?mr=0258201", "http://arxiv.org/abs/math/0406456", "http://doi.org/10.1093%2Fbiomet%2F54.1-2.1", "http://doi.org/10.1093%2Fbiomet%2F64.3.509", "http://doi.org/10.1093%2Fbiomet%2F73.1.43", "http://doi.org/10.1177%2F0016986211422217", "http://doi.org/10.1177%2F0734016807304871", "http://doi.org/10.1214%2F009053604000000067", "http://doi.org/10.1214%2Faos%2F1176343056", "http://doi.org/10.2307%2F1268284", "http://doi.org/10.2307%2F1402501", "http://doi.org/10.2307%2F2285891", "http://doi.org/10.2307%2F2290063", "http://doi.org/10.2307%2F2683577", "http://www.jstor.org/stable/1268284", "http://www.jstor.org/stable/1402501", "http://www.jstor.org/stable/2285891", "http://www.jstor.org/stable/2290063", "http://www.jstor.org/stable/2333849", "http://www.jstor.org/stable/2336270", "http://www.jstor.org/stable/2345326", "http://www.jstor.org/stable/2346178", "http://www.jstor.org/stable/2346776", "http://www.jstor.org/stable/2347363", "http://www.jstor.org/stable/2348005", "http://www.jstor.org/stable/2683577", "http://www.jstor.org/stable/2958945", "http://www.jstor.org/stable/3448465", "http://www.geocities.ws/diylf/DIYLF.html", "https://books.google.com/books?id=0g-PAuKub3QC&pg=PA19", "https://books.google.com/books?id=MjNv6rGv8NIC&pg=PA1", "https://phet.colorado.edu/en/simulation/least-squares-regression", "https://people.cs.pitt.edu/~milos/courses/cs2750-Spring03/lectures/class6.pdf", "https://web.archive.org/web/20110611114740/http://www.ec.gc.ca/esee-eem/default.asp?lang=En&n=453D78FC-1"]}, "Robust statistics": {"categories": ["All articles needing additional references", "All articles needing expert attention", "All articles that are too technical", "All articles to be expanded", "All articles with unsourced statements", "Articles needing additional references from February 2012", "Articles needing expert attention from June 2010", "Articles to be expanded from July 2008", "Articles using small message boxes", "Articles with unsourced statements from April 2014", "Articles with unsourced statements from February 2008", "Articles with unsourced statements from July 2016", "Robust statistics", "Wikipedia articles that are too technical from June 2010"], "title": "Robust statistics", "method": "Robust statistics", "url": "https://en.wikipedia.org/wiki/Robust_statistics", "summary": "Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from parametric distributions. For example, robust methods work well for mixtures of two normal distributions with different standard-deviations; under this model, non-robust methods like a t-test work poorly.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/46/Biweight.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/7/78/PsiFunctions.png", "https://upload.wikimedia.org/wikipedia/commons/c/c1/RhoFunctions.png", "https://upload.wikimedia.org/wikipedia/commons/e/e6/SpeedOfLight.png", "https://upload.wikimedia.org/wikipedia/commons/a/a6/SpeedOfLightScale.png", "https://upload.wikimedia.org/wikipedia/commons/9/9b/TDistPsi.png", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Ancillary statistic", "Anderson\u2013Darling test", "Annals of Statistics", "Antarctica", "Arithmetic mean", "Asymptotic theory (statistics)", "Asymptotically unbiased", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias (statistics)", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brian D. 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Press", "Winsorising", "Winsorizing", "Xuming He", "Z-test"], "references": ["http://apps.nrbook.com/empanel/index.html#pg=818", "http://www.wunderground.com/climate/holefaq.asp", "http://jsxgraph.uni-bayreuth.de/wiki/index.php/Analyze_data_with_the_Statistics_software_R", "http://lagrange.math.siu.edu/Olive/ol-bookp.htm", "http://www.ams.org/mathscinet-getitem?mr=0022330", "http://www.ams.org/mathscinet-getitem?mr=0606374", "http://www.ams.org/mathscinet-getitem?mr=0829458", "http://www.ams.org/mathscinet-getitem?mr=0914792", "http://www.ams.org/mathscinet-getitem?mr=1141746", "http://www.ams.org/mathscinet-getitem?mr=1193333", "http://www.ams.org/mathscinet-getitem?mr=1245360", "http://www.ams.org/mathscinet-getitem?mr=1604954", "http://www.ams.org/mathscinet-getitem?mr=1692202", "http://www.ams.org/mathscinet-getitem?mr=1825288", "http://www.ams.org/mathscinet-getitem?mr=2238141", "http://www.ams.org/mathscinet-getitem?mr=2371990", "http://www.ams.org/mathscinet-getitem?mr=2758558", "http://www.ams.org/mathscinet-getitem?mr=3286430", "http://doi.org/10.1002%2F0470010940", "http://doi.org/10.1002%2F0471725382", "http://doi.org/10.1002%2Fwidm.2", "http://doi.org/10.1016%2FB978-0-12-386983-8.00001-9", "http://doi.org/10.1016%2Fs0043-1354(01)00069-0", "http://doi.org/10.1061%2F(asce)0733-9372(2007)133:9(909)", "http://doi.org/10.1198%2Ftast.2010.10159", "http://doi.org/10.1214%2Faoms%2F1177730385", "http://doi.org/10.1214%2Faos%2F1176348910", "http://doi.org/10.2307%2F2289782", "http://doi.org/10.2307%2F2291267", "http://doi.org/10.2307%2F2669782", "http://secamlocal.ex.ac.uk/people/staff/dbs202/", "http://secamlocal.ex.ac.uk/people/staff/dbs202/cag/courses/MT37C/course/node13.html", "http://www.nickfieller.staff.shef.ac.uk/sheff-only/StatModall05.pdf", "https://wis.kuleuven.be/stat/robust/papers/2011/rousseeuwhubert-robuststatisticsforoutlierdetectio.pdf", "https://web.archive.org/web/20121021081319/http://www.stats.ox.ac.uk/pub/StatMeth/Robust.pdf"]}, "Utility maximization problem": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles with unsourced statements", "Articles lacking in-text citations from August 2010", "Articles needing additional references from March 2011", "Articles with unsourced statements from August 2010", "CS1 maint: Multiple names: authors list", "Optimal decisions", "Utility"], "title": "Utility maximization problem", "method": "Utility maximization problem", "url": "https://en.wikipedia.org/wiki/Utility_maximization_problem", "summary": "For a less technical introduction, see Utility.In microeconomics, the utility maximization problem is the problem consumers face: \"how should I spend my money in order to maximize my utility?\" It is a type of optimal decision problem.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Andreu Mas-Colell", "Bounded rationality", "Budget set", "Choice modelling", "Consumer", "Consumption set", "Dot product", "Evolutionary psychology", "Expenditure function", "Expenditure minimization problem", "Hicksian demand", "Income-consumption curve", "International Standard Book Number", "Linear programming", "Marshallian demand", "Marshallian demand correspondence", "Marshallian demand function", "Microeconomics", "Money", "Money illusion", "Optimal decision", "Ordinal utility", "Satisficing", "Substitution effect", "Utility", "Utility function"], "references": ["http://www2.hawaii.edu/~fuleky/anatomy/anatomy.html", "http://plato.stanford.edu/entries/evolutionary-psychology/"]}, "Estimation theory": {"categories": ["CS1 errors: external links", "Estimation theory", "Mathematical and quantitative methods (economics)", "Signal processing"], "title": "Estimation theory", "method": "Estimation theory", "url": "https://en.wikipedia.org/wiki/Estimation_theory", "summary": "Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements. When the data consist of multiple variables and one is estimating the relationship between them, estimation is known as regression analysis.\nIn estimation theory, two approaches are generally considered.\nThe probabilistic approach (described in this article) assumes that the measured data is random with probability distribution dependent on the parameters of interest\nThe set-membership approach assumes that the measured data vector belongs to a set which depends on the parameter vector.", "images": [], "links": ["Adaptive control", "Additive white Gaussian noise", "Advanced Z-transform", "Ali H. 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For example, in a test of achievement in mathematics, if examinees can successfully answer items at one level of difficulty (e.g., summing two 3-digit numbers), they would be able to answer the earlier questions (e.g., summing two 2-digit numbers).", "images": [], "links": ["Achievement test", "Bogardus Social Distance Scale", "Classical test theory", "Item response theory", "Louis Guttman", "Mokken scale", "Questionnaires", "Rasch model"], "references": ["https://academic.oup.com/sf/article/29/2/207/2225654"]}, "Quasi-birth\u2013death process": {"categories": ["All stub articles", "Markov processes", "Probability stubs", "Queueing theory"], "title": "Quasi-birth\u2013death process", "method": "Quasi-birth\u2013death process", "url": "https://en.wikipedia.org/wiki/Quasi-birth%E2%80%93death_process", "summary": "In queueing models, a discipline within the mathematical theory of probability, the quasi-birth\u2013death process describes a generalisation of the birth\u2013death process. As with the birth-death process it moves up and down between levels one at a time, but the time between these transitions can have a more complicated distribution encoded in the blocks.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg"], "links": ["ArXiv", "Birth\u2013death process", "Continuous-time Markov chain", "Countably", "Digital object identifier", "International Standard Book Number", "Jackson network", "Markov chain", "Matrix geometric method", "Probability", "Queueing model", "Semi-Markov process", "Stochastic matrix", "Theory of probability", "Transition rate matrix", "Tridiagonal matrix"], "references": ["http://arxiv.org/abs/math/0503555", "http://doi.org/10.1002/9780470400531.eorms0461", "http://doi.org/10.1007/0-387-21525-5_11", "http://doi.org/10.1007/11569596_26", "http://doi.org/10.1080/15326349808807481", "http://doi.org/10.1214/105051604000000477", "http://doi.org/10.1239/aap/1151337083"]}, "Population (statistics)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2017", "Statistical theory"], "title": "Statistical population", "method": "Population (statistics)", "url": "https://en.wikipedia.org/wiki/Statistical_population", "summary": "In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker). A common aim of statistical analysis is to produce information about some chosen population.In statistical inference, a subset of the population (a statistical sample) is chosen to represent the population in a statistical analysis. The ratio of the size of this statistical sample to the size of the population is called a sampling fraction. If a sample is chosen properly, characteristics of the entire population that the sample is drawn from can be estimated from corresponding characteristics of the sample.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bimodal distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Data collection system", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimating equations", "Estimation theory", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Galaxy", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Infinite set", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "MathWorld", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Milky Way", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mixture model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Overdispersion", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Poker", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling fraction", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Star", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Statistics.com", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Subset", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "W. H. Freeman and Company", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.statistics.com/glossary&term_id=281", "http://www.statistics.com/glossary&term_id=812", "http://bcs.whfreeman.com/yates2e/", "http://mathworld.wolfram.com/Population.html", "http://www.socialresearchmethods.net/kb/sampstat.htm", "https://web.archive.org/web/20050209001108/http://bcs.whfreeman.com/yates2e/"]}, "Statistical parameter": {"categories": ["Statistical parameters"], "title": "Statistical parameter", "method": "Statistical parameter", "url": "https://en.wikipedia.org/wiki/Statistical_parameter", "summary": "A statistical parameter or population parameter is a quantity that indexes a family of probability distributions. It can be regarded as a numerical characteristic of a population or a statistical model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Cambridge University Press", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Concentration parameter", "Conditional probability distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Indexed family", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameter", "Parametric family", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Precision (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random sample", "Random variables", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression coefficient", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Vuong's closeness test": {"categories": ["All articles needing expert attention", "All articles with specifically marked weasel-worded phrases", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Articles with specifically marked weasel-worded phrases from February 2011", "Statistical tests", "Statistics articles needing expert attention"], "title": "Vuong's closeness test", "method": "Vuong's closeness test", "url": "https://en.wikipedia.org/wiki/Vuong%27s_closeness_test", "summary": "In statistics, the Vuong closeness test is likelihood-ratio-based test for model selection using the Kullback-Leibler information criterion. This statistic makes probabilistic statements about two models. They can be nested, non-nested or overlapping. The statistic tests the null hypothesis that the two models are equally close to the true data generating process, against the alternative that one model is closer. It cannot make any decision whether the \"closer\" model is the true model.\nWith non-nested models and iid exogenous variables, model 1 (2) is preferred with significance level \u03b1, if the z statistic\n\n \n \n \n Z\n =\n \n \n \n L\n \n R\n \n N\n \n \n (\n \n \u03b2\n \n M\n L\n ,\n 1\n \n \n ,\n \n \u03b2\n \n M\n L\n ,\n 2\n \n \n )\n \n \n \n \n N\n \n \n \n \u03c9\n \n N\n \n \n \n \n \n \n \n {\\displaystyle Z={\\frac {LR_{N}(\\beta _{ML,1},\\beta _{ML,2})}{{\\sqrt {N}}\\omega _{N}}}}\n with\n\n \n \n \n \n L\n \n R\n \n N\n \n \n (\n \n \u03b2\n \n M\n L\n ,\n 1\n \n \n ,\n \n \u03b2\n \n M\n L\n ,\n 2\n \n \n )\n \n =\n \n L\n \n N\n \n \n 1\n \n \n \u2212\n \n L\n \n N\n \n \n 2\n \n \n \u2212\n \n \n \n \n K\n \n 1\n \n \n \u2212\n \n K\n \n 2\n \n \n \n 2\n \n \n log\n \u2061\n N\n \n \n {\\displaystyle {LR_{N}(\\beta _{ML,1},\\beta _{ML,2})}=L_{N}^{1}-L_{N}^{2}-{\\frac {K_{1}-K_{2}}{2}}\\log N}\n exceeds the positive (falls below the negative) (1 \u2212 \u03b1)-quantile of the standard normal distribution. Here K1 and K2 are the numbers of parameters in models 1 and 2 respectively.\nThe numerator is the difference between the maximum likelihoods of the two models, corrected for the number of coefficients analogous to the BIC, the term in the denominator of the expression for Z, \n \n \n \n \n \u03c9\n \n N\n \n \n \n \n \n {\\displaystyle \\omega _{N}\\,}\n , is defined by setting \n \n \n \n \n \u03c9\n \n N\n \n \n 2\n \n \n \n \n {\\displaystyle \\omega _{N}^{2}}\n equal to either the mean of the squares of the pointwise log-likelihood ratios \n \n \n \n \n \u2113\n \n i\n \n \n \n \n \n {\\displaystyle \\ell _{i}\\,}\n , or to the sample variance of these values, where\n\n \n \n \n \n \u2113\n \n i\n \n \n =\n log\n \u2061\n \n \n \n \n f\n \n 1\n \n \n (\n \n y\n \n i\n \n \n \n |\n \n \n x\n \n i\n \n \n ,\n \n \u03b2\n \n M\n L\n ,\n 1\n \n \n )\n \n \n \n f\n \n 2\n \n \n (\n \n y\n \n i\n \n \n \n |\n \n \n x\n \n i\n \n \n ,\n \n \u03b2\n \n M\n L\n ,\n 2\n \n \n )\n \n \n \n .\n \n \n {\\displaystyle \\ell _{i}=\\log {\\frac {f_{1}(y_{i}|x_{i},\\beta _{ML,1})}{f_{2}(y_{i}|x_{i},\\beta _{ML,2})}}.}\n For nested or overlapping models the statistic\n\n \n \n \n 2\n L\n \n R\n \n N\n \n \n (\n \n \u03b2\n \n M\n L\n ,\n 1\n \n \n ,\n \n \u03b2\n \n M\n L\n ,\n 2\n \n \n )\n \n \n \n {\\displaystyle 2LR_{N}(\\beta _{ML,1},\\beta _{ML,2})\\,}\n has to be compared to critical values from a weighted sum of chi squared distributions. This can be approximated by a gamma distribution:\n\n \n \n \n \n M\n \n m\n \n \n (\n .\n ,\n \n \n \u03bb\n \n \n )\n \u223c\n \u0393\n (\n b\n ,\n p\n )\n \n \n \n {\\displaystyle M_{m}(.,{\\mathbf {\\lambda } })\\sim \\Gamma (b,p)\\,}\n with\n\n \n \n \n \n \n \u03bb\n \n \n =\n (\n \n \u03bb\n \n 1\n \n \n ,\n \n \u03bb\n \n 2\n \n \n ,\n \u2026\n ,\n \n \u03bb\n \n m\n \n \n )\n ,\n \n \n \n {\\displaystyle {\\mathbf {\\lambda } }=(\\lambda _{1},\\lambda _{2},\\dots ,\\lambda _{m}),\\,}\n \n \n \n \n m\n =\n \n K\n \n 1\n \n \n +\n \n K\n \n 2\n \n \n ,\n \n b\n =\n \n \n 1\n 2\n \n \n \n \n \n \u2211\n \n \u03bb\n \n i\n \n \n \n \n \u2211\n \n \u03bb\n \n i\n \n \n 2\n \n \n \n \n \n \n \n {\\displaystyle m=K_{1}+K_{2},\\ b={\\frac {1}{2}}{\\frac {\\sum \\lambda _{i}}{\\sum \\lambda _{i}^{2}}}}\n and\n\n \n \n \n p\n =\n \n \n 1\n 2\n \n \n \n \n \n \n (\n \u2211\n \u03bb\n i\n )\n \n \n 2\n \n \n \n \u2211\n \n \u03bb\n \n i\n \n \n 2\n \n \n \n \n \n .\n \n \n {\\displaystyle p={\\frac {1}{2}}{\\frac {{(\\sum \\lambda i)}^{2}}{\\sum \\lambda _{i}^{2}}}.}\n \n \n \n \n \n \n \u03bb\n \n \n \n \n {\\displaystyle {\\mathbf {\\lambda } }}\n is a vector of eigenvalues of a matrix of conditional expectations. The computation is quite difficult, so that in the overlapping and nested case many authors only derive statements from a subjective evaluation of the Z statistic (is it subjectively \"big enough\" to accept my hypothesis?).\nVuong's test for non-nested models has sometimes been used to determine whether zero-inflation is present in data. As a given model and its zero-inflated counterpart are not non-nested, this is an erroneous use of the test", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["Bayesian information criterion", "Chi squared distribution", "Digital object identifier", "Econometrica", "Eigenvalue", "Expected value", "Gamma distribution", "Iid", "JSTOR", "Kullback\u2013Leibler divergence", "Likelihood-ratio test", "Matrix (mathematics)", "Model selection", "Standard normal distribution", "Statistical model", "Statistics", "Z statistic"], "references": ["http://doi.org/10.1016%2FS0165-1765(01)00566-3", "http://doi.org/10.1016%2Fj.econlet.2014.12.029", "http://www.jstor.org/stable/1912557"]}, "Clinical trial": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from November 2014", "Articles with Japanese-language external links", "Articles with unsourced statements from October 2017", "Clinical pharmacology", "Clinical research", "Clinical trials", "Commons category link is on Wikidata", "Design of experiments", "Drug discovery", "Epidemiology", "Food and Drug Administration", "Medical statistics", "Nursing research", "Pharmaceutical industry", "Product testing", "Use dmy dates from January 2011", "Webarchive template wayback links"], "title": "Clinical trial", "method": "Clinical trial", "url": "https://en.wikipedia.org/wiki/Clinical_trial", "summary": "Clinical trials are experiments or observations done in clinical research. Such prospective biomedical or behavioral research studies on human participants are designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dietary choices, dietary supplements, and medical devices) and known interventions that warrant further study and comparison. Clinical trials generate data on safety and efficacy. They are conducted only after they have received health authority/ethics committee approval in the country where approval of the therapy is sought. These authorities are responsible for vetting the risk/benefit ratio of the trial \u2013 their approval does not mean that the therapy is 'safe' or effective, only that the trial may be conducted.\nDepending on product type and development stage, investigators initially enroll volunteers or patients into small pilot studies, and subsequently conduct progressively larger scale comparative studies. Clinical trials can vary in size and cost, and they can involve a single research center or multiple centers, in one country or in multiple countries. Clinical study design aims to ensure the scientific validity and reproducibility of the results.\nCosts for clinical trials can range into the billions of dollars per approved drug. The sponsor may be a governmental organization or a pharmaceutical, biotechnology or medical device company. Certain functions necessary to the trial, such as monitoring and lab work, may be managed by an outsourced partner, such as a contract research organization or a central laboratory.\nOnly 10 percent of all drugs started in human clinical trials become an approved drug.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/eb/Austin_Bradford_Hill.jpg", "https://upload.wikimedia.org/wikipedia/commons/6/6d/Melingue_Jenner.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/7f/PARAMOUNT_Eli_Lilly_Informed_Consent_Document.djvu", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fc/Clinical_trial_newspaper_advertisements.JPG", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/8/87/Drug_Evaluation_Process.jpg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abdominal aortic aneurysm", "Academic clinical trials", "Accelerated failure time model", "Actuarial science", "Adaptive clinical trial", "Adverse event", "Aeroallergen", "Akaike information criterion", "Alzheimer's disease", "Analysis of clinical trials", "Analysis of covariance", "Analysis of variance", "Ancient Iranian medicine", "Anderson\u2013Darling test", "Animal testing", "Animal testing on non-human primates", "Antiscorbutic", "Approved drug", "Arithmetic mean", "Asymptotic theory (statistics)", "Attributable fraction among the exposed", "Attributable fraction for the population", "Audit", "Austin Bradford Hill", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Avicenna", "Bar chart", "Barley water", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biologic medical product", "Biostatistics", "Biotechnology", "Biplot", "Blind experiment", "Blocking (statistics)", "Book of Daniel", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "British East India Company", "British Medical Association", "British doctors study", "California", "Cannabis product testing", "Canonical correlation", "Cartography", "Case-control study", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Categorical variable", "Catheter", "Census", "Central limit theorem", "Central tendency", "Chemical substance", "Chemical test", "Chemometrics", "Chi-squared test", "Chronic illness", "Cider", "Citrus fruit", "ClinicalTrials.gov", "Clinical Trial Management System", "Clinical Trial Portal", "Clinical Trials", "Clinical Trials (journal)", "Clinical data management system", "Clinical endpoint", "Clinical research", "Clinical research ethics", "Clinical study design", "Clinical trial protocol", "Clinical trials publication", "Clinicaltrials.gov", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Coffee cupping", "Cohen's kappa", "Cohort study", "Cointegration", "Compassionate use", "Completeness (statistics)", "Concise Encyclopedia of Economics", "Confidence interval", "Conformance testing", "Confounding", "Consumer organization", "Contingency table", "Continuous probability distribution", "Contract research organization", "Control chart", "Control group", "Controlled experiment", "Correlation and dependence", "Correlation does not imply causation", "Correlogram", "Count data", "Crash test", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-sectional study", "Cross-validation (statistics)", "Cumulative incidence", "Daniel Henninger", "Data analysis", "Data collection", "Data monitoring committee", "David R. Henderson", "Declaration of Helsinki", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Destructive testing", "Dickey\u2013Fuller test", "Dietary supplement", "Digital object identifier", "Discrimination testing", "Divergence (statistics)", "Drug", "Durbin\u2013Watson statistic", "Ecological study", "Econometrics", "Edward Jenner", "Effect size", "Efficacy", "Efficiency (statistics)", "Electronic data capture", "Electronic patient-reported outcome", "Elisha Perkins", "Elliptical distribution", "Empirical distribution function", "Endovascular aneurysm repair", "Engineering statistics", "Environmental statistics", "Epidemiological methods", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Ethical problems using children in clinical trials", "Ethics committee (European Union)", "Ethnic minority", "European Medicines Agency", "European Union", "Evidence-based medicine", "Evidence-based practice", "Expanded access", "Experiment", "Exponential family", "Exponential smoothing", "Ezekiel J. Emanuel", "F-test", "FDA Accelerated Approval Program", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fetus", "First-hitting-time model", "First-in-man study", "Food and Drug Administration", "Food and Drug Administration (United States)", "Forest plot", "Fourier analysis", "Frederick Akbar Mahomed", "Free Press (publisher)", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George Anson's voyage around the world", "George Anson, 1st Baron Anson", "Geostatistics", "Glossary of clinical research", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Guy's Hospital", "Handle System", "Harmonic mean", "Hazard ratio", "Health Canada", "Health Insurance Portability and Accountability Act", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human subject research", "Hypertension", "Hypothesis", "In vitro", "In vivo", "Incidence (epidemiology)", "Index of dispersion", "Infectivity", "Influenza", "Information technology", "Informed consent", "Inoculation", "Institutional Review Board", "Institutional review board", "Intention-to-treat analysis", "Interaction (statistics)", "Interactive voice response", "International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use", "International Standard Book Number", "Interquartile range", "Interval estimation", "Investigator's brochure", "Isotonic regression", "Jackknife resampling", "James Lind", "James Phipps", "Jarque\u2013Bera test", "Johansen test", "John Haygarth", "John Woodall", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lady Mary Wortley Montagu", "Lehmann\u2013Scheff\u00e9 theorem", "Lemon", "Library of Economics and Liberty", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratios in diagnostic testing", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Lipids", "List of clinical research topics", "List of fields of application of statistics", "List of food safety organisations", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "London", "Longitudinal study", "Loss function", "Lp space", "Lung cancer", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measurement uncertainty", "Median", "Median-unbiased estimator", "Medical Research Council (United Kingdom)", "Medical device", "Medical laboratory", "Medical nutrition therapy", "Medical procedure", "Medical statistics", "Medication", "Meta-analysis", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Ministry of Health, Labour and Welfare (Japan)", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monitoring in clinical trials", "Monotone likelihood ratio", "Morbidity", "Mortality rate", "Multicenter trial", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Cancer Institute", "National Institutes of Health", "National Library of Medicine", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nephritis", "Nested case\u2013control study", "Newspaper advertisement", "Nondestructive testing", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null result", "Number needed to harm", "Number needed to treat", "Nurses' Health Study", "OCLC", "Observation", "Observational studies", "Observational study", "Odds algorithm", "Odds ratio", "Official statistics", "One- and two-tailed tests", "Open-label trial", "Open aortic repair", "Opinion poll", "Optimal decision", "Optimal design", "Orange (fruit)", "Order statistic", "Ordinary least squares", "Orphan disease", "Outline of statistics", "Outsource", "PARAMOUNT trial", "Package testing", "Parametric statistics", "Parkinson's disease", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Patient-reported outcome", "Patient recruitment", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Pediatrics", "Percentile", "Period prevalence", "Permutation test", "Pharmaceutical Research and Manufacturers of America", "Pharmaceutical drug", "Pharmaceutical industry", "Pharmacodynamics", "Pharmacokinetics", "Phases of clinical research", "Physical test", "Pie chart", "Pilot experiment", "Pivotal quantity", "Placebo", "Placebo-controlled studies", "Placebo effect", "Plug-in principle", "Point estimation", "Point prevalence", "Poisson regression", "Population (statistics)", "Population Impact Measures", "Population statistics", "Posterior probability", "Power (statistics)", "Pre- and post-test probability", "Pre-clinical development", "Pre-existing medical conditions", "Prediction interval", "Premarket approval", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Primum non nocere", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Product testing", "Prophylactic", "Proportional hazards model", "Prospective cohort study", "Prospective study", "Protocol (science)", "Psychological therapies", "Psychometrics", "PubMed Central", "PubMed Identifier", "Pulmonary tuberculosis", "Quality control", "Quality of life (healthcare)", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Radiation therapy", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized controlled trials", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regulatory authority", "Relative risk reduction", "Reliability engineering", "Replication (statistics)", "Reproducibility", "Resampling (statistics)", "Retrospective cohort study", "Richard Doll", "Risk/benefit ratio", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Robust regression", "Robust statistics", "Ronald A. Fisher", "Rothamsted experimental station", "Royal Society", "Run chart", "Safety", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Scurvy", "Seasonal adjustment", "Seasonal affective disorder", "Secondary hypertension", "Seeding trial", "Selection bias", "Semiparametric regression", "Sensory analysis", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Sir William Gull, 1st Baronet", "Site management organization", "Skewness", "Skin disease", "Smallpox", "Smallpox vaccine", "Smoking", "Social statistics", "Software testing", "Spatial analysis", "Spearman's rank correlation coefficient", "Specificity and sensitivity", "Spectral density estimation", "Squamous cell cancer", "Standard deviation", "Standard error", "Standards organization", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical packages", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Streptomycin", "Structural break", "Structural equation modeling", "Stuart Pocock", "Student's t-test", "Sufficient statistic", "Sulfuric acid", "Surgical procedures", "Survey methodology", "Survey research", "Survival analysis", "Survival function", "Survivorship bias", "System identification", "Systematic review", "Tax credit", "Test method", "The Canon of Medicine", "The New York Times", "Therapy", "Time domain", "Time series", "Tolerance interval", "Trade organization", "Translational research", "Trend estimation", "Trials (journal)", "U-statistic", "U.S. National Institutes of Health", "US Congress", "Uniformly most powerful test", "Urinary incontinence", "Usability testing", "V-statistic", "Vaccine", "Vaccine trial", "Variance", "Vascular surgery", "Vector autoregression", "Vinegar", "Virulence", "Vital signs", "Vitamin C", "Vitriol", "Volunteering", "Wald test", "Wavelet", "Wayback Machine", "Whisky tasting", "Whittle likelihood", "Wilcoxon signed-rank test", "Wine tasting", "Z-test"], "references": ["http://www.cmaj.ca/cgi/pmidlookup?view=long&pmid=11584570", "http://adisonline.com/pharmaceuticalmedicine/Abstract/2011/25040/Achieving_Ethnic_Diversity_in_Trial_Recruitment.1.aspx", "http://adisonline.com/pharmaceuticalmedicine/Fulltext/2010/24040/EU_Compassionate_Use_Programmes__CUPs___Regulatory.4.aspx", "http://www.centerwatch.com/clinical-trials/volunteering.aspx", "http://www.experiment-resources.com/replication-study.html", "http://www.hhlaw.com/files/Publication/edbf3429-125c-41c9-9442-b552e69b756c/Presentation/PublicationAttachment/972a9053-8c8d-46e4-ac96-ecf4892a8643/Pharma.pdf", "http://journals.lww.com/anesthesia-analgesia/Fulltext/2015/10000/Clinical_Research_Methodology_2___Observational.27.aspx", "http://www.merckmanuals.com/home/drugs/over-the-counter_drugs/overview_of_over-the-counter_drugs.html", "http://www.outsourcing-pharma.com/Clinical-Development/CROs-Slowly-Shifting-to-Adaptive-Clinical-Trial-Designs", "http://www.pharm-olam.com/pdf/POI-Seasonality.pdf", "http://www.pharmabiz.com/NewsDetails.aspx?aid=81931&sid=2", "http://www.sciencedirect.com/science/article/pii/S1936879808001702", "http://www.statisticshowto.com/active-control-comparator/", "http://www.technologyreview.com/news/521496/can-genomics-blow-up-the-clinical-trial/", "http://azcc.arizona.edu/patients/clinical-trials/faq", "http://irb.ucsd.edu/ab_2328_bill_20020826_enrolled.pdf", "http://www.cancer.gov/clinicaltrials", "http://clinicaltrials.gov/", "http://clinicaltrials.gov/ct2/info/glossary", "http://clinicaltrials.gov/ct2/info/understand", "http://www.fda.gov/Drugs/DevelopmentApprovalProcess/", "http://www.fda.gov/Drugs/ResourcesForYou/Consumers/ucm289601.htm", "http://www.fda.gov/downloads/RegulatoryInformation/Guidances/UCM126553.pdf", "http://www.fda.gov/orphan/taxcred.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1126054", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1475627", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1550630", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2308176", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3218552", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3373653", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4792418", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4804244", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC81460", "http://www.ncbi.nlm.nih.gov/pubmed/11584570", "http://www.ncbi.nlm.nih.gov/pubmed/12775622", "http://www.ncbi.nlm.nih.gov/pubmed/15829477", "http://www.ncbi.nlm.nih.gov/pubmed/16603070", "http://www.ncbi.nlm.nih.gov/pubmed/17374817", "http://www.ncbi.nlm.nih.gov/pubmed/1737655", "http://www.ncbi.nlm.nih.gov/pubmed/17497782", "http://www.ncbi.nlm.nih.gov/pubmed/18711161", "http://www.ncbi.nlm.nih.gov/pubmed/18755376", "http://www.ncbi.nlm.nih.gov/pubmed/19463302", "http://www.ncbi.nlm.nih.gov/pubmed/19616703", "http://www.ncbi.nlm.nih.gov/pubmed/19826022", "http://www.ncbi.nlm.nih.gov/pubmed/20142732", "http://www.ncbi.nlm.nih.gov/pubmed/21350072", "http://www.ncbi.nlm.nih.gov/pubmed/21473670", "http://www.ncbi.nlm.nih.gov/pubmed/22102925", "http://www.ncbi.nlm.nih.gov/pubmed/22376222", "http://www.ncbi.nlm.nih.gov/pubmed/22719228", "http://www.ncbi.nlm.nih.gov/pubmed/25391940", "http://www.ncbi.nlm.nih.gov/pubmed/25517397", "http://www.ncbi.nlm.nih.gov/pubmed/26378704", "http://www.ncbi.nlm.nih.gov/pubmed/26908540", "http://www.ncbi.nlm.nih.gov/pubmed/26928437", "http://www.ncbi.nlm.nih.gov/pubmed/26978655", "http://www.ncbi.nlm.nih.gov/pubmed/27019801", "http://www.bruzelius.info/Nautica/Medicine/Lind(1753).html", "http://www.pmda.go.jp/ich/s/s1b_98_7_9e.pdf", "http://hdl.handle.net/10161%2F12742", "http://www.news-medical.net/whitepaper/20130916/Adaptive-Clinical-Trials-for-Overcoming-Research-Challenges.aspx", "http://www.annals.org/cgi/pmidlookup?view=long&pmid=18711161", "http://www.commondreams.org/archive/2007/12/14/5838/", "http://doi.org/10.1001%2Fjama.2009.1426", "http://doi.org/10.1001%2Fjama.297.11.1233", "http://doi.org/10.1002%2F14651858.CD001756.pub6", "http://doi.org/10.1007%2FBF03256820", "http://doi.org/10.1007%2FBF03256863", "http://doi.org/10.1016%2FS0140-6736(09)61309-X", "http://doi.org/10.1016%2Fj.clindermatol.2008.01.016", "http://doi.org/10.1016%2Fj.jcin.2008.01.008", "http://doi.org/10.1016%2Fj.jhealeco.2016.01.012", "http://doi.org/10.1021%2Fja0713781", "http://doi.org/10.1038%2F515177a", "http://doi.org/10.1080%2F10810730.2011.635774", "http://doi.org/10.1097%2FSLA.0b013e3181cf863d", "http://doi.org/10.1136%2Fbmj.326.7400.1193", "http://doi.org/10.1161%2F01.HYP.19.2.212", "http://doi.org/10.1177%2F0968533212465615", "http://doi.org/10.1177%2F1740774515625964", "http://doi.org/10.1185%2F03007995.2011.573546", "http://doi.org/10.1186%2F1745-6215-7-9", "http://doi.org/10.1213%2FANE.0000000000000861", "http://doi.org/10.1258%2Fjmb.2010.010019", "http://doi.org/10.1371%2Fjournal.pmed.1001228", "http://doi.org/10.1371%2Fjournal.pone.0150205", "http://doi.org/10.2196%2Fjmir.7.1.e5", "http://doi.org/10.5662%2Fwjm.v6.i1.101", "http://doi.org/10.7326%2F0003-4819-149-4-200808190-00012", "http://www.econlib.org/library/Enc1/DrugLag.html", "http://www.foxtrialfinder.org", "http://www.ich.org/", "http://www.ich.org/LOB/media/MEDIA482.pdf", "http://www.ich.org/cache/compo/276-254-1.html", "http://www.jmir.org/2005/1/e5/", "http://med-quest.org/electronic-patient-reported-outcomes-benefits/", "http://www.mlanet.org/resources/hlth_tutorial/mod4c.html", "http://www.phrma.org/sites/default/files/pdf/rd_brochure_022307.pdf", "https://cioms.ch/shop/product/evidence-synthesis-and-meta-analysis-report-of-cioms-working-group-x/", "https://cioms.ch/shop/product/management-of-safety-information-from-clinical-trials-report-of-cioms-working-group-vi/", "https://books.google.com/?id=i1oAxuE29MUC&pg=PA3&lpg=PA3", "https://books.google.com/books?id=Zke8ocubNXAC&pg=PA1", "https://books.google.com/books?id=d8GxG0d9rpgC&pg=PA118", "https://books.google.com/books?id=lU4TAAAAQBAJ", "https://www.nytimes.com/2012/04/17/science/rise-in-scientific-journal-retractions-prompts-calls-for-reform.html", "https://www.nytimes.com/2015/09/09/opinion/the-solution-to-drug-prices.html", "https://www.wsj.com/article/PR-CO-20130507-911627.html?mod=googlenews_wsj", "https://www.wsj.com/news/articles/SB10001424052702304361604579290572010514840?KEYWORDS=adaptive+clinical+trial", "https://www.fda.gov/Drugs/DevelopmentApprovalProcess/HowDrugsareDevelopedandApproved/ApprovalApplications/InvestigationalNewDrugINDApplication/ucm226358.htm", "https://www.fda.gov/MedicalDevices/DeviceRegulationandGuidance/HowtoMarketYourDevice/PremarketSubmissions/PremarketApprovalPMA/ucm050419.htm", "https://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM227351.pdf", "https://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/UCM477584.pdf", "https://www.fda.gov/forpatients/clinicaltrials/informedconsent/default.htm", "https://www.ncbi.nlm.nih.gov/pubmedhealth/PMH0011167/", "https://archive.is/20120707082132/http://adisonline.com/pharmaceuticalmedicine/Fulltext/2010/24040/EU_Compassionate_Use_Programmes__CUPs___Regulatory.4.aspx", "https://web.archive.org/web/20070630181341/http://www.ich.org/cache/compo/276-254-1.html", "https://web.archive.org/web/20080625192559/http://www.hhlaw.com/files/Publication/edbf3429-125c-41c9-9442-b552e69b756c/Presentation/PublicationAttachment/972a9053-8c8d-46e4-ac96-ecf4892a8643/Pharma.pdf", "https://web.archive.org/web/20080921193848/http://www.ich.org/LOB/media/MEDIA482.pdf", "https://web.archive.org/web/20081217025300/http://www.pmda.go.jp/ich/s/s1b_98_7_9e.pdf", "https://web.archive.org/web/20110715072506/http://www.pharm-olam.com/pdf/POI-Seasonality.pdf", "https://web.archive.org/web/20111114180004/http://adisonline.com/pharmaceuticalmedicine/Abstract/2011/25040/Achieving_Ethnic_Diversity_in_Trial_Recruitment.1.aspx", "https://web.archive.org/web/20120410030741/http://clinicaltrials.gov/ct2/info/understand", "https://web.archive.org/web/20131003122247/http://www.mlanet.org/resources/hlth_tutorial/mod4c.html", "https://web.archive.org/web/20140204030845/http://online.wsj.com/article/PR-CO-20130507-911627.html?mod=googlenews_wsj", "https://web.archive.org/web/20160314151221/http://www.wsj.com/news/articles/SB10001424052702304361604579290572010514840?KEYWORDS=adaptive+clinical+trial", "https://docs.gatesfoundation.org/documents/clinical_trials.pdf", "https://www.webcitation.org/61BHrqVfM?url=http://clinicaltrials.gov/ct2/info/glossary", "https://www.worldcat.org/oclc/163149563", "https://www.worldcat.org/oclc/317650570", "https://www.worldcat.org/oclc/50016270"]}, "STAR model": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from June 2012", "Nonlinear systems", "Nonlinear time series analysis", "Time series models"], "title": "STAR model", "method": "STAR model", "url": "https://en.wikipedia.org/wiki/STAR_model", "summary": "In statistics, Smooth Transition Autoregressive (STAR) models are typically applied to time series data as an extension of autoregressive models, in order to allow for higher degree of flexibility in model parameters through a smooth transition.\nGiven a time series of data xt, the STAR model is a tool for understanding and, perhaps, predicting future values in this series, assuming that the behaviour of the series changes depending on the value of the transition variable. The transition might depend on the past values of the x series (similar to the SETAR models), or exogenous variables.\nThe model consists of 2 autoregressive (AR) parts linked by the transition function. The model is usually referred to as the STAR(p) models proceeded by the letter describing the transition function (see below) and p is the order of the autoregressive part. Most popular transition function include exponential function and first and second-order logistic functions. They give rise to Logistic STAR (LSTAR) and Exponential STAR (ESTAR) models.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3d/Estar_transition_function.png", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Lstar_transition_function.png", "https://upload.wikimedia.org/wikipedia/commons/0/02/Lstar_transition_function_c1_and_c2.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Autoregressive", "Autoregressive model", "Characterizations of the exponential function", "Digital object identifier", "Exogenous", "Exponential growth", "Exponentiation", "Generalised logistic function", "Logistic distribution", "R (programming language)", "SETAR (model)", "SETAR models", "Statistics", "Time series", "Variance", "White noise"], "references": ["http://intlpress.com/site/pub/files/_fulltext/journals/sii/2011/0004/0002/SII-2011-0004-0002-a001.pdf", "http://www.ssc.wisc.edu/~bhansen/papers/saii_11.pdf", "http://lx2.saas.hku.hk/research/research-report-494.pdf", "http://doi.org/10.1081%2FETC-120008723", "http://doi.org/10.1111%2Fj.1467-9892.1986.tb00501.x", "http://doi.org/10.4310%2Fsii.2011.v4.n2.a4"]}, "Galton\u2013Watson process": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2009", "Genetic genealogy", "Human population genetics", "Stochastic processes", "Surname"], "title": "Galton\u2013Watson process", "method": "Galton\u2013Watson process", "url": "https://en.wikipedia.org/wiki/Galton%E2%80%93Watson_process", "summary": "The Galton\u2013Watson process is a branching stochastic process arising from Francis Galton's statistical investigation of the extinction of family names. The process models family names as patrilineal (passed from father to son), while offspring are randomly either male or female, and names become extinct if the family name line dies out (holders of the family name die without male descendants). This is an accurate description of Y chromosome transmission in genetics, and the model is thus useful for understanding human Y-chromosome DNA haplogroups, and is also of use in understanding other processes (as described below); but its application to actual extinction of family names is fraught. In practice, family names change for many other reasons, and dying out of name line is only one factor, as discussed in examples, below; the Galton\u2013Watson process is thus of limited applicability in understanding actual family name distributions.\nThere was concern amongst the Victorians that aristocratic surnames were becoming extinct. Galton originally posed the question regarding the probability of such an event in an 1873 issue of The Educational Times, and the Reverend Henry William Watson replied with a solution. Together, they then wrote an 1874 paper entitled \"On the probability of the extinction of families\" in the Journal of the Anthropological Institute of Great Britain and Ireland (now the Journal of the Royal Anthropological Institute). Galton and Watson appear to have derived their process independently of the earlier work by I. J. Bienaym\u00e9; see Heyde and Seneta 1977. For a detailed history see Kendall (1966 and 1975).", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3f/Galton_Watson_survival_Poisson.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost surely", "Aristocracy (class)", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Averaged reproduction mean", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "C C Heyde", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Chinese surname", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "David George Kendall", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dutch name", "Dynkin's formula", "E Seneta", "Econometrics", "Educational Times", "Empirical process", "Epidemic", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Exponential growth", "Extinction", "Extreme value theory", "F. Thomas Bruss", "Family name", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "Francis Galton", "G-network", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Han Chinese", "Heath\u2013Jarrow\u2013Morton framework", "Henry William Watson", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Human Y-chromosome DNA haplogroup", "Human Y-chromosome DNA haplogroups", "Hunt process", "Independent and identically-distributed random variables", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Serial Number", "Ipso facto", "Ir\u00e9n\u00e9e-Jules Bienaym\u00e9", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Japanese names", "Journal of Applied Probability", "Journal of the Royal Anthropological Institute", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Li (surname)", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "Luigi Luca Cavalli-Sforza", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Meiji restoration", "Mixing (mathematics)", "Moran process", "Moving-average model", "Mutant", "Napoleonic Wars", "Nguy\u1ec5n", "Non-homogeneous Poisson process", "Nuclear chain reaction", "Optional stopping theorem", "Organism", "Ornstein\u2013Uhlenbeck process", "Patrilineal", "Pedigree collapse", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson distribution", "Poisson point process", "Poisson process", "Population", "Potts model", "Predictable process", "Probability distribution", "Probability generating function", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Resource Dependent Branching Process", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sexual orientation", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistical independence", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Thai name", "The Economist", "The Educational Times", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "Victorian era", "Vietnamese name", "Wang (surname)", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "Y chromosome", "Zhang (surname)"], "references": ["http://hsblogs.stanford.edu/morrison/", "http://hsblogs.stanford.edu/morrison/files/2011/02/27.pdf", "http://hsblogs.stanford.edu/morrison/morrison-institute-working-papers1-pdf/", "http://doi.org/10.1112%2Fblms%2F7.3.225", "http://doi.org/10.1112%2Fjlms%2Fs1-41.1.385", "http://www.worldcat.org/issn/0024-6093", "http://www.worldcat.org/issn/0024-6107", "http://ioearc.da.ulcc.ac.uk/9305/1/Educational%20Times%20Vol%2026%20Iss%20144.PDF", "http://ioearc.da.ulcc.ac.uk/9309/1/Educational%20Times%20Vol%2026%20Iss%20148.PDF", "http://ioearc.da.ulcc.ac.uk/9344/1/Educational%20Times%20Vol%2025%20Iss%20143.PDF", "https://web.archive.org/web/20040401131411/http://www-users.york.ac.uk/~pml1/stats/gwproc.ps", "https://babel.hathitrust.org/cgi/pt?id=mdp.39015027596207;view=1up;seq=166", "https://www.webcitation.org/6bTLDd2kR?url=http://hsblogs.stanford.edu/morrison/files/2011/02/27.pdf"]}, "Central composite design": {"categories": ["Design of experiments", "Educational research", "Mathematical optimization"], "title": "Central composite design", "method": "Central composite design", "url": "https://en.wikipedia.org/wiki/Central_composite_design", "summary": "In statistics, a central composite design is an experimental design, useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level factorial experiment.\nAfter the designed experiment is performed, linear regression is used, sometimes iteratively, to obtain results. Coded variables are often used when constructing this design.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial design", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Internal validity", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MATLAB", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Response variable", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1016%2Fj.biortech.2016.12.073", "https://www.researchgate.net/publication/311881656_Optimization_of_organosolv_pretreatment_of_rice_straw_for_enhanced_biohydrogen_production_using_Enterobacter_aerogenes"]}, "Circular statistics": {"categories": ["Directional statistics", "Statistical data types", "Statistical theory", "Types of probability distributions"], "title": "Directional statistics", "method": "Circular statistics", "url": "https://en.wikipedia.org/wiki/Directional_statistics", "summary": "Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Rn), axes (lines through the origin in Rn) or rotations in Rn. More generally, directional statistics deals with observations on compact Riemannian manifolds.\n\nThe fact that 0 degrees and 360 degrees are identical angles, so that for example 180 degrees is not a sensible mean of 2 degrees and 358 degrees, provides one illustration that special statistical methods are required for the analysis of some types of data (in this case, angular data). Other examples of data that may be regarded as directional include statistics involving temporal periods (e.g. time of day, week, month, year, etc.), compass directions, dihedral angles in molecules, orientations, rotations and so on.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ca/Point_sets_from_Kent_distributions_mapped_onto_a_sphere_-_journal.pcbi.0020131.g004.svg", "https://upload.wikimedia.org/wikipedia/en/4/42/Fb5_cover.jpg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Average", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bessel function", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bioinformatics", "Bivariate normal distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Cartesian Coordinate System", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Central limit theorem for directional statistics", "Chi-squared distribution", "Chi distribution", "Christopher Bingham", "Circular distribution", "Circular uniform distribution", "Complex normal distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Crystallography", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Degree (angle)", "Delaporte distribution", "Digital object identifier", "Dihedral angle", "Dirac delta function", "Direction (geometry)", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geology", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Histogram", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kuiper's test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Line (geometry)", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Matrix von Mises\u2013Fisher distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean of circular quantities", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "N-sphere", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Protein", "PubMed Central", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quaternions", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Rayleigh test", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Riemannian manifold", "Rotation", "Rotation matrix", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Sphere", "Stable distribution", "Statistics", "Stiefel manifold", "Student's t-distribution", "Theta function", "Torus", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Two-dimensional sphere", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unit vector", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal", "Wrapped normal distribution", "Yamartino method", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2440424", "http://doi.org/10.1073%2Fpnas.0801715105", "http://doi.org/10.1093%2Fbiomet%2F59.3.665", "http://doi.org/10.1111%2Fj.1541-0420.2006.00682.x", "http://doi.org/10.1198%2F016214501750332974", "http://doi.org/10.1214%2Faos%2F1176342874", "http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.0020131", "https://books.google.com/books?id=sKqWMGqQXQkC&printsec=frontcover&dq=Jammalamadaka+Topics+in+circular&hl=en&ei=iJ3QTe77NKL00gGdyqHoDQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDcQ6AEwAA#v=onepage&q&f=false"]}, "Completely randomized design": {"categories": ["Analysis of variance", "CS1 maint: Multiple names: authors list", "Design of experiments", "Statistical models", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Completely randomized design", "method": "Completely randomized design", "url": "https://en.wikipedia.org/wiki/Completely_randomized_design", "summary": "In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take other nuisance variables into account. This article describes completely randomized designs that have one primary factor. The experiment compares the values of a response variable based on the different levels of that primary factor. For completely randomized designs, the levels of the primary factor are randomly assigned to the experimental units.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "One-way ANOVA", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Random number generation", "Random number table", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Response variable", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://itfeature.com/design-of-experiment-doe/completely-randomized-design-crd", "http://www.itl.nist.gov/div898/handbook/pri/section3/pri331.htm", "http://www.nist.gov"]}, "Human subject research": {"categories": ["All articles to be expanded", "Articles containing video clips", "Articles to be expanded from July 2015", "Articles using small message boxes", "CS1 Russian-language sources (ru)", "Clinical research", "Commons category link is on Wikidata", "Ethics and statistics", "Human subject research", "Research ethics", "Webarchive template wayback links", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Human subject research", "method": "Human subject research", "url": "https://en.wikipedia.org/wiki/Human_subject_research", "summary": "Human subject research is systematic, scientific investigation that can be either interventional (a \"trial\") or observational (no \"test article\") and involves human beings as research subjects. Human subject research can be either medical (clinical) research or non-medical (e.g., social science) research. Systematic investigation incorporates both the collection and analysis of data in order to answer a specific question. Medical human subject research often involves analysis of biological specimens, epidemiological and behavioral studies and medical chart review studies. (A specific, and especially heavily regulated, type of medical human subject research is the \"clinical trial\", in which drugs, vaccines and medical devices are evaluated.) On the other hand, human subject research in the social sciences often involves surveys which consist of questions to a particular group of people. Survey methodology includes questionnaires, interviews, and focus groups.\nHuman subject research is used in various fields, including research into basic biology, clinical medicine, nursing, psychology, sociology, political science, and anthropology. As research has become formalized, the academic community has developed formal definitions of \"human subject research\", largely in response to abuses of human subjects.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/1/18/National_Advisory_Committee_for_Aeronautics_wind_tests_%281946%29.webm"], "links": ["Abnormal psychology", "Abraham Maslow", "Advisory Committee on Human Radiation Experiments", "Affective neuroscience", "Affective science", "Airbag", "Albert Bandura", "Amos Tversky", "Animal testing", "Anomalistic psychology", "Anthropology", "Applied behavior analysis", "Applied psychology", "Archival research", "Asch conformity experiments", "Automotive industry", "B. F. Skinner", "BBC News", "Basic science (psychology)", "Behavioral epigenetics", "Behavioral neuroscience", "Behaviorism", "Behavioural genetics", "Beijing", "Belmont Report", "Beneficence (ethics)", "Bibb Latane", "Biobank", "Biobank ethics", "Bioethics", "Biological specimens", "Biology", "Biomedical research", "Biotechnology", "Bruce McEwen", "Bystander effect", "Cadaver", "Car", "Carl Jung", "Carl Rogers", "Case study", "Chester M. Southam", "Church Committee", "Clark L. Hull", "Clinical medicine", "Clinical psychology", "Clinical research", "Clinical research ethics", "Clinical study design", "Clinical trial", "Coercion", "Cognitive dissonance", "Cognitive neuroscience", "Cognitive psychology", "Cognitivism (psychology)", "Common Rule", "Community advisory board", "Community psychology", "Comparative psychology", "Confidentiality", "Consent", "Consumer behaviour", "Content analysis", "Contract research organization", "Control group", "Cornell University", "Counseling psychology", "Crash test dummy", "Critical psychology", "Cross-cultural psychology", "Cultural psychology", "Daniel Kahneman", "Data monitoring committee", "Data sharing", "David McClelland", "Declaration of Helsinki", "Developmental psychology", "Dietary supplement", "Differential psychology", "Diffusion of responsibility", "Digital object identifier", "Disability", "Disfigurement", "Dismemberment", "Doctors' Trial", "Donald O. Hebb", "Donald T. Campbell", "Douglas MacArthur", "Duplessis Orphans", "Ecological psychology", "Ed Diener", "Educational psychology", "Edward Thorndike", "Efficacy", "Elliot Aronson", "Endel Tulving", "Epidemiological", "Erik Erikson", "Ernest Hilgard", "Ethics committee", "Evolutionary psychology", "Experiment", "Experimental psychology", "Facebook", "Feminist psychology", "Focus groups", "Food and Drug Administration", "Forensic psychology", "Fort Detrick", "Genie (feral child)", "George Armitage Miller", "Gestalt psychology", "Gordon Allport", "Guangzhou", "Guidelines for human subject research", "Hans Eysenck", "Harbin", "Harry Harlow", "Harvard University", "HeLa", "Health psychology", "Herbert A. Simon", "History of psychology", "Human being", "Human experimentation in North Korea", "Human factors and ergonomics", "Human radiation experiments", "Imperial Japanese Army", "Index of psychology articles", "Industrial and organizational psychology", "Informed consent", "Institutional review board", "Integrated Authority File", "Intelligence", "International Standard Book Number", "International Standard Serial Number", "Interview (research)", "Interviews", "Ivan Pavlov", "J. P. Guilford", "Japanese human experimentations", "Japanese war crimes", "Jean Piaget", "Jerome Bruner", "Jerome Kagan", "Jews", "John B. Watson", "John M. Darley", "John Robert Anderson (psychologist)", "Josef Mengele", "Joseph E. LeDoux", "Justice (ethics)", "Kurt Lewin", "Larry Squire", "Lawrence Kohlberg", "Legal psychology", "Leon Festinger", "List of counseling topics", "List of important publications in psychology", "List of medical ethics cases", "List of psychological research methods", "List of psychological schools", "List of psychologists", "List of psychology disciplines", "List of psychology organizations", "List of psychotherapies", "Manchukuo", "Martin Seligman", "Mathematical psychology", "Media psychology", "Medical device", "Medical ethics", "Medical nutrition therapy", "Medical torture", "Merrill Carlsmith", "Michael Posner (psychologist)", "Milgram Experiment", "Military medical ethics", "Military psychology", "Military vehicle", "Monitoring in clinical trials", "Multicenter trial", "Music psychology", "Muzafer Sherif", "Nanking", "National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research", "National Diet Library", "National Institute of Justice", "National Research Act", "National Science Foundation", "Nazi concentration camps", "Nazi crimes against Soviet POWs", "Nazi human experimentation", "Neal E. Miller", "Neuroimaging", "Neuropsychology", "News Feed", "Noam Chomsky", "Non-human primate experiments", "Nuremberg Code", "Nuremberg Trials", "Nursing", "Observation", "Occupational health psychology", "Ohio Penitentiary", "Operation Whitecoat", "Outline of psychology", "Outsource", "Oxford University Press", "Pastoral psychology", "Paul Ekman", "Penicillin", "Perception", "Personality psychology", "Pharmaceutical drug", "Pharmaceutical industry", "Philip Zimbardo", "Philosophy of psychology", "Pilot experiment", "Poison laboratory of the Soviet secret services", "Poles", "Political psychology", "Political science", "Positive psychology", "Primum non nocere", "Privacy", "Privacy for research participants", "Proceedings of the National Academy of Sciences of the United States of America", "Project MKUltra", "Prospective cohort study", "Psycholinguistics", "Psychological testing", "Psychologist", "Psychology", "Psychology of religion", "Psychometrics", "Psychophysics", "Psychophysiology", "Psychotherapy", "PubMed Central", "PubMed Identifier", "Pure Food and Drug Act", "Qualitative psychological research", "Quantitative psychological research", "Quantitative psychology", "Raymond Cattell", "Realistic conflict theory", "Reproducibility", "Research ethics", "Research participant", "Respect for persons", "Return of results", "Richard Davidson", "Richard E. Nisbett", "Richard Lazarus", "Right to withdraw", "Risk-benefit analysis", "Robert Zajonc", "Roger Brown (psychologist)", "Romani people", "Ronald C. Kessler", "Roy Baumeister", "Safety", "School psychology", "Second Sino-Japanese war", "Self-report inventory", "Shelley E. Taylor", "Shir\u014d Ishii", "Sigmund Freud", "Singapore", "Sinti", "Social influence", "Social media", "Social psychology", "Social research", "Sociology", "Solomon Asch", "Sport psychology", "Stanford University", "Stanford prison experiment", "Stanley Milgram", "Stanley Schachter", "Statistical unit", "Suicidology", "Survey (human research)", "Survey methodology", "Susan Fiske", "Systems psychology", "The Holocaust", "Theoretical psychology", "Therapy", "Timeline of psychology", "Title 32 CFR Part 219", "Title 32 of the Code of Federal Regulations", "Title 45 CFR Part 46", "Title 45 of the Code of Federal Regulations", "Totskoye nuclear exercise", "Traffic psychology", "Trauma (medicine)", "Tuskegee Institute", "Tuskegee syphilis experiment", "Tuttle Publishing", "UNESCO", "Ulric Neisser", "Unethical human experimentation", "Unethical human experimentation in the United States", "Unit 1644", "Unit 1855", "Unit 731", "Unit 8604", "Unit 9420", "United States", "United States Department of Health, Education and Welfare", "United States Department of Health and Human Services", "United States President's Commission on CIA activities within the United States", "United States Public Health Service", "University of California, Irvine", "University of Texas at Austin", "Vaccine", "Vivisection", "Walter Mischel", "Wayback Machine", "Wilhelm Wundt", "William James", "World Medical Association", "World War II", "Yale University"], "references": ["http://www.bt.com.bn/focus/2007/10/31/a_life_haunted_by_wwii_surgical_killings", "http://neuron4.psych.ubc.ca/~schaller/Psyc591Readings/Blass1999.pdf", "http://www.humansubjects.com/", "http://auschwitz.dk/Mengele.htm", "http://muse.jhu.edu/cgi-bin/resolve_openurl.cgi?issn=1049-2089&volume=17&issue=4&spage=698&aulast=Katz", "http://www2.umf.maine.edu/irb/other-links/the-belmont-report/", 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"http://www.ncbi.nlm.nih.gov/pubmed/23679571", "http://www.ncbi.nlm.nih.gov/pubmed/24889601", "http://www.ncbi.nlm.nih.gov/pubmed/5724528", "http://videocast.nih.gov/pdf/ohrp_belmont_report.pdf", "http://www.nij.gov/funding/humansubjects/", "http://www.wma.net/e/press/2000_8.htm", "http://doi.org/10.1007%2Fs10676-010-9227-5", "http://doi.org/10.1037%2Fh0040525", "http://doi.org/10.1073%2Fpnas.1320040111", "http://doi.org/10.1089%2Fcyber.2012.0334", "http://doi.org/10.1111%2Fj.1559-1816.1999.tb00134.x", "http://doi.org/10.1177%2F001872676501800105", "http://doi.org/10.1353%2Fhpu.2006.0126", "http://www.svoboda.org/content/article/27214509.html", "http://www.talyarkoni.org/blog/2014/06/28/in-defense-of-facebook/", "http://unesdoc.unesco.org/images/0014/001461/146180E.pdf", "http://www.worldcat.org/issn/0362-4331", "http://www.worldcat.org/issn/1388-1957", "http://materiais.dbio.uevora.pt/MA/Modulo2/Artigos/SoCRA-Perlman.pdf", "http://scindeks.ceon.rs/article.aspx?artid=0354-73100103179B&lang=en", "http://news.bbc.co.uk/2/hi/programmes/file_on_4/4701196.stm", "https://www.chronicle.com/article/Harvards-Privacy-Meltdown/128166", "https://books.google.com/books?id=4P04DuPIfAYC&pg=PA105#v=onepage&q&f=false", "https://books.google.com/books?id=cprBEpxvexgC&pg=PA109#v=onepage&q&f=false", "https://www.google.com/hostednews/afp/article/ALeqM5ht5P8U54dLa7dH9mqjKyurq0zQMw?hl=en", "https://medium.com/@JamesGrimmelmann/illegal-unethical-and-mood-altering-8b93af772688", "https://www.nytimes.com/2014/07/01/opinion/jaron-lanier-on-lack-of-transparency-in-facebook-study.html", "https://www.scientificamerican.com/article.cfm?id=milgram-nationality-conformity", "https://link.springer.com/article/10.1007/s10676-010-9227-5", "https://www.theguardian.com/commentisfree/2014/jul/07/facebook-study-science-experiment-research", "https://www.thestar.com/news/canada/2013/07/16/hungry_aboriginal_kids_used_unwittingly_in_nutrition_experiments_researcher_says.html", "https://www.gpo.gov/fdsys/delivery/get-cfr.action?TYPE=TEXT&YEAR=current&TITLE=32&PART=219&SECTION=102", "https://www.gpo.gov/fdsys/delivery/get-cfr.action?TYPE=TEXT&YEAR=current&TITLE=45&PART=46&SECTION=102", "https://www.hhs.gov/ohrp/humansubjects/guidance/belmont.htm", "https://www.hhs.gov/ohrp/regulations-and-policy/belmont-report/index.html", "https://d-nb.info/gnd/4038649-1", "https://id.ndl.go.jp/auth/ndlna/01207132", "https://web.archive.org/web/20060927052340/http://www.wma.net/e/press/2000_8.htm", "https://web.archive.org/web/20071029120713/http://ohsr.od.nih.gov/guidelines/nuremberg.html", "https://web.archive.org/web/20110611105753/http://www.garfield.library.upenn.edu/classics1981/A1981LC33300001.pdf", "https://web.archive.org/web/20120207032034/http://www.utexas.edu/research/rsc/humansubjects/whatis.html", "https://web.archive.org/web/20140317024425/https://www.google.com/hostednews/afp/article/ALeqM5ht5P8U54dLa7dH9mqjKyurq0zQMw?hl=en", "https://web.archive.org/web/20141213021214/http://www.bt.com.bn/focus/2007/10/31/a_life_haunted_by_wwii_surgical_killings", "https://docs.gatesfoundation.org/documents/clinical_trials.pdf", "https://www.simplypsychology.org/zimbardo.html", "https://www.webcitation.org/61BHsKgXN?url=http://www.wma.net/en/30publications/10policies/b3/index.html", "https://www.wikidata.org/wiki/Q1331083"]}, "Newcastle\u2013Ottawa scale": {"categories": ["All stub articles", "CS1 maint: Multiple names: authors list", "Meta-analysis", "Statistics stubs"], "title": "Newcastle\u2013Ottawa scale", "method": "Newcastle\u2013Ottawa scale", "url": "https://en.wikipedia.org/wiki/Newcastle%E2%80%93Ottawa_scale", "summary": "In statistics, the Newcastle\u2013Ottawa scale is a tool used for assessing the quality of non-randomized studies included in a systematic review and/or meta-analyses. Using the tool, each study is judged on eight items, categorized into three groups: the selection of the study groups; the comparability of the groups; and the ascertainment of either the exposure or outcome of interest for case-control or cohort studies respectively. Stars awarded for each quality item serve as a quick visual assessment. Stars are awarded such that the highest quality studies are awarded up to nine stars. The method was developed as a collaboration between the University of Newcastle, Australia, and the University of Ottawa, Canada, using a Delphi process to define variables for data extraction. The scale was then tested on systematic reviews and further refined. Separate tools were developed for cohort and case\u2013control studies. It has also been adapted for prevalence studies.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg"], "links": ["Constance Guille", "Delphi method", "Digital object identifier", "Douglas A. Mata", "Emanuele Di Angelantonio", "International Standard Serial Number", "JAMA (journal)", "Marco A. Ramos", "Meta-analysis", "Narinder Bansal", "PubMed Central", "PubMed Identifier", "Rida Khan", "Srijan Sen", "Statistics", "Systematic review", "University of Newcastle (Australia)", "University of Ottawa"], "references": ["http://www.ohri.ca/programs/clinical_epidemiology/oxford.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4866499", "http://www.ncbi.nlm.nih.gov/pubmed/26647259", "http://www.ncbi.nlm.nih.gov/pubmed/27923088", "http://doi.org/10.1001/jama.2015.15845", "http://doi.org/10.1001/jama.2016.17324", "http://doi.org/10.3310/hta7270", "http://www.worldcat.org/issn/1538-3598"]}, "Stepwise regression": {"categories": ["Regression variable selection"], "title": "Stepwise regression", "method": "Stepwise regression", "url": "https://en.wikipedia.org/wiki/Stepwise_regression", "summary": "In statistics, stepwise regression is a method of fitting regression models in which the choice of predictive variables is carried out by an automatic procedure. In each step, a variable is considered for addition to or subtraction from the set of explanatory variables based on some prespecified criterion. Usually, this takes the form of a sequence of F-tests or t-tests, but other techniques are possible, such as adjusted R2, Akaike information criterion, Bayesian information criterion, Mallows's Cp, PRESS, or false discovery rate.\nThe frequent practice of fitting the final selected model followed by reporting estimates and confidence intervals without adjusting them to take the model building process into account has led to calls to stop using stepwise model building altogether or to at least make sure model uncertainty is correctly reflected.", "images": ["https://upload.wikimedia.org/wikipedia/en/0/07/Stepwise.jpg"], "links": ["Adjusted R-squared", "Akaike information criterion", "Annals of Statistics", "Approximation", "Bayesian information criterion", "Biometrika", "Bonferroni", "Box\u2013Behnken design", "Computer simulation", "Cross-validation (statistics)", "Data", "Data dredging", "Data mining", "Degrees of freedom (statistics)", "Design of experiments", "Digital object identifier", "Efficiency (statistics)", "Ensemble learning", "Experiment", "Explanatory variable", "F-test", "False discovery rate", "Freedman's paradox", "Least-angle regression", "Logistic regression", "Mallows's Cp", "Model (abstract)", "Model selection", "National Institute of Standards and Technology", "Occam's razor", "Overfitting", "PRESS statistic", "Parameter", "Regression analysis", "Regression model", "Regression validation", "Residual sum of squares", "Risk function", "Risk inflation", "SAS System", "Sample size", "Statistical survey", "Statistics", "T-test", "Training set", "Validation set", "Variable (mathematics)"], "references": ["http://www.itl.nist.gov/div898/handbook/", "http://www.itl.nist.gov/div898/handbook/pri/section3/pri3362.htm", "https://doi.org/10.1093%2Fbiomet%2F81.3.425", "https://doi.org/10.1214%2Faos%2F1176325766"]}, "Expected value": {"categories": ["Articles containing proofs", "Gambling terminology", "Theory of probability distributions"], "title": "Expected value", "method": "Expected value", "url": "https://en.wikipedia.org/wiki/Expected_value", "summary": "In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents. For example, the expected value in rolling a six-sided die is 3.5, because the average of all the numbers that come up in an extremely large number of rolls is close to 3.5. Less roughly, the law of large numbers states that the arithmetic mean of the values almost surely converges to the expected value as the number of repetitions approaches infinity. The expected value is also known as the expectation, mathematical expectation, EV, average, mean value, mean, or first moment.\nMore practically, the expected value of a discrete random variable is the probability-weighted average of all possible values. In other words, each possible value the random variable can assume is multiplied by its probability of occurring, and the resulting products are summed to produce the expected value. The same principle applies to an absolutely continuous random variable, except that an integral of the variable with respect to its probability density replaces the sum. The formal definition subsumes both of these and also works for distributions which are neither discrete nor absolutely continuous; the expected value of a random variable is the integral of the random variable with respect to its probability measure.The expected value does not exist for random variables having some distributions with large \"tails\", such as the Cauchy distribution. For random variables such as these, the long-tails of the distribution prevent the sum or integral from converging.\nThe expected value is a key aspect of how one characterizes a probability distribution; it is one type of location parameter. By contrast, the variance is a measure of dispersion of the possible values of the random variable around the expected value. The variance itself is defined in terms of two expectations: it is the expected value of the squared deviation of the variable's value from the variable's expected value.\nThe expected value plays important roles in a variety of contexts. In regression analysis, one desires a formula in terms of observed data that will give a \"good\" estimate of the parameter giving the effect of some explanatory variable upon a dependent variable. The formula will give different estimates using different samples of data, so the estimate it gives is itself a random variable. A formula is typically considered good in this context if it is an unbiased estimator\u2014 that is if the expected value of the estimate (the average value it would give over an arbitrarily large number of separate samples) can be shown to equal the true value of the desired parameter.\nIn decision theory, and in particular in choice under uncertainty, an agent is described as making an optimal choice in the context of incomplete information. For risk neutral agents, the choice involves using the expected values of uncertain quantities, while for risk averse agents it involves maximizing the expected value of some objective function such as a von Neumann\u2013Morgenstern utility function. One example of using expected value in reaching optimal decisions is the Gordon\u2013Loeb model of information security investment. According to the model, one can conclude that the amount a firm spends to protect information should generally be only a small fraction of the expected loss (i.e., the expected value of the loss resulting from a cyber or information security breach).", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/82/Beta_first_moment.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Largenumbers.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg"], "links": ["Absolute continuity", "Absolute convergence", "Almost surely", "Antoine Gombaud", "Arithmetic mean", "Berry\u2013Esseen theorem", "Bienaym\u00e9-Chebyshev inequality", "Blaise Pascal", "Cauchy distribution", "Cauchy\u2013Bunyakovsky\u2013Schwarz inequality", "Center of mass", "Central moment", "Central tendency", "Characteristic function (probability)", "Characteristic function (probability theory)", "Chebyshev's inequality", "Christiaan Huygens", "Classical mechanics", "Coin tossing", "Combinant", "Computational formula for the variance", "Conditional convergence", "Conditional expectation", "Conditional expected value", "Convergent sequence", "Convex function", "Covariance", "Cumulant", "Cumulative distribution function", "De M\u00e9r\u00e9's Problem", "Decision theory", "Dependent variable", "Dice", "Digital object identifier", "Discrete random variable", "Disjoint union", "Dominated convergence theorem", "E(X)", "Economics", "Equiprobable", "Errors and residuals in statistics", "Estimation theory", "Estimator", "Estimator bias", "Event (probability theory)", "Expectation (epistemic)", "Expectation value (quantum mechanics)", "Expected utility hypothesis", "Expected value (disambiguation)", "Explanatory variable", "Exponential function", "Fatou's lemma", "Finance", "Fubini theorem", "Geometric series", "Gordon-Loeb Model", "Harmonic series (mathematics)", "Heavy-tailed distribution", "H\u00f6lder\u2019s inequality", "Improper Riemann integral", "Improper integral", "Independent random variables", "Indicator function", "Infinite sum", "Inner product", "International Standard Book Number", "Jensen's inequality", "Kurtosis", "L-moment", "Law of large numbers", "Law of the unconscious statistician", "Law of total expectation", "Lebesgue integral", "Lebesgue integration", "Lebesgue\u2013Stieltjes integration", "Linear operator", "Location parameter", "Machine learning", "Markov's inequality", "Measurable function", "Measure (mathematics)", "Minkowski inequality", "Moment-generating function", "Moment (mathematics)", "Moment about the mean", "Moment generating function", "Monotone convergence theorem", "Monte Carlo methods", "Natural logarithm", "Nonlinear expectation", "Null set", "Objective function", "Outcome (probability)", "Pierre-Simon Laplace", "Pierre de Fermat", "Pip (counting)", "Plancherel theorem", "Pointwise convergence", "Probability-generating function", "Probability density function", "Probability distribution", "Probability mass function", "Probability measure", "Probability space", "Probability theory", "Problem of points", "Quantile function", "Quantum mechanics", "Quantum state", "Random variable", "Raw moment", "Regression analysis", "Richard W Hamming", "Riemann integral", "Riemann rearrangement theorem", "Risk aversion", "Risk neutrality", "Roulette", "Sample size", "Security breach", "Simple function", "Skewness", "St. Petersburg paradox", "Standard deviation", "Statistical dispersion", "Statistical estimation", "Statistical frequency", "Statistical sample", "Strong law of large numbers", "Theory of probability", "Unbiased estimator", "Uncertainty principle", "Variance", "Von Neumann\u2013Morgenstern utility function", "Wald's equation", "Weighted average", "William Allen Whitworth"], "references": ["http://jeff560.tripod.com/stat.html", "http://mathworld.wolfram.com/ExpectationValue.html", "http://doi.org/10.1145%2F581271.581274", "http://doi.org/10.2307%2F2309286", "http://www.york.ac.uk/depts/maths/histstat/huygens.pdf", "https://books.google.com/books?id=12Pk5zZFirEC&pg=PA38", "https://books.google.com/books?id=jX_F-77TA3gC&pg=PA64", "https://books.google.com/books?id=jX_F-77TA3gC&printsec=frontcover#v=onepage&q=Cauchy"]}, "Winsorized mean": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from March 2012", "Articles needing additional references from September 2009", "Means", "Robust statistics"], "title": "Winsorized mean", "method": "Winsorized mean", "url": "https://en.wikipedia.org/wiki/Winsorized_mean", "summary": "A winsorized mean is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean. It involves the calculation of the mean after replacing given parts of a probability distribution or sample at the high and low end with the most extreme remaining values, typically doing so for an equal amount of both extremes; often 10 to 25 percent of the ends are replaced. The winsorized mean can equivalently be expressed as a weighted average of the truncated mean and the quantiles at which it is limited, which corresponds to replacing parts with the corresponding quantiles.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Digital object identifier", "International Standard Book Number", "Mean", "Measure of central tendency", "Median", "Outlier", "Probability distribution", "PubMed Identifier", "Robust estimator", "Sampling (statistics)", "Statistical", "Symmetric probability distribution", "Truncated mean", "Unbiased estimator", "Weighted average", "Winsorising", "Yadolah Dodge"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/14596490", "http://doi.org/10.1037%2F1082-989X.8.3.254"]}, "Encyclopedia of Statistical Sciences": {"categories": ["All stub articles", "Encyclopedia stubs", "Encyclopedias of mathematics", "Mathematics books", "Statistics books", "Statistics stubs"], "title": "Encyclopedia of Statistical Sciences", "method": "Encyclopedia of Statistical Sciences", "url": "https://en.wikipedia.org/wiki/Encyclopedia_of_Statistical_Sciences", "summary": "The Encyclopedia of Statistical Sciences is an encyclopaedia of statistics published by John Wiley & Sons.The first edition, in nine volumes, was edited by Norman Lloyd Johnson and Samuel Kotz and appeared in 1982. The second edition, in 16 volumes, was published in 2006. Samuel Kotz was the senior editor.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/6/61/HK_Britannica_Micropedia_Ready_Reference_Index_1-7.JPG"], "links": ["Encyclopedia", "International Encyclopedia of Statistical Science", "JSTOR", "John Wiley & Sons", "Journal of the American Statistical Association", "Norman Lloyd Johnson", "Samuel Kotz", "Statistics"], "references": ["http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471150444.html", "http://econpapers.repec.org/article/besjnlasa/v_3a102_3ay_3a2007_3am_3aseptember_3ap_3a1074-1075.htm", "https://www.jstor.org/stable/2289675"]}, "SUDAAN": {"categories": ["All articles lacking sources", "Articles lacking sources from June 2008", "Proprietary commercial software for Linux", "Statistical software"], "title": "SUDAAN", "method": "SUDAAN", "url": "https://en.wikipedia.org/wiki/SUDAAN", "summary": "SUDAAN is a proprietary statistical software package for the analysis of correlated data, including correlated data encountered in complex sample surveys. SUDAAN originated in 1972 at RTI International (the trade name of Research Triangle Institute). Individual commercial licenses are sold for $1,460 a year, or $3,450 permanently.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["ADMB", "Analyse-it", "Analytic and enumerative statistical studies", "BMDP", "BV4.1 (software)", "CSPro", "Clinical trial", "Commercial software", "Comparison of statistical packages", "Correlation", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Data clustering", "Data set", "Dataplot", "EViews", "Epi Info", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "Mean", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "Open-source software", "OpenBUGS", "Orange (software)", "OxMetrics", "PSPP", "Proprietary software", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "RTI International", "R (programming language)", "Random digit dialing", "Regression analysis", "Resampling (statistics)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SYSTAT (software)", "SageMath", "Sample survey", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Social statistics", "Stan (software)", "Standard error (statistics)", "StatView", "StatXact", "Stata", "Statistica", "StatsDirect", "Stratified sampling", "TSP (econometrics software)", "Taylor series", "The Unscrambler", "Toxicology", "UNISTAT", "Weight function", "Weighting", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.statmodel.com/resrchpap.shtml", "http://www.rti.org/sudaan/"]}, "Robust confidence intervals": {"categories": ["All articles needing additional references", "Articles needing additional references from November 2015", "Robust statistics"], "title": "Robust confidence intervals", "method": "Robust confidence intervals", "url": "https://en.wikipedia.org/wiki/Robust_confidence_intervals", "summary": "In statistics a robust confidence interval is a robust modification of confidence intervals, meaning that one modifies the non-robust calculations of the confidence interval so that they are not badly affected by outlying or aberrant observations in a data-set.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Bootstrapping (statistics)", "Confidence interval", "Gnumeric", "Median", "Microsoft Excel", "Monte Carlo method", "Normal distribution", "OpenOffice.org Calc", "Outlier", "Robust measures of scale", "Robust statistics", "Spreadsheet", "Standard deviation", "Statistics", "Systematic error", "Truncated mean"], "references": ["http://vertex42.com/ExcelArticles/mc/"]}, "It\u014d isometry": {"categories": ["Stochastic calculus"], "title": "It\u00f4 isometry", "method": "It\u014d isometry", "url": "https://en.wikipedia.org/wiki/It%C3%B4_isometry", "summary": "In mathematics, the It\u00f4 isometry, named after Kiyoshi It\u00f4, is a crucial fact about It\u00f4 stochastic integrals. One of its main applications is to enable the computation of variances for random variables that are given as It\u00f4 integrals.\nLet \n \n \n \n W\n :\n [\n 0\n ,\n T\n ]\n \u00d7\n \u03a9\n \u2192\n \n R\n \n \n \n {\\displaystyle W:[0,T]\\times \\Omega \\to \\mathbb {R} }\n denote the canonical real-valued Wiener process defined up to time \n \n \n \n T\n >\n 0\n \n \n {\\displaystyle T>0}\n , and let \n \n \n \n X\n :\n [\n 0\n ,\n T\n ]\n \u00d7\n \u03a9\n \u2192\n \n R\n \n \n \n {\\displaystyle X:[0,T]\\times \\Omega \\to \\mathbb {R} }\n be a stochastic process that is adapted to the natural filtration \n \n \n \n \n \n \n F\n \n \n \n \u2217\n \n \n W\n \n \n \n \n {\\displaystyle {\\mathcal {F}}_{*}^{W}}\n of the Wiener process. Then\n\n \n \n \n \n E\n \n \n [\n \n \n (\n \n \n \u222b\n \n 0\n \n \n T\n \n \n \n X\n \n t\n \n \n \n \n d\n \n \n W\n \n t\n \n \n \n )\n \n \n 2\n \n \n ]\n \n =\n \n E\n \n \n [\n \n \n \u222b\n \n 0\n \n \n T\n \n \n \n X\n \n t\n \n \n 2\n \n \n \n \n d\n \n t\n \n ]\n \n ,\n \n \n {\\displaystyle \\mathbb {E} \\left[\\left(\\int _{0}^{T}X_{t}\\,\\mathrm {d} W_{t}\\right)^{2}\\right]=\\mathbb {E} \\left[\\int _{0}^{T}X_{t}^{2}\\,\\mathrm {d} t\\right],}\n where \n \n \n \n \n E\n \n \n \n {\\displaystyle \\mathbb {E} }\n denotes expectation with respect to classical Wiener measure. \nIn other words, the It\u00f4 integral, as a function from the space \n \n \n \n \n L\n \n \n a\n d\n \n \n \n 2\n \n \n (\n [\n 0\n ,\n T\n ]\n \u00d7\n \u03a9\n )\n \n \n {\\displaystyle L_{\\mathrm {ad} }^{2}([0,T]\\times \\Omega )}\n of square-integrable adapted processes to the space \n \n \n \n \n L\n \n 2\n \n \n (\n \u03a9\n )\n \n \n {\\displaystyle L^{2}(\\Omega )}\n of square-integrable random variables, is an isometry of normed vector spaces with respect to the norms induced by the inner products\n\n \n \n \n \n \n \n \n (\n X\n ,\n Y\n \n )\n \n \n L\n \n \n a\n d\n \n \n \n 2\n \n \n (\n [\n 0\n ,\n T\n ]\n \u00d7\n \u03a9\n )\n \n \n \n \n \n :=\n \n E\n \n \n (\n \n \n \u222b\n \n 0\n \n \n T\n \n \n \n X\n \n t\n \n \n \n \n Y\n \n t\n \n \n \n \n d\n \n t\n \n )\n \n \n \n \n \n \n \n {\\displaystyle {\\begin{aligned}(X,Y)_{L_{\\mathrm {ad} }^{2}([0,T]\\times \\Omega )}&:=\\mathbb {E} \\left(\\int _{0}^{T}X_{t}\\,Y_{t}\\,\\mathrm {d} t\\right)\\end{aligned}}}\n and\n\n \n \n \n (\n A\n ,\n B\n \n )\n \n \n L\n \n 2\n \n \n (\n \u03a9\n )\n \n \n :=\n \n E\n \n (\n A\n B\n )\n .\n \n \n {\\displaystyle (A,B)_{L^{2}(\\Omega )}:=\\mathbb {E} (AB).}\n As a consequence, the It\u00f4 integral respects these inner products as well, i.e. we can write\n\n \n \n \n \n E\n \n \n [\n \n \n (\n \n \n \u222b\n \n 0\n \n \n T\n \n \n \n X\n \n t\n \n \n \n \n d\n \n \n W\n \n t\n \n \n \n )\n \n \n (\n \n \n \u222b\n \n 0\n \n \n T\n \n \n \n Y\n \n t\n \n \n \n \n d\n \n \n W\n \n t\n \n \n \n )\n \n \n ]\n \n =\n \n E\n \n \n [\n \n \n \u222b\n \n 0\n \n \n T\n \n \n \n X\n \n t\n \n \n \n Y\n \n t\n \n \n \n \n d\n \n t\n \n ]\n \n \n \n {\\displaystyle \\mathbb {E} \\left[\\left(\\int _{0}^{T}X_{t}\\,\\mathrm {d} W_{t}\\right)\\left(\\int _{0}^{T}Y_{t}\\,\\mathrm {d} W_{t}\\right)\\right]=\\mathbb {E} \\left[\\int _{0}^{T}X_{t}Y_{t}\\,\\mathrm {d} t\\right]}\n for \n \n \n \n X\n ,\n Y\n \u2208\n \n L\n \n \n a\n d\n \n \n \n 2\n \n \n (\n [\n 0\n ,\n T\n ]\n \u00d7\n \u03a9\n )\n \n \n {\\displaystyle X,Y\\in L_{\\mathrm {ad} }^{2}([0,T]\\times \\Omega )}\n .", "images": [], "links": ["Adapted process", "Bernt \u00d8ksendal", "Classical Wiener measure", "Expected value", "Filtration (abstract algebra)", "Inner product", "International Standard Book Number", "Isometry", "It\u00f4 calculus", "Kiyoshi It\u00f4", "Mathematics", "Normed vector space", "Stochastic process", "Variance", "Wiener process"], "references": []}, "Statistical proof": {"categories": ["Logic and statistics", "Pages with login required references or sources"], "title": "Statistical proof", "method": "Statistical proof", "url": "https://en.wikipedia.org/wiki/Statistical_proof", "summary": "Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores. Statistical methods are used to increase the understanding of the facts and the proof demonstrates the validity and logic of inference with explicit reference to a hypothesis, the experimental data, the facts, the test, and the odds. Proof has two essential aims: the first is to convince and the second is to explain the proposition through peer and public review.The burden of proof rests on the demonstrable application of the statistical method, the disclosure of the assumptions, and the relevance that the test has with respect to a genuine understanding of the data relative to the external world. There are adherents to several different statistical philosophies of inference, such as Bayes theorem versus the likelihood function, or positivism versus critical rationalism. These methods of reason have direct bearing on statistical proof and its interpretations in the broader philosophy of science.A common demarcation between science and non-science is the hypothetico-deductive proof of falsification developed by Karl Popper, which is a well-established practice in the tradition of statistics. Other modes of inference, however, may include the inductive and abductive modes of proof. Scientists do not use statistical proof as a means to attain certainty, but to falsify claims and explain theory. Science cannot achieve absolute certainty nor is it a continuous march toward an objective truth as the vernacular as opposed to the scientific meaning of the term \"proof\" might imply. Statistical proof offers a kind of proof of a theory's falsity and the means to learn heuristically through repeated statistical trials and experimental error. Statistical proof also has applications in legal matters with implications for the legal burden of proof.", "images": [], "links": ["Abductive reasoning", "Axioms", "Bayes theorem", "Bayesian statistics", "Bernoulli distribution", "Bonnie Gold", "Corroborating evidence", "Critical rationalism", "Data analysis", "Deductive", "Digital object identifier", "Evidence", "Evidence under Bayes theorem", "Experimental data", "Falsifiability", "Heuristics", "Hypothesis", "Hypothetico-deductive", "Inductive reasoning", "Inference", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Karl Popper", "Legal burden of proof", "Likelihood function", "Logical disjunction", "Mathematical proof", "Natural law", "Nature (journal)", "Non-science", "Normal distribution", "Null-hypothesis", "Odds", "P-value", "Philosophic burden of proof", "Poisson distribution", "Positivism", "Prima facie", "Probability distributions", "Proof (truth)", "Proposition", "Randomness", "Reason", "Scientific law", "Scientific theory", "Society of Systematic Biologists", "Statistical hypothesis testing", "Statistical inference", "Statistical proof", "Statistical significance", "Statistical test", "Statistical tests", "Systematic Zoology", "Validity (statistics)"], "references": ["http://www.utm.utoronto.ca/~collinsn/1310/Nov%203/optional/Bayesian%20methods%20in%20conserv%20biol.pdf", "http://www.springerlink.com/content/424p8r420820316l/", "http://bama.ua.edu/~molsyst/page2/assets/Huelsenbeck2001.pdf", "http://users.stat.umn.edu/~sandy/courses/8801/articles/Law/meierlaw.pdf", "http://research.amnh.org/users/desalle/pdf/Helfenbein.2005.MPE.pdf", "http://doi.org/10.1007/s10649-006-9057-x", "http://doi.org/10.1016/j.ympev.2005.01.003", "http://doi.org/10.1038/350371a0", "http://doi.org/10.1046/j.1523-1739.2000.99415.x", "http://doi.org/10.1080/01621459.1986.10478270", "http://doi.org/10.1111/j.1467-9639.1996.tb00300.x", "http://doi.org/10.1126/science.1065889", "http://doi.org/10.2307/1341808", "http://doi.org/10.2307/2412764", "http://doi.org/10.2307/2987595", "http://doi.org/10.5840/monist199477315", "http://www.jstor.org/stable/1341808", "http://www.jstor.org/stable/2412764", "http://www.jstor.org/stable/2987595", "http://www.jstor.org/stable/3312286", "http://www.jstor.org/stable/3312337", "http://www.worldcat.org/issn/0039-7989", "http://www.worldcat.org/issn/1476-4687", "http://www.rsscse-edu.org.uk/tsj/wp-content/uploads/2011/03/bissell1.pdf", "https://books.google.com/books?id=HDOuKjMc0AEC&printsec=frontcover&dq=Thomas+Kuhn's+%22linguistic+turn%22+and+the+legacy+of+logical+empiricism&hl=en&ei=Xz-8TpznC6aPiALPn6mdAw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC4Q6AEwAA#v=onepage&q&f=false", "https://books.google.com/books?id=N6KCNw5NHNkC&dq=biometry&hl=en&ei=_ka7TuLtCObmiAKfuKSDAg&sa=X&oi=book_result&ct=book-thumbnail&resnum=1&ved=0CDUQ6wEwAA", "https://books.google.com/books?id=Uc9C90KKW_UC&printsec=frontcover&dq=A+history+of+parametric+statistical+inference+from+Bernoulli+to+Fisher&hl=en&ei=_fe6Tui3MIiuiQKhw5yMDA&sa=X&oi=book_result&ct=book-thumbnail&resnum=1&ved=0CDAQ6wEwAA#v=onepage&q&f=false", "https://books.google.com/books?id=WlUL_r06GnEC&pg=PA180&lpg=PA180&dq=%22All+that+one+does+in+science+is+assign+degrees+of+belief%22&source=bl&ots=ii2pXy2BzM&sig=FYFilXaMbM-9rRNrJLDs0rhBrD0&hl=en&ei=s328TrqZHKiZiQLA9sGIAw&sa=X&oi=book_result&ct=result&resnum=2&sqi=2&ved=0CCIQ6AEwAQ#v=onepage&q=%22All%20that%20one%20does%20in%20science%20is%20assign%20degrees%20of%20belief%22&f=false", "https://books.google.com/books?id=sJVHoJ2ML40C&printsec=frontcover&dq=statistics+for+biologists&hl=en&ei=9e-6ToGzMq3MiQKrkfiODA&sa=X&oi=book_result&ct=book-thumbnail&resnum=7&ved=0CEgQ6wEwBg#v=onepage&q=parametric&f=false", "https://books.google.com/books?id=wPhwJdjI-dIC&printsec=frontcover&dq=Proof+and+other+dilemmas:+mathematics+and+philosophy&hl=en&ei=SVq7TvQ4g-KIAteutIkC&sa=X&oi=book_result&ct=book-thumbnail&resnum=1&ved=0CDEQ6wEwAA#v=onepage&q&f=false", "https://www.law.cornell.edu/supct/html/historics/USSC_CR_0430_0482_ZS.html", "https://openaccess.leidenuniv.nl/bitstream/handle/1887/11990/9_054_019.pdf?sequence=1"]}, "Correspondence analysis": {"categories": ["Accuracy disputes from April 2016", "All accuracy disputes", "Dimension reduction"], "title": "Correspondence analysis", "method": "Correspondence analysis", "url": "https://en.wikipedia.org/wiki/Correspondence_analysis", "summary": "Correspondence analysis (CA) or reciprocal averaging is a multivariate statistical technique proposed by Herman Otto Hartley (Hirschfeld) and later developed by Jean-Paul Benz\u00e9cri. It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a similar manner to principal component analysis, it provides a means of displaying or summarising a set of data in two-dimensional graphical form.\nAll data should be on the same scale for CA to be applicable, keeping in mind that the method treats rows and columns equivalently. It is traditionally applied to contingency tables \u2014 CA decomposes the chi-squared statistic associated with this table into orthogonal factors. Because CA is a descriptive technique, it can be applied to tables whether or not the \n \n \n \n \n \u03c7\n \n 2\n \n \n \n \n {\\displaystyle \\chi ^{2}}\n statistic is appropriate.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/17/System-search.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/17/20150413103857%21System-search.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/17/20120911200436%21System-search.svg"], "links": ["Canonical correspondence analysis", "Chi-squared statistic", "Contingency table", "Contingency tables", "Detrended correspondence analysis", "Discriminant analysis", "Factor analysis", "Formal concept analysis", "Generalized singular value decomposition", "Herman Otto Hartley", "International Standard Book Number", "Jean-Paul Benz\u00e9cri", "Multiple correspondence analysis", "Orange (software)", "Orthogonality", "Pierre Bourdieu", "Principal component analysis", "Principal components analysis", "R (programming language)", "Routledge", "Statistics"], "references": ["http://www.fbbva.es/TLFU/tlfu/esp/publicaciones/libros/fichalibro/index.jsp?codigo=300", "http://www.multivariatestatistics.org"]}, "Location\u2013scale family": {"categories": ["Location-scale family probability distributions", "Parametric statistics", "Types of probability distributions"], "title": "Location\u2013scale family", "method": "Location\u2013scale family", "url": "https://en.wikipedia.org/wiki/Location%E2%80%93scale_family", "summary": "In probability theory, especially in mathematical statistics, a location\u2013scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter. For any random variable \n \n \n \n X\n \n \n {\\displaystyle X}\n whose probability distribution function belongs to such a family, the distribution function of \n \n \n \n Y\n \n \n \n \n =\n \n \n d\n \n \n \n \n a\n +\n b\n X\n \n \n {\\displaystyle Y{\\stackrel {d}{=}}a+bX}\n also belongs to the family (where \n \n \n \n \n \n \n \n =\n \n \n d\n \n \n \n \n \n \n {\\displaystyle {\\stackrel {d}{=}}}\n means \"equal in distribution\"\u2014that is, \"has the same distribution as\"). Moreover, if \n \n \n \n X\n \n \n {\\displaystyle X}\n and \n \n \n \n Y\n \n \n {\\displaystyle Y}\n are two random variables whose distribution functions are members of the family, and assuming 1) existence of the first two moments and 2) \n \n \n \n X\n \n \n {\\displaystyle X}\n has zero mean and unit variance, then \n \n \n \n Y\n \n \n {\\displaystyle Y}\n can be written as \n \n \n \n Y\n \n \n \n \n =\n \n \n d\n \n \n \n \n \n \u03bc\n \n Y\n \n \n +\n \n \u03c3\n \n Y\n \n \n X\n \n \n {\\displaystyle Y{\\stackrel {d}{=}}\\mu _{Y}+\\sigma _{Y}X}\n , where \n \n \n \n \n \u03bc\n \n Y\n \n \n \n \n {\\displaystyle \\mu _{Y}}\n and \n \n \n \n \n \u03c3\n \n Y\n \n \n \n \n {\\displaystyle \\sigma _{Y}}\n are the mean and standard deviation of \n \n \n \n Y\n \n \n {\\displaystyle Y}\n .\nIn other words, a class \n \n \n \n \u03a9\n \n \n {\\displaystyle \\Omega }\n of probability distributions is a location\u2013scale family if for all cumulative distribution functions \n \n \n \n F\n \u2208\n \u03a9\n \n \n {\\displaystyle F\\in \\Omega }\n and any real numbers \n \n \n \n a\n \u2208\n \n R\n \n \n \n {\\displaystyle a\\in \\mathbb {R} }\n and \n \n \n \n b\n >\n 0\n \n \n {\\displaystyle b>0}\n , the distribution function \n \n \n \n G\n (\n x\n )\n =\n F\n (\n a\n +\n b\n x\n )\n \n \n {\\displaystyle G(x)=F(a+bx)}\n is also a member of \n \n \n \n \u03a9\n \n \n {\\displaystyle \\Omega }\n .\n\nIf \n \n \n \n X\n \n \n {\\displaystyle X}\n has a cumulative distribution function \n \n \n \n \n F\n \n X\n \n \n (\n x\n )\n =\n P\n (\n X\n \u2264\n x\n )\n \n \n {\\displaystyle F_{X}(x)=P(X\\leq x)}\n , then \n \n \n \n Y\n \n =\n \n a\n +\n b\n X\n \n \n {\\displaystyle Y{=}a+bX}\n has a cumulative distribution function \n \n \n \n \n F\n \n Y\n \n \n (\n y\n )\n =\n \n F\n \n X\n \n \n \n (\n \n \n \n y\n \u2212\n a\n \n b\n \n \n )\n \n \n \n {\\displaystyle F_{Y}(y)=F_{X}\\left({\\frac {y-a}{b}}\\right)}\n .\nIf \n \n \n \n X\n \n \n {\\displaystyle X}\n is a discrete random variable with probability mass function \n \n \n \n \n p\n \n X\n \n \n (\n x\n )\n =\n P\n (\n X\n =\n x\n )\n \n \n {\\displaystyle p_{X}(x)=P(X=x)}\n , then \n \n \n \n Y\n \n =\n \n a\n +\n b\n X\n \n \n {\\displaystyle Y{=}a+bX}\n is a discrete random variable with probability mass function \n \n \n \n \n p\n \n Y\n \n \n (\n y\n )\n =\n \n p\n \n X\n \n \n \n (\n \n \n \n y\n \u2212\n a\n \n b\n \n \n )\n \n \n \n {\\displaystyle p_{Y}(y)=p_{X}\\left({\\frac {y-a}{b}}\\right)}\n .\nIf \n \n \n \n X\n \n \n {\\displaystyle X}\n is a continuous random variable with probability density function \n \n \n \n \n f\n \n X\n \n \n (\n x\n )\n \n \n {\\displaystyle f_{X}(x)}\n , then \n \n \n \n Y\n \n =\n \n a\n +\n b\n X\n \n \n {\\displaystyle Y{=}a+bX}\n is a continuous random variable with probability density function \n \n \n \n \n f\n \n Y\n \n \n (\n y\n )\n =\n \n \n 1\n b\n \n \n \n f\n \n X\n \n \n \n (\n \n \n \n y\n \u2212\n a\n \n b\n \n \n )\n \n \n \n {\\displaystyle f_{Y}(y)={\\frac {1}{b}}f_{X}\\left({\\frac {y-a}{b}}\\right)}\n .In decision theory, if all alternative distributions available to a decision-maker are in the same location\u2013scale family, and the first two moments are finite, then a two-moment decision model can apply, and decision-making can be framed in terms of the means and the variances of the distributions.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARGUS distribution", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "American Economic Review", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous random variable", "Control chart", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Cumulative distribution functions", "Dagum distribution", "Data collection", "Davis distribution", "Decision theory", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete random variable", "Discrete uniform distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Ewens's sampling formula", "Expected value", "Experiment", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "Geostatistics", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hans-Werner Sinn", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabolic fractal distribution", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Proportional hazards model", "Psychometrics", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quantile function", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrix", "Random variable", "Random variate", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Review of Economic Studies", "Rice distribution", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable distribution", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Tracy\u2013Widom distribution", "Trend estimation", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Two-moment decision models", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Uniformly most powerful test", "Univariate distribution", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.jstor.org/stable/1804104", "http://www.jstor.org/stable/2297094", "http://www.randomservices.org/random/special/LocationScale.html"]}, "Power transform": {"categories": ["Normal distribution", "Statistical data transformation"], "title": "Power transform", "method": "Power transform", "url": "https://en.wikipedia.org/wiki/Power_transform", "summary": "In statistics, a power transform is a family of functions that are applied to create a monotonic transformation of data using power functions. This is a useful data transformation technique used to stabilize variance, make the data more normal distribution-like, improve the validity of measures of association such as the Pearson correlation between variables and for other data stabilization procedures.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/e/e1/BUPA_BoxCox.JPG"], "links": ["Alanine transaminase", "ArXiv", "Biometrika", "Box\u2013Cox distribution", "Cobb\u2013Douglas", "Confidence interval", "Consistency (statistics)", "Continuous function", "Cram\u00e9r\u2013Rao bound", "Data transformation (statistics)", "David Cox (statistician)", "Derivative", "Digital object identifier", "Dimensional analysis", "Econometrics", "Encyclopedia of Mathematics", "Epidemiology", "Errors and residuals in statistics", "Gamma-glutamyl transpeptidase", "Geometric mean", "George E. P. Box", "Histogram", "Homogeneous function", "International Standard Book Number", "JSTOR", "John Johnston (econometrician)", "Journal of the Royal Statistical Society", "Journal of the Royal Statistical Society, Series B", "Likelihood-ratio test", "Likelihood function", "Local asymptotic normality", "Mathematical Reviews", "Maximum likelihood", "Michiel Hazewinkel", "Monotonic function", "Morris H. DeGroot", "Normal distribution", "Pearson product-moment correlation coefficient", "Peter J. Bickel", "Power (mathematics)", "Power function", "Profile likelihood", "Q-Q plot", "Regression analysis", "Robust regression", "SOCR", "Scatterplot", "Sign function", "Statistics", "Time-series", "Truncated distribution", "Truncated normal distribution"], "references": ["http:ftp://ftp.ics.uci.edu/pub/machine-learning-databases/liver-disorders", "http://www.ime.usp.br/~abe/lista/pdfm9cJKUmFZp.pdf", "http://www.springerlink.com/content/mt81u60813077641/", "http://www.springerlink.com/content/y25q020x24602701/", "http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_PowerTransformFamily_Graphs", "http://wiki.stat.ucla.edu/socr/uploads/b/b8/PowerTransformFamily_Biometrica609.pdf", "http://portal.acm.org/citation.cfm?id=1172964.1173292&coll=&dl=acm&CFID=15151515&CFTOKEN=6184618", "http://www.ams.org/mathscinet-getitem?mr=0192611", "http://arxiv.org/abs/cond-mat/0606104", "http://doi.org/10.1007%2FBF01043245", "http://doi.org/10.1007%2Fs10910-005-9003-7", "http://doi.org/10.1080%2F01621459.1981.10477649", "http://doi.org/10.1111%2Fj.1467-9876.2005.00476.x", "http://doi.org/10.1214%2Fss%2F1177013223", "http://doi.org/10.2307%2F2348250", "http://www.encyclopediaofmath.org/index.php/Box%E2%80%93Cox_transformation", "http://www.jstor.org/stable/2348250", "http://www.jstor.org/stable/2673623", "http://www.jstor.org/stable/2984418", "https://www.stat.umn.edu/arc/yjpower.pdf", "https://www.encyclopediaofmath.org/index.php?title=B/b110790"]}, "S (programming language)": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2015", "Statistical programming languages"], "title": "S (programming language)", "method": "S (programming language)", "url": "https://en.wikipedia.org/wiki/S_(programming_language)", "summary": "S is a statistical programming language developed primarily by John Chambers and (in earlier versions) Rick Becker and Allan Wilks of Bell Laboratories. The aim of the language, as expressed by John Chambers, is \"to turn ideas into software, quickly and faithfully\".The modern implementation of S is R, a part of the GNU free software project. S-PLUS, a commercial product, was formerly sold by TIBCO Software.", "images": [], "links": ["APL (programming language)", "Bell Labs", "C (programming language)", "Class (computer science)", "Digital Equipment Corporation", "Digital object identifier", "Double precision", "Fortran", "GNU", "General Comprehensive Operating System", "Imperative programming", "International Standard Book Number", "JSTOR", "John Chambers (programmer)", "Method (computer science)", "Multi-paradigm programming language", "Object oriented programming", "Polymorphic Programming Language", "PostScript", "Programming language", "Programming language implementation", "Programming paradigm", "R (programming language)", "S-PLUS", "S-plus", "SAS System", "Software developer", "Software license", "Strong typing", "TIBCO Software", "Type system", "UNIX/32V", "Unix", "VAX", "X Window System"], "references": ["http://www2.research.att.com/areas/stat/doc/94.11.ps", "http://ect.bell-labs.com/sl/S/", "http://ect.bell-labs.com/sl/S/history.html", "http://statweb.stanford.edu/~jmc4/papers/96.7.ps", "http://doi.org/10.2307%2F2346786", "http://www.jstor.org/stable/2346786"]}, "Monotone likelihood ratio": {"categories": ["Statistical hypothesis testing", "Theory of probability distributions"], "title": "Monotone likelihood ratio", "method": "Monotone likelihood ratio", "url": "https://en.wikipedia.org/wiki/Monotone_likelihood_ratio", "summary": "In statistics, the monotone likelihood ratio property is a property of the ratio of two probability density functions (PDFs). Formally, distributions \u0192(x) and g(x) bear the property if\n\n \n \n \n \n for every \n \n \n x\n \n 1\n \n \n >\n \n x\n \n 0\n \n \n ,\n \n \n \n \n f\n (\n \n x\n \n 1\n \n \n )\n \n \n g\n (\n \n x\n \n 1\n \n \n )\n \n \n \n \u2265\n \n \n \n f\n (\n \n x\n \n 0\n \n \n )\n \n \n g\n (\n \n x\n \n 0\n \n \n )\n \n \n \n \n \n {\\displaystyle {\\text{for every }}x_{1}>x_{0},\\quad {\\frac {f(x_{1})}{g(x_{1})}}\\geq {\\frac {f(x_{0})}{g(x_{0})}}}\n that is, if the ratio is nondecreasing in the argument \n \n \n \n x\n \n \n {\\displaystyle x}\n .\nIf the functions are first-differentiable, the property may sometimes be stated\n\n \n \n \n \n \n \u2202\n \n \u2202\n x\n \n \n \n \n (\n \n \n \n f\n (\n x\n )\n \n \n g\n (\n x\n )\n \n \n \n )\n \n \u2265\n 0\n \n \n {\\displaystyle {\\frac {\\partial }{\\partial x}}\\left({\\frac {f(x)}{g(x)}}\\right)\\geq 0}\n For two distributions that satisfy the definition with respect to some argument x, we say they \"have the MLRP in x.\" For a family of distributions that all satisfy the definition with respect to some statistic T(X), we say they \"have the MLR in T(X).\"", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/1/1b/MLRP-illustration.png", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes' law", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central moment", "Central tendency", "Characteristic function (probability theory)", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinant", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation", "Expected value", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "First-order stochastic dominance", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hazard rate", "Hazard ratio", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis testing", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karlin\u2013Rubin theorem", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lawrence D. Brown", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mechanism design", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment-generating function", "Moment (mathematics)", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability-generating function", "Probability density function", "Probability distribution", "Probability mass function", "Probability model", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile function", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raw moment", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic dominance", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficiency (statistics)", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly minimum-variance unbiased estimator", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://projecteuclid.org/euclid.aos/1176343543"]}, "Wrapped normal distribution": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from June 2014", "Continuous distributions", "Directional statistics", "Normal distribution", "Pages using deprecated image syntax"], "title": "Wrapped normal distribution", "method": "Wrapped normal distribution", "url": "https://en.wikipedia.org/wiki/Wrapped_normal_distribution", "summary": "In probability theory and directional statistics, a wrapped normal distribution is a wrapped probability distribution that results from the \"wrapping\" of the normal distribution around the unit circle. It finds application in the theory of Brownian motion and is a solution to the heat equation for periodic boundary conditions. It is closely approximated by the von Mises distribution, which, due to its mathematical simplicity and tractability, is the most commonly used distribution in directional statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/4/45/WrappedNormalCDF.png", "https://upload.wikimedia.org/wikipedia/commons/6/69/WrappedNormalPDF.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Brownian motion", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac comb", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Entropy (information theory)", "Erlang distribution", "Euler function", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fourier series", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Jacobi triple product", "Johnson's SU-distribution", "Joint probability distribution", "Kantilal Mardia", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Periodic boundary conditions", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Theta function", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unit circle", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.codeproject.com/Articles/190833/Circular-Values-Math-and-Statistics-with-Cplusplus", "http://doi.org/10.2307%2F2333749", "http://biomet.oxfordjournals.org/cgi/pdf_extract/50/1-2/81", "https://www.amazon.com/Directional-Statistics-Kanti-V-Mardia/dp/0471953334/ref=sr_1_1?s=books&ie=UTF8&qid=1311003484&sr=1-1#reader_0471953334", "https://books.google.com/books?id=IIpeevaNH88C&dq=%22circular+variance%22+fisher&source=gbs_navlinks_s", "https://books.google.com/books?id=R3GpDglVOSEC&printsec=frontcover&source=gbs_navlinks_s#v=onepage&q=&f=false"]}, "Bayesian inference in phylogeny": {"categories": ["Applications of Bayesian inference", "Articles with short description", "Bioinformatics", "Computational phylogenetics"], "title": "Bayesian inference in phylogeny", "method": "Bayesian inference in phylogeny", "url": "https://en.wikipedia.org/wiki/Bayesian_inference_in_phylogeny", "summary": "Bayesian inference of phylogeny uses a likelihood function to create a quantity called the posterior probability of trees using a model of evolution, based on some prior probabilities, producing the most likely phylogenetic tree for the given data. The Bayesian approach has become popular due to advances in computing speeds and the integration of Markov chain Monte Carlo (MCMC) algorithms. Bayesian inference has a number of applications in molecular phylogenetics and systematics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/18/Bayes%27_Theorem_MMB_01.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/17/Divergence_time_estimation_and_ancestral_area_reconstruction_of_porcini_s.s..png", "https://upload.wikimedia.org/wikipedia/commons/c/c8/Robot_metaphor.png", "https://upload.wikimedia.org/wikipedia/commons/8/8e/Tiger_phylogenetic_relationships.png", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/3/39/LongBranch.png", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Autapomorphy", "Basal (phylogenetics)", "Bayes' theorem", "Bayesian inference", "Bootstrapping", "Clade", "Cladistics", "Cladogenesis", "Cladogram", "Computational phylogenetics", "Crown group", "DNA barcoding", "Distance matrices in phylogeny", "Evolutionary biology", "Evolutionary grade", "Evolutionary taxonomy", "Ghost lineage", "Ghost population", "International Standard Book Number", "Least squares inference in phylogeny", "Lineage (evolution)", "List of phylogenetics software", "Long branch attraction", "Markov chain", "Markov chain Monte Carlo", "Maximum likelihood", "Maximum parsimony", "Maximum parsimony (phylogenetics)", "Metropolis-Hastings algorithm", "Molecular phylogenetics", "Monophyly", "Neighbor-joining", "Nexus file", "Paraphyly", "PhyloCode", "Phylogenesis", "Phylogenetic comparative methods", "Phylogenetic network", "Phylogenetic niche conservatism", "Phylogenetic nomenclature", "Phylogenetic tree", "Phylogenetics", "Phylogenomics", "Phylogeography", "Plesiomorphy", "Polyphyly", "Primitive (phylogenetics)", "Sister group", "Supertree", "Symplesiomorphy", "Synapomorphy", "Systematics", "Taxa", "Taxonomy (biology)", "Three-taxon analysis", "UPGMA"], "references": ["http://www.bioinfo.uqam.ca/armadillo", "http://www.geneious.com", "http://www.stat.wisc.edu/~ane/bucky/", "http://mrbayes.sourceforge.net/", "http://www.bali-phy.org", "http://mbe.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=9214744", "http://www.phylobayes.org", "http://www.topali.org", "http://www.maths.abdn.ac.uk/%CB%9Cijw", "http://beast.bio.ed.ac.uk/", "http://beast.bio.ed.ac.uk", "http://www.evolution.rdg.ac.uk/BayesPhy.html"]}, "Huber loss function": {"categories": ["All articles needing additional references", "Articles needing additional references from August 2014", "Loss functions", "M-estimators", "Robust statistics"], "title": "Huber loss", "method": "Huber loss function", "url": "https://en.wikipedia.org/wiki/Huber_loss", "summary": "In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/cc/Huber_loss.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Absolute deviation", "Additive model", "Annals of Statistics", "Arithmetic mean", "Binary classification", "Convex function", "Digital object identifier", "Estimation theory", "Estimator", "Geometric median", "Hinge loss", "International Standard Book Number", "JSTOR", "Loss function", "M-estimator", "Mean squared error", "Median", "Outlier", "Peter J. Huber", "Robust regression", "Robust statistics", "Squared error loss", "Statistical classification", "Statistics", "Support vector machine", "Unbiased estimator", "Winsorizing"], "references": ["http://statweb.stanford.edu/~tibs/ElemStatLearn/", "http://doi.org/10.1109%2F42.61759", "http://doi.org/10.1109%2F83.551699", "http://doi.org/10.1214%2Faoms%2F1177703732", "http://doi.org/10.1214%2Faos%2F1013203451", "http://www.jstor.org/stable/2238020", "http://www.jstor.org/stable/2699986", "https://web.archive.org/web/20150126123924/http://statweb.stanford.edu/~tibs/ElemStatLearn/"]}, "BMDP": {"categories": ["1960s software", "All articles containing potentially dated statements", "Articles containing potentially dated statements from 2017", "Biostatistics", "Statistical software", "Windows-only software"], "title": "BMDP", "method": "BMDP", "url": "https://en.wikipedia.org/wiki/BMDP", "summary": "BMDP was a statistical package developed in 1965 by Wilfrid Dixon at the University of California, Los Angeles. The acronym stands for Bio-Medical Data Package, the word package was added by Dixon as the software consisted of a series of programs (subroutines) which performed different parametric and nonparametric statistical analyses.BMDP was originally distributed for free. It was later sold by Statsols, who originally was a subsidiary of BMDP, but through a management buy-out formed the now independent company Statistical Solutions Ltd, known as Statsols. BMDP is no longer available as of 2017. The company decided to only offer its other statistical product nQuery Sample Size Software.\n\n", "images": [], "links": ["ADMB", "Analyse-it", "BV4.1 (software)", "CSPro", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "EViews", "Epi Info", "Free Online Dictionary of Computing", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "GraphPad InStat", "GraphPad Prism", "Gretl", "H2O (software)", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "LIMDEP", "LISREL", "List of statistical packages", "MATLAB", "MLwiN", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "NCSS (statistical software)", "NQuery Sample Size Software", "Open-source software", "OpenBUGS", "Orange (software)", "OxMetrics", "PSPP", "Public-domain software", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SUDAAN", "SYSTAT (software)", "SageMath", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Stan (software)", "StatView", "StatXact", "Stata", "Statistica", "StatsDirect", "Statsols", "TSP (econometrics software)", "The Unscrambler", "UNISTAT", "University of California, Los Angeles", "Wilfrid Dixon", "WinBUGS", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://senate.universityofcalifornia.edu/WilfridJ.Dixon.html", "http://archive.computerhistory.org/resources/access/text/2012/04/102658169-05-01-acc.pdf", "http://foldoc.org/?BMDP", "https://www.statsols.com/statsols-about", "https://web.archive.org/web/20160303230948/http://senate.universityofcalifornia.edu/WilfridJ.Dixon.html"]}, "Cauchy\u2013Schwarz inequality": {"categories": ["Articles containing proofs", "Inequalities", "Linear algebra", "Mathematical analysis", "Operator theory", "Probabilistic inequalities"], "title": "Cauchy\u2013Schwarz inequality", "method": "Cauchy\u2013Schwarz inequality", "url": "https://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality", "summary": "In mathematics, the Cauchy\u2013Schwarz inequality, also known as the Cauchy\u2013Bunyakovsky\u2013Schwarz inequality, is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas. It is considered to be one of the most important inequalities in all of mathematics.The inequality for sums was published by Augustin-Louis Cauchy (1821), while the corresponding inequality for integrals was first proved by\nViktor Bunyakovsky (1859). The modern proof of the integral inequality was given by Hermann Amandus Schwarz (1888).", "images": [], "links": ["Absolutely convex set", "Absorbing set", "Abstract Wiener space", "Algebraic interior", "Angle", "Augustin-Louis Cauchy", "Balanced set", "Banach algebra", "Banach lattice", "Banach space", "Banach\u2013Alaoglu theorem", "Banach\u2013Mazur theorem", "Banach\u2013Saks theorem", "Barrelled space", "Bessel's inequality", "Bilinear form", "Bilinear map", "Bochner integral", "Bochner space", "Borel functional calculus", "Bornological space", "Bounded operator", "Bounded set (topological vector space)", "Bounding point", "Brauner space", "C*-algebra", "Closed graph theorem", "Closed linear operator", "Closed range theorem", "Compact operator", "Complex conjugate", "Complex numbers", "Cone (linear algebra)", "Continuous function", "Continuous functional calculus", "Continuous linear operator", "Convex cone", "Convex hull", "Convex set", "Covariance", "Densely defined", "Derivative", "Differentiation in Fr\u00e9chet spaces", "Digital object identifier", "Discontinuous linear map", "Discriminant", "Dot product", "Dual norm", "Dual space", "Dual topology", "Dunford integral", "Eberlein\u2013\u0160mulian theorem", "Encyclopedia of Mathematics", "Euclidean space", "Extreme point", "F-space", "Fidelity of quantum states", "Fredholm operator", "Freudenthal spectral theorem", "Fr\u00e9chet derivative", "Fr\u00e9chet space", "Function (mathematics)", "Functional analysis", "Functional calculus", "Functional derivative", "Gelfand\u2013Mazur theorem", "Gelfand\u2013Naimark theorem", "Goldstine theorem", "G\u00e2teaux derivative", "Hahn\u2013Banach theorem", "Hermann Amandus Schwarz", "Hermitian adjoint", "Hilbert space", "Hilbert\u2013Schmidt operator", "Holomorphic functional calculus", "Hyperplane separation theorem", "H\u00f6lder's inequality", "H\u00f6lder inequality", "Inequality (mathematics)", "Infinite-dimensional Lebesgue measure", "Infinite-dimensional holomorphy", "Inner-product space", "Inner product", "Inner product space", "Integral", "Interior (topology)", "International Standard Book Number", "International Standard Serial Number", "Invariant subspace problem", "Inverse function theorem", "JSTOR", "Jensen's inequality", "Kakutani fixed-point theorem", "Krein\u2013Milman theorem", "Kunita\u2013Watanabe inequality", "LF-space", "Linear algebra", "Linear form", "Linear independence", "Linear map", "List of functional analysis topics", "Locally convex topological vector space", "M. Riesz extension theorem", "Mackey space", "Mackey topology", "Mackey\u2013Arens theorem", "Mathematical analysis", "Mathematics", "Mazur's lemma", "Measure (mathematics)", "Michiel Hazewinkel", "Minkowski addition", "Minkowski functional", "Minkowski inequality", "Montel space", "Nash\u2013Moser theorem", "Norm (mathematics)", "Normal operator", "Normed space", "Nuclear operator", "Nuclear space", "Open mapping theorem (functional analysis)", "Operator algebra", "Operator theory", "Operator topologies", "Paley\u2013Wiener integral", "Parallel (geometry)", "Parseval's identity", "Pettis integral", "Pointwise product", "Polar decomposition", "Polar set", "Polarization identity", "Positive linear functional", "Probability theory", "Projection-valued measure", "Pythagorean theorem", "Quasinorm", "Radial set", "Random variable", "Real numbers", "Reflexive space", "Regulated integral", "Richard Kadison", "Richard V. Kadison", "Riesz representation theorem", "Riesz space", "Schauder fixed-point theorem", "Self-adjoint operator", "Sesquilinear form", "Singular value decomposition", "Smith space", "Spectral radius", "Spectral theorem", "Spectral theory", "Spectral theory of ordinary differential equations", "Spectrum (functional analysis)", "Spectrum of a C*-algebra", "Square-integrable", "Star domain", "Stereotype space", "Strictly convex space", "Strictly singular operator", "Strong operator topology", "Strong topology", "Strong topology (polar topology)", "Symmetric set", "Tensor product of Hilbert spaces", "Titu Andreescu", "Topological tensor product", "Topological vector space", "Topology", "Topology of uniform convergence", "Trace class", "Transpose of a linear map", "Triangle inequality", "Ultrastrong topology", "Ultraweak topology", "Unbounded operator", "Unitary operator", "Variance", "Vector algebra", "Vector measure", "Vector projection", "Viktor Bunyakovsky", "Viktor Yakovlevich Bunyakovsky", "W*-algebra", "Weak operator topology", "Weak topology", "Weak topology (polar topology)", "Weakly measurable function", "Webbed space", "Zonotope"], "references": ["http://jipam.vu.edu.au/article.php?sid=301", "http://www.mediafire.com/?1mw1tkgozzu", "http://people.revoledu.com/kardi/tutorial/LinearAlgebra/LinearlyIndependent.html#LinearlyIndependentVectors", "http://jeff560.tripod.com/c.html", "http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/CSMC_index.html", "http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/bunyakovsky.pdf", "http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/Schwarz.pdf", "http://www.uni-miskolc.hu/~matsefi/Octogon/volumes/volume1/article1_19.pdf", "http://doi.org/10.1016%2F0022-247X(65)90016-8", "http://doi.org/10.1016%2Fj.aam.2004.05.001", "http://doi.org/10.15352%2Fafa%2F06-3-20", "http://doi.org/10.2307%2F1969657", "http://www.jstor.org/stable/1969657", "http://www.worldcat.org/issn/1222-5657", "https://artofproblemsolving.com/wiki/index.php?title=Callebaut's_Inequality", "https://books.google.com/books?id=2qru8d7BCAAC", "https://books.google.com/books?id=4hIq6ExH7NoC", "https://books.google.com/books?id=7x8MCAAAQBAJ", "https://books.google.com/books?id=JnMZDAAAQBAJ", "https://books.google.com/books?id=PkHhBwAAQBAJ", "https://books.google.com/books?id=SsbsCgAAQBAJ", "https://books.google.com/books?id=TMSnGkr_DxwC", "https://books.google.com/books?id=VtSFHDABxMIC&pg=PA40", "https://books.google.com/books?id=WDTcBQAAQBAJ", "https://books.google.com/books?id=_lTDAgAAQBAJ", "https://books.google.com/books?id=aVJmcega44cC", "https://books.google.com/books?id=d5TqBwAAQBAJ", "https://books.google.com/books?id=lQtKAIONqwIC", "https://books.google.com/books?id=oOYQVeHmNk4C", "https://books.google.com/books?id=s7bMBQAAQBAJ", "https://books.google.com/books?id=u9M9PFLNpMMC", "https://www.sciencedirect.com/science/article/pii/0022247X65900168", "https://web.archive.org/web/20080720034744/http://jipam.vu.edu.au/article.php?sid=301", "https://arxiv.org/pdf/1112.3003.pdf", "https://www.encyclopediaofmath.org/index.php?title=C/c020880", "https://www.encyclopediaofmath.org/index.php?title=b/b017770"]}, "Statistical literacy": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from September 2010", "Literacy", "Statistics education"], "title": "Statistical literacy", "method": "Statistical literacy", "url": "https://en.wikipedia.org/wiki/Statistical_literacy", "summary": "Statistical literacy is the ability to understand and reason with statistics and data. The abilities to understand and reason with data, or arguments that use data, are necessary for citizens to understand material presented in publications such as newspapers, television, and the Internet. However, scientists also need to develop statistical literacy so that they can both produce rigorous and reproducible research and consume it. Numeracy is an element of being statistically literate and in some models of statistical literacy, or for some populations (e.g., students in kindergarten through 12th grade/end of secondary school), it is a prerequisite skill. Being statistically literate is sometimes taken to include having the abilities to both critically evaluate statistical material and appreciate the relevance of statistically-based approaches to all aspects of life in general or to the evaluating, design, and/or production of scientific work.", "images": [], "links": ["Adolescent literacy", "Agricultural literacy", "Aliteracy", "Asemic writing", "Australian Bureau of Statistics", "Average", "Biased sample", "Computer literacy", "Critical literacy", "Cultural literacy", "Data literacy", "Diaspora literacy", "Dick and Jane", "Digital object identifier", "Dyslexia", "Early literacy", "Ecological literacy", "Electracy", "Emergent literacy", "Emotional literacy", "Family literacy", "Financial literacy", "Frank Laubach", "Functional illiteracy", "Graph literacy", "Griffith Jones (Llanddowror)", "Health literacy", "How to Lie with Statistics", "Information and media literacy", "Information literacy", "International Literacy Association", "International Literacy Day", "International Standard Book Number", "International Statistical Institute", "Internet", "James Paul Gee", "Katherine Wallman", "Lies, damned lies, and statistics", "List of Chinese administrative divisions by illiteracy rate", "List of countries by literacy rate", "Literacy", "Literacy in India", "Literacy test", "Literate", "Marie Clay", "Media consumption", "Media literacy", "Mental health literacy", "Misuse of statistics", "National Council of Teachers of English", "New literacies", "Newspaper", "No Child Left Behind Act", "Numeracy", "OCLC", "Opinion polling", "Oracy", "Oral literature", "Orality", "Paulo Freire", "Phonics", "Postliterate society", "Racial literacy", "Reading education in the United States", "Reproducibility", "Royal Statistical Society", "Ruth Johnson Colvin", "Sampling (statistics)", "Scientific literacy", "Shark attack", "Skill", "Standard deviation", "Statistics", "Statistics Canada", "Technology education", "Television", "Transliteracy", "United Nations Economic Commission for Europe", "Visual literacy", "Whole language", "Writing system"], "references": ["http://www.mdpi.com/2227-7102/7/1/3", "http://www.stat.auckland.ac.nz/~iase/islp/", "http://www.stat.auckland.ac.nz/~iase/publications/isr/02.Gal.pdf", "http://doi.org/10.1080%2F01621459.1940.10500563", "http://doi.org/10.1080%2F01621459.1993.10594283", "http://doi.org/10.3390%2Feducsci7010003", "http://straightstatistics.fullfact.org/resources/making-sense-statistics", "http://www.riskliteracy.org", "http://statlit.org/", "http://www.worldcat.org/oclc/21270160", "http://www.worldcat.org/oclc/36234417", "http://www.worldcat.org/oclc/46932988", "http://www.worldcat.org/oclc/70203994", "https://www.amstat.org/asa/education/Guidelines-for-Assessment-and-Instruction-in-Statistics-Education-Reports.aspx", "https://www.worldcat.org/oclc/21270160", "https://www.worldcat.org/oclc/36234417", "https://www.worldcat.org/oclc/46932988", "https://www.worldcat.org/oclc/70203994"]}, "Kolmogorov's criterion": {"categories": ["Markov processes"], "title": "Kolmogorov's criterion", "method": "Kolmogorov's criterion", "url": "https://en.wikipedia.org/wiki/Kolmogorov%27s_criterion", "summary": "In probability theory, Kolmogorov's criterion, named after Andrey Kolmogorov, is a theorem giving a necessary and sufficient condition for a Markov chain or continuous-time Markov chain to be stochastically identical to its time-reversed version.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/93/Kolmogorov_criterion_dtmc.svg"], "links": ["Andrey Kolmogorov", "Continuous-time Markov chain", "Frank P. Kelly", "Kolmogorov's normability criterion", "Markov chain", "Probability theory", "Stochastic matrix", "Theorem", "Time reversibility", "Transition rate matrix"], "references": ["http://www.statslab.cam.ac.uk/~frank/BOOKS/book/whole.pdf"]}, "Linear probability model": {"categories": ["Generalized linear models"], "title": "Linear probability model", "method": "Linear probability model", "url": "https://en.wikipedia.org/wiki/Linear_probability_model", "summary": "In statistics, a linear probability model is a special case of a binomial regression model. Here the dependent variable for each observation takes values which are either 0 or 1. The probability of observing a 0 or 1 in any one case is treated as depending on one or more explanatory variables. For the \"linear probability model\", this relationship is a particularly simple one, and allows the model to be fitted by simple linear regression.\nThe model assumes that, for a binary outcome (Bernoulli trial), \n \n \n \n Y\n \n \n {\\displaystyle Y}\n , and its associated vector of explanatory variables, \n \n \n \n X\n \n \n {\\displaystyle X}\n ,\n\n \n \n \n Pr\n (\n Y\n =\n 1\n \n |\n \n X\n =\n x\n )\n =\n \n x\n \u2032\n \n \u03b2\n .\n \n \n {\\displaystyle \\Pr(Y=1|X=x)=x'\\beta .}\n For this model,\n\n \n \n \n E\n [\n Y\n \n |\n \n X\n ]\n =\n Pr\n (\n Y\n =\n 1\n \n |\n \n X\n )\n =\n \n x\n \u2032\n \n \u03b2\n ,\n \n \n {\\displaystyle E[Y|X]=\\Pr(Y=1|X)=x'\\beta ,}\n and hence the vector of parameters \u03b2 can be estimated using least squares. This method of fitting would be inefficient, and can be improved by adopting an iterative scheme based on weighted least squares, in which the model from the previous iteration is used to supply estimates of the conditional variances, \n \n \n \n Var\n \u2061\n (\n Y\n \n |\n \n X\n =\n x\n )\n \n \n {\\displaystyle \\operatorname {Var} (Y|X=x)}\n , which would vary between observations. This approach can be related to fitting the model by maximum likelihood.A drawback of this model is that, unless restrictions are placed on \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n , the estimated coefficients can imply probabilities outside the unit interval \n \n \n \n [\n 0\n ,\n 1\n ]\n \n \n {\\displaystyle [0,1]}\n . For this reason, models such as the logit model or the probit model are more commonly used.\n\n", "images": [], "links": ["Bernoulli trial", "Binomial regression", "Dependent and independent variables", "International Standard Book Number", "Least squares", "Logit model", "Maximum likelihood", "Probit model", "Simple linear regression", "Statistics", "Unit interval", "Weighted least squares"], "references": ["https://books.google.com/books?id=0bzGQE14CwEC&pg=PA267"]}, "Simon model": {"categories": ["Power laws"], "title": "Simon model", "method": "Simon model", "url": "https://en.wikipedia.org/wiki/Simon_model", "summary": "In applied probability theory, the Simon model is a class of stochastic models that results in a power-law distribution function. It was proposed by Herbert A. Simon to account for the wide range of empirical distributions following a power-law. It models the dynamics of a system of elements with associated counters (e.g., words and their frequencies in texts, or nodes in a network and their connectivity \n \n \n \n k\n \n \n {\\displaystyle k}\n ). In this model the dynamics of the system is based on constant growth via addition of new elements (new instances of words) as well as incrementing the counters (new occurrences of a word) at a rate proportional to their current values.", "images": [], "links": ["Average path length", "BA model", "Barab\u00e1si-Albert (BA) model", "Clustering coefficient", "Degree distribution", "Frequency distribution", "Generalized scale-free model", "Herbert A. Simon", "Power-law", "Scale-free network", "Stochastic model", "Zipf's law"], "references": ["https://web.archive.org/web/20070128124135/http://austria.phys.nd.edu/netwiki/index.php/Graph_Spectra"]}, "Telegraph process": {"categories": ["Stochastic differential equations"], "title": "Telegraph process", "method": "Telegraph process", "url": "https://en.wikipedia.org/wiki/Telegraph_process", "summary": "In probability theory, the telegraph process is a memoryless continuous-time stochastic process that shows two distinct values.\nIt models burst noise (also called popcorn noise or random telegraph signal).\nIf the two possible states are called a and b, the process can be described by the following master equations:\n\n \n \n \n \n \u2202\n \n t\n \n \n P\n (\n a\n ,\n t\n \n |\n \n x\n ,\n \n t\n \n 0\n \n \n )\n =\n \u2212\n \u03bb\n P\n (\n a\n ,\n t\n \n |\n \n x\n ,\n \n t\n \n 0\n \n \n )\n +\n \u03bc\n P\n (\n b\n ,\n t\n \n |\n \n x\n ,\n \n t\n \n 0\n \n \n )\n \n \n {\\displaystyle \\partial _{t}P(a,t|x,t_{0})=-\\lambda P(a,t|x,t_{0})+\\mu P(b,t|x,t_{0})}\n and\n\n \n \n \n \n \u2202\n \n t\n \n \n P\n (\n b\n ,\n t\n \n |\n \n x\n ,\n \n t\n \n 0\n \n \n )\n =\n \u03bb\n P\n (\n a\n ,\n t\n \n |\n \n x\n ,\n \n t\n \n 0\n \n \n )\n \u2212\n \u03bc\n P\n (\n b\n ,\n t\n \n |\n \n x\n ,\n \n t\n \n 0\n \n \n )\n .\n \n \n {\\displaystyle \\partial _{t}P(b,t|x,t_{0})=\\lambda P(a,t|x,t_{0})-\\mu P(b,t|x,t_{0}).}\n The process is also known under the names Kac process\n, dichotomous random process.", "images": [], "links": ["Abstract Wiener space", "Actuarial mathematics", "Algebraic tail", "ArXiv", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Bibcode", "Biology", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "Burst noise", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Correlation function", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Exponential decay", "Exponential distribution", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Finance", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fluorescence", "Fluorescence intermittency", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Mark Kac", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Master equation", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Memorylessness", "Mixing (mathematics)", "Model building", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Physics", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random telegraph signal", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Single molecule experiment", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Spin (physics)", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stock", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Time reversibility", "Time series", "Time series analysis", "Transcription factor", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://adsabs.harvard.edu/abs/2006JSP...122..137M", "http://arxiv.org/abs/cond-mat/0504454", "http://doi.org/10.1007%2Fs10955-005-8076-9", "http://doi.org/10.1023%2FA:1009437108439"]}, "Sampling bias": {"categories": ["All articles lacking reliable references", "Articles lacking reliable references from November 2014", "Bias", "CS1 maint: Multiple names: authors list", "Design of experiments", "Misuse of statistics", "Sampling (statistics)", "Wikipedia articles needing clarification from August 2014"], "title": "Sampling bias", "method": "Sampling bias", "url": "https://en.wikipedia.org/wiki/Sampling_bias", "summary": "In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population are less likely to be included than others. It results in a biased sample, a non-random sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling.\nMedical sources sometimes refer to sampling bias as ascertainment bias. Ascertainment bias has basically the same definition, but is still sometimes classified as a separate type of bias.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c9/Acid2compliancebyusage.png", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/7/70/Ascertainment_bias.png", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["Academic bias", "Accident (fallacy)", "Acid2", "Acquiescence bias", "Alf Landon", "Ambiguity", "Anchoring", "Anecdotal evidence", "Animistic fallacy", "ArXiv", "Argument from analogy", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "Autosomal recessive", "Base rate fallacy", "Begging the question", "Belief bias", "Bell System", "Berkson's fallacy", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Cave painting", "Censored regression model", "Ceremonial burial", "Cherry picking", "Cherry picking (fallacy)", "Chicago Tribune", "Choice-supportive bias", "Cholecystitis", "Circular analysis", "Circular reasoning", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Comorbidity", "Complex question", "Confirmation bias", "Confounding", "Congruence bias", "Conjunction fallacy", "Continuum fallacy", "Converse accident", "Correlation does not imply causation", "Correlative-based fallacies", "Cultural bias", "Debiasing", "Demarcation Problem", "Denying the correlative", "Dewey Defeats Truman", "Digital object identifier", "Distinction bias", "Double-barreled question", "Double counting (fallacy)", "Dunning\u2013Kruger effect", "Dyslexia", "Ecological fallacy", "Egocentric bias", "Emotional bias", "Equivocation", "External validity", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Fallacies of illicit transference", "Fallacy", "Fallacy of accent", "Fallacy of composition", "Fallacy of division", "Fallacy of the single cause", "False attribution", "False dilemma", "False equivalence", "False precision", "Faulty generalization", "File drawer problem", "Fold change", "Forecast bias", "Franklin Roosevelt", "Friendship paradox", "Fundamental attribution error", "Funding bias", "Furtive fallacy", "Gallup poll", "Gambler's fallacy", "George Gallup", "Halo effect", "Harry S. Truman", "Healthy user bias", "Heterozygote", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "How to Lie with Statistics", "Human migration", "Impact bias", "Impression management", "In-group favoritism", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "Intellectual disability", "Internal validity", "International Standard Book Number", "Internet Explorer", "Inverse gambler's fallacy", "Lead time bias", "Leading question", "Length time bias", "Lies, damned lies, and statistics", "List of cognitive biases", "List of fallacies", "List of memory biases", "Literary Digest", "Loaded language", "Loaded question", "Loki's Wager", "Malmquist bias", "McNamara fallacy", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mendelian inheritance", "Mere-exposure effect", "Midden", "Misleading graph", "Misuse of statistics", "Moving the goalposts", "National Center for Health Statistics", "Negativity bias", "Net bias", "Nirvana fallacy", "No true Scotsman", "Non-response bias", "Normalcy bias", "Omission bias", "Omitted-variable bias", "Online and phone-in polls", "Optimism bias", "Outcome bias", "Overmatching", "Overton window", "Overwhelming exception", "Parameter", "Participation bias", "Phone survey", "Post hoc ergo propter hoc", "Precision bias", "Prehistory", "President-elect", "Pro-innovation bias", "PubMed Identifier", "Publication bias", "Questionable cause", "Quoting out of context", "Recall bias", "Regression fallacy", "Reification (fallacy)", "Reporting bias", "Research ethics", "Response bias", "Restraint bias", "Sampling (statistics)", "Sampling probability", "Scientific fraud", "Secundum quid", "Selection bias", "Self-selection bias", "Self-serving bias", "Slippery slope", "Slothful induction", "Social Register", "Social comparison bias", "Social desirability bias", "Society for Academic Emergency Medicine", "Sorites paradox", "Spectrum bias", "Statistic", "Statistical population", "Statistics", "Status quo bias", "Suppressed correlative", "Survivorship bias", "Syntactic ambiguity", "Systematic error", "Systemic bias", "Telephone directory", "Texas sharpshooter fallacy", "Time-saving bias", "Trait ascription bias", "Truncated regression model", "United States news media and the Vietnam War", "United States presidential election, 1936", "United States presidential election, 1948", "Vagueness", "Verification bias", "Von Restorff effect", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://www.tdx.cat/bitstream/handle/10803/7140/tars.pdf?sequence=1", "http://www.medilexicon.com/medicaldictionary.php?t=10080", "http://www.medilexicon.com/medicaldictionary.php?t=10087", "http://medical-dictionary.thefreedictionary.com/Sample+bias", "http://medical.webends.com/kw/Selection%20Bias", "http://www.cs.nyu.edu/~mohri/postscript/bias.pdf", "http://www.cs.nyu.edu/~mohri/pub/nsmooth.pdf", "http://www.uh.edu/engines/epi1199.htm", "http://web.utk.edu/~orme00/articles/Cuddeback_et_al.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/9504213", "http://arxiv.org/abs/0805.2775", "http://doi.org/10.1007%2F978-3-540-87987-9_8", "http://doi.org/10.1016%2FS0145-2134(97)00131-2", "http://doi.org/10.1016%2Fj.tcs.2013.09.027", "http://doi.org/10.1300%2FJ079v30n03_02", "http://doi.org/10.2307%2F2095230", "http://elearning.saem.org/sites/default/files/issuu/libraries/Panacek_Error_And_Bias_In_Clinical_Research_syllabus_1.pdf", "https://books.google.com/books?id=EBq63uyt87QC", "https://books.google.com/books?id=WY5qAAAAMAAJ", "https://books.google.com/books?id=f0IDHvLiWqUC", "https://www.w3schools.com/browsers/browsers_stats.asp", "https://www.cdc.gov/nchs/about/otheract/minority/minority.htm"]}, "Outline of statistics": {"categories": ["Mathematics-related lists", "Statistics", "Statistics-related lists", "Wikipedia outlines"], "title": "Outline of statistics", "method": "Outline of statistics", "url": "https://en.wikipedia.org/wiki/Outline_of_statistics", "summary": "Statistics is a field of inquiry that studies the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities; it is also used and misused for making informed decisions in all areas of business and government.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikibooks-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/2/24/Wikinews-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1b/Wikiversity-logo-en.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1b/Wikiversity-logo-en.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/0/06/Wiktionary-logo-v2.svg"], "links": ["Academic discipline", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algebra of random variables", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Bar chart", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Biased sample", "Binomial regression", "Bioinformatics", "Biometrics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Business", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central moment", "Central tendency", "Characteristic function (probability theory)", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinatorics", "Completeness (statistics)", "Computational statistics", "Conditional probability", "Conditional probability distribution", "Confidence interval", "Confounding", "Conjugate prior", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data", "Data collection", "Decision theory", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation theory", "Estimator", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Formal science", "Founders of statistics", "Fourier analysis", "Free statistical software", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of probability and statistics", "Goodness of fit", "Government", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "History of probability", "History of statistics", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Humanities", "Index of dispersion", "Index of statistics articles", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kalman filter", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kernel (statistics)", "Kernel density estimation", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of academic disciplines", "List of academic statistical associations", "List of fields of application of statistics", "List of graphical methods", "List of important publications in statistics", "List of national and international statistical services", "List of probability distributions", "List of scientific journals in statistics", "List of statistical packages", "List of statisticians", "List of statistics articles", "List of statistics journals", "Lists of statistics topics", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Markov chain Monte Carlo", "Mathematical sciences", "Mathematical statistics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Median absolute deviation", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Misuse of statistics", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo method", "Moving average", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate kernel density estimation", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Notation in probability and statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of probability", "Outline of regression analysis", "P-value", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Particle filter", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Philosophy of statistics", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior distribution", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior distribution", "Prior probability", "Probabilistic design", "Probability", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile", "Quasi-experiment", "Questionnaire", "Quota sampling", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recursive Bayesian estimation", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Science", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simulation", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spectrum bias", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical survey", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Survivorship bias", "Symmetric probability distribution", "System identification", "Time domain", "Time series", "Time series analysis", "Timeline of probability and statistics", "Tolerance interval", "Trend estimation", "Trimmed estimator", "Type I and type II errors", "U-statistic", "Uniformly most powerful test", "Unimodal probability distribution", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Strong Law of Small Numbers": {"categories": ["1988 documents", "1988 in science", "All stub articles", "Mathematical humor", "Mathematics literature stubs", "Mathematics papers", "Works originally published in American magazines", "Works originally published in science and technology magazines"], "title": "Strong Law of Small Numbers", "method": "Strong Law of Small Numbers", "url": "https://en.wikipedia.org/wiki/Strong_Law_of_Small_Numbers", "summary": "In mathematics, the \"Strong Law of Small Numbers\" is the humorous title of a popular paper by mathematician Richard K. Guy and also the so-called law that proclaims: \n\n\"There aren't enough small numbers to meet the many demands made of them.\"\nIn other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few. Guy's paper gives 35 examples in support of this thesis. This can lead inexperienced mathematicians to conclude that these concepts are related, when in fact they are not.\nGuy's observation has since become part of mathematical folklore, and is commonly referenced by other authors.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a3/Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a3/20120917204659%21Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a3/20100506100358%21Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a3/20070526080805%21Arithmetic_symbols.svg"], "links": ["Academic publishing", "American Mathematical Monthly", "Amos Tversky", "Arithmetic function", "Daniel Kahneman", "Digital object identifier", "Eric W. Weisstein", "Insensitivity to sample size", "International Standard Serial Number", "JSTOR", "Jean-Pierre Serre", "Law (principle)", "Law of large numbers", "Law of small numbers (disambiguation)", "MathWorld", "Mathematical coincidence", "Mathematical folklore", "Mathematics", "Mathematics Magazine", "Pigeonhole principle", "Representativeness heuristic", "Richard K. Guy"], "references": ["http://mathworld.wolfram.com/StrongLawofSmallNumbers.html", "http://sbseminar.wordpress.com/2007/10/27/small-finite-sets/", "http://primes.utm.edu/glossary/page.php?sort=LawOfSmall", "http://psycnet.apa.org/?&fa=main.doiLanding&doi=10.1037/h0031322", "http://doi.org/10.1037/h0031322", "http://doi.org/10.2307/2322249", "http://doi.org/10.2307/2691503", "http://www.jstor.org/stable/2322249", "http://www.jstor.org/stable/2691503", "http://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Guy697-712.pdf", "http://www.worldcat.org/issn/0002-9890"]}, "Blocking (statistics)": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from January 2018", "CS1 maint: Multiple names: authors list", "Design of experiments", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Blocking (statistics)", "method": "Blocking (statistics)", "url": "https://en.wikipedia.org/wiki/Blocking_(statistics)", "summary": "In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algebraic statistics", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anne Penfold Street", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Block design", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinatorial design", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Control group", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Damaraju Raghavarao", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Double blind", "Drug", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Francis J. Anscombe", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Holger Rootz\u00e9n", "Homoscedasticity", "Hyper-Graeco-Latin square design", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "Paired difference test", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Placebo", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R.A. Bailey", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized complete block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sidney Addelman", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Treatment group", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://itfeature.com/design-of-experiment-doe/randomized-complete-block-design", "http://www.nist.gov", "http://www.isid.ac.in/~rbb/", "http://www.ams.org/mathscinet-getitem?mr=0030181", "http://www.ams.org/mathscinet-getitem?mr=1994124", "http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521683579", "http://doi.org/10.1214%2Faoms%2F1177703889", "http://doi.org/10.2307%2F2284277", "http://doi.org/10.2307%2F2333423", "http://doi.org/10.2307%2F2681737", "http://doi.org/10.2307%2F2684574", "http://doi.org/10.2307%2F2984159", "http://www.jstor.org/stable/2238364", "http://www.jstor.org/stable/2284277", "http://www.jstor.org/stable/2333423", "http://www.jstor.org/stable/2681737", "http://www.jstor.org/stable/2684574", "http://www.jstor.org/stable/2984159", "http://www.maths.qmul.ac.uk/~rab/DOEbook/", "http://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm", "https://books.google.com/books?id=T5dsExIP3aAC", "https://www.springer.com/series/694"]}, "Propensity score": {"categories": ["Causal inference", "Epidemiology", "Observational study", "Regression analysis"], "title": "Propensity score matching", "method": "Propensity score", "url": "https://en.wikipedia.org/wiki/Propensity_score_matching", "summary": "In the statistical analysis of observational data, propensity score matching (PSM) is a statistical matching technique that attempts to estimate the effect of a treatment, policy, or other intervention by accounting for the covariates that predict receiving the treatment. PSM attempts to reduce the bias due to confounding variables that could be found in an estimate of the treatment effect obtained from simply comparing outcomes among units that received the treatment versus those that did not. The technique was first published by Paul Rosenbaum and Donald Rubin in 1983, and implements the Rubin causal model for observational studies.\nThe possibility of bias arises because the apparent difference in outcome between these two groups of units may depend on characteristics that affected whether or not a unit received a given treatment instead of due to the effect of the treatment per se. In randomized experiments, the randomization enables unbiased estimation of treatment effects; for each covariate, randomization implies that treatment-groups will be balanced on average, by the law of large numbers. Unfortunately, for observational studies, the assignment of treatments to research subjects is typically not random. Matching attempts to mimic randomization by creating a sample of units that received the treatment that is comparable on all observed covariates to a sample of units that did not receive the treatment.\nFor example, one may be interested to know the consequences of smoking or the consequences of going to university. The people 'treated' are simply those\u2014the smokers, or the university graduates\u2014who in the course of everyday life undergo whatever it is that is being studied by the researcher. In both of these cases it is unfeasible (and perhaps unethical) to randomly assign people to smoking or a university education, so observational studies are required. The treatment effect estimated by simply comparing a particular outcome\u2014rate of cancer or lifetime earnings\u2014between those who smoked and did not smoke or attended university and did not attend university would be biased by any factors that predict smoking or university attendance, respectively. PSM attempts to control for these differences to make the groups receiving treatment and not-treatment more comparable.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alberto Abadie", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Approximation theory", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average treatment effect", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias (statistics)", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calibration curve", "Canonical correlation", "Cartography", "Categorical variable", "Causality", "Census", "Central limit theorem", "Central tendency", "Chebyshev nodes", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "CiteSeerX", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational statistics", "Conditional probability", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curve fitting", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Donald Rubin", "Durbin\u2013Watson statistic", "Econometrica", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation theory", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gary King (political scientist)", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric progression", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "Guido Imbens", "Harmonic mean", "Heckman correction", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Inductive reasoning", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Iteratively reweighted least squares", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Judea Pearl", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear least squares (mathematics)", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local regression", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mahalanobis distance", "Mallows's Cp", "Mann\u2013Whitney U test", "Matching (statistics)", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean and predicted response", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean-square error", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving least squares", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nearest neighbor search", "Nelson\u2013Aalen estimator", "Non-experimental", "Non-linear least squares", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Numerical analysis", "Numerical integration", "Numerical smoothing and differentiation", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal polynomials", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial least squares", "Partition of sums of squares", "Paul Rosenbaum", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Political Analysis (journal)", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quantile regression", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Regression toward the mean", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Ridge regression", "Robust regression", "Robust statistics", "Rubin causal model", "Run chart", "SAS (software)", "SPSS", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Segmented regression", "Selection bias", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistical unit", "Statistics", "Stem-and-leaf display", "Stepwise regression", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Total least squares", "Treatment and control groups", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weighted least squares", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www2.sas.com/proceedings/sugi29/165-29.pdf", "http://onlinelibrary.wiley.com/doi/10.1111/1475-6773.12182/full", "http://fmwww.bc.edu/RePEc/usug2001/psmatch.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.559.6313", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4213057", "http://www.ncbi.nlm.nih.gov/pubmed/24779867", "http://doi.org/10.1093%2Fbiomet%2F70.1.41", "http://doi.org/10.1093%2Fpan%2Fmpl013", "http://doi.org/10.1111%2F1475-6773.12182", "http://doi.org/10.1111%2Fj.1468-0262.2006.00655.x", "http://ideas.repec.org/c/boc/bocode/s432001.html", "https://books.google.com/books?id=lV3DIdV0F9AC&pg=PA206", "https://www.stata.com/manuals13/teteffectspsmatch.pdf", "https://cran.r-project.org/package=MatchIt"]}, "Binomial regression": {"categories": ["All articles with specifically marked weasel-worded phrases", "Articles with specifically marked weasel-worded phrases from November 2018", "Generalized linear models"], "title": "Binomial regression", "method": "Binomial regression", "url": "https://en.wikipedia.org/wiki/Binomial_regression", "summary": "In statistics, binomial regression is a technique in which the response (often referred to as Y) is the result of a series of Bernoulli trials, or a series of one of two possible disjoint outcomes (traditionally denoted \"success\" or 1, and \"failure\" or 0). In binomial regression, the probability of a success is related to explanatory variables: the corresponding concept in ordinary regression is to relate the mean value of the unobserved response to explanatory variables.\nBinomial regression models are essentially the same as binary choice models, one type of discrete choice model. The primary difference is in the theoretical motivation: Discrete choice models are motivated using utility theory so as to handle various types of correlated and uncorrelated choices, while binomial regression models are generally described in terms of the generalized linear model, an attempt to generalize various types of linear regression models. As a result, discrete choice models are usually described primarily with a latent variable indicating the \"utility\" of making a choice, and with randomness introduced through an error variable distributed according to a specific probability distribution. Note that the latent variable itself is not observed, only the actual choice, which is assumed to have been made if the net utility was greater than 0. Binary regression models, however, dispense with both the latent and error variable and assume that the choice itself is a random variable, with a link function that transforms the expected value of the choice variable into a value that is then predicted by the linear predictor. It can be shown that the two are equivalent, at least in the case of binary choice models: the link function corresponds to the quantile function of the distribution of the error variable, and the inverse link function to the cumulative distribution function (CDF) of the error variable. The latent variable has an equivalent if one imagines generating a uniformly distributed number between 0 and 1, subtracting from it the mean (in the form of the linear predictor transformed by the inverse link function), and inverting the sign. One then has a number whose probability of being greater than 0 is the same as the probability of success in the choice variable, and can be thought of as a latent variable indicating whether a 0 or 1 was chosen.\nIn machine learning, binomial regression is considered a special case of probabilistic classification, and thus a generalization of binary classification.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli trial", "Bias of an estimator", "Binary choice model", "Binary classification", "Binomial distribution", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Discrete choice", "Divergence (statistics)", "Dummy variable (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Error variable", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Explanatory variable", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalised linear model", "Generalized extreme value distribution", "Generalized linear model", "Generative model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Identifiability", "Independent variable", "Index of dispersion", "Indicator function", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latent variable", "Latent variable model", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear probability model", "Linear regression", "Link function", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic distribution", "Logistic function", "Logistic regression", "Logit function", "Logit model", "Loss function", "Lp space", "M-estimator", "Machine learning", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal variable", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Predictive modelling", "Principal component analysis", "Prior probability", "Probabilistic classification", "Probabilistic design", "Probability distribution", "Probit model", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile function", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression coefficient", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response variable", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard normal distribution", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Utility theory", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["https://books.google.com/books?id=RBKEwpsxmN4C", "https://books.google.com/books?id=RBKEwpsxmN4C&pg=PA91"]}, "Methods engineering": {"categories": ["All articles needing additional references", "Articles needing additional references from July 2008", "Engineering disciplines", "Engineering statistics", "Industrial engineering", "Wikipedia articles with NDL identifiers"], "title": "Methods engineering", "method": "Methods engineering", "url": "https://en.wikipedia.org/wiki/Methods_engineering", "summary": "Methods engineering is a subspecialty of industrial engineering and manufacturing engineering concerned with human integration in industrial production processes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Cost-benefit analysis", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gantt chart", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Industrial engineering", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Manufacturing engineering", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method engineering", "Method of moments (statistics)", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Motion analysis", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "PERT chart", "Parametric statistics", "Pareto analysis", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raw material", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Value engineering", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Work design", "Z-test"], "references": ["https://id.ndl.go.jp/auth/ndlna/00569942", "https://archive.org/details/MethodsEngineering", "https://www.wikidata.org/wiki/Q6823864"]}, "Generalized linear array model": {"categories": ["Generalized linear models", "Regression models"], "title": "Generalized linear array model", "method": "Generalized linear array model", "url": "https://en.wikipedia.org/wiki/Generalized_linear_array_model", "summary": "In statistics, the generalized linear array model (GLAM) is used for analyzing data sets with array structures. It based on the generalized linear model with the design matrix written as a Kronecker product.", "images": [], "links": ["Design matrix", "Generalized linear model", "Journal of the Royal Statistical Society", "Kronecker product", "Statistics"], "references": []}, "Probable error": {"categories": ["Errors and residuals", "Statistical deviation and dispersion", "Theory of probability distributions"], "title": "Probable error", "method": "Probable error", "url": "https://en.wikipedia.org/wiki/Probable_error", "summary": "In statistics, probable error defines the half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside. \nThus for a symmetric distribution it is equivalent to half the interquartile range, or the median absolute deviation. One such use of the term probable error in this sense is as the name for the scale parameter of the Cauchy distribution, which does not have a standard deviation.\nThe probable error can also be expressed as a multiple of the standard deviation \u03c3,, which requires that at least the second statistical moment of the distribution should exist, whereas the other definition does not. For a normal distribution this is \n\n \n \n \n \u03b3\n =\n 0.6745\n \u00d7\n \u03c3\n \n \n {\\displaystyle \\gamma =0.6745\\times \\sigma }\n (see details)\n\n", "images": [], "links": ["Cauchy distribution", "Central tendency", "Circular error probable", "Half-range", "International Standard Book Number", "Interquartile range", "Median absolute deviation", "Normal distribution", "Scale parameter", "Statistical moment", "Statistics", "Symmetric distribution"], "references": []}, "Optimistic knowledge gradient": {"categories": ["All orphaned articles", "Markov processes", "Mathematical optimization", "Orphaned articles from June 2015"], "title": "Optimistic knowledge gradient", "method": "Optimistic knowledge gradient", "url": "https://en.wikipedia.org/wiki/Optimistic_knowledge_gradient", "summary": "In statistics The optimistic knowledge gradient is a new approximation policy proposed by Xi Chen, Qihang Lin and Dengyong Zhou in 2013. This policy is created to solve the challenge of computationally intractable of large size of optimal computing budget allocation problem in binary/multi-class crowd labeling where each label from the crowd has a certain cost.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/6c/Wiki_letter_w.svg"], "links": ["Bernoulli distribution", "Crowdsourcing", "Dynamic programming", "Labeling", "Markov decision process", "Optimal computing budget allocation", "Random", "Statistics", "Variational Bayesian methods"], "references": ["http://20bits.com/articles/introduction-to-dynamic-programming/", "http://edwardbetts.com/find_link?q=Optimistic_knowledge_gradient", "http://www.eecs.umich.edu/~baveja/", "http://www.eecs.umich.edu/~baveja/Papers/Thesis.ps.gz", "http://www.jmlr.org/papers/volume16/chen15a/chen15a.pdf", "http://www.gatsby.ucl.ac.uk/vbayes/", "https://www.cs.cmu.edu/~xichen/images/ICML_Crowd_Budget.pdf"]}, "Richardson\u2013Lucy deconvolution": {"categories": ["Estimation theory", "Image processing"], "title": "Richardson\u2013Lucy deconvolution", "method": "Richardson\u2013Lucy deconvolution", "url": "https://en.wikipedia.org/wiki/Richardson%E2%80%93Lucy_deconvolution", "summary": "The Richardson\u2013Lucy algorithm, also known as Lucy\u2013Richardson deconvolution, is an iterative procedure for recovering an underlying image that has been blurred by a known point spread function. It was named after William Richardson and Leon Lucy, who described it independently.", "images": [], "links": ["Bibcode", "Blind deconvolution", "Charge coupled device", "Convolution", "Deconvolution", "Digital object identifier", "Iterative procedure", "JOSA", "Journal of the Optical Society of America A", "Modified Richardson iteration", "Photographic film", "Point source", "Point spread function", "PubMed Identifier", "Shift-invariant system"], "references": ["http://adsabs.harvard.edu/abs/1974AJ.....79..745L", "http://adsabs.harvard.edu/abs/1995JOSAA..12...58F", "http://www.math.ufl.edu/~bamair/fish95.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/18238264", "http://doi.org/10.1086%2F111605", "http://doi.org/10.1109%2FTMI.1982.4307558", "http://doi.org/10.1364%2FJOSA.62.000055", "http://doi.org/10.1364%2FJOSAA.12.000058", "http://www.opticsinfobase.org/abstract.cfm?id=54565"]}, "List of probability topics": {"categories": ["Lists of topics", "Mathematics-related lists", "Probability", "Statistics-related lists"], "title": "List of probability topics", "method": "List of probability topics", "url": "https://en.wikipedia.org/wiki/List_of_probability_topics", "summary": "This is a list of probability topics, by Wikipedia page.\nIt overlaps with the (alphabetical) list of statistical topics. There are also the outline of probability and catalog of articles in probability theory. For distributions, see List of probability distributions. For journals, see list of probability journals. For contributors to the field, see list of mathematical probabilists and list of statisticians.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png"], "links": ["Adapted process", "Aleatoric", "Aleatoric music", "Algebra of random variables", "Almost surely", "An inequality on location and scale parameters", "Anderson's theorem", "Anomaly time series", "Applied probability", "Asymptotic equipartition property", "Autoregressive integrated moving average model", "Autoregressive model", "Autoregressive moving average model", "Average", "Azuma's inequality", "Basic affine jump diffusion", "Bayes' theorem", "Bayesian probability", "Bayesianism", "Bean machine", "Belief propagation", "Benford's law", "Bernoulli process", "Bernoulli scheme", "Bernstein inequalities (probability theory)", "Berry\u2013Esseen theorem", "Berry\u2013Ess\u00e9en theorem", "Bertrand's paradox (probability)", "Bible code", "Birthday paradox", "Birthday problem", "Boole's inequality", "Borel's paradox", "Borel\u2013Cantelli lemma", "Box\u2013Muller transform", "Boy or Girl paradox", "Branching process", "Brownian motion", "Buffon's needle", "Canonical correlation", "Carleman's condition", "Catalog of articles in probability theory", "Central limit theorem", "Central tendency", "Chapman\u2013Kolmogorov equation", "Characteristic function (probability theory)", "Charles Wells (gambler)", "Chebyshev's inequality", "Chernoff's inequality", "Chernoff bound", "Chinese restaurant process", "Chung\u2013Erd\u0151s inequality", "Coefficient of variation", "Coherence (philosophical gambling strategy)", "Complementary event", "Concrete illustration of the central limit theorem", "Conditional event algebra", "Conditional expectation", "Conditional independence", "Conditional probability", "Conditional probability distribution", "Conditional random field", "Conditioning (probability)", "Constant random variable", "Continuity correction", "Continuous-time Markov process", "Contraction principle (large deviations theory)", "Convergence of random variables", "Correlation", "Correlation function", "Coupling (probability)", "Coupon collector's problem", "Covariance", "Covariance function", "Covariance matrix", "Cox's theorem", "Cram\u00e9r's theorem (large deviations)", "Credal set", "Cumulant", "Cumulative distribution function", "De Finetti's theorem", "De Moivre\u2013Laplace theorem", "Dempster\u2013Shafer theory", "Detailed balance", "Discrete random variable", "Disintegration theorem", "Donsker's theorem", "Doob martingale", "Dutch book", "Dynkin system", "Edgeworth series", "Elementary event", "Empirical measure", "Empirical process", "Equipossible", "Equiprobable", "Ergodic (adjective)", "Ergodic theory", "Erlang unit", "Etemadi's inequality", "Event (probability theory)", "Ewens's sampling formula", "Examples of Markov chains", "Exchangeable random variables", "Exotic probability", "Expected value", "Exponentially equivalent measures", "Extractor (mathematics)", "Factorial moment", "Factorial moment generating function", "Financial mathematics", "Free probability", "Frequency probability", "Galton\u2013Watson process", "Gambler's fallacy", "Gambler's ruin", "Gambling", "Game of chance", "Gaussian isoperimetric inequality", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Genetics", "Geometric Brownian motion", "Geometric standard deviation", "Gibbs sampling", "Girsanov's theorem", "Glivenko\u2013Cantelli theorem", "Glossary of probability and statistics", "Goodman\u2013Nguyen\u2013van Fraassen algebra", "Hadwiger's theorem", "Hamburger moment problem", "Hardware random number generator", "Hardy\u2013Weinberg principle", "Hausdorff moment problem", "Heavy-tailed distribution", "Hellinger distance", "Helly\u2013Bray theorem", "Hewitt\u2013Savage zero\u2013one law", "Hidden Markov model", "History of probability", "Hoeffding's inequality", "Illustration of the central limit theorem", "Impossible event", "Inclusion\u2013exclusion principle", "Increasing process", "Indecomposable distribution", "Independent and identically-distributed random variables", "Independent identically-distributed random variables", "Index of coincidence", "Infinite divisibility", "Infinite divisibility (probability)", "Infinite monkey theorem", "Information entropy", "Information geometry", "Integral geometry", "Inverse gambler's fallacy", "Inverse transform sampling method", "It\u00f4's lemma", "It\u00f4 calculus", "Jensen's inequality", "Joint probability distribution", "Jump diffusion", "Kelly criterion", "Khintchine inequality", "Kirkwood approximation", "Kolmogorov's inequality", "Kolmogorov's two-series theorem", "Kolmogorov's zero\u2013one law", "Kullback\u2013Leibler divergence", "Kurtosis", "Laplace principle (large deviations theory)", "Large deviations of Gaussian random functions", "Large deviations theory", "Las Vegas algorithm", "Law of large numbers", "Law of the iterated logarithm", "Law of the unconscious statistician", "Law of total cumulance", "Law of total expectation", "Law of total probability", "Law of total variance", "Law of truly large numbers", "Laws of large numbers", "Le Cam's theorem", "List of mathematical probabilists", "List of probability distributions", "List of probability journals", "List of statistical topics", "List of statisticians", "Littlewood's law", "Littlewood\u2013Offord problem", "Locality (statistics)", "Location parameter", "Loop-erased random walk", "Lottery", "Lottery machine", "Luck", "Lyapunov's central limit theorem", "L\u00e9vy's continuity theorem", "L\u00e9vy continuity theorem", "L\u00e9vy flight", "L\u00e9vy metric", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "Malliavin calculus", "Marginal distribution", "Market risk", "Markov's inequality", "Markov chain", "Markov chain mixing time", "Markov partition", "Markov process", "Markov property", "Markovian (disambiguation)", "Martingale (betting system)", "Martingale (probability theory)", "Martingale central limit theorem", "Martingale representation theorem", "Maximal ergodic theorem", "Maximum-entropy Markov model", "Maximum likelihood", "Maxwell's theorem", "Method of moments (probability theory)", "Metropolis algorithm", "Moment-generating function", "Moment (mathematics)", "Moment about the mean", "Moment problem", "Monte Carlo method", "Monty Hall problem", "Moving average model", "Multivariate random variable", "Mutual information", "Mutually exclusive", "Negative probability", "Normalizing constant", "Normally distributed and uncorrelated does not imply independent", "Notation in probability and statistics", "Observational error", "Odds", "Optional stopping theorem", "Outline of probability", "Pachinko", "Pairwise independence", "Paley\u2013Zygmund inequality", "Pareto principle", "Parrondo's paradox", "Pascal's wager", "Piecewise-deterministic Markov process", "Point process", "Poisson process", "Poisson random measure", "Poker probability", "Poker probability (Omaha)", "Poker probability (Texas hold 'em)", "Population genetics", "Population process", "Possibility theory", "Posterior probability", "Pot odds", "Power law", "Principle of indifference", "Principle of maximum entropy", "Prior probability", "Prior probability distribution", "Probabilistic Turing machine", "Probabilistic algorithm", "Probabilistically checkable proof", "Probability", "Probability-generating function", "Probability axioms", "Probability bounds analysis", "Probability box", "Probability density function", "Probability distribution", "Probability distribution function", "Probability interpretations", "Probability mass function", "Probability space", "Probability theory", "Probable prime", "Process with independent increments", "Progressively measurable process", "Pseudorandomness", "Punnett square", "Quantile", "Quasirandomness", "Queueing theory", "Random compact set", "Random element", "Random field", "Random number generation", "Random sequence", "Random variable", "Random walk", "Random walk Monte Carlo", "Randomised algorithm", "Randomization", "Randomness", "Rate function", "Regular conditional probability", "Relative frequency", "Renewal theory", "Risk", "Risk-neutral measure", "Roulette", "Rule of succession", "Sample space", "Schr\u00f6dinger method", "Second moment method", "Skewness", "Skorokhod's embedding theorem", "Skorokhod's representation theorem", "Slutsky's theorem", "Spurious relationship", "Stability (probability)", "Standard deviation", "Standard probability space", "Standardized moment", "Stationary process", "Statistical dispersion", "Statistical independence", "Statistical regularity", "Stein's lemma", "Stieltjes moment problem", "Stochastic calculus", "Stochastic process", "Stochastic programming", "Stratonovich integral", "Talagrand's concentration inequality", "Taylor expansions for the moments of functions of random variables", "Technical analysis", "The Doctrine of Chances", "Tilted large deviation principle", "Time series analysis", "Total variation", "Transferable belief model", "Trigonometric moment problem", "Truncated distribution", "Typical set", "Uncertainty", "Uncorrelated", "Uniform integrability", "Urn problem", "Value at risk", "Varadhan's lemma", "Variance", "Variance-to-mean ratio", "Volatility (finance)", "Voter model", "Vysochanski\u00ef\u2013Petunin inequality", "Wald's equation", "Walk-on-spheres method", "Wasserstein metric", "Weak convergence of measures", "Wendel's theorem", "Wick product", "Wiener equation", "Wiener process", "Wiener sausage", "Zero\u2013one law (disambiguation)", "Zipf's law"], "references": []}, "Ogden tables": {"categories": ["Actuarial science", "Forensic statistics", "Medical malpractice"], "title": "Ogden tables", "method": "Ogden tables", "url": "https://en.wikipedia.org/wiki/Ogden_tables", "summary": "Ogden tables are a set of statistical tables and other information for use in court cases in the UK.\nTheir purpose is to make it easier to calculate future losses in personal injury and fatal accident cases. The tables take into account life expectancy and provide a range of discount rates from -2.0% to 3.0% in steps of 0.5%. The discount rate is fixed by the Lord Chancellor under section 1 of the Damages Act 1996; as of 27 February 2017, this rate is -0.75%.The most recent edition of the tables (7th Edition) makes changes to the discount rate range (previously 0.0% to 5.0% revised to -2.0% to 3.0%) to allow for a revision of the discount rate by the Lord Chancellor (currently under consideration as at 24 October 2011) and to provide for the implications of the case of Helmot v. Simon.The Civil Evidence Act 1995 permitted their use in the UK and they were first used by the House of Lords in Wells v. Wells in July 1999.\nThe full, and official, name of the tables is Actuarial Tables with explanatory notes for use in Personal Injury and Fatal Accident Cases but the unofficial name became common parlance following the Civil Evidence Act 1995, where this shorthand name was used as a subheading \u2013 Sir Michael Ogden QC having been the chairman of the Working Party for the first four editions", "images": [], "links": ["Chairman", "Court case", "Discount window", "Fatal accident", "House of Lords", "Life expectancy", "Lord Chancellor", "Personal injury", "UK"], "references": ["http://www.frenkels.com/ogden-tables-calculator.html", "http://www.gad.gov.uk/services/Other%20Services/Compensation_for_injury_and_death.html", "http://www.legislation.gov.uk/ukpga/1996/48/pdfs/ukpga_19960048_en.pdf", "https://web.archive.org/web/20141130201803/https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/245859/ogden_tables_7th_edition.pdf", "https://web.archive.org/web/20141130202533/https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/309971/Ogden_Tables_5th_edition.pdf", "https://www.gov.uk/government/news/new-discount-rate-for-personal-injury-claims-announced", "https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/245859/ogden_tables_7th_edition.pdf", "https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/309971/Ogden_Tables_5th_edition.pdf"]}, "Filtering problem (stochastic processes)": {"categories": ["Control theory", "Signal estimation", "Stochastic differential equations"], "title": "Filtering problem (stochastic processes)", "method": "Filtering problem (stochastic processes)", "url": "https://en.wikipedia.org/wiki/Filtering_problem_(stochastic_processes)", "summary": "In the theory of stochastic processes, the filtering problem is a mathematical model for a number of state estimation problems in signal processing and related fields. The general idea is to establish a \"best estimate\" for the true value of some system from an incomplete, potentially noisy set of observations on that system. The problem of optimal non-linear filtering (even for the non-stationary case) was solved by Ruslan L. Stratonovich (1959, 1960), see also Harold J. Kushner's work and Moshe Zakai's, who introduced a simplified dynamics for the unnormalized conditional law of the filter known as Zakai equation. The solution, however, is infinite-dimensional in the general case. Certain approximations and special cases are well understood: for example, the linear filters are optimal for Gaussian random variables, and are known as the Wiener filter and the Kalman-Bucy filter. More generally, as the solution is infinite dimensional, it requires finite dimensional approximations to be implemented in a computer with finite memory. A finite dimensional approximated nonlinear filter may be more based on heuristics, such as the Extended Kalman Filter or the Assumed Density Filters, or more methodologically oriented such as for example the Projection Filters, some sub-families of which are shown to coincide with the Assumed Density Filters.In general, if the separation principle applies, then filtering also arises as part of the solution of an optimal control problem. For example, the Kalman filter is the estimation part of the optimal control solution to the linear-quadratic-Gaussian control problem.", "images": [], "links": ["Bernard Hanzon", "Bernt \u00d8ksendal", "Brownian motion", "Conditional expectation", "Damiano Brigo", "Digital object identifier", "Dimension", "Euclidean space", "Extended Kalman Filter", "Filter (disambiguation)", "Filter (signal processing)", "Filtering problem", "Fran\u00e7ois Le Gland", "Harold J. Kushner", "Hilbert space", "International Standard Book Number", "Kalman-Bucy filter", "Kalman filter", "Kiyoshi It\u014d", "Linear-quadratic-Gaussian control", "Linear subspace", "Mathematical Reviews", "Measurable function", "Mireille Chaleyat-Maurel", "Moshe Zakai", "Nonlinear filter", "Optimal control", "Orthogonal projection", "Probability space", "Random variable", "Ruslan L. Stratonovich", "Separation principle", "Sigma algebra", "Signal processing", "Smoothing", "Smoothing (disambiguation)", "Smoothing problem", "Stochastic differential equation", "Stochastic processes", "Wiener filter", "Zakai equation", "Zentralblatt MATH"], "references": ["https://mathscinet.ams.org/mathscinet-getitem?mr=242552", "https://doi.org/10.1007%2FBF00536382", "https://zbmath.org/?format=complete&q=an:0164.19201"]}, "Guess value": {"categories": ["All articles lacking sources", "Articles lacking sources from June 2012", "Computational statistics", "Mathematical optimization", "Regression analysis"], "title": "Guess value", "method": "Guess value", "url": "https://en.wikipedia.org/wiki/Guess_value", "summary": "In mathematical modeling, a guess value is more commonly called a starting value or initial value. These are necessary for most optimization problems which use search algorithms, because those algorithms are mainly deterministic and iterative, and they need to start somewhere. One common type of application is nonlinear regression.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Arithmetic overflow", "Asymptotes", "Deterministic algorithm", "Differential equation", "Dimensions", "Dithering", "Evolutionary algorithms", "Fitness function", "Genetic algorithms", "Guesstimate", "Iterative", "Linear", "Linearization", "Mean", "Nonlinear regression", "Objective function", "Optimization (mathematics)", "Plateau (mathematics)", "Search algorithms", "Simultaneous equations", "Stochastic", "Sum of squared errors of prediction", "Time series"], "references": []}, "Disorder problem": {"categories": ["All stub articles", "Optimal decisions", "Probability stubs", "Stochastic processes"], "title": "Disorder problem", "method": "Disorder problem", "url": "https://en.wikipedia.org/wiki/Disorder_problem", "summary": "In the study of stochastic processes in mathematics, a disorder problem or quickest detection problem (formulated by Kolmogorov) is the problem of using ongoing observations of a stochastic process to detect as soon as possible when the probabilistic properties of the process have changed. This is a type of change detection problem.\nAn example case is to detect the change in the drift parameter of a Wiener process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["Change detection", "Compound Poisson process", "International Standard Book Number", "Kolmogorov", "Mathematics", "Probability", "Shiryaev", "Stochastic processes", "Wiener process"], "references": ["http://projecteuclid.org/euclid.aoap/1106922334"]}, "Panjer recursion": {"categories": ["Actuarial science", "Compound probability distributions", "Theory of probability distributions"], "title": "Panjer recursion", "method": "Panjer recursion", "url": "https://en.wikipedia.org/wiki/Panjer_recursion", "summary": "The Panjer recursion is an algorithm to compute the probability distribution approximation of a compound random variable\n\n \n \n \n S\n =\n \n \u2211\n \n i\n =\n 1\n \n \n N\n \n \n \n X\n \n i\n \n \n \n \n \n {\\displaystyle S=\\sum _{i=1}^{N}X_{i}\\,}\n .\nwhere both \n \n \n \n N\n \n \n \n {\\displaystyle N\\,}\n and \n \n \n \n \n X\n \n i\n \n \n \n \n \n {\\displaystyle X_{i}\\,}\n are random variables and of special types. In more general cases the distribution of S is a compound distribution. The recursion for the special cases considered was introduced in a paper by Harry Panjer (Emeritus professor, University of Waterloo). It is heavily used in actuarial science (see also systemic risk).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/72/Expba07.jpg"], "links": ["(a,b,0) class of distributions", "Actuarial science", "Algorithm", "Compound distribution", "Digital object identifier", "Emeritus professor", "Fr\u00e9chet distribution", "Harry Panjer", "I.i.d.", "International Actuarial Association", "Probability distribution", "Probability generating function", "Random variable", "Random variables", "Systemic risk", "University of Waterloo"], "references": ["http://www.vosesoftware.com/riskwiki/Aggregatemodeling-DePrilsrecursivemethod.php", "http://www.vosesoftware.com/riskwiki/Aggregatemodeling-Panjersrecursivemethod.php", "http://www.risk.net/journal-of-operational-risk/technical-paper/2160851/a-modified-panjer-algorithm-operational-risk-capital-calculations", "http://www.actuaries.org/COUNCIL/Documents/CV_Panjer.pdf", "http://www.casact.org/library/astin/vol12no1/22.pdf", "http://doi.org/10.1080/03461238.1988.10413837", "https://math.uwaterloo.ca/statistics-and-actuarial-science/about/people/harry-panjer"]}, "Ridit scoring": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2011", "Categorical data", "Econometric modeling"], "title": "Ridit scoring", "method": "Ridit scoring", "url": "https://en.wikipedia.org/wiki/Ridit_scoring", "summary": "In econometrics, ridit scoring is a statistical method used to analyze ordered qualitative measurements.\nThe tools of ridit analysis were developed and first applied by Bross, who coined the term \"ridit\" by analogy with other statistical transformations such as probit and logit.", "images": [], "links": ["Digital object identifier", "Econometrics", "Epidemiology", "Health science", "JSTOR", "Logit", "Percentile", "Probit", "PubMed Identifier"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/15102382", "http://doi.org/10.1016%2FS1090-3801(98)90018-0", "https://www.jstor.org/stable/2527727", "https://www.jstor.org/stable/2958658", "https://cran.r-project.org/package=Ridit"]}, "Rasch model estimation": {"categories": ["All Wikipedia articles needing context", "All articles lacking in-text citations", "All articles needing additional references", "All pages needing cleanup", "Articles lacking in-text citations from July 2012", "Articles needing additional references from July 2012", "Articles with multiple maintenance issues", "Maximum likelihood estimation", "Psychometrics", "Wikipedia articles needing context from October 2009", "Wikipedia introduction cleanup from October 2009"], "title": "Rasch model estimation", "method": "Rasch model estimation", "url": "https://en.wikipedia.org/wiki/Rasch_model_estimation", "summary": "Estimation of a Rasch model is used to estimate the parameters of the Rasch model. Various techniques are employed to estimate the parameters from matrices of response data. The most common approaches are types of maximum likelihood estimation, such as joint and conditional maximum likelihood estimation. Joint maximum likelihood (JML) equations are efficient, but inconsistent for a finite number of items, whereas conditional maximum likelihood (CML) equations give consistent and unbiased item estimates. Person estimates are generally thought to have bias associated with them, although weighted likelihood estimation methods for the estimation of person parameters reduce the bias.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bias of an estimator", "Elementary symmetric function", "Expectation-maximization algorithm", "Maximum likelihood", "Newton-Raphson", "Rasch model"], "references": []}, "Bayesian average": {"categories": ["All articles to be merged", "All stub articles", "Articles to be merged from July 2018", "Bayesian estimation", "Statistics stubs"], "title": "Bayesian average", "method": "Bayesian average", "url": "https://en.wikipedia.org/wiki/Bayesian_average", "summary": "A Bayesian average is a method of estimating the mean of a population using outside information, especially a pre-existing belief, that is factored into the calculation. This is a central feature of Bayesian interpretation. This is relevant when the available data set is small.Calculating the Bayesian average uses the prior mean m and a constant C. C is assigned a value that is proportional to the typical data set size. The value is larger when the expected variation between data sets (within the larger population) is small. It is smaller when the data sets are expected to vary substantially from one another.\n\n \n \n \n \n \n \n x\n \u00af\n \n \n \n =\n \n \n \n C\n m\n +\n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n x\n \n i\n \n \n \n \n C\n +\n n\n \n \n \n \n \n {\\displaystyle {\\bar {x}}={Cm+\\sum _{i=1}^{n}x_{i} \\over C+n}}\n This is equivalent to adding C data points of value m to the data set. It is a weighted average of a prior average m and the sample average.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/a/aa/Merge-arrow.svg"], "links": ["Additive smoothing", "Bayesian probability", "Digital object identifier", "Mean", "Statistics"], "references": ["http://fulmicoton.com/posts/bayesian_rating", "http://doi.org/10.1145/2505515.2507885", "http://www.evanmiller.org/bayesian-average-ratings.html"]}, "Exponential-logarithmic distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax", "Survival analysis"], "title": "Exponential-logarithmic distribution", "method": "Exponential-logarithmic distribution", "url": "https://en.wikipedia.org/wiki/Exponential-logarithmic_distribution", "summary": "In probability theory and statistics, the Exponential-Logarithmic (EL) distribution is a family of lifetime distributions with\ndecreasing failure rate, defined on the interval [0, \u221e). This distribution is parameterized by two parameters \n \n \n \n p\n \u2208\n (\n 0\n ,\n 1\n )\n \n \n {\\displaystyle p\\in (0,1)}\n and \n \n \n \n \u03b2\n >\n 0\n \n \n {\\displaystyle \\beta >0}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/60/Hazard_EL.png", "https://upload.wikimedia.org/wikipedia/commons/a/a9/Pdf_EL.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biological", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dilogarithm", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Engineering", "Erlang distribution", "Ewens's sampling formula", "Expectation-maximization algorithm", "Expected value", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Failure rate", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hazard function", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypergeometric function", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Moment generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Parametric family", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Polylogarithm", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Random variate", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Survival function", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.vgtu.lt/leidiniai/leidykla/ASMDA_2009/", "http://www.vgtu.lt/leidiniai/leidykla/ASMDA_2009/PDF/16_sec_081_Ciumara_The_Weibull.pdf", "https://doi.org/10.1016%2Fj.csda.2007.12.002"]}, "Hirschman uncertainty": {"categories": ["Concepts in physics", "Inequalities", "Information theory", "Quantum mechanical entropy"], "title": "Entropic uncertainty", "method": "Hirschman uncertainty", "url": "https://en.wikipedia.org/wiki/Entropic_uncertainty", "summary": "In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. This is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations.\nIn 1957, Hirschman considered a function f and its Fourier transform g such that\n\n \n \n \n g\n (\n y\n )\n \u2248\n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n exp\n \u2061\n (\n \u2212\n 2\n \u03c0\n i\n x\n y\n )\n f\n (\n x\n )\n \n d\n x\n ,\n \n f\n (\n x\n )\n \u2248\n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n exp\n \u2061\n (\n 2\n \u03c0\n i\n x\n y\n )\n g\n (\n y\n )\n \n d\n y\n \n ,\n \n \n {\\displaystyle g(y)\\approx \\int _{-\\infty }^{\\infty }\\exp(-2\\pi ixy)f(x)\\,dx,\\qquad f(x)\\approx \\int _{-\\infty }^{\\infty }\\exp(2\\pi ixy)g(y)\\,dy~,}\n where the \"\u2248\" indicates convergence in L2, and normalized so that (by Plancherel's theorem),\n\n \n \n \n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n \n |\n \n f\n (\n x\n )\n \n \n |\n \n \n 2\n \n \n \n d\n x\n =\n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n \n |\n \n g\n (\n y\n )\n \n \n |\n \n \n 2\n \n \n \n d\n y\n =\n 1\n \n .\n \n \n {\\displaystyle \\int _{-\\infty }^{\\infty }|f(x)|^{2}\\,dx=\\int _{-\\infty }^{\\infty }|g(y)|^{2}\\,dy=1~.}\n He showed that for any such functions the sum of the Shannon entropies is non-negative,\n\n \n \n \n H\n (\n \n |\n \n f\n \n \n |\n \n \n 2\n \n \n )\n +\n H\n (\n \n |\n \n g\n \n \n |\n \n \n 2\n \n \n )\n \u2261\n \u2212\n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n \n |\n \n f\n (\n x\n )\n \n \n |\n \n \n 2\n \n \n log\n \u2061\n \n |\n \n f\n (\n x\n )\n \n \n |\n \n \n 2\n \n \n \n d\n x\n \u2212\n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n \n |\n \n g\n (\n y\n )\n \n \n |\n \n \n 2\n \n \n log\n \u2061\n \n |\n \n g\n (\n y\n )\n \n \n |\n \n \n 2\n \n \n \n d\n y\n \u2265\n 0.\n \n \n {\\displaystyle H(|f|^{2})+H(|g|^{2})\\equiv -\\int _{-\\infty }^{\\infty }|f(x)|^{2}\\log |f(x)|^{2}\\,dx-\\int _{-\\infty }^{\\infty }|g(y)|^{2}\\log |g(y)|^{2}\\,dy\\geq 0.}\n A tighter bound,\n\nwas conjectured by Hirschman and Everett, proven in 1975 by W. Beckner\nand in the same year interpreted by as a generalized quantum mechanical uncertainty principle by Bia\u0142ynicki-Birula and Mycielski.\nThe equality holds in the case of Gaussian distributions.Note, however, that the above entropic uncertainty function is distinctly different from the quantum Von Neumann entropy represented in phase space.", "images": [], "links": ["American Journal of Mathematics", "Annals of Mathematics", "ArXiv", "Babenko\u2013Beckner inequality", "Bibcode", "Bit", "Calculus of variations", "Communications in Mathematical Physics", "Differential entropy", "Digital object identifier", "Fourier Transform", "Fourier analysis", "Fourier transform", "Gaussian distribution", "Hermite functions", "Hugh Everett", "Inequalities in information theory", "Information theory", "Isidore Isaac Hirschman, Jr.", "JSTOR", "Lebesgue measure", "Nat (unit)", "Normal distribution", "Normal probability distribution", "Phase space", "Plancherel theorem", "PubMed Identifier", "Riesz\u2013Thorin theorem", "R\u00e9nyi entropy", "Shannon entropy", "Uncertainty principle", "Variance", "Von Neumann entropy", "William Beckner (mathematician)"], "references": ["http://www.hindawi.com/GetArticle.aspx?doi=10.1155/S0161171286000212", "http://redwood.berkeley.edu/w/images/9/95/2002-26.pdf", "http://adsabs.harvard.edu/abs/1975CMaPh..44..129B", "http://adsabs.harvard.edu/abs/1988PhRvL..60.1103M", "http://adsabs.harvard.edu/abs/1997quant.ph..6015S", "http://adsabs.harvard.edu/abs/2003PhLA..317...32G", "http://adsabs.harvard.edu/abs/2006PhRvA..74e2101B", "http://adsabs.harvard.edu/abs/2007PhRvA..75b2319B", "http://adsabs.harvard.edu/abs/2007PhyA..375..499Z", "http://www.ncbi.nlm.nih.gov/pubmed/10037942", "http://arxiv.org/abs/math/0605510", "http://arxiv.org/abs/quant-ph/0310120", "http://arxiv.org/abs/quant-ph/0606244", "http://arxiv.org/abs/quant-ph/0608116", "http://arxiv.org/abs/quant-ph/9706015", "http://doi.org/10.1007%2FBF01608825", "http://doi.org/10.1016%2Fj.jfa.2003.11.008", "http://doi.org/10.1016%2Fj.physa.2006.09.019", "http://doi.org/10.1016%2Fj.physleta.2003.08.029", "http://doi.org/10.1023%2FA:1007464229188", "http://doi.org/10.1103%2FPhysRevA.74.052101", "http://doi.org/10.1103%2FPhysRevA.75.022319", "http://doi.org/10.1103%2FPhysRevLett.60.1103", "http://doi.org/10.2307%2F1970980", "http://doi.org/10.2307%2F2372390", "http://www.jstor.org/stable/1970980", "http://www.jstor.org/stable/2372390", "https://pure.uva.nl/ws/files/2210736/46650_28y.pdf", "https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.060104", "https://arxiv.org/abs/math/0605510v1", "https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf"]}, "V-optimal histograms": {"categories": ["All articles needing expert attention", "All articles needing rewrite", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Database theory", "Statistical charts and diagrams", "Statistics articles needing expert attention", "Wikipedia articles needing rewrite from May 2009"], "title": "V-optimal histograms", "method": "V-optimal histograms", "url": "https://en.wikipedia.org/wiki/V-optimal_histograms", "summary": "Histograms are most commonly used as visual representations of data. However, database systems use histograms to summarize data internally and provide size estimates for queries. These histograms are not presented to users or displayed visually, so a wider range of options are available for their construction. Simple or exotic histograms are defined by four parameters, Sort Value, Source Value, Partition Class and Partition Rule. The most basic histogram is the equi-width histogram, where each bucket represents the same range of values. That histogram would be defined as having a Sort Value of Value, a Source Value of Frequency, be in the Serial Partition Class and have a Partition Rule stating that all buckets have the same range.\nV-optimal histograms are an example of a more \"exotic\" histogram. V-optimality is a Partition Rule which states that the bucket boundaries are to be placed as to minimize the cumulative weighted variance of the buckets. Implementation of this rule is a complex problem and construction of these histograms is also a complex process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e8/Crystal_Clear_app_kedit.svg"], "links": ["Bucket (computing)", "Database management system", "Digital object identifier", "Histogram", "International Standard Book Number", "Query language"], "references": ["http://www.cs.cmu.edu/~natassa/courses/15-823/current/papers/poosala96improved.pdf", "http://www-static.cc.gatech.edu/computing/Database/readinggroup/articles/p312-ioannidis.pdf", "http://citeseer.ist.psu.edu/poosala96improved.html", "http://doi.org/10.1145/223784.223841", "http://doi.org/10.1145/233269.233342", "http://doi.org/10.1145/93605.98740", "http://reference.kfupm.edu.sa/content/b/a/balancing_histogram_optimality_and_pract_46453.pdf"]}, "Z-factor": {"categories": ["Change detection", "Effect size"], "title": "Z-factor", "method": "Z-factor", "url": "https://en.wikipedia.org/wiki/Z-factor", "summary": "The Z-factor is a measure of statistical effect size. It has been proposed for use in high-throughput screening (where it is also known as Z-prime, and commonly written as Z') to judge whether the response in a particular assay is large enough to warrant further attention.", "images": [], "links": ["Arithmetic mean", "Assay", "Compressibility factor", "Digital object identifier", "Effect size", "Expected value", "High-throughput screening", "Normal distribution", "PubMed Central", "PubMed Identifier", "Robust statistics", "SSMD", "Scientific control", "Standard deviation", "Standard score", "Statistics", "Z-score", "Z-value"], "references": ["http://planetorbitrap.com/data/uploads/4fb692e73c07b.pdf", "http://iccb.med.harvard.edu/screening/Quantitative%20Assay%20Evaluation%20and%20Optimization%20complete%20(3).pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2789971", "http://www.ncbi.nlm.nih.gov/pubmed/10838414", "http://www.ncbi.nlm.nih.gov/pubmed/17218666", "http://www.ncbi.nlm.nih.gov/pubmed/17276655", "http://www.ncbi.nlm.nih.gov/pubmed/18480473", "http://www.ncbi.nlm.nih.gov/pubmed/18567841", "http://www.ncbi.nlm.nih.gov/pubmed/19644458", "http://www.cambridge.org/9780521734448", "http://doi.org/10.1016%2Fj.ygeno.2006.12.014", "http://doi.org/10.1038%2Fnmeth.1351", "http://doi.org/10.1177%2F1087057106296498", "http://doi.org/10.1177%2F1087057108317062", "http://doi.org/10.1177%2F1087057108317145", "http://doi.org/10.1177%2F108705719900400206"]}, "Higher-order statistics": {"categories": ["All articles needing expert attention", "All stub articles", "Articles needing expert attention from February 2009", "Articles needing expert attention with no reason or talk parameter", "Statistics articles needing expert attention", "Statistics stubs", "Summary statistics"], "title": "Higher-order statistics", "method": "Higher-order statistics", "url": "https://en.wikipedia.org/wiki/Higher-order_statistics", "summary": "In statistics, the term higher-order statistics (HOS) refers to functions which use the third or higher power of a sample, as opposed to more conventional techniques of lower-order statistics, which use constant, linear, and quadratic terms (zeroth, first, and second powers). The third and higher moments, as used in the skewness and kurtosis, are examples of HOS, whereas the first and second moments, as used in the arithmetic mean (first), and variance (second) are examples of low-order statistics. HOS are particularly used in estimation of shape parameters, such as skewness and kurtosis, as when measuring the deviation of a distribution from the normal distribution. On the other hand, due to the higher powers, HOS are significantly less robust than lower-order statistics.\nIn statistical theory, one long-established approach to higher-order statistics, for univariate and multivariate distributions is through the use of cumulants and joint cumulants. In time series analysis, the extension of these is to higher order spectra, for example the bispectrum and trispectrum.\nAn alternative to the use of HOS and higher moments is to instead use L-moments, which are linear statistics (linear combinations of order statistics), and thus more robust than HOS.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg"], "links": ["Arithmetic mean", "Bispectrum", "Cumulant", "International Standard Book Number", "Kurtosis", "L-moment", "Moment (mathematics)", "Normal distribution", "Order statistic", "Robust statistics", "Sample (statistics)", "Shape parameter", "Skewness", "Statistical theory", "Statistics", "Time series analysis", "Trispectrum", "Variance"], "references": ["http://www.ics.uci.edu/~welling/publications/papers/RobCum-aistats.pdf", "http://lpce.cnrs-orleans.fr/~ddwit/lalonde/lalonde_presentations/horbury2.pdf", "http://www.maths.leeds.ac.uk/Applied/news.dir/issue2/hos_intro.html"]}, "Ellsberg paradox": {"categories": ["All articles lacking in-text citations", "All articles with style issues", "Articles lacking in-text citations from August 2015", "Articles with multiple maintenance issues", "Decision-making paradoxes", "Pages using web citations with no URL", "Paradoxes in utility theory", "Probability theory paradoxes", "Statistical paradoxes", "Thought experiments", "Wikipedia articles with style issues from December 2010"], "title": "Ellsberg paradox", "method": "Ellsberg paradox", "url": "https://en.wikipedia.org/wiki/Ellsberg_paradox", "summary": "The Ellsberg paradox is a paradox in decision theory in which people's choices violate the postulates of subjective expected utility. It is generally taken to be evidence for ambiguity aversion. The paradox was popularized by Daniel Ellsberg, although a version of it was noted considerably earlier by John Maynard Keynes.The basic idea is that people overwhelmingly prefer taking on risk in situations where they know specific odds rather than an alternative risk scenario in which the odds are completely ambiguous\u2014they will always choose a known probability of winning over an unknown probability of winning even if the known probability is low and the unknown probability could be a guarantee of winning. For example, given a choice of risks to take (such as bets), people \"prefer the devil they know\" rather than assuming a risk where odds are difficult or impossible to calculate.Ellsberg proposed two separate thought experiments, the proposed choices in which contradict subjective expected utility. The 2-color problem involves bets on two urns, both of which contain balls of two different colors. The 3-color problem, described below, involves bets on a single urn, which contains balls of three different colors.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c2/Buridan%27s_bridge.jpg", "https://upload.wikimedia.org/wikipedia/commons/2/22/Deliberations_of_Congress.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f0/PinocchioChiostri22.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/89/Symbol_book_class2.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["Abilene paradox", "Alabama paradox", "Allais paradox", "Ambiguity aversion", "Amos Tversky", "Apportionment paradox", "Argument from free will", "Arrow's impossibility theorem", "Arrow information paradox", "Barber paradox", "Barbershop paradox", "Bayesian probability", "Berry paradox", "Bertrand paradox (economics)", "Bhartrhari's paradox", "Braess's paradox", "Buridan's ass", "Buridan's bridge", "Card paradox", "Catch-22 (logic)", "Chainstore paradox", "Choquet expected utility", "CiteSeerX", "Condorcet paradox", "Crocodile dilemma", "Curry's paradox", "Daniel Ellsberg", "David Schmeidler", "Decision-making paradox", "Decision theory", "Digital object identifier", "Downs\u2013Thomson paradox", "Dream argument", "Drinker paradox", "Easterlin paradox", "Economy", "Edgeworth paradox", "Epicurean paradox", "Epimenides paradox", "European paradox", "Experiment", "Experimental economics", "Fenno's paradox", "Fitch's paradox of knowability", "Fredkin's paradox", "Gibson's paradox", "Giffen good", "Green paradox", "Grelling\u2013Nelson paradox", "Hedgehog's dilemma", "Hilbert's paradox of the Grand Hotel", "I know that I know nothing", "Icarus paradox", "If and only if", "Income and fertility", "Info-gap decision theory", "International Economic Review", "International Standard Book Number", "Inventor's paradox", "JSTOR", "Jevons paradox", "John Maynard Keynes", "Kavka's toxin puzzle", "Kleene\u2013Rosser paradox", "Knightian uncertainty", "Leontief paradox", "Liar paradox", "Liberal paradox", "List of Ship of Theseus examples", "List of paradoxes", "Logic", "Lottery paradox", "Lucas paradox", "Mandeville's paradox", "Mayfield's paradox", "Meno", "Mere addition paradox", "Metzler paradox", "Moore's paradox", "Morton's fork", "Navigation paradox", "New riddle of induction", "New states paradox", "Newcomb's paradox", "No-no paradox", "Omnipotence paradox", "Opposite Day", "Paradox", "Paradox of analysis", "Paradox of competition", "Paradox of entailment", "Paradox of fiction", "Paradox of hedonism", "Paradox of nihilism", "Paradox of prosperity", "Paradox of the Court", "Paradox of thrift", "Paradox of toil", "Paradox of tolerance", "Paradox of value", "Paradox of voting", "Parrondo's paradox", "Philosophy", "Pinocchio paradox", "Plato's beard", "Population paradox", "Preface paradox", "Prevention paradox", "Prisoner's dilemma", "Productivity paradox", "Quarterly Journal of Economics", "Quine's paradox", "Raven paradox", "Resource curse", "Richard's paradox", "Risk aversion", "Ross' paradox", "Russell's paradox", "Satisficing", "Scitovsky paradox", "Service recovery paradox", "Ship of Theseus", "Social Science Research Network", "Sorites paradox", "St. Petersburg paradox", "Subjective expected utility", "The Antitrust Paradox", "Tullock paradox", "Unexpected hanging paradox", "Urn problem", "Utility function", "Utility theory", "What the Tortoise Said to Achilles", "When a white horse is not a horse", "Willpower paradox", "Wittgenstein on Rules and Private Language", "Yablo's paradox", "Zeno's paradoxes"], "references": ["http://ssrn.com/abstract=2389751", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.295.4096", "http://doi.org/10.1007%2Fbf00057884", "http://doi.org/10.2139%2Fssrn.2389751", "http://doi.org/10.2307%2F1884324", "http://doi.org/10.2307%2F1911053", "http://doi.org/10.2307%2F2526866", "http://doi.org/10.2307%2F2946693", "http://www.econport.org/econport/request?page=man_ru_experiments_ellsberg", "http://www.jstor.org/stable/1884324", "http://www.jstor.org/stable/1911053", "http://www.jstor.org/stable/2526866", "http://www.jstor.org/stable/2946693"]}, "Standard score": {"categories": ["Statistical ratios"], "title": "Standard score", "method": "Standard score", "url": "https://en.wikipedia.org/wiki/Standard_score", "summary": "In statistics, the standard score is the signed number of standard deviations by which the value of an observation or data point is above the mean value of what is being observed or measured. Observed values above the mean have positive standard scores, while values below the mean have negative standard scores. The standard score is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing (however, \"normalizing\" can refer to many types of ratios; see normalization for more). \nStandard scores are also called z-values, z-scores, normal scores, and standardized variables. They are most frequently used to compare an observation to a standard normal deviate, though they can be defined without assumptions of normality.\nComputing a z-score requires knowing the mean and standard deviation of the complete population to which a data point belongs; if one only has a sample of observations from the population, then the analogous computation with sample mean and sample standard deviation yields the t-statistic.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/2/25/The_Normal_Distribution.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Altman Z-score", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Dimensionless number", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Erwin Kreyszig", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher transformation", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical statistics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normalization (statistics)", "Observational study", "Official statistics", "Omega ratio", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population mean", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raw score", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard normal deviate", "Standardization", "Standardize", "Standardized testing (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-score", "T-statistic", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-factor", "Z-test", "Z-transform", "Z-value"], "references": ["http://staff.argyll.epsb.ca/jreed/math30p/statistics/standardCurve.htm", "https://books.google.com/?id=gccHkMDikb0C", "https://books.google.com/books?id=57jdRoC4hCoC&pg=PA43", "https://books.google.com/books?id=dejKAgAAQBAJ&pg=PA133", "https://books.google.com/books?id=sMSWbI23RMUC&pg=PA123", "https://www.niams.nih.gov/Health_Info/Bone/Bone_Health/bone_mass_measure.asp#b"]}, "OpenEpi": {"categories": ["All articles needing additional references", "Articles needing additional references from September 2009", "Biostatistics", "CS1 maint: Archived copy as title", "Epidemiology", "Free statistical software", "Pages using deprecated image syntax", "Software using the MIT license"], "title": "OpenEpi", "method": "OpenEpi", "url": "https://en.wikipedia.org/wiki/OpenEpi", "summary": "OpenEpi is a free, web-based, open source, operating system-independent series of programs for use in epidemiology, biostatistics, public health, and medicine, providing a number of epidemiologic and statistical tools for summary data. OpenEpi was developed in JavaScript and HTML, and can be run in modern web browsers. The program can be run from the OpenEpi website or downloaded and run without a web connection. The source code and documentation is downloadable and freely available for use by other investigators. OpenEpi has been reviewed, both by media organizations and in research journals.The OpenEpi developers have had extensive experience in the development and testing of Epi Info, a program developed by the Centers for Disease Control and Prevention (CDC) and widely used around the world for data entry and analysis. OpenEpi was developed to perform analyses found in the DOS version of Epi Info modules StatCalc and EpiTable, to improve upon the types of analyses provided by these modules, and to provide a number of tools and calculations not currently available in Epi Info. It is the first step toward an entirely web-based set of epidemiologic software tools. OpenEpi can be thought of as an important companion to Epi Info and to other programs such as SAS, PSPP, SPSS, Stata, SYSTAT, Minitab, Epidata, and R (see the R programming language). Another functionally similar Windows-based program is Winpepi. See also list of statistical packages and comparison of statistical packages. Both OpenEpi and Epi Info were developed with the goal of providing tools for low and moderate resource areas of the world. The initial development of OpenEpi was supported by a grant from the Bill and Melinda Gates Foundation to Emory University.The types of calculations currently performed by OpenEpi include:\n\nVarious confidence intervals for proportions, rates, standardized mortality ratio, mean, median, percentiles\n2x2 crude and stratified tables for count and rate data\nMatched case-control analysis\nTest for trend with count data\nIndependent t-test and one-way ANOVA\nDiagnostic and screening test analyses with receiver operating characteristic (ROC) curves\nSample size for proportions, cross-sectional surveys, unmatched case-control, cohort, randomized controlled trials, and comparison of two means\nPower calculations for proportions (unmatched case-control, cross-sectional, cohort, randomized controlled trials) and for the comparison of two means\nRandom number generatorFor epidemiologists and other health researchers, OpenEpi performs a number of calculations based on tables not found in most epidemiologic and statistical packages. For example, for a single 2x2 table, in addition to the results presented in other programs, OpenEpi provides estimates for:\n\nEtiologic or prevented fraction in the population and in exposed with confidence intervals, based on risk, odds, or rate data\nThe cross-product and MLE odds ratio estimate\nMid-p exact p-values and confidence limits for the odds ratio\nCalculations of rate ratios and rate differences with confidence intervals and statistical tests.For stratified 2x2 tables with count data, OpenEpi provides:\n\nMantel-Haenszel (MH) and precision-based estimates of the risk ratio and odds ratio\nPrecision-based adjusted risk difference\nTests for interaction for the risk ratio, odds ratio, and risk difference\nFour different confidence limit methods for the odds ratio.Similar to Epi Info, in a stratified analysis, both crude and adjusted estimates are provided so that the assessment of confounding can be made. With rate data, OpenEpi provides adjusted rate ratio\u2019s and rate differences, and tests for interaction. Finally, with count data, OpenEpi also performs a test for trend, for both crude data and stratified data.\nIn addition to being used to analyze data by health researchers, OpenEpi has been used as a training tool for teaching epidemiology to students at: Emory University, University of Massachusetts, University of Michigan, University of Minnesota, Morehouse College, Columbia University, University of Wisconsin, San Jose State University, University of Medicine and Dentistry of New Jersey, University of Washington, and elsewhere. This includes campus-based and distance learning courses. Because OpenEpi is easy to use, requires no programming experience, and can be run on the internet, students can use the program and focus on the interpretation of results. Users can run the program in English, French, Spanish, Portuguese or Italian.\nComments and suggestions for improvements are welcomed and the developers respond to user queries. The developers encourage others to develop modules that could be added to OpenEpi and provide a developer\u2019s tool at the website. Planned future development include improvements to existing modules, development of new modules, translation into other languages, and add the ability to cut and paste data and/or read data files.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/31/Free_and_open-source_software_logo_%282009%29.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/7/73/OpenEpi_screen_22.jpg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ANOVA", "Analysis of variance", "Asymptomatic carrier", "Atlanta, GA", "Auxology", "Bachelor of Science in Public Health", "Behavior change (public health)", "Behavioural change theories", "Bill and Melinda Gates Foundation", "Biological hazard", "Biostatistics", "Carl Rogers Darnall", "Case-control", "Case\u2013control study", "Centers for Disease Control and Prevention", "Chief Medical Officer", "Child mortality", "Cohort study", "Community health", "Comparison of statistical packages", "Computing platform", "Confidence interval", "Confidence intervals", "Confounding", "Council on Education for Public Health", "Count data", "Cross-platform", "Cross-sectional", "Cultural competence in health care", "DOS", "Deviance (sociology)", "Diffusion of innovations", "Digital object identifier", "Disease surveillance", "Doctor of Public Health", "Emergency sanitation", "Emory University", "Environmental health", "Epi Info", "Epidata", "Epidemic", "Epidemiology", "European Centre for Disease Prevention and Control", "European Parliament Committee on the Environment, Public Health and Food Safety", "Euthenics", "Family planning", "Fecal\u2013oral route", "Food additive", "Food chemistry", "Food engineering", "Food microbiology", "Food processing", "Food safety", "Free statistical software", "Genetically modified food", "Germ theory of disease", "Global health", "Globalization and disease", "Good agricultural practice", "Good manufacturing practice", "HACCP", "HTML", "Hand washing", "Health belief model", "Health care reform", "Health communication", "Health economics", "Health education", "Health equity", "Health impact assessment", "Health literacy", "Health policy", "Health promotion", "Health psychology", "Health system", "Human factors and ergonomics", "Human nutrition", "Hygiene", "ISO 22000", "Infant mortality", "Infection control", "Injury prevention", "Interaction", "JavaScript", "John Snow (physician)", "Joseph Lister", "List of epidemics", "List of notifiable diseases", "List of open-source health software", "List of statistical packages", "MIT License", "Margaret Sanger", "Mary Mallon", "Maternal health", "Mean", "Median", "Medical anthropology", "Medical sociology", "Medicine", "Mental health", "Ministry of Health and Family Welfare", "Minitab", "Notifiable disease", "Occupational health nursing", "Occupational hygiene", "Occupational medicine", "Occupational safety and health", "Odds ratio", "Open defecation", "Operating system", "Oral hygiene", "PRECEDE-PROCEED model", "PSPP", "Patient safety", "Patient safety organization", "Pharmaceutical policy", "Pharmacovigilance", "Population health", "Positive deviance", "Preventive healthcare", "Preventive nutrition", "Professional degrees of public health", "Public health", "Public health genomics", "Public health informatics", "Public health intervention", "Public health laboratory", "Public health law", "Public health surveillance", "Quarantine", "ROC curve", "R (programming language)", "Race and health", "Randomized controlled trial", "Randomized controlled trials", "Receiver operating characteristic", "Regression analysis", "Relative risk", "Reproductive health", "Risk ratio", "SAS System", "SPSS", "SYSTAT (statistics)", "Safe sex", "Sample size", "Samuel Jay Crumbine", "Sanitary sewer", "Sanitation", "Sara Josephine Baker", "Sexually transmitted infection", "Smoking cessation", "Social cognitive theory", "Social determinants of health", "Social hygiene movement", "Social medicine", "Social norms approach", "Social psychology", "Sociology of health and illness", "Software categories", "Software developer", "Software license", "Software release life cycle", "Standardized mortality ratio", "Stata", "Statistical hypothesis testing", "Statistics", "Student's t-test", "Theory of planned behavior", "Toledo, Spain", "Transtheoretical model", "Tropical disease", "United States Public Health Service", "Vaccination", "Vaccine trial", "Vector control", "Waterborne diseases", "Web application", "Web based simulation", "Web browsers", "Winpepi", "World Health Organization", "World Toilet Organization", "Z-test"], "references": ["http://www.openepi.com/", "http://thdblog.wordpress.com/2007/09/24/openepi-online/", "http://education.zdnet.com/?p=1220", "http://doi.org/10.1016%2Fj.cosrev.2008.05.002", "http://www.gatesfoundation.org/nr/public/media/annualreports/annualreport01/pdf/BMGF2001GlobalHealth.pdf", "https://web.archive.org/web/20090920020510/http://www.gatesfoundation.org/nr/public/media/annualreports/annualreport01/pdf/BMGF2001GlobalHealth.pdf#"]}, "Semi-log graph": {"categories": ["Charts", "Statistical charts and diagrams", "Technical drawing"], "title": "Semi-log plot", "method": "Semi-log graph", "url": "https://en.wikipedia.org/wiki/Semi-log_plot", "summary": "In science and engineering, a semi-log graph or semi-log plot is a way of visualizing data that are related according to an exponential relationship. One axis is plotted on a logarithmic scale. \nThis kind of plotting method is useful when one of the variables being plotted covers a large range of values and the other has only a restricted range \u2013 the advantage being that it can bring out features in the data that would not easily be seen if both variables had been plotted linearly.All equations of the form \n \n \n \n y\n =\n \u03bb\n \n a\n \n \u03b3\n x\n \n \n \n \n {\\displaystyle y=\\lambda a^{\\gamma x}}\n form straight lines when plotted semi-logarithmically, since taking logs of both sides gives\n\n \n \n \n \n log\n \n a\n \n \n \u2061\n y\n =\n \u03b3\n x\n +\n \n log\n \n a\n \n \n \u2061\n \u03bb\n .\n \n \n {\\displaystyle \\log _{a}y=\\gamma x+\\log _{a}\\lambda .}\n This can easily be seen as a line in slope-intercept form with \n \n \n \n \u03b3\n \n \n {\\displaystyle \\gamma }\n as the slope and \n \n \n \n \n log\n \n a\n \n \n \u2061\n \u03bb\n \n \n {\\displaystyle \\log _{a}\\lambda }\n as the vertical intercept. To facilitate use with logarithmic tables, one usually takes logs to base 10 or e, or sometimes base 2:\n\n \n \n \n log\n \u2061\n (\n y\n )\n =\n (\n \u03b3\n log\n \u2061\n (\n a\n )\n )\n x\n +\n log\n \u2061\n (\n \u03bb\n )\n .\n \n \n {\\displaystyle \\log(y)=(\\gamma \\log(a))x+\\log(\\lambda ).}\n The term log-lin is used to describe a semi-log plot with a logarithmic scale on the y-axis, and a linear scale on the x-axis. Likewise, a lin-log plot uses a logarithmic scale on the x-axis, and a linear scale on the y-axis. Note that the naming is output-input (y-x), the opposite order from (x, y).\nOn a semi-log plot the spacing of the scale on the y-axis (or x-axis) is proportional to the logarithm of the number, not the number itself. It is equivalent to converting the y values (or x values) to their log, and plotting the data on lin-lin scales. A log-log plot uses the logarithmic scale for both axes, and hence is not a semi-log plot.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c0/Bacterial_growth_en.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f8/Influenza-2009-cases-logarithmic.png", "https://upload.wikimedia.org/wikipedia/commons/2/2f/LinLogScale.svg", "https://upload.wikimedia.org/wikipedia/commons/4/46/LogLinScale.svg", "https://upload.wikimedia.org/wikipedia/commons/0/08/Phase_diagram_of_water.svg"], "links": ["2009 outbreak of influenza A (H1N1)", "Abscissa", "Asexual reproduction", "Bacteria", "Base (exponentiation)", "Biological engineering", "Biology", "Chemistry", "Engineering", "Exponential curve", "Ice", "Linear", "Log-log plot", "Logarithmic scale", "Microbes", "Nomograph", "Nonlinear regression", "Ordinate", "Phase (matter)", "Phase diagram", "Physics", "Roman numeral", "Science", "Variable (mathematics)", "Water"], "references": ["http://www.intmath.com/Exponential-logarithmic-functions/7_Graphs-log-semilog.php"]}, "Divisia monetary aggregates index": {"categories": ["Banking", "Econometric modeling", "Macroeconomic indicators", "Monetary economics", "Webarchive template wayback links"], "title": "Divisia monetary aggregates index", "method": "Divisia monetary aggregates index", "url": "https://en.wikipedia.org/wiki/Divisia_monetary_aggregates_index", "summary": "In econometrics and official statistics, and particularly in banking, the Divisia monetary aggregates index is an index of money supply. It uses Divisia index methods.\n\n", "images": [], "links": ["Asset", "Banking", "Central bank", "Divisia index", "Econometrics", "Federal Reserve Board", "Index (economics)", "Microeconomic", "Money supply", "Official statistics", "Opportunity cost", "Salam Fayyad", "Substitute good", "Summation", "Wayback Machine", "Wealth", "Weighted mean", "William A. Barnett", "Yield (finance)"], "references": ["http://econ.ucalgary.ca/serletis.htm", "http://www.sciencedirect.com/science/article/pii/0304407680900706", "http://econ.tepper.cmu.edu/barnett/Welcome.html", "http://www.boi.org.il/en/dataandstatistics/pages/dma.aspx", "http://www.ecb.int/home/html/index.en.html", "http://www.boj.or.jp/en/", "http://www.imf.org/external/index.htm", "http://research.stlouisfed.org/msi/2006msidata.html", "https://books.google.com/books?id=wWjOmQEACAAJ", "https://web.archive.org/web/20061001162140/http://econ.ucalgary.ca/serletis.htm"]}, "Semimartingale": {"categories": ["Martingale theory"], "title": "Semimartingale", "method": "Semimartingale", "url": "https://en.wikipedia.org/wiki/Semimartingale", "summary": "In probability theory, a real valued process X is called a semimartingale if it can be decomposed as the sum of a local martingale and an adapted finite-variation process.\nSemimartingales are \"good integrators\", forming the largest class of processes with respect to which the It\u014d integral and the Stratonovich integral can be defined.\nThe class of semimartingales is quite large (including, for example, all continuously differentiable processes, Brownian motion and Poisson processes). Submartingales and supermartingales together represent a subset of the semimartingales.\n\n", "images": [], "links": ["Absolutely continuous", "Abstract Wiener space", "Actuarial mathematics", "Adapted process", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Bounded variation", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Change of time", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Differentiable manifold", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtered probability space", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "It\u014d's lemma", "It\u014d calculus", "It\u014d integral", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic calculus", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopped process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": []}, "Wilks' theorem": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles needing expert attention", "Articles lacking in-text citations from November 2010", "Articles needing additional references from September 2009", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Statistical ratios", "Statistical tests", "Statistics articles needing expert attention"], "title": "Wilks' theorem", "method": "Wilks' theorem", "url": "https://en.wikipedia.org/wiki/Wilks%27_theorem", "summary": "In statistics, the Wilks' theorem offers an asymptotic distribution of the log-likelihood ratio statistic, which can be used as a test statistic for performing the Likelihood-ratio test.\nIf the distribution of the likelihood ratio corresponding to a particular null and alternative hypothesis can be explicitly determined then it can directly be used to form decision regions (to accept/reject the null hypothesis). In most cases, however, the exact distribution of the likelihood ratio corresponding to specific hypotheses is very difficult to determine.\nA convenient result by Samuel S. Wilks, says that as the sample size \n \n \n \n n\n \n \n {\\displaystyle n}\n approaches \n \n \n \n \u221e\n \n \n {\\displaystyle \\infty }\n , the test statistic \n \n \n \n \u2212\n 2\n log\n \u2061\n (\n \u039b\n )\n \n \n {\\displaystyle -2\\log(\\Lambda )}\n for a nested model asymptotically will be chi-squared distributed (\n \n \n \n \n \u03c7\n \n 2\n \n \n \n \n {\\displaystyle \\chi ^{2}}\n ) with degrees of freedom equal to the difference in dimensionality of \n \n \n \n \u0398\n \n \n {\\displaystyle \\Theta }\n and \n \n \n \n \n \u0398\n \n 0\n \n \n \n \n {\\displaystyle \\Theta _{0}}\n , when \n \n \n \n \n H\n \n 0\n \n \n \n \n {\\displaystyle H_{0}}\n holds true. This means that for a great variety of hypotheses, a practitioner can compute the likelihood ratio \n \n \n \n \u039b\n \n \n {\\displaystyle \\Lambda }\n for the data and compare \n \n \n \n \u2212\n 2\n log\n \u2061\n (\n \u039b\n )\n \n \n {\\displaystyle -2\\log(\\Lambda )}\n to the \n \n \n \n \n \u03c7\n \n 2\n \n \n \n \n {\\displaystyle \\chi ^{2}}\n value corresponding to a desired statistical significance as an approximate statistical test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Edward Arnold (publisher)", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Infinity", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Philosophical Transactions of the Royal Society of London", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Random effects model", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted maximum likelihood", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel S. Wilks", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sup-LR test", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://adsabs.harvard.edu/abs/1933RSPTA.231..289N", "http://doi.org/10.1098%2Frsta.1933.0009", "http://doi.org/10.1146%2Fannurev.ecolsys.28.1.437", "http://doi.org/10.1214%2Faoms%2F1177732360", "http://www.jstor.org/stable/91247", "http://www.stats.org.uk/statistical-inference/NeymanPearson1933.pdf", "https://stephens999.github.io/fiveMinuteStats/wilks.html"]}, "posterior probability": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2009", "Bayesian statistics", "Wikipedia articles needing clarification from March 2018"], "title": "Posterior probability", "method": "posterior probability", "url": "https://en.wikipedia.org/wiki/Posterior_probability", "summary": "In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence or background is taken into account. Similarly, the posterior probability distribution is the probability distribution of an unknown quantity, treated as a random variable, conditional on the evidence obtained from an experiment or survey. \"Posterior\", in this context, means after taking into account the relevant evidence related to the particular case being examined. For instance, there is a (\"non-posterior\") probability of a person finding buried treasure if they dig in a random spot, and a posterior probability of finding buried treasure if they dig in a spot where their metal detector rings.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Admissible decision rule", "Approximate Bayesian computation", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bayesian structural time series", "Bernstein\u2013von Mises theorem", "Bertrand's box paradox", "Class membership probabilities", "Conditional probability", "Conditional probability distribution", "Conjugate prior", "Credible interval", "Cromwell's rule", "Empirical Bayes method", "Hyperparameter", "Hyperprior", "International Standard Book Number", "John Wiley & Sons", "Law of total probability", "Likelihood function", "Markov chain Monte Carlo", "Maximum a posteriori estimation", "Monty Hall Problem", "Normalizing constant", "Posterior predictive distribution", "Prediction interval", "Principle of indifference", "Principle of maximum entropy", "Prior probability", "Prior probability distribution", "Probability density function", "Probability distribution", "Probability distribution function", "Probability interpretations", "Probability of success", "Radical probabilism", "Random event", "Random variable", "Schwarz criterion", "Scientific evidence", "Spike and slab variable selection", "Statistical classification", "Statistics", "Three Prisoners Problem"], "references": ["http://www-users.york.ac.uk/~pml1/bayes/book.htm"]}, "Nonlinear dimensionality reduction": {"categories": ["CS1 errors: dates", "Dimension reduction"], "title": "Nonlinear dimensionality reduction", "method": "Nonlinear dimensionality reduction", "url": "https://en.wikipedia.org/wiki/Nonlinear_dimensionality_reduction", "summary": "High-dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. If the manifold is of low enough dimension, the data can be visualised in the low-dimensional space.\n\nBelow is a summary of some of the important algorithms from the history of manifold learning and nonlinear dimensionality reduction (NLDR). Many of these non-linear dimensionality reduction methods are related to the linear methods listed below. Non-linear methods can be broadly classified into two groups: those that provide a mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa), and those that just give a visualisation. In the context of machine learning, mapping methods may be viewed as a preliminary feature extraction step, after which pattern recognition algorithms are applied. Typically those that just give a visualisation are based on proximity data \u2013 that is, distance measurements.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fd/Lle_hlle_swissroll.png", "https://upload.wikimedia.org/wikipedia/commons/b/bb/SOMsPCA.PNG", "https://upload.wikimedia.org/wikipedia/commons/4/48/SlideQualityLife.png", "https://upload.wikimedia.org/wikipedia/en/e/e1/Letters_pca.png", "https://upload.wikimedia.org/wikipedia/en/9/9c/Nldr.jpg"], "links": ["Alexander Nikolaevich Gorban", "Autoencoder", "Backpropagation", "Broken line", "Charles-Augustin de Coulomb", "CiteSeerX", "Concentration of measure", "Coulomb's law", "Curie Institute (Paris)", "Curse of Dimensionality", "Curse of dimensionality", "Curvilinear component analysis", "Degree matrix", "Density networks", "Diffeomorphic", "Diffusion", "Diffusion map", "Digital object identifier", "Dimensionality reduction", "Discriminant analysis", "Distance", "Distance matrix", "Dynamic time warping", "Dynamical systems", "Eigendecomposition of a matrix", "Elastic map", "Embedding", "Euclidean distance", "Expectation-maximization algorithm", "Factor analysis", "Feature extraction", "Feature learning", "Floyd\u2013Warshall algorithm", "Fourier series", "Fraction of variance unexplained", "Gaussian process", "Gaussian process latent variable model", "Generative topographic mapping", "Geodesic", "Geodesic distance", "Global cascades model", "Graduated optimization", "Gross domestic product", "Growing self-organizing map", "Hamming space", "Hessian LLE", "High-dimensional", "Higher-dimensional space", "Independent component analysis", "Infant mortality", "Institut des Hautes \u00c9tudes Scientifiques", "International Journal of Neural Systems", "International Standard Book Number", "International Standard Serial Number", "Isomap", "Journal of Machine Learning Research", "K-nearest neighbor algorithm", "Karhunen\u2013Lo\u00e8ve transform", "Kernel principal component analysis", "Kernel trick", "Klein bottle", "Laplace\u2013Beltrami operator", "Latent variable model", "Life expectancy", "Local tangent space alignment", "Locally-Linear Embedding", "Locally linear embeddings", "MIT Press", "Machine learning", "Manifold", "Manifold alignment", "Manifold learning", "Manifold regularization", "Markov Chain", "Maximum Variance Unfolding", "Maximum variance unfolding", "Multidimensional Scaling", "Multidimensional scaling", "Neural network", "NeuroScale", "Nonlinear dimensionality reduction", "Ohio State University", "Partha Niyogi", "Pattern recognition", "Principal component analysis", "Principal curve", "Projective space", "Radial basis function network", "Random walk", "Reproducing kernel Hilbert space", "Restricted Boltzmann machine", "Sammon's mapping", "Sammon's projection", "Sammon mapping", "Self-organizing map", "Similarity matrix", "Singular value decomposition", "Sparse matrix", "Sphere", "Stress majorization", "Swiss roll", "T-distributed stochastic neighbor embedding", "Topologically Constrained Isometric Embedding", "Torus", "Trevor Hastie", "Tuberculosis", "United Nations", "University Of Chicago", "Vision-based activity recognition", "Yale University"], "references": ["http://www.dice.ucl.ac.be/Proceedings/esann/esannpdf/es2010-107.pdf", "http://www.miketipping.com/thesis.htm", "http://www.palgrave-journals.com/ivs/journal/v3/n1/pdf/9500051a.pdf", "http://www.VisuMap.com", "http://axon.cs.byu.edu/papers/gashler2007nips.pdf", "http://axon.cs.byu.edu/papers/gashler2011ijcnn2.pdf", "http://jmlr.csail.mit.edu/papers/v6/lawrence05a.html", "http://www.cse.ohio-state.edu/~mbelkin/algorithms/algorithms.html", "http://www.cse.ohio-state.edu/~mbelkin/papers/papers.html#thesis", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.211.9957", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.382", "http://www.cs.toronto.edu/~roweis/lle/", "http://people.cs.umass.edu/~chwang/papers/ICML-2008.pdf", "http://bioinfo-out.curie.fr/projects/vidaexpert/", "http://sy.lespi.free.fr/DD-HDS-homepage.html", "http://sy.lespi.free.fr/RankVisu-homepage.html", "http://www.ihes.fr", "http://www.ihes.fr/~zinovyev/vida/ViDaExpert/ViDaOverView.pdf", "http://waffles.sourceforge.net/", "http://www.visumap.net/index.aspx?p=Resources/RpmOverview", "http://doi.org/10.1016%2Fj.acha.2015.10.004", "http://doi.org/10.1137%2Fs1064827502419154", "http://doi.org/10.1162%2Fneco.2006.18.10.2509", "http://ieeexplore.ieee.org/abstract/document/6985586/", "http://jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf", "http://www.jmlr.org/papers/v13/lawrence12a.html", "http://www.nlpca.org/", "http://www.worldcat.org/issn/0899-7667", "http://www.worldcat.org/issn/1063-5203", "http://pca.narod.ru/contentsgkwz.htm", "http://www.math.le.ac.uk/people/ag153/homepage/PCA_SOM/PCA_SOM.html", "http://www.dcs.shef.ac.uk/~neil/gplvm/", "https://www.researchgate.net/publication/271642170_Principal_Manifolds_for_Data_Visualisation_and_Dimension_Reduction_LNCSE_58", "https://web.archive.org/web/20040411051530/http://isomap.stanford.edu/", "https://web.archive.org/web/20090204021348/http://www.ncrg.aston.ac.uk/GTM/", "https://web.archive.org/web/20111002023651/http://tx.technion.ac.il/~rc/diffusion_maps.pdf", "https://arxiv.org/abs/1001.1122", "https://doi.org/10.1016/j.acha.2015.10.004", "https://www.mitpressjournals.org/doi/10.1162/neco.2006.18.10.2509"]}, "Candlestick chart": {"categories": ["All articles needing additional references", "Articles needing additional references from July 2010", "Articles needing additional references from March 2018", "Commons category link is on Wikidata", "Financial charts", "Pages using citations with accessdate and no URL"], "title": "Candlestick chart", "method": "Candlestick chart", "url": "https://en.wikipedia.org/wiki/Candlestick_chart", "summary": "A candlestick chart (also called Japanese candlestick chart) is a style of financial chart used to describe price movements of a security, derivative, or currency. Each \"candlestick\" typically shows one day, thus a one-month chart may show the 20 trading days as 20 \"candlesticks\". Shorter intervals than one day are common on computer charts, longer are possible. \nIt is like a combination of line-chart and a bar-chart: each bar represents all four important pieces of information for that day: The open, the close, the high and the low. Being densely packed with information, they tend to represent trading patterns over short periods of time, often a few days or a few trading sessions.Candlestick charts are most often used in technical analysis of equity and currency price patterns. They are visually similar to box plots, though box plots show different information.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/92/Candlestick_chart_scheme_01-en.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ea/Candlestick_chart_scheme_03-en.svg", "https://upload.wikimedia.org/wikipedia/commons/1/14/Order_book_depth_chart.gif", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accumulation/distribution index", "Advance\u2013decline line", "Average directional movement index", "Average true range", "Bollinger Bands", "Bottom (technical analysis)", "Box plot", "Breadth of market", "Breakout (technical analysis)", "Broadening top", "Bullish", "Candle wick", "Candlestick pattern", "Chart pattern", "Commodity channel index", "Commodity trading", "Coppock curve", "Cup and handle", "Currency", "Dead cat bounce", "Derivative (finance)", "Detrended price oscillator", "Digital object identifier", "Doji", "Donchian channel", "Double top and double bottom", "Dow theory", "Ease of movement", "Elliott wave principle", "Fibonacci retracement", "Financial instrument", "Flag and pennant patterns", "Force index", "Foreign exchange trading", "Gap (chart pattern)", "Hammer (candlestick pattern)", "Hanging man (candlestick pattern)", "Head and shoulders (chart pattern)", "Hikkake pattern", "Ichimoku Kink\u014d Hy\u014d", "International Standard Book Number", "Inverted hammer", "Island reversal", "Japanese language", "Kagi chart", "Keltner channel", "Know sure thing oscillator", "Line chart", "MACD", "Market trend", "Marubozu", "Mass index", "McClellan oscillator", "Momentum (finance)", "Money flow index", "Morning star (candlestick pattern)", "Moving average", "Munehisa Homma", "Negative volume index", "On-balance volume", "Open-high-low-close chart", "Option trading", "Order book (trading)", "Parabolic SAR", "Pivot point (stock market)", "Point and figure chart", "Price channels", "Put/call ratio", "Relative strength index", "Security (finance)", "Shooting star (candlestick pattern)", "Smart money index", "Spinning top (candlestick pattern)", "Standard deviation", "Steve Nison", "Stochastic oscillator", "Stock trading", "Support and resistance", "TRIN (finance)", "Technical analysis", "Technical indicator", "Three black crows", "Three white soldiers", "Top (technical analysis)", "Trading", "Trading session", "Trend line (technical analysis)", "Triangle (chart pattern)", "Triple top and triple bottom", "Trix (technical analysis)", "True strength index", "Ulcer index", "Ultimate oscillator", "VIX", "Volatility (finance)", "Volume (finance)", "Volume\u2013price trend", "Vortex indicator", "Wedge pattern", "Williams %R"], "references": ["http://www.investopedia.com/articles/technical/02/121702.asp", "http://www.investopedia.com/articles/technical/04/092204.asp", "http://www.sciencedirect.com/science/article/pii/S1058330012000092", "http://stockcharts.com/school/doku.php?id=chart_school:chart_analysis:introduction_to_candlesticks", "http://doi.org/10.1016%2Fj.rfe.2012.02.001"]}, "Conditionality principle": {"categories": ["Statistical principles"], "title": "Conditionality principle", "method": "Conditionality principle", "url": "https://en.wikipedia.org/wiki/Conditionality_principle", "summary": "The conditionality principle is a Fisherian principle of statistical inference that Allan Birnbaum formally defined and studied in his 1962 JASA article. Informally, the conditionality principle can be taken as the claim that experiments which were not actually performed are statistically irrelevant.\nTogether with the sufficiency principle, Birnbaum's version of the principle implies the famous likelihood principle. Although the relevance of the proof to data analysis remains controversial among statisticians, many Bayesians and likelihoodists consider the likelihood principle foundational for statistical inference.\n\n", "images": [], "links": ["Allan Birnbaum", "Ancillary statistic", "Bayesian inference", "Bioinformatics", "Digital object identifier", "International Standard Book Number", "JSTOR", "Journal of the American Statistical Association", "Likelihood principle", "Mathematical Reviews", "Statistical inference", "Sufficiency principle"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0138176", "http://doi.org/10.1007%2Fs10539-014-9455-x", "http://doi.org/10.1093%2Fbiomet%2F62.2.251", "http://doi.org/10.2307%2F2281640", "http://www.jstor.org/stable/2281640", "https://dx.doi.org/10.1007/s10539-014-9455-x"]}, "Peirce's criterion": {"categories": ["CS1 maint: Uses editors parameter", "Statistical outliers"], "title": "Peirce's criterion", "method": "Peirce's criterion", "url": "https://en.wikipedia.org/wiki/Peirce%27s_criterion", "summary": "In robust statistics, Peirce's criterion is a rule for eliminating outliers from data sets, which was devised by Benjamin Peirce.\n\n", "images": [], "links": ["American Academy of Arts and Sciences", "Benjamin Peirce", "Chapman and Hall", "Charles Sanders Peirce", "Coast Survey", "Data set", "Digital object identifier", "Francis J. Anscombe", "Gaussian distribution", "International Standard Book Number", "JSTOR", "Likelihood-ratio test", "Mathematical Reviews", "Median", "Outlier", "Robust statistic", "Robust statistics", "Significance test", "Stephen M. Stigler", "Stephen Stigler", "United States Coast Survey", "William Chauvenet"], "references": ["http://adsabs.harvard.edu/full/1855AJ......4...81G", "http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1852AJ......2..161P;data_type=PDF_HIGH", "http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1852AJ......2..176P;data_type=PDF_HIGH", "http://newton.newhaven.edu/sross/piercescriterion.pdf", "http://www.eol.ucar.edu/system/files/piercescriterion.pdf", "http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0019.PDF#page=215", "http://docs.lib.noaa.gov/rescue/cgs/data_rescue_cgs_annual_reports.html", "http://www.ams.org/mathscinet-getitem?mr=0483118", "http://doi.org/10.1214%2Faos%2F1176344123", "http://doi.org/10.2307%2F25138498", "http://www.jstor.org/stable/25138498", "http://www.jstor.org/stable/2958876", "http://mathforum.org/kb/message.jspa?messageID=6449606", "http://projecteuclid.org/euclid.aos/1176344123", "https://www.jstor.org/stable/2958876", "https://r-forge.r-project.org/scm/viewvc.php/*checkout*/pkg/Peirce/Peirce-manual.pdf?root=peirce", "https://r-forge.r-project.org/scm/viewvc.php/*checkout*/pkg/Peirce/PeirceSub.pdf?root=peirce"]}, "Randomness tests": {"categories": ["Algorithmic information theory", "Statistical randomness", "Statistical tests", "Wikipedia articles needing clarification from November 2017"], "title": "Randomness tests", "method": "Randomness tests", "url": "https://en.wikipedia.org/wiki/Randomness_tests", "summary": "Randomness tests (or tests for randomness), in data evaluation, are used to analyze the distribution of a set of data to see if it is random (patternless). In stochastic modeling, as in some computer simulations, the hoped-for randomness of potential input data can be verified, by a formal test for randomness, to show that the data are valid for use in simulation runs. In some cases, data reveals an obvious non-random pattern, as with so-called \"runs in the data\" (such as expecting random 0\u20139 but finding \"4 3 2 1 0 4 3 2 1...\" and rarely going above 4). If a selected set of data fails the tests, then parameters can be changed or other randomized data can be used which does pass the tests for randomness.\nThere are many practical measures of randomness for a binary sequence. These include measures based on statistical tests, transforms, and complexity or a mixture of these. A widely used collection of tests introduced by Marsaglia is called the Diehard Battery of Tests.", "images": [], "links": ["Algorithmically random sequence", "Basis function", "Binary sequence", "CAcert.org", "Chi-squared test", "Complexity", "Computer simulation", "Diehard tests", "Digital object identifier", "Duke University", "George Marsaglia", "Hadamard transform", "International Standard Book Number", "Journal of Statistical Software", "Kolmogorov complexity", "Linear-feedback shift register", "Linear congruential generator", "National Institute of Standards and Technology", "Pseudo-random", "Pseudorandom binary sequence", "RANDU", "Random", "Random number generator attack", "Randomness", "Rule 30", "Seven states of randomness", "Statistical randomness", "Statistical tests", "Stephen Wolfram", "Stochastic modeling", "String (computer science)", "Subhash Kak", "TestU01", "Wald\u2013Wolfowitz runs test"], "references": ["http://www.cacert.at/random/", "http://www.ciphersbyritter.com/RES/RANDTEST.HTM", "http://www.phy.duke.edu/~rgb/General/dieharder.php", "http://webpages.uncc.edu/yonwang/", "http://csrc.nist.gov/groups/ST/toolkit/rng/", "http://doi.org/10.1142/S012918319600017X", "http://www.jstatsoft.org/v07/i03/paper"]}, "Bayesian inference using Gibbs sampling": {"categories": ["All articles needing additional references", "All stub articles", "Articles needing additional references from March 2013", "Computational statistics", "Statistics stubs", "Webarchive template wayback links"], "title": "Bayesian inference using Gibbs sampling", "method": "Bayesian inference using Gibbs sampling", "url": "https://en.wikipedia.org/wiki/Bayesian_inference_using_Gibbs_sampling", "summary": "Bayesian inference using Gibbs sampling (BUGs) is a software package for performing Bayesian inference using Markov chain Monte Carlo (based on Gibbs sampling).\nBUGs is used in the following software:\nJust another Gibbs sampler\nOpenBUGS\nWinBUGS", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayesian inference", "Bayesian structural time series", "Digital object identifier", "Gibbs sampling", "Just another Gibbs sampler", "Markov chain Monte Carlo", "OpenBUGS", "PubMed Identifier", "Spike and slab variable selection", "Statistics", "Wayback Machine", "WinBUGS"], "references": ["http://w3.jouy.inra.fr/unites/miaj/public/matrisq/Contacts/applibugs.bugs_project.evolution.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/19630097", "https://web.archive.org/web/20120915083751/http://w3.jouy.inra.fr/unites/miaj/public/matrisq/Contacts/applibugs.bugs_project.evolution.pdf", "https://doi.org/10.1002%2Fsim.3680"]}, "Econometrics": {"categories": ["Applied statistics", "CS1 maint: Archived copy as title", "Commons category link from Wikidata", "Commons category link is on Wikidata", "Econometrics", "EngvarB from October 2017", "Formal sciences", "Mathematical and quantitative methods (economics)", "Use dmy dates from October 2017", "Webarchive template wayback links", "Wikipedia articles with GND identifiers", "Wikipedia articles with NARA identifiers", "Wikipedia articles with NDL identifiers"], "title": "Econometrics", "method": "Econometrics", "url": "https://en.wikipedia.org/wiki/Econometrics", "summary": "Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. More precisely, it is \"the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference\". An introductory economics textbook describes econometrics as allowing economists \"to sift through mountains of data to extract simple relationships\". The first known use of the term \"econometrics\" (in cognate form) was by Polish economist Pawe\u0142 Ciompa in 1910. Jan Tinbergen is considered by many to be one of the founding fathers of econometrics. Ragnar Frisch is credited with coining the term in the sense in which it is used today.A basic tool for econometrics is the multiple linear regression model. Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, and consistency. Applied econometrics uses theoretical econometrics and real-world data for assessing economic theories, developing econometric models, analysing economic history, and forecasting.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f3/Emblem-money.svg", "https://upload.wikimedia.org/wikipedia/commons/d/db/Okuns_law_differences_1948_to_mid_2011.png", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Adam Smith", "Adaptive expectations", "Aggregate demand", "Aggregation problem", "Agricultural economics", "Alfred Marshall", "Amartya Sen", "Anarchist economics", "Ancient economic thought", "Applied Econometrics and International Development", "Applied economics", "Arthur Cecil Pigou", "Asia-Pacific Economic Cooperation", "Augmented Dickey\u2013Fuller test", "Austrian School", "Average cost", "Balance of payments", "Bayes estimator", "Bayesian statistics", "Behavioral economics", "Bias of an estimator", "Bilateral monopoly", "Buddhist economics", "Budget set", "Business cycle", "Business economics", "Capacity utilization", "Capital flight", "Central bank", "Chicago school of economics", "Choice modelling", "Classical economics", "Clive Granger", "Cognate", "Competition (economics)", "Computational economics", "Consistent estimator", "Consumer choice", "Consumer confidence", "Contrived experiment", "Control theory", "Convexity in economics", "Cost\u2013benefit analysis", "Covariate", "Cowles Foundation", "Criticisms of econometrics", "Cultural economics", "Currency", "David Card", "David Ricardo", "Deadweight loss", "Decision theory", "Deflation", "Deidre McCloskey", "Deirdre McCloskey", "Demand for money", "Demand shock", "Demographic economics", "Depression (economics)", "Development economics", "Digital object identifier", "Distribution (economics)", "Dynamic stochastic general equilibrium", "Ecological economics", "Econometric Reviews", "Econometric Theory", "Econometric model", "Econometric software", "Econometrica", "Econometrics Journal", "Economic Cooperation Organization", "Economic cost", "Economic data", "Economic equilibrium", "Economic forecast", "Economic geography", "Economic growth", "Economic history", "Economic indicator", "Economic methodology", "Economic planning", "Economic policy", "Economic rent", "Economic sociology", "Economic statistics", "Economic surplus", "Economic system", "Economic theory", "Economics", "Economics (textbook)", "Economics Network", "Economics of digitization", "Economies of scale", "Economies of scope", "Economist", "Education economics", "Edward Leamer", "Effective demand", "Efficiency (statistics)", "Elasticity (economics)", "Empirical", "Engineering economics", "Environmental economics", "Equilibrium (economics)", "Estimation theory", "Estimator", "European Free Trade Association", "Evolutionary economics", "Expected utility hypothesis", "Expeditionary economics", "Experiment", "Experimental economics", "Exploratory data analysis", "Externality", "Feminist economics", "Financial econometrics", "Financial economics", "Financial modelling", "Fiscal policy", "Francis Ysidro Edgeworth", "Fran\u00e7ois Quesnay", "Frequentist probability", "Friedrich Hayek", "Game theory", "Gary Becker", "Gauss-Markov (disambiguation)", "General equilibrium theory", "Generalized least squares", "Generalized method of moments", "Georgism", "Glossary of economics", "Granger causality", "Great Depression", "Harold Hotelling", "Health economics", "Herbert A. Simon", "Herman Wold", "Heterodox economics", "Historical school of economics", "History of economic thought", "Hyperinflation", "Hypothesis test", "IS\u2013LM model", "Index of economics articles", "Indifference curve", "Industrial organization", "Inflation", "Information economics", "Input\u2013output model", "Institutional economics", "Integrated Authority File", "Interest", "Interest rate", "International Monetary Fund", "International Standard Book Number", "International Standard Serial Number", "International economics", "International organization", "Intertemporal choice", "Investment (macroeconomics)", "JEL classification codes", "JSTOR", "Jacob Marschak", "Jan Tinbergen", "John Maynard Keynes", "John Stuart Mill", "John von Neumann", "Joseph Schumpeter", "Journal of Applied Econometrics", "Journal of Business & Economic Statistics", "Journal of Econometrics", "Karl Marx", "Kenneth Arrow", "Keynesian economics", "Knowledge economy", "Labour economics", "Lausanne School", "Law and economics", "Linear regression", "List of economics journals", "List of economists", "List of important publications in economics", "List of publications in economics", "L\u00e9on Walras", "M. Hashem Pesaran", "Macroeconomic model", "Macroeconomics", "Mainstream economics", "Malthusianism", "Managerial economics", "Marginal cost", "Marginal utility", "Marginalism", "Market (economics)", "Market failure", "Market structure", "Marxian economics", "Mathematical economics", "Mathematical finance", "Mathematical statistics", "Maximum likelihood estimation", "Measures of national income and output", "Mechanism design", "Mercantilism", "Methodological individualism", "Methodology of econometrics", "Microeconomics", "Microfoundations", "Milton Friedman", "Model selection", "Monetary economics", "Monetary policy", "Money", "Money supply", "Monopolistic competition", "Monopoly", "Monopsony", "Multiple linear regression", "Mutualism (economic theory)", "NAIRU", "National Archives and Records Administration", "National Diet Library", "National accounts", "Natural experiment", "Natural logarithm", "Natural resource economics", "Neo-Keynesian economics", "Neo-Marxian economics", "Neoclassical economics", "New Keynesian economics", "New classical macroeconomics", "New institutional economics", "Non-convexity (economics)", "Null hypothesis", "OECD", "Observational studies", "Observational study", "Okun's law", "Oligopoly", "Oligopsony", "Omitted-variable bias", "Operations research", "Opportunity cost", "Ordinary least squares", "Organizational economics", "Outline of economics", "P-value", "Parameter identification problem", "Pareto efficiency", "Paul Krugman", "Paul Samuelson", "Perfect competition", "Personnel economics", "Phenomena", "Physiocracy", "Political economy", "Polynomial least squares", "Post-Keynesian economics", "Predetermined variables", "Preference (economics)", "Price", "Price level", "Production set", "Profit (economics)", "Public choice", "Public economics", "Public good", "Purchasing power parity", "Quasi-experiment", "Ragnar Anton Kittil Frisch", "Ragnar Frisch", "Rate of profit", "Rational expectations", "Rationing", "Real business-cycle theory", "Recession", "Regional economics", "Regression analysis", "Returns to scale", "Review of Economics and Statistics", "Richard Stone", "Richard Thaler", "Risk aversion", "Robert Lucas Jr.", "Robert Solow", "Ronald A. Fisher", "Rural economics", "Saving", "Scarcity", "Schools of economic thought", "Service economy", "Shortage", "Shrinkflation", "Simultaneous equation methods (econometrics)", "Single equation methods (econometrics)", "Social choice theory", "Social cost", "Socialist economics", "Socioeconomics", "Spatial econometrics", "Spurious relationship", "Stagflation", "Statistical methods", "Statistical model", "Statistical significance", "Statistical theory", "Stephen Ziliak", "Stockholm school (economics)", "Sunk cost", "Supply-side economics", "Supply and demand", "Supply shock", "System identification", "Systems analysis", "Tests of significance", "The General Theory of Employment, Interest and Money", "The New Palgrave: A Dictionary of Economics", "The New Palgrave Dictionary of Economics", "Theory of the firm", "Thermoeconomics", "Thomas Robert Malthus", "Tjalling Koopmans", "Trade", "Transaction cost", "Transport economics", "Type II error", "Uncertainty", "Unemployment", "Unit root", "Urban economics", "Utility", "Value (economics)", "Vilfredo Pareto", "Wage", "Wayback Machine", "Welfare", "Welfare economics", "William D. Nordhaus", "World Bank", "World Trade Organization"], "references": ["http://www.aea-eu.com", "http://www.dictionaryofeconomics.com/article?id=pde2008_E000007&edition=current&q=Econometrics&topicid=&result_number=2", "http://www.dictionaryofeconomics.com/article?id=pde2008_F000161&edition=current&q=forecast&topicid=&result_number=7", "http://www.dictionaryofeconomics.com/article?id=pde2008_S000502&edition=current&q=statistics&topicid=&result_number=1", "http://www.dictionaryofeconomics.com/article?id=pde2008_S000200&edition=current&q=Specification%20problems%20in%20econometrics&topicid=&result_number=1", "http://www.econometriclinks.com", "http://www.wiley.com/bw/journal.asp?ref=1368-4221", "http://sofie.stern.nyu.edu/", "http://faculty.roosevelt.edu/Ziliak/doc/Size%20Matters%20Journal%20of%20Socio-Economics%20Ziliak%20and%20McCloskey.pdf", "http://www.elsevierweekblad.nl/Economie/achtergrond/2015/10/1969---Jan-Tinbergen-Nobelprijs-economie-2700626W/?masterpageid=5573", "http://doi.org/10.1257%2Fjep.24.2.3", "http://www.econometricsociety.org", "http://www.ectj.org", "http://www.jstor.org/stable/1803924", "http://www.oecd.org/sdd/41746710.pdf", "http://jfec.oxfordjournals.org/", "http://philpapers.org/rec/BRACAI-3", "http://www.worldcat.org/issn/0895-3309", "http://www.dziejekrakowa.pl/biogramy/index.php?id=516", "http://www.economicsnetwork.ac.uk/subjects/econometrics.htm", "https://books.google.com/books?id=gBsgr7BPJsoC&dq=econometrics&printsec=find&pg=PA1=false#v=onepage&q&f=false", "https://books.google.com/books?id=gBsgr7BPJsoC&dq=econometrics&printsec=find&pg=PA2=false#v=onepage&q&f=false", "https://catalog.archives.gov/id/10639172", "https://d-nb.info/gnd/4132280-0", "https://id.ndl.go.jp/auth/ndlna/00565373", "https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.24.2.3", "https://web.archive.org/web/20100625163446/http://faculty.roosevelt.edu/Ziliak/doc/Size%20Matters%20Journal%20of%20Socio-Economics%20Ziliak%20and%20McCloskey.pdf", "https://web.archive.org/web/20120518001558/http://www.dictionaryofeconomics.com/article?id=pde2008_E000007&edition=current&q=Econometrics&topicid=&result_number=2", "https://web.archive.org/web/20120518001702/http://www.dictionaryofeconomics.com/article?id=pde2008_S000502&edition=current&q=statistics&topicid=&result_number=1", "https://web.archive.org/web/20120518001935/http://www.dictionaryofeconomics.com/article?id=pde2008_F000161&edition=current&q=forecast&topicid=&result_number=7", "https://web.archive.org/web/20140502005854/http://www.dziejekrakowa.pl/biogramy/index.php?id=516", "https://web.archive.org/web/20150923231333/http://www.dictionaryofeconomics.com/article?id=pde2008_S000200&edition=current&q=Specification%20problems%20in%20econometrics&topicid=&result_number=1", "https://web.archive.org/web/20180501212351/https://www.elsevierweekblad.nl/Economie/achtergrond/2015/10/1969---Jan-Tinbergen-Nobelprijs-economie-2700626W/?masterpageid=5573", "https://www.jstor.org/pss/1907538", "https://www.jstor.org/pss/1912787", "https://www.wikidata.org/wiki/Q160039"]}, "Multiresolution analysis": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "Time\u2013frequency analysis", "Wavelets"], "title": "Multiresolution analysis", "method": "Multiresolution analysis", "url": "https://en.wikipedia.org/wiki/Multiresolution_analysis", "summary": "A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms (DWT) and the justification for the algorithm of the fast wavelet transform (FWT). It was introduced in this context in 1988/89 by Stephane Mallat and Yves Meyer and has predecessors in the microlocal analysis in the theory of differential equations (the ironing method) and the pyramid methods of image processing as introduced in 1981/83 by Peter J. Burt, Edward H. Adelson and James L. Crowley.\n\n", "images": [], "links": ["Algebraic closure", "Algorithm", "Ali Akansu", "C. Sidney Burrus", "Compact support", "Complete metric space", "Dense set", "Differential equation", "Dilation (metric space)", "Discrete wavelet transform", "Fast wavelet transform", "Father wavelets", "Image processing", "Infinity", "Ingrid Daubechies", "Integer", "International Standard Book Number", "Intersection", "Linear hull", "Linear subspace", "Lp space", "Microlocal analysis", "Multiple (mathematics)", "Multiscale modeling", "Orthogonal direct sum", "Orthonormal wavelet", "Piecewise continuous", "Pyramid (image processing)", "Scale space", "Scaling (geometry)", "Self-similarity", "Sequence", "Stephane Mallat", "Topologically closed", "Wavelet", "Yves Meyer", "Zero element"], "references": ["http://www-prima.inrialpes.fr/Prima/Homepages/jlc/jlc.html", "http://www-prima.inrialpes.fr/Prima/Homepages/jlc/papers/Crowley-Thesis81.pdf", "http://www.cmap.polytechnique.fr/~mallat/book.html"]}, "Cohort effect": {"categories": ["Cohort study methods", "Epidemiology", "Medical statistics", "Social research"], "title": "Cohort effect", "method": "Cohort effect", "url": "https://en.wikipedia.org/wiki/Cohort_effect", "summary": "The term cohort effect is used in social science to describe variations in the characteristics of an area of study (such as the incidence of a characteristic or the age at onset) over time among individuals who are defined by some shared temporal experience or common life experience, such as year of birth, or year of exposure to radiation.\nCohort effects are important to epidemiologists searching for patterns in illnesses. Certain illnesses may be socially affected via the anticipation phenomenon, and cohort effects can be an indicator of this sort of phenomenon.\nCohort effects are important to resource dependency and economics theorists when these groups affect structures of influence within their larger organizations. Cohorts in organizations are often defined by entry or birth date, and retain some common characteristic (size, cohesiveness, competition) that can affect the organization. For example, cohort effects are critical issues in school enrollment. \nIn order to determine whether a cohort effect is present, a researcher may conduct a cohort study.\n\n", "images": [], "links": ["Anticipation (genetics)", "Cohort study", "Epidemiologists", "Political socialization", "Social science", "Socialization"], "references": ["http://www.spirxpert.com/longitudinal2.htm", "http://ideas.repec.org/p/hhs/ifswps/2003_003.html"]}, "Confusion of the inverse": {"categories": ["All articles with incomplete citations", "Articles with incomplete citations from November 2012", "Misuse of statistics", "Probability fallacies"], "title": "Confusion of the inverse", "method": "Confusion of the inverse", "url": "https://en.wikipedia.org/wiki/Confusion_of_the_inverse", "summary": "Confusion of the inverse, also called the conditional probability fallacy or the inverse fallacy, is a logical fallacy whereupon a conditional probability is equivocated with its inverse: That is, given two events A and B, the probability of A happening given that B has happened is assumed to be about the same as the probability of B given A. More formally, P(A|B) is assumed to be approximately equal to P(B|A).", "images": [], "links": ["Amos Tversky", "Base rate fallacy", "Bayes' theorem", "Conditional probability", "Daniel Kahneman", "David M. Eddy", "Digital object identifier", "Equivocation", "False positive paradox", "Illicit conversion", "Informal fallacy", "International Standard Book Number", "Marijuana", "Monty Hall problem", "Paul Slovic", "Prior probability", "Prosecutor's fallacy", "Reid Hastie", "Robyn Dawes", "Scott Plous", "Slashdot"], "references": ["http://www.springerlink.com/content/2337k223787544t9/", "http://doi.org/10.3758%2FBF03195278", "http://it.slashdot.org/it/08/04/03/1943247.shtml"]}, "Heston model": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from November 2010", "Derivatives (finance)", "Financial models"], "title": "Heston model", "method": "Heston model", "url": "https://en.wikipedia.org/wiki/Heston_model", "summary": "In finance, the Heston model, named after Steven Heston, is a mathematical model describing the evolution of the volatility of an underlying asset. It is a stochastic volatility model: such a model assumes that the volatility of the asset is not constant, nor even deterministic, but follows a random process.", "images": [], "links": ["Abstract Wiener space", "Actuarial mathematics", "ArXiv", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "CIR process", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "CiteSeerX", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Del", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov's theorem", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "JSTOR", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Least squares", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local minima", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical model", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Numerical derivative", "Objective function", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random process", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk-neutral measure", "Risk process", "Ruin theory", "SABR Volatility Model", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Social Science Research Network", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Steven L. Heston", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stochastic volatility", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Underlying", "Uniform integrability", "Usual hypotheses", "Vanilla option", "Variance gamma process", "Variance swap", "Vasicek model", "Volatility (finance)", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "Wilmott"], "references": ["http://www.aessweb.com/journals/5002", "http://www.readcube.com/articles/10.1002/wilm.10201?locale=en", "http://ssrn.com/abstract=1367955", "http://ssrn.com/abstract=1434853", "http://ssrn.com/abstract=1447362", "http://www.math.uni-wuppertal.de/~kahl/publications/NotSoComplexLogarithmsInTheHestonModel.pdf", "http://www.math.nyu.edu/research/carrp/papers/pdf/jcfpub.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.170.9335", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.657.6271", "http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=SJFMBJ000002000001000255000001&idtype=cvips&doi=10.1137/090756119&prog=normal", "http://arxiv.org/abs/1511.08718", "http://doi.org/10.1002%2Fwilm.10201", "http://doi.org/10.1093%2Frfs%2F6.2.327", "http://doi.org/10.2139%2Fssrn.1367955", "http://www.jstor.org/stable/2962057", "https://github.com/jcfrei/Heston"]}, "Point-biserial correlation coefficient": {"categories": ["Covariance and correlation", "Psychometrics"], "title": "Point-biserial correlation coefficient", "method": "Point-biserial correlation coefficient", "url": "https://en.wikipedia.org/wiki/Point-biserial_correlation_coefficient", "summary": "The point biserial correlation coefficient (rpb) is a correlation coefficient used when one variable (e.g. Y) is dichotomous; Y can either be \"naturally\" dichotomous, like whether a coin lands heads or tails, or an artificially dichotomized variable. In most situations it is not advisable to dichotomize variables artificially. When a new variable is artificially dichotomized the new dichotomous variable may be conceptualized as having an underlying continuity. If this is the case, a biserial correlation would be the more appropriate calculation.\nThe point-biserial correlation is mathematically equivalent to the Pearson (product moment) correlation, that is, if we have one continuously measured variable X and a dichotomous variable Y, rXY = rpb. This can be shown by assigning two distinct numerical values to the dichotomous variable.", "images": [], "links": ["Allyn & Bacon", "Biserial correlation", "Correlation", "Correlation coefficient", "Dichotomy", "International Standard Book Number", "Mann\u2013Whitney U", "Normal distribution", "Student's t-distribution", "Student's t-test"], "references": ["http://www.andrews.edu/~calkins/math/edrm611/edrm13.htm#POINTB", "http://www.rasch.org/rmt/rmt221e.htm"]}, "Cook's distance": {"categories": ["Regression diagnostics", "Statistical distance", "Statistical outliers", "Wikipedia articles needing clarification from July 2010"], "title": "Cook's distance", "method": "Cook's distance", "url": "https://en.wikipedia.org/wiki/Cook%27s_distance", "summary": "In statistics, Cook's distance or Cook's D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis. In a practical ordinary least squares analysis, Cook's distance can be used in several ways: to indicate influential data points that are particularly worth checking for validity; or to indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.\n\n", "images": [], "links": ["American Statistical Association", "DFFITS", "Design matrix", "Digital object identifier", "Edwin Kuh", "Errors and residuals", "F-distribution", "Influential observation", "Influential observations", "International Standard Book Number", "J. Scott Long", "JSTOR", "Journal of the American Statistical Association", "Kenneth A. Bollen", "Least squares", "Leverage (statistics)", "Mathematical Reviews", "Mean squared error", "Ordinary least squares", "Outlier", "Partial leverage", "Projection matrix", "R. Dennis Cook", "Regression analysis", "Sanford Weisberg", "Statistics", "Studentized residual"], "references": ["http://se.mathworks.com/help/stats/cooks-distance.html", "http://www.ams.org/mathscinet-getitem?mr=0436478", "http://www.ams.org/mathscinet-getitem?mr=0529533", "http://doi.org/10.1016%2FS1573-4412(83)01015-6", "http://doi.org/10.1177%2F1094428112470848", "http://doi.org/10.2307%2F1268249", "http://doi.org/10.2307%2F2286747", "http://www.jstor.org/stable/1268249", "http://www.jstor.org/stable/2286747", "https://books.google.com/books?id=MVSqAAAAIAAJ", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA21", "https://books.google.com/books?id=X0dPBOJ_L4UC&pg=PA22", "https://books.google.com/books?id=co3gBwAAQBAJ&pg=PA312", "https://www.stat.purdue.edu/~jennings/stat514/stat512notes/topic3.pdf#page=9", "https://www.researchgate.net/profile/Herman_Aguinis/publication/258174106_Best-Practice_Recommendations_for_Defining_Identifying_and_Handling_Outliers/links/004635276b1ff93ba8000000.pdf"]}, "Multinomial logistic regression": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from November 2011", "Articles with unsourced statements from September 2017", "Classification algorithms", "Logistic regression", "Regression models"], "title": "Multinomial logistic regression", "method": "Multinomial logistic regression", "url": "https://en.wikipedia.org/wiki/Multinomial_logistic_regression", "summary": "In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.).\nMultinomial logistic regression is known by a variety of other names, including polytomous LR, multiclass LR, softmax regression, multinomial logit, the maximum entropy (MaxEnt) classifier, and the conditional maximum entropy model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bayesian linear regression", "Bayesian multivariate linear regression", "Binary variable", "Blood pressure", "Categorical distribution", "Categorical variable", "Continuous variable", "Coordinate descent", "Dependent variable", "Differentiation (mathematics)", "Digital object identifier", "Discrete choice", "Dot product", "Error propagation", "Errors-in-variables models", "Errors and residuals in statistics", "Extreme value distribution", "Fixed effects model", "Gaussian distribution", "Gauss\u2013Markov theorem", "General linear model", "Generalized iterative scaling", "Generalized least squares", "Generalized linear model", "Gibbs measure", "Goodness of fit", "Gradient-based optimization", "Hepatitis", "Identifiability", "Independence of irrelevant alternatives", "Independent identically distributed", "Independent variable", "Indicator function", "International Standard Book Number", "Isotonic regression", "Iteratively reweighted least squares", "Journal of Business Research", "L-BFGS", "Latent variable", "Least-angle regression", "Least absolute deviations", "Least squares", "Level of measurement", "Linear combination", "Linear discriminant analysis", "Linear least squares", "Linear predictor function", "Linear regression", "Local regression", "Location parameter", "Logarithm", "Logistic distribution", "Logistic function", "Logistic regression", "Mathematical optimization", "Maximum a posteriori", "Maximum likelihood", "Mean and predicted response", "Mixed logit", "Mixed model", "Multiclass classification", "Multicollinearity", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multinomial regression", "Naive Bayes classifier", "Natural language processing", "Nested logit", "Non-linear least squares", "Non-negative least squares", "Nonidentifiable", "Nonlinear regression", "Nonparametric regression", "Normalization factor", "Odds ratio", "Order statistic", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Partition function (mathematics)", "Perceptron", "Perfect substitute", "Poisson regression", "Polynomial regression", "Predictive modelling", "Principal component regression", "Prior distribution", "Probability", "Probability distribution", "Probit model", "Quantile regression", "Random effects model", "Random variable", "Regression analysis", "Regression coefficient", "Regression model validation", "Regularization (mathematics)", "Regularized least squares", "Robust regression", "Scale parameter", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Smooth function", "Softmax activation function", "Softmax function", "Statistical classification", "Statistical independence", "Statistically independent", "Statistics", "Studentized residual", "Support vector machine", "Tikhonov regularization", "Total least squares", "Utility", "Weighted average", "Weighted least squares", "William Greene (economist)"], "references": ["http://aclweb.org/anthology/W/W02/W02-2018.pdf", "http://doi.org/10.1007%2Fs10994-010-5221-8", "http://doi.org/10.1016%2FS0148-2963(99)00058-2", "http://doi.org/10.1111%2Fj.1467-9574.1988.tb01238.x", "http://doi.org/10.1214%2Faoms%2F1177692379", "http://projecteuclid.org/download/pdf_1/euclid.aoms/1177692379", "http://www.csie.ntu.edu.tw/~cjlin/papers/maxent_dual.pdf"]}, "Data binning": {"categories": ["All articles needing expert attention", "All stub articles", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Statistical data coding", "Statistics articles needing expert attention", "Statistics stubs"], "title": "Data binning", "method": "Data binning", "url": "https://en.wikipedia.org/wiki/Data_binning", "summary": "Data binning (also called Discrete binning or bucketing) is a data pre-processing technique used to reduce the effects of minor observation errors. The original data values which fall in a given small interval, a bin, are replaced by a value representative of that interval, often the central value. It is a form of quantization.\nStatistical data binning is a way to group a number of more or less continuous values into a smaller number of \"bins\". For example, if you have data about a group of people, you might want to arrange their ages into a smaller number of age intervals (for example, grouping every five years together). It can also be used in multivariate statistics, binning in several dimensions at once.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg"], "links": ["Atomic mass unit", "Chemical shift", "Data pre-processing", "Digital camera", "Discretization of continuous features", "Euclidean vector", "Frequency distribution", "Grouped data", "Histogram", "Image processing", "Interval (mathematics)", "Level of measurement", "Mass spectrometry", "Multivariate statistics", "NMR", "Nuclear magnetic resonance", "One-dimensional space", "Pattern recognition", "Pixel", "Quantization (signal processing)", "Statistics"], "references": ["http://www.microscopyu.com/tutorials/java/digitalimaging/signaltonoise/index.html", "http://www.starrywonders.com/binning.html"]}, "Model output statistics": {"categories": ["Climate and weather statistics", "Weather forecasting"], "title": "Model output statistics", "method": "Model output statistics", "url": "https://en.wikipedia.org/wiki/Model_output_statistics", "summary": "Model Output Statistics (MOS) is a multiple linear regression technique in which predictands, often near-surface quantities, such as 2-meter (AGL) air temperature, horizontal visibility, and wind direction, speed and gusts, are related statistically to one or more predictors. The predictors are typically forecasts from a numerical weather prediction (NWP) model, climatic data, and, if applicable, recent surface observations. Thus, output from NWP models can be transformed by the MOS technique into sensible weather parameters that are familiar to the \"person on the street\".", "images": ["https://upload.wikimedia.org/wikipedia/en/e/e9/MaxT2_CONUS_08072014.png"], "links": ["ADCIRC", "ADMS 3", "AERMOD", "ATSTEP", "AUSTAL2000", "Atmospheric dispersion modeling", "Atmospheric model", "Bibcode", "CALPUFF", "CGCM", "CLaMS", "Canadian Land Surface Scheme", "Ceiling (cloud)", "Chemical transport model", "Climate Forecast System", "Climate model", "Community Climate System Model", "Community Earth System Model", "Computer simulation", "DISPERSION21", "Digital object identifier", "ECHAM", "Ensemble forecasting", "Environmental Modeling Center", "European Centre for Medium-Range Weather Forecasts", "FESOM", "Finite Volume Community Ocean Model", "Flow-following, finite-volume Icosahedral Model", "GEOS-Chem", "GFDL CM2.X", "GME of Deutscher Wetterdienst", "Global Environmental Multiscale Model", "Global Forecast System", "Guam", "HIRLAM", "HWRF", "HadCM3", "HadGEM1", "ISC3", "Integrated Forecast System", "Interaction Soil-Biosphere-Atmosphere", "Intermediate General Circulation Model", "International Standard Book Number", "JULES", "Linear regression", "MEMO Model", "MERCURE", "METAR", "MIT General Circulation Model", "MM5 (weather model)", "MOZART (model)", "Mathematical model", "Mesonet", "Meteorological reanalysis", "Model for Prediction Across Scales", "Modular ocean model", "NAME (dispersion model)", "NOAA", "National Hurricane Center", "National Weather Service", "Navy Global Environmental Model", "Navy Operational Global Atmospheric Prediction System", "Nested Grid Model", "North American Ensemble Forecast System", "North American Mesoscale Model", "Northern Mariana Islands", "Numerical weather prediction", "Operational Street Pollution Model", "Overcast", "PUFF-PLUME", "Parametrization (atmospheric modeling)", "Planetary boundary layer", "Princeton ocean model", "Probability of precipitation", "RIMPUFF", "Rapid Refresh", "Rapid Update Cycle", "Regional Atmospheric Modeling System", "Regional Ocean Modeling System", "Royal Netherlands Meteorological Institute", "SAFE AIR", "Scientific modelling", "Statistical model", "Storm Prediction Center", "Temperature", "Thunderstorm", "Tropical cyclone forecast model", "Unified Model", "Upper-atmospheric models", "Visibility", "Weather", "Weather Prediction Center", "Weather Research and Forecasting model", "Wind", "Wind direction", "Wind gust", "Wind speed"], "references": ["http://adsabs.harvard.edu/abs/1963JAtS...20..130L", "http://adsabs.harvard.edu/abs/1989WtFor...4..401C", "http://adsabs.harvard.edu/abs/1991WtFor...6..142E", "http://adsabs.harvard.edu/abs/2002WtFor..17..206W", "http://adsabs.harvard.edu/abs/2005WtFor..20..134S", "http://adsabs.harvard.edu/abs/2007MWRv..135.2379W", "http://adsabs.harvard.edu/abs/2009WtFor..24..520G", "http://adsabs.harvard.edu/abs/2010WtFor..25.1161R", "http://adsabs.harvard.edu/abs/2011APJAS..47..199K", "http://adsabs.harvard.edu/abs/2013MWRv..141.2467V", "http://madis.noaa.gov/network_info.html", "http://www.emc.ncep.noaa.gov/NAM/clog.php#TAB4", "http://www.emc.ncep.noaa.gov/gmb/STATS/html/model_changes.html", "http://www.emc.ncep.noaa.gov/gmb/wd20rt/vsdb/prhw14/www/scorecard/mainindex.html", "http://www.mdl.nws.noaa.gov/~naefs_ekdmos/", "http://www.mdl.nws.noaa.gov/~qa/pdf_files/TDL_Office_Note_00-1.pdf", "http://www.nws.noaa.gov/mdl/gfslamp/gfslamp.shtml", "http://www.nws.noaa.gov/mdl/survey/2011/results/MDL_Survey_2011_FINAL.pdf", "http://www.nws.noaa.gov/mdl/synop/avnmosmap.php", "http://www.nws.noaa.gov/mdl/synop/mavcard.php", "http://www.nws.noaa.gov/mdl/synop/mrfmosmap.php", "http://www.nws.noaa.gov/mdl/synop/nammosmap.php", "http://www.nws.noaa.gov/tdl/", "http://graphical.weather.gov/gmos/index.php", "http://web.kma.go.kr", "http://www.knmi.nl/bibliotheek/knmipubIR/IR2012-01.pdf", "http://doi.org/10.1007%2Fs13143-011-0009-8", "http://doi.org/10.1175%2F1520-0434(1989)004%3C0401:SFBOTN%3E2.0.CO;2", "http://doi.org/10.1175%2F1520-0434(1991)006%3C0142:ETIORC%3E2.0.CO;2", "http://doi.org/10.1175%2F1520-0434(2002)017%3C0206:TCUMOS%3E2.0.CO;2", "http://doi.org/10.1175%2F1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2", "http://doi.org/10.1175%2F2008WAF2007080.1", "http://doi.org/10.1175%2F2010WAF2222383.1", "http://doi.org/10.1175%2FMWR-D-12-00191.1", "http://doi.org/10.1175%2FMWR3402.1", "http://doi.org/10.1175%2FWAF840.1", "https://ams.confex.com/ams/91Annual/webprogram/Paper179368.html", "https://ams.confex.com/ams/annual2002/techprogram/paper_27642.htm", "https://ams.confex.com/ams/pdfpapers/154242.pdf"]}, "Recursive partitioning": {"categories": ["Biostatistics", "Statistical classification"], "title": "Recursive partitioning", "method": "Recursive partitioning", "url": "https://en.wikipedia.org/wiki/Recursive_partitioning", "summary": "Recursive partitioning is a statistical method for multivariable analysis. Recursive partitioning creates a decision tree that strives to correctly classify members of the population by splitting it into sub-populations based on several dichotomous independent variables. The process is termed recursive because each sub-population may in turn be split an indefinite number of times until the splitting process terminates after a particular stopping criterion is reached.\n\nRecursive partitioning methods have been developed since the 1980s. Well known methods of recursive partitioning include Ross Quinlan's ID3 algorithm and its successors, C4.5 and C5.0 and Classification and Regression Trees. Ensemble learning methods such as Random Forests help to overcome a common criticism of these methods - their vulnerability to overfitting of the data - by employing different algorithms and combining their output in some way.\nThis article focuses on recursive partitioning for medical diagnostic tests,\nbut the technique has far wider applications.\nSee decision tree.\nAs compared to regression analysis, which creates a formula that health care providers can use to calculate the probability that a patient has a disease, recursive partition creates a rule such as 'If a patient has finding x, y, or z they probably have disease q'.\nA variation is 'Cox linear recursive partitioning'.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f3/CART_tree_titanic_survivors.png"], "links": ["C4.5", "C5.0", "Decision tree learning", "Diagnostic", "Digital object identifier", "Ensemble learning", "ID3 algorithm", "Independent variable", "International Standard Book Number", "Multivariable analysis", "Myocardial infarction", "Overfitting", "PubMed Identifier", "Random forest", "Recursion", "Sensitivity (tests)", "Specificity (tests)", "Statistics", "Titanic"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/10891517", "http://www.ncbi.nlm.nih.gov/pubmed/11597285", "http://www.ncbi.nlm.nih.gov/pubmed/15687312", "http://www.ncbi.nlm.nih.gov/pubmed/16149128", "http://www.ncbi.nlm.nih.gov/pubmed/16482368", "http://www.ncbi.nlm.nih.gov/pubmed/3060613", "http://www.ncbi.nlm.nih.gov/pubmed/6501544", "http://www.ncbi.nlm.nih.gov/pubmed/7110205", "http://www.ncbi.nlm.nih.gov/pubmed/8594242", "http://www.ncbi.nlm.nih.gov/pubmed/9790741", "http://doi.org/10.1001/jama.275.8.611", "http://doi.org/10.1001/jama.286.15.1841", "http://doi.org/10.1001/jama.293.5.572", "http://doi.org/10.1002/sim.2154", "http://doi.org/10.1006/cbmr.1998.1488", "http://doi.org/10.1016/0021-9681(84)90041-9", "http://doi.org/10.1056/NEJM198209023071004", "http://doi.org/10.1056/NEJM200007133430204"]}, "Logit": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2010", "CS1 maint: Archived copy as title", "Logarithms", "Special functions"], "title": "Logit", "method": "Logit", "url": "https://en.wikipedia.org/wiki/Logit", "summary": "In statistics, the logit ( LOH-jit) function or the log-odds is the logarithm of the odds p/(1 \u2212 p) where p is the probability.. It is a type of function that creates a map of probability values from \n \n \n \n [\n 0\n ,\n 1\n ]\n \n \n {\\displaystyle [0,1]}\n to \n \n \n \n [\n \u2212\n \u221e\n ,\n +\n \u221e\n ]\n \n \n {\\displaystyle [-\\infty ,+\\infty ]}\n . It is the inverse of the sigmoidal \"logistic\" function or logistic transform used in mathematics, especially in statistics.\nIn deep learning, the term logits layer is popularly used for the last neuron layer of neural network for classification task which produces raw prediction values as real numbers ranging from \n \n \n \n [\n \u2212\n \u221e\n ,\n +\n \u221e\n ]\n \n \n {\\displaystyle [-\\infty ,+\\infty ]}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/39/Logit-probit.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c8/Logit.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Additive function", "Arcsin", "Bayesian statistics", "Bernoulli distribution", "Binary entropy function", "Charles Sanders Peirce", "Chester Ittner Bliss", "Cumulative distribution function", "Daniel McFadden", "Data transformation (statistics)", "Deep learning", "Derivative", "Digital object identifier", "Discrete choice", "E (mathematical constant)", "G. A. Barnard", "Generalized linear model", "Hartley (unit)", "International Standard Book Number", "International Standard Serial Number", "Inverse function", "Joseph Berkson", "Limited dependent variable", "Link function", "Logarithm", "Logarithmic unit", "Logistic distribution", "Logistic function", "Logistic regression", "Logit analysis (in marketing)", "Logit function", "Logit model", "Mathematics", "Measurement", "Mixed logit", "Multinomial logit", "Nat (unit)", "Natural logarithm", "Nobel Prize in Economics", "Normal distribution", "Odds", "Odds ratio", "Ogee", "Ordered logit", "Perceptron", "Probability", "Probability distribution", "Probit", "Probit function", "Probit model", "Quantile function", "Rasch model", "Ridit scoring", "Shannon (unit)", "Sigmoid function", "Stephen M. Stigler"], "references": ["http://www.stat.ucl.ac.be/ISdidactique/Rhelp/library/msm/html/expit.html", "http://www.cs.cmu.edu/~16831-f12/notes/F12/16831_lecture05_vh.pdf", "http://www.columbia.edu/~so33/SusDev/Lecture_9.pdf", "http://itl.nist.gov/div898/software/dataplot/refman2/auxillar/logoddra.htm", "http://www.cambridge.org/resources/0521815886/1208_default.pdf", "http://doi.org/10.1023%2FA:1025584807625", "http://doi.org/10.1109%2FACCESS.2015.2454533", "http://ieeexplore.ieee.org/document/7161279/", "http://www.worldcat.org/issn/0929-5593", "http://www.worldcat.org/issn/2169-3536", "https://books.google.com/books?id=1Od2d72pPXUC&pg=PA13", "https://books.google.com/books?id=tmHMBQAAQBAJ&pg=PA3", "https://link.springer.com/article/10.1023/A:1025584807625", "https://web.archive.org/web/20110706132209/http://www.stat.ucl.ac.be/ISdidactique/Rhelp/library/msm/html/expit.html", "https://www.tensorflow.org/tutorials/estimators/cnn#logits_layer"]}, "Correlation function": {"categories": ["All articles lacking sources", "Articles lacking sources from December 2009", "Covariance and correlation", "Spatial data analysis", "Time series", "Wikipedia articles needing clarification from July 2016"], "title": "Correlation function", "method": "Correlation function", "url": "https://en.wikipedia.org/wiki/Correlation_function", "summary": "A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables representing the same quantity measured at two different points then this is often referred to as an autocorrelation function, which is made up of autocorrelations. Correlation functions of different random variables are sometimes called cross-correlation functions to emphasize that different variables are being considered and because they are made up of cross-correlations.\nCorrelation functions are a useful indicator of dependencies as a function of distance in time or space, and they can be used to assess the distance required between sample points for the values to be effectively uncorrelated. In addition, they can form the basis of rules for interpolating values at points for which there are no observations.\nCorrelation functions used in astronomy, financial analysis, econometrics, and statistical mechanics differ only in the particular stochastic processes they are applied to. In quantum field theory there are correlation functions over quantum distributions.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/21/Comparison_convolution_correlation.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Autocorrelation", "Autocorrelation function", "Convolution", "Correlation", "Correlation does not imply causation", "Correlation function (astronomy)", "Correlation function (disambiguation)", "Correlation function (quantum field theory)", "Correlation function (statistical mechanics)", "Covariance function", "Cross-correlation", "Econometrics", "Financial analysis", "Function (mathematics)", "Gaussian processes", "Irreducible representation", "It\u014d calculus", "Minkowski spacetime", "Mutual information", "Path integral formulation", "Pearson product-moment correlation coefficient", "Probability distribution", "Probability distributions", "Quantum field theory", "Radial distribution function", "Random variable", "Random vector", "Random walk", "Rate distortion theory", "Reflection positivity", "Renormalization", "Spacetime symmetries", "Statistical mechanics", "Trace (matrix)", "Wick rotation"], "references": []}, "G-test": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2011", "Articles with unsourced statements from January 2016", "Statistical tests for contingency tables", "Webarchive template wayback links"], "title": "G-test", "method": "G-test", "url": "https://en.wikipedia.org/wiki/G-test", "summary": "In statistics, G-tests are likelihood-ratio or maximum likelihood statistical significance tests that are increasingly being used in situations where chi-squared tests were previously recommended.The general formula for G is\n\n \n \n \n G\n =\n 2\n \n \u2211\n \n i\n \n \n \n \n O\n \n i\n \n \n \u22c5\n ln\n \u2061\n \n (\n \n \n \n O\n \n i\n \n \n \n E\n \n i\n \n \n \n \n )\n \n \n ,\n \n \n {\\displaystyle G=2\\sum _{i}{O_{i}\\cdot \\ln \\left({\\frac {O_{i}}{E_{i}}}\\right)},}\n where \n \n \n \n \n O\n \n i\n \n \n \u2265\n 0\n \n \n {\\textstyle O_{i}\\geq 0}\n is the observed count in a cell, \n \n \n \n \n E\n \n i\n \n \n >\n 0\n \n \n {\\textstyle E_{i}>0}\n is the expected count under the null hypothesis, \n \n \n \n ln\n \n \n {\\textstyle \\ln }\n denotes the natural logarithm, and the sum is taken over all non-empty cells. Furthermore, the total observed count should be equal to the total expected count:where \n \n \n \n N\n \n \n {\\textstyle N}\n is the total number of observations.\nG-tests have been recommended at least since the 1981 edition of the popular statistics textbook by Robert R. Sokal and F. James Rohlf.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Statistics", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational Linguistics (journal)", "Computational linguistics", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Entropy (information theory)", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "F. James Rohlf", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's exact test", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "IEEE Transactions on Information Theory", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Java (programming language)", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kullback\u2013Leibler divergence", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratio test", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-likelihood ratio", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimate", "McDonald\u2013Kreitman test", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial test", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Mutual information", "National accounts", "Natural experiment", "Natural logarithm", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R programming language", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robert R. Sokal", "Robust regression", "Robust statistics", "Run chart", "SAS System", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stata", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical genetics", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taylor series", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.biostathandbook.com/gtestgof.html", "http://www.biostathandbook.com/gtestind.html", "http://www.biostathandbook.com/small.html", "http://adsabs.harvard.edu/abs/1929RSPSA.125...54F", "http://adsabs.harvard.edu/abs/2012arXiv1202.1125H", "http://acl.ldc.upenn.edu/J/J93/J93-1003.pdf", "http://rforge.net/doc/packages/Deducer/html/00Index.html", "http://rforge.net/doc/packages/Deducer/likelihood.test.html", "http://arxiv.org/abs/1202.1125", "http://arxiv.org/abs/1206.4881", "http://doi.org/10.1098%2Frspa.1929.0151", "http://doi.org/10.1109%2Ftit.2007.911155", "http://doi.org/10.1214%2Faos%2F1176349550", "http://cran.r-project.org/package=AMR", "http://cran.r-project.org/package=Rfast", "http://ucrel.lancs.ac.uk/llwizard.html", "https://commons.apache.org/proper/commons-math/javadocs/api-3.3/org/apache/commons/math3/stat/inference/GTest.html", "https://web.archive.org/web/20111215212356/http://acl.ldc.upenn.edu/J/J93/J93-1003.pdf", "https://cran.r-project.org/web/packages/GeneCycle/"]}, "Singular spectrum analysis": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "Multivariate time series", "Time domain analysis"], "title": "Singular spectrum analysis", "method": "Singular spectrum analysis", "url": "https://en.wikipedia.org/wiki/Singular_spectrum_analysis", "summary": "In time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. Its roots lie in the classical Karhunen (1946)\u2013Lo\u00e8ve (1945, 1978) spectral decomposition of time series and random fields and in the Ma\u00f1\u00e9 (1981)\u2013Takens (1981) embedding theorem. SSA can be an aid in the decomposition of time series into a sum of components, each having a meaningful interpretation. The name \"singular spectrum analysis\" relates to the spectrum of eigenvalues in a singular value decomposition of a covariance matrix, and not directly to a frequency domain decomposition.\n\n", "images": [], "links": ["Attractor", "Autoregressive", "Autoregressive model", "Basis function", "Blind source separation", "Change detection", "Cosine", "Covariance matrix", "Cross-validation (statistics)", "Decomposition of time series", "Density Estimation", "Dynamical systems", "Eigenvalue", "Empirical orthogonal functions", "Estimation of signal parameters via rotational invariance techniques", "Fourier Analysis", "Fourier analysis", "Fourier transform", "Frequency domain decomposition", "Frequency estimation", "Hankel matrix", "Independent Component Analysis", "International Standard Book Number", "Karhunen\u2013Loeve theorem", "Kari Karhunen", "Least squares", "Linear filters", "Linear prediction", "Michel Lo\u00e8ve", "Missing data", "Multitaper", "Multivariate statistics", "Noise reduction", "Nonparametric statistics", "Periodic function", "Principal component analysis", "Principal components analysis", "Prony's method", "Random fields", "Recurrence relation", "Regression analysis", "Seasonal adjustment", "Short-time Fourier transform", "Signal processing", "Signal subspace", "Sine", "Singular Value Decomposition", "Singular value decomposition", "Smoothing", "Spectral decomposition", "Spectral decomposition (Matrix)", "Spectral density estimation", "State Space Model", "Stationary process", "Takens' theorem", "Time series", "Time series analysis", "Trend estimation", "Unevenly spaced time series", "Varimax rotation"], "references": ["http://www.gistatgroup.com/cat/", "http://www.gistatgroup.com/cat/books.html", "http://www.gistatgroup.com/gus/mssa2.pdf", "http://www.spectraworks.com/web/welcome.html", "http://www.atmos.ucla.edu/tcd/PREPRINTS/2000RG.pdf", "http://www.atmos.ucla.edu/tcd/ssa", "http://www.nonlin-processes-geophys.net/13/151/2006/npg-13-151-2006.html", "http://r-forge.r-project.org/projects/simsalabim/", "https://www.amazon.com/Singular-Spectrum-Analysis-Biomedical-Signals/dp/1466589272", "https://www.amazon.com/dp/1584881941", "https://www.amazon.com/dp/3642349129", "https://www.scribd.com/doc/106788415/Singular-Spectrum-Analysis-Demo-With-VBA", "https://dept.atmos.ucla.edu/tcd/m-ssa-tutorial-matlab", "https://dept.atmos.ucla.edu/tcd/ssa-tutorial-matlab", "https://ssa-with-r-book.github.io", "https://mdecarvalho.shinyapps.io/decarvalho2017/", "https://cran.r-project.org/web/packages/ASSA/index.html", "https://cran.r-project.org/web/packages/Rssa/index.html", "https://www.maths.ed.ac.uk/~mdecarv/papers/decarvalho2012d.pdf", "https://www.maths.ed.ac.uk/~mdecarv/papers/decarvalho2017.pdf"]}, "Cartography": {"categories": ["All articles with unsourced statements", "Articles with short description", "Articles with unsourced statements from July 2011", "CS1 errors: dates", "CS1 maint: Extra text: authors list", "Cartography", "Wikipedia articles with GND identifiers", "Wikipedia articles with HDS identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NARA identifiers", "Wikipedia articles with NDL identifiers"], "title": "Cartography", "method": "Cartography", "url": "https://en.wikipedia.org/wiki/Cartography", "summary": "Cartography (; from Greek \u03c7\u03ac\u03c1\u03c4\u03b7\u03c2 chart\u0113s, \"papyrus, sheet of paper, map\"; and \u03b3\u03c1\u03ac\u03c6\u03b5\u03b9\u03bd graphein, \"write\") is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.\nThe fundamental problems of traditional cartography are to:\n\nSet the map's agenda and select traits of the object to be mapped. This is the concern of map editing. Traits may be physical, such as roads or land masses, or may be abstract, such as toponyms or political boundaries.\nRepresent the terrain of the mapped object on flat media. This is the concern of map projections.\nEliminate characteristics of the mapped object that are not relevant to the map's purpose. This is the concern of generalization.\nReduce the complexity of the characteristics that will be mapped. This is also the concern of generalization.\nOrchestrate the elements of the map to best convey its message to its audience. This is the concern of map design.Modern cartography constitutes many theoretical and practical foundations of geographic information systems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/7d/Bedolina_roccia_1_foto_rilievo.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f0/Claudius_Ptolemy-_The_World.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/bc/Easter_Island_map-en.svg", "https://upload.wikimedia.org/wikipedia/commons/8/86/Europe_As_A_Queen_Sebastian_Munster_1570.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/79/Gfi-set01-airport.png", "https://upload.wikimedia.org/wikipedia/commons/2/2f/Gfi-set01-airport1.png", "https://upload.wikimedia.org/wikipedia/commons/6/68/Gfi-set01-castle.png", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Gfi-set01-castle1.png", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Gfi-set01-hostel.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5c/Gfi-set01-info.png", "https://upload.wikimedia.org/wikipedia/commons/d/de/Gfi-set01-memorial.png", "https://upload.wikimedia.org/wikipedia/commons/4/4a/Gfi-set01-railway.png", "https://upload.wikimedia.org/wikipedia/commons/5/55/Gfi-set01-railway1.png", "https://upload.wikimedia.org/wikipedia/commons/3/38/Info_Simple.svg", "https://upload.wikimedia.org/wikipedia/commons/1/10/Legenda_Michelin_kaart_1940.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/08/Livingston-Greenwich-map.jpg", "https://upload.wikimedia.org/wikipedia/commons/c/c4/Maps-for-free_Sierra_Nevada.png", "https://upload.wikimedia.org/wikipedia/commons/3/31/Orienteringskort_bygholm_2005_detail.jpg", "https://upload.wikimedia.org/wikipedia/commons/c/ce/Paspardo_roccia_Vite29_rilievo_foto.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/ac/Schlaegel_und_Eisen_nach_DIN_21800.svg", "https://upload.wikimedia.org/wikipedia/commons/6/62/Schlaegel_und_Eisen_nach_DIN_21800_gedreht_um_180_Grad.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5e/Set01-church.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Set01-church1.svg", "https://upload.wikimedia.org/wikipedia/commons/4/42/Structureforet.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/70/T_and_O_map_Guntherus_Ziner_1472.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a1/TabulaRogeriana_upside-down.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikibooks-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/2/24/Wikinews-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1b/Wikiversity-logo-en.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1b/Wikiversity-logo-en.svg", "https://upload.wikimedia.org/wikipedia/commons/9/95/World_map_green.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fc/Fern%C3%A3o_Vaz_Dourado_1571-1.jpg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/0/06/Wiktionary-logo-v2.svg"], "links": ["Ade Olufeko", "Adolphe Quetelet", "Aerial photography", "Aesthetics", "Africa", "Age of Exploration", "Agricultural geography", "Airport", "Alan MacEachren", "Anatolian Studies", "Anaximander", "Ancient China", "Ancient Greeks", "Animated mapping", "Arabic script", "Arthur H. Robinson", "Assyria", "Atlas", "Atmospheric science", "August Kekul\u00e9", "Babylon", "Babylonia", "Babylonian world map", "Bang Wong", "Bangkok", "Bar scale", "Battista Agnese", "Bedolina Map", "Behavioral geography", "Ben Shneiderman", "Berlin Conference", "Biogeography", "Biological data visualization", "Bonne projection", "Boulder County, Colorado", "British Columbia", "Bruce H. McCormick", "Burh", "Cadastre", "Cambridge University Press", "Cartogram", "Cartographer", "Cartographer (disambiguation)", "Cartographic generalization", "Cartographic labeling", "Cartographic propaganda", "Cartographic relief depiction", "Cartography of India", "Castle", "Chapel", "Charles Joseph Minard", "Chart", "Chartjunk", "Chemical imaging", "China", "Choropleth map", "Christopher R. Johnson", "Church (building)", "City map", "Clifford A. Pickover", "Climate", "Climatology", "Coastal geography", "Compass", "Compass rose", "Computer-aided design", "Computer graphics", "Computer graphics (computer science)", "Computer hardware", "Continental divide", "Contour line", "Cornell University Library", "Cosmographia (Sebastian M\u00fcnster)", "Counter-mapping", "Crime mapping", "Critical cartography", "Cultural geography", "Cyberspace", "Cyrillic", "Data visualization", "Database", "David Woodward", "Deconstruction", "Deconstructionism", "Development geography", "Diagram", "Diego Ribero", "Digital mapping", "Digital object identifier", "Digital raster graphic", "Early world maps", "Earth science", "Earth system science", "Easter Island", "Easter egg (media)", "Ecology", "Economic geography", "Ecumene", "Edaphology", "Edward Tufte", "Engineering drawing", "Environmental geography", "Environmental science", "Environmental social science", "Environmental studies", "Epistemology", "Etymology", "Euphrates", "Europa regina", "Europe", "Exonym", "Fantasy map", "Far East", "Fernanda Vi\u00e9gas", "Fern\u00e3o Vaz Dourado", "Fictitious entry", "Figure-ground in map design", "Florence Nightingale", "Flow visualization", "Fran\u00e7ois Du Creux", "Fraser Stoddart", "Fukuoka", "GPS", "Gamut", "Gaspard Monge", "Geo-literacy", "Geo warping", "Geobiology", "Geochronology", "Geodesy", "Geographia", "Geographic information system", "Geography", "Geography (Ptolemy)", "Geography in medieval Islam", "Geoinformatics", "Geologic map", "Geologic modelling", "Geology", "Geomathematics", "Geomatics", "Geomorphology", "Geophysics", "George Dow", "George Furnas", "George G. Robertson", "Geostatistics", "Geovisualization", "Gerardus Mercator", "Glaciology", "Graph drawing", "Graph of a function", "Graphic design", "Graphic organizer", "Greek language", "Ground track", "Ground truth", "Guadalajara", "Hammer and pick", "Hanspeter Pfister", "Harry Beck", "Hartmann Schedel", "Health geography", "Herman Moll", "Historical Dictionary of Switzerland", "Historical cartography", "Historical geography", "History of Cartography Project", "History of cartography", "History of geography", "Ho Chi Minh City", "Hotel", "Howard Wainer", "Human body", "Human geography", "Hydrography", "Hydrology", "Ideogram", "Imaging science", "Index of geography articles", "Indian Ocean", "Infographic", "Information science", "Information visualization", "Integrated Authority File", "Integrated geography", "International Geography Olympiad", "International Standard Book Number", "Isidore of Seville", "Italy", "Ivory Coast", "JSTOR", "Jacques Bertin", "Jock D. Mackinlay", "Johannes Werner", "John Brian Harley", "John Wiley & Sons", "Karl Wilhelm Pohlke", "Kassites", "Kluwer Academic Publishers", "Labeling (map design)", "Lance Wyman", "Landscape architecture", "Landscape ecology", "Laser rangefinder", "Latin script", "Latitude", "Lawrence J. Rosenblum", "Library of Congress", "Library of Congress Control Number", "Limnology", "Linguistic map", "List of Graeco-Roman geographers", "List of cartographers", "List of geographical societies", "List of geoscience organizations", "Lithography", "Locator map", "Louis Hennepin", "Magnetic compass", "Magnetic storage", "Manuel Lima", "Map", "Map coloring", "Map projection", "Mappa mundi", "Maps", "Mark Ovenden", "Martin Behaim", "Martin M. Wattenberg", "Martin Waldseem\u00fcller", "Mathematical diagram", "Medical imaging", "Mental image", "Mercator 1569 world map", "Mercator projection", "Meteorology", "Mexico City Metro", "Michael Friendly", "Michael Maltz", "Mining", "Minoan civilization", "Miriah Meyer", "Misleading graph", "Mocha, Yemen", "Molecular graphics", "Monastery", "Monterrey", "Monument", "Mount Bego", "Muhammad al-Idrisi", "Myanmar", "National Archives and Records Administration", "National Diet Library", "National mapping agency", "Nautical chart", "Neuroimaging", "Nicolas de Fer", "Nigel Holmes", "Nippur", "North Star", "Oceanography", "Oceanus", "OpenStreetMap", "Ordnance Survey", "Otto Neurath", "Outline of cartography", "Outline of geography", "Palaeogeography", "Paleoclimatology", "Paper townsite", "Passenger", "Pat Hanrahan", "Patent drawing", "Pedology (soil study)", "Penguin Books", "Photogrammetry", "Photograph", "Photography", "Physical geography", "Phytogeography", "Pictogram", "Pictorial map", "Pictorial maps", "Pinyin", "Planetary cartography", "Plot (graphics)", "Pole star", "Political geography", "Population geography", "Portugal", "Princeton University Press", "Printing", "Printing press", "Ptolemy", "Ptolemy's world map", "Public transport", "Qin (state)", "Quadrant (instrument)", "Quaternary science", "Railway station", "Rand McNally", "Regional geography", "Remote sensing", "River Thames", "Rock Drawings in Valcamonica", "Rocky Mountains", "Roger II of Sicily", "Roman Empire", "Rudolf Modley", "Rugged computer", "Sandy Island (New Caledonia)", "Satellite imagery", "Schematic", "Science", "Scientific modelling", "Scientific visualization", "Scribing (cartography)", "Sebastian M\u00fcnster", "Settlement geography", "Sextant", "Sierra Nevada (Spain)", "Sinusoidal projection", "Skeletal formula", "Software", "Software visualization", "Soil science", "Spatial analysis", "Spatial citizenship", "Star map", "Statistical graphics", "Stuart Card", "Su Song", "Surveying", "Symbology", "TO map", "Table (information)", "Tabula Rogeriana", "Tamara Munzner", "Technical drawing", "Technical illustration", "Telescope", "Terrain", "Thematic map", "Thomas A. DeFanti", "Time geography", "Topographic map", "Topographic mapping", "Topography", "Topological map", "Toponomy", "Toponymy", "Tourist information", "Transcription (linguistics)", "Transliteration", "Trap streets", "Treatise", "Tube map", "United States Geological Survey", "Universalis Cosmographia", "University of Chicago Press", "Urartu", "Urban geography", "Urban rail and metro maps", "User interface", "User interface design", "Val Camonica", "Vector graphics", "Vernier scale", "Virtual world", "Visual analytics", "Visual culture", "Visual perception", "Visualization (computer graphics)", "Visualization (graphics)", "Volume cartography", "Volume rendering", "Wade-Giles", "Warring States period", "Washington Metro", "Watermark", "Weather map", "Werner projection", "William Playfair", "World map", "Writing system", "Zoogeography", "\u00c7atalh\u00f6y\u00fck", "\u2641"], "references": ["http://www.collectionscanada.gc.ca/forgery/002035-3000-e.html", "http://www.hls-dhs-dss.ch/textes/f/F8258.php", "http://archive.aramcoworld.com/issue/200401/mapping.arabia.htm", "http://discovermagazine.com/1999/may/archeologist", "http://encarta.msn.com/encyclopedia_761552030_3/geography.html", "http://au.encarta.msn.com/encyclopedia_781534525/cartography_history_of.html", "http://www.geo.hunter.cuny.edu/~jochen/gtech201/201syllabusSp05.htm", "http://www.geo.hunter.cuny.edu/~jochen/gtech201/lectures/lec6concepts/map%20coordinate%20systems/how%20to%20choose%20a%20projection.htm", "http://www.press.uchicago.edu/books/HOC/HOC_V1/HOC_VOLUME1_chapter4.pdf", "http://quod.lib.umich.edu/p/passages/4761530.0003.008/--deconstructing-the-map?rgn=main;view=fulltext", "http://www.carto.net/", "http://www.cartogis.org/", "http://doi.org/10.1080%2F03085699608592846", "http://www.icaci.org/", "http://www.jstor.org/stable/1151277", "http://www.jstor.org/stable/20065543", "http://www.nacis.org/", "http://www.newberry.org/collections/conbib.html", "http://wiki.openstreetmap.org/wiki/Copyright_Easter_Eggs", "http://www.bl.uk/learning/artimages/maphist/mappinghistory.html", "http://www.soc.org.uk/", "https://www.amazon.com/Mapping-World-Illustrated-History-Cartography/dp/0792265254/ref=pd_sim_b_4", "https://www.britannica.com/biography/Gerardus-Mercator", "https://www.britannica.com/science/Mercator-projection", "https://www.tandfonline.com/doi/abs/10.1559/152304006777323118", "https://www.academia.edu/1154206/Arc%C3%A0_Andrea_2004._The_topographic_engravings_of_the_alpine_rock-art_fields_settlements_and_agricultural_landscapes", "https://persuasivemaps.library.cornell.edu/", "https://www.e-education.psu.edu/geog486/node/1848", "https://oi.uchicago.edu/research/projects/nippur-expedition", "https://www.press.uchicago.edu/books/HOC/HOC_V3_Pt1/HOC_VOLUME3_Part1_chapter10.pdf", "https://catalog.archives.gov/id/10639651", "https://id.loc.gov/authorities/subjects/sh85020515", "https://www.loc.gov/rr/geogmap/guide/gmillgtm.html", "https://www.loc.gov/rr/geogmap/guide/gmilltoc.html", "https://pubs.er.usgs.gov/publication/pp1395", "https://d-nb.info/gnd/4029823-1", "https://id.ndl.go.jp/auth/ndlna/00573134", "https://web.archive.org/web/20070202062403/http://www.antiquemaps.co.uk/contents.html", "https://icaci.org/eduard-imhof-1895-1986/", "https://www.webcitation.org/5kwQdtmEV?url=http://encarta.msn.com/encyclopedia_761552030_3/geography.html", "https://www.webcitation.org/5kwQeQNdg?url=http://au.encarta.msn.com/encyclopedia_781534525/cartography_history_of.html", "https://www.wikidata.org/wiki/Q42515"]}, "Multidimensional panel data": {"categories": ["All articles needing additional references", "Articles needing additional references from December 2008", "Multivariate time series", "Statistical data types"], "title": "Multidimensional panel data", "method": "Multidimensional panel data", "url": "https://en.wikipedia.org/wiki/Multidimensional_panel_data", "summary": "In econometrics, a multidimensional panel data is data of a phenomenon observed over three or more dimensions. This comes in contrast with panel data, observed over two dimensions (typically, time and cross-sections). An example is a data set containing forecasts of one or multiple macroeconomic variables produced by multiple individuals (the first dimension), in multiple series (the second dimension) at multiple times periods (the third dimension) and for multiple horizons (the fourth dimension).", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Cross-sectional study", "Digital object identifier", "Econometrics", "Heteroskedasticity", "International Standard Book Number", "Journal of Econometrics", "Panel analysis", "Panel data", "Regression model", "Survey of Professional Forecasters", "Time series"], "references": ["http://doi.org/10.1016%2F0304-4076(94)01649-K"]}, "Newman\u2013Keuls method": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2014", "CS1 maint: Multiple names: authors list", "Multiple comparisons"], "title": "Newman\u2013Keuls method", "method": "Newman\u2013Keuls method", "url": "https://en.wikipedia.org/wiki/Newman%E2%80%93Keuls_method", "summary": "The Newman\u2013Keuls or Student\u2013Newman\u2013Keuls (SNK) method is a stepwise multiple comparisons procedure used to identify sample means that are significantly different from each other. It was named after Student (1927), D. Newman, and M. Keuls. This procedure is often used as a post-hoc test whenever a significant difference between three or more sample means has been revealed by an analysis of variance (ANOVA). The Newman\u2013Keuls method is similar to Tukey's range test as both procedures use studentized range statistics. Unlike Tukey's range test, the Newman\u2013Keuls method uses different critical values for different pairs of mean comparisons. Thus, the procedure is more likely to reveal significant differences between group means and to commit type I errors by incorrectly rejecting a null hypothesis when it is true. In other words, the Neuman-Keuls procedure is more powerful but less conservative than Tukey's range test.", "images": [], "links": ["Analysis of variance", "Arithmetic mean", "Critical value", "Degrees of freedom (statistics)", "Digital object identifier", "False discovery rate", "Familywise error rate", "International Standard Book Number", "John Tukey", "Mean squared error", "Multiple comparisons", "Null hypothesis", "Post-hoc analysis", "PubMed Identifier", "Sample (statistics)", "Statistical power", "Statistical significance", "Studentized range", "T-test", "Tukey's range test", "Type I errors", "William Sealy Gosset"], "references": ["http://www.wias-berlin.de/people/dickhaus/downloads/MultipleTests-SoSe-2010/keuls1952.pdf", "http://engr.case.edu/ray_soumya/mlrg/controlling_fdr_benjamini95.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/17342955", "http://psycnet.apa.org/journals/bul/110/3/577.pdf", "http://doi.org/10.1002%2Fbimj.200610297", "http://doi.org/10.1007%2Fbf01908269", "http://doi.org/10.1037%2F0033-2909.110.3.577", "http://doi.org/10.1093%2Fbiomet%2F31.1-2.20", "http://doi.org/10.2307%2F2332181", "http://biomet.oxfordjournals.org/content/19/1-2/151.full.pdf+html", "http://biomet.oxfordjournals.org/content/31/1-2/20.full.pdf+html", "https://web.archive.org/web/20141104043438/http://www.wias-berlin.de/people/dickhaus/downloads/MultipleTests-SoSe-2010/keuls1952.pdf"]}, "Noncentral hypergeometric distributions": {"categories": ["Discrete distributions"], "title": "Noncentral hypergeometric distributions", "method": "Noncentral hypergeometric distributions", "url": "https://en.wikipedia.org/wiki/Noncentral_hypergeometric_distributions", "summary": "In statistics, the hypergeometric distribution is the discrete probability distribution generated by picking colored balls at random from an urn without replacement.\nVarious generalizations to this distribution exist for cases where the picking of colored balls is biased so that balls of one color are more likely to be picked than balls of another color.\nThis can be illustrated by the following example. Assume that an opinion poll is conducted by calling random telephone numbers. Unemployed people are more likely to be home and answer the phone than employed people are. Therefore, unemployed respondents are likely to be over-represented in the sample. The probability distribution of employed versus unemployed respondents in a sample of n respondents can be described as a noncentral hypergeometric distribution.\nThe description of biased urn models is complicated by the fact that there is more than one noncentral hypergeometric distribution. Which distribution you get depends on whether items (e.g. colored balls) are sampled one by one in a manner where there is competition between the items, or they are sampled independently of each other.\nThere is widespread confusion about this fact. The name noncentral hypergeometric distribution has been used for two different distributions, and several scientists have used the wrong distribution or erroneously believed that the two distributions were identical.\nThe use of the same name for two different distributions has been possible because these two distributions were studied by two different groups of scientists with hardly any contact with each other.\nAgner Fog (2007, 2008) has suggested that the best way to avoid confusion is to use the name Wallenius' noncentral hypergeometric distribution for the distribution of a biased urn model where a predetermined number of items are drawn one by one in a competitive manner, while the name Fisher's noncentral hypergeometric distribution is used where items are drawn independently of each other, so that the total number of items drawn is known only after the experiment. The names refer to Kenneth Ted Wallenius and R. A. Fisher who were the first to describe the respective distributions.\nFisher's noncentral hypergeometric distribution has previously been given the name extended hypergeometric distribution, but this name is rarely used in the scientific literature, except in handbooks that need to distinguish between the two distributions. Some scientists are strongly opposed to using this name.\nA thorough explanation of the difference between the two noncentral hypergeometric distributions is obviously needed here.", "images": ["https://upload.wikimedia.org/wikipedia/en/2/22/FishersNoncentralHypergeometric1.png", "https://upload.wikimedia.org/wikipedia/en/1/1a/NoncentralHypergeometricCompare1.png", "https://upload.wikimedia.org/wikipedia/en/7/7d/NoncentralHypergeometricCompare2.png", "https://upload.wikimedia.org/wikipedia/en/f/fe/WalleniusNoncentralHypergeometric1.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias (statistics)", "Biased sample", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Competition", "Compound Poisson distribution", "Conditional probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's noncentral hypergeometric distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Odds", "Opinion poll", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poisson process", "Poly-Weibull distribution", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Ronald Fisher", "Sample (statistics)", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Urn problem", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wallenius' noncentral hypergeometric distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.agner.org/random/theory/", "http://doi.org/10.1080%2F03610910701790269"]}, "Star plot": {"categories": ["CS1 German-language sources (de)", "Charts", "Statistical charts and diagrams", "Webarchive template wayback links", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Radar chart", "method": "Star plot", "url": "https://en.wikipedia.org/wiki/Radar_chart", "summary": "A radar chart is a graphical method of displaying multivariate data in the form of a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point. The relative position and angle of the axes is typically uninformative.\nThe radar chart is also known as web chart, spider chart, star chart, star plot, cobweb chart, irregular polygon, polar chart, or Kiviat diagram. It is equivalent to a parallel coordinates plot in polar coordinates.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/09/MER_Star_Plot.gif", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/1/18/Spider_Chart2.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Star_Plot_of_16_cars.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/d/d7/Star_plot_Detail.gif"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Background variables", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Cadillac", "Canonical correlation", "Car", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chart", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Commonality", "Completeness (statistics)", "Confidence interval", "Confounding", "Consumer Reports", "Contingency table", "Continuous probability distribution", "Control chart", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data", "Data collection", "Data set", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Foreground", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Georg von Mayr", "Geostatistics", "Glyph plot", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Harvey Balls", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of graphical methods", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michael Friendly", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "NIST", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal scale", "Ordinary least squares", "Outlier", "Outline of statistics", "Parallel coordinates", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Performance metric", "Permutation test", "Pie chart", "Pivotal quantity", "Plot (graphics)", "Plug-in principle", "Point estimation", "Poisson regression", "Polar area diagram", "Polar coordinates", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quality management", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Sparkline", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spider chart", "Spider diagram", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.math.yorku.ca/SCS/Gallery/milestone/milestone.pdf", "http://www.math.yorku.ca/SCS/sugi/sugi16-paper.html", "http://i-ocean.blogspot.com/2008/08/clock-this.html", "http://i-ocean.blogspot.com/2008/09/reorderable-tables-ii-bertin-versus.html", "http://www.content-workshops.com/toolbox/2015/2/find-content-gaps-using-radar-charts", "http://www.excelcharts.com/blog/charting-around-the-clock/", "http://howtowatchsports.com/spider-graphs-charting-basketball-statistics/", "http://peltiertech.com/WordPress/rock-around-the-clock/", "http://processtrends.com/toc_data_visualization.htm", "http://supportanalytics.com/blog/2007/12/qualitative-comparison/", "http://www.itl.nist.gov/div898/handbook/eda/section3/starplot.htm", "http://www.nist.gov", "http://chandoo.org/wp/2008/09/18/better-radar-charts-excel/", "http://doi.org/10.1145%2F1113644.1113647", "http://openlibrary.org/books/OL23294909M/Die_Gesetzm%C3%A4ssigkeit_im_Gesellschaftsleben", "https://msdn.microsoft.com/en-us/library/dd239337.aspx", "https://web.archive.org/web/20100325233432/http://processtrends.com/toc_data_visualization.htm", "https://web.archive.org/web/20120408192509/http://supportanalytics.com/blog/2007/12/qualitative-comparison/"]}, "Efficient estimator": {"categories": ["All accuracy disputes", "All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from May 2010", "Articles with disputed statements from February 2012", "Articles with unsourced statements from December 2011", "Articles with unsourced statements from February 2012", "Estimator"], "title": "Efficient estimator", "method": "Efficient estimator", "url": "https://en.wikipedia.org/wiki/Efficient_estimator", "summary": "In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some \u201cbest possible\u201d manner. The notion of \u201cbest possible\u201d relies upon the choice of a particular loss function \u2014 the function which quantifies the relative degree of undesirability of estimation errors of different magnitudes. The most common choice of the loss function is quadratic, resulting in the mean squared error criterion of optimality.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Admissible procedure", "Asymptotically", "Bayes estimator", "Bias of an estimator", "Binomial distribution", "Consistent estimator", "Cram\u00e9r\u2013Rao inequality", "Dominating decision rule", "Efficiency (statistics)", "Erich Leo Lehmann", "Estimator", "Exponential family", "Fisher information", "Fisher information matrix", "Hodges\u2019 estimator", "Iid", "International Standard Book Number", "James\u2013Stein estimator", "Johann Pfanzagl", "Loss function", "Mathematical Reviews", "Maximum likelihood", "Mean squared error", "Minimum variance unbiased estimator", "Multinomial distribution", "Multivariate statistics", "Normal distribution", "Parametric model", "Poisson distribution", "Quadratic loss function", "Sample mean", "Statistics", "Variance"], "references": ["http://www.ams.org/mathscinet-getitem?mr=1291393"]}, "Risk adjusted mortality rate": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from November 2011", "Articles needing additional references from November 2011", "Articles with multiple maintenance issues", "Medical aspects of death", "Medical statistics"], "title": "Risk adjusted mortality rate", "method": "Risk adjusted mortality rate", "url": "https://en.wikipedia.org/wiki/Risk_adjusted_mortality_rate", "summary": "The risk adjusted mortality rate (RAMR) is a mortality rate that is adjusted for predicted risk of death. It is usually utilized to observe and/or compare the performance of certain institution(s) or person(s), e.g., hospitals or surgeons.\nIt can be found as:\nRAMR = (Observed Mortality Rate/Predicted Mortality Rate)* Overall (Weighted) Mortality Rate\nIn medical science, RAMR could be a predictor of mortality that takes into account the predicted risk for a group of patients. For example, for a group of patients first we need to find the observed mortality rates for all the hospitals of interest. Then we can build/construct a model or use an existing model to predict mortality rates for each of the hospitals. It is expected that the number of patients in each hospital will be different and hence we need an overall (weighted) mortality rate for all these hospitals. Once we have the above three rates, then we can utilize the above formula to find the risk adjusted mortality rate which will reflect the actual mortality rate of a particular hospital without being biased from the observed mortality.\nIn the English NHS the Summary Hospital-level Mortality Indicator, the Hospital Standardised Mortality Rate and the Risk Adjusted Mortality Index are all used. The BBC produced a table in 2011 comparing mortality on various measures across all NHS acute trusts.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bias", "English NHS", "Hospital", "Medical science", "Mortality rate", "Patient", "Surgeon"], "references": ["http://content.digital.nhs.uk/shmi", "https://www.bbc.co.uk/news/health-15897345?sort1"]}, "Curve fitting": {"categories": ["Commons category link is defined as the pagename", "Geometric algorithms", "Interpolation", "Numerical analysis", "Regression analysis"], "title": "Curve fitting", "method": "Curve fitting", "url": "https://en.wikipedia.org/wiki/Curve_fitting", "summary": "Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a \"smooth\" function is constructed that approximately fits the data. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8c/Big-o-approx-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7f/Curve_fitting.svg", "https://upload.wikimedia.org/wikipedia/commons/4/46/Gohana_inverted_S-curve.png", "https://upload.wikimedia.org/wikipedia/commons/7/73/Regression_circulaire_coope_arc_de_cercle.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b6/Regression_elliptique_distance_algebrique_donnees_gander.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a8/Regression_pic_assymetrique.gif", "https://upload.wikimedia.org/wikipedia/commons/5/55/Wp_ellfitting.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Adjustment of observations", "Agriculture", "Angle", "Approximation", "Arc length", "Best fit", "Big O notation", "Cauchy distribution", "Chord distance", "Cloverleaf interchange", "Collinear points", "Computer representation of surfaces", "Conic sections", "Curvature", "Curve", "Curve-fitting compaction", "Data points", "Digital object identifier", "Distribution fitting", "Estimation theory", "Extrapolation", "False precision", "Fragmentation (computer)", "Function (mathematics)", "Function approximation", "GNU Octave", "GNU Scientific Library", "Gauss\u2013Newton algorithm", "Generalization error", "Goodness of fit", "Inflection point", "International Standard Book Number", "Interpolating spline", "Interpolation", "Jaan Kiusalaas", "Jerk (physics)", "Least squares", "Levenberg\u2013Marquardt algorithm", "Line fitting", "List of numerical analysis software", "List of statistical packages", "MATLAB", "MLAB", "Magnitude (mathematics)", "Maple (software)", "Mathematica", "Mollifier", "Nonlinear regression", "Normal distribution", "Order of approximation", "Ordinary least squares", "Osculating circle", "Overfitting", "Parametric curve", "Plane curve", "Polynomial", "Polynomial interpolation", "Polynomial regression", "R (programming language)", "Range (mathematics)", "Regression analysis", "Runge's phenomenon", "Scale analysis (mathematics)", "SciPy", "Scientific modelling", "Sigmoid function", "Significant figures", "Slope", "Smoothing", "Smoothing spline", "Spline (mathematics)", "Statistical inference", "Taylor series", "The Signal and the Noise", "Time series", "Total least squares", "Trend estimation", "Trigonometric functions", "Uncertainty", "Voigt function"], "references": ["http://people.cas.uab.edu/~mosya/cl/", "http://doi.org/10.1007%2F978-3-540-79246-8_29", "http://doi.org/10.1007%2FBF00939613", "http://doi.org/10.3745%2FJIPS.2008.4.4.153", "http://jips-k.org/dlibrary/JIPS_v04_no4_paper4.pdf", "https://books.google.com.br/books?id=S7d1pjJHsRgC&lpg=PA51&ots=2x1_wUTUxJ&dq=arc-length%20curve%20fitting&pg=PA51#v=onepage&q=arc-length%20curve%20fitting&f=false", "https://books.google.com/books?id=SI-VqAT4_hYC", "https://books.google.com/books?id=hhdVr9F-JfAC", "https://books.google.com/books?id=rJ23LWaZAqsC&pg=PA69", "https://www.waterlog.info/sigmoid.htm", "https://web.archive.org/web/20140313084307/http://jips-k.org/dlibrary/JIPS_v04_no4_paper4.pdf"]}, "Edgeworth series": {"categories": ["Mathematical series", "Statistical approximations"], "title": "Edgeworth series", "method": "Edgeworth series", "url": "https://en.wikipedia.org/wiki/Edgeworth_series", "summary": "The Gram\u2013Charlier A series (named in honor of J\u00f8rgen Pedersen Gram and Carl Charlier), and the Edgeworth series (named in honor of Francis Ysidro Edgeworth) are series that approximate a probability distribution in terms of its cumulants. The series are the same; but, the arrangement of terms (and thus the accuracy of truncating the series) differ. The key idea of these expansions is to write the characteristic function of the distribution whose probability density function f is to be approximated in terms of the characteristic function of a distribution with known and suitable properties, and to recover f through the inverse Fourier transform.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f0/Edgeworth_expansion_of_the_density_of_the_sample_mean_of_three_Chi2_variables.png"], "links": ["Annals of Statistics", "Approximation error", "ArXiv", "Asymptotic expansion", "Bell polynomials", "Bibcode", "Carl Charlier", "Central limit theorem", "Characteristic function (probability theory)", "Cornish\u2013Fisher expansion", "Cumulant", "Cumulative distribution function", "David Cox (statistician)", "Differential operator", "Digital object identifier", "Edgeworth binomial tree", "Encyclopedia of Mathematics", "Eric W. Weisstein", "Fourier transform", "Francis Ysidro Edgeworth", "Gamma distribution", "Harald Cram\u00e9r", "Hermite polynomial", "Independent and identically distributed", "International Standard Book Number", "JSTOR", "J\u00f8rgen Pedersen Gram", "MathWorld", "Michiel Hazewinkel", "Normal distribution", "Ole Barndorff-Nielsen", "Peter McCullagh", "Polynomial", "Probability density function", "Probability distribution", "Series (mathematics)"], "references": ["http://mathworld.wolfram.com/EdgeworthSeries.html", "http://adsabs.harvard.edu/abs/1998A&AS..130..193B", "http://aas.aanda.org/articles/aas/pdf/1998/10/h0596.pdf", "http://arxiv.org/abs/astro-ph/9711239", "http://doi.org/10.1051%2Faas:1998221", "http://doi.org/10.1214%2Faoms%2F1177706528", "http://doi.org/10.1214%2Faos%2F1176347637", "http://doi.org/10.21314%2FJOR.2017.365", "http://www.jstor.org/stable/2242145", "https://www.encyclopediaofmath.org/index.php?title=p/e035060"]}, "Measurement invariance": {"categories": ["All articles to be expanded", "Articles to be expanded from March 2018", "Articles using small message boxes", "CS1 maint: Explicit use of et al.", "Latent variable models", "Psychometrics"], "title": "Measurement invariance", "method": "Measurement invariance", "url": "https://en.wikipedia.org/wiki/Measurement_invariance", "summary": "Measurement invariance or measurement equivalence is a statistical property of measurement that indicates that the same construct is being measured across some specified groups. For example, measurement invariance can be used to study whether a given measure is interpreted in a conceptually similar manner by respondents representing different genders or cultural backgrounds. Violations of measurement invariance may preclude meaningful interpretation of measurement data. Tests of measurement invariance are increasingly used in fields such as psychology to supplement evaluation of measurement quality rooted in classical test theory.Measurement invariance is often tested in the framework of multiple-group confirmatory factor analysis (CFA). In the context of structural equation models, including CFA, measurement invariance is often termed factorial invariance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg"], "links": ["Classical test theory", "Confirmatory factor analysis", "Construct (philosophy of science)", "Differential item functioning", "Digital object identifier", "Factor analysis", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Likelihood ratio test", "PubMed Central", "PubMed Identifier", "Structural equation modeling"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2848495", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4516821", "http://www.ncbi.nlm.nih.gov/pubmed/12741671", "http://www.ncbi.nlm.nih.gov/pubmed/26283995", "http://doi.org/10.1016%2Fs0160-2896(03)00051-5", "http://doi.org/10.1037%2F1082-989x.8.1.16", "http://doi.org/10.1057%2Feps.2011.11", "http://doi.org/10.1086%2F209528", "http://doi.org/10.1111%2Fj.1750-8606.2009.00110.x", "http://doi.org/10.1177%2F109442810031002", "http://doi.org/10.1207%2Fs15328007sem0902_5", "http://doi.org/10.1207%2Fs15328007sem1203_7", "http://doi.org/10.3389%2Ffpsyg.2015.01064", "http://journal.frontiersin.org/article/10.3389/fpsyg.2015.01064/full", "http://www.jstor.org/stable/10.1086/209528", "http://www.worldcat.org/issn/0093-5301", "http://www.worldcat.org/issn/1082-989X", "http://www.worldcat.org/issn/1680-4333", "https://academic.oup.com/jcr/article/25/1/78/1807396", "https://link.springer.com/article/10.1057/eps.2011.11"]}, "Explanatory variable": {"categories": ["Design of experiments", "Independence (probability theory)", "Mathematical terminology", "Regression analysis", "Webarchive template wayback links"], "title": "Dependent and independent variables", "method": "Explanatory variable", "url": "https://en.wikipedia.org/wiki/Dependent_and_independent_variables", "summary": "In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables. The dependent variables represent the output or outcome whose variation is being studied. The independent variables, also known in a statistical context as regressors, represent inputs or causes, that is, potential reasons for variation. In an experiment, any variable that the experimenter manipulates can be called an independent variable. Models and experiments test the effects that the independent variables have on the dependent variables. Sometimes, even if their influence is not of direct interest, independent variables may be included for other reasons, such as to account for their potential confounding effect.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f8/Polynomialdeg2.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg"], "links": ["Abscissa", "Bias (statistics)", "Blocking (statistics)", "Calculus", "Cartesian product", "Confounding", "Control variable", "Covariance", "Data mining", "Dependent variable", "Design of experiments", "Digital object identifier", "Econometrics", "Errors and residuals", "Experimental science", "Feature (machine learning)", "Function (mathematics)", "Goodness of fit", "Graph of a function", "Horizontal axis", "Hypothesis", "Independence (probability theory)", "International Standard Book Number", "Linear model", "Machine learning", "Manifold (mathematics)", "Mathematical modeling", "Medical statistics", "Multivariable calculus", "Multivariate statistics", "Omitted variable bias", "Ordinate", "Pattern recognition", "Prediction", "RapidMiner", "Reliability theory", "Risk factor", "Set (mathematics)", "Set theory", "Simulation", "Statistical model", "Stochastic", "Subset", "Supervised learning", "Test data", "Variable and attribute (research)", "Vector-valued functions", "Vertical axis", "Wayback Machine"], "references": ["http://1xltkxylmzx3z8gd647akcdvov.wpengine.netdna-cdn.com/wp-content/uploads/2013/10/rapidminer-5.0-manual-english_v1.0.pdf", "http://onlinestatbook.com/2/introduction/variables.html", "http://doi.org/10.1080%2F15210608709379549", "https://web.archive.org/web/20140210002634/http://1xltkxylmzx3z8gd647akcdvov.wpengine.netdna-cdn.com/wp-content/uploads/2013/10/rapidminer-5.0-manual-english_v1.0.pdf"]}, "Step detection": {"categories": ["Change detection", "Feature detection (computer vision)", "Nonlinear filters", "Statistical signal processing"], "title": "Step detection", "method": "Step detection", "url": "https://en.wikipedia.org/wiki/Step_detection", "summary": "In statistics and signal processing, step detection (also known as step smoothing, step filtering, shift detection, jump detection or edge detection) is the process of finding abrupt changes (steps, jumps, shifts) in the mean level of a time series or signal. It is usually considered as a special case of the statistical method known as change detection or change point detection. Often, the step is small and the time series is corrupted by some kind of noise, and this makes the problem challenging because the step may be hidden by the noise. Therefore, statistical and/or signal processing algorithms are often required.\nThe step detection problem occurs in multiple scientific and engineering contexts, for example in statistical process control (the control chart being the most directly related method), in exploration geophysics (where the problem is to segment a well-log recording into stratigraphic zones), in genetics (the problem of separating microarray data into similar copy-number regimes), and in biophysics (detecting state transitions in a molecular machine as recorded in time-position traces). For 2D signals, the related problem of edge detection has been studied intensively for image processing.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/5/56/Step_signal.png"], "links": ["Bandwidth (signal processing)", "Bibcode", "Bilateral filter", "Biophysics", "CUSUM", "Change detection", "Control chart", "Convex function", "Convex optimization", "Copy-number variation", "Cosmic ray", "DNA microarray", "Digital object identifier", "Edge detection", "Fourier transform", "Genetics", "Geophysics", "Hidden Markov Models", "Image processing", "K-means clustering", "Level set", "Low pass filter", "Markov chain", "Mean-shift", "Mean shift", "Median filter", "Microarray", "Molecular machine", "Molecular motors", "Neutron monitor", "Noise", "Nonlinear filter", "Online algorithm", "Piecewise constant", "Proceedings of the Royal Society A", "PubMed Central", "PubMed Identifier", "Rhodobacter sphaeroides", "Sequential analysis", "Signal processing", "Spline (mathematics)", "Statistical process control", "Statistics", "Stratigraphy", "Student's t-test", "Time-series segmentation", "Time series", "Total variation denoising", "Wavelet", "Well logging"], "references": ["http://pottslab.de/", "http://adsabs.harvard.edu/abs/2003InvPr..19S.165S", "http://adsabs.harvard.edu/abs/2005Natur.437..916S", "http://adsabs.harvard.edu/abs/2006Natur.442..709K", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1544307", "http://www.ncbi.nlm.nih.gov/pubmed/11687795", "http://www.ncbi.nlm.nih.gov/pubmed/16208378", "http://www.ncbi.nlm.nih.gov/pubmed/16766620", "http://www.beringclimate.noaa.gov/regimes/rodionov_overview.pdf", "http://www.maxlittle.net/software/", "http://doi.org/10.1038%2Fnature04003", "http://doi.org/10.1038%2Fnature04928", "http://doi.org/10.1038%2Fng754", "http://doi.org/10.1088%2F0266-5611%2F19%2F6%2F059", "http://doi.org/10.1093%2Fbiomet%2F42.3-4.523", "http://doi.org/10.1098%2Frspa.2010.0671", "http://doi.org/10.1109%2F18.119727", "http://doi.org/10.1306%2F5d25ca35-16c1-11d7-8645000102c1865d", "http://doi.org/10.1529%2Fbiophysj.106.082487", "http://rspa.royalsocietypublishing.org/content/467/2135/3088.short"]}, "Poincar\u00e9 plot": {"categories": ["All stub articles", "Applied mathematics stubs", "Chaos theory", "Dynamical systems", "Scaling symmetries", "Statistical charts and diagrams"], "title": "Poincar\u00e9 plot", "method": "Poincar\u00e9 plot", "url": "https://en.wikipedia.org/wiki/Poincar%C3%A9_plot", "summary": "A Poincar\u00e9 plot, named after Henri Poincar\u00e9, is a species of recurrence plot used to quantify self-similarity in processes, usually periodic functions. It is also known as a return map. Poincar\u00e9 plots can be used to distinguish chaos from randomness by embedding a data set into a higher-dimensional state space.\nGiven a time series of the form\n\n \n \n \n \n x\n \n t\n \n \n ,\n \n x\n \n t\n +\n 1\n \n \n ,\n \n x\n \n t\n +\n 2\n \n \n ,\n \u2026\n ,\n \n \n {\\displaystyle x_{t},x_{t+1},x_{t+2},\\ldots ,}\n a return map in its simplest form first plots (xt, xt+1), then plots (xt+1, xt+2), then (xt+2, xt+3), and so on.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a3/Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a3/20120917204659%21Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a3/20100506100358%21Arithmetic_symbols.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a3/20070526080805%21Arithmetic_symbols.svg"], "links": ["Applied mathematics", "Atrium (heart)", "Autonomic nervous system", "Chaos theory", "Depolarization", "Digital object identifier", "Electrocardiogram", "Heart rate", "Heart rate turbulence", "Heart rate variability", "Henri Poincar\u00e9", "International Standard Serial Number", "Periodic function", "Poincar\u00e9 map", "PubMed Central", "PubMed Identifier", "Recurrence plot", "Repolarization", "Self-similarity", "Sinoatrial node", "State space", "Ventricle (heart)"], "references": ["http://users.math.yale.edu/public_html/People/frame/Fractals/Chaos/ReturnMap/ReturnExpl.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4368686", "http://www.ncbi.nlm.nih.gov/pubmed/10618303", "http://www.ncbi.nlm.nih.gov/pubmed/25793605", "http://circ.ahajournals.org/cgi/content/full/101/1/47", "http://doi.org/10.1161%2F01.CIR.101.1.47", "http://doi.org/10.1371%2Fjournal.pone.0118504", "http://www.worldcat.org/issn/1524-4539", "http://www.worldcat.org/issn/1932-6203", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4368686/", "https://www.researchgate.net/publication/316061441", "https://web.archive.org/web/20110722032226/http://www.cbi.dongnocchi.it/glossary/ReturnMap.html", "https://physionet.org/physiotools/mpp/"]}, "Poisson random numbers": {"categories": ["All articles with unsourced statements", "Articles with example pseudocode", "Articles with unsourced statements from April 2012", "Articles with unsourced statements from May 2012", "Articles with unsourced statements from May 2018", "Conjugate prior distributions", "Factorial and binomial topics", "Infinitely divisible probability distributions", "Pages using deprecated image syntax", "Poisson distribution", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers"], "title": "Poisson distribution", "method": "Poisson random numbers", "url": "https://en.wikipedia.org/wiki/Poisson_distribution", "summary": "In probability theory and statistics, the Poisson distribution (French pronunciation: \u200b[pwas\u0254\u0303]; in English often rendered ), named after French mathematician Sim\u00e9on Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume.\nFor instance, an individual keeping track of the amount of mail they receive each day may notice that they receive an average number of 4 letters per day. If receiving any particular piece of mail does not affect the arrival times of future pieces of mail, i.e., if pieces of mail from a wide range of sources arrive independently of one another, then a reasonable assumption is that the number of pieces of mail received in a day obeys a Poisson distribution. Other examples that may follow a Poisson include the number of phone calls received by a call center per hour and the number of decay events per second from a radioactive source.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fb/Binomial_versus_poisson.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7c/Poisson_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/1/16/Poisson_pmf.svg"], "links": ["ARGUS distribution", "Abraham de Moivre", "Addison Wesley", "Admissible decision rule", "Agner Krarup Erlang", "Anscombe transform", "Arcsine distribution", "Astronomy", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bayesian inference", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli trial", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biology", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "C (programming language)", "Call centre", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Causal Set", "Cell membrane", "Cells (biology)", "Characteristic function (probability theory)", "Chemistry", "Chernoff bound", "Chi-square distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Coefficient of variation", "Combinatorics", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Conjugate prior", "Continuity correction", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation", "Coverage probability", "Cram\u00e9r\u2013Rao lower bound", "Cumulant", "Cumulative distribution function", "DNA", "Dagum distribution", "Data transformation (statistics)", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Dobinski's formula", "Donald Knuth", "E (mathematical constant)", "Earthquake seismology", "Electric current", "Elementary charge", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exact statistics", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Factorial", "Factorial moment", "Finance and insurance", "Fisher's z-distribution", "Fisher information", "Floor function", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fortran", "France", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Generating function", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Guinness", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hermite distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "I. J. Good", "Incomplete gamma function", "Index of dispersion", "Infinite divisibility (probability)", "Information entropy", "Integrated Authority File", "International Agency for Research on Cancer", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverse transform sampling", "Irwin\u2013Hall distribution", "JSTOR", "John Nelder", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the Royal Statistical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kullback\u2013Leibler divergence", "Kumaraswamy distribution", "Ladislaus Bortkiewicz", "Landau distribution", "Laplace distribution", "Library of Congress Control Number", "List of probability distributions", "Living polymerization", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Luc Devroye", "L\u00e9vy distribution", "MATLAB", "Management", "Marchenko\u2013Pastur distribution", "Mathematica", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mean absolute deviation", "Median", "Minimax estimator", "Minimum-variance unbiased estimator", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Molar mass distribution", "Moment-generating function", "Moment (mathematics)", "Multinomial distribution", "Multiplicity of infection", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Mutation", "Nakagami distribution", "National Diet Library", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nick Day", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Norman Breslow", "Parabolic fractal distribution", "Pareto distribution", "Partition of a set", "Pearson distribution", "Peter McCullagh", "Phase-type distribution", "Photons", "Poisson binomial distribution", "Poisson clumping", "Poisson distribution", "Poisson limit theorem", "Poisson point process", "Poisson process", "Poisson regression", "Poisson sampling", "Poisson wavelet", "Poly-Weibull distribution", "Posterior predictive distribution", "Prime number", "Probability-generating function", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Prussia", "Pseudo-random number sampling", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quantile function", "Queueing theory", "R (programming language)", "Rademacher distribution", "Radioactivity", "Raikov's theorem", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Receptor (biochemistry)", "Reciprocal distribution", "Rectified Gaussian distribution", "Rejection sampling", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Renewal theory", "Rice distribution", "Robbins lemma", "Scale parameter", "Scaled inverse chi-squared distribution", "SciPy", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Shot noise", "Silver", "Sim\u00e9on Denis Poisson", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Space", "Special case", "Stable distribution", "Standard deviation", "Standard normal deviate", "Statistical independence", "Statistics", "Stein's example", "Stigler's law", "Stirling numbers of the second kind", "Student's t-distribution", "Student center", "Sufficient statistic", "Support (mathematics)", "Telecommunication", "The Art of Computer Programming", "Time", "Touchard polynomials", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Unbiased estimator", "Uniform distribution (continuous)", "Upper incomplete gamma function", "V-1 flying bomb", "Variance", "Variance-gamma distribution", "Variance-stabilizing transformation", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Web server", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "William Sealy Gosset", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zero-inflated model", "Zero-truncated Poisson distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.sciencedirect.com/science/article/pii/0167715282900104", "http://www.sciencedirect.com/science/article/pii/S0167668714001279", "http://www.vosesoftware.com/ModelRiskHelp/index.htm#Probability_theory_and_statistics/Stochastic_processes/Some_Poisson_models.htm", "http://reference.wolfram.com/language/ref/MultivariatePoissonDistribution.html", "http://reference.wolfram.com/language/ref/PoissonDistribution.html", "http://www.umass.edu/wsp/resources/poisson/index.html", "http://www.iarc.fr/en/publications/pdfs-online/stat/sp82/index.php", "http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc331.htm", "http://www.sportsbettingonline.net/strategy/football-prediction-model-poisson-distribution/", "http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7266644", "http://cnx.org/content/m13500/latest/?collection=col10343/latest", "http://luc.devroye.org/chapter_ten.pdf", "http://luc.devroye.org/rnbookindex.html", "http://doi.org/10.1007%2FBF02293108", "http://doi.org/10.1016%2F0167-7152(82)90010-4", "http://doi.org/10.1016%2Fj.insmatheco.2014.09.012", "http://doi.org/10.1021%2Fja01863a066", "http://doi.org/10.1080%2F00031305.1984.10483195", "http://doi.org/10.1080%2F01621459.1975.10482497", "http://doi.org/10.1080%2F03610926.2014.901375", "http://doi.org/10.1093%2Fbiomet%2F28.3-4.437", "http://doi.org/10.1112%2Fs0025579300016442", "http://doi.org/10.1137%2F1030059", "http://doi.org/10.1145%2F355993.355997", "http://doi.org/10.1214%2Faoms%2F1177732430", "http://doi.org/10.2307%2F1403045", "http://doi.org/10.2307%2F2340091", "http://doi.org/10.2307%2F2530708", "http://doi.org/10.3844%2Famjbsp.2013.17.29", "http://www.jstor.org/stable/10.2307/2340091", "http://www.jstor.org/stable/1403045", "http://www.jstor.org/stable/2530708", "http://www.proofwiki.org/wiki/Expectation_of_Poisson_Distribution", "http://www.proofwiki.org/wiki/Variance_of_Poisson_Distribution", "http://www.rasch.org/memo1963.pdf", "https://books.google.com/?id=SKUXe_PjtRMC&pg=PA5&dq=%22law+of+rare+events%22+poisson#v=onepage&q=%22law%20of%20rare%20events%22%20poisson&f=false", "https://books.google.com/books?id=o_k3AAAAMAAJ&pg=PA1#v=onepage&q&f=false", "https://books.google.com/books?id=o_k3AAAAMAAJ&pg=PA23#v=onepage&q&f=false", "https://books.google.com/books?id=uovoFE3gt2EC&pg=PA206#v=onepage&q&f=false", "https://www.wired.com/2012/12/what-does-randomness-look-like/", "https://id.loc.gov/authorities/subjects/sh85103956", "https://d-nb.info/gnd/4253010-6", "https://id.ndl.go.jp/auth/ndlna/00569122", "https://arxiv.org/pdf/1502.01975v1.pdf,", "https://www.cambridge.org/core/journals/journal-of-the-institute-of-actuaries/article/an-application-of-the-poisson-distribution/F75111847FDA534103BD4941BD96A78E", "https://cran.r-project.org/web/packages/KFAS/vignettes/KFAS.pdf", "https://www.wikidata.org/wiki/Q205692"]}, "Quantum (Statistical programming language)": {"categories": ["All articles needing additional references", "All articles with topics of unclear notability", "Articles needing additional references from February 2009", "Articles with multiple maintenance issues", "Articles with topics of unclear notability from February 2009", "Products articles with topics of unclear notability", "Statistical programming languages", "Statistical survey software"], "title": "Quantum (statistical programming language)", "method": "Quantum (Statistical programming language)", "url": "https://en.wikipedia.org/wiki/Quantum_(statistical_programming_language)", "summary": "Quantum is a software package and programming language for statistical survey data validation and manipulation and tabulation. Originally developed by Quantime to run on Unix systems, it was incorporated into SPSS Inc.'s SPSS MR product line [1] after its acquisition of Quantime on September 1997.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Application software", "Data validation", "Freeware", "Programming language", "Quantime", "SPSS Inc.", "Statistical survey", "Tabulation"], "references": ["http://findarticles.com/p/articles/mi_m0EIN/is_1997_Sept_11/ai_19742267", "http://scholar.google.com/scholar?q=%22Quantum%22+statistical+programming+language", "http://www.google.com/search?&q=%22Quantum%22+statistical+programming+language+site:news.google.com/newspapers&source=newspapers", "http://www.google.com/search?as_eq=wikipedia&q=%22Quantum%22+statistical+programming+language&num=50", "http://www.google.com/search?tbm=nws&q=%22Quantum%22+statistical+programming+language+-wikipedia", "http://www.google.com/search?tbs=bks:1&q=%22Quantum%22+statistical+programming+language+-wikipedia", "http://www.spss.com/products/result.cfm?keybrand_id=21&type=keybrands", "https://web.archive.org/web/20070626153616/http://investor.spss.com/phoenix.zhtml?c=118415&p=irol-newsArticle_Print&ID=519136&highlight=", "https://web.archive.org/web/20080209194624/http://pan-data.dyndns.org/ccount/", "https://www.jstor.org/action/doBasicSearch?Query=%22Quantum%22+statistical+programming+language&acc=on&wc=on"]}, "Chernoff's inequality": {"categories": ["Probabilistic inequalities"], "title": "Chernoff bound", "method": "Chernoff's inequality", "url": "https://en.wikipedia.org/wiki/Chernoff_bound", "summary": "In probability theory, the Chernoff bound, named after Herman Chernoff but due to Herman Rubin, gives exponentially decreasing bounds on tail distributions of sums of independent random variables. It is a sharper bound than the known first- or second-moment-based tail bounds such as Markov's inequality or Chebyshev's inequality, which only yield power-law bounds on tail decay. However, the Chernoff bound requires that the variates be independent \u2013 a condition that neither Markov's inequality nor Chebyshev's inequality require, although Chebyshev's inequality does require the variates to be pairwise independent.\nIt is related to the (historically prior) Bernstein inequalities and to Hoeffding's inequality.", "images": [], "links": ["Andreas Winter", "Annals of Mathematical Statistics", "Annals of Probability", "Approximation error", "ArXiv", "Avner Magen", "Bernoulli distribution", "Bernoulli random variable", "Bernstein inequalities (probability theory)", "Chebyshev's inequality", "Computational learning theory", "Concentration inequality", "Convex function", "Cumulative distribution function", "Digital object identifier", "Entropic value at risk", "Herman Chernoff", "Hoeffding's inequality", "I.i.d.", "IEEE Transactions on Information Theory", "Information Processing Letters", "International Standard Book Number", "JSTOR", "Jane-Ling Wang", "Journal of the American Statistical Association", "Kullback\u2013Leibler divergence", "Markov's inequality", "Mathematical Reviews", "Matrix Chernoff bound", "Network congestion", "Packet (information technology)", "Probability theory", "Probably approximately correct learning", "Routing", "Rudolf Ahlswede", "Sergei Bernstein", "Set balancing", "Sparse graph", "Statistical independence", "Wassily Hoeffding", "Zentralblatt MATH"], "references": ["http://www.crcpress.com/product/isbn/9781482204964", "http://www.cs.berkeley.edu/~sinclair/cs271/n13.pdf", "http://www.ams.org/mathscinet-getitem?mr=0057518", "http://www.ams.org/mathscinet-getitem?mr=0614640", "http://arxiv.org/abs/1004.4389", "http://arxiv.org/abs/1005.2724", "http://arxiv.org/abs/1102.2684", "http://arxiv.org/abs/quant-ph/0012127", "http://arxiv.org/archive/cs.DM", "http://arxiv.org/archive/cs.IT", "http://doi.org/10.1007%2F3-540-44676-1_35", "http://doi.org/10.1007%2Fs10208-011-9099-z", "http://doi.org/10.1016%2F0020-0190(90)90214-I", "http://doi.org/10.1109%2F18.985947", "http://doi.org/10.1214%2Faoms%2F1177729330", "http://doi.org/10.1214%2Faop%2F1176994428", "http://doi.org/10.2307%2F2282952", "http://www.jstor.org/stable/2236576", "http://www.jstor.org/stable/2243541", "http://www.jstor.org/stable/2282952", "http://nisla05.niss.org/copss/past-present-future-copss.pdf", "http://zbmath.org/?format=complete&q=an:0048.11804", "http://zbmath.org/?format=complete&q=an:0457.60014", "https://www.desmos.com/calculator/eqvyjug0re", "https://www.desmos.com/calculator/nxurzg7bqj", "https://books.google.com/books?id=0bAYl6d7hvkC", "https://books.google.com/books?id=0bAYl6d7hvkC&printsec=frontcover&source=gbs_summary_r&cad=0#PPA71,M1", "https://books.google.com/books?id=0bAYl6d7hvkC&printsec=frontcover&source=gbs_summary_r&cad=0#PPA72,M1"]}, "Sparsity-of-effects principle": {"categories": ["Design of experiments", "Statistical principles"], "title": "Sparsity-of-effects principle", "method": "Sparsity-of-effects principle", "url": "https://en.wikipedia.org/wiki/Sparsity-of-effects_principle", "summary": "In the statistical analysis of the results from factorial experiments, the sparsity-of-effects principle states that a system is usually dominated by main effects and low-order interactions. Thus it is most likely that main (single factor) effects and two-factor interactions are the most significant responses in a factorial experiment. In other words, higher order interactions such as three-factor interactions are very rare. This is sometimes referred to as the hierarchical ordering principle. The sparsity-of-effects principle actually refers to the idea that only a few effects in a factorial experiment will be statistically significant.This principle is only valid on the assumption of a factor space far from a stationary point.", "images": [], "links": ["C.F. Jeff Wu", "Factorial experiment", "George E. P. Box", "Interaction (statistics)", "International Standard Book Number", "Main effect", "Occam's Razor", "Pareto principle", "Statistics"], "references": []}, "Linear discriminant analysis": {"categories": ["All articles with dead external links", "Articles with dead external links from December 2017", "Articles with permanently dead external links", "CS1 maint: Archived copy as title", "Classification algorithms", "Market research", "Market segmentation", "Statistical classification", "Wikipedia articles needing clarification from April 2012", "Wikipedia articles needing page number citations from April 2012"], "title": "Linear discriminant analysis", "method": "Linear discriminant analysis", "url": "https://en.wikipedia.org/wiki/Linear_discriminant_analysis", "summary": "Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.\nLDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (i.e. the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain a categorical variable by the values of continuous independent variables. These other methods are preferable in applications where it is not reasonable to assume that the independent variables are normally distributed, which is a fundamental assumption of the LDA method.\nLDA is also closely related to principal component analysis (PCA) and factor analysis in that they both look for linear combinations of variables which best explain the data. LDA explicitly attempts to model the difference between the classes of data. PCA on the other hand does not take into account any difference in class, and factor analysis builds the feature combinations based on differences rather than similarities. Discriminant analysis is also different from factor analysis in that it is not an interdependence technique: a distinction between independent variables and dependent variables (also called criterion variables) must be made.\nLDA works when the measurements made on independent variables for each observation are continuous quantities. When dealing with categorical independent variables, the equivalent technique is discriminant correspondence analysis.Discriminant analysis is used when groups are known a priori (unlike in cluster analysis). Each case must have a score on one or more quantitative predictor measures, and a score on a group measure. In simple terms, discriminant function analysis is classification - the act of distributing things into groups, classes or categories of the same type.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/46/R._A._Fischer.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA", "Accelerated failure time model", "Actuarial science", "Affine transformation", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Eugenics", "Anomaly detection", "ArXiv", "Arithmetic mean", "Artificial intelligence", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Asymptotic theory (statistics)", "Autocorrelation", "Autoencoder", "Automated machine learning", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "BIRCH", "Bankruptcy prediction", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bias-variance dilemma", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Boosting (machine learning)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box's M test", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brian Ripley", "C. R. Rao", "CURE data clustering algorithm", "Calyampudi Radhakrishna Rao", "Canonical coordinates", "Canonical correlation", "Canonical correlation analysis", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational learning theory", "Concentration of measure", "Conditional random field", "Conference on Neural Information Processing Systems", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous variable", "Control chart", "Convolutional neural network", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curse of dimensionality", "DBSCAN", "Data collection", "Data mining", "Decision tree learning", "Decomposition of time series", "DeepDream", "Deep learning", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension reduction", "Dimensionality reduction", "Divergence (statistics)", "Dot product", "Durbin\u2013Watson statistic", "Econometrics", "Edward Altman", "Effect size", "Efficiency (statistics)", "Eigenfaces", "Eigenvalue", "Eigenvalue, eigenvector and eigenspace", "Eigenvalues and eigenvectors", "Eigenvector", "Elliptical distribution", "Empirical distribution function", "Empirical risk minimization", "Engineering statistics", "Ensemble learning", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expectation\u2013maximization algorithm", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Facial recognition system", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feature engineering", "Feature learning", "Features (pattern recognition)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gated recurrent unit", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of artificial intelligence", "Goodness of fit", "Grammar induction", "Granger causality", "Graphical model", "Grouped data", "Handle System", "Harmonic mean", "Hermitian matrix", "Heteroscedasticity", "Hidden Markov model", "Hierarchical clustering", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedastic", "Homoscedasticity", "Hyperplane", "IEEE Transactions on Pattern Analysis and Machine Intelligence", "Independent component analysis", "Independent variables", "Index of dispersion", "Instrumental variable", "Interaction (statistics)", "International Conference on Machine Learning", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Machine Learning Research", "Journal of the American Statistical Association", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kernel Fisher discriminant analysis", "Kernel trick", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latent Dirichlet allocation", "Latent variable", "Learning to rank", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear Discriminant Analysis", "Linear classifier", "Linear combination", "Linear regression", "Linear subspace", "List of datasets for machine-learning research", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local outlier factor", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logarithmically concave measure", "Logistic regression", "Logit", "Long short-term memory", "Loss function", "Lp space", "M-estimator", "MANOVA", "Machine Learning (journal)", "Machine learning", "Mann\u2013Whitney U test", "Marketing", "Mathematical Reviews", "Maximum a posteriori", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McNemar's test", "Mean", "Mean-shift", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multicollinearity", "Multidimensional scaling", "Multilayer perceptron", "Multiple comparisons", "Multiple discriminant analysis", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Naive Bayes classifier", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-negative matrix factorization", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "OPTICS algorithm", "Observational study", "Occam learning", "Official statistics", "One- and two-tailed tests", "Online machine learning", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Otsu's method", "Outline of machine learning", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pattern recognition", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perceptron", "Perceptual mapping", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Positioning (marketing)", "Posterior probability", "Power (statistics)", "Prediction interval", "Preference regression", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probably approximately correct learning", "Probit regression", "Product management", "Proportional hazards model", "Pseudo inverse", "Psychometrics", "PubMed Central", "Q-learning", "Quadratic classifier", "Quality control", "Quantitative marketing research", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R language", "Radar chart", "Random assignment", "Random forest", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recurrent neural network", "Regression analysis", "Regression model validation", "Reinforcement learning", "Relevance vector machine", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted Boltzmann machine", "Robust regression", "Robust statistics", "Ronald A. Fisher", "Ronald Fisher", "Run chart", "SAS programming language", "SPSS", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Self-organizing map", "Semi-supervised learning", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shrinkage estimator", "Sign test", "Signal-to-noise ratio", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social salience", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "State\u2013action\u2013reward\u2013state\u2013action", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical survey", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Structured prediction", "Student's t-test", "Sufficient statistic", "Supervised learning", "Support vector machine", "Surface normal", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-distributed stochastic neighbor embedding", "Talagrand's concentration inequality", "Temporal difference learning", "Time domain", "Time series", "Tolerance interval", "Training set", "Trend estimation", "U-Net", "U-statistic", "Uniformly most powerful test", "Unsupervised learning", "V-statistic", "Vapnik\u2013Chervonenkis theory", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Wilks' lambda distribution", "YouTube", "Z-Score Financial Analysis Tool", "Z-test"], "references": ["http://ajbasweb.com/old/ajbas/2010/564-576.pdf", "http://people.revoledu.com/kardi/tutorial/LDA/", "http://people.revoledu.com/kardi/tutorial/LDA/index.html", "http://www.sciencedirect.com/science/article/pii/S0031320314005214", "http://www.sciencedirect.com/science/article/pii/S0047259X00919249", "http://www.sciencedirect.com/science/article/pii/S0047259X01920342", "http://www.psychometrica.de/lds.html", "http://www.psychstat.missouristate.edu/multibook/mlt03m.html", "http://www2.chass.ncsu.edu/garson/pa765/discrim.htm", "http://www.ece.osu.edu/~aleix/pami01.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.9904", "http://userwww.sfsu.edu/~efc/classes/biol710/discrim/discrim.pdf", "http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-4389.pdf", "http://www.utdallas.edu/~herve/Abdi-DCA2007-pretty.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2976202", "http://www.alglib.net/dataanalysis/lineardiscriminantanalysis.php", "http://hdl.handle.net/2440%2F15227", "http://www.ams.org/mathscinet-getitem?mr=0999675", "http://www.ams.org/mathscinet-getitem?mr=1190469", "http://www.ams.org/mathscinet-getitem?mr=1802993", "http://arxiv.org/abs/0903.2003", "http://doi.org/10.1006%2Fjmva.2000.1924", "http://doi.org/10.1006%2Fjmva.2001.2034", "http://doi.org/10.1016%2Fj.patcog.2014.12.012", "http://doi.org/10.1016%2Fj.patrec.2004.08.005", "http://doi.org/10.1016%2Fs0031-3203(00)00162-x", "http://doi.org/10.1016%2Fs0169-2607(02)00011-1", "http://doi.org/10.1109%2F34.908974", "http://doi.org/10.1109%2F72.572105", "http://doi.org/10.1109%2FNNSP.1999.788121", "http://doi.org/10.1109%2FTIFS.2016.2569061", "http://doi.org/10.1111%2Fj.1469-1809.1936.tb02137.x", "http://doi.org/10.1128%2Faem.00726-10", "http://doi.org/10.1128%2Faem.01589-09", "http://doi.org/10.1214%2F09-aoas277", "http://doi.org/10.2307%2F2289860", "http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=572105&url=http%253A%252F%252Fieeexplore.ieee.org%252Fiel4%252F72%252F12383%252F00572105", "http://www.jstor.org/stable/2289860", "http://www.jstor.org/stable/2983775", "http://projecteuclid.org/euclid.aoas/1273584465", "http://www.worldcat.org/issn/0167-8655", "http://www.worldcat.org/issn/1045-9227", "https://github.com/mhaghighat/dcaFuse", "https://www.youtube.com/watch?v=azXCzI57Yfc", "https://www.researchgate.net/publication/326592545_Correction_of_AI_systems_by_linear_discriminants_Probabilistic_foundations", "https://web.archive.org/web/20080312065328/http://www2.chass.ncsu.edu/garson/pA765/discrim.htm", "https://web.archive.org/web/20150405124836/http://biostat.katerynakon.in.ua/en/prognosis/discriminant-analysis.html", "https://arxiv.org/list/cs.LG/recent", "https://arxiv.org/pdf/0906.2530.pdf", "https://arxiv.org/pdf/1011.0943.pdf", "https://dx.doi.org/10.1016/j.patrec.2004.08.005"]}, "Location test": {"categories": ["All articles lacking sources", "Articles lacking sources from August 2009", "Statistical tests"], "title": "Location test", "method": "Location test", "url": "https://en.wikipedia.org/wiki/Location_test", "summary": "A location test is a statistical hypothesis test that compares the location parameter of a statistical population to a given constant, or that compares the location parameters of two statistical populations to each other. Most commonly, the location parameter (or parameters) of interest are expected values, but location tests based on medians or other measures of location are also used.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anova", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Barnard's test", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Binomial test", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's exact test", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis test", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nominal data", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon rank-sum test", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Variable-order Bayesian network": {"categories": ["Bayesian networks", "CS1 errors: dates", "Markov models"], "title": "Variable-order Bayesian network", "method": "Variable-order Bayesian network", "url": "https://en.wikipedia.org/wiki/Variable-order_Bayesian_network", "summary": "Variable-order Bayesian network (VOBN) models provide an important extension of both the Bayesian network models and the variable-order Markov models. VOBN models are used in machine learning in general and have shown great potential in bioinformatics applications.\nThese models extend the widely used position weight matrix (PWM) models, Markov models, and Bayesian network (BN) models.\nIn contrast to the BN models, where each random variable depends on a fixed subset of random variables, in VOBN models these subsets may vary based on the specific realization of observed variables. The observed realizations are often called the context and, hence, VOBN models are also known as context-specific Bayesian networks.\nThe flexibility in the definition of conditioning subsets of variables turns out to be a real advantage in classification and analysis applications, as the statistical dependencies between random variables in a sequence of variables (not necessarily adjacent) may be taken into account efficiently, and in a position-specific and context-specific manner.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["Artificial intelligence", "Bayesian network", "Bioinformatics", "Digital object identifier", "Examples of Markov chains", "Machine learning", "Markov chain", "Markov chain Monte Carlo", "Markov model", "Markov process", "Position weight matrix", "PubMed Central", "PubMed Identifier", "Semi-Markov process", "Variable-order Markov models", "Variable order Markov models"], "references": ["http://www.informatik.uni-trier.de/~ley/db/conf/uai/uai1996.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1538886", "http://www.ncbi.nlm.nih.gov/pubmed/15797905", "http://www.ncbi.nlm.nih.gov/pubmed/16845064", "http://www.eng.tau.ac.il/~bengal/VOMBAT.pdf", "http://doi.org/10.1093%2Fbioinformatics%2Fbti410", "http://doi.org/10.1093%2Fnar%2Fgkl212", "http://bioinformatics.oxfordjournals.org/cgi/reprint/bti410?ijkey=KkxNhRdTSfvtvXY&keytype=ref", "https://www2.informatik.uni-halle.de:8443/VOMBAT/"]}, "Quantitative research": {"categories": ["All articles needing additional references", "All articles needing expert attention", "Articles needing additional references from May 2009", "Articles needing expert attention from November 2009", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "CS1 maint: Multiple names: authors list", "Quantitative research", "Sociology articles needing expert attention"], "title": "Quantitative research", "method": "Quantitative research", "url": "https://en.wikipedia.org/wiki/Quantitative_research", "summary": "In natural sciences and social sciences, quantitative research is the systematic empirical investigation of observable phenomena via statistical, mathematical, or computational techniques. The objective of quantitative research is to develop and employ mathematical models, theories, and hypotheses pertaining to phenomena. The process of measurement is central to quantitative research because it provides the fundamental connection between empirical observation and mathematical expression of quantitative relationships.\nQuantitative data is any data that is in numerical form such as statistics, percentages, etc. The researcher analyses the data with the help of statistics and hopes the numbers will yield an unbiased result that can be generalized to some larger population. Qualitative research, on the other hand, inquires deeply into specific experiences, with the intention of describing and exploring meaning through text, narrative, or visual-based data, by developing themes exclusive to that set of participants.In social sciences, quantitative research is widely used in psychology, economics, demography, sociology, marketing, community health, health & human development, gender and political science, and less frequently in anthropology and history. Research in mathematical sciences, such as physics, is also \"quantitative\" by definition, though this use of the term differs in context. In the social sciences, the term relates to empirical methods, originating in both philosophical positivism and the history of statistics, which contrast with qualitative research methods.\nQualitative research produces information only on the particular cases studied, and any more general conclusions are only hypotheses. Quantitative methods can be used to verify which of such hypotheses are true. A comprehensive analysis of 1274 articles published in the top two American sociology journals between 1935 and 2005 found that roughly two thirds of these articles used quantitative method.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Anthropology", "Antipositivism", "Auguste Comte", "Bias (statistics)", "Bibcode", "Biological science", "Case study research", "Clive Granger", "Correlation does not imply causation", "Covariance", "Demography", "Descriptive statistics", "Deterministic", "Digital object identifier", "Econometrics", "Economics", "Empirical", "Empirical research", "Ernst Heinrich Weber", "Factor analysis", "Falsifiability", "Finance", "General linear model", "Granger causality", "Gustav Fechner", "Hedge fund", "History", "History of statistics", "Hypothesis", "International Standard Book Number", "International Standard Serial Number", "Item response theory", "JSTOR", "Market research", "Marketing", "Mathematical model", "Measurement", "Methodology", "Mixed-methods research", "Natural science", "OCLC", "Observation", "Observational study", "Pearson plc", "Phenomenon", "Physical science", "Physics", "Political science", "Positivism", "Positivist", "Proxy (statistics)", "Psychology", "Psychometrics", "Psychophysics", "Qualitative research", "Quantification (science)", "Quantitative marketing research", "Quantitative psychology", "R (programming language)", "Randomly", "Rasch model", "SAGE Publications", "SPSS", "Scientific method", "Scientific theory", "Social anthropology", "Social science", "Sociological positivism", "Sociology", "Spurious relationship", "Statistical mechanics", "Statistical survey", "Statistics", "Stock market", "Survey research", "Temperature record of the past 1000 years", "Trading Strategy Index", "VISQ", "Variable (mathematics)"], "references": ["http://adsabs.harvard.edu/abs/2001JGR...106.2929B", "http://www.climateaudit.info/pdf/others/Briffa.2001.jgr.pdf", "http://eprints.uthm.edu.my/268/", "http://www.qualitative-research.net/index.php/fqs/article/view/72", "http://doi.org/10.1007%2Fs11192-007-1901-y", "http://doi.org/10.1007%2Fs12108-008-9042-1", "http://doi.org/10.1029%2F2000JD900617", "http://doi.org/10.1086%2F349468", "http://www.jstor.org/stable/228678", "http://eprints.rclis.org/12286/", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Quantitative+research", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Quantitative+research&library=0CHOOSE0", "http://www.worldcat.org/issn/0024-2586", "http://www.worldcat.org/oclc/464594493", "https://journals.ala.org/index.php/ltr/article/view/6325", "https://www.worldcat.org/oclc/464594493"]}, "Cross-correlation": {"categories": ["All articles with specifically marked weasel-worded phrases", "Articles with specifically marked weasel-worded phrases from May 2015", "Bilinear operators", "Covariance and correlation", "Signal processing", "Time domain analysis", "Wikipedia articles needing clarification from May 2015"], "title": "Cross-correlation", "method": "Cross-correlation", "url": "https://en.wikipedia.org/wiki/Cross-correlation", "summary": "In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology.\nFor continuous functions f and g, the cross-correlation is defined as:\n\n \n \n \n (\n f\n \u22c6\n g\n )\n (\n \u03c4\n )\n \n \n \n \n \n =\n \n \n \n d\n e\n f\n \n \n \n \n \n \n \u222b\n \n \u2212\n \u221e\n \n \n \u221e\n \n \n \n f\n \n \u2217\n \n \n (\n t\n )\n \n g\n (\n t\n +\n \u03c4\n )\n \n d\n t\n \n \n {\\displaystyle (f\\star g)(\\tau )\\ {\\stackrel {\\mathrm {def} }{=}}\\int _{-\\infty }^{\\infty }f^{*}(t)\\ g(t+\\tau )\\,dt}\n ,where \n \n \n \n \n f\n \n \u2217\n \n \n \n \n {\\displaystyle f^{*}}\n denotes the complex conjugate of \n \n \n \n f\n \n \n {\\displaystyle f}\n , and \n \n \n \n \u03c4\n \n \n {\\displaystyle \\tau }\n is the displacement, also known as lag (a feature in f at t occurs in g at \n \n \n \n t\n +\n \u03c4\n \n \n {\\displaystyle t+\\tau }\n ).\nSimilarly, for discrete functions, the cross-correlation is defined as:\n\n \n \n \n (\n f\n \u22c6\n g\n )\n [\n n\n ]\n \n \n \n \n \n =\n \n \n \n d\n e\n f\n \n \n \n \n \n \n \u2211\n \n m\n =\n \u2212\n \u221e\n \n \n \u221e\n \n \n \n f\n \n \u2217\n \n \n [\n m\n ]\n \n g\n [\n m\n +\n n\n ]\n .\n \n \n {\\displaystyle (f\\star g)[n]\\ {\\stackrel {\\mathrm {def} }{=}}\\sum _{m=-\\infty }^{\\infty }f^{*}[m]\\ g[m+n].}\n The cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal energy.\nIn probability and statistics, the term cross-correlations is used for referring to the correlations between the entries of two random vectors X and Y, while the correlations of a random vector X are considered to be the correlations between the entries of X itself, those forming the correlation matrix (matrix of correlations) of X. If each of X and Y is a scalar random variable which is realized repeatedly in temporal sequence (a time series), then the correlations of the various temporal instances of X are known as autocorrelations of X, and the cross-correlations of X with Y across time are temporal cross-correlations.\nFurthermore, in probability and statistics the definition of correlation always includes a standardising factor in such a way that correlations have values between \u22121 and +1.\nIf \n \n \n \n X\n \n \n {\\displaystyle X}\n and \n \n \n \n Y\n \n \n {\\displaystyle Y}\n are two independent random variables with probability density functions f and g, respectively, then the probability density of the difference \n \n \n \n Y\n \u2212\n X\n \n \n {\\displaystyle Y-X}\n is formally given by the cross-correlation (in the signal-processing sense) \n \n \n \n f\n \u22c6\n g\n \n \n {\\displaystyle f\\star g}\n ; however this terminology is not used in probability and statistics. In contrast, the convolution \n \n \n \n f\n \u2217\n g\n \n \n {\\displaystyle f*g}\n (equivalent to the cross-correlation of f(t) and g(\u2212t) ) gives the probability density function of the sum \n \n \n \n X\n +\n Y\n \n \n {\\displaystyle X+Y}\n .\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/21/Comparison_convolution_correlation.svg", "https://upload.wikimedia.org/wikipedia/commons/7/71/Cross_correlation_animation.gif", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arg max", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autocovariance", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Averaging", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Coherence (signal processing)", "Cointegration", "Completeness (statistics)", "Complex-valued function", "Complex conjugate", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convolution", "Convolution theorem", "Correlation", "Correlation and dependence", "Correlation function", "Correlation matrix", "Correlogram", "Count data", "Covariance and correlation", "Credible interval", "Crime statistics", "Cross-covariance", "Cross-spectrum", "Cross-validation (statistics)", "Cryptanalysis", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital image correlation", "Digital object identifier", "Discrete Fourier transform", "Divergence (statistics)", "Dot product", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Electron tomography", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fast Fourier transform", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fourier transform", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Functional analysis", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hermitian function", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent (probability)", "Index of dispersion", "Inner product", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate random variable", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Neurophysiology", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pattern recognition", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase correlation", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled correlation", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal processing", "Similarity measure", "Simple linear regression", "Simultaneous equations model", "Single particle analysis", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic process", "Stochastic processes", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Template matching", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Unit vector", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wide-sense stationary", "Wide sense stationary", "Wiener\u2013Khinchin theorem", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://mathworld.wolfram.com/Cross-Correlation.html", "http://d-scholarship.pitt.edu/9773/", "http://www.phys.ufl.edu/LIGO/stochastic/sign05.pdf", "http://doi.org/10.1007%2Fs10596-012-9287-1", "http://doi.org/10.1109%2FICSPCS.2015.7391783", "http://doi.org/10.1115%2FIMECE2009-10798", "http://ieeexplore.ieee.org/document/7391783/", "http://scribblethink.org/Work/nvisionInterface/nip.html", "http://www.staff.ncl.ac.uk/oliver.hinton/eee305/Chapter6.pdf"]}, "Probabilistic forecasting": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2011", "Climate and weather statistics", "Probability assessment", "Statistical forecasting", "Weather forecasting", "Wikipedia articles needing clarification from June 2011"], "title": "Probabilistic forecasting", "method": "Probabilistic forecasting", "url": "https://en.wikipedia.org/wiki/Probabilistic_forecasting", "summary": "Probabilistic forecasting summarizes what is known about, or opinions about, future events. In contrast to single-valued forecasts (such as forecasting that the maximum temperature at a given site on a given day will be 23 degrees Celsius, or that the result in a given football match will be a no-score draw), probabilistic forecasts assign a probability to each of a number of different outcomes, and the complete set of probabilities represents a probability forecast. Thus, probabilistic forecasting is a type of probabilistic classification. \nWeather forecasting represents a service in which probability forecasts are sometimes published for public consumption, although it may also be used by weather forecasters as the basis of a simpler type of forecast. For example forecasters may combine their own experience together with computer-generated probability forecasts to construct a forecast of the type \"we expect heavy rainfall\".\nSports betting is another field of application where probabilistic forecasting can play a role. The pre-race odds published for a horse race can be considered to correspond to a summary of bettors' opinions about the likely outcome of a race, although this needs to be tempered with caution as bookmakers' profits needs to be taken into account. In sports betting, probability forecasts may not be published as such, but may underlie bookmakers' activities in setting pay-off rates, etc.", "images": [], "links": ["Annual Energy Outlook", "Bookmaker", "Brier score", "Consensus Economics", "Consensus forecast", "Continuous ranked probability score", "Digital object identifier", "Economic forecasting", "Electricity price forecasting", "Energy forecasting", "Ensemble forecasting", "Eugenia Kalnay", "Forecast skill", "Forecasting", "Global Energy Forecasting Competition", "International Standard Book Number", "International Standard Serial Number", "Journal of the American Statistical Association", "Load forecasting", "Monetary Authority of Singapore", "Numerical weather prediction", "Probabilistic classification", "Probability of precipitation", "Quantile regression", "Quantile regression averaging", "Quantitative precipitation forecast", "Scoring rule", "Solar power forecasting", "Sports betting", "Weather forecasting", "Wind power forecasting"], "references": ["http://www.wmo.ch/web/www/DPS/EPS-HOME/eps-home.htm", "http://www.consensuseconomics.com/special_data.htm#Probs", "http://blog.drhongtao.com/2013/10/probabilistic-energy-forecasting.html", "http://www.sciencedirect.com/science/article/pii/S0169207014001083", "http://www.springerlink.com/content/42u8j5r230v5805w", "http://www.maxlittle.net/publications/mwr2614_glms.pdf", "http://doi.org/10.1007%2Fs00180-014-0523-0", "http://doi.org/10.1016%2Fj.ijforecast.2014.08.008", "http://doi.org/10.1111%2Fj.1538-4632.2006.00693.x", "http://www.worldcat.org/issn/0943-4062", "http://www.mas.gov.sg/~/media/resource/publications/macro_review/2015/MROct15_Macroeconomic%20Review.pdf", "https://www.le.ac.uk/economics/research/RePEc/lec/leecon/econ00-4.pdf"]}, "McNemar's test": {"categories": ["All articles needing expert attention", "All articles that are too technical", "All articles with unsourced statements", "Articles needing expert attention from November 2012", "Articles with unsourced statements from June 2011", "Nonparametric statistics", "Pages using web citations with no URL", "Statistical tests", "Summary statistics for contingency tables", "Wikipedia articles that are too technical from November 2012"], "title": "McNemar's test", "method": "McNemar's test", "url": "https://en.wikipedia.org/wiki/McNemar%27s_test", "summary": "In statistics, McNemar's test is a statistical test used on paired nominal data. It is applied to 2 \u00d7 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whether the row and column marginal frequencies are equal (that is, whether there is \"marginal homogeneity\"). It is named after Quinn McNemar, who introduced it in 1947.\nAn application of the test in genetics is the transmission disequilibrium test for detecting linkage disequilibrium.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "American Statistical Association", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bhapkar's test", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biometrika Trust", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's Q test", "Cochran\u2013Mantel\u2013Haenszel test", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dichotomous", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Duxbury Press", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Hodgkin's lymphoma", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Liddell's exact test", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Linkage disequilibrium", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nominal data", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability mass function", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Quinn McNemar", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "SAS (software)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Stuart\u2013Maxwell test", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "The British Journal of Psychiatry", "Time domain", "Time series", "Tolerance interval", "Transmission disequilibrium test", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Warren Ewens", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://john-uebersax.com/stat/mcnemar.htm", "http://www.john-uebersax.com/stat/mcnemar.htm#bhapkar", "http://rimarcik.com/en/navigator/z-nominal.html", "http://dij.sagepub.com/content/46/4/434", "http://www2.sas.com/proceedings/forum2008/382-2008.pdf", "http://www3.interscience.wiley.com/journal/104545274/abstract", "http://onlinelibrary.wiley.com/doi/10.1002/bimj.201000035/abstract", "http://faculty.vassar.edu/lowry/propcorr.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1682161", "http://www.ncbi.nlm.nih.gov/pubmed/12872299", "http://www.ncbi.nlm.nih.gov/pubmed/20254758", "http://www.ncbi.nlm.nih.gov/pubmed/20976694", "http://www.ncbi.nlm.nih.gov/pubmed/8447318", "http://doi.org/10.1002%2Fbimj.201000035", "http://doi.org/10.1002%2Fsim.1438", "http://doi.org/10.1007%2FBF02295996", "http://doi.org/10.1007%2Fbf02289261", "http://doi.org/10.1080%2F01621459.1961.10482105", "http://doi.org/10.1177%2F0092861512442021", "http://doi.org/10.1186%2F1471-2288-13-91", "http://www.jstor.org/stable/2283057", "http://www.jstor.org/stable/2333387", "http://www.jstor.org/stable/2988087", "http://bjp.rcpsych.org/content/116/535/651.full.pdf", "https://mathdept.iut.ac.ir/sites/mathdept.iut.ac.ir/files/AGRESTI.PDF"]}, "Park test": {"categories": ["Regression diagnostics", "Statistical tests"], "title": "Park test", "method": "Park test", "url": "https://en.wikipedia.org/wiki/Park_test", "summary": "In econometrics, the Park test is a test for heteroscedasticity. The test is based on the method proposed by Rolla Edward Park for estimating linear regression parameters in the presence of heteroscedastic error terms.", "images": [], "links": ["Econometrica", "Econometrics", "Errors and residuals in statistics", "Gauss\u2013Markov theorem", "Glejser test", "Heteroscedastic", "Heteroscedasticity", "Homoscedasticity", "International Standard Book Number", "JSTOR", "Linear regression", "Ordinary least squares", "Regression analysis", "Richard E. Quandt", "Stephen Goldfeld", "Variance", "White test"], "references": ["http://www.jstor.org/stable/1910108"]}, "Delta method": {"categories": ["Articles containing proofs", "Estimation methods", "Statistical approximations", "Statistics articles needing expert attention"], "title": "Delta method", "method": "Delta method", "url": "https://en.wikipedia.org/wiki/Delta_method", "summary": "In statistics, the delta method is a result concerning the approximate probability distribution for a function of an asymptotically normal statistical estimator from knowledge of the limiting variance of that estimator. It was first described in 1938 by Robert Dorfman", "images": [], "links": ["Asymptotic distribution", "Big O in probability notation", "Binomial distribution", "Central limit theorem", "Consistency (statistics)", "Continuous function", "Continuous mapping theorem", "Convergence in distribution", "Convergence in probability", "Digital object identifier", "Estimator", "Function (mathematics)", "Gradient", "Harald Cram\u00e9r", "J. Scott Long", "JSTOR", "Lawrence Klein", "Mean value theorem", "Probability distribution", "Relative risk", "Robert Dorfman", "Sequence (mathematics)", "Slutsky's theorem", "Statistics", "Taylor's theorem", "Taylor expansions for the moments of functions of random variables", "Taylor series", "Variance", "Variance-stabilizing transformation", "William Greene (economist)"], "references": ["http://data.imf.au.dk/courses/advsimmethod/Fall05/notes/1209.pdf", "http://www.indiana.edu/~jslsoc/stata/ci_computations/spost_deltaci.pdf", "http://doi.org/10.1080%2F00031305.1992.10475842", "http://www.jstor.org/stable/2684406", "https://books.google.com/books?id=0x_vAAAAMAAJ", "https://books.google.com/books?id=CRTKKaJO0DYC&pg=PA353", "https://books.google.com/books?id=JJkWAQAAMAAJ&pg=PA913", "https://books.google.com/books?id=gQyIGGAiN4AC&pg=PA33", "https://books.google.com/books?id=uzwiAAAAMAAJ&pg=PA258", "https://www.stata.com/support/faqs/stat/deltam.html", "https://www.jstor.org/stable/pdf/23339471.pdf?casa_token=9I5bSEzyIpUAAAAA:KPPYNHKhxiKwZy3VnR6V_cgUiGNJy_s7Ptl2WBWUiCFFA6WzaJa6CCCX6NfnVvg1juvxxZ6RXQo31A5Ct6DsfFyjD0HeqXV8oPK_WLU2zHTqAg1dg2c"]}, "Standard normal deviate": {"categories": ["All stub articles", "Normal distribution", "Statistics stubs"], "title": "Standard normal deviate", "method": "Standard normal deviate", "url": "https://en.wikipedia.org/wiki/Standard_normal_deviate", "summary": "A standard normal deviate (or standard normal variable) is a normally distributed random variable with expected value 0 and variance 1. A fuller term is standard normal random variable. Where collections of such random variables are used, there is often an associated (possibly unstated) assumption that members of such collections are statistically independent.\nStandard normal variables play a major role in theoretical statistics in the description of many types of model, particularly in regression analysis, the analysis of variance and time series analysis.\nWhen the term \"deviate\" is used, rather than \"variable\", there is a connotation that the value concerned is treated as the no-longer-random outcome of a standard norm random variable. The terminology here is the same as that for random variable and random variate. Standard normal deviates arise in practical statistics in two ways.\n\nGiven a model for a set of observed data, a set of manipulations of the data can result in a derived quantity which, assuming that the model is a true representation of reality, is a standard normal deviate (perhaps in an approximate sense). This enables a significance test to be made for the validity of the model.\nIn the computer generation of a pseudorandom number sequence, the aim may be to generate random numbers having a normal distribution: these can be obtained from standard normal deviates (themselves the output of a pseudorandom number sequence) by multiplying by the scale parameter and adding the location parameter. More generally, the generation of pseudorandom number sequence having other marginal distributions may involve manipulating sequences of standard normal deviates: an example here is the chi-squared distribution, random values of which can be obtained by adding the squares of standard normal deviates (although this would seldom be the fastest method of generating such values).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Analysis of variance", "Chi-squared distribution", "Expected value", "International Standard Book Number", "Marginal distribution", "Normal distribution", "Pseudorandom number sequence", "Random variable", "Random variate", "Regression analysis", "Significance test", "Standard normal table", "Statistically independent", "Statistics", "Time series analysis", "Variance"], "references": []}, "Compositional data": {"categories": ["Statistical data types"], "title": "Compositional data", "method": "Compositional data", "url": "https://en.wikipedia.org/wiki/Compositional_data", "summary": "In statistics, compositional data are quantitative descriptions of the parts of some whole, conveying relative information. Measurements involving probabilities, proportions, percentages or ppm can all be thought of as compositional data.\nThe original definition, given by John Aitchison (1986) has several consequences:\n\nA compositional data point, or composition for short, can be represented by a positive real vector with as many parts as considered. Sometimes, if the total amount is fixed and known, one component of the vector can be omitted.\nAs compositions only carry relative information, the only information is given by the ratios between components. Consequently, a composition multiplied by any positive constant contains the same information as the former. Therefore, proportional positive vectors are equivalent when considered as compositions.Compositional data can be represented by constant sum real vectors with positive components, and this vectors span a simplex, defined as\n \n \n \n \n \n \n S\n \n \n \n D\n \n \n =\n \n {\n \n \n x\n \n =\n [\n \n x\n \n 1\n \n \n ,\n \n x\n \n 2\n \n \n ,\n \u2026\n ,\n \n x\n \n D\n \n \n ]\n \u2208\n \n \n R\n \n \n D\n \n \n \n \n |\n \n \n \n x\n \n i\n \n \n >\n 0\n ,\n i\n =\n 1\n ,\n 2\n ,\n \u2026\n ,\n D\n ;\n \n \u2211\n \n i\n =\n 1\n \n \n D\n \n \n \n x\n \n i\n \n \n =\n \u03ba\n \n \n \n \n }\n \n .\n \n \n \n {\\displaystyle {\\mathcal {S}}^{D}=\\left\\{\\mathbf {x} =[x_{1},x_{2},\\dots ,x_{D}]\\in \\mathbb {R} ^{D}\\,\\left|\\,x_{i}>0,i=1,2,\\dots ,D;\\sum _{i=1}^{D}x_{i}=\\kappa \\right.\\right\\}.\\ }\n \nThe sample space \n \n \n \n \n \n \n \n S\n \n \n \n D\n \n \n \n \n \n {\\displaystyle \\scriptstyle {\\mathcal {S}}^{D}}\n is also known as the Aitchison simplex. It turns out that an alternative vector space structure can be defined on the Aitchison simplex, which motivated the development of Aitchison geometry.\nEach composition represents an equivalence class. Any two compositions \n \n \n \n x\n ,\n y\n \u2208\n \n S\n \n D\n \n \n \n \n {\\displaystyle x,y\\in S^{D}}\n are said to be equivalent if \n \n \n \n y\n =\n \u03bb\n x\n \n \n {\\displaystyle y=\\lambda x}\n for any \n \n \n \n \u03bb\n >\n 0\n \n \n {\\displaystyle \\lambda >0}\n . \nFor example, if these two compositions where \n \n \n \n x\n =\n [\n 0.5\n ,\n 0.25\n ,\n 0.25\n ]\n \n \n {\\displaystyle x=[0.5,0.25,0.25]}\n and \n \n \n \n y\n =\n [\n 50\n ,\n 25\n ,\n 25\n ]\n \n \n {\\displaystyle y=[50,25,25]}\n , they are equivalent since one could multiply \n \n \n \n x\n \n \n {\\displaystyle x}\n by 100 to obtain \n \n \n \n y\n \n \n {\\displaystyle y}\n . \nEquivalent compositions can be represented by positive vectors whose components add to a given constant \n \n \n \n \n \u03ba\n \n \n \n {\\displaystyle \\scriptstyle \\kappa }\n . The vector operation assigning the constant sum representative is called closure and is denoted by \n \n \n \n \n \n \n C\n \n \n [\n \n \u22c5\n \n ]\n \n \n \n {\\displaystyle \\scriptstyle {\\mathcal {C}}[\\,\\cdot \\,]}\n :\n\n \n \n \n \n \n C\n \n \n [\n \n x\n \n 1\n \n \n ,\n \n x\n \n 2\n \n \n ,\n \u2026\n ,\n \n x\n \n D\n \n \n ]\n =\n \n [\n \n \n \n \n x\n \n 1\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n D\n \n \n \n x\n \n i\n \n \n \n \n \n ,\n \n \n \n x\n \n 2\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n D\n \n \n \n x\n \n i\n \n \n \n \n \n ,\n \u2026\n ,\n \n \n \n x\n \n D\n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n D\n \n \n \n x\n \n i\n \n \n \n \n \n \n ]\n \n ,\n \n \n \n {\\displaystyle {\\mathcal {C}}[x_{1},x_{2},\\dots ,x_{D}]=\\left[{\\frac {x_{1}}{\\sum _{i=1}^{D}x_{i}}},{\\frac {x_{2}}{\\sum _{i=1}^{D}x_{i}}},\\dots ,{\\frac {x_{D}}{\\sum _{i=1}^{D}x_{i}}}\\right],\\ }\n where D is the number of parts (components) and \n \n \n \n [\n \u22c5\n ]\n \n \n {\\displaystyle [\\cdot ]}\n denotes a row vector.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/cd/Aitchison-simplex.jpg"], "links": ["Aitchison geometry", "Aitchison simplex", "Data set", "John Aitchison", "Simplex", "Statistics", "Vera Pawlowsky-Glahn"], "references": ["http://www.compositionaldata.com/", "http://hdl.handle.net/10256/297", "https://github.com/juliohm/CoDa.jl", "https://cran.r-project.org/web/packages/coda.base/index.html", "https://cran.r-project.org/web/packages/compositions/index.html"]}, "Descriptive statistics": {"categories": ["Descriptive statistics", "Psychometrics", "Summary statistics", "Wikipedia articles with GND identifiers"], "title": "Descriptive statistics", "method": "Descriptive statistics", "url": "https://en.wikipedia.org/wiki/Descriptive_statistics", "summary": "A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information, while descriptive statistics in the mass noun sense is the process of using and analyzing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aims to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent. This generally means that descriptive statistics, unlike inferential statistics, is not developed on the basis of probability theory, and are frequently nonparametric statistics. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented. For example, in papers reporting on human subjects, typically a table is included giving the overall sample size, sample sizes in important subgroups (e.g., for each treatment or exposure group), and demographic or clinical characteristics such as the average age, the proportion of subjects of each sex, the proportion of subjects with related comorbidities, etc.\nSome measures that are commonly used to describe a data set are measures of central tendency and measures of variability or dispersion. Measures of central tendency include the mean, median and mode, while measures of variability include the standard deviation (or variance), the minimum and maximum values of the variables, kurtosis and skewness.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average", "Bar chart", "Basketball", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comorbidity", "Completeness (statistics)", "Conditional distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Count noun", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic", "Demographic statistics", "Density estimation", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Grade point average", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Histograms", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Information", "Integrated Authority File", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mass noun", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Methods in Molecular Biology", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's r", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentage", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "Quality control", "Quantitative research", "Quartiles", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scatterplot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spearman's rho", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Summary statistic", "Summary statistics", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Univariate analysis", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-score", "Z-test"], "references": ["http://www.investopedia.com/terms/d/descriptive_statistics.asp#axzz2DxCoTnMM", "http://www.pitt.edu/~super1/lecture/lec0421/index.htm", "http://www.socialresearchmethods.net/kb/statdesc.php", "http://doi.org/10.1007%2F978-1-59745-530-5_3", "https://d-nb.info/gnd/4070313-7", "https://www.wikidata.org/wiki/Q380344"]}, "Bayes linear statistics": {"categories": ["Bayesian statistics", "Probability interpretations"], "title": "Bayes linear statistics", "method": "Bayes linear statistics", "url": "https://en.wikipedia.org/wiki/Bayes_linear_statistics", "summary": "Bayes linear statistics is a subjectivist statistical methodology and framework. Traditional subjective Bayesian analysis is based upon fully specified probability distributions, which are very difficult to specify at the necessary level of detail. Bayes linear analysis attempts to solve this problem by developing theory and practise for using partially specified probability models. Bayes linear in its current form has been primarily developed by Michael Goldstein. Mathematically and philosophically it extends Bruno de Finetti's Operational Subjective approach to probability and statistics.", "images": [], "links": ["AFM Smith", "Bayesian analysis", "Bruno de Finetti", "De Finetti's theorem", "Exchangeability", "Imprecise probability", "International Standard Book Number", "Journal of the Royal Statistical Society", "Moore\u2013Penrose pseudoinverse", "Operational Subjective", "Partition of a set", "Prevision", "Probability distribution"], "references": ["http://www.numdam.org/item?id=AIHP_1937__7_1_1_0", "http://maths.dur.ac.uk/stats/bayeslin/", "https://web.archive.org/web/20151004174936/http://ba.stat.cmu.edu/journal/2006/vol01/issue03/goldstein.pdf"]}, "Empirical likelihood": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from January 2018", "Probability distribution fitting"], "title": "Empirical likelihood", "method": "Empirical likelihood", "url": "https://en.wikipedia.org/wiki/Empirical_likelihood", "summary": "Empirical likelihood (EL) is an estimation method in statistics. Empirical likelihood estimates require fewer assumptions about the error distribution compared to similar methods like maximum likelihood. The estimation method requires that the data are independent and identically distributed (iid). It performs well even when the distribution is asymmetric or censored. EL methods can also handle constraints and prior information on parameters. Art Owen pioneered work in this area with his 1988 paper.", "images": [], "links": ["Art Owen", "Biometrika", "Bootstrapping (statistics)", "Cambridge University Press", "Chapman & Hall", "Digital object identifier", "Estimating function", "Independent and identically distributed", "International Standard Book Number", "Jackknife (statistics)", "Journal of Econometrics", "Lagrange multiplier", "Likelihood function", "Maximum entropy probability distribution", "Maximum likelihood", "Statistics"], "references": ["http://doi.org/10.1016%2Fs0304-4076(01)00113-0", "http://doi.org/10.1093%2Fbiomet%2F75.2.237"]}, "One-class classification": {"categories": ["All stub articles", "Artificial intelligence stubs", "Classification algorithms", "Statistical classification", "Statistics stubs"], "title": "One-class classification", "method": "One-class classification", "url": "https://en.wikipedia.org/wiki/One-class_classification", "summary": "In machine learning, one-class classification, also known as unary classification or class-modelling, tries to identify objects of a specific class amongst all objects, by primarily learning from a training set containing only the objects of that class, although there exist variants of one-class classifiers where counter-examples are used to further refine the classification boundary. This is different from and more difficult than the traditional classification problem, which tries to distinguish between two or more classes with the training set containing objects from all the classes. An example is the classification of the operational status of a nuclear plant as 'normal': In this scenario, there are few, if any, examples of catastrophic system states; only the statistics of normal operation are known. The term one-class classification was coined by Moya & Hush (1996) and many applications can be found in scientific literature, for example outlier detection, anomaly detection, novelty detection. A feature of one-class classification is that it uses only sample points from the assigned class, so that a representative sampling is not strictly required for non-target classes.While many of the above approaches focus on the case of removing a small number of outliers or anomalies, one can also learn the other extreme, where the single class covers a small coherent subset of the data, using an information bottleneck approach.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/LampFlowchart.svg"], "links": ["Anomaly detection", "Artificial intelligence", "Binary classification", "Bioinformatics", "Classification (machine learning)", "Digital object identifier", "Expectation-maximization", "Information bottleneck method", "Machine learning", "Multiclass classification", "Novelty detection", "Outlier detection", "Philip S. Yu", "Semi-supervised learning", "Statistics", "Supervised learning", "Text classification", "Training set"], "references": ["http://linkinghub.elsevier.com/retrieve/pii/S0003267017306050", "http://www.sciencedirect.com/science/article/pii/S0169743916302799", "http://homepage.tudelft.nl/n9d04/thesis.pdf", "http://doi.org/10.1016%2Fj.aca.2017.05.013", "http://doi.org/10.1016%2Fj.chemolab.2016.10.002", "https://dl.acm.org/citation.cfm?id=1015399", "https://doi.org/10.1016%2F0893-6080(95)00120-4"]}, "Ordinary least squares": {"categories": ["All articles to be expanded", "All articles with unsourced statements", "Articles to be expanded from February 2017", "Articles using small message boxes", "Articles with unsourced statements from February 2010", "Articles with unsourced statements from October 2018", "Least squares", "Parametric statistics"], "title": "Ordinary least squares", "method": "Ordinary least squares", "url": "https://en.wikipedia.org/wiki/Ordinary_least_squares", "summary": "In statistics, ordinary least squares (OLS) is a type of linear least squares method for estimating the unknown parameters in a linear regression model. OLS chooses the parameters of a linear function of a set of explanatory variables by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being predicted) in the given dataset and those predicted by the linear function. \nGeometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression surface \u2013 the smaller the differences, the better the model fits the data. The resulting estimator can be expressed by a simple formula, especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation.\nThe OLS estimator is consistent when the regressors are exogenous, and optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated. Under these conditions, the method of OLS provides minimum-variance mean-unbiased estimation when the errors have finite variances. Under the additional assumption that the errors are normally distributed, OLS is the maximum likelihood estimator.\nOLS is used in fields as diverse as economics (econometrics), political science, psychology and engineering (control theory and signal processing).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e7/HeightWeightResiduals.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/OLS_example_weight_vs_height_fitted_line.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e2/OLS_example_weight_vs_height_residuals.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c1/OLS_example_weight_vs_height_scatterplot.svg", "https://upload.wikimedia.org/wikipedia/commons/8/87/OLS_geometric_interpretation.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Okuns_law_quarterly_differences.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a7/Split-arrows.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg"], "links": ["Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Annihilator matrix", "Approximation theory", "Arthur Goldberger", "Asymptotic theory (statistics)", "Autocorrelation", "Bayesian experimental design", "Bayesian linear regression", "Bayesian multivariate linear regression", "Best linear unbiased estimator", "Bias of an estimator", "Binomial regression", "Calibration curve", "Central limit theorem", "Chebyshev nodes", "Chebyshev polynomials", "Chi-squared distribution", "Chow test", "Coefficient of determination", "Coefficients", "Cointegration", "Column rank", "Column space", "Computational statistics", "Conditional expectation", "Confidence interval", "Confounding", "Consistent estimator", "Control theory", "Convergence of random variables", "Correlation", "Correlation and dependence", "Cram\u00e9r\u2013Rao bound", "Cross-sectional data", "Curve fitting", "Data collection", "Dataset", "Degrees of freedom (statistics)", "Dependent variable", "Design matrix", "Design of experiments", "Discrete choice", "Durbin\u2013Watson statistic", "Econometrics", "Economics", "Endogeneity (economics)", "Engineering", "Ergodic process", "Errors-in-variables models", "Errors and residuals in statistics", "Estimator bias", "Euclidean space", "Exogenous", "Experiment", "Explanatory variable", "Extrapolation", "F-test", "Fama\u2013MacBeth regression", "Fixed effects model", "Frisch\u2013Waugh\u2013Lovell theorem", "Gaussian quadrature", "Gauss\u2013Markov theorem", "General linear model", "Generalized least squares", "Generalized linear model", "Generalized method of moments", "Goodness of fit", "Gramian matrix", "Growth curve (statistics)", "Hat matrix", "Hessian matrix", "Heteroscedasticity", "Homoscedastic", "Homoscedasticity", "Hyperplane", "Hypothesis testing", "Idempotent matrix", "Identity matrix", "Iid", "Independent and identically distributed", "Independent random variables", "Influential observation", "Instrumental variable", "International Standard Book Number", "Interval estimate", "Isotonic regression", "Iteratively reweighted least squares", "Jackknife method", "Karl Pearson", "Kendall tau rank correlation coefficient", "Law of large numbers", "Least-angle regression", "Least absolute deviations", "Least squares", "Leverage (statistics)", "Likelihood ratio test", "Linear equation", "Linear function", "Linear least squares", "Linear least squares (mathematics)", "Linear projection", "Linear regression", "Linear regression model", "Linear span", "Linear subspace", "Linearly independent", "List of statistical packages", "List of statistics articles", "Local regression", "Logistic regression", "Macroeconomics", "Mallows's Cp", "Martingale difference sequence", "Mathematical optimization", "Matrix (mathematics)", "Maximum likelihood estimator", "Mean and predicted response", "Mean response", "Mean squared error", "Minimum mean-square error", "Minimum mean square error", "Mixed logit", "Mixed model", "Model selection", "Moment matrix", "Moore\u2013Penrose pseudoinverse", "Moving least squares", "Multicollinearity", "Multilevel model", "Multinomial logit", "Multinomial probit", "Multivariate analysis of variance", "Multivariate normal distribution", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonlinear system identification", "Nonnegative-definite matrix", "Nonparametric regression", "Norm (mathematics)", "Normal distribution", "Normal equations", "Normal matrix", "Nuisance parameter", "Null hypothesis", "Numerical analysis", "Numerical integration", "Numerical methods for linear least squares", "Numerical smoothing and differentiation", "Observational study", "Okun's law", "Optimal design", "Ordered logit", "Ordered probit", "Orthogonal polynomials", "Outline of statistics", "Overdetermined system", "P-value", "Panel data", "Partial correlation", "Partial least squares", "Partial least squares regression", "Partition of sums of squares", "Pearson product-moment correlation coefficient", "Point estimate", "Poisson regression", "Political science", "Polynomial least squares", "Polynomial regression", "Positive-definite matrix", "Positive semi-definite matrix", "Predicted response", "Prediction interval", "Principal component regression", "Probability distribution", "Probit model", "Projection (linear algebra)", "Projection matrix", "Proofs involving ordinary least squares", "Psychology", "Quadratic form (statistics)", "Quantile function", "Quantile regression", "Quantization error model", "Random effects model", "Random sample", "Rank correlation", "Reduced chi-squared", "Regression analysis", "Regression model validation", "Regressor", "Regressors", "Regular estimator", "Regularized least squares", "Response surface methodology", "Ridge regression", "Robust regression", "Row and column vectors", "Scatterplot", "Schwarz criterion", "Segmented regression", "Semiparametric regression", "Signal processing", "Simple linear regression", "Spearman's rank correlation coefficient", "Standard error", "Standard error (statistics)", "Stationary process", "Statistical error", "Statistical estimation", "Statistical model", "Statistical parameter", "Statistical population", "Statistical significance", "Statistical unit", "Statistics", "Stepwise regression", "Stochastic process", "Studentized residual", "Symmetric matrix", "System identification", "T-statistic", "Tikhonov regularization", "Time series", "Total least squares", "Transpose", "UMVU", "Udny Yule", "Uncorrelated", "Variance", "Variance-covariance matrix", "Vector decomposition", "Wald test", "Weighted least squares"], "references": ["http://stat.smmu.edu.cn/DOWNLOAD/ebook/econometric.pdf", "http://mlmadesimple.com/2014/05/07/line-estimation/", "http://www.pareonline.net/getvn.asp?v=18&n=11", "https://books.google.com.br/books?id=Np7y43HU_m8C&lpg=PA227&dq=cofactor%20matrix%20least%20squares&pg=PA263#v=onepage&q&f=false", "https://books.google.com.br/books?id=hZ4mAOXVowoC&lpg=PA538&dq=cofactor&pg=PA160#v=onepage&q&f=false", "https://books.google.com.br/books?id=peYFZ69HqEsC&lpg=PA151&dq=cofactor%20matrix%20least%20squares&pg=PA134#v=onepage&q&f=false", "https://books.google.com/books?id=KZq5AAAAIAAJ&pg=PA156", "https://cran.r-project.org/doc/contrib/Faraway-PRA.pdf"]}, "Confounding": {"categories": ["All articles with unsourced statements", "Analysis of variance", "Articles with short description", "Articles with unsourced statements from April 2012", "Causal inference", "Design of experiments"], "title": "Confounding", "method": "Confounding", "url": "https://en.wikipedia.org/wiki/Confounding", "summary": "In statistics, a confounder (also confounding variable, confounding factor or lurking variable) is a variable that influences both the dependent variable and independent variable causing a spurious association. Confounding is a causal concept, and as such, cannot be described in terms of correlations or associations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/Confounding.PNG", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b8/Simple_Confounding_Case.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alaska", "American Journal of Epidemiology", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anecdotal evidence", "Antidepressant", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Berkson's paradox", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Case-control study", "Categorical variable", "Causal inference", "Causality", "Cause", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort study", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding Factor (games company)", "Confounding factor", "Confusion", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Donald Rubin", "Double blinding", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiological method", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Health", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Judea Pearl", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Leslie Kish", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Lippincott Williams & Wilkins", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Medieval Latin", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New England Journal of Medicine", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational studies", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Peer review", "Percentile", "Permutation test", "Pesticide", "Pie chart", "Pivotal quantity", "Placebo effect", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Risk assessment", "Risk ratio", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "SSRI", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific Reports", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sherry L Mayrent", "Sign test", "Simple linear regression", "Simpson's Paradox", "Simpson's paradox", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratification (statistics)", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tricyclic antidepressant", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.une.edu.au/WebStat/unit_materials/c1_behavioural_science_research/confounds.html", "http://adsabs.harvard.edu/abs/2014NatSR...4E6085L", "http://ftp.cs.ucla.edu/pub/stat_ser/R256.pdf", "http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1009818", "http://www.ncbi.nlm.nih.gov/pubmed/11565527", "http://arxiv.org/abs/1304.0564", "http://doi.org/10.1037%2Fh0037350", "http://doi.org/10.1038%2Fsrep06085", "http://doi.org/10.1056%2Fnejm200109203451211", "http://doi.org/10.1093%2Faje%2F154.3.276", "http://doi.org/10.1093%2Fije%2F15.3.413", "http://doi.org/10.1136%2Fjech.2010.112565", "http://doi.org/10.1136%2Foem.46.8.505", "http://doi.org/10.1214%2F12-aos1058", "http://doi.org/10.1214%2Fss%2F1009211805"]}, "Data stream clustering": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2017", "Cluster analysis algorithms"], "title": "Data stream clustering", "method": "Data stream clustering", "url": "https://en.wikipedia.org/wiki/Data_stream_clustering", "summary": "In computer science, data stream clustering is defined as the clustering of data that arrive continuously such as telephone records, multimedia data, financial transactions etc. Data stream clustering is usually studied as a streaming algorithm and the objective is, given a sequence of points, to construct a good clustering of the stream, using a small amount of memory and time.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/4/45/Small-Space.jpg"], "links": ["Approximation algorithm", "BIRCH (data clustering)", "C2ICM(incremental clustering)", "CURE data clustering algorithm", "Category utility", "CiteSeerX", "Cluster analysis", "Cobweb (clustering)", "Computer science", "Decision tree learning", "Digital object identifier", "Divide-and-conquer algorithm", "Hierarchical clustering", "K-means clustering", "K-medoids", "Local search (optimization)", "Streaming algorithm"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.9554", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.1927", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.9914", "http://dl.acm.org/citation.cfm?doid=130226.134466", "http://doi.acm.org/10.1145/235968.233324", "http://portal.acm.org/citation.cfm?id=796509", "http://doi.org/10.1016%2F0304-3975(80)90061-4", "http://doi.org/10.1023%2FA:1022852608280", "http://doi.org/10.1145%2F130226.134466", "http://doi.org/10.1145%2F235968.233324", "http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4567985", "https://link.springer.com/article/10.1023%2FA:1022852608280"]}, "Logarithmic mean": {"categories": ["All articles needing additional references", "Articles needing additional references from April 2009", "Means"], "title": "Logarithmic mean", "method": "Logarithmic mean", "url": "https://en.wikipedia.org/wiki/Logarithmic_mean", "summary": "In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient. In symbols:\n\n \n \n \n \n \n \n \n \n M\n \n lm\n \n \n (\n x\n ,\n y\n )\n \n \n \n =\n \n lim\n \n (\n \u03be\n ,\n \u03b7\n )\n \u2192\n (\n x\n ,\n y\n )\n \n \n \n \n \n \u03b7\n \u2212\n \u03be\n \n \n ln\n \u2061\n (\n \u03b7\n )\n \u2212\n ln\n \u2061\n (\n \u03be\n )\n \n \n \n \n \n \n \n \n \n =\n \n \n {\n \n \n \n 0\n \n \n \n if \n \n x\n =\n 0\n \n or \n \n y\n =\n 0\n ,\n \n \n \n \n x\n \n \n \n if \n \n x\n =\n y\n ,\n \n \n \n \n \n \n \n y\n \u2212\n x\n \n \n ln\n \u2061\n (\n y\n )\n \u2212\n ln\n \u2061\n (\n x\n )\n \n \n \n \n \n \n otherwise,\n \n \n \n \n \n \n \n \n \n \n \n \n \n {\\displaystyle {\\begin{aligned}M_{\\text{lm}}(x,y)&=\\lim _{(\\xi ,\\eta )\\to (x,y)}{\\frac {\\eta -\\xi }{\\ln(\\eta )-\\ln(\\xi )}}\\\\[6pt]&={\\begin{cases}0&{\\text{if }}x=0{\\text{ or }}y=0,\\\\x&{\\text{if }}x=y,\\\\{\\frac {y-x}{\\ln(y)-\\ln(x)}}&{\\text{otherwise,}}\\end{cases}}\\end{aligned}}}\n for the positive numbers \n \n \n \n x\n ,\n y\n \n \n {\\displaystyle x,y}\n .\nThis calculation is applicable in engineering problems involving heat and mass transfer.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/dd/Logarithmic_mean_3D_plot_from_0_to_100.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Area", "Arithmetic mean", "Derivative", "Difference (mathematics)", "Digital object identifier", "Divided difference", "Engineering", "Eric W. Weisstein", "Exponential function", "Function (mathematics)", "Geometric mean", "Heat transfer", "Homogeneous function", "Logarithm", "Logarithmic mean temperature difference", "Mass transfer", "MathWorld", "Mathematics", "Mean value theorem", "Mean value theorem (divided differences)", "Monotonic function", "Number", "Quotient", "Simplex", "Stolarsky mean"], "references": ["http://mathworld.wolfram.com/Arithmetic-Logarithmic-GeometricMeanInequality.html", "http://doi.org/10.1090%2Fs0002-9939-1966-0188497-6", "https://web.archive.org/web/20060215011645/http://jipam-old.vu.edu.au/v4n4/088_03.html", "https://www.jstor.org/stable/2689825"]}, "Per-protocol analysis": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2010", "Clinical research", "Clinical trials"], "title": "Analysis of clinical trials", "method": "Per-protocol analysis", "url": "https://en.wikipedia.org/wiki/Analysis_of_clinical_trials", "summary": "The analysis of clinical trials involves a large number of related topics including:\n\nthe choice of an estimand (measure of effect size) of interest that is closely linked to the objectives of the trial,\nthe choice and definition of analysis sets,\nthe choice of an appropriate statistical model for the type of data being studied,\nappropriate accounting for the treatment assignment process,\nhandling of missing data,\nhandling of multiple comparisons or endpoints,\naccounting for interim analyses and trial adaptations,\nand appropriate data presentation.One basic guidance document on this topic is the International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use guidance E9.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["AIDS", "Academic clinical trials", "Adaptive clinical trial", "Adverse effect", "Animal testing", "Animal testing on non-human primates", "Attributable fraction among the exposed", "Attributable fraction for the population", "Bias (statistics)", "Blind experiment", "Bootstrapping (statistics)", "Cancer", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Clinical endpoint", "Clinical research", "Clinical study design", "Clinical trial", "Clinical trial protocol", "Cohort study", "Compliance (medicine)", "Confidence interval", "Correlation does not imply causation", "Cross-sectional study", "Cumulative incidence", "Declaration of Helsinki", "Design of experiments", "Digital object identifier", "Ecological study", "Effect size", "Epidemiological methods", "Estimand", "Ethical imperative", "Evidence-based medicine", "Exclusion criteria", "Experiment", "First-in-man study", "Food and Drug Administration", "Generalized estimating equation", "Glossary of clinical research", "Hazard ratio", "Heart failure", "Imputation (statistics)", "In vitro", "In vivo", "Incidence (epidemiology)", "Inclusion criteria", "Infectivity", "Intention-to-treat analysis", "Intention to treat analysis", "Interim analysis", "International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use", "International Standard Book Number", "International Standard Serial Number", "Likelihood ratios in diagnostic testing", "List of clinical research topics", "Longitudinal study", "Meta-analysis", "Missing data", "Morbidity", "Mortality rate", "Multicenter trial", "Multiple comparisons problem", "Multiple imputation", "National Academy of Sciences", "Nested case\u2013control study", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Odds ratio", "Open-label trial", "Period prevalence", "Point prevalence", "Population Impact Measures", "Pre- and post-test probability", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Prospective cohort study", "Protocol (science)", "PubMed Central", "PubMed Identifier", "Randomization", "Randomized controlled trial", "Relative risk reduction", "Reproducibility", "Research participant", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Robust statistics", "Rubin causal model", "Scientific control", "Seeding trial", "Selection bias", "Sensitivity analysis", "Specificity and sensitivity", "Statistical model", "Statistical power", "Survivorship bias", "Systematic review", "Type I error", "Underestimated", "Vaccine trial", "Virulence"], "references": ["http://www.nap.edu/openbook.php?record_id=12955", "http://www.fda.gov/downloads/Drugs/GuidanceComplianceRegulatoryInformation/Guidances/ucm073137.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2553855", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3230230", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3771340", "http://www.ncbi.nlm.nih.gov/pubmed/18718673", "http://www.ncbi.nlm.nih.gov/pubmed/18838445", "http://www.ncbi.nlm.nih.gov/pubmed/20442226", "http://www.ncbi.nlm.nih.gov/pubmed/24983040", "http://doi.org/10.1016%2Fj.psychres.2007.08.005", "http://doi.org/10.1136%2Fbmj.c2073", "http://doi.org/10.1503%2Fcmaj.080820", "http://doi.org/10.17226%2F12955", "http://www.worldcat.org/issn/1756-1833"]}, "Semantic mapping (statistics)": {"categories": ["All Wikipedia articles needing context", "All pages needing cleanup", "Dimension reduction", "Wikipedia articles needing context from November 2010", "Wikipedia introduction cleanup from November 2010"], "title": "Semantic mapping (statistics)", "method": "Semantic mapping (statistics)", "url": "https://en.wikipedia.org/wiki/Semantic_mapping_(statistics)", "summary": "Semantic mapping (SM) is a method in statistics for dimensionality reduction that can be used in a set of multidimensional vectors of features to extract a few new features that preserves the main data characteristics. SM performs dimensionality reduction by clustering the original features in semantic clusters and combining features mapped in the same cluster to generate an extracted feature. Given a data set, this method constructs a projection matrix that can be used to map a data element from a high-dimensional space into a reduced dimensional space. SM can be applied in construction of text mining and information retrieval systems, as well as systems managing vectors of high dimensionality.\nSM is an alternative to random mapping, principal components analysis and latent semantic indexing methods.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Cluster analysis", "Data element", "Data set", "Dimensionality reduction", "Euclidean vector", "High-dimensional space", "Information retrieval", "International Standard Book Number", "Latent semantic indexing", "Principal components analysis", "Projection matrix", "Random mapping", "Statistics", "Text mining", "Unification (computer science)"], "references": ["http://renatocorrea.googlepages.com/", "http://biecoll.ub.uni-bielefeld.de/volltexte/2007/133", "https://dx.doi.org/10.1016/j.neucom.2006.07.007"]}, "It\u014d calculus": {"categories": ["Definitions of mathematical integration", "Stochastic calculus"], "title": "It\u00f4 calculus", "method": "It\u014d calculus", "url": "https://en.wikipedia.org/wiki/It%C3%B4_calculus", "summary": "It\u00f4 calculus, named after Kiyoshi It\u00f4, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations.\nThe central concept is the It\u00f4 stochastic integral, a stochastic generalization of the Riemann\u2013Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes:\n\n \n \n \n \n Y\n \n t\n \n \n =\n \n \u222b\n \n 0\n \n \n t\n \n \n \n H\n \n s\n \n \n \n d\n \n X\n \n s\n \n \n ,\n \n \n {\\displaystyle Y_{t}=\\int _{0}^{t}H_{s}\\,dX_{s},}\n where H is a locally square-integrable process adapted to the filtration generated by X (Revuz & Yor 1999, Chapter IV), which is a Brownian motion or, more generally, a semimartingale. The result of the integration is then another stochastic process. Concretely, the integral from 0 to any particular t is a random variable, defined as a limit of a certain sequence of random variables. The paths of Brownian motion fail to satisfy the requirements to be able to apply the standard techniques of calculus. So with the integrand a stochastic process, the It\u00f4 stochastic integral amounts to an integral with respect to a function which is not differentiable at any point and has infinite variation over every time interval. \nThe main insight is that the integral can be defined as long as the integrand H is adapted, which loosely speaking means that its value at time t can only depend on information available up until this time. Roughly speaking, one chooses a sequence of partitions of the interval from 0 to t and construct Riemann sums. Every time we are computing a Riemann sum, we are using a particular instantiation of the integrator. It is crucial which point in each of the small intervals is used to compute the value of the function. The limit then is taken in probability as the mesh of the partition is going to zero. Numerous technical details have to be taken care of to show that this limit exists and is independent of the particular sequence of partitions. Typically, the left end of the interval is used.\nImportant results of It\u00f4 calculus include the integration by parts formula and It\u00f4's lemma, which is a change of variables formula. These differ from the formulas of standard calculus, due to quadratic variation terms.\nIn mathematical finance, the described evaluation strategy of the integral is conceptualized as that we are first deciding what to do, then observing the change in the prices. The integrand is how much stock we hold, the integrator represents the movement of the prices, and the integral is how much money we have in total including what our stock is worth, at any given moment. The prices of stocks and other traded financial assets can be modeled by stochastic processes such as Brownian motion or, more often, geometric Brownian motion (see Black\u2013Scholes). Then, the It\u00f4 stochastic integral represents the payoff of a continuous-time trading strategy consisting of holding an amount Ht of the stock at time t. In this situation, the condition that H is adapted corresponds to the necessary restriction that the trading strategy can only make use of the available information at any time. This prevents the possibility of unlimited gains through high-frequency trading: buying the stock just before each uptick in the market and selling before each downtick. Similarly, the condition that H is adapted implies that the stochastic integral will not diverge when calculated as a limit of Riemann sums (Revuz & Yor 1999, Chapter IV).", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/4/43/ItoIntegralWienerProcess.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/ItoProcess1D.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Adapted process", "ArXiv", "Associativity", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bernt \u00d8ksendal", "Bessel process", "Biased random walk on a graph", "Bibcode", "Birkhaueser", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes", "Black\u2013Scholes model", "Bochner integral", "Boolean network", "Bounded variation", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "Burkill integral", "B\u00fchlmann model", "Cambridge University Press", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chain rule", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Colored noise", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous linear extension", "Continuous stochastic process", "Contour integration", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Daniell integral", "Darboux integral", "Diffeomorphism", "Differential form", "Differentiation under the integral sign", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Dol\u00e9ans measure", "Dominated convergence theorem", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Einstein notation", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtered probability space", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian integral", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Haar measure", "Hagen Kleinert", "Heath\u2013Jarrow\u2013Morton framework", "Hellinger integral", "Henstock\u2013Kurzweil integral", "Heston model", "Hidden Markov model", "High-frequency trading", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Improper integral", "Independent and identically distributed random variables", "Independent increments", "Infinitesimal generator (stochastic processes)", "Integral", "Integration by partial fractions", "Integration by parts", "Integration by reduction formulae", "Integration by substitution", "Integration using Euler's formula", "Integration using parametric derivatives", "Interacting particle system", "International Standard Book Number", "Inverse function integration", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 isometry", "It\u00f4 process", "Jump diffusion", "Jump process", "Khinchin integral", "Khintchine inequality", "Kiyoshi It\u00f4", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kolmogorov integral", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Langevin equation", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Lebesgue integration", "Lebesgue\u2013Stieltjes integral", "Lebesgue\u2013Stieltjes integration", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mesh (mathematics)", "Mexican hat wavelet", "Mixing (mathematics)", "Monotone class lemma", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Numerical integration", "Optional stopping theorem", "Order of integration (calculus)", "Ornstein\u2013Uhlenbeck process", "Partition of an interval", "Percolation theory", "Pettis integral", "Pfeffer integral", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Pullback (differential geometry)", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Regulated integral", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Riemann integral", "Riemann sum", "Riemann\u2013Stieltjes integral", "Right-continuous", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic calculus", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "Supersymmetric theory of stochastic dynamics", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Trigonometric substitution", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "\u03a3-algebra"], "references": ["http://www.physik.fu-berlin.de/~kleinert/b5", "http://adsabs.harvard.edu/abs/2007PhRvE..76a1123L", "http://arxiv.org/abs/0707.2234", "http://doi.org/10.1103%2FPhysRevE.76.011123"]}, "Wald test": {"categories": ["Statistical tests"], "title": "Wald test", "method": "Wald test", "url": "https://en.wikipedia.org/wiki/Wald_test", "summary": "The Wald test is a parametric statistical test named after the statistician Abraham Wald. Whenever a relationship within or between data items can be expressed as a statistical model with parameters to be estimated from a sample, the Wald test can be used to test the true value of the parameter based on the sample estimate.\nSuppose a social scientist, who has data on social class and shoe size, wonders whether social class is associated with shoe size. Say \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n is the average increase in shoe size for upper-class people compared to middle-class people: then the Wald test can be used to test whether \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n is 0 (in which case social class has no association with shoe size) or non-zero (shoe size varies between social classes). Here, \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n , the hypothetical difference in shoe sizes between upper and middle-class people in the whole population, is a parameter. An estimate of \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n might be the difference in shoe size between upper and middle-class people in the sample. In the Wald test, the social scientist uses the estimate and an estimate of variability (see below) to draw conclusions about the unobserved true \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n . Or, for a medical example, suppose smoking multiplies the risk of lung cancer by some number R: then the Wald test can be used to test whether R = 1 (i.e. there is no effect of smoking) or is greater (or less) than 1 (i.e. smoking alters risk).\nA Wald test can be used in a great variety of different models including models for dichotomous variables and models for continuous variables.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abraham Wald", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chow test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran\u2013Mantel\u2013Haenzel test", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Delta method", "Demographic statistics", "Density estimation", "Derivative", "Descriptive statistics", "Design of experiments", "Dichotomous", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher information", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fumio Hayashi", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jan Kmenta", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monotonic", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robert F. Engle", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Slutsky's theorem", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard error (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sup-Wald test", "Survey methodology", "Survival analysis", "Survival function", "System identification", "The American Statistician", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variable (mathematics)", "Variance", "Vector autoregression", "Wavelet", "Welch's t-test", "Whittle likelihood", "Wilcoxon signed-rank test", "William Greene (economist)", "Z-test"], "references": ["http://jeff560.tripod.com/mathword.html", "http://jeff560.tripod.com/w.html", "http://doi.org/10.1080%2F00031305.1996.10474384", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA489", "https://cran.r-project.org/web/packages/SPRT/SPRT.pdf"]}, "Order statistic": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from December 2010", "Nonparametric statistics", "Permutations", "Summary statistics"], "title": "Order statistic", "method": "Order statistic", "url": "https://en.wikipedia.org/wiki/Order_statistic", "summary": "In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Together with rank statistics, order statistics are among the most fundamental tools in non-parametric statistics and inference.\nImportant special cases of the order statistics are the minimum and maximum value of a sample, and (with some qualifications discussed below) the sample median and other sample quantiles.\nWhen using probability theory to analyze order statistics of random samples from a continuous distribution, the cumulative distribution function is used to reduce the analysis to the case of order statistics of the uniform distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/cb/Order_Statistics_Exponential_PDF.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute continuity", "Accelerated failure time model", "Acta Mathematica Hungarica", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Mathematical Statistics", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bapat\u2013Beg theorem", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernstein polynomial", "Beta distribution", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Concomitant (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Delta method", "Demographic statistics", "Density estimation", "Density function", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Eric W. Weisstein", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Even and odd numbers", "Experiment", "Exploratory data analysis", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher\u2013Tippett distribution", "Forest plot", "Fourier analysis", "Frederick Mosteller", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent (statistics)", "Independent and identically distributed", "Index of dispersion", "Institute of Mathematical Statistics", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-estimator", "L-moment", "Laplace distribution", "Laplace transform", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marginal distribution", "MathWorld", "Maximum", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric inference", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "PlanetMath", "Plug-in principle", "Point estimate", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile", "Quantile function", "Quartile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Raghu Raj Bahadur", "Random assignment", "Random sample", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank-size distribution", "Rank correlation", "Rank statistics", "Rankit", "Rao\u2013Blackwell theorem", "Realization (probability)", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample maximum and minimum", "Sample mean", "Sample median", "Sample range", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sampling in order", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Selection algorithm", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Sorting algorithm", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Susan P. Holmes", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "Unit interval", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://onlinelibrary.wiley.com/doi/10.1002/0471722162.ch2/summary", "http://mathworld.wolfram.com/OrderStatistic.html", "http://www-stat.stanford.edu/~susan/courses/s116/node79.html", "http://doi.org/10.1002%2F0471722162", "http://doi.org/10.1002%2F0471722162.ch2", "http://doi.org/10.1007%2FBF02127580", "http://doi.org/10.1016%2Fj.spl.2009.09.006", "http://doi.org/10.1016%2Fj.stamet.2008.04.001", "http://doi.org/10.1214%2Faoms%2F1177730881", "http://www.mathunion.org/ICM/ICM1954.1/Main/icm1954.1.0508.0510.ocr.pdf", "http://planetmath.org/OrderStatistics", "http://projecteuclid.org/euclid.aoms/1177730881", "https://github.com/xtaci/algorithms/blob/master/include/dos_tree.h", "https://books.google.com/books?id=mQ5KAAAAQBAJ&pg=PA63", "https://web.archive.org/web/20161009020918/http://www.mathunion.org/ICM/ICM1954.1/Main/icm1954.1.0508.0510.ocr.pdf"]}, "Post-hoc analysis": {"categories": ["Articles with short description", "Clinical research", "Data analysis", "Medical statistics", "Multiple comparisons"], "title": "Post hoc analysis", "method": "Post-hoc analysis", "url": "https://en.wikipedia.org/wiki/Post_hoc_analysis", "summary": "In a scientific study, post hoc analysis (from Latin post hoc, \"after this\") consists of statistical analyses that were not specified before the data was seen. This typically creates a multiple testing problem because each potential analysis is effectively a statistical test. Multiple testing procedures are sometimes used to compensate, but that is often difficult or impossible to do precisely. Post hoc analysis that is conducted and interpreted without adequate consideration of this problem is sometimes called data dredging by critics, in part because the statistical associations that it finds may be spurious.", "images": [], "links": ["Astrological sign", "Br J Cancer", "Data dredging", "Digital object identifier", "Food and Drug Administration", "International Standard Serial Number", "Latin language", "Multiple testing", "Post hoc (disambiguation)", "Post hoc theorizing", "Richard Peto", "Secondary prevention", "Statistical hypothesis testing", "Statistics", "Subgroup analysis", "Testing hypotheses suggested by the data"], "references": ["http://www.worldcat.org/issn/0362-4331", "https://www.nytimes.com/2017/11/28/magazine/a-failure-to-heal.html", "https://doi.org/10.1038%2Fbjc.2011.79"]}, "Law of total cumulance": {"categories": ["Algebra of random variables", "Statistical laws", "Statistical theorems", "Theory of probability distributions"], "title": "Law of total cumulance", "method": "Law of total cumulance", "url": "https://en.wikipedia.org/wiki/Law_of_total_cumulance", "summary": "In probability theory and mathematical statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of total expectation, and the law of total variance. It has applications in the analysis of time series. It was introduced by David Brillinger.It is most transparent when stated in its most general form, for joint cumulants, rather than for cumulants of a specified order for just one random variable. In general, we have\n\n \n \n \n \u03ba\n (\n \n X\n \n 1\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n )\n =\n \n \u2211\n \n \u03c0\n \n \n \u03ba\n (\n \u03ba\n (\n \n X\n \n i\n \n \n :\n i\n \u2208\n B\n \u2223\n Y\n )\n :\n B\n \u2208\n \u03c0\n )\n ,\n \n \n {\\displaystyle \\kappa (X_{1},\\dots ,X_{n})=\\sum _{\\pi }\\kappa (\\kappa (X_{i}:i\\in B\\mid Y):B\\in \\pi ),}\n where\n\n\u03ba(X1, ..., Xn) is the joint cumulant of n random variables X1, ..., Xn, and\nthe sum is over all partitions \n \n \n \n \u03c0\n \n \n {\\displaystyle \\pi }\n of the set { 1, ..., n } of indices, and\n\"B \u2208 \u03c0;\" means B runs through the whole list of \"blocks\" of the partition \u03c0, and\n\u03ba(Xi : i \u2208 B | Y) is a conditional cumulant given the value of the random variable Y. It is therefore a random variable in its own right\u2014a function of the random variable Y.", "images": [], "links": ["Central moment", "Cumulant", "Expected value", "Law of total expectation", "Law of total probability", "Law of total variance", "Mathematics", "Moment (mathematics)", "Normal distribution", "Partition of a set", "Poisson distribution", "Probability theory", "Random variable", "Statistical independence", "Statistics", "Time series"], "references": []}, "Idempotent matrix": {"categories": ["Algebra", "Matrices", "Regression analysis"], "title": "Idempotent matrix", "method": "Idempotent matrix", "url": "https://en.wikipedia.org/wiki/Idempotent_matrix", "summary": "In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix M is idempotent if and only if MM = M. For this product MM to be defined, M must necessarily be a square matrix. Viewed this way, idempotent matrices are idempotent elements of matrix rings.", "images": [], "links": ["Bias (statistics)", "Circle", "Column space", "Dependent and independent variables", "Diagonal matrix", "Diagonalizable", "Econometrics", "Eigenvalue", "Hat matrix", "Idempotence", "Idempotent element (ring theory)", "Identity matrix", "International Standard Book Number", "Linear algebra", "Matrix (mathematics)", "Matrix multiplication", "Matrix ring", "Nilpotent", "Null space", "Ordinary least squares", "Orthogonal projection", "Projection (linear algebra)", "Quadratic equation", "Rank (linear algebra)", "Regression analysis", "Singular matrix", "Square matrix", "Statistics", "Symmetric matrix", "Trace (linear algebra)", "Transpose", "Variance"], "references": ["https://books.google.com/books?id=PlYQN0ypTwEC&pg=PA148&dq=%22every+idempotent+matrix+is+diagonalizable%22"]}, "Hurst exponent": {"categories": ["Autocorrelation", "Fractals", "Wikipedia articles needing clarification from August 2011", "Wikipedia articles needing page number citations from September 2010"], "title": "Hurst exponent", "method": "Hurst exponent", "url": "https://en.wikipedia.org/wiki/Hurst_exponent", "summary": "The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases.\nStudies involving the Hurst exponent were originally developed in hydrology for the practical matter of determining optimum dam sizing for the Nile river's volatile rain and drought conditions that had been observed over a long period of time. The name \"Hurst exponent\", or \"Hurst coefficient\", derives from Harold Edwin Hurst (1880\u20131978), who was the lead researcher in these studies; the use of the standard notation H for the coefficient relates to his name also.\nIn fractal geometry, the generalized Hurst exponent has been denoted by H or Hq in honor of both Harold Edwin Hurst and Ludwig Otto H\u00f6lder (1859\u20131937) by Beno\u00eet Mandelbrot (1924\u20132010). H is directly related to fractal dimension, D, and is a measure of a data series' \"mild\" or \"wild\" randomness.The Hurst exponent is referred to as the \"index of dependence\" or \"index of long-range dependence\". It quantifies the relative tendency of a time series either to regress strongly to the mean or to cluster in a direction. A value H in the range 0.5\u20131 indicates a time series with long-term positive autocorrelation, meaning both that a high value in the series will probably be followed by another high value and that the values a long time into the future will also tend to be high. A value in the range 0 \u2013 0.5 indicates a time series with long-term switching between high and low values in adjacent pairs, meaning that a single high value will probably be followed by a low value and that the value after that will tend to be high, with this tendency to switch between high and low values lasting a long time into the future. A value of H=0.5 can indicate a completely uncorrelated series, but in fact it is the value applicable to series for which the autocorrelations at small time lags can be positive or negative but where the absolute values of the autocorrelations decay exponentially quickly to zero. This in contrast to the typically power law decay for the 0.5 < H < 1 and 0 < H < 0.5 cases.", "images": [], "links": ["Algebraic structure", "Anomalous diffusion", "ArXiv", "Autocorrelation", "Band gap", "Beno\u00eet Mandelbrot", "Bibcode", "Bootstrapping (statistics)", "Brown noise", "CiteSeerX", "DNA", "Detrended fluctuation analysis", "Digital object identifier", "Euler Gamma Function", "Expected value", "Fractal dimension", "Fractal geometry", "Fractional Brownian motion", "Frequency domain", "H (disambiguation)", "Harold Edwin Hurst", "Hydrology", "International Standard Book Number", "International Standard Serial Number", "Long-range dependency", "L\u00e9vy stable process", "Markov process", "Mean", "Multifractal system", "Nile river", "Otto Ludwig Holder", "Pink noise", "Power law", "PubMed Central", "PubMed Identifier", "Range (statistics)", "Rescaled range", "Self-similarity", "Standard deviation", "Time domain", "Time series", "Truncated L\u00e9vy process", "White noise"], "references": ["http://www.nature.com/ncomms/2015/150916/ncomms9269/full/ncomms9269.html?WT.ec_id=NCOMMS-20150923", "http://www.sciencedirect.com/science/article/pii/S0378437102009615", "http://onlinelibrary.wiley.com/doi/10.1029/WR005i005p00967/abstract", "http://edoc.hu-berlin.de/dissertationen/kleinow-torsten-2002-07-04/PDF/Kleinow.pdf", "http://adsabs.harvard.edu/abs/1968WRR.....4..909M", "http://adsabs.harvard.edu/abs/1969WRR.....5..967M", "http://adsabs.harvard.edu/abs/1985PhyS...32..257M", "http://adsabs.harvard.edu/abs/1998PhRvE..58.2779S", "http://adsabs.harvard.edu/abs/2001PhRvE..63f2102H", "http://adsabs.harvard.edu/abs/2001PhyA..295..441K", "http://adsabs.harvard.edu/abs/2002PhyA..312..285W", "http://adsabs.harvard.edu/abs/2002PhyA..316...87K", "http://adsabs.harvard.edu/abs/2002PhyA..316..496G", "http://adsabs.harvard.edu/abs/2003PhRvL..91v8101R", "http://adsabs.harvard.edu/abs/2004SIAMR..46..269G", "http://adsabs.harvard.edu/abs/2009NJPh...11i3024P", "http://adsabs.harvard.edu/abs/2011PhyA..390.4426B", "http://adsabs.harvard.edu/abs/2015NatCo...6E8269Y", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.207", "http://complex.phys.uh.edu", "http://www.uh.edu/~jmccaul2/", "http://users.math.yale.edu/~bbm3/web_pdfs/112selfAffinity.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4595658", "http://www.ncbi.nlm.nih.gov/pubmed/14683275", "http://www.ncbi.nlm.nih.gov/pubmed/26373616", "http://havlin.biu.ac.il/Publications.php?keyword=Detecting+long-range+correlations+with+detrended+fluctuation+analysis++&year=*&match=all", "http://havlin.biu.ac.il/Publications.php?keyword=Multifractal+detrended+fluctuation+analysis+of+nonstationary+time+series&year=*&match=all", "http://www.aureliofernandez.net/", "http://link.aps.org/doi/10.1103/PhysRevE.58.2779", "http://link.aps.org/doi/10.1103/PhysRevLett.91.228101", "http://arxiv.org/abs/0706.1062", "http://arxiv.org/abs/1501.02591", "http://arxiv.org/abs/cond-mat/0007011", "http://arxiv.org/abs/cond-mat/0102214", "http://arxiv.org/abs/cond-mat/0103510", "http://arxiv.org/abs/cond-mat/0205482", "http://arxiv.org/abs/cond-mat/0309463", "http://arxiv.org/abs/cond-mat/9707153", "http://arxiv.org/abs/physics/0109031", "http://arxiv.org/abs/physics/0202070", "http://doi.org/10.1016%2FS0378-4371(01)00144-3", "http://doi.org/10.1016%2FS0378-4371(02)00961-5", "http://doi.org/10.1016%2Fj.physa.2011.07.032", "http://doi.org/10.1016%2Fs0378-4371(02)01021-x", "http://doi.org/10.1016%2Fs0378-4371(02)01383-3", "http://doi.org/10.1029%2FWR005i005p00967", "http://doi.org/10.1029%2Fwr004i005p00909", "http://doi.org/10.1038%2Fncomms9269", "http://doi.org/10.1088%2F0031-8949%2F32%2F4%2F001", "http://doi.org/10.1088%2F1367-2630%2F11%2F9%2F093024", "http://doi.org/10.1093%2Fbiomet%2F63.1.111", "http://doi.org/10.1103%2FPhysRevE.58.2779", "http://doi.org/10.1103%2FPhysRevE.63.062102", "http://doi.org/10.1103%2FPhysRevLett.91.228101", "http://doi.org/10.1111%2Fj.1467-9892.1983.tb00371.x", "http://doi.org/10.1137%2F070710111", "http://doi.org/10.1137%2Fs0036144501394387", "http://doi.org/10.1214%2Faos%2F1176324317", "http://www.iop.org/EJ/abstract/1367-2630/11/9/093024/", "http://biomet.oxfordjournals.org/content/63/1/111", "http://www.worldcat.org/issn/0006-3444", "http://www.worldcat.org/issn/1944-7973", "https://github.com/Mottl/hurst", "https://arxiv.org/abs/0710.2583", "https://ideas.repec.org/s/wuu/hscode.html"]}, "Locality (statistics)": {"categories": ["Probability theory", "Summary statistics"], "title": "Central tendency", "method": "Locality (statistics)", "url": "https://en.wikipedia.org/wiki/Central_tendency", "summary": "In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution. It may also be called a center or location of the distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s.The most common measures of central tendency are the arithmetic mean, the median and the mode. A central tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote \"the tendency of quantitative data to cluster around some central value.\"The central tendency of a distribution is typically contrasted with its dispersion or variability; dispersion and central tendency are the often characterized properties of distributions. Analysts may judge whether data has a strong or a weak central tendency based on its dispersion.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average absolute deviation", "Averages", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calculus of variations", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Centrality", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Coercive function", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convex function", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric median", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "International Statistical Institute", "Interquartile mean", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum deviation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Midhinge", "Midrange", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiplicative inverse", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric skew", "Nonparametric statistics", "Normal distribution", "Nth root", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-norm", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quadratic mean", "Quality control", "Quartile", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Root mean square", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simplex", "Simplicial depth", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Strictly convex", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Trimean", "Truncated mean", "Tukey median", "U-statistic", "Uniformly most powerful test", "Unimodal distribution", "V-statistic", "Variance", "Variation ratio", "Vector autoregression", "Wald test", "Wavelet", "Weighted arithmetic mean", "Whittle likelihood", "Wilcoxon signed-rank test", "Winsorized mean", "Z-test"], "references": []}, "True variance": {"categories": ["All articles lacking in-text citations", "All articles with incomplete citations", "All articles with unsourced statements", "Articles containing proofs", "Articles lacking in-text citations from November 2018", "Articles with excessive see also sections from May 2017", "Articles with incomplete citations from March 2013", "Articles with inconsistent citation formats", "Articles with unsourced statements from February 2012", "Articles with unsourced statements from June 2015", "Articles with unsourced statements from September 2016", "CS1 maint: Uses authors parameter", "Moment (mathematics)", "Statistical deviation and dispersion", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "Variance", "method": "True variance", "url": "https://en.wikipedia.org/wiki/Variance", "summary": "In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of (random) numbers are spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n {\\displaystyle \\sigma ^{2}}\n , \n \n \n \n \n s\n \n 2\n \n \n \n \n {\\displaystyle s^{2}}\n , or \n \n \n \n Var\n \u2061\n (\n X\n )\n \n \n {\\displaystyle \\operatorname {Var} (X)}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f9/Comparison_standard_deviations.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/6/60/Scaled_chi_squared.svg", "https://upload.wikimedia.org/wikipedia/commons/9/97/Scaled_chi_squared_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/6/64/Variance_visualisation.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Algebraic formula for the variance", "Algorithms for calculating variance", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average absolute deviation", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bessel's correction", "Bhatia\u2013Davis inequality", "Bias of an estimator", "Biased estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biometry", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box test", "Box\u2013Anderson test", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cantor distribution", "Capon test", "Cartography", "Catastrophic cancellation", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central moment", "Central tendency", "Characteristic function (probability theory)", "Chebyshev's inequality", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi square test", "CiteSeerX", "Classical mechanics", "Classical test theory", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinant", "Common-method variance", "Completeness (statistics)", "Complex conjugate", "Complex number", "Concave function", "Conditional expectation", "Conditional variance", "Confidence interval", "Confounding", "Conjugate transpose", "Consistent estimator", "Contingency table", "Continuous distribution", "Continuous probability distribution", "Continuous random variable", "Control chart", "Correlated", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Covariance matrix", "Credible interval", "Crime statistics", "Cronbach's alpha", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulative distribution function", "Data collection", "Data set", "Decomposition of time series", "Definite integral", "Degrees of freedom (statistics)", "Delta method", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Deviation (statistics)", "Dice", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete probability distribution", "Discrete random variable", "Distance variance", "Divergence (statistics)", "Downside risk", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation of covariance matrices", "Estimation theory", "Estimator", "Euclidean distance", "Excess kurtosis", "Expected value", "Experiment", "Explained variance", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "F test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Floating point arithmetic", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heavy-tailed distribution", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis testing", "Independence (probability theory)", "Index of dispersion", "Integrated Authority File", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Invariant (mathematics)", "Investment", "Ir\u00e9n\u00e9e-Jules Bienaym\u00e9", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jensen's inequality", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Klotz test", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Law of total variance", "Lehmann test", "Lehmann\u2013Scheff\u00e9 theorem", "Leo Goodman", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean absolute difference", "Mean absolute error", "Mean preserving spread", "Mean square error", "Mean squared error", "Measurement error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michel Lo\u00e8ve", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment-generating function", "Moment (mathematics)", "Moment (physics)", "Moment of inertia", "Moment of inertia tensor", "Monotone likelihood ratio", "Monte Carlo method", "Mood test", "Moses test", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Observations", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outlier", "Outline of statistics", "Parametric statistics", "Pareto distribution", "Pareto index", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Pooled variance", "Popoviciu's inequality on variances", "Population (statistics)", "Population statistics", "Positive definite matrix", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability-generating function", "Probability density function", "Probability distribution", "Probability mass function", "Probability theory", "Proportional hazards model", "Psychometrics", "Qualitative variation", "Quality control", "Quantile function", "Quasi-experiment", "Quasi-variance", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raw moment", "Reduced chi-squared", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Root mean square deviation", "Run chart", "Sample (statistics)", "Sample covariance", "Sample mean", "Sample mean and covariance", "Sample median", "Sample size determination", "Sample standard deviation", "Sampling (statistics)", "Sampling distribution", "Samuelson's inequality", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Semivariance", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shrinkage estimator", "Sigma", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spearman\u2013Brown prediction formula", "Spectral density estimation", "Square root", "Squared deviations", "Standard deviation", "Standard error", "Standard error (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sukhatme test", "Sum of normally distributed random variables", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taylor's law", "Taylor expansion", "Taylor expansions for the moments of functions of random variables", "The Correlation Between Relatives on the Supposition of Mendelian Inheritance", "Time domain", "Time series", "Tolerance interval", "Trace (linear algebra)", "Transpose", "Trend estimation", "U-statistic", "Unbiased estimation of standard deviation", "Uncorrelated", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-covariance matrix", "Variance (disambiguation)", "Vector autoregression", "Vector space", "Wald test", "Wavelet", "Weighted mean", "Weighted variance", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15097/1/9.pdf", "http://www.mathstatica.com/book/Mathematical_Statistics_with_Mathematica.pdf", "http://mathworld.wolfram.com/SampleVarianceDistribution.html", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.551.9397", "http://www.ijpam.eu/contents/2005-21-3/10/10.pdf", "http://www.ijpam.eu/contents/2009-52-1/5/5.pdf", "http://gallica.bnf.fr/ark:/12148/bpt6k16411c/f166.image.n19", "http://visualiseur.bnf.fr/CadresFenetre?O=NUMM-2994&I=313", "http://sites.mathdoc.fr/JMPA/PDF/JMPA_1867_2_12_A10_0.pdf", "http://krishikosh.egranth.ac.in/bitstream/1/2025521/1/G2257.pdf", "http://doi.org/10.1006%2Fjmaa.1999.6688", "http://doi.org/10.1016%2FS0167-7152(98)00041-8", "http://doi.org/10.1080%2F01621459.1968.10480944", "http://doi.org/10.2307%2F2281592", "http://doi.org/10.7153%2Fjmi-02-11", "http://www.jstor.org/stable/2281592", "http://www.jstor.org/stable/2285901", "https://d-nb.info/gnd/4078739-4", "https://id.ndl.go.jp/auth/ndlna/00561029", "https://www.wikidata.org/wiki/Q175199"]}, "Climate ensemble": {"categories": ["Climate", "Climate and weather statistics"], "title": "Climate ensemble", "method": "Climate ensemble", "url": "https://en.wikipedia.org/wiki/Climate_ensemble", "summary": "A climate ensemble involves slightly different models of the climate system. There are at least four different types, to be described below. For the equivalent in numerical weather prediction, see ensemble forecasting.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/25/CPGrandensemble.PNG"], "links": ["ADCIRC", "ADMS 3", "AERMOD", "ATSTEP", "AUSTAL2000", "Atmospheric dispersion modeling", "Atmospheric model", "CALPUFF", "CGCM", "CLaMS", "Canadian Land Surface Scheme", "Chemical transport model", "Climate Forecast System", "Climate model", "Climateprediction.net", "Community Climate System Model", "Community Earth System Model", "Computer simulation", "DISPERSION21", "ECHAM", "Ensemble (fluid mechanics)", "Ensemble forecasting", "FESOM", "Finite Volume Community Ocean Model", "Flow-following, finite-volume Icosahedral Model", "GEOS-Chem", "GFDL CM2.X", "GME of Deutscher Wetterdienst", "Global Environmental Multiscale Model", "Global Forecast System", "HIRLAM", "HWRF", "HadCM3", "HadGEM1", "ISC3", "Integrated Forecast System", "Interaction Soil-Biosphere-Atmosphere", "Intermediate General Circulation Model", "JULES", "MEMO Model", "MERCURE", "MIT General Circulation Model", "MM5 (weather model)", "MOZART (model)", "Mathematical model", "Meteorological reanalysis", "Model for Prediction Across Scales", "Model output statistics", "Modular ocean model", "NAME (dispersion model)", "National Climate Projections", "Navy Global Environmental Model", "Navy Operational Global Atmospheric Prediction System", "Nested Grid Model", "North American Ensemble Forecast System", "North American Mesoscale Model", "Numerical weather prediction", "Operational Street Pollution Model", "PUFF-PLUME", "Parametrization (atmospheric modeling)", "Princeton ocean model", "Probability distribution function", "RIMPUFF", "Rapid Refresh", "Rapid Update Cycle", "Regional Atmospheric Modeling System", "Regional Ocean Modeling System", "SAFE AIR", "Scientific modelling", "Sensitivity analysis", "Special Report on Emissions Scenarios", "Statistical model", "Tropical cyclone forecast model", "Uncertainty analysis", "Unified Model", "Upper-atmospheric models", "Weather Research and Forecasting model"], "references": ["http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8487303", "https://www.scribd.com/doc/208284648/Climate-Prediction-CPU"]}, "Inverse distribution": {"categories": ["Algebra of random variables", "All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from April 2013", "Articles with unsourced statements from April 2013", "Types of probability distributions"], "title": "Inverse distribution", "method": "Inverse distribution", "url": "https://en.wikipedia.org/wiki/Inverse_distribution", "summary": "In probability theory and statistics, an inverse distribution is the distribution of the reciprocal of a random variable. Inverse distributions arise in particular in the Bayesian context of prior distributions and posterior distributions for scale parameters. In the algebra of random variables, inverse distributions are special cases of the class of ratio distributions, in which the numerator random variable has a degenerate distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Algebra of random variables", "Bayesian inference", "Big O notation", "Bimodal", "Bimodal distribution", "Cauchy distribution", "Continuous probability distribution", "Cumulative distribution function", "Degenerate distribution", "Degrees of freedom", "Expected value", "F distribution", "Harmonic mean", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse distribution function", "Inverse matrix gamma distribution", "Median", "Multiplicative inverse", "Normally distributed", "Posterior distribution", "Prior distribution", "Probability density function", "Probability distribution", "Probability theory", "Proportionality (mathematics)", "Ratio distribution", "Reciprocal distribution", "Relationships among probability distributions", "Richard Hamming", "Scale parameter", "Statistics", "Student's t-distribution", "Support (mathematics)", "Uniform distribution (continuous)", "Variance"], "references": ["http://lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf"]}, "Empirical orthogonal functions": {"categories": ["Spatial data analysis", "Statistical signal processing"], "title": "Empirical orthogonal functions", "method": "Empirical orthogonal functions", "url": "https://en.wikipedia.org/wiki/Empirical_orthogonal_functions", "summary": "In statistics and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. It is similar to performing a principal components analysis on the data, except that the EOF method finds both time series and spatial patterns. The term is also interchangeable with the geographically weighted PCAs in geophysics.The i th basis function is chosen to be orthogonal to the basis functions from the first through i \u2212 1, and to minimize the residual variance. That is, the basis functions are chosen to be different from each other, and to account for as much variance as possible.\nThe method of EOF analysis is similar in spirit to harmonic analysis, but harmonic analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed frequencies. In some cases the two methods may yield essentially the same results.\nThe basis functions are typically found by computing the eigenvectors of the covariance matrix of the data set. A more advanced technique is to form a kernel out of the data, using a fixed kernel. The basis functions from the eigenvectors of the kernel matrix are thus non-linear in the location of the data (see Mercer's theorem and the kernel trick for more information).", "images": [], "links": ["Basis function", "Biometrika", "Blind signal separation", "Covariance matrix", "Eigenvector", "Frequency", "Geophysics", "Harmonic analysis", "Kernel (matrix)", "Kernel (statistics)", "Kernel trick", "Mercer's theorem", "Multilinear PCA", "Multilinear subspace learning", "Nonlinear dimensionality reduction", "Orthogonal", "Orthogonal matrix", "Principal components analysis", "Signal processing", "Signal separation", "Statistics", "Three-dimensional space", "Time series", "Transform coding", "Variance", "Varimax rotation"], "references": ["http://brunnur.vedur.is/pub/halldor/TEXT/eofsvd.html", "http://www.gfi.uib.no/~nilsg/kurs/notes/", "http://www.gfi.uib.no/~nilsg/kurs/notes/node87.html", "http://www.uib.no/people/ngbnk/kurs/notes/node87.html", "http://journals.ametsoc.org/doi/pdf/10.1175/1520-0485(1984)014%3C0035:REOFAO%3E2.0.CO;2", "https://dx.doi.org/10.1093/biomet/86.4.815"]}, "DFFITS": {"categories": ["Regression diagnostics"], "title": "DFFITS", "method": "DFFITS", "url": "https://en.wikipedia.org/wiki/DFFITS", "summary": "DFFITS is a diagnostic meant to show how influential a point is in a statistical regression. It was proposed in 1980. It is defined as the Studentized DFFIT, where the latter is the change in the predicted value for a point, obtained when that point is left out of the regression; Studentization is achieved by dividing by the estimated standard deviation of the fit at that point:\n\n \n \n \n \n DFFITS\n \n =\n \n \n \n \n \n \n \n y\n \n i\n \n \n ^\n \n \n \n \u2212\n \n \n \n \n y\n \n i\n (\n i\n )\n \n \n ^\n \n \n \n \n \n \n s\n \n (\n i\n )\n \n \n \n \n \n h\n \n i\n i\n \n \n \n \n \n \n \n \n \n {\\displaystyle {\\text{DFFITS}}={{\\widehat {y_{i}}}-{\\widehat {y_{i(i)}}} \\over s_{(i)}{\\sqrt {h_{ii}}}}}\n where \n \n \n \n \n \n \n \n y\n \n i\n \n \n ^\n \n \n \n \n \n {\\displaystyle {\\widehat {y_{i}}}}\n and \n \n \n \n \n \n \n \n y\n \n i\n (\n i\n )\n \n \n ^\n \n \n \n \n \n {\\displaystyle {\\widehat {y_{i(i)}}}}\n are the prediction for point i with and without point i included in the regression,\n\n \n \n \n \n s\n \n (\n i\n )\n \n \n \n \n {\\displaystyle s_{(i)}}\n is the standard error estimated without the point in question, and \n \n \n \n \n h\n \n i\n i\n \n \n \n \n {\\displaystyle h_{ii}}\n is the leverage for the point.\nDFFITS is very similar to the externally Studentized residual, and is in fact equal to the latter times \n \n \n \n \n \n \n h\n \n i\n i\n \n \n \n /\n \n (\n 1\n \u2212\n \n h\n \n i\n i\n \n \n )\n \n \n \n \n {\\displaystyle {\\sqrt {h_{ii}/(1-h_{ii})}}}\n .As when the errors are Gaussian the externally Studentized residual is distributed as Student's t (with a number of degrees of freedom equal to the number of residual degrees of freedom minus one), DFFITS for a particular point will be distributed according to this same Student's t distribution multiplied by the leverage factor \n \n \n \n \n \n \n h\n \n i\n i\n \n \n \n /\n \n (\n 1\n \u2212\n \n h\n \n i\n i\n \n \n )\n \n \n \n \n {\\displaystyle {\\sqrt {h_{ii}/(1-h_{ii})}}}\n for that particular point. Thus, for low leverage points, DFFITS is expected to be small, whereas as the leverage goes to 1 the distribution of the DFFITS value widens infinitely.\nFor a perfectly balanced experimental design (such as a factorial design or balanced partial factorial design), the leverage for each point is p/n, the number of parameters divided by the number of points. This means that the DFFITS values will be distributed (in the Gaussian case) as \n \n \n \n \n \n \n p\n \n n\n \u2212\n p\n \n \n \n \n \u2248\n \n \n \n p\n n\n \n \n \n \n \n {\\displaystyle {\\sqrt {p \\over n-p}}\\approx {\\sqrt {p \\over n}}}\n times a t variate. Therefore, the authors suggest investigating those points with DFFITS greater than \n \n \n \n 2\n \n \n \n p\n n\n \n \n \n \n \n {\\displaystyle 2{\\sqrt {p \\over n}}}\n .\nAlthough the raw values resulting from the equations are different, Cook's distance and DFFITS are conceptually identical and there is a closed-form formula to convert one value to the other.", "images": [], "links": ["Cook's distance", "DFBETA", "Degrees of freedom (statistics)", "Factorial design", "Gaussian", "Influential point", "International Standard Book Number", "John Wiley & Sons", "Leverage (statistics)", "Statistical regression", "Student's t", "Studentized residual"], "references": ["https://books.google.com/books?id=0yR4KUL4VDkC&pg=PA218", "https://books.google.com/books?id=GECBEUJVNe0C&pg=PA11"]}, "Studentization": {"categories": ["All stub articles", "Statistical ratios", "Statistics stubs"], "title": "Studentization", "method": "Studentization", "url": "https://en.wikipedia.org/wiki/Studentization", "summary": "In statistics, Studentization, named after William Sealy Gosset, who wrote under the pseudonym Student, is the adjustment consisting of division of a first-degree statistic derived from a sample, by a sample-based estimate of a population standard deviation. The term is also used for the standardisation of a higher-degree statistic by another statistic of the same degree: for example, an estimate of the third central moment would be standardised by dividing by the cube of the sample standard deviation.\nA simple example is the process of dividing a sample mean by the sample standard deviation when data arise from a location-scale family. The consequence of \"Studentization\" is that the complication of treating the probability distribution of the mean, which depends on both the location and scale parameters, has been reduced to considering a distribution which depends only on the location parameter. However, the fact that a sample standard deviation is used, rather than the unknown population standard deviation, complicates the mathematics of finding the probability distribution of a Studentized statistic.\nIn computational statistics, the idea of using Studentized statistics is of some importance in the development of confidence intervals with improved properties in the context of resampling and, in particular, bootstrapping.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational statistics", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location-scale family", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Pseudonym", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student", "Student's t-test", "Studentized range", "Studentized residual", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Sealy Gosset", "Z-test"], "references": []}, "Lead time bias": {"categories": ["Bias", "Epidemiology", "Medical statistics"], "title": "Lead time bias", "method": "Lead time bias", "url": "https://en.wikipedia.org/wiki/Lead_time_bias", "summary": "Lead time is the length of time between the detection of a disease (usually based on new, experimental criteria) and its usual clinical presentation and diagnosis (based on traditional criteria). It is the time between early diagnosis with screening and the time in which diagnosis would have been made without screening. It is an important factor when evaluating the effectiveness of a specific test.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/02/Lead_time_bias.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8b/Nuvola_apps_kalzium.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d8/Nuvola_apps_package_favorite.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d6/WHO_Rod.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Academic bias", "Acquiescence bias", "Anchoring", "Attentional bias", "Attribution bias", "Authority bias", "Automation bias", "Belief bias", "Bias", "Bias (statistics)", "Bias blind spot", "Bias in education", "Bias of an estimator", "Choice-supportive bias", "Cognitive bias", "Cognitive bias in animals", "Cognitive bias mitigation", "Confirmation bias", "Congruence bias", "Cultural bias", "Debiasing", "Distinction bias", "Dunning\u2013Kruger effect", "Egocentric bias", "Emotional bias", "Extrinsic incentives bias", "FUTON bias", "Fading affect bias", "Five-year survival rate", "Forecast bias", "Fundamental attribution error", "Funding bias", "Halo effect", "Healthy user bias", "Heuristics in judgment and decision-making", "Hindsight bias", "Horn effect", "Hostile attribution bias", "Huntington's disease", "Impact bias", "In-group favoritism", "Inductive bias", "Information bias (epidemiology)", "Infrastructure bias", "Inherent bias", "International Standard Book Number", "Length time bias", "List of cognitive biases", "List of memory biases", "Media bias", "Media bias in Norway", "Media bias in South Asia", "Media bias in Sweden", "Media bias in the United States", "Media coverage of the Arab\u2013Israeli conflict", "Media portrayal of the Ukrainian crisis", "Mere-exposure effect", "Negativity bias", "Net bias", "Normalcy bias", "Omission bias", "Omitted-variable bias", "Optimism bias", "Outcome bias", "Overton window", "Participation bias", "Precision bias", "Pro-innovation bias", "Publication bias", "Recall bias", "Reporting bias", "Response bias", "Restraint bias", "Sampling bias", "Screening (medicine)", "Selection bias", "Self-selection bias", "Self-serving bias", "Social comparison bias", "Social desirability bias", "Spectrum bias", "Status quo bias", "Survivorship bias", "Symptom", "Systematic error", "Systemic bias", "Time-saving bias", "Trait ascription bias", "United States news media and the Vietnam War", "Verification bias", "Von Restorff effect", "Wet bias", "White hat bias", "Zero-risk bias"], "references": ["http://www.gpnotebook.co.uk/simplepage.cfm?ID=577437764"]}, "Half-logistic distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax"], "title": "Half-logistic distribution", "method": "Half-logistic distribution", "url": "https://en.wikipedia.org/wiki/Half-logistic_distribution", "summary": "In probability theory and statistics, the half-logistic distribution is a continuous probability distribution\u2014the distribution of the absolute value of a random variable following the logistic distribution. That is, for\n\n \n \n \n X\n =\n \n |\n \n Y\n \n |\n \n \n \n \n {\\displaystyle X=|Y|\\!}\n where Y is a logistic random variable, X is a half-logistic random variable.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/dc/Half-logistic_distribution_cdf.svg", "https://upload.wikimedia.org/wikipedia/commons/9/93/Half-logistic_distribution_pdf.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "International Standard Serial Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://interstat.statjournals.net/YEAR/2003/articles/0302002.pdf", "http://www.worldcat.org/issn/1941-689X"]}, "Predictive analytics": {"categories": ["Actuarial science", "All articles needing additional references", "All articles with unsourced statements", "All articles with vague or ambiguous time", "Articles needing additional references from June 2011", "Articles with short description", "Articles with unsourced statements from August 2016", "Articles with unsourced statements from March 2014", "Big data", "Business intelligence", "CS1 maint: Extra text: authors list", "CS1 maint: Multiple names: authors list", "Financial crime prevention", "Prediction", "Statistical analysis", "Types of analytics", "Vague or ambiguous time from October 2011"], "title": "Predictive analytics", "method": "Predictive analytics", "url": "https://en.wikipedia.org/wiki/Predictive_analytics", "summary": "Predictive analytics encompasses a variety of statistical techniques from data mining, predictive modelling, and machine learning, that analyze current and historical facts to make predictions about future or otherwise unknown events.In business, predictive models exploit patterns found in historical and transactional data to identify risks and opportunities. Models capture relationships among many factors to allow assessment of risk or potential associated with a particular set of conditions, guiding decision making for candidate transactions.The defining functional effect of these technical approaches is that predictive analytics provides a predictive score (probability) for each individual (customer, employee, healthcare patient, product SKU, vehicle, component, machine, or other organizational unit) in order to determine, inform, or influence organizational processes that pertain across large numbers of individuals, such as in marketing, credit risk assessment, fraud detection, manufacturing, healthcare, and government operations including law enforcement.\nPredictive analytics is used in actuarial science, marketing, financial services, insurance, telecommunications, retail, travel, mobility, healthcare, child protection, pharmaceuticals, capacity planning, social networking and other fields.\nOne of the best-known applications is credit scoring, which is used throughout financial services. Scoring models process a customer's credit history, loan application, customer data, etc., in order to rank-order individuals by their likelihood of making future credit payments on time.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/3b/Predictive_Analytics_Process.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Actuarial science", "Actuate Corporation", "Algorithmic trading", "Alpine Data Labs", "Alteryx", "Alzheimer's disease", "Amyotrophic lateral sclerosis", "Angoss", "Apache Mahout", "ArXiv", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive moving average model", "Backpropagation", "Bankruptcy", "Basis function", "Bibcode", "Big data", "Binary logit model", "Binary numeral system", "Box\u2013Jenkins", "Business record", "Capacity planning", "Capital asset pricing model", "Child protection", "Clinical decision support system", "Cognition", "Cognitive neuroscience", "Cognitive psychology", "Computational sociology", "Conjugate gradient method", "Control theory", "Cost per action", "Cost per order", "Credit card fraud", "Credit history", "Credit scoring", "Criminal Reduction Utilising Statistical History", "Cross-selling", "Curse of dimensionality", "Customer acquisition management", "Customer attrition", "Customer lifecycle management", "Customer relationship management", "Customer retention", "Customer satisfaction", "Data mining", "Database management", "Decision making", "Decision model", "Decision tree learning", "Decision trees", "Default (finance)", "Delphi method", "Digital object identifier", "Disease surveillance", "Economic mobility", "Engineering", "Explanatory variable", "Face recognition", "Feed forward (control)", "Finance", "Financial services", "Financial transaction", "Forecasting", "Fraud", "GNU Octave", "Gary King (political scientist)", "Gauss\u2013Markov theorem", "Geospatial predictive modeling", "Hadoop", "Hazard rate", "Healthcare", "Heuristics", "Hillsborough County, Florida", "Hopfield network", "Huntington's disease", "Identity theft", "Iid", "In-database processing", "Industrial Internet Consortium", "Information extraction", "Insurance", "Insurance claim", "Internal Revenue Service", "International Standard Book Number", "International Standard Serial Number", "K-nearest neighbors algorithm", "KNIME", "KXEN Inc.", "Kaplan-Meier", "LabVIEW", "Learning analytics", "Likelihood-ratio test", "Linear regression", "Linear regression model", "Loan application", "Logistic distribution", "Logistic regression", "Logit model", "MATLAB", "Machine learning", "MapReduce", "Mark Nigrini", "Marketing", "Massive parallel processing", "Mathematica", "Medical diagnostics", "Medicine", "Minitab", "Model (abstract)", "Moving-average model", "Multilayer perceptron", "Multinomial logit", "Multinomial logit model", "Multivariate adaptive regression splines", "Naive Bayes classifier", "Neural Designer", "Neural network", "Neural networks", "Neurodegeneration", "Non-parametric statistics", "Nonlinearity", "Normal distribution", "Odds algorithm", "Odds ratio", "Open-source software", "OpenNN", "Optimal discriminant analysis", "Oracle Corporation", "Orange (software)", "Ordinary least squares", "Overfit", "Parkinson's disease", "Pattern detection", "Pattern recognition", "Perceptron", "Pervasive Software", "Pharmaceutical company", "Physics", "Piecewise", "Predictive Model Markup Language", "Predictive inference", "Predictive modeling", "Predictive modelling", "Predictive policing", "Predixion Software", "Prescriptive analytics", "Presenso", "Probabilistic risk assessment", "Probit", "Probit model", "Prognostics and health management", "Project risk management", "Pruning (decision trees)", "RCASE", "RFID", "R (programming language)", "Radial basis function", "Random forests", "Random multinomial logit", "RapidMiner", "Regression analysis", "Regression spline", "Retail", "Revolution Analytics", "Roger Jones (physicist and entrepreneur)", "SAP HANA", "SAS (software)", "SPSS", "SPSS Modeler", "Scikit-learn", "Self-organizing map", "Sensor network", "Sidetrade", "Sigmoid function", "Social media analytics", "Social network", "Social networking service", "Speech recognition", "Stata", "Statgraphics", "Statistica", "Statistical classification", "Stock market", "Supervised learning", "Support vector machine", "Survival analysis", "Tax fraud", "Telecommunications", "Text analytics", "Tibco Software", "Time series", "Touch point", "Travel", "Trend analysis", "Underwrite", "Underwriting", "Unstructured data", "Unsupervised learning", "Wald test", "Web log", "Weka (machine learning)"], "references": ["http://www.cameronalverson.com/2012/09/polling-and-statistical-models-cant.html", "http://www.destinationcrm.com/Articles/Editorial/Magazine-Features/CRM---Predictive-Analytics-Why-It-All-Adds-Up-74700.aspx", "http://www.destinationcrm.com/articles/Web-Exclusives/Web-Only-Bonus-Articles/The-New-Prescription-for-Pharma-55774.aspx", "http://www.hcltech.com/sites/default/files/key_to_monetizing_big_data_via_predictive_analytics.pdf", "http://www.hpcwire.com/hpcwire/2011-04-21/the_opportunity_for_predictive_analytics_in_finance.html", "http://www.huffingtonpost.com/marquis-cabrera/florida-leverages-predictive_b_8586712.html", "http://www.information-management.com/infodirect/20060707/1057744-1.html", "http://www.information-management.com/issues/21_6/the-top-5-trends-in-redictive-an-alytics-10021460-1.html", "http://www.insurancetech.com/business-intelligence/210600271", "http://sine.ni.com/nips/cds/view/p/lang/en/nid/210191", "http://www.personali.com/answers/predictive-analytics/", "http://presenso.com", "http://go.sap.com/product/analytics/predictive-analytics.html", "http://help.sap.com/saphelp_hanaplatform/helpdata/en/32/731a7719f14e488b1f4ab0afae995b/frameset.htm", "http://www.sciencedirect.com/science/article/pii/S0957417415006053", "http://www.sciencedirect.com/science/article/pii/S1474034604000102", "http://www.targetmarketingmag.com/article/7-best-uses-predictive-analytics-modeling-multichannel-marketing/1#", "http://www.times-standard.com/business/ci_19561141", "http://www.travelmarketreport.com/technology?articleID=4259&LP=1,", "http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470890460.html", "http://adsabs.harvard.edu/abs/2016PLoSO..1157077D", "http://hbswk.hbs.edu/archive/1590.html", "http://www.eng.tau.ac.il/~bengal/DID.pdf", "http://www.eng.tau.ac.il/~bengal/genre_statistics.pdf", "http://www.imscenter.net/front-page/Resources/WD.pdf", "http://www.win.tue.nl/~mpechen/publications/pubs/PA_EDS_HPCS15.pdf", "http://dl.acm.org/citation.cfm?id=1961191", "http://dl.acm.org/citation.cfm?id=593502", "http://arxiv.org/abs/1101.0891", "http://doi.org/10.1007%2Fs10115-013-0619-9", "http://doi.org/10.1016%2Fj.aei.2004.07.005", "http://doi.org/10.1016%2Fj.eswa.2015.08.048", "http://doi.org/10.1109%2FCSCITA.2017.8066548", "http://doi.org/10.1214%2F10-STS330", "http://doi.org/10.1371%2Fjournal.pone.0157077", "http://static.eckerd.org/wp-content/uploads/Eckerd.pdf", "http://www.eckerd.org/2016/03/23/eckerd-rapid-safety-feedback-highlighted-national-report-commission-eliminate-child-abuse-neglect-fatalities/", "http://jamia.oxfordjournals.org/content/14/2/141.short", "http://projecteuclid.org/euclid.ss/1294167961", "http://tdwi.org/Articles/2012/03/06/Predictive-Analytics-Growth.aspx?Page=1", "http://tdwi.org/articles/2007/05/10/predictive-analytics.aspx?sc_lang=en", "http://tdwi.org/articles/2012/05/01/5-predictive-analytics-myths.aspx", "http://www.worldcat.org/issn/0883-4237", "https://www.hisa.org.au/slides/tue/AndraeGaeth.pdf", "https://www.the-digital-insurer.com/wp-content/uploads/2013/12/78-Predictive-Modeling-White-Paper.pdf", "https://www.acf.hhs.gov/sites/default/files/cb/cecanf_final_report.pdf", "https://web.archive.org/web/20150910175014/http://www.travelmarketreport.com/technology?articleID=4259&LP=1,", "https://chronicleofsocialchange.org/blogger-co-op/new-strategies-long-overdue-measuring-child-welfare-risk/15442", "https://ieeexplore.ieee.org/document/8066548", "https://www.npr.org/2012/10/08/162397787/predicting-the-future-fantasy-or-a-good-algorithm"]}, "Point estimation": {"categories": ["Estimation theory"], "title": "Point estimation", "method": "Point estimation", "url": "https://en.wikipedia.org/wiki/Point_estimation", "summary": "In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate or statistic) which is to serve as a \"best guess\" or \"best estimate\" of an unknown population parameter (for example, the population mean). More formally, it is the application of a point estimator to the data to obtain a point estimate.\nPoint estimation can be contrasted with interval estimation: such interval estimates are typically either confidence intervals in the case of frequentist inference, or credible intervals in the case of Bayesian inference.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407084002%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407083328%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407082944%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20110430032449%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20090922000234%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041048%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041018%21Fisher_iris_versicolor_sepalwidth.svg"], "links": ["Admissible procedure", "Algorithmic inference", "Bayes estimator", "Bayes filter", "Bayesian estimation", "Bayesian inference", "Best linear unbiased estimator", "Bias of an estimator", "Central tendency", "Computational statistics", "Confidence interval", "Cram\u00e9r\u2013Rao bound", "Credible intervals", "Data", "Digital object identifier", "Erich Leo Lehmann", "Estimator", "Frequentist inference", "Gauss", "Generalized method of moments", "Induction (philosophy)", "Information theory", "International Standard Book Number", "Interval estimation", "Iterative method", "JSTOR", "Kalman filter", "Laplace", "Loss function", "Lucien Le Cam", "Markov chain Monte Carlo", "Maximum a posteriori", "Maximum likelihood estimator", "Median-unbiased estimator", "Method of moments (statistics)", "Minimum Message Length", "Minimum mean square error", "Minimum mean squared error", "Minimum variance unbiased estimator", "Parameter", "Particle filter", "Philosophy of statistics", "Population mean", "Posterior distribution", "Predictive inference", "Risk function", "Statistic", "Statistical sample", "Statistics", "Thomas S. Ferguson", "Wiener filter"], "references": ["http://doi.org/10.1080%2F01621459.1982.10477894", "http://www.jstor.org/stable/2287314"]}, "Calibration (probability)": {"categories": ["Bayesian statistics", "Probability assessment"], "title": "Calibrated probability assessment", "method": "Calibration (probability)", "url": "https://en.wikipedia.org/wiki/Calibrated_probability_assessment", "summary": "Calibrated probability assessments are subjective probabilities assigned by individuals who have been trained to assess probabilities in a way that historically represents their uncertainty. For example, when a person has calibrated a situation and says they are \"80% confident\" in each of 100 predictions they made, they will get about 80% of them correct. Likewise, they will be right 90% of the time they say they are 90% certain, and so on.\nCalibration training improves subjective probabilities because most people are either \"overconfident\" or \"under-confident\" (usually the former). By practicing with a series of trivia questions, it is possible for subjects to fine-tune their ability to assess probabilities. For example, a subject may be asked:\n\nTrue or False: \"A hockey puck fits in a golf hole\"\nConfidence: Choose the probability that best represents your chance of getting this question right...\n50% 60% 70% 80% 90% 100%If a person has no idea whatsoever, they will say they are only 50% confident. If they are absolutely certain they are correct, they will say 100%. But most people will answer somewhere in between. If a calibrated person is asked a large number of such questions, they will get about as many correct as they expected. An uncalibrated person who is systematically overconfident may say they are 90% confident in a large number of questions where they only get 70% of them correct. On the other hand, an uncalibrated person who is systematically underconfident may say they are 50% confident in a large number of questions where they actually get 70% of them correct.\nAlternatively, the trainee will be asked to provide a numeric range for a question like, \"In what year did Napoleon invade Russia?\", with the instruction that the provided range is to represent a 90% confidence interval. That is, the test-taker should be 90% confident that the range contains the correct answer. \nCalibration training generally involves taking a battery of such tests. Feedback is provided between tests and the subjects refine their probabilities. Calibration training may also involve learning other techniques that help to compensate for consistent over- or under-confidence. Since subjects are better at placing odds when they pretend to bet money, subjects are taught how to convert calibration questions into a type of betting game which is shown to improve their subjective probabilities. Various collaborative methods have been developed, such as prediction market, so that subjective estimates from multiple individuals can be taken into account.\nStochastic modeling methods such as the Monte Carlo method often use subjective estimates from \"subject matter experts\". However, since research shows that such experts are very likely to be statistically overconfident, the model will tend to underestimate uncertainty and risk. The Applied Information Economics method systematically uses calibration training as part of a decision modeling process.", "images": [], "links": ["Applied Information Economics", "Calibration (statistics)", "De Finetti's game", "Monte Carlo method", "Paul J. H. Schoemaker", "Prediction market", "Subjective probability"], "references": ["http://credencecalibration.com/"]}, "Unit (statistics)": {"categories": ["CS1 errors: external links", "CS1 maint: Multiple names: authors list", "Sampling (statistics)"], "title": "Statistical unit", "method": "Unit (statistics)", "url": "https://en.wikipedia.org/wiki/Statistical_unit", "summary": "A unit in a statistical analysis is one member of a set of entities being studied. It is the material source for the mathematical abstraction of a \"random variable\". Common examples of a unit would be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied.\nUnits are often referred to as being either experimental units, sampling units or units of observation:\n\nAn \"experimental unit\" is typically thought of as one member of a set of objects that are initially equivalent, with each object then subjected to one of several experimental treatments. Put simply, it is the smallest entity to which a treatment is applied.\nA \"sampling unit\" is typically thought of as an object that has been sampled from a statistical population. This term is commonly used in opinion polling and survey sampling.For example, in an experiment on educational methods, methods may be applied to classrooms of students. This would indicate the classroom as the experimental unit. Measurements of progress may be obtained on individual students, as observational units. But the treatment (teaching method) being applied to the class would not be applied independently to the individual students. Hence the student could not be regarded as the experimental unit. The class, or the teacher by method combination if the teacher had multiple classes, would be the appropriate experimental unit.\nIn most statistical studies, the goal is to generalize from the observed units to a larger set consisting of all comparable units that exist but are not directly observed. For example, if we randomly sample 100 people and ask them which candidate they intend to vote for in an election, our main interest is in the voting behavior of all eligible voters, not exclusively on the 100 observed units.\nIn some cases, the observed units may not form a sample from any meaningful population, but rather constitute a convenience sample, or may represent the entire population of interest. In this situation, we may study the units descriptively, or we may study their dynamics over time. But it typically does not make sense to talk about generalizing to a larger population of such units. Studies involving countries or business firms are often of this type. Clinical trials also typically use convenience samples, however the aim is often to make inferences about the efficacy of treatments in other patients, and given the inclusion and exclusion criteria for some clinical trials, the sample may not be representative of the majority of patients with the condition or disease.\nIn simple data sets, the units are in one-to-one correspondence with the data values. In more complex data sets, multiple measurements are made for each unit. For example, if blood pressure measurements are made daily for a week on each subject in a study, there would be seven data values for each statistical unit. Multiple measurements taken on an individual are not independent (they will be more alike compared to measurements taken on different individuals). Ignoring these dependencies during the analysis can lead to an inflated sample size or pseudoreplication.\nWhile a unit is often the lowest level at which observations are made, in some cases, a unit can be further decomposed as a statistical assembly.\nMany statistical analyses use quantitative data that have units of measurement. This is a distinct and non-overlapping use of the term \"unit.\"\n\nStatistical unit are divided into two theye are \n\nA:unit of collection \nB:unit of analysis and interpretation \n\n Unit of collection are those units in which figures relating to a particular problem are either enumerated or estimated .the units of collection may be simple or composite .a simple unit is one which represent a singel condition without any qualification .a composite unit is one which is formed by adding a qualification word or phrase to a simple unit \n\nExample -:labour-hours and passenger-killometer \nUnit of analysis and interpretation are those unit in term of which statistical data are analysed and interpreted \nExample -:ratios ,percentage ,co-efficient ect...", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Accidental sampling", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Business", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Country", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dynamic model", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent and identically distributed random variables", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laboratory specimen", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Opinion polling", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Oscar Kempthorne", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Pseudoreplication", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Random variable", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Research subject", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical assembly", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survey sampling", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Unit of analysis", "Unit of observation", "Units of measurement", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Gemmell Cochran", "Z-test"], "references": ["http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471727563.html", "http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521683579", "http://www.maths.qmul.ac.uk/~rab/DOEbook/", "http://www.maths.qmw.ac.uk/~rab/", "https://books.google.com/books?id=T3wWj2kVYZgC&printsec=frontcover&cad=4_0"]}, "Optimal design": {"categories": ["CS1 maint: Multiple names: authors list", "CS1 maint: Uses editors parameter", "Design of experiments", "Industrial engineering", "Mathematical optimization", "Optimal decisions", "Regression analysis", "Statistical process control", "Statistical theory", "Systems engineering"], "title": "Optimal design", "method": "Optimal design", "url": "https://en.wikipedia.org/wiki/Optimal_design", "summary": "In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith.In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation.\nThe optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with designing experiments.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7f/Theb1982.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abraham Wald", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Approximation", "Arithmetic mean", "Armijo rule", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benchmarking", "Best linear unbiased estimator", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Calyampudi Radhakrishna Rao", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Charles Loewner", "Charles Sanders Peirce", "Charles Sanders Peirce bibliography", "Chebyshev polynomials", "Chemometrics", "Chi-squared test", "CiteSeerX", "Clinical study design", "Clinical trial", "Clinical trials", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Computer experiment", "Confidence interval", "Confounding", "Conical combination", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Control theory", "Convex analysis", "Convex conjugate", "Convex function", "Convex functions", "Convex optimization", "Coordinate vector", "Correlation and dependence", "Correlogram", "Count data", "Covariance matrix", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "David R. Cox", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Determinant", "Diagonal", "Dickey\u2013Fuller test", "Differential entropy", "Digital object identifier", "Discretization", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Eigenvalue", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Entropy (information theory)", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation", "Estimation theory", "Estimators", "Expected value", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Fenchel's duality theorem", "First-hitting-time model", "Fisher information", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Friedrich Pukelsheim", "Functional (mathematics)", "G-test", "Gauss\u2013Markov theorem", "General linear model", "Generalized linear model", "Generalized linear models", "Generalized randomized block design", "Geographic information system", "Geometric mean", "George E. P. Box", "Geostatistics", "Global optimization", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Greenland", "Grouped data", "Gustav Elfving", "Hadamard's maximal determinant problem", "Harmonic mean", "Harold J. Kushner", "Hat matrix", "Henry P. Wynn", "Herman Chernoff", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Information matrix", "Information theory", "Ingram Olkin", "Institute of Mathematical Statistics", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Invariant theory", "Inverse matrix", "Invertible matrix", "Isotonic regression", "JSTOR", "Jack Kiefer (mathematician)", "Jackknife resampling", "Jacob Wolfowitz", "Jarque\u2013Bera test", "Jerome Sacks", "Johansen test", "Johns Hopkins University", "Jonckheere's trend test", "Joseph Diaz Gergonne", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kirstine Smith", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "Kyushu University", "L-moment", "Latin hypercube sampling", "Latin square", "Lawrence D. Brown", "Least squares", "Legendre transformation", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear algebra", "Linear combination", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Lloyd Shapley", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Matrix (mathematics)", "Matrix trace", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimisation (clinical trials)", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Moment problem", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Neil Sloane", "Nelson\u2013Aalen estimator", "Nicholas Logothetis", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance parameter", "Nuisance variable", "Objective function", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal control", "Optimal decision", "Optimization (mathematics)", "Order statistic", "Ordered vector space", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Oxford University Press", "Parameter", "Parametric model", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partial order", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pharmacodynamics", "Pharmacokinetics", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Polynomial regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Predictive inference", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability measure", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Quasiconvex function", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Real number", "Reciprocal (mathematics)", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Rosemary A. Bailey", "Run chart", "SAS System", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Samuel Karlin", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semidefinite programming", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape optimization", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Society for Industrial and Applied Mathematics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Science", "Statistical classification", "Statistical decision theory", "Statistical dispersion", "Statistical distance", "Statistical efficiency", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stephen M. Stigler", "Stochastic approximation", "Stochastic optimization", "Stochastic programming", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Subgradient method", "Sufficient statistic", "Summary statistics", "Support (measure theory)", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Systems analysis", "Taguchi methods", "Theodolite", "Thorvald N. Thiele", "Time domain", "Time series", "Tolerance interval", "Trace (linear algebra)", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.biw.kuleuven.be/biosyst/mebios/biostatistics-group", "http://users.telenet.be/peter.goos/springer.htm", "http://www.webdoe.cc/publications/kirstine.php", "http://www.ec-securehost.com/SIAM/CL50.html", "http://www.us.oup.com/us/catalog/general/subject/Mathematics/ProbabilityStatistics/~~/dmlldz11c2EmY2k9OTc4MDE5OTI5NjYwNg", "http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-20/2/df451ec5fbb7c044d0f4d900af80ec86", "http://www.sciencedirect.com/science/article/B6WG9-4D7JMHH-1Y/2/680c7ada0198761e9866197d53512ab4", "http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470744618.html", "http://www.math.uni-augsburg.de/stochastik/pukelsheim/", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.5355", "http://www-stat.stanford.edu/people/faculty/olkin/", "http://www.stanford.edu/~boyd/cvxbook/", "http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf", "http://www.cceb.upenn.edu/faculty/index.php?id=60", "http://docs.lib.noaa.gov/rescue/cgs/001_pdf/CSC-0025.PDF#page=222", "http://www.isid.ac.in/~rbb/", "http://www.ams.org/mathscinet-getitem?mr=1722074", "http://www.ams.org/mathscinet/pdf/153090.pdf", "http://doi.org/10.1016%2F0315-0860(74)90033-0", "http://doi.org/10.1016%2F0315-0860(74)90034-2", "http://doi.org/10.1111%2Fj.1751-5823.2009.00069.x", "http://doi.org/10.1214%2Faoms%2F1177731118", "http://doi.org/10.1214%2Fss%2F1009212244", "http://doi.org/10.1214%2Fss%2F1177009939", "http://doi.org/10.1287%2Fopre.15.4.643", "http://doi.org/10.2206%2Fkyushumfs.16.114", "http://doi.org/10.2307%2F2331929", "http://www.jstor.org/stable/2235829", "http://www.jstor.org/stable/2331929", "http://www.jstor.org/stable/2676737", "http://www.niss.org/people/sacks.html", "http://projecteuclid.org/euclid.ss/1009212244", "http://www.siam.org/books/series/cl.php", "http://www.ipu.ru/labs/lab7/eng/staff/polyak.htm", "http://www.lse.ac.uk/collections/cats/People/HenryPage.htm", "http://www.maths.manchester.ac.uk/undergraduate/ugstudies/units/2008-09/level3/MATH38082/index.php", "http://www.maths.qmul.ac.uk/~rab/DOEbook", "https://books.google.com/books?id=5ZcfDZUJ4F8C", "https://books.google.com/books?id=5ZcfDZUJ4F8C&pg=PA212&lpg=PA212&dq=Kiefer+Wolfowitz&source=bl&ots=u0F1j-W3CF&sig=-bWiYksuk7RIOeZ_qZnB9Jpj0tk&hl=sv&ei=izghSvvUCs6zsgajuo24Bg&sa=X&oi=book_result&ct=result&resnum=10", "https://books.google.com/books?id=E0YFAAAAQAAJ&pg=PA11&dq=%22Logic+will+not+undertake+to+inform%22+%22unfortunately+practice+generally%22", "https://www.jmp.com/en_nl/events/analytically-speaking/thought-leaders/jones-bradley.html", "https://www.springer.com/math/algebra/book/978-0-387-98871-9?cm_mmc=Google-_-Book%20Search-_-Springer-_-0", "https://www.springer.com/series/694", "https://www.amstat.org/meetings/jsm/2009/index.cfm?fuseaction=workshops#mon", "https://web.archive.org/web/20090810040534/http://www.webdoe.cc/publications/kirstine.php", "https://www.jstor.org/stable/168276"]}, "Bhattacharyya distance": {"categories": ["All articles needing expert attention", "Articles needing expert attention from May 2008", "Articles needing expert attention with no reason or talk parameter", "Mathematics articles needing expert attention", "Statistical deviation and dispersion", "Statistical distance"], "title": "Bhattacharyya distance", "method": "Bhattacharyya distance", "url": "https://en.wikipedia.org/wiki/Bhattacharyya_distance", "summary": "In statistics, the Bhattacharyya distance measures the similarity of two probability distributions. It is closely related to the Bhattacharyya coefficient which is a measure of the amount of overlap between two statistical samples or populations. Both measures are named after Anil Kumar Bhattacharya, a statistician who worked in the 1930s at the Indian Statistical Institute.The coefficient can be used to determine the relative closeness of the two samples being considered. It is used to measure the separability of classes in classification and it is considered to be more reliable than the Mahalanobis distance, as the Mahalanobis distance is a particular case of the Bhattacharyya distance when the standard deviations of the two classes are the same. Consequently, when two classes have similar means but different standard deviations, the Mahalanobis distance would tend to zero, whereas the Bhattacharyya distance grows depending on the difference between the standard deviations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20091021223050%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010627%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20081112010514%21Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/b/b4/20080513160307%21Ambox_important.svg"], "links": ["Anil Kumar Bhattacharya", "ArXiv", "Bhattacharyya angle", "Bhattacharyya distance", "Calcutta Mathematical Society", "Chernoff bound", "Digital object identifier", "Domain of a function", "Encyclopedia of Mathematics", "Hellinger distance", "IEEE Transactions on Pattern Analysis and Machine Intelligence", "Indian Statistical Institute", "Integral", "International Standard Book Number", "Kullback\u2013Leibler divergence", "Linear discriminant analysis", "Mahalanobis distance", "Mathematical Reviews", "Measurement", "Michiel Hazewinkel", "Multivariate normal", "Partition of an interval", "Probability distribution", "R\u00e9nyi entropy", "Similarity measure", "Statistical classification", "Statistician", "Statistics", "Triangle inequality"], "references": ["http://www.mtm.ufsc.br/~taneja/book/node20.html", "http://coewww.rutgers.edu/riul/research/papers/pdf/trackmo.pdf", "http://www.ams.org/mathscinet-getitem?mr=0010358", "http://arxiv.org/abs/1004.5049", "http://doi.org/10.1109%2F34.41388", "http://doi.org/10.1109%2FTCOM.1967.1089532", "http://doi.org/10.1109%2FTIT.2011.2159046", "https://arxiv.org/pdf/1709.10498.pdf", "https://www.encyclopediaofmath.org/index.php?title=p/b110490"]}, "Z score": {"categories": ["Statistical ratios"], "title": "Standard score", "method": "Z score", "url": "https://en.wikipedia.org/wiki/Standard_score", "summary": "In statistics, the standard score is the signed number of standard deviations by which the value of an observation or data point is above the mean value of what is being observed or measured. Observed values above the mean have positive standard scores, while values below the mean have negative standard scores. The standard score is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing (however, \"normalizing\" can refer to many types of ratios; see normalization for more). \nStandard scores are also called z-values, z-scores, normal scores, and standardized variables. They are most frequently used to compare an observation to a standard normal deviate, though they can be defined without assumptions of normality.\nComputing a z-score requires knowing the mean and standard deviation of the complete population to which a data point belongs; if one only has a sample of observations from the population, then the analogous computation with sample mean and sample standard deviation yields the t-statistic.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/2/25/The_Normal_Distribution.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Altman Z-score", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Dimensionless number", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Erwin Kreyszig", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher transformation", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical statistics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normalization (statistics)", "Observational study", "Official statistics", "Omega ratio", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population mean", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raw score", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard normal deviate", "Standardization", "Standardize", "Standardized testing (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-score", "T-statistic", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-factor", "Z-test", "Z-transform", "Z-value"], "references": ["http://staff.argyll.epsb.ca/jreed/math30p/statistics/standardCurve.htm", "https://books.google.com/?id=gccHkMDikb0C", "https://books.google.com/books?id=57jdRoC4hCoC&pg=PA43", "https://books.google.com/books?id=dejKAgAAQBAJ&pg=PA133", "https://books.google.com/books?id=sMSWbI23RMUC&pg=PA123", "https://www.niams.nih.gov/Health_Info/Bone/Bone_Health/bone_mass_measure.asp#b"]}, "Restricted maximum likelihood": {"categories": ["All stub articles", "Maximum likelihood estimation", "Statistics stubs"], "title": "Restricted maximum likelihood", "method": "Restricted maximum likelihood", "url": "https://en.wikipedia.org/wiki/Restricted_maximum_likelihood", "summary": "In statistics, the restricted (or residual, or reduced) maximum likelihood (REML) approach is a particular form of maximum likelihood estimation that does not base estimates on a maximum likelihood fit of all the information, but instead uses a likelihood function calculated from a transformed set of data, so that nuisance parameters have no effect.In the case of variance component estimation, the original data set is replaced by a set of contrasts calculated from the data, and the likelihood function is calculated from the probability distribution of these contrasts, according to the model for the complete data set. In particular, REML is used as a method for fitting linear mixed models. In contrast to the earlier maximum likelihood estimation, REML can produce unbiased estimates of variance and covariance parameters.The idea underlying REML estimation was put forward by M. S. Bartlett in 1937. The first description of the approach applied to estimating components of variance in unbalanced data was by Desmond Patterson and Robin Thompson of the University of Edinburgh in 1971, although they did not use the term REML. \nA review of the early literature was given by Harville.REML estimation is available in a number of general-purpose statistical software packages, including Genstat (the REML directive), SAS (the MIXED procedure), SPSS (the MIXED command), Stata (the mixed command), JMP (statistical software), and R (especially the lme4 and older nlme packages),\nas well as in more specialist packages such as MLwiN, HLM, ASReml, (ai)remlf90, wombat, Statistical Parametric Mapping and CropStat.\nREML estimation is implemented in Surfstat a Matlab toolbox for the statistical analysis of univariate and multivariate surface and volumetric neuroimaging data using linear mixed effects models and random field theory.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["ASReml", "Bias (statistics)", "Bibcode", "Contrast (statistics)", "Desmond Patterson", "Digital object identifier", "Genstat", "International Standard Book Number", "JMP (statistical software)", "Likelihood function", "M. S. Bartlett", "MLwiN", "Maximum likelihood", "Mixed model", "Nuisance parameter", "R (programming language)", "Robin Thompson (statistician)", "SAS (software)", "SPSS", "Stata", "Statistical Parametric Mapping", "Statistical software", "Statistics", "University of Edinburgh", "Variance component", "Yadolah Dodge"], "references": ["http://didgeridoo.une.edu.au/km/wombat.php", "http://www.math.mcgill.ca/keith/noniso/noniso.pdf", "http://www.math.mcgill.ca/keith/surfstat/", "http://homepage.usask.ca/~rjb609/stats4.html", "http://www.ssicentral.com/hlm/", "http://adsabs.harvard.edu/abs/1937RSPSA.160..268B", "http://nce.ads.uga.edu/wiki/doku.php?id=start", "http://doi.org/10.1093%2Fbiomet%2F58.3.545", "http://doi.org/10.1098%2Frspa.1937.0109", "http://doi.org/10.2307%2F2286796", "http://archive.irri.org/science/software/cropstat.asp", "https://web.archive.org/web/20080630063659/http://homepage.usask.ca/~rjb609/stats4.html", "https://cran.r-project.org/web/packages/lme4/index.html", "https://cran.r-project.org/web/packages/nlme/index.html"]}, "Maximum spacing estimation": {"categories": ["Estimation methods", "Good articles", "Probability distribution fitting"], "title": "Maximum spacing estimation", "method": "Maximum spacing estimation", "url": "https://en.wikipedia.org/wiki/Maximum_spacing_estimation", "summary": "In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model. The method requires maximization of the geometric mean of spacings in the data, which are the differences between the values of the cumulative distribution function at neighbouring data points.\nThe concept underlying the method is based on the probability integral transform, in that a set of independent random samples derived from any random variable should on average be uniformly distributed with respect to the cumulative distribution function of the random variable. The MPS method chooses the parameter values that make the observed data as uniform as possible, according to a specific quantitative measure of uniformity.\nOne of the most common methods for estimating the parameters of a distribution from data, the method of maximum likelihood (MLE), can break down in various cases, such as involving certain mixtures of continuous distributions. In these cases the method of maximum spacing estimation may be successful.\nApart from its use in pure mathematics and statistics, the trial applications of the method have been reported using data from fields such as hydrology, econometrics, magnetic resonance imaging, and others.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/bd/J-shaped_density.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b3/J-shaped_density_-_corresponding_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ed/Spacing_Estimation_plot_for_MSE_example.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f2/Spacings.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/94/Symbol_support_vote.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cardiff University", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Convergence in probability", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Critical value", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dirichlet cell", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation", "Estimator", "Euler\u2013Mascheroni constant", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-divergence", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gamma distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hydrology", "Iid", "Index of dispersion", "Inequality of arithmetic and geometric means", "Inflection point", "Interaction (statistics)", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kullback\u2013Leibler divergence", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Magnetic resonance imaging", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McNemar's test", "Mean", "Mean-squared error", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mixture (probability)", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural logarithm", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameter space", "Parametric model", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pat Moran (statistician)", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability integral transform", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random sample", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Round-off error", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Supremum", "Survey methodology", "Survival analysis", "Survival function", "Swedish University of Agricultural Sciences", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniform distribution (continuous)", "Uniformly minimum variance unbiased", "Uniformly most powerful test", "Univariate distribution", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.menem.com/ilya/digital_library/entropy/beirlant_etal_97.pdf", "http://www.pstat.ucsb.edu/faculty/jammalam/html/research%20publication_files/MSP2.pdf", "http://www.hydrol-earth-syst-sci.net/8/235/2004/hess-8-235-2004.pdf", "http://arxiv.org/abs/math/0702830v1", "http://doi.org/10.1016%2Fj.jspi.2004.06.059", "http://doi.org/10.1017%2FS0266466605050255", "http://doi.org/10.1093%2Fbiomet%2F76.2.385", "http://doi.org/10.1214%2F074921706000001102", "http://doi.org/10.5194%2Fhess-8-235-2004", "http://www.jstor.org/stable/2345411", "http://www.jstor.org/stable/2345793", "http://www.jstor.org/stable/4615946", "http://www.worldcat.org/issn/0035-9246", "http://www.worldcat.org/issn/0303-6898", "http://www.worldcat.org/issn/0345-3928", "http://www.worldcat.org/issn/1027-5606", "http://www.worldcat.org/issn/1055-7490", "http://home.agh.edu.pl/pieciak/publikacje_pieciak/2014_ICIP_Pieciak.pdf", "http://fir.nes.ru/~gkosenok/MPS.pdf", "http://www.matstat.umu.se/varia/reports/rep9705.ps.gz", "http://www.matstat.umu.se/varia/reports/rep9706.ps.gz", "https://web.archive.org/web/20050505044534/http://www.menem.com/ilya/digital_library/entropy/beirlant_etal_97.pdf", "https://web.archive.org/web/20070214143042/http://www.matstat.umu.se/varia/reports/rep9705.ps.gz", "https://web.archive.org/web/20070214143052/http://www.matstat.umu.se/varia/reports/rep9706.ps.gz"]}, "Rubin causal model": {"categories": ["All accuracy disputes", "All articles with unsourced statements", "Articles with disputed statements from February 2018", "Articles with unsourced statements from February 2018", "Causal inference", "Econometric models", "Experiments", "Observational study", "Statistical models"], "title": "Rubin causal model", "method": "Rubin causal model", "url": "https://en.wikipedia.org/wiki/Rubin_causal_model", "summary": "The Rubin causal model (RCM), also known as the Neyman\u2013Rubin causal model, is an approach to the statistical analysis of cause and effect based on the framework of potential outcomes, named after Donald Rubin. The name \"Rubin causal model\" was first coined by Rubin's graduate school colleague, Paul W. Holland. The potential outcomes framework was first proposed by Jerzy Neyman in his 1923 Master's thesis, though he discussed it only in the context of completely randomized experiments. Rubin, together with other contemporary statisticians, extended it into a general framework for thinking about causation in both observational and experimental studies.", "images": [], "links": ["Blood pressure", "Cambridge University Press", "Causality", "Causality (book)", "Conceptual framework", "Counterfactual conditional", "Digital object identifier", "Donald Rubin", "Dorota Dabrowska", "Guido Imbens", "Instrumental variable", "International Standard Book Number", "International Statistical Review", "JSTOR", "James Heckman", "Jerzy Neyman", "Journal of Educational Psychology", "Journal of Educational Statistics", "Journal of the American Statistical Association", "Judea Pearl", "Mahalanobis metric", "Paul W. Holland", "Principal stratification", "Propensity score matching", "Sociological Methodology", "Stable unit treatment value assumption", "Statistical analysis", "Structural Equation Modeling", "The Annals of Statistics", "Variance"], "references": ["http://www.dictionaryofeconomics.com/article?id=pde2008_R000247", "http://sekhon.berkeley.edu/papers/SekhonOxfordHandbook.pdf", "http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf", "http://doi.org/10.1037%2Fh0037350", "http://doi.org/10.1080%2F01621459.1986.10478354", "http://doi.org/10.1080%2F01621459.1996.10476902", "http://doi.org/10.1111%2Fj.1751-5823.2007.00024.x", "http://doi.org/10.1198%2F016214504000001880", "http://www.jstor.org/stable/2289064", "http://www.jstor.org/stable/4148843", "https://web.archive.org/web/20090120153714/http://www.wjh.harvard.edu/~cwinship/cfa.html"]}, "Multidimensional scaling": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from February 2011", "Articles with unsourced statements from September 2012", "Commons category link is on Wikidata", "Dimension reduction", "Marketing research", "Psychometrics", "Quantitative marketing research", "Wikipedia articles with NDL identifiers"], "title": "Multidimensional scaling", "method": "Multidimensional scaling", "url": "https://en.wikipedia.org/wiki/Multidimensional_scaling", "summary": "Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. It refers to a set of related ordination techniques used in information visualization, in particular to display the information contained in a distance matrix. It is a form of non-linear dimensionality reduction. An MDS algorithm aims to place each object in N-dimensional space such that the between-object distances are preserved as well as possible. Each object is then assigned coordinates in each of the N dimensions. The number of dimensions of an MDS plot N can exceed 2 and is specified a priori. Choosing N=2 optimizes the object locations for a two-dimensional scatterplot.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/b/be/RecentVotes.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["A priori and a posteriori", "Algorithm", "Bibcode", "Cayley\u2013Menger determinant", "Centering matrix", "Coordinate", "Data clustering", "Diagonal matrix", "Digital object identifier", "Dimension", "Dimensionality reduction", "Discriminant analysis", "Distance geometry", "Distance matrix", "ELKI", "Eigendecomposition of a matrix", "Eigenvalues and eigenvectors", "Embedding", "Euclidean distance", "Factor analysis", "Generalized multidimensional scaling", "Information visualization", "International Standard Book Number", "Isotonic regression", "Jaccard index", "Joseph Kruskal", "Likert scale", "Loss function", "Louis Guttman", "MATLAB", "Marketing", "Marketing research", "Metric (mathematics)", "Monotonic", "Monte Carlo method", "National Diet Library", "Non-linear dimensionality reduction", "Non-parametric", "Nonlinear dimensionality reduction", "Norm (mathematics)", "Optimization (mathematics)", "Orange (software)", "Ordination (statistics)", "Patrick Groenen", "Perceptual mapping", "Positioning (marketing)", "Product management", "PubMed Central", "PubMed Identifier", "R-squared", "R (programming language)", "Real numbers", "Sammon mapping", "Scatterplot", "Scikit-learn", "Semantic differential", "Similarity measure", "Sorenson index", "Stress majorization", "Taxonomy (general)", "United States House of Representatives"], "references": ["http://adsabs.harvard.edu/abs/2006PNAS..103.1168B", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1360551", "http://www.ncbi.nlm.nih.gov/pubmed/16432211", "http://doi.org/10.1007%2FBF02289565", "http://doi.org/10.1073%2Fpnas.0508601103", "http://doi.org/10.2307%2F1250799", "http://www.pnas.org/cgi/pmidlookup?view=long&pmid=16432211", "http://scikit-learn.org/stable/modules/generated/sklearn.manifold.MDS.html", "https://id.ndl.go.jp/auth/ndlna/01160098", "https://www.wikidata.org/wiki/Q620538"]}, "Truncated distribution": {"categories": ["All articles needing additional references", "Articles needing additional references from September 2009", "Theory of probability distributions", "Types of probability distributions"], "title": "Truncated distribution", "method": "Truncated distribution", "url": "https://en.wikipedia.org/wiki/Truncated_distribution", "summary": "In statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution. Truncated distributions arise in practical statistics in cases where the ability to record, or even to know about, occurrences is limited to values which lie above or below a given threshold or within a specified range. For example, if the dates of birth of children in a school are examined, these would typically be subject to truncation relative to those of all children in the area given that the school accepts only children in a given age range on a specific date. There would be no information about how many children in the locality had dates of birth before or after the school's cutoff dates if only a direct approach to the school were used to obtain information.\nWhere sampling is such as to retain knowledge of items that fall outside the required range, without recording the actual values, this is known as censoring, as opposed to the truncation here.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/d/df/TnormPDF.png"], "links": ["Bayes' rule", "Censoring (statistics)", "Conditional distribution", "Continuous distribution", "Cumulative distribution function", "Discrete distribution", "Expected value", "International Standard Book Number", "Median", "Probability density function", "Probability distribution", "Statistics", "Support (mathematics)", "Tobit model", "Truncated mean", "Truncated normal distribution", "Truncation (statistics)"], "references": []}, "Nonprobability sampling": {"categories": ["Sampling techniques"], "title": "Nonprobability sampling", "method": "Nonprobability sampling", "url": "https://en.wikipedia.org/wiki/Nonprobability_sampling", "summary": "Sampling is the use of a subset of the population to represent the whole population or to inform about (social) processes that are meaningful beyond the particular cases, individuals or sites studied. Probability sampling, or random sampling, is a sampling technique in which the probability of getting any particular sample may be calculated. Nonprobability sampling does not meet this criterion and, as any methodological decision, should adjust to the research question that one envisages to answer. Nonprobability sampling techniques are not intended to be used to infer from the sample to the general population in statistical terms. Instead, for example, grounded theory can be produced through iterative non-probability sampling until theoretical saturation is reached (Strauss and Corbin, 1990).\nThus, one cannot say the same on the basis of a nonprobability sample than on the basis of a probability sample. The grounds for drawing generalizations (e.g., propose new theory, propose policy) from studies based on nonprobability samples are based on the notion of \"theoretical saturation\" and \"analytical generalization\" (Yin, 2014) instead of on statistical generalization. \nResearchers working with the notion of purposive sampling assert that while probability methods are suitable for large-scale studies concerned with representativeness, non-probability approaches are more suitable for in-depth qualitative research in which the focus is often to understand complex social phenomena (e.g., Marshall 1996; Small 2009). One of the advantages of nonprobability sampling is its lower cost compared to probability sampling. Moreover, the in-depth analysis of a small-N purposive sample or a case study enables the \"discovery\" and identification of patterns and causal mechanisms that do not draw time and context-free assumptions.\nNon-probability sampling is often not appropriate in statistical quantitative research, though, as these assertions raise some questions \u2014how can one understand a complex social phenomenon by drawing only the most convenient expressions of that phenomenon into consideration? What assumption about homogeneity in the world must one make to justify such assertions? Alas, the consideration that research can only be based in statistical inference focuses on the problems of bias linked to nonprobability sampling and acknowledges only one situation in which a non-probability sample can be appropriate \u2014if one is interested only in the specific cases studied (for example, if one is interested in the Battle of Gettysburg), one does not need to draw a probability sample from similar cases (Lucas 2014a).\nNon-probability sampling is however widely used in qualitative research. Examples of nonprobability sampling include:\n\nConvenience, haphazard or accidental sampling \u2013 members of the population are chosen based on their relative ease of access. To sample friends, co-workers, or shoppers at a single mall, are all examples of convenience sampling. Such samples are biased because researchers may unconsciously approach some kinds of respondents and avoid others (Lucas 2014a), and respondents who volunteer for a study may differ in unknown but important ways from others (Wiederman 1999).\nConsecutive sampling \u2013 also known as total enumerative sampling, is a sampling technique in which every subject meeting the criteria of inclusion is selected until the required sample size is achieved.\nSnowball sampling \u2013 The first respondent refers an acquaintance. The friend also refers a friend, and so on. Such samples are biased because they give people with more social connections an unknown but higher chance of selection (Berg 2006), but lead to higher response rates.\nJudgmental sampling or purposive sampling \u2013 The researcher chooses the sample based on who they think would be appropriate for the study. This is used primarily when there is a limited number of people that have expertise in the area being researched, or when the interest of the research is on a specific field or a small group. Different types of purposive sampling include:\nDeviant case \u2013 The researcher obtains cases that substantially differ from the dominant pattern (a special type of purposive sample). The case is selected in order to obtain information on unusual cases that can be specially problematic or specially good.\nCase study \u2013 The research is limited to one group, often with a similar characteristic or of small size.\nAd hoc quotas \u2013 A quota is established (e.g. 65% women) and researchers are free to choose any respondent they wish as long as the quota is met.Nonprobability sampling should not intend to meet the same type of results neither to be assessed with the quality criteria of probabilistic sampling (Steinke, 2004).\nStudies intended to use probability sampling sometimes end up using nonprobability samples because of characteristics of the sampling method. For example, using a sample of people in the paid labor force to analyze the effect of education on earnings is to use a non-probability sample of persons who could be in the paid labor force. Because the education people obtain could determine their likelihood of being in the paid labor force, technically the sample in the paid labor force is a nonprobability sample for the question at issue. In such cases results are biased.\nThe statistical model one uses can also render the data a non-probability sample. For example, Lucas (2014b) notes that several published studies that use multilevel modeling have been based on samples that are probability samples in general, but nonprobability samples for one or more of the levels of analysis in the study. Evidence indicates that in such cases the bias is poorly behaved, such that inferences from such analyses are unjustified.\nThese problems occur in the academic literature, but they may be more common in non-academic research. For example, in public opinion polling by private companies (or other organizations unable to require response), the sample can be self-selected rather than random. This often introduces an important type of error, self-selection bias, in which a potential participant's willingness to volunteer for the sample may be determined by characteristics such as submissiveness or availability. The samples in such surveys should be treated as non-probability samples of the population, and the validity of the findings based on them is unknown and cannot be established.\n\n", "images": [], "links": ["Accidental sampling", "Cluster sampling", "Consecutive sampling", "International Standard Book Number", "Judgment sample", "Multistage sampling", "Population (statistics)", "Probability", "Quota sampling", "Random sampling", "Sampling (statistics)", "Self-selection bias", "Simple random sample", "Snowball sampling", "Stratified sampling", "Systematic sampling"], "references": ["http://www.springerlink.com/content/u272h22kx2124037/fulltext.pdf", "http://www.li.suu.edu/library/circulation/Stein/Comm%206020ksStraussCorbinBasicsQualitativeFall07.pdf", "https://books.google.com/books?id=9RyMBgAAQBAJ&pg=PA224&dq=%22consecutive+sampling%22&hl=en&sa=X&ved=0ahUKEwjv4rnYy8nWAhUH-2MKHSxbAXI4ChDoAQgxMAI#v=onepage&q=%22consecutive%20sampling%22&f=false", "https://books.google.com/books?id=C7pZftbI0ZMC&pg=PA46&dq=%22consecutive+sampling%22&hl=en&sa=X&ved=0ahUKEwjC-tWaycnWAhWEKWMKHdaiDQ0Q6AEIQDAE#v=onepage&q=%22consecutive%20sampling%22&f=false", "https://books.google.com/books?id=t729l9LE9NUC&pg=PT46&dq=Consecutive+sampling&hl=en&sa=X&ei=PlszVe6qCJGTuASnioHgDw&redir_esc=y#v=onepage&q=Consecutive%20sampling&f=false", "https://link.springer.com/content/pdf/10.1007%2Fs11135-013-9865-x.pdf"]}, "Anomaly time series": {"categories": ["Climate and weather statistics", "Geophysics", "Time series"], "title": "Anomaly (natural sciences)", "method": "Anomaly time series", "url": "https://en.wikipedia.org/wiki/Anomaly_(natural_sciences)", "summary": "In the natural sciences, especially in atmospheric and Earth sciences involving applied statistics, an anomaly is the deviation in a quantity from its expected value, e.g., the difference between a measurement and a mean or a model prediction. \nSimilarly, a standardized anomaly equals an anomaly divided by a standard deviation. \nA group of anomalies can be analyzed spatially, as a map, or temporally, as a time series.\nThere are examples in atmospheric sciences and in geophysics.", "images": [], "links": ["Annual cycle", "Applied statistics", "Atmospheric sciences", "Bouguer anomaly", "Central tendency", "Climate oscillation", "Data transformation (statistics)", "Deviation (statistics)", "Earth sciences", "El Ni\u00f1o", "Europe", "Free-air anomaly", "Gravity anomaly", "Innovation (signal processing)", "International Standard Book Number", "Iridium anomaly", "Kursk Magnetic Anomaly", "Magnetic anomaly", "Natural sciences", "North Atlantic oscillation", "Outlier", "Robust statistics", "Southern Oscillation", "Standard deviation", "Storm track", "Temagami Magnetic Anomaly", "Weather"], "references": []}, "Taleb distribution": {"categories": ["All articles lacking reliable references", "All articles with unsourced statements", "Articles lacking reliable references from November 2015", "Articles with unsourced statements from April 2013", "Financial risk", "Mathematical finance", "Types of probability distributions"], "title": "Taleb distribution", "method": "Taleb distribution", "url": "https://en.wikipedia.org/wiki/Taleb_distribution", "summary": "In economics and finance, a Taleb distribution is the statistical profile of an investment which normally provides a payoff of small positive returns, while carrying a small but significant risk of catastrophic losses. The term was coined by journalist Martin Wolf and economist John Kay to describe investments with a \"high probability of a modest gain and a low probability of huge losses in any period.\"The concept is named after Nassim Nicholas Taleb, based on ideas outlined in his book Fooled by Randomness.\nAccording to Taleb in Silent Risk, the term should be called \"payoff\" to reflect the importance of the payoff function of the underlying probability distribution, rather than the distribution itself. The term is meant to refer to an investment returns profile in which there is a high probability of a small gain, and a small probability of a very large loss, which more than outweighs the gains. In these situations the expected value is very much less than zero, but this fact is camouflaged by the appearance of low risk and steady returns. It is a combination of kurtosis risk and skewness risk: overall returns are dominated by extreme events (kurtosis), which are to the downside (skew).\nMore detailed and formal discussion of the bets on small probability events is in the academic essay by Taleb, called \"Why Did the Crisis of 2008 Happen?\" and in the 2004 paper in the Journal of Behavioral Finance called \"Why Do We Prefer Asymmetric Payoffs?\" in which he writes \"agents risking other people\u2019s capital would have the incentive to camouflage the properties by showing a steady income. Intuitively, hedge funds are paid on an annual basis while disasters happen every four or five years, for example. The fund manager does not repay his incentive fee.\"", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Antifragile", "Antifragility", "Barbell strategy", "Black swan theory", "Carry trade", "Cognitive bias", "Decision theory", "Digital object identifier", "Economics", "Epistemology", "Expected utility", "Expected value", "Fat-tailed distribution", "Finance", "Financial Times", "Financial leverage", "Fooled by Randomness", "Gambler's ruin", "Hedge fund", "Hedge funds", "Holy grail distribution", "Info-gap decision theory", "Investment return", "Investment strategy", "John Kay (economist)", "John Kenneth Galbraith", "Journal of Behavioral Finance", "Knightian uncertainty", "Kurtosis risk", "Lindy effect", "Ludic fallacy", "Mark-to-market accounting", "Martin Wolf", "Minimax", "Minimax regret", "Moral hazard", "Nassim Nicholas Taleb", "Option (finance)", "Probability", "Probability distribution", "Return (finance)", "Risk", "Risk of ruin", "Robust decision", "Scenario analysis", "Security (finance)", "Sensitivity analysis", "Skewness risk", "Skin in the Game (book)", "Speculative bubble", "Stress test (financial)", "Stress testing", "Tailgating", "The Bed of Procrustes", "The Black Swan: The Impact of the Highly Improbable", "Traffic accident", "Uncertainty"], "references": ["http://www.fooledbyrandomness.com/bleedblowup.pdf", "http://www.johnkay.com/2003/01/16/a-strategy-for-hedge-funds-and-dangerous-drivers/", "http://www.johnkay.com/2008/10/15/banks-got-burned-by-their-own-%E2%80%98innocent-fraud%E2%80%99/", "http://www.nakedcapitalism.com/2008/03/are-hedge-funds-scam.html", "http://seekingalpha.com/article/2530925-holy-grail-distribution", "http://doi.org/10.1207%2Fs15427579jpfm0501_1", "https://www.forbes.com/forbes/2011/0627/money-guide-11-spitznagel-black-swan-cnbc-protect-tail.html", "https://www.ft.com/content/c8941ad4-f503-11dc-a21b-000077b07658", "https://drive.google.com/file/d/0B8nhAlfIk3QIR1o1dnk5ZmRaaGs/view", "https://www.researchgate.net/publication/233246782_Bleed_or_Blowup_Why_Do_We_Prefer_Asymmetric_Payoffs"]}, "Conjoint analysis (in marketing)": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from August 2017", "Articles with unsourced statements from May 2017", "Dynamic lists", "Market research", "Product management", "Psychometrics", "Regression analysis"], "title": "Conjoint analysis", "method": "Conjoint analysis (in marketing)", "url": "https://en.wikipedia.org/wiki/Conjoint_analysis", "summary": "'Conjoint analysis' is a survey-based statistical technique used in market research that helps determine how people value different attributes (feature, function, benefits) that make up an individual product or service.\nThe objective of conjoint analysis is to determine what combination of a limited number of attributes is most influential on respondent choice or decision making. A controlled set of potential products or services is shown to survey respondents and by analyzing how they make preferences between these products, the implicit valuation of the individual elements making up the product or service can be determined. These implicit valuations (utilities or part-worths) can be used to create market models that estimate market share, revenue and even profitability of new designs.\nConjoint originated in mathematical psychology and was developed by marketing professor Paul E. Green at the Wharton School of the University of Pennsylvania. Other prominent conjoint analysis pioneers include professor V. \"Seenu\" Srinivasan of Stanford University who developed a linear programming (LINMAP) procedure for rank ordered data as well as a self-explicated approach, Richard Johnson who developed the Adaptive Conjoint Analysis technique in the 1980s and Jordan Louviere (University of Iowa) who invented and developed choice-based approaches to conjoint analysis and related techniques such as best\u2013worst scaling.\nToday it is used in many of the social sciences and applied sciences including marketing, product management, and operations research. It is used frequently in testing customer acceptance of new product designs, in assessing the appeal of advertisements and in service design. It has been used in product positioning, but there are some who raise problems with this application of conjoint analysis.\nConjoint analysis techniques may also be referred to as multiattribute compositional modelling, discrete choice modelling, or stated preference research, and is part of a broader set of trade-off analysis tools used for systematic analysis of decisions. These tools include Brand-Price Trade-Off, Simalto, and mathematical approaches such as AHP, evolutionary algorithms or rule-developing experimentation.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/89/Ice-cream-experiment-example.png", "https://upload.wikimedia.org/wikipedia/commons/5/50/Sample-output-of-conjoint-analysis.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["1000minds", "Advertising", "Analytic hierarchy process", "Application software", "Bayesian estimator", "Bayesian probability", "Best\u2013worst scaling", "Choice-based conjoint analysis", "Configurator", "Digital object identifier", "Discrete choice", "Discrete choice analysis", "Dummy variable (statistics)", "Econometric modeling", "Evolutionary algorithms", "Fractional factorial design", "Linear regression", "Logistic regression", "Marketing", "Marketing research", "Mathematical psychology", "Maximum likelihood estimation", "New Zealand", "New product development", "Open-source software", "Operations research", "Paul E. Green", "Positioning (marketing)", "Product management", "Proprietary software", "Provo, Utah", "PubMed Identifier", "Quantitative marketing research", "R (programming language)", "Regression analysis", "Revealed preference", "Rule-developing experimentation", "San Francisco", "Sawtooth Software", "Service design", "Simalto", "Software as a service", "Sydney", "TURF Analysis", "Test market", "V Srinivasan", "Value-based pricing", "Wharton School of the University of Pennsylvania"], "references": ["http://www.sawtoothsoftware.com/products/all-products", "http://www.sawtoothsoftware.com/support/technical-papers/conference-proceedings/proceedings2001", "http://onlinelibrary.wiley.com/doi/10.1111/j.1540-5915.1988.tb00268.x/abstract", "http://www.mit.edu/~hauser/Papers/GreenTributeConjoint092302.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/22185216", "http://www.conjoint.online/", "http://www.conjoint.online/reports.html", "http://doi.org/10.1071%2FCP10320", "http://doi.org/10.2165%2F11587140-000000000-00000", "http://www.ispor.org/taskforces/documents/ISPOR-CA-in-Health-TF-Report-Checklist.pdf", "http://hbanaszak.mjr.uw.edu.pl/TempTxt/GreenEtAl_1981_GeneralApproachToProductDesignOptimisationViaConJointAnalysis.pdf", "https://www.1000minds.com/", "https://www.criterioneconomics.com/using-conjoint-analysis-to-apportion-patent-damages.html", "https://mychoicesurveys.com", "https://www.qualtrics.com/research-core/conjoint-analysis/", "https://www.sawtoothsoftware.com/products/pricing-ordering", "https://surveyanalytics.com/", "https://run.conjoint.ly/study/163/3ewoipzq36", "https://conjoint.online/conjoint-analysis/", "https://conjoint.online/pricing", "https://web.archive.org/web/20120212051120/http://www.ericmarder.com/articles/cjmr1.pdf", "https://www.jstor.org/stable/1251756", "https://www.jstor.org/stable/2489001", "https://cran.r-project.org/web/packages/support.CEs/index.html"]}, "Optimal matching": {"categories": ["Data mining", "Quantitative research", "Statistical distance"], "title": "Optimal matching", "method": "Optimal matching", "url": "https://en.wikipedia.org/wiki/Optimal_matching", "summary": "Optimal matching is a sequence analysis method used in social science, to assess the dissimilarity of ordered arrays of tokens that usually represent a time-ordered sequence of socio-economic states two individuals have experienced. Once such distances have been calculated for a set of observations (e.g. individuals in a cohort) classical tools (such as cluster analysis) can be used. The method was tailored to social sciences from a technique originally introduced to study molecular biology (protein or genetic) sequences (see sequence alignment). Optimal matching uses the Needleman-Wunsch algorithm.", "images": [], "links": ["Algebras", "Cluster analysis", "Cohort (statistics)", "Counterfactual conditional", "Digital object identifier", "Maximum matching", "Needleman-Wunsch algorithm", "R (programming language)", "Sequence alignment", "Social science", "Symmetric", "Transitive relation"], "references": ["http://traminer.unige.ch/", "http://smr.sagepub.com/cgi/content/abstract/29/1/3", "http://smr.sagepub.com/cgi/content/refs/29/1/41", "http://www.stat.ruhr-uni-bochum.de/tda.html", "http://ideas.repec.org/a/tsj/stataj/v6y2006i4p435-460.html", "https://doi.org/10.1177%2F0049124100029001001", "https://doi.org/10.1177%2F0049124100029001003"]}, "Challenge\u2013dechallenge\u2013rechallenge": {"categories": ["Design of experiments", "Medical tests"], "title": "Challenge\u2013dechallenge\u2013rechallenge", "method": "Challenge\u2013dechallenge\u2013rechallenge", "url": "https://en.wikipedia.org/wiki/Challenge%E2%80%93dechallenge%E2%80%93rechallenge", "summary": "Challenge\u2013dechallenge\u2013rechallenge (CDR) is a medical testing protocol in which a medicine or drug is administered, withdrawn, then re-administered, while being monitored for adverse effects at each stage. The protocol is used when statistical testing is inappropriate due to an idiosyncratic reaction by a specific individual, or a lack of sufficient test subjects and unit of analysis is the individual. During the withdraw phase, the medication is allowed to wash out of the system in order to determine what effect the medication is having on an individual.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["Adverse drug reaction", "Adverse effect (medicine)", "Akathisia", "CDR computerized assessment system", "Clinical trial", "Digital object identifier", "Eli Lilly and Company", "Fluoxetine", "Food and Drug Administration", "International Standard Book Number", "Medical diagnosis", "Peter Breggin", "Philadelphia", "Protocol (natural sciences)", "PubMed Central", "PubMed Identifier", "Randomized controlled trial", "Single-subject design", "Statistics", "Suicidal ideation"], "references": ["http://www.fda.gov/medwatch/report/cberguid/define.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC193979", "http://www.ncbi.nlm.nih.gov/pubmed/10268556", "http://www.ncbi.nlm.nih.gov/pubmed/12601224", "http://www.ncbi.nlm.nih.gov/pubmed/14517576", "http://www.ncbi.nlm.nih.gov/pubmed/16111835", "http://www.ncbi.nlm.nih.gov/pubmed/1752848", "http://www.ncbi.nlm.nih.gov/pubmed/3821430", "http://www.oism.info/en/therapy/theory/suicide_and_neuropsychiatric_adverse_effects_of_ssri.htm", "http://doi.org/10.1016/j.mehy.2005.07.013", "http://doi.org/10.1159/000068691", "http://doi.org/10.1177/009286158401800314", "http://doi.org/10.4103/0253-7613.132157", "https://web.archive.org/web/20071007215452/http://www.fda.gov/medwatch/report/cberguid/define.htm", "https://web.archive.org/web/20081120204712/http://www.oism.info/en/therapy/theory/suicide_and_neuropsychiatric_adverse_effects_of_ssri.htm"]}, "Mexican paradox": {"categories": ["Epidemiology", "Health in Mexico", "Health paradoxes", "Obstetrics", "Public health"], "title": "Mexican paradox", "method": "Mexican paradox", "url": "https://en.wikipedia.org/wiki/Mexican_paradox", "summary": "The Mexican paradox is the observation that the Mexican people exhibit a surprisingly low incidence of low birth weight (LBW), contrary to what would be expected from their socioeconomic status (SES). This appears as an outlier in graphs correlating SES with low-birth-weight rates.\nIt has been proposed that resistance to changes in diet is responsible for the positive birth weight association for Mexican-American mothers.Nevertheless, the medical causes of lower rates of low birth weights among birthing Mexican mothers has been called into question.The results of the study showed that the mean birth weight of Mexican-American babies was 3.34 kg (7.37 lbs), while that of non-Hispanic White babies was 3.39 kg (7.48 lbs.). This finding re-emphasized the independence of mean birth weight and LBW. This however did not refute the discrepancies in LBW for Mexicans.\nThe study also showed that the overall preterm birth rate was higher among Mexican Americans (10.6%) than non-Hispanic Whites (9.3%).\nThe overall hypothesis of the authors was that this finding reflected an error in recorded gestational age, described in a strongly bimodal birth-weight distribution at young gestational ages for Mexican-Americans.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["Bimodal", "Demographics of Mexico", "Diet (nutrition)", "Digital object identifier", "French paradox", "Gestational age", "Hispanic paradox", "International Standard Serial Number", "List of paradoxes", "Low birth weight", "Low birth weight paradox", "Outlier", "Preterm birth", "PubMed Central", "PubMed Identifier", "Socioeconomic status", "White Hispanic and Latino Americans"], "references": ["http://linkinghub.elsevier.com/retrieve/pii/S0306987706004361", "http://www.indyweek.com/gyrobase/Content?oid=oid:18907", "http://heb.sagepub.com/cgi/content/abstract/22/1/96", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1448590", "http://www.ncbi.nlm.nih.gov/pubmed/10968379", "http://www.ncbi.nlm.nih.gov/pubmed/15569952", "http://www.ncbi.nlm.nih.gov/pubmed/16935435", "http://www.ncbi.nlm.nih.gov/pubmed/7721605", "http://www.ajph.org/cgi/pmidlookup?view=long&pmid=15569952", "http://doi.org/10.1016%2Fj.mehy.2006.05.059", "http://doi.org/10.1093%2Faje%2F152.4.347", "http://doi.org/10.1177%2F109019819502200109", "http://doi.org/10.1353%2Fsof.2002.0014", "http://doi.org/10.2105%2FAJPH.94.12.2062", "http://aje.oxfordjournals.org/cgi/content/full/152/4/347", "http://www.worldcat.org/issn/0037-7732"]}, "One-factor-at-a-time method": {"categories": ["Design of experiments"], "title": "One-factor-at-a-time method", "method": "One-factor-at-a-time method", "url": "https://en.wikipedia.org/wiki/One-factor-at-a-time_method", "summary": "The one-factor-at-a-time method, also known as one-variable-at-a-time, OFAT, OF@T,\nOFaaT, OVAT, OV@T, OVaaT, or monothetic analysis is a method of designing experiments involving the testing of factors, or causes, one at a time instead of multiple factors simultaneously.", "images": [], "links": ["Balance puzzle", "Ceteris paribus", "Design of experiments", "Digital object identifier", "Efficiency (statistics)", "Factorial design", "Fractional factorial design", "International Standard Serial Number", "Plackett-Burman design", "Ronald Fisher"], "references": ["http://doi.org/10.1002%2F2014wr016527", "http://www.worldcat.org/issn/0043-1397", "https://www.questia.com/googleScholar.qst?docId=5001888588", "https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2014WR016527"]}, "Testing hypotheses suggested by the data": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from January 2008", "Articles with unsourced statements from February 2011", "Misuse of statistics", "Multiple comparisons", "Statistical hypothesis testing"], "title": "Testing hypotheses suggested by the data", "method": "Testing hypotheses suggested by the data", "url": "https://en.wikipedia.org/wiki/Testing_hypotheses_suggested_by_the_data", "summary": "In statistics, hypotheses suggested by a given dataset, when tested with the same dataset that suggested them, are likely to be accepted even when they are not true. This is because circular reasoning (double dipping) would be involved: something seems true in the limited data set, therefore we hypothesize that it is true in general, therefore we (wrongly) test it on the same limited data set, which seems to confirm that it is true. Generating hypotheses based on data already observed, in the absence of testing them on new data, is referred to as post hoc theorizing (from Latin post hoc, \"after this\").\nThe correct procedure is to test any hypothesis on a data set that was not used to generate the hypothesis.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Academic publishing", "Analysis of variance", "Biometrika", "Bonferroni correction", "Confirmation sample", "Cross-validation (statistics)", "Data", "Data analysis", "Data dredging", "Data mining", "Digital object identifier", "Exploratory data analysis", "Henry Scheff\u00e9", "Hypothesis", "Latin language", "Machine learning", "Multiple comparisons", "Overfitting", "Placebo", "Post-hoc analysis", "Post hoc analysis", "Predictive analytics", "Probability", "Publication bias", "Scheff\u00e9 test", "Scientific evidence", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical noise", "Texas sharpshooter fallacy", "Trial and error", "Type I and type II errors", "Type I error", "Uncomfortable science"], "references": ["https://doi.org/10.1093%2Fbiomet%2F40.1-2.87"]}, "Bar chart": {"categories": ["Commons category link is on Wikidata", "Statistical charts and diagrams"], "title": "Bar chart", "method": "Bar chart", "url": "https://en.wikipedia.org/wiki/Bar_chart", "summary": "A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a line graph.\nA bar graph shows comparisons among discrete categories. One axis of the chart shows the specific categories being compared, and the other axis represents a measured value. Some bar graphs present bars clustered in groups of more than one, showing the values of more than one measured variable.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/35/Human_losses_of_world_war_two_by_country.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete variable", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Enhanced Metafile Format", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Height", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "James R. Beniger", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Length", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "MS PowerPoint", "Mann\u2013Whitney U test", "Marshall Clagett", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Misleading graph", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Center for Education Statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nicole Oresme", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rectangle", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Playfair", "Z-test"], "references": ["http://nces.ed.gov/nceskids/createagraph/", "http://www.dmoz.org/Science/Math/Software/Graphing/", "http://doi.org/10.1080%2F00031305.1978.10479235", "http://www.jstor.org/stable/2683467", "https://livegap.com/charts/", "https://books.google.ru/books?id=kB8bBAAAQBAJ&printsec=frontcover#v=onepage"]}, "Granger causality": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from February 2018", "Multivariate time series", "Time series statistical tests", "Webarchive template wayback links"], "title": "Granger causality", "method": "Granger causality", "url": "https://en.wikipedia.org/wiki/Granger_causality", "summary": "The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969. Ordinarily, regressions reflect \"mere\" correlations, but Clive Granger argued that causality in economics could be tested for by measuring the ability to predict the future values of a time series using prior values of another time series. Since the question of \"true causality\" is deeply philosophical, and because of the post hoc ergo propter hoc fallacy of assuming that one thing preceding another can be used as a proof of causation, econometricians assert that the Granger test finds only \"predictive causality\".A time series X is said to Granger-cause Y if it can be shown, usually through a series of t-tests and F-tests on lagged values of X (and with lagged values of Y also included), that those X values provide statistically significant information about future values of Y.\nGranger also stressed that some studies using \"Granger causality\" testing in areas outside economics reached \"ridiculous\" conclusions. \"Of course, many ridiculous papers appeared\", he said in his Nobel lecture. However, it remains a popular method for causality analysis in time series due to its computational simplicity. The original definition of Granger causality does not account for latent confounding effects and does not capture instantaneous and non-linear causal relationships, though several extensions have been proposed to address these issues.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/7d/GrangerCausalityIllustration.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregression", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Bradford Hill criteria", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Causality", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Clive Granger", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Conditional intensity function", "Conditional probability", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convergent cross mapping", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrician", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Explanatory power", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forecasting", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Functional connectivity", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Graphical model", "Grouped data", "Harmonic mean", "Helmut L\u00fctkepohl", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Humean definition of causality", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kevin Hoover", "Koch postulate", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lag operator", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Neural population", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Point process", "Poisson process", "Poisson regression", "Population (statistics)", "Population statistics", "Post hoc ergo propter hoc", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Refractory period (physiology)", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Schwarz information criterion", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Small-world networks", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spike train", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic processes", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "The New Palgrave Dictionary of Economics", "Time domain", "Time series", "Tolerance interval", "Transfer entropy", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://research.economics.unsw.edu.au/vpanchenko/papers/2006_GC_JEDC.pdf", "http://research.economics.unsw.edu.au/vpanchenko/papers/2009_SLFIRMS_JEF.pdf", "http://www.dictionaryofeconomics.com/article?id=pde2008_G000190", "http://people.dbmi.columbia.edu/samantha/papers/kleinberg_jbi11_preprint.pdf", "http://adsabs.harvard.edu/abs/2007SchpJ...2.1667S", "http://adsabs.harvard.edu/abs/2011PLSCB...7E1110K", "http://adsabs.harvard.edu/abs/2015PhLRv..15..107M", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3063721", "http://www.ncbi.nlm.nih.gov/pubmed/17569852", "http://www.ncbi.nlm.nih.gov/pubmed/20202481", "http://www.ncbi.nlm.nih.gov/pubmed/21455283", "http://www.ncbi.nlm.nih.gov/pubmed/26429630", "http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=229894", "http://researchers-sbe.unimaas.nl/michaeleichler/wp-content/uploads/sites/31/2014/02/causalstatistics.pdf", "http://doi.org/10.1007%2Fs00181-011-0484-x", "http://doi.org/10.1016%2F0165-1889(80)90069-X", "http://doi.org/10.1016%2Fj.econmod.2012.02.014", "http://doi.org/10.1016%2Fj.jedc.2005.08.008", "http://doi.org/10.1016%2Fj.jempfin.2009.08.003", "http://doi.org/10.1016%2Fj.neuroimage.2010.02.059", "http://doi.org/10.1016%2Fj.plrev.2015.09.002", "http://doi.org/10.1080%2F00036840500405763", "http://doi.org/10.1086%2F294632", "http://doi.org/10.1126%2Fscience.1144677", "http://doi.org/10.1257%2F0002828041464669", "http://doi.org/10.1371%2Fjournal.pcbi.1001110", "http://doi.org/10.2307%2F1912791", "http://doi.org/10.4249%2Fscholarpedia.1667", "http://www.jstor.org/stable/1912791", "http://www.worldcat.org/issn/1843-2298", "https://web.archive.org/web/20120430094823/http://people.dbmi.columbia.edu/samantha/papers/kleinberg_jbi11_preprint.pdf", "https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2003/granger-lecture.pdf", "https://ideas.repec.org/a/spr/empeco/v43y2012i1p447-456.html", "https://ideas.repec.org/a/taf/applec/v38y2006i13p1489-1500.html"]}, "Trimmed estimator": {"categories": ["All articles lacking sources", "Articles lacking sources from April 2013", "Estimator", "Robust statistics"], "title": "Trimmed estimator", "method": "Trimmed estimator", "url": "https://en.wikipedia.org/wiki/Trimmed_estimator", "summary": "In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation. This is generally done to obtain a more robust statistic, and the extreme values are considered outliers. Trimmed estimators also often have higher efficiency for mixture distributions and heavy-tailed distributions than the corresponding untrimmed estimator, at the cost of lower efficiency for other distributions, such as the normal distribution.\nGiven an estimator, the n% trimmed version is obtained by discarding the n% lowest and highest observations: it is a statistic on the middle of the data. For instance, the 5% trimmed mean is obtained by taking the mean of the 5% to 95% range. In some cases a trimmed estimator discards a fixed number of points (such as maximum and minimum) instead of a percentage.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Cauchy distribution", "Consistent estimator", "Core inflation", "Efficiency (statistics)", "Error function", "Estimator", "Expected value", "Extreme value", "Heavy-tailed distribution", "Interdecile range", "Interquartile mean", "Interquartile range", "L-estimator", "Location parameter", "Median", "Median absolute deviation", "Mid-range", "Midhinge", "Mixture distribution", "Modified mean", "Nonparametric skew", "Normal distribution", "Outlier", "Parameter estimation", "Pearson's skewness coefficients", "Percentile", "Population variance", "Quantiles", "Range (statistics)", "Robust measures of scale", "Robust statistic", "Scale factor", "Scale parameter", "Skewness", "Standard deviation", "Statistics", "Trimmed mean", "Truncation (statistics)", "Unbiased estimator", "Winsorising"], "references": []}, "Wombling": {"categories": ["All stub articles", "Change detection", "Spatial data analysis", "Statistics stubs"], "title": "Wombling", "method": "Wombling", "url": "https://en.wikipedia.org/wiki/Wombling", "summary": "In statistics, Wombling is any of a number of techniques used for identifying zones of rapid change, typically in some quantity as it varies across some geographical or Euclidean space. It is named for statistician William H. Womble.\nThe technique may be applied to gene frequency in a population of organisms, and to evolution of language.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Bayesian Analysis (journal)", "Biometrics (journal)", "Digital object identifier", "Ecology (journal)", "Euclidean space", "Evolutionary linguistics", "Gene frequency", "Journal of the American Statistical Association", "Rate of change (mathematics)", "Science (journal)", "Statistics", "William H. Womble", "Womble (disambiguation)"], "references": ["http://ba.stat.cmu.edu/journal/2007/vol02/issue02/ma.pdf", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2835372/", "https://doi.org/10.1111%2Fj.1541-0420.2009.01203.x", "https://doi.org/10.1126%2Fscience.114.2961.315", "https://doi.org/10.1198%2F016214506000000041", "https://doi.org/10.1890%2F10-0807.1"]}, "Conjoint analysis (in healthcare)": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from August 2017", "Articles with unsourced statements from May 2017", "Dynamic lists", "Market research", "Product management", "Psychometrics", "Regression analysis"], "title": "Conjoint analysis", "method": "Conjoint analysis (in healthcare)", "url": "https://en.wikipedia.org/wiki/Conjoint_analysis", "summary": "'Conjoint analysis' is a survey-based statistical technique used in market research that helps determine how people value different attributes (feature, function, benefits) that make up an individual product or service.\nThe objective of conjoint analysis is to determine what combination of a limited number of attributes is most influential on respondent choice or decision making. A controlled set of potential products or services is shown to survey respondents and by analyzing how they make preferences between these products, the implicit valuation of the individual elements making up the product or service can be determined. These implicit valuations (utilities or part-worths) can be used to create market models that estimate market share, revenue and even profitability of new designs.\nConjoint originated in mathematical psychology and was developed by marketing professor Paul E. Green at the Wharton School of the University of Pennsylvania. Other prominent conjoint analysis pioneers include professor V. \"Seenu\" Srinivasan of Stanford University who developed a linear programming (LINMAP) procedure for rank ordered data as well as a self-explicated approach, Richard Johnson who developed the Adaptive Conjoint Analysis technique in the 1980s and Jordan Louviere (University of Iowa) who invented and developed choice-based approaches to conjoint analysis and related techniques such as best\u2013worst scaling.\nToday it is used in many of the social sciences and applied sciences including marketing, product management, and operations research. It is used frequently in testing customer acceptance of new product designs, in assessing the appeal of advertisements and in service design. It has been used in product positioning, but there are some who raise problems with this application of conjoint analysis.\nConjoint analysis techniques may also be referred to as multiattribute compositional modelling, discrete choice modelling, or stated preference research, and is part of a broader set of trade-off analysis tools used for systematic analysis of decisions. These tools include Brand-Price Trade-Off, Simalto, and mathematical approaches such as AHP, evolutionary algorithms or rule-developing experimentation.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/89/Ice-cream-experiment-example.png", "https://upload.wikimedia.org/wikipedia/commons/5/50/Sample-output-of-conjoint-analysis.png", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["1000minds", "Advertising", "Analytic hierarchy process", "Application software", "Bayesian estimator", "Bayesian probability", "Best\u2013worst scaling", "Choice-based conjoint analysis", "Configurator", "Digital object identifier", "Discrete choice", "Discrete choice analysis", "Dummy variable (statistics)", "Econometric modeling", "Evolutionary algorithms", "Fractional factorial design", "Linear regression", "Logistic regression", "Marketing", "Marketing research", "Mathematical psychology", "Maximum likelihood estimation", "New Zealand", "New product development", "Open-source software", "Operations research", "Paul E. Green", "Positioning (marketing)", "Product management", "Proprietary software", "Provo, Utah", "PubMed Identifier", "Quantitative marketing research", "R (programming language)", "Regression analysis", "Revealed preference", "Rule-developing experimentation", "San Francisco", "Sawtooth Software", "Service design", "Simalto", "Software as a service", "Sydney", "TURF Analysis", "Test market", "V Srinivasan", "Value-based pricing", "Wharton School of the University of Pennsylvania"], "references": ["http://www.sawtoothsoftware.com/products/all-products", "http://www.sawtoothsoftware.com/support/technical-papers/conference-proceedings/proceedings2001", "http://onlinelibrary.wiley.com/doi/10.1111/j.1540-5915.1988.tb00268.x/abstract", "http://www.mit.edu/~hauser/Papers/GreenTributeConjoint092302.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/22185216", "http://www.conjoint.online/", "http://www.conjoint.online/reports.html", "http://doi.org/10.1071%2FCP10320", "http://doi.org/10.2165%2F11587140-000000000-00000", "http://www.ispor.org/taskforces/documents/ISPOR-CA-in-Health-TF-Report-Checklist.pdf", "http://hbanaszak.mjr.uw.edu.pl/TempTxt/GreenEtAl_1981_GeneralApproachToProductDesignOptimisationViaConJointAnalysis.pdf", "https://www.1000minds.com/", "https://www.criterioneconomics.com/using-conjoint-analysis-to-apportion-patent-damages.html", "https://mychoicesurveys.com", "https://www.qualtrics.com/research-core/conjoint-analysis/", "https://www.sawtoothsoftware.com/products/pricing-ordering", "https://surveyanalytics.com/", "https://run.conjoint.ly/study/163/3ewoipzq36", "https://conjoint.online/conjoint-analysis/", "https://conjoint.online/pricing", "https://web.archive.org/web/20120212051120/http://www.ericmarder.com/articles/cjmr1.pdf", "https://www.jstor.org/stable/1251756", "https://www.jstor.org/stable/2489001", "https://cran.r-project.org/web/packages/support.CEs/index.html"]}, "Dickey\u2013Fuller test": {"categories": ["All articles with dead external links", "Articles with dead external links from December 2016", "Articles with permanently dead external links", "Time series statistical tests"], "title": "Dickey\u2013Fuller test", "method": "Dickey\u2013Fuller test", "url": "https://en.wikipedia.org/wiki/Dickey%E2%80%93Fuller_test", "summary": "In statistics, the Dickey\u2013Fuller test tests the null hypothesis that a unit root is present in an autoregressive model. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity. It is named after the statisticians David Dickey and Wayne Fuller, who developed the test in 1979.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Augmented Dickey\u2013Fuller test", "Autocorrelation", "Autoregressive", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "David Dickey", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller distribution", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Equivalence relation", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finite difference", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Economic Education", "Journal of Economic Surveys", "Journal of the American Statistical Association", "KPSS test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phillips\u2013Perron test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random walk", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationarity (statistics)", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistician", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Trend stationary", "U-statistic", "Uniformly most powerful test", "Unit root", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Wayne Fuller", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.economics.utoronto.ca/jfloyd/stats/statabs.ps", "http://doi.org/10.1080%2F00220480109595179", "http://doi.org/10.1080%2F01621459.1979.10482531", "http://doi.org/10.1111%2Fj.1467-6419.1990.tb00088.x", "http://doi.org/10.2307%2F3585053", "http://www.jstor.org/stable/2286348", "http://www.jstor.org/stable/3585053", "http://cesis.abe.kth.se/documents/CESISWP213.pdf", "https://books.google.com/books?id=ZQsaRNl5J60C&pg=PA48", "https://www.scribd.com/doc/80877200/How-to-do-a-Dickey-Fuller-Test-using-Excel", "https://dash.harvard.edu/bitstream/handle/1/3374863/campbell_pitfalls.pdf?sequence=2", "https://ideas.repec.org/p/hhs/cesisp/0214.html"]}, "Watts and Strogatz model": {"categories": ["CS1 maint: Multiple names: authors list", "Networks", "Random graphs", "Social networks"], "title": "Watts\u2013Strogatz model", "method": "Watts and Strogatz model", "url": "https://en.wikipedia.org/wiki/Watts%E2%80%93Strogatz_model", "summary": "The Watts\u2013Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering. It was proposed by Duncan J. Watts and Steven Strogatz in their joint 1998 Nature paper. The model also became known as the (Watts) beta model after Watts used \n \n \n \n \u03b2\n \n \n {\\displaystyle \\beta }\n to formulate it in his popular science book Six Degrees.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/2b/Watts-Strogatz_small-world_model_100nodes.png", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Watts_strogatz.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d2/Internet_map_1024.jpg"], "links": ["Adjacency list", "Adjacency matrix", "Agent-based model", "Alfr\u00e9d R\u00e9nyi", "ArXiv", "Artificial neural network", "Assortativity", "Average path length", "BA model", "Balance theory", "Barab\u00e1si\u2013Albert model", "Betweenness centrality", "Bibcode", "Biological network", "Bipartite graph", "Boolean network", "Budding yeast", "Caenorhabditis elegans", "Centrality", "Clique (graph theory)", "Closeness (graph theory)", "Clustering coefficient", "Combinatorial optimization", "Community structure", "Complete graph", "Complex contagion", "Complex network", "Computer network", "Connected component (graph theory)", "Cut (graph theory)", "Cycle (graph theory)", "Degree (graph theory)", "Degree distribution", "Dependency network", "Digital object identifier", "Dirac delta function", "Directed graph", "Distance (graph theory)", "Duncan J. Watts", "Edge (graph theory)", "Efficiency (network science)", "Epidemic model", "Erd\u0151s\u2013R\u00e9nyi model", "Evolving networks", "Exponential random graph models", "Fitness model (network theory)", "Flow network", "Graph (abstract data type)", "Graph (discrete mathematics)", "Graph drawing", "Hierarchical network model", "Homophily", "Hyperbolic geometric graph", "Hypergraph", "Incidence list", "Incidence matrix", "Interdependent networks", "Lancichinetti\u2013Fortunato\u2013Radicchi benchmark", "Lattice (group)", "Limiting case (mathematics)", "Link analysis", "List of algorithms", "List of network scientists", "List of network theory topics", "Loop (graph theory)", "Metrics (networking)", "Modularity (networks)", "Multigraph", "Nature (journal)", "Neighbourhood (graph theory)", "Network controllability", "Network effect", "Network motif", "Network on a chip", "Network science", "Network theory", "PageRank", "Path (graph theory)", "Paul Erd\u0151s", "Percolation theory", "Poisson distribution", "Power law", "Preferential attachment", "PubMed Central", "PubMed Identifier", "Random geometric graph", "Random graph", "Reciprocity (network science)", "SIR model", "Scale-free network", "Scale-free networks", "Scientific collaboration network", "Semantic network", "Six Degrees: The Science of a Connected Age", "Small-world network", "Small-world networks", "Social capital", "Social influence", "Social network", "Social network analysis software", "Social networks", "Spatial network", "Steven Strogatz", "Stochastic block model", "Telecommunications network", "Transitive relation", "Transport network", "Triadic closure", "Undirected graph", "Vertex (graph theory)", "Watts and Strogatz model", "Weighted network"], "references": ["http://www.springerlink.com/index/0HGUCD51T90CKB12.pdf", "http://worrydream.com/refs/Watts-CollectiveDynamicsOfSmallWorldNetworks.pdf", "http://adsabs.harvard.edu/abs/1998Natur.393..440W", "http://adsabs.harvard.edu/abs/2002RvMP...74...47A", "http://adsabs.harvard.edu/abs/2002Sci...297.1551R", "http://adsabs.harvard.edu/abs/2015PLSCB..11E4264A", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4447291", "http://www.ncbi.nlm.nih.gov/pubmed/26020510", "http://www.ncbi.nlm.nih.gov/pubmed/9623998", "http://arxiv.org/abs/cond-mat/0106096", "http://arxiv.org/abs/cond-mat/0209244", "http://arxiv.org/abs/cond-mat/9903411", "http://doi.org/10.1007%2Fs100510050067", "http://doi.org/10.1038%2F30918", "http://doi.org/10.1103%2FRevModPhys.74.47", "http://doi.org/10.1126%2Fscience.1073374", "http://doi.org/10.1371%2Fjournal.pcbi.1004264"]}, "Lot quality assurance sampling": {"categories": ["All stub articles", "Quality assurance", "Sampling (statistics)", "Statistics stubs"], "title": "Lot quality assurance sampling", "method": "Lot quality assurance sampling", "url": "https://en.wikipedia.org/wiki/Lot_quality_assurance_sampling", "summary": "Lot quality assurance sampling (LQAS) is a random sampling methodology, originally developed in the 1920s as a method of quality control in industrial production. Compared to similar sampling techniques like stratified and cluster sampling, LQAS provides less information but often requires substantially smaller sample sizes.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Cluster sampling", "Digital object identifier", "PubMed Central", "PubMed Identifier", "Quality control", "Random sample", "Random sampling", "Statistical inference", "Statistics", "Stratified sampling", "World Health Organization"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2912491", "http://www.ncbi.nlm.nih.gov/pubmed/1949879", "http://www.ncbi.nlm.nih.gov/pubmed/20139435", "http://extranet.who.int/ivb_docs/documents/1049", "http://doi.org/10.1093%2Fije%2Fdyp363", "https://archive.org/details/bstj8-4-613"]}, "Consistency (statistics)": {"categories": ["Asymptotic theory (statistics)"], "title": "Consistency (statistics)", "method": "Consistency (statistics)", "url": "https://en.wikipedia.org/wiki/Consistency_(statistics)", "summary": "In statistics, consistency of procedures, such as computing confidence intervals or conducting hypothesis tests, is a desired property of their behaviour as the number of items in the data set to which they are applied increases indefinitely. In particular, consistency requires that the outcome of the procedure with unlimited data should identify the underlying truth.\nUse of the term in statistics derives from Sir Ronald Fisher in 1922.Use of the terms consistency and consistent in statistics is restricted to cases where essentially the same procedure can be applied to any number of data items. In complicated applications of statistics, there may be several ways in which the number of data items may grow. For example, records for rainfall within an area might increase in three ways: records for additional time periods; records for additional sites with a fixed area; records for extra sites obtained by extending the size of the area. In such cases, the property of consistency may be limited to one or more of the possible ways a sample size can grow.", "images": [], "links": ["Confidence interval", "Consistent estimator", "Convergence of random variables", "Fisher consistency", "Hypothesis test", "Internal consistency", "International Standard Book Number", "Random variable", "Reliability (statistics)", "Ronald Fisher", "Statistical classification", "Statistical hypothesis testing", "Statistical power", "Statistics"], "references": ["http://normaldeviate.wordpress.com/2013/09/11/consistency-sparsistency-and-presistency/"]}, "Markov chain Monte Carlo": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2015", "Bayesian estimation", "Computational statistics", "Markov chain Monte Carlo", "Markov models", "Monte Carlo methods"], "title": "Markov chain Monte Carlo", "method": "Markov chain Monte Carlo", "url": "https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo", "summary": "In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by observing the chain after a number of steps. The more steps there are, the more closely the distribution of the sample matches the actual desired distribution.\nRandom-walk Monte Carlo methods make up a large subclass of Markov chain Monte Carlo methods.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5e/Metropolis_algorithm_convergence_example.png"], "links": ["Admissible decision rule", "Algorithm", "Andrew Gelman", "Annals of Statistics", "Approximate Bayesian computation", "ArXiv", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian inference using Gibbs sampling", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernd A. Berg", "Bernstein\u2013von Mises theorem", "Bibcode", "Biometrika", "Bull. Amer. Math. Soc.", "Cambridge University Press", "Chapman and Hall", "Chinese restaurant process", "Computational biology", "Computational linguistics", "Computational physics", "Computer simulation", "Conditional distribution", "Conjugate prior", "Correlation", "Coupling from the past", "Credible interval", "Cromwell's rule", "Curse of dimensionality", "David Spiegelhalter", "Digital object identifier", "Dirichlet process", "Donald B. Rubin", "Donald Geman", "Empirical Bayes method", "Genetic algorithm", "Gibbs sampling", "Grand canonical ensemble", "Hamiltonian dynamics", "Hybrid Monte Carlo", "Hyperparameter", "Hyperprior", "IEEE Control Systems Magazine", "IEEE Transactions on Pattern Analysis and Machine Intelligence", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "John Wiley & Sons", "Journal of the American Statistical Association", "Just another Gibbs sampler", "Koksma-Hlawka inequality", "Likelihood function", "Low-discrepancy sequence", "MCSim", "Markov chain", "Markov chain mixing time", "Maximum a posteriori estimation", "Mean field particle methods", "Metropolis-adjusted Langevin algorithm", "Metropolis\u2013Hastings algorithm", "Momentum", "Monte Carlo integration", "Monte Carlo method", "Multiple-try Metropolis", "Multiple integral", "Nonparametric", "Numerical analysis", "OpenBUGS", "Operations Research: A Journal of the Institute for Operations Research and the Management Sciences", "Particle filter", "Persi Diaconis", "Posterior predictive distribution", "Posterior probability", "Principle of indifference", "Principle of maximum entropy", "Prior probability", "Probabilistic programming language", "Probability distribution", "Probability interpretations", "Pseudo-random number sampling", "PubMed Central", "PubMed Identifier", "PyMC3", "Quasi-Monte Carlo method", "R (programming language)", "Radical probabilism", "Random walk", "Rare event sampling", "Reversible-jump", "Running time", "Saul Teukolsky", "Schwarz criterion", "Signal processing", "Simulated annealing", "Slice sampling", "Stan (software)", "Statistical ensemble", "Statistical physics", "Statistically independent", "Statistics", "TensorFlow", "The American Mathematical Monthly", "The American Statistician", "William H. Press", "WinBUGS", "World Scientific"], "references": ["http://www.cs.utoronto.ca/~radford/review.abstract.html", "http://www.crcpress.com/product/isbn/9781466504059", "http://apps.nrbook.com/empanel/index.html#pg=824", "http://www.tandfonline.com/doi/abs/10.1080/01621459.2000.10473908", "http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9868.2006.00553.x/abstract", "http://adsabs.harvard.edu/abs/1992StaSc...7..457G", "http://adsabs.harvard.edu/abs/2015ITSP...63.3123M", "http://www.cs.princeton.edu/courses/archive/spr06/cos598C/papers/AndrieuFreitasDoucetJordan2003.pdf", "http://www.math.ucsb.edu/~atzberg/spring2006/monteCarloMethod.pdf", "http://stat.wharton.upenn.edu/~stjensen/stat542/lecture14.mcmchistory.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4946376", "http://www.ncbi.nlm.nih.gov/pubmed/11917018", "http://www.ncbi.nlm.nih.gov/pubmed/27429455", "http://www.ncbi.nlm.nih.gov/pubmed/29315405", "http://dfm.io/emcee/current/", "http://a2rms.sourceforge.net", "http://www.ams.org/bull/2009-46-02/S0273-0979-08-01238-X/S0273-0979-08-01238-X.pdf", "http://arxiv.org/abs/1201.0646", "http://arxiv.org/abs/1205.5494", "http://arxiv.org/abs/cond-mat/0212648", "http://doi.org/10.1002%2Faic.14409", "http://doi.org/10.1007%2Fbfb0103798", "http://doi.org/10.1007%2Fs00180-013-0429-2", "http://doi.org/10.1016%2Fj.coal.2016.08.024", "http://doi.org/10.1016%2Fs0378-4754(98)00096-2", "http://doi.org/10.1023%2FA:1010090512027", "http://doi.org/10.1080%2F01621459.1990.10476213", "http://doi.org/10.1080%2F01621459.1996.10476956", "http://doi.org/10.1080%2F01621459.2000.10473908", "http://doi.org/10.1090%2Fs0273-0979-08-01238-x", "http://doi.org/10.1093%2Fbiomet%2F82.4.711", "http://doi.org/10.1093%2Fnar%2Fgkx1313", "http://doi.org/10.1109%2FTSP.2015.2420537", "http://doi.org/10.1109%2Fmcs.2003.1188770", "http://doi.org/10.1111%2Fj.1467-9868.2006.00553.x", "http://doi.org/10.1214%2Faos%2F1056562461", "http://doi.org/10.1214%2Fss%2F1177011136", "http://doi.org/10.1287%2Fopre.32.6.1296", "http://doi.org/10.2307%2F2347565", "http://doi.org/10.2307%2F2685208", "http://doi.org/10.2307%2F2986138", "http://doi.org/10.4169%2F000298910x485923", "http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7080917", "http://www.jstor.org/stable/2347565", "http://www.jstor.org/stable/2986138", "http://www.jstor.org/stable/3448413", "http://micans.org/mcl/", "http://archive.numdam.org/ARCHIVE/SPS/SPS_2000__34_/SPS_2000__34__1_0/SPS_2000__34__1_0.pdf", "http://www.worldcat.org/issn/0162-1459", "http://www.worldcat.org/issn/0943-4062", "http://www.worldcat.org/issn/1053-587X", "http://www.bioss.ac.uk/students/alexm/MCMCintroPresentation.pdf", "https://link.springer.com/article/10.1007/s00180-013-0429-2", "https://www.springer.com/mathematics/probability/book/978-0-387-20268-6", "https://greta-dev.github.io/greta/", "https://greta-dev.github.io/greta/software.html", "https://pymc-devs.github.io/pymc/", "https://www.researchgate.net/publication/307626119_Stochastic_Shale_Permeability_Matching_Three-Dimensional_Characterization_and_Modeling", "https://web.archive.org/web/20110531150413/http://www.bioss.ac.uk/students/alexm/MCMCintroPresentation.pdf", "https://bitbucket.org/azadcse/hipmcl/wiki/Home", "https://www.multibugs.org/", "https://r-nimble.org/", "https://www.tensorflow.org/probability/"]}, "Time\u2013frequency representation": {"categories": ["CS1 maint: Multiple names: authors list", "Signal estimation", "Time\u2013frequency analysis"], "title": "Time\u2013frequency representation", "method": "Time\u2013frequency representation", "url": "https://en.wikipedia.org/wiki/Time%E2%80%93frequency_representation", "summary": "A time\u2013frequency representation (TFR) is a view of a signal (taken to be a function of time) represented over both time and frequency. Time\u2013frequency analysis means analysis into the time\u2013frequency domain provided by a TFR. This is achieved by using a formulation often called \"Time\u2013Frequency Distribution\", abbreviated as TFD.\nTFRs are often complex-valued fields over time and frequency, where the modulus of the field represents either amplitude or \"energy density\" (the concentration of the root mean square over time and frequency), and the argument of the field represents phase.", "images": [], "links": ["Absolute value", "Argument (complex analysis)", "Bilinear time\u2013frequency distribution", "Continuous wavelet transform", "Digital object identifier", "Eugene Wigner", "Fourier transform", "Fractional Fourier transform", "Frequency", "Function (mathematics)", "Linear canonical transformation", "Linear transform", "Magnitude (mathematics)", "Newland transform", "Quadratic function", "Quantum mechanics", "Reassignment method", "Root mean square", "Scaleogram", "Short-time Fourier transform", "Signal processing", "Spectrogram", "Stationary phase approximation", "Symplectic form", "Time\u2013frequency analysis", "Time\u2013frequency analysis for music signals", "Wigner\u2013Ville distribution"], "references": ["http://tfd.sourceforge.net/", "http://doi.org/10.1109%2F18.119728", "http://tftb.nongnu.org/", "https://link.springer.com/article/10.1007/s00034-018-0834-4", "https://hal.archives-ouvertes.fr/hal-01222729/document", "https://www.researchgate.net/publication/3091384_Time-stretched_short-time_Fourier_transform/", "https://doi.org/10.1109%2F29.90380"]}, "Comparison of statistical packages": {"categories": ["CS1 maint: Archived copy as title", "CS1 maint: BOT: original-url status unknown", "Comparisons of mathematical software", "Mathematical and quantitative methods (economics)", "Statistical software", "Statistics-related lists"], "title": "Comparison of statistical packages", "method": "Comparison of statistical packages", "url": "https://en.wikipedia.org/wiki/Comparison_of_statistical_packages", "summary": "The following tables compare general and technical information for a number of statistical analysis packages.\n\n", "images": [], "links": ["ADMB", "ADaMSoft", "ANOVA", "ARIMA", "ASReml", "Affero General Public License", "Analyse-it", "BMDP", "BSD license", "BV4.1 (software)", "Bar chart", "Berkeley Software Distribution", "Box plot", "C++", "CSPro", "C (programming language)", "C Sharp (programming language)", "Charts", "Cointegration test", "Command-line interface", "Command line interface", "Commercial software", "Comparison of computer algebra systems", "Comparison of deep learning software", "Comparison of numerical analysis software", "Comparison of survey software", "Correlogram", "Cox regression", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "Diagrams", "Digital object identifier", "ELKI", "EViews", "Enthought", "Epi Info", "Fortran", "Freeware", "GARCH", "GAUSS (software)", "GNU GPL", "GNU General Public License", "GNU Octave", "GNU Project", "GenStat", "General linear model", "Generalized linear models", "GraphPad InStat", "GraphPad Prism", "Graphical user interface", "Gretl", "H2O (software)", "Histogram", "IBM", "International Standard Book Number", "JASP", "JMP (statistical software)", "JMulTi", "JSTOR", "Java (programming language)", "Java SDK", "Journal of Applied Econometrics", "Journal of Economic Literature", "Julia (programming language)", "Just another Gibbs sampler", "LGPL", "LIMDEP", "LISREL", "Latin squares", "Least absolute deviation", "Line chart", "Linux", "List of scientific journals in statistics", "List of statistical packages", "Logistic regression", "Ludwig Maximilian University of Munich", "MANOVA", "MATLAB", "MLwiN", "Mac OS", "Maple (software)", "Mathcad", "Mathematica", "MaxStat", "MedCalc", "Microfit", "Microsoft Excel", "Microsoft Windows", "Minitab", "Mixed model", "Multiple linear regression", "Multivariate GARCH", "NCSS (statistical software)", "NCSS Statistical Software", "NLOGIT", "NMath Stats", "Nonlinear least squares", "NumPy", "NumXL", "Open-source software", "OpenBUGS", "OpenEpi", "Open source", "Orange (software)", "Ordinary least squares", "Origin (data analysis software)", "OxMetrics", "Ox programming language", "PSPP", "PSPP-Perl", "Pearson Education", "Perl", "Poisson regression", "Post-hoc analysis", "Primer-E Primer", "Probit model", "Proprietary software", "Public-domain software", "Public domain", "Python (programming language)", "Python SDK", "Quantile regression", "RATS (software)", "RATS (statistical package)", "RExcel", "RKWard", "ROOT", "RPy", "RStudio", "R (programming language)", "R Commander", "R programming language", "Regression analysis", "Revolution Analytics", "S-PLUS", "SAS (software)", "SAS Institute", "SAS System", "SAS language", "SHAZAM (software)", "SOCR", "SOFA Statistics", "SPC XL", "SPSS", "SPSS Modeler", "SPlus", "SQL", "SUDAAN", "SYSTAT (software)", "SYSTAT (statistics)", "SageMath", "Salstat", "Scatterplot", "SciPy", "SegReg", "Shell (computing)", "SigmaStat", "SigmaXL", "Sigmaxl", "SimFiT", "Skytree, Inc", "SmartPLS", "Software", "Software as a service", "Software developer", "Software license", "Stan (software)", "StatCrunch", "StatPlus", "StatView", "StatXact", "Stata", "StataCorp LLC", "Statgraphics", "Statistica", "Statistical", "Statistical analysis", "StatsDirect", "Statsmodels", "Stepwise regression", "TSP (econometrics software)", "The Unscrambler", "Time series analysis", "Two-stage least squares", "UCLA", "UNISTAT", "Unit root test", "University of Ljubljana", "University of Michigan", "Unix", "User interface", "Vector autoregression", "WINKS", "WINdows KwikStat", "Weighted least squares", "WinBUGS", "Winpepi", "World Programming", "World Programming System", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://librestats.com/2011/08/27/how-much-of-r-is-written-in-r/", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/BarChart&term=BarChart", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/BoxPlot&term=BoxPlot", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/LineChart&term=LineChart", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/ScatterPlot&term=Scatterplot", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=ProcessControl&term=processcontrol", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/OneWayANOVA", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/NonlinearFit", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/Histogram", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/ShapiroWilkWTest", "http://www.maplesoft.com/support/help/Maple/view.aspx?path=Statistics/GridPlot", "http://www.mathworks.com/help/curvefit/least-squares-fitting.html", "http://reference.wolfram.com/mathematica/BarCharts/ref/BarChart.html", "http://reference.wolfram.com/mathematica/Histograms/ref/Histogram.html", "http://reference.wolfram.com/mathematica/guide/SurvivalAnalysis.html", "http://reference.wolfram.com/mathematica/ref/ARIMAProcess.html", "http://reference.wolfram.com/mathematica/ref/ARProcess.html", "http://reference.wolfram.com/mathematica/ref/BoxWhiskerChart.html", "http://reference.wolfram.com/mathematica/ref/CoxModelFit.html", "http://reference.wolfram.com/mathematica/ref/GARCHProcess.html", "http://reference.wolfram.com/mathematica/ref/GeneralizedLinearModelFit.html", "http://reference.wolfram.com/mathematica/ref/LinearModelFit.html", "http://reference.wolfram.com/mathematica/ref/ListLinePlot.html", "http://reference.wolfram.com/mathematica/ref/ListPlot.html", "http://reference.wolfram.com/mathematica/ref/ListPointPlot3D.html", "http://reference.wolfram.com/mathematica/ref/LogitModelFit.html", "http://reference.wolfram.com/mathematica/ref/NormFunction.html", "http://reference.wolfram.com/mathematica/ref/ProbitModelFit.html", "http://reference.wolfram.com/mathematica/ref/UnitRootTest.html", "http://www.wolfram.com/mathematica/quick-revision-history.html", "http://search.cpan.org/~pdonelan/PSPP-Perl/", "http://doi.org/10.1002%2F(SICI)1099-1255(199903%2F04)14:2%3C191::AID-JAE524%3E3.0.CO;2-K", "http://www.jstor.org/stable/2565215", "http://www.nait.org/jit/Articles/zhu031105.pdf", "http://www.sagemath.org/", "https://books.google.com/books?id=CZg42jo02CEC", "https://www.maplesoft.com/support/help/Maple/view.aspx?path=MOLS", "https://web.archive.org/web/20051025165844/http://nait.org/jit/Articles/zhu031105.pdf", "https://savannah.gnu.org/forum/forum.php?forum_id=8936", "https://www.webcitation.org/5ElLwqoZN?url=http://www.partek.com/", "https://www.webcitation.org/5gbmX1GNH?url=http://rkward.sourceforge.net/"]}, "Heart rate variability": {"categories": ["All articles with unsourced statements", "All pages needing factual verification", "Articles with unsourced statements from August 2015", "Cardiology", "Medical signs", "Medical statistics", "Statistical signal processing", "Wikipedia articles needing factual verification from January 2013"], "title": "Heart rate variability", "method": "Heart rate variability", "url": "https://en.wikipedia.org/wiki/Heart_rate_variability", "summary": "Heart rate variability (HRV) is the physiological phenomenon of variation in the time interval between heartbeats. It is measured by the variation in the beat-to-beat interval.\nOther terms used include: \"cycle length variability\", \"RR variability\" (where R is a point corresponding to the peak of the QRS complex of the ECG wave; and RR is the interval between successive Rs), and \"heart period variability\".\nMethods used to detect beats include: ECG, blood pressure,\nballistocardiograms,\nand the pulse wave signal derived from a photoplethysmograph (PPG). ECG is considered superior because it provides a clear waveform, which makes it easier to exclude heartbeats not originating in the sinoatrial node. The term \"NN\" is used in place of RR to emphasize the fact that the processed beats are \"normal\" beats.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fd/Heart_rate_variability_ECG.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/4a/Neurovisceral_integration_model.png"], "links": ["ArXiv", "Autonomic nervous system", "Ballistocardiography", "Baroreceptor", "Baroreflex", "Bibcode", "Biofeedback", "Cardiac transplant", "Chaotic behavior", "Cirrhosis", "Congestive heart failure", "Correlation dimension", "Detrended fluctuation analysis", "Diabetic neuropathy", "Digital object identifier", "Discrete Fourier transform", "ECG", "European Society of Cardiology", "Heart Rhythm Society", "Heart rate", "Heart rate turbulence", "Hertz", "Hormones", "Humoral factor", "International Standard Book Number", "International Standard Serial Number", "Journal of Physiology", "Limbic system", "Mayer waves", "Myocardial infarction", "Native American flute", "Parasympathetic nervous system", "Photoplethysmograph", "Poincar\u00e9 plot", "Polyvagal theory", "Post-traumatic stress disorder", "Power spectral density", "Prefrontal cortex", "Preterm birth", "Psychophysiology", "PubMed Central", "PubMed Identifier", "QRS complex", "Respiratory sinus arrhythmia", "R\u2013R interval", "Sample entropy", "Scatterplot", "Sinoatrial node", "Sinus rhythm", "Sleep-wake cycle", "Standard deviation", "Stress (biology)", "Sudden infant death syndrome", "Sympathetic nervous system", "Thermoregulation"], "references": ["http://www.brainandheart.at/Param.php", "http://www.Flutopedia.com/refs/MillerGoss_2014_PhysioNAF_v2.pdf", "http://webcache.googleusercontent.com/search?q=cache:650hJp1_khQJ:http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/lorenz.htm%2BLorenz+curve++NIST&hl=en-AU&gbv=1&ct=clnk", "http://www.hrvcourse.com/blog", "http://adsabs.harvard.edu/abs/1993PhRvL..70.1343P", "http://adsabs.harvard.edu/abs/1995Chaos...5...82P", "http://adsabs.harvard.edu/abs/2000PhRvL..85.3736B", "http://adsabs.harvard.edu/abs/2001PhyA..295..441K", "http://adsabs.harvard.edu/abs/2002PhRvL..89f8102C", "http://adsabs.harvard.edu/abs/2006NYASA1088..361T", "http://adsabs.harvard.edu/abs/2009RSPTA.367..277V", "http://adsabs.harvard.edu/abs/2011JSMTE..08..014E", "http://adsabs.harvard.edu/abs/2013PLoSO...872854S", "http://adsabs.harvard.edu/abs/2013arXiv1308.6018G", "http://adsabs.harvard.edu/abs/2014arXiv1401.6004M", "http://adsabs.harvard.edu/abs/2015Cmplx..20c..84D", "http://adsabs.harvard.edu/abs/2017PLoSO..1281833N", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1767394", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1868418", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2603289", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2643913", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3576706", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3764113", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5469891", 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"http://www.ncbi.nlm.nih.gov/pubmed/18524629", "http://www.ncbi.nlm.nih.gov/pubmed/18977726", "http://www.ncbi.nlm.nih.gov/pubmed/19023029", "http://www.ncbi.nlm.nih.gov/pubmed/21316386", "http://www.ncbi.nlm.nih.gov/pubmed/21421447", "http://www.ncbi.nlm.nih.gov/pubmed/22249221", "http://www.ncbi.nlm.nih.gov/pubmed/22875239", "http://www.ncbi.nlm.nih.gov/pubmed/23294659", "http://www.ncbi.nlm.nih.gov/pubmed/23431279", "http://www.ncbi.nlm.nih.gov/pubmed/24039811", "http://www.ncbi.nlm.nih.gov/pubmed/28659811", "http://www.ncbi.nlm.nih.gov/pubmed/28771509", "http://www.ncbi.nlm.nih.gov/pubmed/29896113", "http://www.ncbi.nlm.nih.gov/pubmed/3812275", "http://www.ncbi.nlm.nih.gov/pubmed/4702060", "http://www.ncbi.nlm.nih.gov/pubmed/7987529", "http://www.ncbi.nlm.nih.gov/pubmed/8598068", "http://www.ncbi.nlm.nih.gov/pubmed/8737210", "http://www.ncbi.nlm.nih.gov/pubmed/8867095", "http://www.ncbi.nlm.nih.gov/pubmed/9821570", "http://itl.nist.gov/div898/software/dataplot/refman1/auxillar/lorenz.htm", "http://arxiv.org/abs/1004.4186", "http://arxiv.org/abs/1308.6018", "http://arxiv.org/abs/1401.6004", "http://arxiv.org/abs/cond-mat/0102214", "http://doi.org/10.1002%2Fcplx.21508", "http://doi.org/10.1007%2FBF01824992", "http://doi.org/10.1007%2FBF02688699", "http://doi.org/10.1016%2F0002-9149(87)90795-8", "http://doi.org/10.1016%2F0165-1838(95)00104-2", "http://doi.org/10.1016%2FS0006-3223(97)00475-7", "http://doi.org/10.1016%2FS0031-9384(03)00156-2", "http://doi.org/10.1016%2FS0378-4371(01)00144-3", "http://doi.org/10.1016%2Fj.biopsycho.2006.06.009", "http://doi.org/10.1016%2Fj.compbiomed.2007.01.012", "http://doi.org/10.1016%2Fj.ijpsycho.2006.07.016", "http://doi.org/10.1016%2Fj.ijpsycho.2006.08.002", "http://doi.org/10.1016%2Fj.neuroimage.2008.04.238", "http://doi.org/10.1016%2Fj.pbiomolbio.2011.02.001", "http://doi.org/10.1046%2Fj.1540-8167.2003.02367.x", "http://doi.org/10.1063%2F1.166141", "http://doi.org/10.1080%2F00140137308924479", "http://doi.org/10.1080%2F10803548.2012.11076959", "http://doi.org/10.1088%2F1742-5468%2F2011%2F08%2FP08014", "http://doi.org/10.1093%2Foxfordjournals.eurheartj.a014868", "http://doi.org/10.1097%2Fshk.0b013e318240b4be", "http://doi.org/10.1098%2Frsta.2008.0232", "http://doi.org/10.1103%2FPhysRevLett.70.1343", "http://doi.org/10.1103%2FPhysRevLett.85.3736", "http://doi.org/10.1103%2Fphysrevlett.89.068102", "http://doi.org/10.1109%2FTBME.2012.2211356", "http://doi.org/10.1109%2FTITB.2011.2128337", "http://doi.org/10.1111%2Fj.1540-8167.1994.tb01300.x", "http://doi.org/10.1136%2Fheart.88.4.378", "http://doi.org/10.1152%2Fajpgi.90488.2008", "http://doi.org/10.1152%2Fajpheart.2000.278.6.H2039", "http://doi.org/10.1152%2Fjappl.1992.73.3.1122", "http://doi.org/10.1161%2F01.CIR.85.1.164", "http://doi.org/10.1161%2F01.cir.93.5.1043", "http://doi.org/10.1196%2Fannals.1366.014", "http://doi.org/10.1203%2F01.pdr.0000088074.97781.4f", "http://doi.org/10.1371%2Fjournal.pone.0072854", "http://doi.org/10.1371%2Fjournal.pone.0181833", "http://doi.org/10.1518%2Fhfes.45.4.575.27094", "http://doi.org/10.1542%2Fpeds.107.1.97", "http://doi.org/10.3389%2Ffphys.2013.00026", "http://doi.org/10.3389%2Ffphys.2017.00360", "http://doi.org/10.3389%2Ffphys.2018.00623", "http://jp.physoc.org/cgi/reprint/542/3/669?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&author1=taylor&fulltext=variability&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&sortspec=relevance&resourcetype=HWCIT", "http://www.worldcat.org/issn/0378-4371", "https://neurostat-mit.appspot.com/"]}, "Shewhart individuals control chart": {"categories": ["CS1 errors: external links", "Quality control tools", "Statistical charts and diagrams"], "title": "Shewhart individuals control chart", "method": "Shewhart individuals control chart", "url": "https://en.wikipedia.org/wiki/Shewhart_individuals_control_chart", "summary": "In statistical quality control, the individual/moving-range chart is a type of control chart used to monitor variables data from a business or industrial process for which it is impractical to use rational subgroups.The chart is necessary in the following situations:\nWhere automation allows inspection of each unit, so rational subgrouping has less benefit.\nWhere production is slow so that waiting for enough samples to make a rational subgroup unacceptably delays monitoring\nFor processes that produce homogeneous batches (e.g., chemical) where repeat measurements vary primarily because of measurement errorThe \"chart\" actually consists of a pair of charts: one, the individuals chart, displays the individual measured values; the other, the moving range chart, displays the difference from one point to the next. As with other control charts, these two charts enable the user to monitor a process for shifts in the process that alter the mean or variance of the measured statistic.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/27/Individuals_chart_for_a_paired_individuals_and_MR_chart.svg", "https://upload.wikimedia.org/wikipedia/commons/6/66/MR_chart_for_a_paired_individuals_and_MR_chart.svg"], "links": ["Autocorrelation", "Business process", "Control chart", "Donald J. Wheeler", "Hoboken, New Jersey", "Indefinite pronoun", "International Standard Book Number", "John Wiley & Sons", "List of industrial processes", "Measuring instrument", "National Institute of Standards and Technology", "Normal distribution", "OCLC", "Statistical process control", "Variable and attribute (research)", "Verification and Validation (software)", "Walter A. Shewhart", "Xbar and R chart", "Xbar and s chart"], "references": ["http://www.qualitydigest.com/inside/health-care-column/good-limits-bad-data.html", "http://www.qualitydigest.com/inside/quality-insider-column/individual-charts-done-right-and-wrong.html", "http://www.qualitydigest.com/inside/quality-insider-column/when-can-we-trust-limits-process-behavior-chart.html", "http://www.qualitydigest.com/inside/quality-insider-column/do-you-have-leptokurtophobia.html", "http://www.eas.asu.edu/~masmlab/montgomery/", "http://www.itl.nist.gov/div898/handbook/index.htm", "http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc322.htm", "http://www.worldcat.org/oclc/56729567", "https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/"]}, "L\u00e9vy's continuity theorem": {"categories": ["Paul L\u00e9vy (mathematician)", "Probability theorems", "Statistical theorems"], "title": "L\u00e9vy's continuity theorem", "method": "L\u00e9vy's continuity theorem", "url": "https://en.wikipedia.org/wiki/L%C3%A9vy%27s_continuity_theorem", "summary": "In probability theory, L\u00e9vy\u2019s continuity theorem (or L\u00e9vy's convergence theorem), named after the French mathematician Paul L\u00e9vy, connects convergence in distribution of the sequence of random variables with pointwise convergence of their characteristic functions. \nThis theorem is the basis for one approach to prove the central limit theorem and it is one of the major theorems concerning characteristic functions.", "images": [], "links": ["Central limit theorem", "Characteristic function (probability theory)", "Continuous function", "Convergence in distribution", "Convergence of random variables", "David Williams (mathematician)", "Expected value", "International Standard Book Number", "Mathematician", "Paul L\u00e9vy (mathematician)", "Pointwise convergence", "Probability space", "Probability theory", "Random variable", "Tightness of measures"], "references": ["https://www.springer.com/birkhauser/applied+probability+and+statistics/book/978-0-8176-3807-8"]}, "Phase-type distribution": {"categories": ["Continuous distributions", "Types of probability distributions"], "title": "Phase-type distribution", "method": "Phase-type distribution", "url": "https://en.wikipedia.org/wiki/Phase-type_distribution", "summary": "A phase-type distribution is a probability distribution constructed by a convolution or mixture of exponential distributions. It results from a system of one or more inter-related Poisson processes occurring in sequence, or phases. The sequence in which each of the phases occur may itself be a stochastic process. The distribution can be represented by a random variable describing the time until absorption of a Markov process with one absorbing state. Each of the states of the Markov process represents one of the phases.\nIt has a discrete time equivalent the discrete phase-type distribution.\nThe set of phase-type distributions is dense in the field of all positive-valued distributions, that is, it can be used to approximate any positive-valued distribution.\n\n", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous-time Markov process", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "David Aldous", "David Cox (statistician)", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete time", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expectation\u2013maximization algorithm", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heavy-tailed distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyper-exponential distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Lawrence Shepp", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "MATLAB", "Marchenko\u2013Pastur distribution", "Markov process", "Mathematica", "Mathematical Proceedings of the Cambridge Philosophical Society", "Matrix-exponential distribution", "Matrix (mathematics)", "Matrix exponential", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Mor Harchol-Balter", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Poisson binomial distribution", "Poisson distribution", "Poisson process", "Poly-Weibull distribution", "Probability", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Queueing theory", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Row vector", "Scaled inverse chi-squared distribution", "Sequence", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Stochastic process", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Transition rate matrix", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://copa.uniandes.edu.co/?p=141", "http://wwwprof.uniandes.edu.co/~jf.perez33/data/PerezRiano_SMC_2006.pdf", "http://www.mi.fu-berlin.de/inf/groups/ag-tech/projects/HyperStar/index.html", "http://home.imf.au.dk/asmus/pspapers.html", "http://ftp.stat.berkeley.edu/~aldous/Papers/me32-scan.PDF", "http://www.cs.cmu.edu/~osogami/code/momentmatching/index.html", "http://webspn.hit.bme.hu/~telek/cikkek/horv02h.ps.gz", "http://webspn.hit.bme.hu/~telek/tools.htm", "http://webspn.hit.bme.hu/~telek/tools/butools/butools.html", "http://doi.org/10.1002%2F0471200581.ch3", "http://doi.org/10.1007%2F3-540-46029-2_5", "http://doi.org/10.1007%2F978-3-642-30782-9_19", "http://doi.org/10.1016%2Fj.camwa.2012.03.016", "http://doi.org/10.1016%2Fj.peva.2005.06.002", "http://doi.org/10.1017%2FCBO9781139226424.026", "http://doi.org/10.1017%2FS0305004100030231", "http://doi.org/10.1080%2F15326348708807067", "http://doi.org/10.1145%2F1190366.1190370", "http://doi.org/10.1287%2Finte.1050.0155", "http://www.jstor.org/stable/4616418", "https://www.smp.uq.edu.au/people/YoniNazarathy/teaching_projects/studentWork/Min_Two_Phase_Types.pdf"]}, "Mathematical biology": {"categories": ["All articles lacking reliable references", "All articles needing additional references", "All articles with dead external links", "All articles with unsourced statements", "Articles lacking reliable references from August 2010", "Articles needing additional references from April 2017", "Articles with dead external links from March 2010", "Articles with dead external links from September 2017", "Articles with permanently dead external links", "Articles with unsourced statements from May 2011", "CS1 maint: Archived copy as title", "Commons category link from Wikidata", "Mathematical and theoretical biology", "Webarchive template wayback links"], "title": "Mathematical and theoretical biology", "method": "Mathematical biology", "url": "https://en.wikipedia.org/wiki/Mathematical_and_theoretical_biology", "summary": "Mathematical and theoretical biology is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.Mathematical biology aims at the mathematical representation and modeling of biological processes, using techniques and tools of applied mathematics. It has both theoretical and practical applications in biological, biomedical and biotechnology research. Describing systems in a quantitative manner means their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter. This requires precise mathematical models.\nMathematical biology employs many components of mathematics, and has contributed to the development of new techniques.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a7/Cell_cycle_bifurcation_diagram.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abiogenesis", "Alan Turing", "Allele", "Analysis of variance", "Anatomy", "Anthony Bartholomay", "Applied mathematics", "ArXiv", "Array data structure", "Artery", "Astrobiology", "Automata theory", "Autopoiesis", "Bibcode", "Bidomain", "Bifurcation diagram", "Bifurcation theory", "Biochemistry", "Biogeography", "Biohistory", "Bioinformatics", "Biological applications of bifurcation theory", "Biological classification", "Biological pattern formation", "Biological process", "Biology", "Biomechanics", "Biophysics", "Biostatistics", "Botany", "Budapest University of Technology and Economics", "Cancer", "Category theory", "Cell biology", "Cell cycle", "Cell cycle checkpoint", "Cellular automata", "Cellular automaton", "Cellular microbiology", "Cellular model", "Chaos theory", "Chaotic system", "Charles Darwin", "Chemical biology", "Chemical kinetics", "Chronobiology", "Coalescent theory", "Computational biology", "Computational neuroscience", "Computational phylogenetics", "Computer", "Computer modeling", "Conservation biology", "Continuous-time Markov process", "Cytogenetics", "D'Arcy Thompson", "Daniel Bernoulli", "Deterministic system", "Developmental biology", "Difference equations", "Digital object identifier", "Dynamic Monte Carlo method", "Dynamical system", "Ecology", "Embryology", "Entropy and life", "Enzyme kinetics", "Epidemiology", "Epigenetics", "Equilibrium point", "Evolution", "Evolutionary biology", "Evolutionary ecology", "Evolutionary game theory", "Evolutionary invasion analysis", "Ewens's sampling formula", "Experimental biology", "Fibonacci", "Fibonacci series", "Fokker-Planck equation", "Francisco Varela", "Freshwater biology", "Fritz M\u00fcller", "Gene", "Genetic network", "Genetic recombination", "Genetics", "Genomics", "Genotype", "Geobiology", "George R. Price", "Gillespie algorithm", "Goldbeter\u2013Koshland kinetics", "Hans Leo Przibram", "Heart", "Histology", "Hopf bifurcation", "Human biology", "Humberto Maturana", "Immunology", "In silico", "Infections", "Infinite period bifurcation", "Infinitesimal", "International Standard Book Number", "JSTOR", "Jack Copeland", "James Mallet", "Johannes Reinke", "John Maynard Smith", "Jonathan Bowen", "Journal of Theoretical Biology", "Life science", "Linkage disequilibrium", "Locus (genetics)", "Lotka\u2013Volterra equation", "Lyapunov stability", "Malthus", "Malthusian growth model", "Marine biology", "Markov process", "Master equation", "Mathematical model", "Mathematical modelling of infectious disease", "Metabolic network modelling", "Michael C. Reed", "Michael P Barnett", "Michaelis-Menten kinetics", "Microbiology", "Molecular biology", "Molecular modelling", "Molecular structure", "Monodomain model", "Monte Carlo method", "Morphogenesis", "Morphometrics", "Mutation", "Mycology", "M\u00fcllerian mimicry", "National Institute for Mathematical and Biological Synthesis", "Neontology", "Neural net", "Neuron", "Neuroscience", "Nicolas Rashevsky", "Notices of the American Mathematical Society", "Numerical ordinary differential equations", "Numerical partial differential equations", "Nutrition", "On Growth and Form", "Ordinary differential equation", "Ordinary differential equations", "Organism", "Oscillation", "Oxford University Press", "Paleontology", "Parasitology", "Partial differential equations", "Pathology", "Pharmacology", "Philip Maini", "Philosophical Transactions of the Royal Society", "Phylogenetics", "Physiology", "Pierre Francois Verhulst", "Population dynamics", "Population genetics", "Population growth", "Probability distribution", "Proteomics", "PubMed Central", "PubMed Identifier", "Quantitative genetics", "Quantum biology", "Quantum computers", "Quasi-linkage equilibrium", "Random variable", "Reaction rate", "Robert Rosen (theoretical biologist)", "Robin Wilson (mathematician)", "Ronald Fisher", "Saddle point", "Science (journal)", "Simulation", "Society for Mathematical Biology", "Sociobiology", "Statistical genetics", "Stochastic", "Stochastic differential equation", "Stochastic process", "Structural biology", "Stuart Kauffman", "Swarming behaviour", "Symbolic computation", "Systematics", "Systems biology", "Teratology", "Tessellation", "The Chemical Basis of Morphogenesis", "The Turing Guide", "Theoretical ecology", "Thomas Malthus", "Thomas Robert Malthus", "Toxicology", "Turing pattern", "Vector field", "Virginia Tech", "Virology", "Virophysics", "Vito Volterra", "Wayback Machine", "Wiener process", "Zoology"], "references": 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"http://doi.org/10.1109%2FTNB.2004.833694", "http://doi.org/10.1126%2Fscience.1094442", "http://doi.org/10.1187%2Fcbe.10-03-0019", "http://doi.org/10.2307%2F3545216", "http://www.esmtb.org/", "http://www.jstor.org/stable/3545216", "http://planetmath.org/?op=getobj&from=objects&id=10770", "http://planetphysics.org/encyclopedia/AbstractRelationalBiologyARB.html", "http://planetphysics.org/encyclopedia/BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics.html", "http://planetphysics.org/encyclopedia/BibliographyForMathematicalBiophysicsAndMathematicalMedicine.html", "http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html", "http://www.smb.org/", "http://theorylab.org/node/56690", "http://www.worldcat.org/title/lifes-other-secret-the-new-mathematics-of-the-living-world/oclc/37211069", "http://www.bath.ac.uk/cmb/mathBiology/", "http://www.maths.gla.ac.uk/research/groups/biology/kal.htm", "http://www.maths.gla.ac.uk/~rwo/research_areas.htm", "http://www.ma.hw.ac.uk/~jas/researchinterests/index.html", "http://www.ma.hw.ac.uk/~jas/researchinterests/scartissueformation.html", "http://www.integrativebiology.ox.ac.uk/heartmodel.html", "http://www.maths.ox.ac.uk/~maini/public/gallery/bpf.htm", "http://www.maths.ox.ac.uk/~maini/public/gallery/mctom.htm", "http://www.maths.ox.ac.uk/~maini/public/gallery/twwha.htm", "https://tspace.library.utoronto.ca/bitstream/1807/2951/2/compauto.pdf", "https://tspace.library.utoronto.ca/retrieve/4969/QuantumInteractomicsInCancer_Sept13k4E_cuteprt.pdf", "https://cdsweb.cern.ch/record/746663/files/COMPUTER_MODEL_AND_AUTOMATA_THEORY_IN_BIOLOGY2p.pdf", "https://www.amazon.com/Life-Itself-Comprehensive-Fabrication-Complexity/dp/0231075650/ref=sr_1_3?s=books&ie=UTF8&qid=1484657576&sr=1-3&keywords=life+itself", "https://books.google.com/books/about/MAKING_SENSE_OF_LIFE.html?id=NdtbR_N_vKYC", "https://books.google.com/books?id=l0_0q_e-u_UC", "https://books.google.com/books?id=uR8i2qetjSAC", "https://www.academia.edu/27958448/Modeling_mammary_organogenesis_from_biological_first_principles_cells_and_their_physical_constraints", "https://web.archive.org/web/20040109164805/http://bioinformatics.weizmann.ac.il/istmb/", "https://web.archive.org/web/20060616135155/http://www.princeton.edu/~allengrp/ms/annobib/mb.pdf", "https://web.archive.org/web/20070713122039/http://cogprints.org/3701/01/ANeuralGenNetworkLuknTopos_oknu4.pdf", "https://web.archive.org/web/20070728091004/http://mpf.biol.vt.edu/Tyson%20Lab.html", "https://web.archive.org/web/20070728093149/http://mpf.biol.vt.edu/Research.html", "https://web.archive.org/web/20080911022733/http://www.necker.fr/sfbt/", "https://web.archive.org/web/20090113215021/http://www.integrativebiology.ox.ac.uk/heartmodel.html", "https://web.archive.org/web/20090202005852/http://www.maths.gla.ac.uk/~rwo/research_areas.htm", "https://web.archive.org/web/20090326215300/http://acube.org/volume_23/v23-1p11-36.pdf", "https://web.archive.org/web/20110604124206/http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=7195", "https://web.archive.org/web/20110728100340/http://theorylab.org/node/56690", "https://web.archive.org/web/20120210210021/http://cellcycle.mkt.bme.hu/", "https://web.archive.org/web/20160107152607/http://planetphysics.org/encyclopedia/AbstractRelationalBiologyARB.html", "https://web.archive.org/web/20160107152607/http://planetphysics.org/encyclopedia/BibliographyForCategoryTheoryAndAlgebraicTopologyApplicationsInTheoreticalPhysics.html", "https://web.archive.org/web/20160107152607/http://planetphysics.org/encyclopedia/BibliographyForMathematicalBiophysicsAndMathematicalMedicine.html", "https://web.archive.org/web/20160107152607/http://planetphysics.org/encyclopedia/CategoryOfMolecularSets2.html"]}, "Probability mass function": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from April 2012", "Articles with short description", "Articles with unsourced statements from April 2012", "Types of probability distributions"], "title": "Probability mass function", "method": "Probability mass function", "url": "https://en.wikipedia.org/wiki/Probability_mass_function", "summary": "In probability and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.\nA probability mass function differs from a probability density function (pdf) in that the latter is associated with continuous rather than discrete random variables; the values of the probability density function are not probabilities as such: a pdf must be integrated over an interval to yield a probability.The value of the random variable having the largest probability mass is called the mode.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/85/Discrete_probability_distrib.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Fair_dice_probability_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Bernoulli distribution", "Binomial distribution", "Categorical distribution", "Central moment", "Characteristic function (probability theory)", "Combinant", "Countable", "Counting measure", "Cumulant", "Cumulative distribution function", "Dice", "Discrete probability distribution", "Discrete random variable", "Domain of a function", "Expected value", "Image (mathematics)", "Integration (mathematics)", "International Standard Book Number", "Joint probability distribution", "Kurtosis", "L-moment", "Measure space", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate random variable", "Probability-generating function", "Probability density function", "Probability distribution", "Probability space", "Probability theory", "Pushforward measure", "Quantile function", "Radon\u2013Nikodym derivative", "Raw moment", "Real number", "Sample space", "Scalar variable", "Sigma algebra", "Skewness", "Standard deviation", "Statistics", "Variance"], "references": ["http://mathworld.wolfram.com/ProbabilityFunction.html", "https://books.google.com/books?id=XsX20uCFJbYC&pg=PA22", "https://books.google.com/books?id=ZfRyBS1WbAQC&pg=PT105", "https://books.google.com/books?id=nuoryE4IwMoC&pg=PA717"]}, "Bingham distribution": {"categories": ["Continuous distributions", "Directional statistics"], "title": "Bingham distribution", "method": "Bingham distribution", "url": "https://en.wikipedia.org/wiki/Bingham_distribution", "summary": "In statistics, the Bingham distribution, named after Christopher Bingham, is an antipodally symmetric probability distribution on the n-sphere. It is a generalization of the Watson distribution and a special case of the Kent and Fisher-Bingham distributions.\nThe Bingham distribution is widely used in paleomagnetic data analysis, and has been reported as being of use in the field of computer vision.Its probability density function is given by\n\n \n \n \n f\n (\n \n x\n \n \n ;\n \n M\n ,\n Z\n )\n \n d\n \n S\n \n n\n \u2212\n 1\n \n \n \n =\n \n \n \n\n \n \n 1\n \n \n \n F\n \n 1\n \n \n (\n \n \n \n \n 1\n 2\n \n \n \n \n ;\n \n \n \n \n n\n 2\n \n \n \n \n ;\n Z\n \n )\n \n \u2212\n 1\n \n \n \n \u22c5\n \n exp\n \u2061\n \n (\n \n \n \n tr\n \n \n \n Z\n \n M\n \n T\n \n \n \n x\n \n \n \n x\n \n \n T\n \n \n M\n \n )\n \n \n d\n \n S\n \n n\n \u2212\n 1\n \n \n \n \n {\\displaystyle f(\\mathbf {x} \\,;\\,M,Z)\\;dS^{n-1}\\;=\\;{}_{1}F_{1}({\\textstyle {\\frac {1}{2}}};{\\textstyle {\\frac {n}{2}}};Z)^{-1}\\;\\cdot \\;\\exp \\left({{\\textrm {tr}}\\;ZM^{T}\\mathbf {x} \\mathbf {x} ^{T}M}\\right)\\;dS^{n-1}}\n which may also be written\n\n \n \n \n f\n (\n \n x\n \n \n ;\n \n M\n ,\n Z\n )\n \n d\n \n S\n \n n\n \u2212\n 1\n \n \n \n =\n \n \n \n\n \n \n 1\n \n \n \n F\n \n 1\n \n \n (\n \n \n \n \n 1\n 2\n \n \n \n \n ;\n \n \n \n \n n\n 2\n \n \n \n \n ;\n Z\n \n )\n \n \u2212\n 1\n \n \n \n \u22c5\n \n exp\n \u2061\n \n (\n \n \n \n x\n \n \n T\n \n \n M\n Z\n \n M\n \n T\n \n \n \n x\n \n \n )\n \n \n d\n \n S\n \n n\n \u2212\n 1\n \n \n \n \n {\\displaystyle f(\\mathbf {x} \\,;\\,M,Z)\\;dS^{n-1}\\;=\\;{}_{1}F_{1}({\\textstyle {\\frac {1}{2}}};{\\textstyle {\\frac {n}{2}}};Z)^{-1}\\;\\cdot \\;\\exp \\left({\\mathbf {x} ^{T}MZM^{T}\\mathbf {x} }\\right)\\;dS^{n-1}}\n where x is an axis (i.e., a unit vector), M is an orthogonal orientation matrix, Z is a diagonal concentration matrix, and\n\n \n \n \n \n \n\n \n \n 1\n \n \n \n F\n \n 1\n \n \n (\n \u22c5\n ;\n \u22c5\n ,\n \u22c5\n )\n \n \n {\\displaystyle {}_{1}F_{1}(\\cdot ;\\cdot ,\\cdot )}\n is a confluent hypergeometric function of matrix argument. The matrices M and Z are the result of diagonalizing the positive-definite covariance matrix of the Gaussian distribution that underlies the Bingham distribution.\n\n", "images": [], "links": ["ARGUS distribution", "Antipodal symmetry", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Christopher Bingham", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Computer vision", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Diagonalizable matrix", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypergeometric function of a matrix argument", "Hypersphere", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Orthogonal matrix", "Paleomagnetic", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Positive-definite matrix", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://web.mit.edu/newsoffice/2013/better-robot-vision-1007.html", "http://doi.org/10.1007%2F978-3-540-88690-7_58", "http://opus.bath.ac.uk/56745/1/2008_eccv.pdf"]}, "Mendelian randomization": {"categories": ["All articles with unsourced statements", "Applications of randomness", "Articles with unsourced statements from April 2016", "Articles with unsourced statements from September 2017", "Epidemiology", "Genetics"], "title": "Mendelian randomization", "method": "Mendelian randomization", "url": "https://en.wikipedia.org/wiki/Mendelian_randomization", "summary": "In epidemiology, Mendelian randomization is a method of using measured variation in genes of known function to examine the causal effect of a modifiable exposure on disease in observational studies. The design was first proposed in 1986 and subsequently described by Gray and Wheatley as a method for obtaining unbiased estimates of the effects of a putative causal variable without conducting a traditional randomised trial. These authors also coined the term Mendelian randomization. The design has a powerful control for reverse causation and confounding, which often impede or mislead epidemiological studies.\n\n", "images": [], "links": ["Cardiovascular disease", "Confounding", "Digital object identifier", "Epidemiology", "Genetic association", "Genetic correlation", "Genetic polymorphism", "Genotype", "Heterogeneous", "Hormone replacement therapy (menopause)", "Instrumental variables", "Linkage disequilibrium", "Meiosis", "Observational studies", "Panmixia", "Pleiotropy", "Population stratification", "PubMed Central", "PubMed Identifier", "Public health", "R.A. Fisher", "Randomised trial", "Reverse causation"], "references": ["http://epidemiologic.blogspot.com/2006/03/mendelian-randomization-perfect-causal.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC557238", "http://www.ncbi.nlm.nih.gov/pubmed/12117397", "http://www.ncbi.nlm.nih.gov/pubmed/12689998", "http://www.ncbi.nlm.nih.gov/pubmed/15075141", "http://www.ncbi.nlm.nih.gov/pubmed/15879400", "http://www.ncbi.nlm.nih.gov/pubmed/16243094", "http://www.ncbi.nlm.nih.gov/pubmed/17715159", "http://www.ncbi.nlm.nih.gov/pubmed/1855097", "http://www.ncbi.nlm.nih.gov/pubmed/20176585", "http://www.ncbi.nlm.nih.gov/pubmed/26162196", "http://www.ncbi.nlm.nih.gov/pubmed/2869248", "http://www.ncbi.nlm.nih.gov/pubmed/28847336", "http://doi.org/10.1001%2Fjama.288.3.321", "http://doi.org/10.1016%2FS0140-6736(05)67601-5", "http://doi.org/10.1016%2Fs0140-6736(86)92972-7", "http://doi.org/10.1017%2FS0033291717002318", "http://doi.org/10.1093%2Fije%2Fdyg070", "http://doi.org/10.1093%2Fije%2Fdyh048", "http://doi.org/10.1093%2Fije%2Fdyp379", "http://doi.org/10.1136%2Fbmj.330.7499.1076", "http://doi.org/10.1177%2F0962280206077743", "http://doi.org/10.1177%2F1745691610383505", "http://www.genestat.org/index.php?n=GeneStat.MendelianRandomisation", "http://www.jameslindlibrary.org", "https://www.youtube.com/watch?v=LoTgfGotaQ4", "https://web.archive.org/web/20071103105404/http://www.jameslindlibrary.org/trial_records/20th_Century/1990s/gray/gray-commentary.html"]}, "Complete spatial randomness": {"categories": ["All articles needing expert attention", "All articles to be merged", "Articles needing expert attention from June 2009", "Articles needing expert attention with no reason or talk parameter", "Articles to be merged from August 2018", "Point processes", "Spatial data analysis", "Spatial processes", "Statistical randomness", "Statistics articles needing expert attention"], "title": "Complete spatial randomness", "method": "Complete spatial randomness", "url": "https://en.wikipedia.org/wiki/Complete_spatial_randomness", "summary": "Complete spatial randomness (CSR) describes a point process whereby point events occur within a given study area in a completely random fashion. It is synonymous with a homogeneous spatial Poisson process. Such a process is modeled using only one parameter \n \n \n \n \u03c1\n \n \n {\\displaystyle \\rho }\n , i.e. the density of points within the defined area. The term complete spatial randomness is commonly used in Applied Statistics in the context of examining certain point patterns, whereas in most other statistical contexts it is referred to the concept of a spatial Poisson process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/aa/Merge-arrow.svg"], "links": ["Average", "Carol A. Gotway Crawford", "Factorial", "Gamma function", "International Standard Book Number", "Monte Carlo method", "Point process", "Poisson distribution", "Social sciences", "Spatial Poisson process", "Statistics", "Uniform probability distribution"], "references": ["http://www.galaxy.gmu.edu/interface/I02/I2002Proceedings/HauckSteven/HauckSteven.presentation.ppt", "http://handle.dtic.mil/100.2/ADA291151"]}, "Fisher information": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2010", "Design of experiments", "Estimation theory", "Information theory", "Wikipedia articles needing page number citations from February 2012"], "title": "Fisher information", "method": "Fisher information", "url": "https://en.wikipedia.org/wiki/Fisher_information", "summary": "In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter \u03b8 of a distribution that models X. \nFormally, it is the variance of the score, or the expected value of the observed information. In Bayesian statistics, the Asymptotic distribution of the posterior mode depends on the Fisher information and not on the prior (according to the Bernstein\u2013von Mises theorem, which was anticipated by Laplace for exponential families). The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized by the statistician Ronald Fisher (following some initial results by Francis Ysidro Edgeworth). The Fisher information is also used in the calculation of the Jeffreys prior, which is used in Bayesian statistics.\nThe Fisher-information matrix is used to calculate the covariance matrices associated with maximum-likelihood estimates. It can also be used in the formulation of test statistics, such as the Wald test.\nStatistical systems of a scientific nature (physical, biological, etc.) whose likelihood functions obey shift invariance have been shown to obey maximum Fisher information. The level of the maximum depends upon the nature of the system constraints.", "images": [], "links": ["Annals of Statistics", "ArXiv", "Artificial neural networks", "Asymptotic distribution", "B. Roy Frieden", "Bayesian statistics", "Bernoulli trial", "Bernstein\u2013von Mises theorem", "Bibcode", "Biometrika", "Catastrophic interference", "Cauchy\u2013Schwarz inequality", "Central moment", "Charles Loewner", "Column vector", "Continuously differentiable", "Covariance matrices", "Covariance matrix", "Cram\u00e9r\u2013Rao bound", "Curvature", "Determinant", "Differential geometry", "Digital object identifier", "Dimension", "Eigenvalue", "Elastic weight consolidation", "Entropy (information theory)", "Erich Leo Lehmann", "Estimator", "Euclidean metric", "Expected value", "Exponential families", "Fisher information metric", "Formation matrix", "Francis Ysidro Edgeworth", "Fubini\u2013Study metric", "Functional (mathematics)", "Hessian matrix", "IEEE Transactions on Information Theory", "If and only if", "Independent and identically distributed random variables", "Information", "Information geometry", "Information theory", "International Standard Book Number", "International Standard Serial Number", "Invariant theory", "JSTOR", "Jacobian matrix", "Jeffreys prior", "Journal of Machine Learning Research", "Journal of the Royal Statistical Society", "Kullback\u2013Leibler divergence", "Laplace", "Least squares", "Leonard J. Savage", "Likelihood Principle", "Likelihood function", "Linear model", "Lucien Le Cam", "Machine learning", "Mathematical statistics", "Matrix (mathematics)", "Matrix trace", "Maximum-likelihood estimation", "Maximum likelihood", "Maximum likelihood estimation", "Mode (statistics)", "Moment (mathematics)", "Multivariate normal distribution", "Mutual information", "Natural logarithm", "Nonlinear regression", "Observed information", "Optimal design", "Order parameter", "Ordered vector space", "Parameter", "Parameter space", "Partial derivative", "Partial order", "Phase transitions", "Positive semidefinite matrix", "Posterior distribution", "Prior distribution", "Probability density function", "Probability mass function", "Proceedings of the 2015 ACM Conference on Foundations of Genetic Algorithms XIII", "Product rule", "PubMed Central", "PubMed Identifier", "Random variable", "Regular parametric model", "Relative entropy", "Riemannian manifold", "Riemannian metric", "Ronald Fisher", "Score (statistics)", "Self-information", "Square matrix", "Statistic", "Statistical Science", "Statistical independence", "Statistical model", "Statistical theory", "Stephen Stigler", "Sufficiency (statistics)", "Sufficient statistic", "Summary statistics", "Support curve", "Trace (matrix)", "Transpose", "Unbiased estimator", "Variance", "Wald test", "Wilks' theorem", "World Scientific"], "references": ["http://adsabs.harvard.edu/abs/2004PhyA..336..181J", "http://adsabs.harvard.edu/abs/2011PhRvE..84d1116P", "http://adsabs.harvard.edu/abs/2013PhRvE..88d2144F", "http://www.stat.tamu.edu/~suhasini/teaching613/inference.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5380101", "http://www.ncbi.nlm.nih.gov/pubmed/28292907", "http://arxiv.org/abs/1405.0007", "http://arxiv.org/abs/cond-mat/0401092", "http://doi.org/10.1016%2Fj.physa.2004.01.023", "http://doi.org/10.1073%2Fpnas.1611835114", "http://doi.org/10.1093%2Fbiomet%2F71.1.135", "http://doi.org/10.1103%2FPhysRevE.84.041116", "http://doi.org/10.1103%2FPhysRevE.88.042144", "http://doi.org/10.1109%2F18.669301", "http://doi.org/10.1145%2F2725494.2725510", "http://doi.org/10.1214%2Faos%2F1176343456", "http://doi.org/10.1214%2Faos%2F1176343457", "http://doi.org/10.1214%2Fss%2F1009212248", "http://doi.org/10.2307%2F2339293", "http://doi.org/10.2307%2F2339378", "http://doi.org/10.2307%2F2339461", "http://doi.org/10.2307%2F2344804", "http://www.jstor.org/stable/2339293", "http://www.jstor.org/stable/2339378", "http://www.jstor.org/stable/2339461", "http://www.jstor.org/stable/2344804", "http://www.jstor.org/stable/2676741", "http://www.jstor.org/stable/2958221", "http://www.jstor.org/stable/2958222", "http://www.pnas.org/content/114/13/3521", "http://www.worldcat.org/issn/0027-8424", "https://books.google.com/books?id=gqI-pAP2JZ8C&pg=PA87"]}, "Survival function": {"categories": ["Applied probability", "Survival analysis"], "title": "Survival function", "method": "Survival function", "url": "https://en.wikipedia.org/wiki/Survival_function", "summary": "The survival function is a function that gives the probability that a patient, device, or other object of interest will survive beyond any given specified time.The survival function is also known as the survivor function or reliability function.The term reliability function is common in engineering while the term survival function is used in a broader range of applications, including human mortality. Another name for the survival function is the complementary cumulative distribution function.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d7/AC_Time_to_failure_LT_100_hours.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ed/CDF_for_AC_failures.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d1/Distribution_of_AC_failure_times.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e0/Four_survival_functions.svg", "https://upload.wikimedia.org/wikipedia/commons/2/26/Median_survival_greater_than_10_months.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b3/Survival_function_1.svg", "https://upload.wikimedia.org/wikipedia/commons/1/10/Survival_function_2.svg", "https://upload.wikimedia.org/wikipedia/commons/5/54/Survival_function_2_median_survival.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9c/Survival_function_is_1_-_CDF.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequency of exceedance", "Frequentist inference", "Friedman test", "Function (mathematics)", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean time to failure", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monotonic function", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random variable", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Residence time (statistics)", "Right-continuous", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survivorship curve", "System identification", "Time", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Slash distribution": {"categories": ["Continuous distributions", "Normal distribution", "Pages using deprecated image syntax", "Probability distributions with non-finite variance", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Slash distribution", "method": "Slash distribution", "url": "https://en.wikipedia.org/wiki/Slash_distribution", "summary": "In probability theory, the slash distribution is the probability distribution of a standard normal variate divided by an independent standard uniform variate. In other words, if the random variable Z has a normal distribution with zero mean and unit variance, the random variable U has a uniform distribution on [0,1] and Z and U are statistically independent, then the random variable X = Z / U has a slash distribution. The slash distribution is an example of a ratio distribution. The distribution was named by William H. Rogers and John Tukey in a paper published in 1972.The probability density function (pdf) is\n\n \n \n \n f\n (\n x\n )\n =\n \n \n \n \u03c6\n (\n 0\n )\n \u2212\n \u03c6\n (\n x\n )\n \n \n x\n \n 2\n \n \n \n \n .\n \n \n {\\displaystyle f(x)={\\frac {\\varphi (0)-\\varphi (x)}{x^{2}}}.}\n where \u03c6(x) is the probability density function of the standard normal distribution. The result is undefined at x = 0, but the discontinuity is removable:\n\n \n \n \n \n lim\n \n x\n \u2192\n 0\n \n \n f\n (\n x\n )\n =\n \n \n \n \u03c6\n (\n 0\n )\n \n 2\n \n \n =\n \n \n 1\n \n 2\n \n \n 2\n \u03c0\n \n \n \n \n \n \n \n {\\displaystyle \\lim _{x\\to 0}f(x)={\\frac {\\varphi (0)}{2}}={\\frac {1}{2{\\sqrt {2\\pi }}}}}\n The most common use of the slash distribution is in simulation studies. It is a useful distribution in this context because it has heavier tails than a normal distribution, but it is not as pathological as the Cauchy distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6c/Slashcdf.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b3/Slashpdf.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Copyright status of work by the U.S. government", "Cumulative distribution function", "Dagum distribution", "David V. Hinkley", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Heavy tail", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "John Tukey", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "National Institute of Standards and Technology", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pathological (mathematics)", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Ratio distribution", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Removable discontinuity", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Simulation", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Soliton distribution", "Stable distribution", "Statistically independent", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/slapdf.htm", "http://www.nist.gov", "http://www.cambridge.org/us/knowledge/isbn/item1154176/?site_locale=en_US", "http://doi.org/10.1111%2Fj.1467-9574.1972.tb00191.x"]}, "Location estimation in sensor networks": {"categories": ["All pages needing cleanup", "Articles needing cleanup from July 2009", "Cleanup tagged articles without a reason field from July 2009", "Detection theory", "Estimation theory", "Wikipedia pages needing cleanup from July 2009", "Wireless sensor network"], "title": "Location estimation in sensor networks", "method": "Location estimation in sensor networks", "url": "https://en.wikipedia.org/wiki/Location_estimation_in_sensor_networks", "summary": "Location estimation in wireless sensor networks is the problem of estimating the location of an object from a set of noisy measurements. These measurements are acquired in a distributed\nmanner by a set of sensors.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/1/15/LocationEstimation_WSN.JPG"], "links": ["6LoWPAN", "802.15.4", "ANT (network)", "Academic conference", "Academic journal", "Ad hoc On-Demand Distance Vector Routing", "Application software", "Arduino", "Bernoulli distribution", "Bluetooth", "Bluetooth Low Energy", "C (programming language)", "CodeBlue system", "Communications protocol", "Computer hardware", "Conference on Embedded Networked Sensor Systems", "Contiki", "DASH7", "Dynamic Source Routing", "ERIKA Enterprise", "Estimation theory", "European Conference on Wireless Sensor Networks", "Georgios B. Giannakis", "Harvard university", "ISA100.11a", "International Conference on Information Processing in Sensor Networks", "Iris Mote", "Key distribution in wireless sensor networks", "LabVIEW", "LinuxMCE", "LiteOS", "Maximum likelihood estimator", "Mean squared error", "MiWi", "Nano-RK", "Near field communication", "NesC", "Normal distribution", "Ns (simulator)", "OCARI", "ONE-NET", "OPNET", "OSIAN", "OpenTag", "OpenWSN", "Operating system", "Probability density function", "Programming language", "RIOT (operating system)", "Routing protocol", "Sensor network queries processor", "Sensor web", "Software", "Sun SPOT", "TSMP", "Telemetry", "Thread (network protocol)", "TinyOS", "Unbiased estimator", "WirelessHART", "Wireless powerline sensor", "Wireless sensor network", "Wireless sensor networks", "Xbee", "Z-Wave", "Zigbee"], "references": ["http://www.eecs.harvard.edu/~mdw/proj/codeblue/", "https://web.archive.org/web/20080430133030/http://www.eecs.harvard.edu/~mdw/proj/codeblue/"]}, "VC theory": {"categories": ["Computational learning theory", "Empirical process"], "title": "Vapnik\u2013Chervonenkis theory", "method": "VC theory", "url": "https://en.wikipedia.org/wiki/Vapnik%E2%80%93Chervonenkis_theory", "summary": "Vapnik\u2013Chervonenkis theory (also known as VC theory) was developed during 1960\u20131990 by Vladimir Vapnik and Alexey Chervonenkis. The theory is a form of computational learning theory, which attempts to explain the learning process from a statistical point of view.\nVC theory is related to statistical learning theory and to empirical processes. Richard M. Dudley and Vladimir Vapnik, among others, have applied VC-theory to empirical processes.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["0-1 loss", "Aad van der Vaart", "Alexey Chervonenkis", "Anomaly detection", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Autoencoder", "Automated machine learning", "BIRCH", "Bayesian network", "Bias-variance dilemma", "Boosting (machine learning)", "Bootstrap aggregating", "CURE data clustering algorithm", "Canonical correlation analysis", "Central limit theorem", "Cluster analysis", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Consistency (statistics)", "Convolutional neural network", "Covering number", "DBSCAN", "Data mining", "Decision tree learning", "DeepDream", "Deep learning", "Dimensionality reduction", "Dirac measure", "Dudley's theorem", "Empirical processes", "Empirical risk minimization", "Ensemble learning", "Expectation\u2013maximization algorithm", "Factor analysis", "Feature engineering", "Feature learning", "Gated recurrent unit", "Glossary of artificial intelligence", "Grammar induction", "Graphical model", "Hidden Markov model", "Hierarchical clustering", "Hoeffding's inequality", "Hypograph (mathematics)", "Independent component analysis", "International Conference on Machine Learning", "International Standard Book Number", "Jensen's inequality", "John Wiley & Sons", "Journal of Machine Learning Research", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Law of large numbers", "Learning to rank", "Linear discriminant analysis", "Linear regression", "List of datasets for machine-learning research", "Local outlier factor", "Logistic regression", "Long short-term memory", "Machine Learning (journal)", "Machine learning", "Mean-shift", "Multilayer perceptron", "Naive Bayes classifier", "Non-negative matrix factorization", "OPTICS algorithm", "Occam learning", "Online machine learning", "Outline of machine learning", "Perceptron", "Principal component analysis", "Probably approximately correct learning", "Q-learning", "Rademacher complexity", "Random forest", "Recurrent neural network", "Regression analysis", "Reinforcement learning", "Relevance vector machine", "Restricted Boltzmann machine", "Richard M. Dudley", "Sauer\u2013Shelah lemma", "Self-organizing map", "Semi-supervised learning", "Shattered set", "Slutsky's theorem", "Springer-Verlag", "Stability (learning theory)", "State\u2013action\u2013reward\u2013state\u2013action", "Statistical classification", "Statistical learning theory", "Structured prediction", "Supervised learning", "Support vector machine", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "U-Net", "Unsupervised learning", "VC dimension", "Vladimir Vapnik"], "references": ["https://arxiv.org/list/cs.LG/recent", "https://books.google.com.ua/books?id=zdDkBwAAQBAJ"]}, "Cohen's class distribution function": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2013", "Digital signal processing", "Fourier analysis", "Signal processing", "Time\u2013frequency analysis"], "title": "Bilinear time\u2013frequency distribution", "method": "Cohen's class distribution function", "url": "https://en.wikipedia.org/wiki/Bilinear_time%E2%80%93frequency_distribution", "summary": "Bilinear time\u2013frequency distributions, or quadratic time\u2013frequency distributions, arise in a sub-field of signal analysis and signal processing called time\u2013frequency signal processing, and, in the statistical analysis of time series data. Such methods are used where one needs to deal with a situation where the frequency composition of a signal may be changing over time; this sub-field used to be called time\u2013frequency signal analysis, and is now more often called time\u2013frequency signal processing due to the progress in using these methods to a wide range of signal-processing problems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/2/27/Ax_to_Wx.jpg", "https://upload.wikimedia.org/wikipedia/en/b/bf/Cross-term_remove.jpg", "https://upload.wikimedia.org/wikipedia/en/6/65/Relationship_between_Ax_Rx_Wx.jpg"], "links": ["Acoustics", "Ambiguity function", "Auto-correlation", "Choi\u2013Williams distribution", "Cone-shape distribution function", "Cumulative distribution function", "Fourier transform", "Frequency domain", "International Standard Book Number", "Modified Wigner distribution function", "Power spectral density", "Rihaczek distribution", "Short-time Fourier transform", "Signal analysis", "Signal processing", "Statistical analysis", "Time domain", "Time series", "Time series analysis", "Time\u2013frequency analysis", "Time\u2013frequency representation", "Transformation between distributions in time-frequency analysis", "Transformation between distributions in time\u2013frequency analysis", "Wigner distribution function", "Window function"], "references": []}, "Bayesian statistics": {"categories": ["All articles needing additional references", "Articles needing additional references from May 2016", "Bayesian statistics"], "title": "Bayesian statistics", "method": "Bayesian statistics", "url": "https://en.wikipedia.org/wiki/Bayesian_statistics", "summary": "Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event, which can change as new information is gathered, rather than a fixed value based upon frequency or propensity. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation that views probability as the limit of the relative frequency of an event after a large number of trials.Bayesian statistical methods use Bayes' theorem to compute and update probabilities after obtaining new data. Bayes' theorem describes the conditional probability of an event based on data as well as prior information or beliefs about the event or conditions related to the event. For example, in Bayesian inference, Bayes' theorem can be used to estimate the parameters of a probability distribution or statistical model. Since Bayesian statistics treats probability as a degree of belief, Bayes' theorem can directly assign a probability distribution that quantifies the belief to the parameter or set of parameters.Bayesian statistics was named after Thomas Bayes, who formulated a specific case of Bayes' theorem in his paper published in 1763. In several papers spanning from the late-1700s to the early-1800s, Pierre-Simon Laplace developed the Bayesian interpretation of probability. Laplace used methods that would now be considered as Bayesian methods to solve a number of statistical problems. Many Bayesian methods were developed by later authors, but the term was not commonly used to describe such methods until the 1950s. During much of the 20th century, Bayesian methods were unfavorable with many statisticians due to philosophical and practical considerations. Many Bayesian methods required a lot of computation to complete, and most methods that were widely used during the century were based on the frequentist interpretation. However, with the advent of powerful computers and new algorithms like Markov chain Monte Carlo, Bayesian methods have seen increasing use within statistics coming into the 21st century.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Admissible decision rule", "Algorithm", "An Essay towards solving a Problem in the Doctrine of Chances", "Andrew Gelman", "Approximate Bayesian computation", "Bayes' theorem", "Bayes factor", "Bayesian design of experiments", "Bayesian efficiency", "Bayesian estimator", "Bayesian hierarchical modeling", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian networks", "Bayesian probability", "Bernstein\u2013von Mises theorem", "Conditional probability", "Conjugate prior", "Credible interval", "Cromwell's rule", "David Spiegelhalter", "Digital object identifier", "Donald Rubin", "Dynamic Yield", "Empirical Bayes method", "Event (probability theory)", "Frequentist inference", "Frequentist probability", "Hyperparameter", "Hyperprior", "Integral", "International Standard Book Number", "Law of large numbers", "Law of total probability", "Likelihood function", "Limit of a sequence", "Markov chain Monte Carlo", "Mathematical optimization", "Maximum a posteriori", "Maximum a posteriori estimation", "Mode (statistics)", "Multi-armed bandit problem", "Nat. Methods", "Outcome (probability)", "Parameter", "Partition of a set", "Pierre-Simon Laplace", "Posterior distribution", "Posterior predictive distribution", "Posterior probability", "Principle of indifference", "Principle of maximum entropy", "Prior distribution", "Prior probability", "Probability", "Probability distribution", "Probability interpretations", "Probability theory", "Proposition", "Radical probabilism", "Random variable", "Sample space", "Scholarpedia", "Schwarz criterion", "Sequential analysis", "Statistical graphics", "Statistical inference", "Statistical model", "Statistics", "Thomas Bayes", "Variational Bayesian methods"], "references": ["http://bayesmodels.com/", "http://greenteapress.com/wp/think-bayes/", "http://www.nature.com/nmeth/journal/v12/n5/full/nmeth.3368.html", "http://www.yudkowsky.net/rational/bayes", "http://doi.org/10.1038%2Fnmeth.3368", "http://blog.efpsa.org/2015/08/03/bayesian-statistics-why-and-how/", "http://www.scholarpedia.org/article/Bayesian_statistics", "https://marketing.dynamicyield.com/bayesian-calculator/", "https://kupdf.com/download/a-gentle-tutorial-in-bayesian-statisticspdf_59b0ed86dc0d602e3b568edc_pdf", "https://www.springer.com/gp/book/9783662486368", "https://www.statmodel.com/download/introBayes.pdf", "https://deepai.org/machine-learning-glossary-and-terms/bayesian-statistics", "https://projecteuclid.org/euclid.ba/1340371071"]}, "Partial residual plot": {"categories": ["CS1 maint: Multiple names: authors list", "Regression diagnostics", "Statistical charts and diagrams", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Partial residual plot", "method": "Partial residual plot", "url": "https://en.wikipedia.org/wiki/Partial_residual_plot", "summary": "In applied statistics, a partial residual plot is a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["Applied statistics", "Copyright status of work by the U.S. government", "Digital object identifier", "Errors and residuals in statistics", "Full model", "Graphical technique", "Independent variable", "JSTOR", "Linear regression", "National Institute of Standards and Technology", "Partial leverage plot", "Partial regression plot", "Response variable", "Scatter plot", "Statistical model", "Variance inflation factor"], "references": ["http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/partresi.htm", "http://www.nist.gov", "http://doi.org/10.2307/2683296", "http://www.jstor.org/stable/2683296", "https://books.google.com/books?id=qozaTQMdC0EC&pg=PA54"]}, "U-chart": {"categories": ["Quality control tools", "Statistical charts and diagrams"], "title": "U-chart", "method": "U-chart", "url": "https://en.wikipedia.org/wiki/U-chart", "summary": "In statistical quality control, the u-chart is a type of control chart used to monitor \"count\"-type data where the sample size is greater than one, typically the average number of nonconformities per unit.\nThe u-chart differs from the c-chart in that it accounts for the possibility that the number or size of inspection units for which nonconformities are to be counted may vary. Larger samples may be an economic necessity or may be necessary to increase the area of opportunity in order to track very low nonconformity levels.Examples of processes suitable for monitoring with a u-chart include:\n\nMonitoring the number of nonconformities per lot of raw material received where the lot size varies\nMonitoring the number of new infections in a hospital per day\nMonitoring the number of accidents for delivery trucks per dayAs with the c-chart, the Poisson distribution is the basis for the chart and requires the same assumptions.\nThe control limits for this chart type are \n \n \n \n \n \n \n u\n \u00af\n \n \n \n \u00b1\n 3\n \n \n \n \n \n u\n \u00af\n \n \n n\n \n \n \n \n \n {\\displaystyle {\\bar {u}}\\pm 3{\\sqrt {\\frac {\\bar {u}}{n}}}}\n where \n \n \n \n \n \n \n u\n \u00af\n \n \n \n \n \n {\\displaystyle {\\bar {u}}}\n is the estimate of the long-term process mean established during control-chart setup. The observations \n \n \n \n \n u\n \n i\n \n \n =\n \n \n \n x\n \n i\n \n \n \n n\n \n i\n \n \n \n \n \n \n {\\displaystyle u_{i}={\\frac {x_{i}}{n_{i}}}}\n are plotted against these control limits, where xi is the number of nonconformities for the ith subgroup and ni is the number of inspection units in the ith subgroup.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9f/U_control_chart.svg"], "links": ["C-chart", "Control chart", "Hoboken, New Jersey", "International Standard Book Number", "John Wiley & Sons", "OCLC", "Poisson distribution", "Statistical process control", "Variable and attribute (research)", "Walter A. Shewhart"], "references": ["http://www.eas.asu.edu/~masmlab/montgomery/", "http://www.worldcat.org/oclc/56729567", "https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/"]}, "Canonical analysis": {"categories": ["All Wikipedia articles needing clarification", "Articles containing Ancient Greek-language text", "Regression analysis", "Wikipedia articles needing clarification from June 2016"], "title": "Canonical analysis", "method": "Canonical analysis", "url": "https://en.wikipedia.org/wiki/Canonical_analysis", "summary": "In statistics, canonical analysis (from Ancient Greek: \u03ba\u03b1\u03bd\u03c9\u03bd bar, measuring rod, ruler) belongs to the family of regression methods for data analysis. Regression analysis quantifies a relationship between a predictor variable and a criterion variable by the coefficient of correlation r, coefficient of determination r2, and the standard regression coefficient \u03b2. Multiple regression analysis expresses a relationship between a set of predictor variables and a single criterion variable by the multiple correlation R, multiple coefficient of determination R\u00b2, and a set of standard partial regression weights \u03b21, \u03b22, etc. Canonical variate analysis captures a relationship between a set of predictor variables and a set of criterion variables by the canonical correlations \u03c11, \u03c12, ..., and by the sets of canonical weights C and D.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Ancient Greek language", "ArXiv", "Biometrika", "Canonical correlation", "Canonical correlation analysis", "Correlation", "Digital object identifier", "Eigenvalues", "Eigenvectors", "Factor analysis", "Harold Hotelling", "JSTOR", "Journal of the Royal Statistical Society, Series D", "Measuring rod", "Minkowski spacetime", "Multiple correlation", "Principal components analysis", "RV coefficient", "Regression analysis", "Social Science Research Network", "Statistics"], "references": ["http://ssrn.com/abstract=1353202", "http://arxiv.org/abs/1109.0725", "http://doi.org/10.1093%2Fbiomet%2F28.3-4.321", "http://doi.org/10.1111%2F1467-9884.00195", "http://doi.org/10.1177%2F001316447603600320", "http://doi.org/10.1207%2Fs15327906mbr3004_4", "http://www.jstor.org/stable/2333955"]}, "Cram\u00e9r\u2019s decomposition theorem": {"categories": ["CS1 maint: Multiple names: authors list", "Characterization of probability distributions", "Probability theorems", "Statistical theorems"], "title": "Cram\u00e9r\u2019s decomposition theorem", "method": "Cram\u00e9r\u2019s decomposition theorem", "url": "https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%99s_decomposition_theorem", "summary": "Cram\u00e9r\u2019s decomposition theorem for a normal distribution is a result of probability theory. It is well known that, given independent normally distributed random variables \u03be1, \u03be2, their sum is normally distributed as well. It turns out that the converse is also true. The latter result, initially announced by Paul L\u00e9vy, has been proved by Harald Cram\u00e9r. This became a starting point for a new subfield in probability theory, decomposition theory for random variables as sums of independent variables (also known as arithmetic of probabilistic distributions).", "images": [], "links": ["Digital object identifier", "Entire function", "Harald Cram\u00e9r", "Independence (probability theory)", "Normal distribution", "Paul L\u00e9vy (mathematician)", "Random variable"], "references": ["http://doi.org/10.1007%2FBF01180430"]}, "Hyperprior": {"categories": ["Bayesian statistics"], "title": "Hyperprior", "method": "Hyperprior", "url": "https://en.wikipedia.org/wiki/Hyperprior", "summary": "In Bayesian statistics, a hyperprior is a prior distribution on a hyperparameter, that is, on a parameter of a prior distribution.\nAs with the term hyperparameter, the use of hyper is to distinguish it from a prior distribution of a parameter of the model for the underlying system. They arise particularly in the use of conjugate priors.\nFor example, if one is using a beta distribution to model the distribution of the parameter p of a Bernoulli distribution, then:\n\nThe Bernoulli distribution (with parameter p) is the model of the underlying system;\np is a parameter of the underlying system (Bernoulli distribution);\nThe beta distribution (with parameters \u03b1 and \u03b2) is the prior distribution of p;\n\u03b1 and \u03b2 are parameters of the prior distribution (beta distribution), hence hyperparameters;\nA prior distribution of \u03b1 and \u03b2 is thus a hyperprior.In principle, one can iterate the above: if the hyperprior itself has hyperparameters, these may be called hyperhyperparameters, and so forth.\nOne can analogously call the posterior distribution on the hyperparameter the hyperposterior, and, if these are in the same family, call them conjugate hyperdistributions or a conjugate hyperprior. However, this rapidly becomes very abstract and removed from the original problem.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ed/Bayes_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg"], "links": ["Admissible decision rule", "Approximate Bayesian computation", "Bayes' theorem", "Bayes factor", "Bayesian efficiency", "Bayesian estimator", "Bayesian inference", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bayesian statistics", "Bernoulli distribution", "Bernstein\u2013von Mises theorem", "Beta distribution", "Conjugate prior", "Convex combination", "Convex set", "Credible interval", "Cromwell's rule", "Dynamical system", "Empirical Bayes method", "Hyperparameter", "International Standard Book Number", "Likelihood function", "Markov chain Monte Carlo", "Maximum a posteriori estimation", "Mixture density", "Posterior predictive distribution", "Posterior probability", "Principle of indifference", "Principle of maximum entropy", "Prior distribution", "Prior probability", "Probability interpretations", "Radical probabilism", "Schwarz criterion", "Statistics"], "references": ["https://books.google.com/books?id=11nSgIcd7xQC"]}, "Probability distribution": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles with unsourced statements", "Articles lacking in-text citations from July 2011", "Articles needing additional references from July 2011", "Articles with multiple maintenance issues", "Articles with unsourced statements from March 2018", "Mathematical and quantitative methods (economics)", "Probability distributions", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers"], "title": "Probability distribution", "method": "Probability distribution", "url": "https://en.wikipedia.org/wiki/Probability_distribution", "summary": "In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. For instance, if the random variable X is used to denote the outcome of a coin toss (\"the experiment\"), then the probability distribution of X would take the value 0.5 for X = heads, and 0.5 for X = tails (assuming the coin is fair). Examples of random phenomena can include the results of an experiment or survey.\nA probability distribution is defined in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed. The sample space may be the set of real numbers or a higher-dimensional vector space, or it may be a list of non-numerical values; for example, the sample space of a coin flip would be {heads, tails} .\nProbability distributions are generally divided into two classes. A discrete probability distribution (applicable to the scenarios where the set of possible outcomes is discrete, such as a coin toss or a roll of dice) can be encoded by a discrete list of the probabilities of the outcomes, known as a probability mass function. On the other hand, a continuous probability distribution (applicable to the scenarios where the set of possible outcomes can take on values in a continuous range (e.g. real numbers), such as the temperature on a given day) is typically described by probability density functions (with the probability of any individual outcome actually being 0). The normal distribution is a commonly encountered continuous probability distribution. More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures.\nA probability distribution whose sample space is the set of real numbers is called univariate, while a distribution whose sample space is a vector space is called multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution (a joint probability distribution) gives the probabilities of a random vector \u2013 a list of two or more random variables \u2013 taking on various combinations of values. Important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is a commonly encountered multivariate distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/1/12/Dice_Distribution_%28bar%29.svg", "https://upload.wikimedia.org/wikipedia/commons/8/85/Discrete_probability_distrib.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fb/Discrete_probability_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Loglogisticpdf_no-labels.svg", "https://upload.wikimedia.org/wikipedia/commons/6/64/Mixed_probability_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e8/Normal_probability_distribution.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ARGUS distribution", "Absolute continuity", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Almost surely", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Antiderivative", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Cache language model", "Cambridge University Press", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central moment", "Central tendency", "Characteristic function (probability theory)", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Chi squared distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinant", "Complement (set theory)", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confounding", "Conjugate prior", "Contingency table", "Continuous and discrete variables", "Continuous function", "Continuous probability distribution", "Continuous time", "Continuous uniform distribution", "Control chart", "Convex combination", "Convex subset", "Convolution", "Conway\u2013Maxwell\u2013Poisson distribution", "Copula (statistics)", "Correlation and dependence", "Correlogram", "Count data", "Countable", "Countable set", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulant", "Cumulative distribution function", "Dagum distribution", "Data collection", "Davis distribution", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dice", "Dickey\u2013Fuller test", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Disjoint set", "Distribution (disambiguation)", "Distribution (mathematics)", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Empirical probability", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Event (probability theory)", "Ewens's sampling formula", "Expected value", "Experiment", "Experiment (probability theory)", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finite set", "First-hitting-time model", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "Fundamental particles", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Genetic variability", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "Geostatistics", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Half-open interval", "Harmonic mean", "Heavy-tailed distribution", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent (statistics)", "Index of dispersion", "Indicator function", "Infinitesimal", "Infinity", "Integral", "Integration (mathematics)", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval (mathematics)", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Jump discontinuity", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kinetic theory of gases", "Kirkwood approximation", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Lebesgue integration", "Lebesgue measure", "Lehmann\u2013Scheff\u00e9 theorem", "Library of Congress Control Number", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Limit (mathematics)", "Linear combination", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistical topics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Measurable function", "Measurable space", "Measure theory", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment-generating function", "Moment (mathematics)", "Monotone likelihood ratio", "Monte Carlo method", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate hypergeometric distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Nakagami distribution", "National Diet Library", "National accounts", "Natural experiment", "Natural exponential family", "Natural language processing", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Non-negative definite", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Number", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outcome (probability)", "Outline of statistics", "Parabolic fractal distribution", "Paradox", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Polya urn scheme", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Power law", "Precision (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability-generating function", "Probability density function", "Probability mass function", "Probability measure", "Probability space", "Probability theory", "Proportional hazards model", "Pseudo-random number sampling", "Pseudorandom number generator", "Pseudorandomness", "Psychometrics", "PubMed Identifier", "Pushforward measure", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quantile function", "Quantum mechanical", "Quasi-experiment", "Quasiprobability distribution", "Questionnaire", "Q\u2013Q plot", "R-squared", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrix", "Random variable", "Random variate", "Random vector", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Randomness", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raw moment", "Rayleigh distribution", "Real numbers", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rice distribution", "Rician fading", "Riemann\u2013Stieltjes integral", "Robust regression", "Robust statistics", "Run chart", "Sample (statistics)", "Sample median", "Sample size determination", "Sample space", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Sampling without replacement", "Scalar (mathematics)", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Set (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singleton (mathematics)", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Springer Publishing", "Stable distribution", "Standard deviation", "Standard error", "Standard normal", "Standardized moment", "Stationary process", "Statistic", "Statistical Language Model", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic processes", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Student's t distribution", "Sufficient statistic", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "Symmetric probability distribution", "System identification", "Time domain", "Time series", "Tolerance interval", "Tracy\u2013Widom distribution", "Trend estimation", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniform distribution (discrete)", "Uniformly most powerful test", "Univariate distribution", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Vector space", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "Weibull distribution", "Weighted average", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://threeplusone.com/FieldGuide.pdf", "http://www.ncbi.nlm.nih.gov/pubmed/25059432", "http://doi.org/10.1016%2Fj.ejmp.2014.05.002", "https://id.loc.gov/authorities/subjects/sh85038545", "https://id.ndl.go.jp/auth/ndlna/00564751", "https://www.encyclopediaofmath.org/index.php?title=p/p074900", "https://www.wikidata.org/wiki/Q200726"]}, "Median absolute deviation": {"categories": ["Robust statistics", "Statistical deviation and dispersion"], "title": "Median absolute deviation", "method": "Median absolute deviation", "url": "https://en.wikipedia.org/wiki/Median_absolute_deviation", "summary": "In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample.\nFor a univariate data set X1, X2, ..., Xn, the MAD is defined as the median of the absolute deviations from the data's median \n \n \n \n \n \n \n X\n ~\n \n \n \n =\n median\n \u2061\n (\n X\n )\n \n \n {\\displaystyle {\\tilde {X}}=\\operatorname {median} (X)}\n :\n\n \n \n \n MAD\n =\n median\n \u2061\n (\n \n |\n \n \n X\n \n i\n \n \n \u2212\n \n \n \n X\n ~\n \n \n \n \n |\n \n )\n \n \n {\\displaystyle \\operatorname {MAD} =\\operatorname {median} (|X_{i}-{\\tilde {X}}|)}\n that is, starting with the residuals (deviations) from the data's median, the MAD is the median of their absolute values.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute deviation", "Absolute value", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average absolute deviation", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Carl Friedrich Gauss", "Cartography", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Complex number", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Deviation (statistics)", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geometric median", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Half-normal distribution", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least absolute deviations", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiplicative inverse", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Rousseeuw", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Population variance", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probable error", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile function", "Quantitative data", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative mean absolute difference", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust measures of scale", "Robust regression", "Robust statistic", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale factor", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard normal distribution", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical estimation", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "Univariate", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://doi.org/10.1016%2Fj.jesp.2013.03.013", "http://doi.org/10.1080%2F01621459.1993.10476408", "https://books.google.co.uk/books?id=i2bD50PbIikC&pg=PA118#v=onepage"]}, "Plackett\u2013Burman design": {"categories": ["Design of experiments", "Wikipedia articles incorporating text from the National Institute of Standards and Technology"], "title": "Plackett\u2013Burman design", "method": "Plackett\u2013Burman design", "url": "https://en.wikipedia.org/wiki/Plackett%E2%80%93Burman_design", "summary": "Plackett\u2013Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply.\nTheir goal was to find experimental designs for investigating the dependence of some measured quantity on a number of independent variables (factors), each taking L levels, in such a way as to minimize the variance of the estimates of these dependencies using a limited number of experiments. Interactions between the factors were considered negligible. The solution to this problem is to find an experimental design where each combination of levels for any pair of factors appears the same number of times, throughout all the experimental runs (refer to table). A complete factorial design would satisfy this criterion, but the idea was to find smaller designs.\n\nFor the case of two levels (L = 2), Plackett and Burman used the method found in 1933 by Raymond Paley for generating orthogonal matrices whose elements are all either 1 or \u22121 (Hadamard matrices). Paley's method could be used to find such matrices of size N for most N equal to a multiple of 4. In particular, it worked for all such N up to 100 except N = 92. If N is a power of 2, however, the resulting design is identical to a fractional factorial design, so Plackett\u2013Burman designs are mostly used when N is a multiple of 4 but not a power of 2 (i.e. N = 12, 20, 24, 28, 36 \u2026). If one is trying to estimate less than N parameters (including the overall average), then one simply uses a subset of the columns of the matrix.\nFor the case of more than two levels, Plackett and Burman rediscovered designs that had previously been given by Raj Chandra Bose and K. Kishen at the Indian Statistical Institute.\nPlackett and Burman give specifics for designs having a number of experiments equal to the number of levels L to some integer power, for L = 3, 4, 5, or 7.\nWhen interactions between factors are not negligible, they are often confounded in Plackett\u2013Burman designs with the main effects, meaning that the designs do not permit one to distinguish between certain main effects and certain interactions. This is called aliasing or confounding.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alias (statistics)", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Block design", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Copyright status of work by the U.S. government", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental design", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial design", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Hadamard matrix", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Independent variable", "Index of dispersion", "Indian Agricultural Statistics Research Institute", "Indian Statistical Institute", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "J. P. Burman", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "K. Kishen", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Ministry of Supply", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "NIST", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonal matrix", "Orthogonality", "Outline of statistics", "Paley construction", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Raj Chandra Bose", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Raymond Paley", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robin L. Plackett", "Robust regression", "Robust statistics", "Run chart", "SEMATECH", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sankhya (journal)", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Technometrics", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.itl.nist.gov/div898/handbook/pri/section3/pri335.htm", "http://www.nist.gov", "http://www.iasri.res.in/design/Supersaturated_Design/SSD/Supersaturated.html", "https://doi.org/10.1093%2Fbiomet%2F33.4.305", "https://www.jstor.org/stable/25047628"]}, "Innovation (signal processing)": {"categories": ["Statistical signal processing"], "title": "Innovation (signal processing)", "method": "Innovation (signal processing)", "url": "https://en.wikipedia.org/wiki/Innovation_(signal_processing)", "summary": "In time series analysis (or forecasting) \u2014 as conducted in statistics, signal processing, and many other fields \u2014 the innovation is the difference between the observed value of a variable at time t and the optimal forecast of that value based on information available prior to time t. If the forecasting method is working correctly, successive innovations are uncorrelated with each other, i.e., constitute a white noise time series. Thus it can be said that the innovation time series is obtained from the measurement time series by a process of 'whitening', or removing the predictable component. The use of the term innovation in the sense described here is due to Hendrik Bode and Claude Shannon (1950) in their discussion of the Wiener filter problem, although the notion was already implicit in the work of Kolmogorov.", "images": [], "links": ["Claude Shannon", "Errors and residuals in statistics", "Filtering problem (stochastic processes)", "Hendrik Bode", "Innovation butterfly", "International Standard Book Number", "Kalman filter", "Kolmogorov", "Signal processing", "Statistics", "Time series analysis", "White noise", "Wiener filter"], "references": []}, "Semantic relatedness": {"categories": ["All articles covered by WikiProject Wikify", "All articles needing additional references", "All articles needing references cleanup", "All articles with unsourced statements", "Articles covered by WikiProject Wikify from December 2010", "Articles needing additional references from December 2010", "Articles with multiple maintenance issues", "Articles with unsourced statements from February 2016", "CS1 maint: Multiple names: authors list", "Computational linguistics", "Semantics", "Statistical distance", "Wikipedia references cleanup from December 2010"], "title": "Semantic similarity", "method": "Semantic relatedness", "url": "https://en.wikipedia.org/wiki/Semantic_similarity", "summary": "Semantic similarity is a metric defined over a set of documents or terms, where the idea of distance between them is based on the likeness of their meaning or semantic content as opposed to similarity which can be estimated regarding their syntactical representation (e.g. their string format). These are mathematical tools used to estimate the strength of the semantic relationship between units of language, concepts or instances, through a numerical description obtained according to the comparison of information supporting their meaning or describing their nature. The term semantic similarity is often confused with semantic relatedness. Semantic relatedness includes any relation between two terms, while semantic similarity only includes \"is a\" relations.\nFor example, \"car\" is similar to \"bus\", but is also related to \"road\" and \"driving\".\nComputationally, semantic similarity can be estimated by defining a topological similarity, by using ontologies to define the distance between terms/concepts. For example, a naive metric for the comparison of concepts ordered in a partially ordered set and represented as nodes of a directed acyclic graph (e.g., a taxonomy), would be the shortest-path linking the two concept nodes. Based on text analyses, semantic relatedness between units of language (e.g., words, sentences) can also be estimated using statistical means such as a vector space model to correlate words and textual contexts from a suitable text corpus.\nSeveral tools are used to measure the semantic similarity between concepts such as WNetSS API, which is a Java API manipulating a wide variety of semantic similarity measurements based on the WordNet semantic resource.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/d/de/Globe_of_letters.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Alessandro Vespignani", "Analogy", "Antonymy", "ArXiv", "Bibcode", "ChEBI", "CiteSeerX", "Coherence (linguistics)", "Concept maps", "Correlation", "DiShIn", "Digital object identifier", "Dijkstra's algorithm", "Directed acyclic graph", "Filippo Menczer", "Gene Ontology", "Gene ontology", "Genes", "GraSM", "Human Phenotype Ontology", "Information content", "International Standard Book Number", "International Standard Serial Number", "Jaccard index", "Latent semantic analysis", "Levenshtein distance", "Lowest common ancestor", "Medical Subject Headings", "Meronymy", "Mind maps", "Natural language processing", "Normalized Compression Distance", "Normalized Google distance", "Ontology (computer science)", "OpenStreetMap", "Open Biomedical Ontologies", "Open Directory Project", "Partially ordered set", "Pixel", "Pointwise mutual information", "Proteins", "PubMed Central", "PubMed Identifier", "RDF Schema", "SNOMED CT", "Second-order co-occurrence pointwise mutual information", "Semantic Web", "Semantic differential", "Semantic folding", "Semantic similarity network", "Sequence similarity", "SimRank", "Similarity learning", "Syntax", "Taxonomy (general)", "Terminology extraction", "Text corpus", "Topological", "UniProt", "Vector space model", "WNetSS API", "Web Ontology Language", "Wikipedia", "Word2vec", "WordNet"], "references": ["http:ftp://www-vhost.cs.toronto.edu/public_html/public_html/pub/gh/Budanitsky+Hirst-2001.pdf", "http://www.oegai.at/konvens2012/proceedings/23_panchenko12p/23_panchenko12p.pdf", "http://serelex.cental.be/", "http://iknowate.blogspot.com/2011/10/google-similarity-distance.html", "http://chronicle.com/wiredcampus/article/3041/six-degrees-of-wikipedia", "http://downloads.hindawi.com/journals/cin/2015/712835.pdf", "http://www.morganclaypool.com/doi/10.2200/S00639ED1V01Y201504HLT027", "http://www.samerhassan.com/images/4/48/Hassan.pdf", "http://semantic-link.com/", "http://www.f%C3%A4hndrich.de", "http://www.linguatools.de/disco/disco-builder.html", "http://www.linguatools.de/disco/disco_en.html", "http://www.similarity-blog.de/?page_id=3", "http://www.stat.cmu.edu/~cshalizi/350/2008/readings/Landauer-Dumais.pdf", "http://lsa.colorado.edu/papers/dp1.LSAintro.pdf", "http://adsabs.harvard.edu/abs/2009LNCS.5872..848D", "http://adsabs.harvard.edu/abs/2009PLSCB...5E0443P", "http://adsabs.harvard.edu/abs/2010PLSCB...6E0937F", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.55.1832&rep=rep1&type=pdf", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.893.7406&rep=rep1&type=pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.5544", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.6956", "http://www.personal.psu.edu/kuj13/janowicz_etal_simdl_geos2007.pdf", "http://csjarchive.cogsci.rpi.edu/Proceedings/2006/docs/p2624.pdf", "http://www.cogsci.rpi.edu/vekslv/pubs/pp718-veksler.pdf", "http://swoogle.umbc.edu/SimService/", "http://sitemaker.umich.edu/iccm2007.org/files/lindsey__veksler__grintsvayg____gray.pdf", "http://atlas.ahc.umn.edu/", "http://www.d.umn.edu/~tpederse/Pubs/prath-thesis.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1130488", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2375122", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2712090", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2756558", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2944781", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3098105", "http://www.ncbi.nlm.nih.gov/pubmed/15468759", "http://www.ncbi.nlm.nih.gov/pubmed/15901854", "http://www.ncbi.nlm.nih.gov/pubmed/18221506", "http://www.ncbi.nlm.nih.gov/pubmed/19649320", "http://www.ncbi.nlm.nih.gov/pubmed/19800049", "http://www.ncbi.nlm.nih.gov/pubmed/20885779", "http://www.ncbi.nlm.nih.gov/pubmed/21122125", "http://www.ncbi.nlm.nih.gov/pubmed/21702778", "http://www.ncbi.nlm.nih.gov/pubmed/22138322", "http://takelab.fer.hr/sts/", "http://irserver.ucd.ie/bitstream/handle/10197/3973/2012_-_Geographic_Knowledge_Extraction_and_Semantic_Similarity_in_OpenStreetMap_-_Ballatore_et_al.pdf?sequence=1", "http://www.cs.technion.ac.il/~gabr/papers/ijcai-2007-sim.pdf", "http://www.di.uniba.it/~cdamato/PhDThesis_dAmato.pdf", "http://wwwusers.di.uniroma1.it/~navigli/pubs/ACL_2013_Pilehvar_Jurgens_Navigli.pdf", "http://www.dsi.uniroma1.it/~navigli/pubs/PAMI_2010_Navigli_Lapata.pdf", "http://lcl.uniroma1.it/adw/", "http://lcl.uniroma1.it/nasari/", "http://disi.unitn.it/~p2p/RelatedWork/Matching/Gracia_wise08.pdf", "http://hdl.handle.net/10455/2935", "http://umls-similarity.sourceforge.net/", "http://wn-similarity.sourceforge.net/", "http://ilk.uvt.nl/~swubben/publications/wubben2008-techrep.pdf", "http://www.aaai.org/Papers/IJCAI/2007/IJCAI07-272.pdf", "http://aclweb.org/anthology/N/N15/N15-1059.pdf", "http://aclweb.org/anthology/P/P15/P15-1072.pdf", "http://doi.acm.org/10.1145/1232425.1232448", "http://arxiv.org/abs/1704.05295", "http://arxiv.org/abs/cs/0412098", "http://www.babelnet.org/", "http://www.bioconductor.org/", "http://cogprints.org/3779/01/cogsci04_2.pdf", "http://doi.org/10.1007%2F3-540-44963-9_8", "http://doi.org/10.1007%2F978-3-642-05290-3_103", "http://doi.org/10.1007%2Fs00500-016-2438-x", "http://doi.org/10.1016%2FB978-0-12-809633-8.20401-9", "http://doi.org/10.1016%2Fj.ajhg.2009.09.003", "http://doi.org/10.1016%2Fj.datak.2006.05.003", "http://doi.org/10.1017%2FS0269888917000029", "http://doi.org/10.1037%2F0033-295x.104.2.211", "http://doi.org/10.1080%2F01638539809545028", "http://doi.org/10.1081%2FBIP-200025659", "http://doi.org/10.1093%2Fbib%2Fbbr066", "http://doi.org/10.1093%2Fnar%2Fgki573", "http://doi.org/10.1109%2FTKDE.2007.48", "http://doi.org/10.1145%2F1054972.1054980", "http://doi.org/10.1145%2F1099554.1099658", "http://doi.org/10.1186%2F1471-2105-11-588", "http://doi.org/10.1186%2F1471-2105-9-50", "http://doi.org/10.1186%2F2041-1480-2-5", "http://doi.org/10.1207%2Fs15516709cog0000_20", "http://doi.org/10.1207%2Fs15516709cog2703_7", "http://doi.org/10.1371%2Fjournal.pcbi.1000443", "http://doi.org/10.1371%2Fjournal.pcbi.1000937", "http://doi.org/10.2200%2FS00639ED1V01Y201504HLT027", "http://doi.org/10.3115%2F1072228.1072318", "http://doi.org/10.5311%2Fjosis.2011.2.3", "http://www.josis.org/index.php/josis/article/view/26/23", "http://wiki.openstreetmap.org/wiki/OSM_Semantic_Network", "http://www.semantic-measures-library.org/", "http://semanticsimilarity.org/", "http://www.worldcat.org/issn/1432-7643", "http://wwwconference.org/proceedings/www2005/docs/p107.pdf", "http://xldb.di.fc.ul.pt/biotools/cmpsim/", "http://labs.fc.ul.pt/dishin/", "http://webpages.fc.ul.pt/~fjcouto/files/journal%20fcouto-jbcb2013%20preprint.pdf", "http://xldb.fc.ul.pt/biotools/cessm/", "http://xldb.fc.ul.pt/biotools/proteinon/", "http://xldb.fc.ul.pt/wiki/Geo-Net-PT_02_in_English", "http://xldb.fc.ul.pt/wiki/Geographic_Similarity_calculator_GeoSSM", "http://xldb.fc.ul.pt/xldb/publications/Ferreira.etal:GenericSemanticRelatedness:2011_document.pdf", "https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-9-S5-S4", "https://github.com/lasigeBioTM/DiShIn", "https://www.hindawi.com/journals/cin/2015/712835/", "https://link.springer.com/article/10.1007/s00500-016-2438-x", "https://link.springer.com/chapter/10.1007/978-3-642-36973-5_97?no-access=true", "https://www.researchgate.net/publication/220105255_A_context-aware_semantic_similarity_model_for_ontology", "https://www.researchgate.net/publication/44241193_A_Hybrid_Concept_Similarity_Measure_Model_for_Ontology_Environment", "https://www.aclweb.org/aclwiki/index.php?title=Similarity_(State_of_the_art)", "https://dl.acm.org/citation.cfm?id=1434078", "https://arxiv.org/pdf/1402.3371", "https://arxiv.org/pdf/cmp-lg/9709008.pdf", "https://arxiv.org/pdf/cs/0212033", "https://www.cambridge.org/core/journals/natural-language-engineering/article/recent-advances-in-methods-of-lexical-semantic-relatedness-a-survey/35BA94697B86B4B797FCF3ACCDE24FBD", "https://doi.org/10.1007%2F978-3-540-87696-0_7", "https://dx.doi.org/10.1371/journal.pcbi.1000937", "https://cloudfront.escholarship.org/dist/prd/content/qt0p7528tp/qt0p7528tp.pdf", "https://www.cs.york.ac.uk/semeval-2012/task6/"]}, "Correlation function (astronomy)": {"categories": ["Covariance and correlation", "Extragalactic astronomy"], "title": "Correlation function (astronomy)", "method": "Correlation function (astronomy)", "url": "https://en.wikipedia.org/wiki/Correlation_function_(astronomy)", "summary": "In astronomy, a correlation function describes the distribution of galaxies in the universe. By default, \"correlation function\" refers to the two-point autocorrelation function. For a given distance, the two-point autocorrelation function is a function of one variable (distance) which describes the probability that two galaxies are separated by this particular distance. It can be thought of as a lumpiness factor - the higher the value for some distance scale, the more lumpy the universe is at that distance scale.\nThe following definition (from Peebles 1980) is often cited: \n\nGiven a random galaxy in a location, the correlation function describes the probability that another galaxy will be found within a given distance.However, it can only be correct in the statistical sense that it is averaged over a large number of galaxies chosen as the first, random galaxy. If just one random galaxy is chosen, then the definition is no longer correct, firstly because it is meaningless to talk of just one \"random\" galaxy, and secondly because the function will vary wildly depending on which galaxy is chosen, in contradiction with its definition as a function.\nThe spatial correlation function \n \n \n \n \u03be\n (\n r\n )\n \n \n {\\displaystyle \\xi (r)}\n is related to the Fourier space power spectrum of the galaxy distribution, \n \n \n \n P\n (\n k\n )\n \n \n {\\displaystyle P(k)}\n , as\n\n \n \n \n \u03be\n (\n r\n )\n =\n \n \n 1\n \n 2\n \n \u03c0\n \n 2\n \n \n \n \n \n \u222b\n d\n k\n \n \n k\n \n 2\n \n \n P\n (\n k\n )\n \n \n \n \n sin\n \u2061\n (\n k\n r\n )\n \n \n k\n r\n \n \n \n \n \n {\\displaystyle \\xi (r)={\\frac {1}{2\\pi ^{2}}}\\int dk\\,k^{2}P(k)\\,{\\frac {\\sin(kr)}{kr}}}\n \nThe n-point autocorrelation functions for n greater than 2 or cross-correlation functions for particular object types are defined similarly to the two-point autocorrelation function.\nThe correlation function is important for theoretical models of physical cosmology because it provides a means of testing models which assume different things about the contents of the universe.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/e9/Gravitational_inverse-square_law.png", "https://upload.wikimedia.org/wikipedia/commons/3/3c/Ilc_9yr_moll4096.png", "https://upload.wikimedia.org/wikipedia/commons/0/00/Crab_Nebula.jpg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["2dF Galaxy Redshift Survey", "Accelerating expansion of the universe", "Age of the universe", "Alan Guth", "Albert Einstein", "Alexander Friedmann", "Alexei Starobinsky", "Andrei Linde", "Arno Allan Penzias", "Astronomy", "BOOMERanG experiment", "Baryonic matter", "Big Bang", "Big Bang nucleosynthesis", "Big Bounce", "Big Crunch", "Big Rip", "Brian Schmidt", "Chronology of the universe", "Cold dark matter", "Correlation function", "Correlation function (disambiguation)", "Cosmic Background Explorer", "Cosmic background radiation", "Cosmic infrared background", "Cosmic microwave background", "Cosmic neutrino background", "Cross-correlation", "Dark Ages (cosmology)", "Dark Energy Survey", "Dark energy", "Dark matter", "Dark radiation", "Discovery of cosmic microwave background radiation", "Edwin Hubble", "Energy", "Euclid (spacecraft)", "Expansion of the universe", "Fourier space", "Friedmann equations", "Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker metric", "Function (mathematics)", "Future of an expanding universe", "Galaxy", "Galaxy cluster", "Galaxy filament", "Galaxy formation and evolution", "Galaxy group", "Galileo Galilei", "George F. R. Ellis", "George Gamow", "George Smoot", "Georges Lema\u00eetre", "Grand unification epoch", "Gravitational wave background", "Hadron epoch", "Hannes Alfv\u00e9n", "Heat death of the universe", "History of the Big Bang theory", "Hot dark matter", "Hubble's law", "Illustris project", "Inflation (cosmology)", "Inhomogeneous cosmology", "Isaac Newton", "John C. Mather", "J\u00fcrgen Ehlers", "Lambda-CDM model", "Large Synoptic Survey Telescope", "Large quasar group", "Lepton epoch", "List of cosmologists", "Local Group", "Marc Aaronson", "Nicholas B. Suntzeff", "Nicolaus Copernicus", "Observable universe", "Observational cosmology", "Paul Steinhardt", "Phantom energy", "Photon epoch", "Physical cosmology", "Planck (spacecraft)", "Planck epoch", "Point process", "Power spectrum", "Probability", "Quark epoch", "Quintessence (physics)", "Radiation", "Ralph Asher Alpher", "Rashid Sunyaev", "Redshift", "Reionization", "Religious interpretations of the Big Bang theory", "Richard C. Tolman", "Robert H. Dicke", "Robert Woodrow Wilson", "Roger Penrose", "Shape of the universe", "Sloan Digital Sky Survey", "Somnath Bharadwaj", "Spatial descriptive statistics", "Stephen Hawking", "Structure formation", "Supercluster", "Timeline of cosmological theories", "Ultimate fate of the universe", "Universe", "Variable (mathematics)", "Vera Rubin", "Void (astronomy)", "Warm dark matter", "Wilkinson Microwave Anisotropy Probe", "Willem de Sitter", "Yakov Borisovich Zel'dovich"], "references": ["http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1980lssu.book.....P&db_key=AST"]}, "Singular distribution": {"categories": ["All stub articles", "Probability stubs", "Statistics stubs", "Types of probability distributions"], "title": "Singular distribution", "method": "Singular distribution", "url": "https://en.wikipedia.org/wiki/Singular_distribution", "summary": "In probability, a singular distribution is a probability distribution concentrated on a set of Lebesgue measure zero, where the probability of each point in that set is zero. \n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg"], "links": ["ARGUS distribution", "Absolutely continuous", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Cantor function", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Continuous function", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Lebesgue's decomposition theorem", 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"https://books.google.com/books?id=hos6AAAAIAAJ", "https://books.google.com/books?id=xxdJgnFzNRsC&pg=PA37", "https://www.wired.com/wiredenterprise/2013/02/computer-based-math-in-estonia/", "https://blogs.wsj.com/tech-europe/2013/02/11/estonian-schools-to-teach-computer-based-math/", "https://apps3.cehd.umn.edu/artist/glossary.html", "https://www.stat.auckland.ac.nz/~iase/serj/SERJ7(2).pdf", "https://www.amstat.org/sections/educ/newsletter/v7n1/Perusing.html"]}, "Spaghetti plot": {"categories": ["Climate and weather statistics", "Commons category link is on Wikidata", "Graphic software in meteorology", "Metaphors referring to spaghetti", "Statistical charts and diagrams"], "title": "Spaghetti plot", "method": "Spaghetti plot", "url": "https://en.wikipedia.org/wiki/Spaghetti_plot", "summary": "A spaghetti plot (also known as a spaghetti chart, spaghetti diagram, or spaghetti model) is a method of viewing data to visualize possible flows through systems. Flows depicted in this manner appear like noodles, hence the coining of this term. This method of statistics was first used to track routing through factories. Visualizing flow in this manner can reduce inefficiency within the flow of a system. In regards to animal populations and weather buoys drifting through the ocean, they are drawn to study distribution and migration patterns. Within meteorology, these diagrams can help determine confidence in a specific weather forecast, as well as positions and intensities of high and low pressure systems. They are composed of deterministic forecasts from atmospheric models or their various ensemble members. Within medicine, they can illustrate the effects of drugs on patients during drug trials.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/44/Nov192001h5spaghetti5640m.png", "https://upload.wikimedia.org/wikipedia/commons/b/bb/Workflowspaghetti.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["Ade Olufeko", "Adolphe Quetelet", "Alan MacEachren", "Anticyclone", "Arthur H. Robinson", "Atmospheric model", "August Kekul\u00e9", "Bang Wong", "Ben Shneiderman", "Biological data visualization", "Blood plasma", "Borehole", "Bruce H. McCormick", "Butterfly", "Cartography", "Charles Joseph Minard", "Chart", "Chartjunk", "Chemical imaging", "Christopher R. Johnson", "Clifford A. Pickover", "Climatology", "Computer graphics", "Computer graphics (computer science)", "Crime mapping", "Cyclone", "Data visualization", "Diagram", "Edward Tufte", "Engineering drawing", "Ensemble forecasting", "Environmental Modeling Center", "Fernanda Vi\u00e9gas", "Florence Nightingale", "Flow visualization", "Fraser Stoddart", "Gaspard Monge", "George Furnas", "George G. Robertson", "Geovisualization", "Glucometer", "Graph drawing", "Graph of a function", "Graphic design", "Graphic organizer", "Hanspeter Pfister", "High-pressure area", "Howard Wainer", "Ice age", "Ideogram", "Imaging science", "Infographic", "Information science", "Information visualization", "International Standard Book Number", "Jacques Bertin", "Jock D. Mackinlay", "Karl Wilhelm Pohlke", "Lawrence J. Rosenblum", "Low-pressure area", "Mammal", "Manuel Lima", "Map", "Martin M. Wattenberg", "Mathematical diagram", "Medical imaging", "Medicine", "Mental image", "Meteorological", "Meteorology", "Michael Friendly", "Michael Maltz", "Miriah Meyer", "Misleading graph", "Molecular graphics", "Mortgage loan", "National Hurricane Center", "National Oceanic and Atmospheric Administration", "Neuroimaging", "Nigel Holmes", "North America", "Nurse", "Ocean", "Otto Neurath", "Paleotempestology", "Pat Hanrahan", "Patent drawing", "Photograph", "Pictogram", "Plot (graphics)", "Precipitation (meteorology)", "Pressure", "Progesterone", "Rudolf Modley", "Schematic", "Scientific modelling", "Scientific visualization", "Skeletal formula", "Software visualization", "Spaghetti", "Spatial analysis", "Statistical graphics", "Stuart Card", "Table (information)", "Tamara Munzner", "Technical drawing", "Technical illustration", "Temperature", "Thomas A. DeFanti", "Tropical cyclone track forecasting", "User interface", "User interface design", "Visual analytics", "Visual culture", "Visual perception", "Visualization (computer graphics)", "Visualization (graphics)", "Volume cartography", "Volume rendering", "Weather buoy", "Weather forecast", "William Playfair"], "references": ["http://www.ncl.ucar.edu/Applications/tigge.shtml", "http://www.emc.ncep.noaa.gov/gmb/ens/spaghetti/spag_frame.htm", "http://www.nhc.noaa.gov/archive/2007/ep02/ep022007.discus.003.shtml", "https://books.google.com/books?id=0p6ccHR5b6QC&pg=PA97&dq=spaghetti+diagram+book&hl=en&ei=TkddTbqJLcnKgQf-k5H2DA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CEUQ6AEwAQ#v=onepage&q=spaghetti%20diagram%20book&f=false", "https://books.google.com/books?id=4IklOX1KAEwC&pg=PA130&dq=spaghetti+diagram+book&hl=en&ei=rlFdTdKnKo2ugQfPqtHQDA&sa=X&oi=book_result&ct=result&resnum=7&ved=0CFEQ6AEwBjgK#v=onepage&q=spaghetti%20diagram%20book&f=false", "https://books.google.com/books?id=Ax2d94PODgIC&pg=PA341&dq=spaghetti+diagram+forecast+model+book&hl=en&ei=EVNdTYW5EoHMgQf_gK2iDQ&sa=X&oi=book_result&ct=result&resnum=6&ved=0CFcQ6AEwBQ#v=onepage&q&f=false", "https://books.google.com/books?id=K-gT2_Ukk0QC&pg=PA264&dq=spaghetti+plot+book&hl=en&ei=fXldTaeFAcKclgeJ6JTXCg&sa=X&oi=book_result&ct=result&resnum=7&ved=0CGAQ6AEwBg#v=onepage&q=spaghetti%20plot%20book&f=false", "https://books.google.com/books?id=Ny0Rs1PwRiQC&pg=PA2&dq=spaghetti+plot+book&hl=en&ei=fXldTaeFAcKclgeJ6JTXCg&sa=X&oi=book_result&ct=result&resnum=6&ved=0CFoQ6AEwBQ#v=onepage&q=spaghetti%20plot%20book&f=false", "https://books.google.com/books?id=Oa5m8gZcGjMC&pg=PA103&dq=spaghetti+diagram+history+book&hl=en&ei=92ldTdWCH5D3gAeTpYSPDQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CD0Q6AEwAA#v=onepage&q=spaghetti%20diagram%20history%20book&f=false", "https://books.google.com/books?id=TRwucwebYMcC&pg=PA54&dq=spaghetti+plot+book&hl=en&ei=fXldTaeFAcKclgeJ6JTXCg&sa=X&oi=book_result&ct=result&resnum=4&ved=0CE4Q6AEwAw#v=onepage&q=spaghetti%20plot%20book&f=false", "https://books.google.com/books?id=ZNroiySUreQC&pg=PT31&dq=spaghetti+plot+flaw&hl=en&ei=onNdTcuVCMXZgQeOh9CVBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCcQ6AEwAA#v=onepage&q&f=false", "https://books.google.com/books?id=ev54lAwS2KIC&pg=PA128&dq=spaghetti+diagram+book&hl=en&ei=PPhbTbSDAcXPgAfJhfWVDQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CEAQ6AEwAA#v=onepage&q=spaghetti%20diagram%20book&f=false", "https://books.google.com/books?id=gJFJ1A7aR-8C&pg=PA127&dq=spaghetti+diagram+book&hl=en&ei=TkddTbqJLcnKgQf-k5H2DA&sa=X&oi=book_result&ct=result&resnum=3&ved=0CEoQ6AEwAg#v=onepage&q=spaghetti%20diagram%20book&f=false", "https://books.google.com/books?id=tJjmtOqWhrMC&pg=PA52&dq=spaghetti+diagram+history+book&hl=en&ei=92ldTdWCH5D3gAeTpYSPDQ&sa=X&oi=book_result&ct=result&resnum=7&ved=0CF0Q6AEwBg#v=onepage&q=spaghetti%20diagram%20history%20book&f=false", "https://books.google.com/books?id=w2Jye1p-MBEC&pg=PA76&dq=spaghetti+diagram+history+book&hl=en&ei=92ldTdWCH5D3gAeTpYSPDQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CE0Q6AEwAw#v=onepage&q=spaghetti%20diagram&f=false"]}, "Inverse probability": {"categories": ["Bayesian statistics", "Probability interpretations", "Statistical inference"], "title": "Inverse probability", "method": "Inverse probability", "url": "https://en.wikipedia.org/wiki/Inverse_probability", "summary": "In probability theory, inverse probability is an obsolete term for the probability distribution of an unobserved variable.\nToday, the problem of determining an unobserved variable (by whatever method) is called inferential statistics, the method of inverse probability (assigning a probability distribution to an unobserved variable) is called Bayesian probability, the \"distribution\" of data given the unobserved variable is rather the likelihood function (which is not a probability distribution), and the distribution of an unobserved variable, given both data and a prior distribution, is the posterior distribution. The development of the field and terminology from \"inverse probability\" to \"Bayesian probability\" is described by Fienberg (2006).\n\nThe term \"inverse probability\" appears in an 1837 paper of De Morgan, in reference to Laplace's method of probability (developed in a 1774 paper, which independently discovered and popularized Bayesian methods, and 1812 book), though the term \"inverse probability\" does not occur in these. Fisher uses the term in 1922, referring to \"the fundamental paradox of inverse probability\" as the source of the confusion between statistical terms that refer to the true value to be estimated, with the actual value arrived at by the estimation method, which is subject to error. \n, (See reprint in \n.)\nLater Jeffreys uses the term in his defense of the methods of Bayes and Laplace, in 1939. The term \"Bayesian\", which displaced \"inverse probability\", was introduced by Ronald Fisher around 1950.\nInverse probability, variously interpreted, was the dominant approach to statistics until the development of frequentism in the early 20th century by Ronald Fisher, Jerzy Neyman and Egon Pearson. Following the development of frequentism, the terms frequentist and Bayesian developed to contrast these approaches, and became common in the 1950s.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/aa/Youngronaldfisher2.JPG", "https://upload.wikimedia.org/wikipedia/commons/archive/a/aa/20180707072216%21Youngronaldfisher2.JPG"], "links": ["Astronomy", "Augustus De Morgan", "Bayes' theorem", "Bayesian probability", "Bayesian statistics", "Biology", "Digital object identifier", "Egon Pearson", "Frequentist inference", "Frequentist probability", "Inferential statistics", "Jerzy Neyman", "Laplace", "Likelihood function", "Navigation", "Posterior distribution", "Prior distribution", "Probability distribution", "Probability theory", "Ronald Fisher"], "references": ["http://doi.org/10.1214%2F06-BA101", "https://projecteuclid.org/download/pdf_1/euclid.ba/1340371071"]}, "Hidden Markov random field": {"categories": ["Markov networks"], "title": "Hidden Markov random field", "method": "Hidden Markov random field", "url": "https://en.wikipedia.org/wiki/Hidden_Markov_random_field", "summary": "In statistics, a hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying Markov random field.\nSuppose that we observe a random variable \n \n \n \n \n Y\n \n i\n \n \n \n \n {\\displaystyle Y_{i}}\n , where \n \n \n \n i\n \u2208\n S\n \n \n {\\displaystyle i\\in S}\n . Hidden Markov random fields assume that the probabilistic nature of \n \n \n \n \n Y\n \n i\n \n \n \n \n {\\displaystyle Y_{i}}\n is determined by the unobservable Markov random field \n \n \n \n \n X\n \n i\n \n \n \n \n {\\displaystyle X_{i}}\n , \n \n \n \n i\n \u2208\n S\n \n \n {\\displaystyle i\\in S}\n .\nThat is, given the neighbors \n \n \n \n \n N\n \n i\n \n \n \n \n {\\displaystyle N_{i}}\n of \n \n \n \n \n X\n \n i\n \n \n ,\n \n X\n \n i\n \n \n \n \n {\\displaystyle X_{i},X_{i}}\n is independent of all other \n \n \n \n \n X\n \n j\n \n \n \n \n {\\displaystyle X_{j}}\n (Markov property).\nThe main difference with a hidden Markov model is that neighborhood is not defined in 1 dimension but within a network, i.e. \n \n \n \n \n X\n \n i\n \n \n \n \n {\\displaystyle X_{i}}\n is allowed to have more than the two neighbors that it would have in a Markov chain. The model is formulated in such a way that given \n \n \n \n \n X\n \n i\n \n \n \n \n {\\displaystyle X_{i}}\n , \n \n \n \n \n Y\n \n i\n \n \n \n \n {\\displaystyle Y_{i}}\n are independent (conditional independence of the observable variables given the Markov random field).\nIn the vast majority of the related literature, the number of possible latent states is considered a user-defined constant. However, ideas from nonparametric Bayesian statistics, which allow for data-driven inference of the number of states, have been also recently investigated with success, e.g.", "images": [], "links": ["Bayesian network", "Hidden Markov model", "Markov chain", "Markov network", "Markov random field"], "references": ["http://ieeexplore.ieee.org/document/5458106/", "http://www.fmrib.ox.ac.uk/analysis/techrep/tr00yz1/tr00yz1/node5.html", "http://www.fmrib.ox.ac.uk/analysis/techrep/tr00yz1/tr00yz1/tr00yz1.html"]}, "Erd\u0151s\u2013R\u00e9nyi model": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2015", "Paul Erd\u0151s", "Random graphs"], "title": "Erd\u0151s\u2013R\u00e9nyi model", "method": "Erd\u0151s\u2013R\u00e9nyi model", "url": "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model", "summary": "In the mathematical field of graph theory, the Erd\u0151s\u2013R\u00e9nyi model is either of two closely related models for generating random graphs. They are named after mathematicians Paul Erd\u0151s and Alfr\u00e9d R\u00e9nyi, who first introduced one of the models in 1959, while Edgar Gilbert introduced the other model contemporaneously and independently of Erd\u0151s and R\u00e9nyi. In the model of Erd\u0151s and R\u00e9nyi, all graphs on a fixed vertex set with a fixed number of edges are equally likely; in the model introduced by Gilbert, each edge has a fixed probability of being present or absent, independently of the other edges. These models can be used in the probabilistic method to prove the existence of graphs satisfying various properties, or to provide a rigorous definition of what it means for a property to hold for almost all graphs.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/13/Erdos_generated_network-p0.01.jpg", "https://upload.wikimedia.org/wikipedia/commons/d/d2/Internet_map_1024.jpg"], "links": ["Adjacency list", "Adjacency matrix", "Agent-based model", "Alfr\u00e9d R\u00e9nyi", "Almost all", "Almost surely", "ArXiv", "Artificial neural network", "Assortativity", "Balance theory", "Barab\u00e1si\u2013Albert model", "Betweenness centrality", "Bibcode", "Binomial distribution", "Biological network", "Bipartite graph", "Boolean network", "Centrality", "Clique (graph theory)", "Closeness (graph theory)", "Clustering coefficient", "Combinatorial optimization", "Community structure", "Complete graph", "Complex contagion", "Complex network", "Computer network", "Connected component (graph theory)", "Connectedness", "Countability", "Cut (graph theory)", "Cycle (graph theory)", "Degree (graph theory)", "Degree distribution", "Dependency network", "Digital object identifier", "Directed graph", "Distance (graph theory)", "Dual-phase evolution", "Edgar Gilbert", "Edge (graph theory)", "Efficiency (network science)", "Epidemic model", "Evolving networks", "Exponential random graph models", "Fitness model (network theory)", "Flow network", "Giant component", "Graph (abstract data type)", "Graph (discrete mathematics)", "Graph drawing", "Graph theory", "Hamiltonian path", "Hierarchical network model", "Homophily", "Hyperbolic geometric graph", "Hypergraph", "Incidence list", "Incidence matrix", "Interdependent networks", "International Standard Book Number", "Lancichinetti\u2013Fortunato\u2013Radicchi benchmark", "Lattice (group)", "Law of large numbers", "Link analysis", "List of algorithms", "List of network scientists", "List of network theory topics", "Loop (graph theory)", "Mean field theory", "Metrics (networking)", "Modularity (networks)", "Monotonic function", "Multigraph", "NP-complete", "Neighbourhood (graph theory)", "Network controllability", "Network effect", "Network motif", "Network on a chip", "Network science", "Network theory", "PageRank", "Path (graph theory)", "Paul Erd\u0151s", "Percolation theory", "Physics", "Poisson distribution", "Preferential attachment", "Probabilistic method", "PubMed Identifier", "Rado graph", "Random geometric graph", "Random graph", "Reciprocity (network science)", "SIR model", "Scale-free network", "Scientific collaboration network", "Semantic network", "Shlomo Havlin", "Small-world network", "Social capital", "Social influence", "Social network", "Social network analysis software", "Spatial network", "Statistical independence", "Stochastic block model", "Telecommunications network", "Threshold function", "Transitive relation", "Transport network", "Triadic closure", "Vertex (graph theory)", "Watts and Strogatz model", "Weighted network"], "references": ["http://adsabs.harvard.edu/abs/1976MPCPS..80..419B", "http://adsabs.harvard.edu/abs/2001PhRvE..64b6118N", "http://adsabs.harvard.edu/abs/2003PhRvE..67d6107R", "http://adsabs.harvard.edu/abs/2010Natur.464.1025B", "http://www.ncbi.nlm.nih.gov/pubmed/20393559", "http://www.renyi.hu/~p_erdos/1959-11.pdf", "http://www.renyi.hu/~p_erdos/1960-10.pdf", "http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all", "http://havlin.biu.ac.il/Shlomo%20Havlin%20books_com_net.php", "http://arxiv.org/abs/0907.1182", "http://arxiv.org/abs/cond-mat/0007235", "http://arxiv.org/abs/cond-mat/0212469", "http://doi.org/10.1017%2FS0305004100053056", "http://doi.org/10.1038%2Fnature08932", "http://doi.org/10.1103%2FPhysRevE.64.026118", "http://doi.org/10.1103%2FPhysRevE.67.046107", "http://doi.org/10.1214%2Faoms%2F1177706098"]}, "Mean percentage error": {"categories": ["Summary statistics"], "title": "Mean percentage error", "method": "Mean percentage error", "url": "https://en.wikipedia.org/wiki/Mean_percentage_error", "summary": "In statistics, the mean percentage error (MPE) is the computed average of percentage errors by which forecasts of a model differ from actual values of the quantity being forecast.\nThe formula for the mean percentage error is:\n\n \n \n \n \n MPE\n \n =\n \n \n \n 100\n %\n \n n\n \n \n \n \u2211\n \n t\n =\n 1\n \n \n n\n \n \n \n \n \n \n a\n \n t\n \n \n \u2212\n \n f\n \n t\n \n \n \n \n a\n \n t\n \n \n \n \n \n \n {\\displaystyle {\\text{MPE}}={\\frac {100\\%}{n}}\\sum _{t=1}^{n}{\\frac {a_{t}-f_{t}}{a_{t}}}}\n where at is the actual value of the quantity being forecast, ft is the forecast, and n is the number of different times for which the variable is forecast.\nBecause actual rather than absolute values of the forecast errors are used in the formula, positive and negative forecast errors can offset each other; as a result the formula can be used as a measure of the bias in the forecasts.\nA disadvantage of this measure is that it is undefined whenever a single actual value is zero.", "images": [], "links": ["Bias (statistics)", "Errors and residuals in statistics", "International Standard Book Number", "Mean absolute percentage error", "Mean squared error", "Mean squared prediction error", "Minimum mean-square error", "Peak signal-to-noise ratio", "Percentage error", "Root mean square deviation", "Squared deviations", "Statistics"], "references": []}, "Correlation does not imply causation": {"categories": ["All accuracy disputes", "All articles with unsourced statements", "Articles with disputed statements from November 2017", "Articles with short description", "Articles with unsourced statements from August 2016", "Articles with unsourced statements from July 2009", "Articles with unsourced statements from July 2015", "Articles with unsourced statements from June 2017", "CS1 maint: Multiple names: authors list", "Causal fallacies", "Causal inference", "Covariance and correlation", "English phrases", "Misuse of statistics", "Webarchive template wayback links", "Wikipedia articles needing clarification from August 2016"], "title": "Correlation does not imply causation", "method": "Correlation does not imply causation", "url": "https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation", "summary": "In statistics, many statistical tests calculate correlations between variables and when two variables are found to be correlated, it is tempting to assume that this shows that one variable causes the other. That \"correlation proves causation\" is considered a questionable cause logical fallacy when two events occurring together are taken to have established a cause-and-effect relationship. This fallacy is also known as cum hoc ergo propter hoc, Latin for \"with this, therefore because of this\", and \"false cause\". A similar fallacy, that an event that followed another was necessarily a consequence of the first event, is the post hoc ergo propter hoc (Latin for \"after this, therefore because of this.\") fallacy.\nFor example, in a widely studied case, numerous epidemiological studies showed that women taking combined hormone replacement therapy (HRT) also had a lower-than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD. But randomized controlled trials showed that HRT caused a small but statistically significant increase in risk of CHD. Re-analysis of the data from the epidemiological studies showed that women undertaking HRT were more likely to be from higher socio-economic groups (ABC1), with better-than-average diet and exercise regimens. The use of HRT and decreased incidence of coronary heart disease were coincident effects of a common cause (i.e. the benefits associated with a higher socioeconomic status), rather than a direct cause and effect, as had been supposed.As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not imply that the resulting conclusion is false. In the instance above, if the trials had found that hormone replacement therapy does in fact have a negative incidence on the likelihood of coronary heart disease the assumption of causality would have been correct, although the logic behind the assumption would still have been flawed. Indeed, a few go further, using correlation as a basis for testing a hypothesis to try to establish a true causal relationship; examples are the Granger causality test, convergent cross mapping, and Liang-Kleeman information flow.", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/d/db/Symbol_list_class.svg"], "links": ["Accident (fallacy)", "Affirming the consequent", "Al-Ghazali", "Alignments of random points", "Ambiguity", "Anecdotal evidence", "Animistic fallacy", "Apophenia", "Argument from analogy", "Aristotle", "Bald\u2013hairy", "Base rate fallacy", "Begging the question", "Bible code", "Biology", "Body mass index", "British Medical Association", "Butterfly effect", "CNN", "Carbon dioxide", "Causality", "Causality (physics)", "Cherry picking", "Cheshire, Connecticut", "Cholesterol", "Circular analysis", "Circular cause and consequence", "Circular logic", "Circular reasoning", "Classical mechanics", "Coefficient of determination", "Coincidence", "Complex question", "Confounding", "Confusion of the inverse", "Conjunction fallacy", "Continuum fallacy", "Convergent cross mapping", "Converse accident", "Coronary heart disease", "Correlation and dependence", "Correlation does not imply causation", "Correlative-based fallacies", "Counterfactual", "Data dredging", "David Hume", "Denying the correlative", "Dependent and independent variables", "Descartes", "Design of experiments", "Digital object identifier", "Direct election", "Discipline (specialism)", "Double-barreled question", "Double-blind", "Double counting (fallacy)", "Drunkenness", "East Lansing, Michigan", "Ecological fallacy", "Economics", "Education economics", "Edward Tufte", "Effect size", "Epidemiological study", "Equivocation", "Exogenous", "Experiment", "Fallacies of illicit transference", "Fallacy", "Fallacy of accent", "Fallacy of composition", "Fallacy of division", "Fallacy of the single cause", "False attribution", "False dilemma", "False equivalence", "False precision", "Faulty generalization", "Fever", "Field (physics)", "Four causes", "French paradox", "Furtive fallacy", "GDP", "Gambler's fallacy", "Gateway drug theory", "George Davey Smith", "Granger causality", "Graphics Press", "High-density lipoprotein", "Hormone replacement therapy (menopause)", "How to Lie with Statistics", "Human capital", "Human swimming", "Illusory correlation", "Immanuel Kant", "Impact (mechanics)", "Impression management", "Inertia", "Infant", "Informal fallacy", "Instrumental variables", "International Standard Book Number", "Inverse gambler's fallacy", "JSTOR", "Joint effect", "Journal of the American Statistical Association", "Latin", "Law", "Leading question", "Lies, damned lies, and statistics", "Life-time of correlation", "List of fallacies", "Loaded language", "Loaded question", "Logic", "Logical consequence", "Loki's Wager", "London", "Look-elsewhere effect", "Louse", "Lurking variable", "Marijuana", "Material conditional", "McNamara fallacy", "Mechanism (philosophy)", "Michigan State University Press", "Middle Ages", "Mierscheid law", "Misleading graph", "Misuse of statistics", "Moving the goalposts", "Multiple comparisons problem", "Myopia", "NRS social grade", "Nate Silver", "Nature (journal)", "Nature Publishing Group", "New York City", "Nirvana fallacy", "No true Scotsman", "Nonlinear system", "Normally distributed and uncorrelated does not imply independent", "Obesity", "Occasionalism", "Ohio State University", "Overwhelming exception", "P-value", "Penguin Books", "Penn Presbyterian Medical Center", "Philosophy", "Physical activity", "Physical law", "Physics", "Pirates in terms of global warming", "Post hoc analysis", "Post hoc ergo propter hoc", "Potential energy", "Predation", "Problem of induction", "Psychiatric disorder", "PubMed Identifier", "Quantum mechanics", "Questionable cause", "Quoting out of context", "Randomized controlled trials", "Recreational drug use", "Redskins Rule", "Regression analysis", "Regression fallacy", "Reification (fallacy)", "Reproducibility", "Ronald Fisher", "Sampling bias", "Screening (economics)", "Second law of thermodynamics", "Secundum quid", "Self medication", "Signalling (economics)", "Slippery slope", "Slothful induction", "Social Democratic Party of Germany", "Social science", "Socio-economic group", "Sorites paradox", "Spacetime", "Spurious relationship", "Statistical mechanics", "Statistical significance", "Statistical tests", "Statistics", "Sufficient condition", "Suppressed correlative", "Syntactic ambiguity", "Television", "Testing hypotheses suggested by the data", "Texas sharpshooter fallacy", "The BMJ", "The Signal and the Noise", "Thermodynamic free energy", "Thermodynamics", "Thermometer", "Tobacco and lung cancer", "Tobacco industry", "Twin study", "United States Presidential Election 2004", "United States Presidential Election 2012", "University of Pennsylvania", "Vagueness", "Variable (mathematics)", "Verificationism", "Washington Redskins", "Wayback Machine"], "references": ["http://www.cnn.com/HEALTH/9905/12/children.lights/index.html", "http://www.edwardtufte.com/tufte/powerpoint", "http://www.huffingtonpost.com/dr-dean-ornish/cholesterol-the-good-the-_b_870655.html", "http://www.opifexphoenix.com/reasoning/fallacies/ignorecc.htm", "http://tylervigen.com/spurious-correlations", "http://www.tylervigen.com/", "http://researchnews.osu.edu/archive/nitelite.htm", "http://plato.stanford.edu/archives/spr2001/entries/hume/#CausationN", "http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf", "http://singapore.cs.ucla.edu/LECTURE/lecture_sec1.htm", "http://www.ncbi.nlm.nih.gov/pubmed/10335839", "http://www.ncbi.nlm.nih.gov/pubmed/10724157", "http://www.ncbi.nlm.nih.gov/pubmed/10724158", "http://www.ncbi.nlm.nih.gov/pubmed/15166201", "http://www.ncbi.nlm.nih.gov/pubmed/29957352", "http://www.americanscientist.org/issues/pub/what-everyone-should-know-about-statistical-correlation", "http://doi.org/10.1016%2Fj.envint.2018.06.023", "http://doi.org/10.1038%2F182108a0", "http://doi.org/10.1038%2F182596a0", "http://doi.org/10.1038%2F20094", "http://doi.org/10.1038%2F35004661", "http://doi.org/10.1038%2F35004663", "http://doi.org/10.1038%2F35004665", "http://doi.org/10.1080%2F01621459.1986.10478354", "http://doi.org/10.1093%2Fije%2Fdyh124", "http://doi.org/10.1136%2Fbmj.2.5035.43", "http://doi.org/10.1136%2Fbmj.2.5039.297-b", "http://doi.org/10.1163%2F156852876x00101", "http://doi.org/10.1214%2Fss%2F1177009870", "http://www.jstor.org/stable/2246135", "http://www.jstor.org/stable/25383068", "http://www.jstor.org/stable/25383439", "http://www.jstor.org/stable/4181986", "http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/", "http://www.sciencebasedmedicine.org/evidence-in-medicine-correlation-and-causation/", "http://www.sciencebasedmedicine.org/index.php/evidence-in-medicine-correlation-and-causation/", "http://www.economics.soton.ac.uk/staff/aldrich/spurious.pdf", "https://books.google.com/books?id=1gJPXv5wQbIC", "https://books.google.com/books?id=yWWEIvNgUQ4C", "https://www.mdpi.com/1099-4300/15/1/327", "https://krugman.blogs.nytimes.com/2013/04/16/reinhart-rogoff-continued/?_r=0", "https://www.sciencedirect.com/science/article/pii/S0160412018307098", "https://web.archive.org/web/20060219042545/http://www.economics.soton.ac.uk/staff/aldrich/spurious.pdf", "https://web.archive.org/web/20060901152949/http://researchnews.osu.edu/archive/nitelite.htm", "https://web.archive.org/web/20090522103015/http://www.opifexphoenix.com/reasoning/fallacies/ignorecc.htm", "https://www.york.ac.uk/depts/maths/histstat/fisher272.pdf", "https://www.york.ac.uk/depts/maths/histstat/fisher274.pdf", "https://www.york.ac.uk/depts/maths/histstat/fisher275.pdf", "https://www.york.ac.uk/depts/maths/histstat/fisher276.pdf"]}, "Weibull distribution": {"categories": ["All articles lacking in-text citations", "All articles with unsourced statements", "Articles lacking in-text citations from June 2010", "Articles with unsourced statements from December 2017", "Articles with unsourced statements from June 2010", "Articles with unsourced statements from May 2011", "Continuous distributions", "Exponential family distributions", "Extreme value data", "Pages using deprecated image syntax", "Survival analysis"], "title": "Weibull distribution", "method": "Weibull distribution", "url": "https://en.wikipedia.org/wiki/Weibull_distribution", "summary": "In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1951, although it was first identified by Fr\u00e9chet (1927) and first applied by Rosin & Rammler (1933) to describe a particle size distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/2/29/FitWeibullDistr.tif", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7e/Weibull_CDF.svg", "https://upload.wikimedia.org/wikipedia/commons/5/58/Weibull_PDF.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asbestosis", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Bathtub curve", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Channel (communications)", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Comminution", "Compound Poisson distribution", "Confidence belt", "Conway\u2013Maxwell\u2013Poisson distribution", "Crusher", "CumFreq", "Cumulative distribution function", "Cumulative frequency analysis", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Delivery (commerce)", "Diffusion of innovations", "Digital object identifier", "Dirac delta distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Distribution fitting", "Electrical engineering", "Elliptical distribution", "Empirical cumulative distribution function", "Encyclopedia of Mathematics", "Entropy (information theory)", "Erlang distribution", "Euler\u2013Mascheroni constant", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponentiated Weibull distribution", "Extended negative binomial distribution", "Extreme value theory", "F-distribution", "Fading channel", "Failure analysis", "Failure rate", "Fisher's z-distribution", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General insurance", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Granular material", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hydrology", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Industrial engineering", "Information entropy", "Information retrieval", "International Standard Book Number", "Interpolation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "John Wiley & Sons", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "Lindy effect", "List of probability distributions", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Manufacturing", "Marchenko\u2013Pastur distribution", "Mass fraction (chemistry)", "Materials science", "Mathematical Reviews", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maurice Fr\u00e9chet", "Maximum entropy distribution", "Maximum entropy probability distribution", "Maximum likelihood estimation", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Meijer G-function", "Michiel Hazewinkel", "Mill (grinding)", "Mineral processing", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Moment generating function", "Monotonic function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "National Institute of Standards and Technology", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Particle-size distribution", "Particle size distribution", "Pearson distribution", "Phase-type distribution", "Plotting position", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Power series", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Q plot", "Q-Weibull distribution", "Q-exponential distribution", "Radar", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Raw moment", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Reinsurance", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Rice distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Shape parameter", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Spreadsheet", "Stable distribution", "Statistics", "Stretched exponential function", "Student's t-distribution", "Support (mathematics)", "Survival analysis", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unimodal function", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Waloddi Weibull", "Weather forecasting", "Weibull fading", "Weibull modulus", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wind power", "Wireless", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.mathworks.com.au/help/stats/rayleigh-distribution.html", "http://www.barringer1.com/wa_files/Weibull-ASME-Paper-1951.pdf", "http://www.crgraph.com/Weibull.pdf", "http://www.mathpages.com/home/kmath122/kmath122.htm", "http://www.reliafy.com/", "http://www.statsoft.com/textbook/survival-failure-time-analysis/#distribution", "http://www.sys-ev.com/reliability01.htm", "http://www.math.wm.edu/~leemis/chart/UDR/UDR.html", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm", "http://www.itl.nist.gov/div898/handbook/eda/section3/weibplot.htm", "http://dl.acm.org/citation.cfm?id=1835449.1835513", "http://www.ams.org/mathscinet-getitem?mr=1299979", "http://www.ams.org/mathscinet-getitem?mr=2237527", "http://doi.org/10.1016%2F0040-1625(80)90026-8", "http://doi.org/10.1016%2Fj.coastaleng.2007.05.001", "http://doi.org/10.1016%2Fj.ress.2011.09.003", "http://doi.org/10.1080%2F01621459.1973.10481432", "http://doi.org/10.1109%2FTIT.2005.855598", "http://doi.org/10.1145%2F1835449.1835513", "http://www.erpt.org/014Q/nelsa-06.htm", "http://reliawiki.org/index.php/The_Weibull_Distribution", "http://www.reuk.co.uk/Wind-Speed-Distribution-Weibull.htm", "https://www.waterlog.info/cumfreq.htm", "https://www.encyclopediaofmath.org/index.php?title=p/w097370"]}, "Brownian bridge": {"categories": ["Empirical process", "Wiener process"], "title": "Brownian bridge", "method": "Brownian bridge", "url": "https://en.wikipedia.org/wiki/Brownian_bridge", "summary": "A Brownian bridge is a continuous-time stochastic process B(t) whose probability distribution is the conditional probability distribution of a Wiener process W(t) (a mathematical model of Brownian motion) subject to the condition (when standardized) that W(T) = 0, so that the process is pinned at the origin at both t=0 and t=T. More precisely:\n\n \n \n \n \n B\n \n t\n \n \n :=\n (\n \n W\n \n t\n \n \n \u2223\n \n W\n \n T\n \n \n =\n 0\n )\n ,\n \n t\n \u2208\n [\n 0\n ,\n T\n ]\n \n \n {\\displaystyle B_{t}:=(W_{t}\\mid W_{T}=0),\\;t\\in [0,T]}\n The expected value of the bridge is zero, with variance \n \n \n \n \n \n \n \n t\n (\n T\n \u2212\n t\n )\n \n T\n \n \n \n \n \n {\\displaystyle \\textstyle {\\frac {t(T-t)}{T}}}\n , implying that the most uncertainty is in the middle of the bridge, with zero uncertainty at the nodes. The covariance of B(s) and B(t) is s(T \u2212 t)/T if s < t.\nThe increments in a Brownian bridge are not independent.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/6b/Brownian_bridge.png"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Conditional probability distribution", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Covariance", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Expected value", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Independent identically distributed", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Karhunen\u2013Lo\u00e8ve theorem", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kolmogorov\u2013Smirnov test", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Normal distribution", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistical inference", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": []}, "Probabilistic metric space": {"categories": ["All stub articles", "Mathematical analysis stubs", "Metric geometry", "Probability distributions"], "title": "Probabilistic metric space", "method": "Probabilistic metric space", "url": "https://en.wikipedia.org/wiki/Probabilistic_metric_space", "summary": "A probabilistic metric space is a generalization of metric spaces where the distance has no longer values in non-negative real numbers, but in distribution functions. \nLet D+ be the set of all probability distribution functions F such that F(0) = 0 (F is a nondecreasing, left\ncontinuous mapping from \n \n \n \n \n R\n \n \n \n {\\displaystyle \\mathbb {R} }\n into [0, 1] such that max(F) = 1).\nThe ordered pair (S,F) is said to be a probabilistic metric space if S is a nonempty set and F: S\u00d7S \u2192\nD+ (F(p, q) is denoted by Fp,q for every (p, q) \u2208 S \u00d7 S) satisfies the following conditions:\n\nFu,v(x) = 1 for every x > 0 \u21d4 u = v (u, v \u2208 S).\nFu,v = Fv,u for every u, v \u2208 S.\nFu,v(x) = 1 and Fv,w(y) = 1 \u21d2 Fu,w(x + y) = 1 f or u, v, w \u2208 S and x, y \u2208 R+.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c9/Lebesgue_Icon.svg", "https://upload.wikimedia.org/wikipedia/commons/1/13/Probability_metric_DNN.png"], "links": ["Continuous mapping", "Dirac delta", "Distance", "Error function", "Euclidean metric", "Expected value", "Identity of indiscernibles", "Mathematical analysis", "Maximum", "Mean", "Metric (mathematics)", "Metric space", "Metric spaces", "Nonempty set", "Normal distribution", "Ordered pair", "Probability distribution function", "Random variable", "Random vector", "Real number", "Standard deviation"], "references": []}, "Principal component analysis": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2014", "Articles with unsourced statements from March 2011", "Articles with unsourced statements from May 2018", "CS1 maint: Multiple names: authors list", "CS1 maint: Uses authors parameter", "Commons category link from Wikidata", "Dimension reduction", "Matrix decompositions", "Wikipedia articles needing clarification from March 2011", "Wikipedia articles needing page number citations from June 2011"], "title": "Principal component analysis", "method": "Principal component analysis", "url": "https://en.wikipedia.org/wiki/Principal_component_analysis", "summary": "Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables (entities each of which takes on various numerical values) into a set of values of linearly uncorrelated variables called principal components. If there are \n \n \n \n n\n \n \n {\\displaystyle n}\n observations with \n \n \n \n p\n \n \n {\\displaystyle p}\n variables, then the number of distinct principal components is \n \n \n \n min\n (\n n\n \u2212\n 1\n ,\n p\n )\n \n \n {\\displaystyle \\min(n-1,p)}\n . This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components. The resulting vectors (each being a linear combination of the variables and containing n observations) are an uncorrelated orthogonal basis set. PCA is sensitive to the relative scaling of the original variables.\nPCA was invented in 1901 by Karl Pearson, as an analogue of the principal axis theorem in mechanics; it was later independently developed and named by Harold Hotelling in the 1930s. Depending on the field of application, it is also named the discrete Karhunen\u2013Lo\u00e8ve transform (KLT) in signal processing, the Hotelling transform in multivariate quality control, proper orthogonal decomposition (POD) in mechanical engineering, singular value decomposition (SVD) of X (Golub and Van Loan, 1983), eigenvalue decomposition (EVD) of XTX in linear algebra, factor analysis (for a discussion of the differences between PCA and factor analysis see Ch. 7 of Jolliffe's Principal Component Analysis), Eckart\u2013Young theorem (Harman, 1960), or empirical orthogonal functions (EOF) in meteorological science, empirical eigenfunction decomposition (Sirovich, 1987), empirical component analysis (Lorenz, 1956), quasiharmonic modes (Brooks et al., 1988), spectral decomposition in noise and vibration, and empirical modal analysis in structural dynamics.\nPCA is mostly used as a tool in exploratory data analysis and for making predictive models. It is often used to visualize genetic distance and relatedness between populations. PCA can be done by eigenvalue decomposition of a data covariance (or correlation) matrix or singular value decomposition of a data matrix, usually after a normalization step of the initial data. The normalization of each attribute consists of mean centering \u2013 subtracting each data value from its variable\u2019s measured mean so that its empirical mean (average) is zero \u2013 and, possibly, normalizing each variable\u2019s variance to make it equal to 1; see Z-scores. The results of a PCA are usually discussed in terms of component scores, sometimes called factor scores (the transformed variable values corresponding to a particular data point), and loadings (the weight by which each standardized original variable should be multiplied to get the component score). If component scores are standardized to unit variance loadings must contain the data variance in them (and that is the magnitude of eigenvalues). If component scores are not standardized (therefore they contain the data variance) then loadings must be unit-scaled, (\"normalized\") and these weights are called eigenvectors; they are the cosines of orthogonal rotation of variables into principal components or back.\nPCA is the simplest of the true eigenvector-based multivariate analyses. Often, its operation can be thought of as revealing the internal structure of the data in a way that best explains the variance in the data. If a multivariate dataset is visualised as a set of coordinates in a high-dimensional data space (1 axis per variable), PCA can supply the user with a lower-dimensional picture, a projection of this object when viewed from its most informative viewpoint. This is done by using only the first few principal components so that the dimensionality of the transformed data is reduced.\nPCA is closely related to factor analysis. Factor analysis typically incorporates more domain specific assumptions about the underlying structure and solves eigenvectors of a slightly different matrix.\nPCA is also related to canonical correlation analysis (CCA). CCA defines coordinate systems that optimally describe the cross-covariance between two datasets while PCA defines a new orthogonal coordinate system that optimally describes variance in a single dataset.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/84/Elmap_breastcancer_wiki.png", "https://upload.wikimedia.org/wikipedia/commons/f/f2/Fractional_Residual_Variances_comparison%2C_PCA_and_NMF.pdf", "https://upload.wikimedia.org/wikipedia/commons/f/f5/GaussianScatterPCA.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/6/69/PCA_of_Haplogroup_J_using_37_STRs.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": [".NET Framework", "ALGLIB", "AbdiWilliams", 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"Blocking (statistics)", "Boosting (machine learning)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breast cancer", "Breusch\u2013Godfrey test", "C++", "CURE data clustering algorithm", "CUR matrix approximation", "Canonical correlation", "Canonical correlation analysis", "Canonical correspondence analysis", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared statistic", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Confidence interval", "Confounding", "Conjugate transpose", "Contingency table", "Contingency tables", "Continuous probability distribution", "Control chart", "Convolutional neural network", "Coordinate system", "Correlation", "Correlation and dependence", "Correlation clustering", "Correlation matrix", "Correlogram", "Correspondence analysis", "Count data", "Covariance", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curie Institute (Paris)", "Curve", "DBSCAN", "Data collection", "Data matrix (multivariate statistics)", "Data mining", "Decision tree learning", "Decomposition of time series", "DeepDream", "Deep learning", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Detrended correspondence analysis", "Diagonal", "Diagonal matrix", "Diagonalizable matrix", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension (metadata)", "Dimensionality reduction", "Discrete cosine transform", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dynamic mode decomposition", "ELKI", "Eckart\u2013Young theorem", "Econometrics", "Effect size", "Efficiency (statistics)", "Eigendecomposition", "Eigendecomposition of a matrix", "Eigenface", "Eigenvalue", "Eigenvalues", "Eigenvalues and eigenvectors", "Eigenvector", "Eigenvectors", "Eigenvectors and eigenvalues", "Elastic map", "Electric current", "Electrophysiology", "Ellipsoid", "Elliptical distribution", "Empirical component analysis", "Empirical distribution function", "Empirical eigenfunction decomposition", "Empirical mean", "Empirical orthogonal functions", "Empirical risk minimization", "Engineering statistics", "Ensemble learning", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Euclidean space", "Expectation\u2013maximization algorithm", "Experiment", "Explanatory variable", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factor analysis of mixed data", "Factorial code", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feature engineering", "Feature learning", "First-hitting-time model", "Forest plot", "Fourier analysis", "Free software", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Frobenius norm", "Functional principal component analysis", "G-test", "GNU Octave", "Gated recurrent unit", "General linear model", "Generalized linear model", "Genomics", "Geographic information system", "Geometric data analysis", "Geometric mean", "Geostatistics", "Glossary of artificial intelligence", "Goodness of fit", "Grammar induction", "Gram\u2013Schmidt", "Granger causality", "Graphical model", "Grouped data", "Haplotype", "Harmonic mean", "Harold Hotelling", "Heteroscedasticity", "Hidden Markov model", "Hierarchical clustering", "High dimensional data", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "IDL (programming language)", "Iid", "Independent component analysis", "Index of dispersion", "Interaction (statistics)", "Interactive Data Language", "Interest rate derivative", "International Conference on Machine Learning", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jean-Paul Benz\u00e9cri", "Johansen test", "Jonckheere's trend test", "Journal of Educational Psychology", "Journal of Machine Learning Research", "Julia language", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "KNIME", "Kaplan\u2013Meier estimator", "Karhunen\u2013Lo\u00e8ve theorem", "Karl Pearson", "Kendall rank correlation coefficient", "Kernel PCA", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kullback\u2013Leibler divergence", "Kurtosis", "L-moment", "L1-norm principal component analysis", "LOBPCG", "Lanczos algorithm", "Learning to rank", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear regression", "Linear transformation", "List of datasets for machine-learning research", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local outlier factor", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Long short-term memory", "Loss function", "Low-rank approximation", "Lp space", "Ludovic Lebart", "M-estimator", "MATLAB", "Machine Learning (journal)", "Machine learning", "Manifold", "Mann\u2013Whitney U test", "Mathematica", "Matplotlib", "Matrix-free methods", "Matrix (mathematics)", "Matrix algebra", "Matrix decomposition", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean-shift", "Median", "Median-unbiased estimator", "Medical statistics", "Metabolomics", "Method of moments (statistics)", "Methods engineering", "Microarray", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean square error", "Missing data", "Mixed model", "Mlpack", "Mode (statistics)", "Mode shape", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multilayer perceptron", "Multilinear principal component analysis", "Multilinear subspace learning", "Multiple comparisons", "Multiple correspondence analysis", "Multivariate Gaussian distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate dataset", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Mutual information", "NAG Numerical Library", "NMath", "Naive Bayes classifier", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Neuron", "Neuroscience", "Non-linear iterative partial least squares", "Non-negative matrix factorization", "Nonlinear dimensionality reduction", "Nonlinear 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assignment", "Random forest", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank (linear algebra)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh quotient", "Recurrent neural network", "Regression analysis", "Regression model validation", "Reinforcement learning", "Relevance vector machine", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted Boltzmann machine", "Risk management", "Robust principal component analysis", "Robust regression", "Robust statistics", "Round-off errors", "Run chart", "SAS (software)", "Sample median", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "SciPy", "Scientific control", "Scientific visualization", "Scikit-learn", "Score test", "Seasonal adjustment", "Self-organizing map", "Semi-supervised learning", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal-to-noise ratio", "Signal processing", "Simple linear regression", "Simultaneous equations model", "Singular spectrum analysis", "Singular value decomposition", "Skewness", "Social statistics", "Sparse PCA", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spectral theorem", "Spike-triggered covariance", "Spike sorting", "Standard deviation", "Standard error", "State\u2013action\u2013reward\u2013state\u2013action", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stock", "Stock selection criterion", "Stratified sampling", "Structural break", "Structural equation modeling", "Structured prediction", "Student's t-test", "Sufficient statistic", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "Swap (finance)", "System identification", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "The Lancet", "Time domain", "Time series", "Tolerance interval", "Transform coding", "Transpose", "Trend estimation", "Tucker decomposition", "U-Net", "U-statistic", "Uniformly most powerful test", "Unit vector", "University of Canterbury", "Unsupervised learning", "V-statistic", "Vapnik\u2013Chervonenkis theory", "Variance", "Vector autoregression", "Vector space", "Wald test", "Wavelet", "Weighted least squares", "Weka (machine learning)", "White noise", "Whitening transformation", "Whittle likelihood", "Wilcoxon signed-rank test", "Y-STR", "YouTube", "Z-score", "Z-test"], "references": 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"http://adsabs.harvard.edu/abs/2016ApJ...824..117P", "http://adsabs.harvard.edu/abs/2018ApJ...852..104R", "http://adsabs.harvard.edu/abs/2018ISPM...35...32V", "http://ranger.uta.edu/~chqding/papers/KmeansPCA1.pdf", "http://ranger.uta.edu/~chqding/papers/Zha-Kmeans.pdf", "http://bioinfo-out.curie.fr/projects/vidaexpert/", "http://factominer.free.fr/", "http://www.ihes.fr/~zinovyev/princmanif2006/", "http://www.ncbi.nlm.nih.gov/pubmed/19772385", "http://www.ncbi.nlm.nih.gov/pubmed/27735002", "http://www.ncbi.nlm.nih.gov/pubmed/8054384", "http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc552.htm", "http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf", "http://arxiv.org/abs/0811.1081", "http://arxiv.org/abs/0811.4413", "http://arxiv.org/abs/0912.3599", "http://arxiv.org/abs/1108.4372", "http://arxiv.org/abs/1205.6935", "http://arxiv.org/abs/1206.5538", "http://arxiv.org/abs/1207.4197", "http://arxiv.org/abs/1405.6785", "http://arxiv.org/abs/1410.6801", "http://arxiv.org/abs/1511.01245", "http://arxiv.org/abs/1604.06097", "http://arxiv.org/abs/1612.06037", "http://arxiv.org/abs/1711.09492", "http://arxiv.org/abs/1712.10317", "http://arxiv.org/abs/1804.10253", "http://arxiv.org/abs/astro-ph/0606170", "http://arxiv.org/archive/astro-ph.IM", "http://arxiv.org/archive/stat.ML", "http://doi.org/10.1002%2Fwics.101", "http://doi.org/10.1007%2F978-3-540-69497-7_27", "http://doi.org/10.1007%2Fb98835", "http://doi.org/10.1007%2Fbf00198909", "http://doi.org/10.1016%2F0003-2670(86)80028-9", "http://doi.org/10.1016%2FS0140-6736(05)17947-1", "http://doi.org/10.1016%2Fj.cosrev.2016.11.001", "http://doi.org/10.1016%2Fj.patcog.2011.01.004", "http://doi.org/10.1023%2Fb:mach.0000033113.59016.96", "http://doi.org/10.1039%2FC6IB00100A", "http://doi.org/10.1080%2F14786440109462720", "http://doi.org/10.1086%2F510127", "http://doi.org/10.1088%2F2041-8205%2F755%2F2%2FL28", "http://doi.org/10.1089%2Fcmb.2008.0221", "http://doi.org/10.1109%2F2.36", 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"https://stats.idre.ucla.edu/sas/output/principal-components-analysis/", "https://ijpam.eu/contents/2017-115-1/12/12.pdf", "https://www.researchgate.net/publication/271642170_Principal_Manifolds_for_Data_Visualisation_and_Dimension_Reduction_LNCSE_58", "https://ir.canterbury.ac.nz/bitstream/handle/10092/10293/thesis.pdf?sequence=1", "https://arxiv.org/abs/0809.0490", "https://arxiv.org/abs/1404.1100", "https://arxiv.org/list/cs.LG/recent", "https://arxiv.org/pdf/1108.4372.pdf"]}, "Normal distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2010", "Articles with unsourced statements from June 2011", "CS1 Latin-language sources (la)", "Commons category link is on Wikidata", "Conjugate prior distributions", "Continuous distributions", "Exponential family distributions", "Location-scale family probability distributions", "Normal distribution", "Pages using deprecated image syntax", "Pages with login required references or sources", "Stable distributions", "Use mdy dates from August 2012"], "title": "Normal distribution", "method": "Normal distribution", "url": "https://en.wikipedia.org/wiki/Normal_distribution", "summary": "In probability theory, the normal (or Gaussian or Gauss or Laplace\u2013Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.\nThe normal distribution is useful because of the central limit theorem. In its most general form, under some conditions (which include finite variance), it states that averages of samples of observations of random variables independently drawn from independent distributions converge in distribution to the normal, that is, they become normally distributed when the number of observations is sufficiently large. Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal. Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.\nThe normal distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped (such as the Cauchy, Student's t, and logistic distributions).\nThe probability density of the normal distribution is\n\n \n \n \n f\n (\n x\n \u2223\n \u03bc\n ,\n \n \u03c3\n \n 2\n \n \n )\n =\n \n \n 1\n \n 2\n \u03c0\n \n \u03c3\n \n 2\n \n \n \n \n \n \n e\n \n \u2212\n \n \n \n (\n x\n \u2212\n \u03bc\n \n )\n \n 2\n \n \n \n \n 2\n \n \u03c3\n \n 2\n \n \n \n \n \n \n \n \n \n {\\displaystyle f(x\\mid \\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}}\n where\n\n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n is the mean or expectation of the distribution (and also its median and mode),\n\n \n \n \n \u03c3\n \n \n {\\displaystyle \\sigma }\n is the standard deviation, and\n\n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n {\\displaystyle \\sigma ^{2}}\n is the variance.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9b/Carl_Friedrich_Gauss.jpg", 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"http://stat.smmu.edu.cn/history/pearson1901.pdf", "http://www.wise.xmu.edu.cn/Master/Download/..%5C..%5CUploadFiles%5Cpaper-masterdownload%5C2009519932327055475115776.pdf", "http://aidanlyon.com/aidanlyon.com/media/publications/Lyon-normal_distributions.pdf", "http://www.encyclopedia.com/topic/Normal_Distribution.aspx#3", "http://www.fxsolver.com/browse/formulas/Normal+Distribution", "http://www.ifa.com/", "http://jeff560.tripod.com/b.html", "http://jeff560.tripod.com/e.html", "http://jeff560.tripod.com/g.html", "http://jeff560.tripod.com/mathword.html", "http://jeff560.tripod.com/n.html", "http://jeff560.tripod.com/s.html", "http://jeff560.tripod.com/stat.html", "http://www.wilmott.com/pdfs/090721_west.pdf", "http://mathworld.wolfram.com/NormalDistribution.html", "http://mathworld.wolfram.com/NormalDistributionFunction.html", "http://mathworld.wolfram.com/NormalProductDistribution.html", 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"http://www.worldcat.org/oclc/476909537", "http://www.math.uni.wroc.pl/~pms/publicationsArticle.php?nr=14.2&nrA=8&ppB=257&ppE=263", "http://www.york.ac.uk/depts/maths/histstat/demoivre.pdf", "https://books.google.com/books?id=1TIAAAAAQAAJ", "https://books.google.com/books?id=tTN4HuUNXjgC&pg=PA592", "https://www.youtube.com/watch?v=AUSKTk9ENzg", "https://www.youtube.com/watch?v=kB_kYUbS_ig", "https://lccn.loc.gov/65012253", "https://web.archive.org/web/20090325160012/http://www.eng.tau.ac.il/~jo/academic/Q.pdf", "https://web.archive.org/web/20100716035328/http://saluc.engr.uconn.edu/refs/crypto/rng/leva92afast.pdf", "https://www.encyclopediaofmath.org/index.php?title=p/n067460", "https://www.jstor.org/stable/2245476"]}, "Sequential Monte Carlo methods": {"categories": ["All Wikipedia articles needing clarification", "All articles needing expert attention", "All articles that are too technical", "All articles with unsourced statements", "Articles needing expert attention from August 2012", "Articles needing expert attention from June 2017", "Articles using small message boxes", "Articles with unsourced statements from October 2011", "CS1 maint: Multiple names: authors list", "Computational statistics", "Control theory", "Monte Carlo methods", "Nonlinear filters", "Robot control", "Sampling techniques", "Statistical mechanics", "Stochastic simulation", "Wikipedia articles needing clarification from October 2011", "Wikipedia articles that are too technical from August 2012", "Wikipedia articles that are too technical from June 2017"], "title": "Particle filter", "method": "Sequential Monte Carlo methods", "url": "https://en.wikipedia.org/wiki/Particle_filter", "summary": "Particle filters or Sequential Monte Carlo (SMC) methods are a set of genetic, Monte Carlo algorithms used to solve filtering problems arising in signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made, and random perturbations are present in the sensors as well as in the dynamical system. The objective is to compute the posterior distributions of the states of some Markov process, given some noisy and partial observations. The term \"particle filters\" was first coined in 1996 by Del Moral in reference to mean field interacting particle methods used in fluid mechanics since the beginning of the 1960s. The terminology \"sequential Monte Carlo\" was proposed by Liu and Chen in 1998.\nParticle filtering uses a genetic mutation-selection sampling approach, with a set of particles (also called samples) to represent the posterior distribution of some stochastic process given noisy and/or partial observations. The state-space model can be nonlinear and the initial state and noise distributions can take any form required. Particle filter techniques provide a well-established methodology for generating samples from the required distribution without requiring assumptions about the state-space model or the state distributions. However, these methods do not perform well when applied to very high-dimensional systems.\nParticle filters implement the prediction-updating transitions of the filtering equation directly by using a genetic type mutation-selection particle algorithm. The samples from the distribution are represented by a set of particles; each particle has a likelihood weight assigned to it that represents the probability of that particle being sampled from the probability density function. Weight disparity leading to weight collapse is a common issue encountered in these filtering algorithms; however it can be mitigated by including a resampling step before the weights become too uneven. Several adaptive resampling criteria can be used, including the variance of the weights and the relative entropy with respect to the uniform distribution. In the resampling step, the particles with negligible weights are replaced by new particles in the proximity of the particles with higher weights.\nFrom the statistical and probabilistic point of view, particle filters can be interpreted as mean field particle interpretations of Feynman-Kac probability measures. These particle integration techniques were developed in molecular chemistry and computational physics by Theodore E. Harris and Herman Kahn in 1951, Marshall N. Rosenbluth and Arianna W. Rosenbluth in 1955 and more recently by Jack H. Hetherington in 1984. In computational physics, these Feynman-Kac type path particle integration methods are also used in Quantum Monte Carlo, and more specifically Diffusion Monte Carlo methods. Feynman-Kac interacting particle methods are also strongly related to mutation-selection genetic algorithms currently used in evolutionary computing to solve complex optimization problems.\nThe particle filter methodology is used to solve Hidden Markov Model (HMM) and nonlinear filtering problems. With the notable exception of linear-Gaussian signal-observation models (Kalman filter) or wider classes of models (Benes filter) Mireille Chaleyat-Maurel and Dominique Michel proved in 1984 that the sequence of posterior distributions of the random states of the signal given the observations (a.k.a. optimal filter) have no finitely recursive recursion. Various numerical methods based on fixed grid approximations, Markov Chain Monte Carlo techniques (MCMC), conventional linearization, extended Kalman filters, or determining the best linear system (in expect cost-error sense) have never really coped with large scale systems, unstable processes or when the nonlinearities are not sufficiently smooth.\nParticle filters and Feynman-Kac particle methodologies find application in signal and image processing, Bayesian inference, machine learning, risk analysis and rare event sampling, engineering and robotics, artificial intelligence, bioinformatics, phylogenetics, computational science, Economics and mathematical finance, molecular chemistry, computational physics, pharmacokinetic and other fields.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", 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"http://www.springerlink.com/content/q6452k2x37357l3r/", "http://adsabs.harvard.edu/abs/1955JChPh..23..356R", "http://adsabs.harvard.edu/abs/1984PhRvA..30.2713H", "http://adsabs.harvard.edu/abs/1993PhRvL..71.2159C", "http://adsabs.harvard.edu/abs/2000PhRvE..61.4566A", "http://adsabs.harvard.edu/abs/2001AnIHP..37..155D", "http://adsabs.harvard.edu/abs/2002ITSP...50..174A", "http://adsabs.harvard.edu/abs/2011SMaS...20g5021L", "http://www.people.fas.harvard.edu/~junliu/TechRept/94folder/klw94.pdf", "http://www.people.fas.harvard.edu/~junliu/TechRept/95folder/liu&chen95_s.pdf", "http://www.people.fas.harvard.edu/~junliu/TechRept/98folder/liu&chen98_2.pdf", "http://blogs.oregonstate.edu/hess/code/particles/", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.107.7415", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.137.5199", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.190.7092", "http://people.bordeaux.inria.fr/pierre.delmoral/delmoral96nonlinear.pdf", 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"http://doi.org/10.1007%2Fbfb0103798", "http://doi.org/10.1007%2Fs004400050131", "http://doi.org/10.1007%2Fs004400050249", "http://doi.org/10.1007%2Fs11222-011-9271-y", "http://doi.org/10.1007%2Fs11222-013-9429-x", "http://doi.org/10.1016%2FS0304-4149(99)00094-0", "http://doi.org/10.1016%2Fj.cviu.2011.06.001", "http://doi.org/10.1016%2Fs0246-0203(00)01064-5", "http://doi.org/10.1023%2FA:1008935410038", "http://doi.org/10.1049%2Fip-f-2.1993.0015", "http://doi.org/10.1051%2Fm2an%2F2010048", "http://doi.org/10.1051%2Fproc%2F201444001", "http://doi.org/10.1051%2Fps:2003001", "http://doi.org/10.1063%2F1.1741967", "http://doi.org/10.1080%2F01621459.1994.10476469", "http://doi.org/10.1080%2F01621459.1998.10473765", "http://doi.org/10.1080%2F07362994.2013.879262", "http://doi.org/10.1080%2F07362999908809648", "http://doi.org/10.1080%2F17442508408833312", "http://doi.org/10.1088%2F0964-1726%2F20%2F7%2F075021", "http://doi.org/10.1093%2Fmind%2FLIX.236.433", "http://doi.org/10.1103%2FPhysRevA.30.2713", "http://doi.org/10.1103%2Fphysreve.61.4566", "http://doi.org/10.1103%2Fphysrevlett.71.2159", "http://doi.org/10.1109%2F78.978374", "http://doi.org/10.1109%2FJPROC.2007.893250", "http://doi.org/10.1109%2Ftpami.2007.1081", "http://doi.org/10.1111%2Fj.1467-9868.2009.00736.x", "http://doi.org/10.1137%2Fs0036139996307371", "http://doi.org/10.1177%2F0278364910364165", "http://doi.org/10.1214%2F10-AAP716", "http://doi.org/10.1214%2Faoap%2F1015345399", "http://doi.org/10.1214%2Faoap%2F1028903535", "http://doi.org/10.1214%2Faoap%2F1029962742", "http://doi.org/10.2307%2F1390750", "http://doi.org/10.2307%2F2291068", "http://doi.org/10.2307%2F2670179", "http://doi.org/10.3150%2F10-bej335", "http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=210672&url=http%25253A%25252F%25252Fieeexplore.ieee.org%25252Fxpls%25252Fabs_all.jsp%25253Farnumber%25253D210672", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=210672", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=978374", "http://www.jstatsoft.org/v30/i06/", "http://www.jstor.org/stable/1390750", "http://www.jstor.org/stable/2670179", "http://www.jstor.org/stable/2984008", "http://archive.numdam.org/ARCHIVE/SPS/SPS_2000__34_/SPS_2000__34__1_0/SPS_2000__34__1_0.pdf", "http://mind.oxfordjournals.org/content/LIX/236/433", "http://projecteuclid.org/download/pdf_1/euclid.aoap/1028903535", "http://projecteuclid.org/euclid.aoap/1015345399", "http://projecteuclid.org/euclid.aoap/1029962742", "http://projecteuclid.org/euclid.aoap/1307020390", "http://www.worldcat.org/issn/0090-9491", "http://www.worldcat.org/issn/0178-8051", "http://www.worldcat.org/issn/0736-2994", "http://www.worldcat.org/issn/0956-375X", "http://www.worldcat.org/issn/0960-3174", "http://www.worldcat.org/issn/1050-5164", "http://www-sigproc.eng.cam.ac.uk/smc/", "https://www.crcpress.com/product/isbn/9781466504059", "https://www.questia.com/PM.qst?a=o&se=gglsc&d=5002321997", "https://link.springer.com/article/10.1007/PL00008786", "https://link.springer.com/article/10.1007/s11222-011-9271-y", "https://www.springer.com/gp/book/9780387202686", "https://www.springer.com/mathematics/probability/book/978-0-387-20268-6", "https://www.springer.com/us/book/9780387202686#reviews", "https://www.youtube.com/watch?v=bO_GajDgGJ4/", "https://mitpress.mit.edu/index.php?q=books/adaptation-natural-and-artificial-systems", "https://dornsifecms.usc.edu/assets/sites/520/docs/kahnharris.pdf", "https://www.laas.fr/public/en", "https://zhouyan.github.io/vSMC/", "https://web.archive.org/web/20060612210237/http://www.cs.washington.edu/ai/Mobile_Robotics/mcl/", "https://web.archive.org/web/20141107015724/http://qmcchem.ups-tlse.fr/files/caffarel/31.pdf"]}, "K-statistic": {"categories": ["All stub articles", "Estimator", "Statistics stubs"], "title": "K-statistic", "method": "K-statistic", "url": "https://en.wikipedia.org/wiki/K-statistic", "summary": "In statistics, a k-statistic is a minimum-variance unbiased estimator of a cumulant.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Cumulant", "Statistics", "Unbiased estimator", "Wolfram MathWorld"], "references": ["http://mathworld.wolfram.com/k-Statistic.html"]}, "Fractional Brownian motion": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2018", "Autocorrelation"], "title": "Fractional Brownian motion", "method": "Fractional Brownian motion", "url": "https://en.wikipedia.org/wiki/Fractional_Brownian_motion", "summary": "In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process BH(t) on [0, T], which starts at zero, has expectation zero for all t in [0, T], and has the following covariance function:\n\n \n \n \n E\n [\n \n B\n \n H\n \n \n (\n t\n )\n \n B\n \n H\n \n \n (\n s\n )\n ]\n =\n \n \n \n 1\n 2\n \n \n \n (\n \n |\n \n t\n \n \n |\n \n \n 2\n H\n \n \n +\n \n |\n \n s\n \n \n |\n \n \n 2\n H\n \n \n \u2212\n \n |\n \n t\n \u2212\n s\n \n \n |\n \n \n 2\n H\n \n \n )\n ,\n \n \n {\\displaystyle E[B_{H}(t)B_{H}(s)]={\\tfrac {1}{2}}(|t|^{2H}+|s|^{2H}-|t-s|^{2H}),}\n where H is a real number in (0, 1), called the Hurst index or Hurst parameter associated with the fractional Brownian motion. The Hurst exponent describes the raggedness of the resultant motion, with a higher value leading to a smoother motion. It was introduced by Mandelbrot & van Ness (1968).\nThe value of H determines what kind of process the fBm is:\n\nif H = 1/2 then the process is in fact a Brownian motion or Wiener process;\nif H > 1/2 then the increments of the process are positively correlated;\nif H < 1/2 then the increments of the process are negatively correlated.The increment process, X(t) = BH(t+1) \u2212 BH(t), is known as fractional Gaussian noise.\nThere is also a generalization of fractional Brownian motion: n-th order fractional Brownian motion, abbreviated as n-fBm. n-fBm is a Gaussian, self-similar, non-stationary process whose increments of order n are stationary. For n = 1, n-fBm is classical fBm.\nLike the Brownian motion that it generalizes, fractional Brownian motion is named after 19th century biologist Robert Brown; fractional Gaussian noise is named after mathematician Carl Friedrich Gauss.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/93/BrownFractionalH15.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3b/BrownFractionalH55.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e2/BrownFractionalH75Seed0.svg", "https://upload.wikimedia.org/wikipedia/commons/4/41/BrownFractionalH75Seed1.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3d/BrownFractionalH75Seed2.svg", "https://upload.wikimedia.org/wikipedia/commons/5/57/BrownFractionalH95.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Almost nowhere", "Almost surely", "ArXiv", "Autoregressive conditional heteroskedasticity", "Autoregressive fractionally integrated moving average", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Benoit Mandelbrot", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Bibcode", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Box dimension", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Brownian surface", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Carl Friedrich Gauss", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Cholesky decomposition", "Circulant embedding", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Correlation", "Covariance function", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Eigenvalues", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Euler hypergeometric integral", "Exchangeable random variables", "Expectation (mathematics)", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractal", "Fractional integration", "G-network", "GNU Scientific Library", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian", "Gaussian process", "Gaussian quadrature", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Hausdorff dimension", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Hurst exponent", "H\u00f6lder condition", "IEEE Transactions on Signal Processing", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "Ito calculus", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "JSTOR", "Journal of Mathematical Physics", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kronecker delta", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Long-range dependence", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Multifractal", "Non-homogeneous Poisson process", "Nowhere differentiable", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pink noise", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Positive-definite matrix", "Potts model", "Predictable process", "Probability distribution", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Riemann\u2013Liouville integral", "Risk process", "Robert Brown (Scottish botanist from Montrose)", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Self-similarity", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "Symmetric matrix", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Tweedie distributions", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "Weyl integral", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://www.mathworks.com/matlabcentral/fileexchange/38935", "http://www2.isye.gatech.edu/~adieker3/fbm/thesis.pdf", "http://adsabs.harvard.edu/abs/1992JMP....33.3128S", "http://adsabs.harvard.edu/abs/2013arXiv1308.0399K", "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.201.5698&rep=rep1&type=pdf", "http://arxiv.org/abs/1308.0399", "http://doi.org/10.1007%2FBF00534922", "http://doi.org/10.1063%2F1.529976", "http://doi.org/10.1137%2F1010093", "http://doi.org/10.1137%2Fs1064827592240555", "http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=917808", "http://www.jstor.org/stable/2027184", "https://doi.org/10.1109%2F78.917808"]}, "One-way analysis of variance": {"categories": ["Analysis of variance", "Statistical tests", "Wikipedia articles needing clarification from September 2014"], "title": "One-way analysis of variance", "method": "One-way analysis of variance", "url": "https://en.wikipedia.org/wiki/One-way_analysis_of_variance", "summary": "In statistics, one-way analysis of variance (abbreviated one-way ANOVA) is a technique that can be used to compare means of two or more samples (using the F distribution). This technique can be used only for numerical response data, the \"Y\", usually one variable, and numerical or (usually) categorical input data, the \"X\", always one variable, hence \"one-way\".The ANOVA tests the null hypothesis that samples in all groups are drawn from populations with the same mean values. To do this, two estimates are made of the population variance. These estimates rely on various assumptions (see below). The ANOVA produces an F-statistic, the ratio of the variance calculated among the means to the variance within the samples. If the group means are drawn from populations with the same mean values, the variance between the group means should be lower than the variance of the samples, following the central limit theorem. A higher ratio therefore implies that the samples were drawn from populations with different mean values.Typically, however, the one-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by a t-test (Gosset, 1908). When there are only two means to compare, the t-test and the F-test are equivalent; the relation between ANOVA and t is given by F = t2. An extension of one-way ANOVA is two-way analysis of variance that examines the influence of two different categorical independent variables on one dependent variable.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/5a/F-dens-2-15df.svg"], "links": ["ANOVA on ranks", "Analysis of variance", "Central limit theorem", "Digital object identifier", "Errors and residuals in statistics", "Expected value", "F-distribution", "F-test", "F distribution", "F test", "George Casella", "Homoscedasticity", "Independent and identically distributed", "International Standard Book Number", "JSTOR", "Journal of the American Statistical Association", "Kruskal\u2013Wallis one-way analysis of variance", "Mixed model", "Multivariate analysis of variance", "Normal distribution", "Normally distributed", "Null hypothesis", "Ordinal scale", "P-value", "Repeated measures", "Robust statistics", "Simple random sample", "Springer Science+Business Media", "Standard error", "Statistical significance", "Statistics", "T-test", "Two-way ANOVA", "Two-way analysis of variance", "Type I error", "Welch's t-test"], "references": ["http://doi.org/10.1080/01621459.1971.10482371", "http://doi.org/10.2307/2332579", "http://doi.org/10.3102/00346543051004499", "http://doi.org/10.3102/00346543060001091", "http://www.jstor.org/stable/2332579", "https://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-75964-7", "https://www.statsoft.com/textbook/elementary-statistics-concepts/", "https://www.rand.org/pubs/research_memoranda/RM5072.html"]}, "Score (statistics)": {"categories": ["All articles to be expanded", "Articles to be expanded from December 2009", "Articles using small message boxes", "Maximum likelihood estimation"], "title": "Score (statistics)", "method": "Score (statistics)", "url": "https://en.wikipedia.org/wiki/Score_(statistics)", "summary": "In statistics, the score, score function, efficient score or informant indicates how sensitive a likelihood function \n \n \n \n \n \n L\n \n \n (\n \u03b8\n ;\n X\n )\n \n \n {\\displaystyle {\\mathcal {L}}(\\theta ;X)}\n is to its parameter \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n . Explicitly, the score for \n\n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n is the gradient of the log-likelihood with respect to \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n .\nThe score plays an important role in several aspects of inference. For example:\n\nin formulating a test statistic for a locally most powerful test;\nin approximating the error in a maximum likelihood estimate;\nin demonstrating the asymptotic sufficiency of a maximum likelihood estimate;\nin the formulation of confidence intervals;\nin demonstrations of the Cram\u00e9r\u2013Rao inequality.The score function also plays an important role in computational statistics, as it can play a part in the computation of\nmaximum likelihood estimates.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128143823%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128140726%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110427033551%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110424212543%21Wiki_letter_w_cropped.svg"], "links": ["Bernoulli process", "Bernoulli trial", "Chain rule", "Computational statistics", "Confidence interval", "Cram\u00e9r\u2013Rao bound", "Digital object identifier", "Encyclopedia of Mathematics", "Epidemiology (journal)", "Estimator", "Expected value", "Fisher information", "Gradient", "Information theory", "International Standard Book Number", "Leibniz integral rule", "Likelihood function", "Log-likelihood", "Logarithm", "Maximum likelihood", "Michiel Hazewinkel", "Natural logarithm", "Numerical analysis", "Parametric model", "Partial derivative", "Probability density function", "PubMed Central", "Random process", "Score test", "Scoring algorithm", "Sensitivity analysis", "Statistic", "Statistical inference", "Statistical power", "Statistical regularity", "Statistics", "Support curve", "Test statistic", "Variance"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3575184", "http://doi.org/10.1097%2FEDE.0b013e3181c30fb2", "https://www.encyclopediaofmath.org/index.php?title=i/i051030"]}, "Social statistics": {"categories": ["All articles needing additional references", "All articles with specifically marked weasel-worded phrases", "Articles needing additional references from December 2014", "Articles with Curlie links", "Articles with specifically marked weasel-worded phrases from December 2011", "Articles with specifically marked weasel-worded phrases from January 2018", "CS1 maint: Multiple names: authors list", "Social statistics", "Wikipedia articles with NDL identifiers", "Wikipedia external links cleanup from November 2015", "Wikipedia spam cleanup from November 2015"], "title": "Social statistics", "method": "Social statistics", "url": "https://en.wikipedia.org/wiki/Social_statistics", "summary": "Social statistics is the use of statistical measurement systems to study human behavior in a social environment. This can be accomplished through polling a group of people, evaluating a subset of data obtained about a group of people, or by observation and statistical analysis of a set of data that relates to people and their behaviors.\nSocial scientists use social statistics for many purposes, including:\n\nthe evaluation of the quality of services available to a group or organization,\nanalyzing behaviors of groups of people in their environment and special situations,\ndetermining the wants of people through statistical sampling.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikibooks-logo.svg", "https://upload.wikimedia.org/wikipedia/commons/f/ff/Wikidata-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anthropology", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian method", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Causality", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curlie", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Harvard", "Harvard Law School", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Item response theory", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latent class model", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistical packages", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multilevel models", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Diet Library", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Political science", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Program evaluation", "Proportional hazards model", "Psychology", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Service (economics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Sociology", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural Equation Modeling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survey sampling", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.socialsciencestatistics.com/", "http://www.socialsciencestatistics.com/index.php?option=com_weblinks&catid=17&Itemid=22", "http://www.unionstats.com/", "http://www.ciser.cornell.edu/", "http://www.iq.harvard.edu/", "http://www.law.harvard.edu/programs/lwp/unionstats.html", "http://steinhardt.nyu.edu/priism/", "http://www.icpsr.umich.edu/", "http://www2.irss.unc.edu/irss/home.asp", "http://www.csss.washington.edu/", "http://blogs.helsinki.fi/methodology/", "http://www.bls.gov", "http://postyour.info/", "http://www.arts.auckland.ac.nz/departments/index.cfm?P=8770", "http://laborsta.ilo.org/", "http://www.laborresearch.org/econ_stats.php", "http://www.oecd.org/home/0,2987,en_2649_201185_1_1_1_1_1,00.html", "http://unstats.un.org/unsd/demographic/products/socind/", "http://www.ncrm.ac.uk/", "http://www.southampton.ac.uk/socsci/socstats/index.shtml", "https://books.google.com/books?id=95tXSwNvVR8C&printsec=frontcover&dq=measurement+social#v=onepage&q&f=false", "https://books.google.com/books?id=sgoHv5ZP6dcC&printsec=frontcover&dq=measurement+social#", "https://id.ndl.go.jp/auth/ndlna/00571921", "https://curlie.org/Science/Math/Statistics/", "https://www.wikidata.org/wiki/Q3274962"]}, "Welch's method": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from November 2011", "Digital signal processing", "Frequency-domain analysis", "Waves"], "title": "Welch's method", "method": "Welch's method", "url": "https://en.wikipedia.org/wiki/Welch%27s_method", "summary": "In physics, engineering, and applied mathematics, Welch's method, named after P.D. Welch, is used for estimating the power of a signal at different frequencies: that is, it is an approach to spectral density estimation. The method is based on the concept of using periodogram spectrum estimates, which are the result of converting a signal from the time domain to the frequency domain. Welch's method is an improvement on the standard periodogram spectrum estimating method and on Bartlett's method, in that it reduces noise in the estimated power spectra in exchange for reducing the frequency resolution. Due to the noise caused by imperfect and finite data, the noise reduction from Welch's method is often desired.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Bartlett's method", "Digital object identifier", "Discrete Fourier transform", "Electric power", "Engineering", "Fast Fourier transform", "Frequency", "International Standard Book Number", "Mathematics", "Modified discrete cosine transform", "P.D. Welch", "Periodogram", "Physics", "Power spectrum", "Short-time Fourier transform", "Signal (electrical engineering)", "Spectral density estimation", "Window function"], "references": ["http://doi.org/10.1109%2FTAU.1967.1161901"]}, "Gy's sampling theory": {"categories": ["Sampling (statistics)"], "title": "Gy's sampling theory", "method": "Gy's sampling theory", "url": "https://en.wikipedia.org/wiki/Gy%27s_sampling_theory", "summary": "Gy's sampling theory is a theory about the sampling of materials, developed by Pierre Gy from the 1950s to beginning 2000s in articles and books including:\n\n(1960) Sampling nomogram\n(1979) Sampling of particulate materials; theory and practice\n(1982) Sampling of particulate materials; theory and practice; 2nd edition\n(1992) Sampling of Heterogeneous and Dynamic Material Systems: Theories of Heterogeneity, Sampling and Homogenizing\n(1998) Sampling for Analytical PurposesThe abbreviation \"TOS\" is also used to denote Gy's sampling theory.Gy's sampling theory uses a model in which the sample taking is represented by independent Bernoulli trials for every particle in the parent population from which the sample is drawn. The two possible outcomes of each Bernoulli trial are: (1) the particle is selected and (2) the particle is not selected. The probability of selecting a particle may be different during each Bernoulli trial. The model used by Gy is mathematically equivalent to Poisson sampling. Using this model, the following equation for the variance of the sampling error in the mass concentration in a sample was derived by Gy:\n\n \n \n \n V\n =\n \n \n 1\n \n (\n \n \u2211\n \n i\n =\n 1\n \n \n N\n \n \n \n q\n \n i\n \n \n \n m\n \n i\n \n \n \n )\n \n 2\n \n \n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n N\n \n \n \n q\n \n i\n \n \n (\n 1\n \u2212\n \n q\n \n i\n \n \n )\n \n m\n \n i\n \n \n 2\n \n \n \n \n (\n \n \n a\n \n i\n \n \n \u2212\n \n \n \n \n \u2211\n \n j\n =\n 1\n \n \n N\n \n \n \n q\n \n j\n \n \n \n a\n \n j\n \n \n \n m\n \n j\n \n \n \n \n \n \u2211\n \n j\n =\n 1\n \n \n N\n \n \n \n q\n \n j\n \n \n \n m\n \n j\n \n \n \n \n \n \n )\n \n \n 2\n \n \n .\n \n \n {\\displaystyle V={\\frac {1}{(\\sum _{i=1}^{N}q_{i}m_{i})^{2}}}\\sum _{i=1}^{N}q_{i}(1-q_{i})m_{i}^{2}\\left(a_{i}-{\\frac {\\sum _{j=1}^{N}q_{j}a_{j}m_{j}}{\\sum _{j=1}^{N}q_{j}m_{j}}}\\right)^{2}.}\n in which V is the variance of the sampling error, N is the number of particles in the population (before the sample was taken), q i is the probability of including the ith particle of the population in the sample (i.e. the first-order inclusion probability of the ith particle), m i is the mass of the ith particle of the population and a i is the mass concentration of the property of interest in the ith particle of the population.\nIt is noted that the above equation for the variance of the sampling error is an approximation based on a linearization of the mass concentration in a sample.\nIn the theory of Gy, correct sampling is defined as a sampling scenario in which all particles have the same probability of being included in the sample. This implies that q i no longer depends on i, and can therefore be replaced by the symbol q. Gy's equation for the variance of the sampling error becomes:\n\n \n \n \n V\n =\n \n \n \n 1\n \u2212\n q\n \n \n q\n \n M\n \n batch\n \n \n 2\n \n \n \n \n \n \n \u2211\n \n i\n =\n 1\n \n \n N\n \n \n \n m\n \n i\n \n \n 2\n \n \n \n \n (\n \n \n a\n \n i\n \n \n \u2212\n \n a\n \n batch\n \n \n \n )\n \n \n 2\n \n \n .\n \n \n {\\displaystyle V={\\frac {1-q}{qM_{\\text{batch}}^{2}}}\\sum _{i=1}^{N}m_{i}^{2}\\left(a_{i}-a_{\\text{batch}}\\right)^{2}.}\n where abatch is the concentration of the property of interest in the population from which the sample is to be drawn and Mbatch is the mass of the population from which the sample is to be drawn. It has been noted that a similar equation had already been derived in 1935 by Kassel and Guy.", "images": [], "links": ["Bernoulli trials", "Correct sampling", "Digital object identifier", "First-order inclusion probability", "Heterogeneous", "Linearization", "Pierre Gy", "Poisson sampling", "Sampling error", "Scientific model", "Scientific theory", "Statistical independence", "Statistical sampling", "Variance"], "references": ["http://doi.org/10.1002%2Fasmb.878", "http://doi.org/10.1111%2Fj.1751-908X.2004.tb00742.x"]}, "Product form solution": {"categories": ["Queueing theory"], "title": "Product-form solution", "method": "Product form solution", "url": "https://en.wikipedia.org/wiki/Product-form_solution", "summary": "In probability theory, a product-form solution is a particularly efficient form of solution for determining some metric of a system with distinct sub-components, where the metric for the collection of components can be written as a product of the metric across the different components. Using capital Pi notation a product-form solution has algebraic form\n\n \n \n \n \n P\n \n (\n \n x\n \n 1\n \n \n ,\n \n x\n \n 2\n \n \n ,\n \n x\n \n 3\n \n \n ,\n \u2026\n ,\n \n x\n \n n\n \n \n )\n =\n B\n \n \u220f\n \n i\n =\n 1\n \n \n n\n \n \n \n P\n \n (\n \n x\n \n i\n \n \n )\n \n \n {\\displaystyle {\\text{P}}(x_{1},x_{2},x_{3},\\ldots ,x_{n})=B\\prod _{i=1}^{n}{\\text{P}}(x_{i})}\n where B is some constant. Solutions of this form are of interest as they are computationally inexpensive to evaluate for large values of n. Such solutions in queueing networks are important for finding performance metrics in models of multiprogrammed and time-shared computer systems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Annals of Applied Probability", "ArXiv", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Capital Pi notation", "Chemical reaction network", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Equilibrium distribution", "Erlang (unit)", "Erlang distribution", "Erol Gelenbe", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "Frank Kelly (mathematician)", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell network", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Independence (probability theory)", "Information system", "International Standard Book Number", "J. Michael Harrison", "JSTOR", "Jackson's theorem (queueing theory)", "Jackson network", "James R. Jackson", "Jane Hillston", "Jean Walrand", "Journal of the ACM", "K.M. Chandy", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Local balance", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Management Science: A Journal of the Institute for Operations Research and the Management Sciences", "Markov chain", "Markovian arrival process", "Martin Feinberg", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Onno J. Boxma", "PEPA", "Performance metric", "Peter G. Harrison", "Petri nets", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product (mathematics)", "PubMed Identifier", "Quality of service", "Quasireversibility", "Queueing Systems", "Queueing theory", "RCAT", "Random neural network", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Ruth J. Williams", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Stochastic", "Teletraffic engineering", "Traffic equations"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/20306147", "http://arxiv.org/abs/0803.3042", "http://arxiv.org/abs/math/0512119", "http://doi.org/10.1007/978-3-642-02424-5_8", "http://doi.org/10.1007/978-3-642-15784-4_14", "http://doi.org/10.1007/978-3-642-39408-9_3", "http://doi.org/10.1007/BF02033315", "http://doi.org/10.1007/BF02411466", "http://doi.org/10.1007/s11538-010-9517-4", "http://doi.org/10.1016/0166-5316(92)90019-D", "http://doi.org/10.1016/0166-5316(93)90017-O", "http://doi.org/10.1016/S0166-5316(02)00127-X", "http://doi.org/10.1016/S0166-5316(99)00005-X", "http://doi.org/10.1016/S0304-3975(02)00375-4", "http://doi.org/10.1016/j.peva.2012.06.003", "http://doi.org/10.1017/S0269964800002953", "http://doi.org/10.1109/72.737488", "http://doi.org/10.1145/2422.322419", "http://doi.org/10.1145/322003.322009", "http://doi.org/10.1145/322186.322193", "http://doi.org/10.1145/322358.322369", "http://doi.org/10.1162/neco.1989.1.4.502", "http://doi.org/10.1162/neco.1993.5.1.154", "http://doi.org/10.1214/aoap/1177005704", "http://doi.org/10.1214/aoms/1177704275", "http://doi.org/10.1214/aoms/1177706889", "http://doi.org/10.1287/mnsc.10.1.131", "http://doi.org/10.1287/moor.1070.0259", "http://doi.org/10.2307/1426623", "http://doi.org/10.2307/1426680", "http://doi.org/10.2307/1426753", "http://doi.org/10.2307/3214499", "http://doi.org/10.2307/3214781", "http://www.jstor.org/stable/1426753", "http://www.jstor.org/stable/2345774", "http://pubs.doc.ic.ac.uk/rcat/"]}, "National accounts": {"categories": ["All articles with dead external links", "Articles with dead external links from September 2018", "Articles with permanently dead external links", "Categories which are included in the JEL classification codes", "Economic data", "National accounts", "Official statistics", "Webarchive template other archives", "Wikipedia articles with GND identifiers", "Wikipedia articles with NDL identifiers"], "title": "National accounts", "method": "National accounts", "url": "https://en.wikipedia.org/wiki/National_accounts", "summary": "National accounts or national account systems (NAS) are the implementation of complete and consistent accounting techniques for measuring the economic activity of a nation. These include detailed underlying measures that rely on double-entry accounting. By design, such accounting makes the totals on both sides of an account equal even though they each measure different characteristics, for example production and the income from it. As a method, the subject is termed national accounting or, more generally, social accounting. Stated otherwise, national accounts as systems may be distinguished from the economic data associated with those systems. While sharing many common principles with business accounting, national accounts are based on economic concepts. One conceptual construct for representing flows of all economic transactions that take place in an economy is a social accounting matrix with accounts in each respective row-column entry.National accounting has developed in tandem with macroeconomics from the 1930s with its relation of aggregate demand to total output through interaction of such broad expenditure categories as consumption and investment. Economic data from national accounts are also used for empirical analysis of economic growth and development.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/f/f3/Emblem-money.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Accounting identity", "Actuarial science", "Adam Smith", "Adaptive expectations", "Aggregate demand", "Aggregation problem", "Agricultural economics", "Akaike information criterion", "Alfred Marshall", "Amartya Sen", "Analysis of covariance", "Analysis of variance", "Anarchist economics", "Ancient economic thought", "Anderson\u2013Darling test", "Applied economics", "Arithmetic mean", "Arthur Cecil Pigou", "Asia-Pacific Economic Cooperation", "Asymptotic theory (statistics)", "Austrian School", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Average cost", "Balance of payments", "Balance sheet", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Behavioral economics", "Bias of an estimator", "Bilateral monopoly", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Buddhist economics", "Budget deficit", "Budget set", "Business cycle", "Business economics", "Canonical correlation", "Capacity utilization", "Capital (economics)", "Capital account", "Capital flight", "Cartography", "Categorical variable", "Census", "Central bank", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Chicago school of economics", "Classical economics", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Colin Clark (economist)", "Competition (economics)", "Completeness (statistics)", "Computational economics", "Confidence interval", "Confounding", "Consumer choice", "Consumer confidence", "Contingency table", "Continuous probability distribution", "Control chart", "Convexity in economics", "Correlation and dependence", "Correlogram", "Cost-of-living index", "Cost\u2013benefit analysis", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cultural economics", "Currency", "Data collection", "David Ricardo", "David Romer", "Deadweight loss", "Decision theory", "Decomposition of time series", "Deflation", "Degrees of freedom (statistics)", "Demand for money", "Demand shock", "Demographic economics", "Demographic statistics", "Density estimation", "Depression (economics)", "Descriptive statistics", "Design of experiments", "Developed country", "Developing country", "Development economics", "Dickey\u2013Fuller test", "Digital divide", "Digital object identifier", "Distribution (economics)", "Divergence (statistics)", "Double-entry accounting", "Durbin\u2013Watson statistic", "Dynamic stochastic general equilibrium", "Ecological economics", "Econometrics", "Economic Cooperation Organization", "Economic cost", "Economic data", "Economic development", "Economic equilibrium", "Economic geography", "Economic growth", "Economic history", "Economic indicator", "Economic methodology", "Economic planning", "Economic policy", "Economic rent", "Economic sociology", "Economic statistics", "Economic surplus", "Economic system", "Economic theory", "Economics", "Economics of digitization", "Economies of scale", "Economies of scope", "Economist", "Education economics", "Effect size", "Effective demand", "Efficiency (statistics)", "Elasticity (economics)", "Elliptical distribution", "Empirical distribution function", "Engineering economics", "Engineering statistics", "Environmental accounting", "Environmental assets", "Environmental economics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "European Free Trade Association", "European System of Accounts", "Evolutionary economics", "Expected utility hypothesis", "Expeditionary economics", "Experiment", "Experimental economics", "Exponential family", "Exponential smoothing", "Externality", "F-test", "Factor analysis", "Factorial experiment", "Factors of production", "Failure rate", "Fan chart (statistics)", "Feminist economics", "Financial economics", "First-hitting-time model", "First World", "Fiscal policy", "Flow of Funds", "Forest plot", "Fourier analysis", "Fourth World", "Francis Ysidro Edgeworth", "Fran\u00e7ois Quesnay", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Friedrich Hayek", "G-test", "GDP gap", "Game theory", "Gary Becker", "General equilibrium theory", "General linear model", "Generalized linear model", "Generational accounting", "Geographic information system", "Geometric mean", "Georgism", "Geostatistics", "Glossary of economics", "Goodness of fit", "Granger causality", "Graphical model", "Great Depression", "Green national accounting", "Greg Mankiw", "Gross National Happiness", "Gross domestic product", "Gross national income", "Grouped data", "Growth accounting", "Harmonic mean", "Harold Hotelling", "Health economics", "Heavily indebted poor countries", "Herbert A. Simon", "Heterodox economics", "Heteroscedasticity", "Histogram", "Historical school of economics", "History of economic thought", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Household income", "Human Development Index", "Human Poverty Index", "Human development (humanity)", "Hyperinflation", "ICT Development Index", "IS\u2013LM model", "Index of dispersion", "Index of economics articles", "Indifference curve", "Industrial organization", "Inflation", "Inflation rate", "Information economics", "Input-output model", "Input\u2013output model", "Institutional economics", "Intangible asset", "Integrated Authority File", "Interaction (statistics)", "Interest", "Interest rate", "International Monetary Fund", "International Standard Book Number", "International economics", "International organization", "Interquartile range", "Intertemporal choice", "Interval estimation", "Investment (macroeconomics)", "Isotonic regression", "JEL classification codes", "Jackknife resampling", "Jacob Marschak", "Jarque\u2013Bera test", "Johansen test", "John Maynard Keynes", "John Stuart Mill", "John von Neumann", "Jonckheere's trend test", "Joseph Schumpeter", "Kaplan\u2013Meier estimator", "Karl Marx", "Kendall rank correlation coefficient", "Kenneth Arrow", "Keynesian", "Keynesian economics", "Knowledge economy", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Labor force participation rate", "Labour economics", "Laurence J. Kotlikoff", "Lausanne School", "Law and economics", "Least Developed Countries", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of European countries by average wage", "List of countries by GDP (PPP)", "List of countries by GDP (PPP) per capita", "List of countries by GDP (PPP) per hour worked", "List of countries by GDP (PPP) per person employed", "List of countries by GDP (nominal)", "List of countries by GDP (nominal) per capita", "List of countries by GNI (PPP) per capita", "List of countries by GNI (nominal, Atlas method) per capita", "List of countries by Human Development Index", "List of countries by average wage", "List of countries by employee compensation (per hour)", "List of countries by future GDP (PPP) estimates", "List of countries by future GDP (PPP) per capita estimates", "List of countries by inequality-adjusted HDI", "List of countries by median wage", "List of countries by net international investment position per capita", "List of countries by number of Internet users", "List of countries by number of broadband Internet subscriptions", "List of countries by past and future GDP (nominal)", "List of countries by past and future GDP (nominal) per capita", "List of countries by percentage of population living in poverty", "List of countries by research and development spending", "List of countries by smartphone penetration", "List of countries by wealth per adult", "List of economics journals", "List of economists", "List of fields of application of statistics", "List of important publications in economics", "List of minimum wages by country", "List of minimum wages in Canada", "List of sovereign states in Europe by minimum wage", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "L\u00e9on Walras", "M-estimator", "Macroeconomic", "Macroeconomics", "Mainstream economics", "Malthusianism", "Managerial economics", "Mann\u2013Whitney U test", "Marginal cost", "Marginal utility", "Marginalism", "Market (economics)", "Market failure", "Market structure", "Marxian economics", "Material Product System", "Mathematical economics", "Mathematical finance", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measures of national income and output", "Mechanism design", "Median", "Median-unbiased estimator", "Medical statistics", "Mercantilism", "Method of moments (statistics)", "Methodology", "Methods engineering", "Microeconomics", "Microfoundations", "Milton Friedman", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum wage in the United States", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monetary economics", "Monetary policy", "Money", "Money supply", "Monopolistic competition", "Monopoly", "Monopsony", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Mutualism (economic theory)", "NAIRU", "National Bureau of Economic Research", "National Diet Library", "National Income and Product Accounts", "National wealth", "Natural experiment", "Natural resource economics", "Nelson\u2013Aalen estimator", "Neo-Keynesian economics", "Neo-Marxian economics", "Neoclassical economics", "Net international investment position", "Net material product", "New Keynesian economics", "New classical macroeconomics", "New institutional economics", "Newly industrialized country", "Non-convexity (economics)", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "OECD", "Observational study", "Official statistics", "Oligopoly", "Oligopsony", "One- and two-tailed tests", "Operations research", "Opinion poll", "Opportunity cost", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Organizational economics", "Oskar Morgenstern", "Outline of economics", "Outline of statistics", "Parametric statistics", "Pareto efficiency", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Paul Krugman", "Paul Samuelson", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Penn World Table", "Percentile", "Perfect competition", "Permutation test", "Personal consumption expenditure", "Personal consumption expenditures price index", "Personnel economics", "Physiocracy", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Political economy", "Population (statistics)", "Population statistics", "Post-Keynesian economics", "Posterior probability", "Potential GDP", "Power (statistics)", "Prediction interval", "Preference (economics)", "Price", "Price index", "Price level", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Production set", "Profit (economics)", "Proportional hazards model", "Psychometrics", "Public choice", "Public economics", "Public good", "Public policy", "Purchasing power parity", "Quality control", "Quarterly Journal of Economics", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Ragnar Frisch", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rate of profit", "Rational expectations", "Rationing", "Real business-cycle theory", "Real versus nominal value (economics)", "Recession", "Regional economics", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Returns to scale", "Richard Stone", "Richard Thaler", "Risk aversion", "Robert J. Gordon", "Robert Lucas Jr.", "Robert Solow", "Robust regression", "Robust statistics", "Run chart", "Rural economics", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Saving", "Savings identity", "Scale parameter", "Scarcity", "Scatter plot", "Schools of economic thought", "Scientific control", "Scientific technique", "Score test", "Seasonal adjustment", "Second World", "Sectoral balances", "Semiparametric regression", "Service economy", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shortage", "Shrinkflation", "Sign test", "Simon Kuznets", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social Progress Index", "Social accounting", "Social accounting matrix", "Social choice theory", "Social cost", "Social health insurance", "Social insurance", "Social security", "Social statistics", "Socialist economics", "Socioeconomics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stagflation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical survey", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stock and flow", "Stockholm school (economics)", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Sunk cost", "Supply-side economics", "Supply and demand", "Supply shock", "Survey methodology", "Survival analysis", "Survival function", "Sustainable economy", "System identification", "Tax burden", "Technological change", "The Economist", "The General Theory of Employment, Interest and Money", "The New Palgrave: A Dictionary of Economics", "The New Palgrave Dictionary of Economics", "Theory of the firm", "Thermoeconomics", "Third World", "Thomas Robert Malthus", "Three-World Model", "Time domain", "Time series", "Tjalling Koopmans", "Tolerance interval", "Trade", "Transaction cost", "Transport economics", "Trend estimation", "U-statistic", "Uncertainty", "Unemployment", "Unemployment rate", "Uniformly most powerful test", "United Nations", "United Nations System of National Accounts", "Unpaid work", "Urban economics", "Utility", "V-statistic", "Value (economics)", "Variance", "Vector autoregression", "Vilfredo Pareto", "Wage", "Wald test", "Wavelet", "Wealth (economics)", "Welfare", "Welfare economics", "Whittle likelihood", "Wilcoxon signed-rank test", "World Bank", "World Bank high-income economy", "World Trade Organization", "Z-test"], "references": ["http://www.dictionaryofeconomics.com/article?id=pde2008_A000019&edition=current&q=national%20accounting&topicid=&result_number=10", "http://www.dictionaryofeconomics.com/article?id=pde2008_G000203&q=generational%20accounting&topicid=&result_number=1", "http://www.dictionaryofeconomics.com/article?id=pde2008_G000196&edition=current&q=environment&topicid=&result_number=5", "http://www.dictionaryofeconomics.com/article?id=pde2008_G000209&edition=current&q=national%20economic%20accounting&topicid=&result_number=3", "http://www.dictionaryofeconomics.com/article?id=pde2008_G000126", "http://www.dictionaryofeconomics.com/article?id=pde2008_I000299&edition=&field=keyword&q=national%20accounting&topicid=&result_number=2", "http://www.dictionaryofeconomics.com/article?id=pde2008_N000007&q=national%20income&topicid=&result_number=1", "http://www.dictionaryofeconomics.com/article?id=pde2008_N000160&q=National%20Income%20and%20Product%20Accounts%20(USA)&topicid=&result_number=1", "http://www.dictionaryofeconomics.com/article?id=pde2008_S000482&edition=current&q=sustainability&topicid=&result_number=1", "http://www.dictionaryofeconomics.com/article?id=pde2008_U000016&edition=current&q=unemployment&topicid=&result_number=1", "http://www.dictionaryofeconomics.com/article?id=pde2008_U000074&edition=current&q=unemployment&topicid=&result_number=4", "http://www.economist.com/research/Economics/searchActionTerms.cfm?query=generational+accounting", "http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B7MRM-4MT09VJ-4TK&_rdoc=18&_hierId=151000134&_refWorkId=21&_explode=151000131,151000134&_fmt=summary&_orig=na&_docanchor=&_idxType=SC&view=c&_ct=28&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=ca21bd9f0990f078143dcbf9ca76bb8f", "http://www.brookings.edu/~/media/Files/Programs/ES/BPEA/1984_2_bpea_papers/1984b_bpea_gordon_clark.pdf", "http://www.gmu.edu/depts/rae/archives/VOL17_4_2004/5_holcombe.pdf", "http://books.nap.edu/openbook.php?record_id=4844&page=R1", "http://cowles.econ.yale.edu/P/cm/m13/m13-16.pdf", "http://doi.org/10.2307%2F2118477", "http://www.nber.org/booksbyseries/SIW.html", "http://www.oecdbookshop.org/oecd/display.asp?sf1=identifiers&st1=9789264025660", "http://ntj.tax.org/wwtax/ntjrec.nsf/D119187747E6619285256863004B1F2F/$FILE/v49n4597.pdfhttps://www.jstor.org/pss/4007493", "http://unstats.un.org/unsd/nationalaccount/data.asp", "http://unstats.un.org/unsd/nationalaccount/sna.asp", "http://unstats.un.org/unsd/nationalaccount/sna2008.asp", "http://unstats.un.org/unsd/publication/SeriesF/seriesF_85.pdf", "http://arquivo.pt/wayback/20160521063357/http://www.brookings.edu/~/media/Files/Programs/ES/BPEA/1984_2_bpea_papers/1984b_bpea_gordon_clark.pdf", "http://www.bibliotekar.ru/economicheskaya-teoriya/index.htm", "https://books.google.com/books?id=BEFmbH-TNJMC&printsec=find&pg=PA5=#v=onepage&q&f=false", "https://www.bea.gov/about/pdf/jep_spring2008.pdf", "https://d-nb.info/gnd/4063886-8", "https://id.ndl.go.jp/auth/ndlna/00566368", "https://web.archive.org/web/20070613041057/http://www.cato.org/pubs/articles/gokhale-generational_accounting.pdf", "https://www.jstor.org/pss/2283115", "https://www.jstor.org/stable/2723639", "https://www.wikidata.org/wiki/Q350151"]}, "Memorylessness": {"categories": ["All articles covered by WikiProject Wikify", "All pages needing cleanup", "Articles covered by WikiProject Wikify from January 2018", "Characterization of probability distributions", "Markov processes", "Theory of probability distributions", "Wikipedia introduction cleanup from January 2018"], "title": "Memorylessness", "method": "Memorylessness", "url": "https://en.wikipedia.org/wiki/Memorylessness", "summary": "In probability and statistics, memorylessness is a property of certain probability distributions. It usually refers to the cases when the distribution of a \"waiting time\" until a certain event, does not depend on how much time has elapsed already. Only two kinds of distributions are memoryless: exponential distributions of non-negative real numbers and the geometric distributions of non-negative integers.\nMost phenomena are not memoryless, which means that observers will obtain information about them over time. For example, suppose that X is a random variable, the lifetime of a car engine, expressed in terms of \"number of miles driven until the engine breaks down\". It is clear, based on our intuition, that an engine which has already been driven for 300,000 miles will have a much lower X than would a second (equivalent) engine which has only been driven for 1,000 miles. Hence, this random variable would not have the memorylessness property.\nIn contrast, let us examine a situation which would exhibit memorylessness. Imagine a long hallway, lined on one wall with thousands of safes. Each safe has a dial with 500 positions, and each has been assigned an opening position at random. Imagine that an eccentric person walks down the hallway, stopping once at each safe to make a single random attempt to open it. In this case, we might define random variable X as the lifetime of their search, expressed in terms of \"number of attempts the person must make until they successfully open a safe\". In this case, E[X] will always be equal to the value of 500, regardless of how many attempts have already been made. Each new attempt has a (1/500) chance of succeeding, so the person is likely to open exactly one safe sometime in the next 500 attempts -- but with each new failure they make no \"progress\" toward ultimately succeeding. Even if the safe-cracker has just failed 499 consecutive times (or 4,999 times), we expect to wait 500 more attempts until we observe the next success. If, instead, this person focused their attempts on a single safe, and \"remembered\" their previous attempts to open it, they would be guaranteed to open the safe after, at most, 500 attempts (and, in fact, at onset would only expect to need 250 attempts, not 500).\nReal-life examples of memorylessness include the time until a given radioactive particle decays, the time until the discovery of a new Bitcoin block, and (over the short term) the time a storekeeper must wait before the arrival of their next customer.\nTo model these situations accurately, we must constantly 'forget' which state the system is in: the probabilities would not be influenced by the history of the process.In the context of Markov processes, memorylessness refers to the Markov property, an even stronger assumption which implies that the properties of random variables related to the future depend only on relevant information about the current time, not on information from further in the past. The present article describes the use outside the Markov property.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Bernoulli trial", "Bitcoin", "Characterization (mathematics)", "Conditional probability", "Discrete random variable", "Exponential distribution", "Exponential function", "Functional equation", "Geometric distribution", "Hysteresis", "Integer", "International Standard Book Number", "Intuition", "Markov process", "Markov property", "Materials science", "Monotonic function", "Monotonically decreasing", "Negative binomial distribution", "Probability", "Probability distribution", "Queueing theory", "Radioactive decay", "Random variable", "Rational number", "Real number", "Statistical independence", "Statistics", "Survival function", "William Feller"], "references": ["http://math.arizona.edu/~klin/courses/spring10-stoch/download/memoryless.pdf", "https://www.cs.princeton.edu/courses/archive/fall05/cos521/markov.pdf"]}, "Gamma process": {"categories": ["All Wikipedia articles needing context", "All articles needing expert attention", "All articles with unsourced statements", "All pages needing cleanup", "All stub articles", "Articles needing expert attention from November 2008", "Articles needing expert attention with no reason or talk parameter", "Articles with multiple maintenance issues", "Articles with unsourced statements from February 2012", "L\u00e9vy processes", "Mathematics articles needing expert attention", "Probability stubs", "Wikipedia articles needing context from March 2010", "Wikipedia introduction cleanup from March 2010"], "title": "Gamma process", "method": "Gamma process", "url": "https://en.wikipedia.org/wiki/Gamma_process", "summary": "A gamma process is a random process with independent gamma distributed increments. Often written as \n \n \n \n \u0393\n (\n t\n ;\n \u03b3\n ,\n \u03bb\n )\n \n \n {\\displaystyle \\Gamma (t;\\gamma ,\\lambda )}\n , it is a pure-jump increasing L\u00e9vy process with intensity measure \n \n \n \n \u03bd\n (\n x\n )\n =\n \u03b3\n \n x\n \n \u2212\n 1\n \n \n exp\n \u2061\n (\n \u2212\n \u03bb\n x\n )\n ,\n \n \n {\\displaystyle \\nu (x)=\\gamma x^{-1}\\exp(-\\lambda x),}\n for positive \n \n \n \n x\n \n \n {\\displaystyle x}\n . Thus jumps whose size lies in the interval \n \n \n \n [\n x\n ,\n x\n +\n d\n x\n )\n \n \n {\\displaystyle [x,x+dx)}\n occur as a Poisson process with intensity \n \n \n \n \u03bd\n (\n x\n )\n d\n x\n .\n \n \n {\\displaystyle \\nu (x)dx.}\n The parameter \n \n \n \n \u03b3\n \n \n {\\displaystyle \\gamma }\n controls the rate of jump arrivals and the scaling parameter \n \n \n \n \u03bb\n \n \n {\\displaystyle \\lambda }\n inversely controls the jump size. It is assumed that the process starts from a value 0 at t=0.\nThe gamma process is sometimes also parameterised in terms of the mean (\n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n ) and variance (\n \n \n \n v\n \n \n {\\displaystyle v}\n ) of the increase per unit time, which is equivalent to \n \n \n \n \u03b3\n =\n \n \u03bc\n \n 2\n \n \n \n /\n \n v\n \n \n {\\displaystyle \\gamma =\\mu ^{2}/v}\n and \n \n \n \n \u03bb\n =\n \u03bc\n \n /\n \n v\n \n \n {\\displaystyle \\lambda =\\mu /v}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma distribution", "Gamma function", "Gamma process (astrophysics)", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Increasing", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Marginal distribution", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random process", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistical independence", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": []}, "Stanine": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from November 2010", "CS1 maint: Archived copy as title", "Comparison of assessments", "Educational assessment and evaluation", "Psychometrics", "Scales"], "title": "Stanine", "method": "Stanine", "url": "https://en.wikipedia.org/wiki/Stanine", "summary": "Stanine (STAndard NINE) is a method of scaling test scores on a nine-point standard scale with a mean of five and a standard deviation of two.\nSome web sources attribute stanines to the U.S. Army Air Forces during World War II. Psychometric legend has it that a 1-9 scale was used because of the compactness of recording the score as a single digit but Thorndike claims that by reducing scores to just nine values, stanines \"reduce the tendency to try to interpret small score differences (p. 131)\". The earliest known use of stanines was by the U.S. Army Air Forces in 1943.", "images": [], "links": ["Edmonton, Alberta", "Educational Records Bureau", "Mean", "NZCER", "Normal distribution", "Normal score", "Otis-Lennon School Ability Test", "Standard deviation", "Stanene", "Sten scores", "United States Army Air Forces", "University of Alberta", "World War II"], "references": ["http://www.registrar.ualberta.ca/ro.cfm?id=184", "http://www.afhso.af.mil/shared/media/document/AFD-101105-019.pdf", "http://www.pballew.net/arithme3.html#stanine", "http://www.nzcersupport.org.nz/marking/?p=75", "http://www.gl-assessment.co.uk/products/cat4-cognitive-abilities-test-fourth-edition", "https://web.archive.org/web/20061212012831/http://www.registrar.ualberta.ca/ro.cfm?id=184", "https://web.archive.org/web/20080514031604/http://www.boydstonfoundation.org/WINGS32.html"]}, "SOFA Statistics": {"categories": ["All articles lacking reliable references", "All articles with a promotional tone", "Articles lacking reliable references from November 2014", "Articles with a promotional tone from March 2013", "Articles with multiple maintenance issues", "Cross-platform free software", "Cross-platform software", "Free statistical software", "Numerical software", "Pages using Infobox software with unknown parameters", "Pages using deprecated image syntax", "Science software for Linux", "Science software for MacOS", "Science software for Windows", "Software that uses wxPython", "Software using the GNU AGPL license", "Wikipedia articles with possible conflicts of interest from November 2014"], "title": "SOFA Statistics", "method": "SOFA Statistics", "url": "https://en.wikipedia.org/wiki/SOFA_Statistics", "summary": "SOFA Statistics is an open-source statistical package. The name stands for Statistics Open For All. It has a graphical user interface and can connect directly to MySQL, PostgreSQL, SQLite, MS Access (mdb), Microsoft SQL Server, and CUBRID. Data can also be imported from CSV and Tab-Separated files or spreadsheets (Microsoft Excel, OpenOffice.org Calc, Gnumeric, Google Docs). The main statistical tests available are Independent and Paired t-tests, Wilcoxon signed ranks, Mann\u2013Whitney U, Pearson's chi squared, Kruskal Wallis H, one-way ANOVA, Spearman's R, and Pearson's R. Nested tables can be produced with row and column percentages, totals, sd, mean, median, lower and upper quartiles, and sum.\nInstallation packages are available for several Operating Systems such as Microsoft Windows, Ubuntu, ArchLinux, Linux Mint, and macOS (Leopard upwards).\nSOFA Statistics is written in Python, and the widget toolkit used is wxPython. The statistical analyses are based on functions available through the Scipy stats module.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/3/31/Free_and_open-source_software_logo_%282009%29.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d6/Sofa_main_screen.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Unbalanced_scales.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["ADMB", "Affero General Public License", "Analyse-it", "Analysis of variance", "ArchLinux", "Arithmetic mean", "BMDP", "BV4.1 (software)", "CSPro", "CUBRID", "Comma-separated values", "Commercial software", "Comparison of statistical packages", "Cross-platform", "CumFreq", "DAP (software)", "Data Desk", "Dataplot", "EViews", "Epi Info", "Freeware", "GAUSS (software)", "GNU Octave", "GenStat", "Gnumeric", "Google Docs", "GraphPad InStat", "GraphPad Prism", "Graphical user interface", "Gretl", "H2O (software)", "JASP", "JMP (statistical software)", "JMulTi", "Julia (programming language)", "Just another Gibbs sampler", "Kruskal\u2013Wallis one-way analysis of variance", "LIMDEP", "LISREL", "Linux Mint", "List of statistical packages", "MATLAB", "MLwiN", "MS Access", "MacOS", "Mann\u2013Whitney U", "Maple (software)", "Mathcad", "Mathematica", "MedCalc", "Median", "Microfit", "Microsoft Excel", "Microsoft SQL Server", "Microsoft Windows", "Minitab", "MySQL", "NCSS (statistical software)", "Open-source", "Open-source software", "OpenBUGS", "OpenOffice.org Calc", "Operating System", "Operating system", "Orange (software)", "OxMetrics", "PSPP", "Pearson's chi-squared test", "Pearson product-moment correlation coefficient", "PostgreSQL", "Public-domain software", "Python (programming language)", "Quartile", "RATS (software)", "RExcel", "RStudio", "R (programming language)", "Revolution Analytics", "S-PLUS", "SAS (software)", "SHAZAM (software)", "SPC XL", "SPSS", "SPSS Modeler", "SQLite", "SUDAAN", "SYSTAT (software)", "SageMath", "Scipy", "SegReg", "SigmaStat", "SigmaXL", "SimFiT", "SmartPLS", "Software categories", "Software developer", "Software license", "Software release life cycle", "Spearman's rank correlation coefficient", "Stan (software)", "Standard deviation", "StatView", "StatXact", "Stata", "Statistica", "Statistical package", "Statistics", "StatsDirect", "TSP (econometrics software)", "T test", "Tab-separated values", "The Unscrambler", "UNISTAT", "Ubuntu (operating system)", "Widget toolkit", "Wilcoxon signed-rank test", "WinBUGS", "World Programming System", "WxPython", "X-12-ARIMA", "XLfit (software)", "XLispStat", "XploRe"], "references": ["http://www.sofastatistics.com", "http://www.sofastatistics.com/home.php", "https://launchpad.net/sofastatistics/", "https://sourceforge.net/projects/sofastatistics/", "https://web.archive.org/web/20100211142619/http://showmedo.com/videotutorials/video?name=7520010&fromSeriesID=752"]}, "Latent variable model": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "Articles lacking in-text citations from April 2011", "Articles needing additional references from April 2011", "Articles with multiple maintenance issues", "Latent variable models"], "title": "Latent variable model", "method": "Latent variable model", "url": "https://en.wikipedia.org/wiki/Latent_variable_model", "summary": "A latent variable model is a statistical model that relates a set of observable variables (so-called manifest variables) to a set of latent variables.\nIt is assumed that \nthe responses on the indicators or manifest variables are the result of an individual's position on the latent variable(s), and \nthat the manifest variables have nothing in common after controlling for the latent variable (local independence).\nDifferent types of the latent variable model can be grouped according to whether the manifest and \nlatent variables are categorical or continuous:\n\nThe Rasch model represents the simplest form of item response theory. Mixture models are central to latent profile analysis.\nIn factor analysis and latent trait analysis the latent variables are treated as continuous normally distributed variables, and in latent profile analysis and latent class analysis as from a multinomial distribution. The manifest variables in factor analysis and latent profile analysis are continuous and in most cases, their conditional distribution given the latent variables is assumed to be normal. In latent trait analysis and latent class analysis, the manifest variables are discrete. These variables could be dichotomous, ordinal or nominal variables. Their conditional distributions are assumed to be binomial or multinomial.\nBecause the distribution of a continuous latent variable can be approximated by a discrete distribution, the distinction between continuous and discrete variables turns out not to be fundamental at all. Therefore, there may be a psychometrical latent variable, but not a psychological psychometric variable.\nRecently DSDs and Latent Variable modeling were applied for the first time to the optimization of an extraction procedure in order to analyze target compounds present in wine samples. Latent Variable modeling can be a relevant tool for the optimization of analytical techniques, contributing to the implementation of rigorous, systematic and more efficient optimization protocols", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Factor analysis", "International Standard Book Number", "Item response theory", "Latent class analysis", "Latent profile analysis", "Latent trait analysis", "Latent variable", "Local independence", "Mixture models", "Multinomial distribution", "Normal distribution", "Observable variable", "Partial least squares path modeling", "Partial least squares regression", "Psychology", "Rasch model", "Statistical model", "Structural equation modeling"], "references": ["https://www.sciencedirect.com/science/article/pii/S0169743918300947"]}, "Qualitative data": {"categories": ["All articles lacking sources", "Articles lacking sources from March 2013", "Measurement"], "title": "Qualitative property", "method": "Qualitative data", "url": "https://en.wikipedia.org/wiki/Qualitative_property", "summary": "Qualitative properties are properties that are observed and can generally not be measured with a numerical result. They are contrasted to quantitative properties which have numerical characteristics. \nSome engineering and scientific properties are qualitative. A test method can result in qualitative data about something. This can be a categorical result or a binary classification (e.g., pass/fail, go/no go, conform/non-conform). It can sometimes be an engineering judgement.\nThe data that all share a qualitative property form a nominal category. A variable which codes for the presence or absence of such a property is called a binary categorical variable, or equivalently a dummy variable.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Behaviour", "Binary classification", "Categorical variable", "Child labour", "Conformity", "Corporate governance", "Dummy variable (statistics)", "Emotional", "Environmental issues", "Ethical issues", "Go/no go", "Human factors", "Human work capital", "Illegal dumping", "Level of measurement", "Manufacturing", "Motivation", "Nominal category", "Qualitative research", "Quantitative property", "Quantitative research", "Shareholder", "Statistical data type", "Test method"], "references": []}, "Distance correlation": {"categories": ["Covariance and correlation", "Statistical distance", "Theory of probability distributions"], "title": "Distance correlation", "method": "Distance correlation", "url": "https://en.wikipedia.org/wiki/Distance_correlation", "summary": "In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables.\nDistance correlation can be used to perform a statistical test of dependence with a permutation test. One first computes the distance correlation (involving the re-centering of Euclidean distance matrices) between two random vectors, and then compares this value to the distance correlations of many shuffles of the data.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/99/Distance_Correlation_Examples.svg"], "links": ["Annals of Statistics", "ArXiv", "Biometrika", "Brownian motion", "Canonical correlation analysis", "Characteristic function (probability theory)", "Corrado Gini", "Correlation", "Covariance", "Digital object identifier", "Distance correlation", "Distance matrix", "Energy distance", "Euclidean distance", "Euclidean norm", "Euclidean vector", "Expected value", "Grand mean", "G\u00e1bor J. Sz\u00e9kely", "Hilbert space", "Independence (probability theory)", "Independent component analysis", "Isometry", "Karolinum Press", "Mean absolute difference", "Metric space", "Moment (mathematics)", "Norm (mathematics)", "Orthonormal matrix", "Pearson's correlation", "Pearson product-moment correlation coefficient", "Permutation test", "Probability theory", "Proceedings of the Royal Society", "RV coefficient", "R (programming language)", "Random variable", "Random variables", "Random vector", "Skewness", "Statistical hypothesis testing", "Statistical power", "Statistical sample", "Statistics", "The Annals of Applied Statistics", "Wiener process"], "references": ["http://personal.bgsu.edu/~mrizzo/energy.htm", "http://doi.org/10.1016/j.spl.2012.08.007", "http://projecteuclid.org/download/pdfview_1/euclid.aoas/1267453934", "http://projecteuclid.org/download/pdfview_1/euclid.aoas/1267453933", "http://projecteuclid.org/euclid.aos/1413810731", "http://cran.us.r-project.org/web/packages/energy/index.html", "https://arxiv.org/pdf/1010.0822v2.pdf", "https://arxiv.org/pdf/1310.2926.pdf", "https://doi.org/10.1214%2F09-AOAS312", "https://doi.org/10.1214%2F09-AOAS312A", "https://doi.org/10.1214%2F09-AOAS312B", "https://dx.doi.org/10.1214/009053607000000505"]}, "Probability": {"categories": ["All articles to be expanded", "All articles with incomplete citations", "All articles with unsourced statements", "Articles to be expanded from April 2017", "Articles using small message boxes", "Articles with Italian-language external links", "Articles with incomplete citations from November 2012", "Articles with unsourced statements from February 2012", "Articles with unsourced statements from July 2012", "Articles with unsourced statements from June 2012", "Articles with unsourced statements from October 2015", "Commons category link from Wikidata", "Dimensionless numbers", "Probability", "Use dmy dates from October 2013", "Wikipedia articles needing clarification from July 2014", "Wikipedia articles needing clarification from June 2012", "Wikipedia articles needing page number citations from June 2012", "Wikipedia articles with GND identifiers"], "title": "Probability", "method": "Probability", "url": "https://en.wikipedia.org/wiki/Probability", "summary": "Probability is the measure of the likelihood that an event will occur. See glossary of probability and statistics. Probability quantifies as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes (\"heads\" and \"tails\") are both equally probable; the probability of \"heads\" equals the probability of \"tails\"; and since no other outcomes are possible, the probability of either \"heads\" or \"tails\" is 1/2 (which could also be written as 0.5 or 50%).\nThese concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/33/Bendixen_-_Carl_Friedrich_Gau%C3%9F%2C_1828.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/0/03/Cardano.jpg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Christiaan_Huygens-painting.jpeg", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/7/7c/Logic_portal.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png", "https://upload.wikimedia.org/wikipedia/commons/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg", "https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/d/df/Wikibooks-logo-en-noslogan.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg"], "links": ["A priori and a posteriori", "Abductive reasoning", "Abraham de Moivre", "Actuarial science", "Adolphe Quetelet", "Adrien-Marie Legendre", "Agnosticism", "Albert Einstein", "Almost surely", "An Anthology of Chance Operations", "Analytic\u2013synthetic distinction", "Andrey Kolmogorov", "Andrey Markov", "Antinomy", "Approximation", "ArXiv", "Areas of study", "Argumentation theory", "Ars Conjectandi", "Artemas Martin", "Artificial intelligence", "Augustus De Morgan", "Aumann's agreement theorem", "Authority", "Automobiles", "Avogadro constant", "Axiology", "BBC", "Balance of probabilities", "Bayes' rule", "Bayesian probability", "Behavioral finance", "Belief", "Blaise Pascal", "Bruno de Finetti", "Cache language model", "Cambridge University Press", "Carl Friedrich Gauss", "Catalog of articles in probability theory", "Certainty", "Chance (disambiguation)", "Chaos theory", "Christiaan Huygens", "Christian August Friedrich Peters", "Class membership probabilities", "Complementary event", "Complex systems", "Computer science", "Conditional probability", "Contingency (philosophy)", "Continuous random variable", "Continuous uniform distribution", "Copenhagen interpretation", "Cox's theorem", "Critical thinking", "Daniel Bernoulli", "Deductive reasoning", "Definition", "Dempster\u2013Shafer theory", "Description", "Determinism", "Dice", "Digital object identifier", "Doubt", "Edwin Thompson Jaynes", "Empirical evidence", "Environmental regulation", "Epistemology", "Equiprobability", "Erwin Schr\u00f6dinger", "Estimation Theory", "Estimators", "Etymology", "Eudaemons", "Europe", "Event (probability theory)", "Experiment", "Fallibilism", "Fatalism", "Finance", "Financial regulation", "Frequentist probability", "Friedrich Bessel", "Function (mathematics)", "GNU Free Documentation License", "Gambling", "Game theory", "Games of chance", "George Boole", "Gerolamo Cardano", "Giovanni Schiaparelli", "Glossary of aerospace engineering", "Glossary of archaeology", "Glossary of architecture", "Glossary of areas of mathematics", "Glossary of artificial intelligence", "Glossary of astronomy", "Glossary of biology", "Glossary of botany", "Glossary of calculus", "Glossary of chemistry terms", "Glossary of civil engineering", "Glossary of clinical research", "Glossary of computer science", "Glossary of ecology", "Glossary of economics", "Glossary of electrical and electronics engineering", "Glossary of engineering", "Glossary of entomology terms", "Glossary of environmental science", "Glossary of genetics", "Glossary of geography terms", "Glossary of geology", "Glossary of machine vision", "Glossary of mechanical engineering", "Glossary of medicine", "Glossary of meteorology", "Glossary of physics", "Glossary of probability and statistics", "Glossary of psychiatry", "Glossary of robotics", "Glossary of speciation", "Glossary of structural engineering", "Groupthink", "Hermann Laurent", "Heuristics in judgment and decision-making", "History of logic", "History of probability", "History of statistics", "Hypothesis", "Ian Hacking", "In Our Time (radio series)", "Independence (probability theory)", "Index of logic articles", "Inductive reasoning", "Inference", "Instrumentalism", "Integral geometry", "Integrated Authority File", "International Standard Book Number", "Inverse probability", "Italians", "Jakob Bernoulli", "James Franklin (philosopher)", "James Ivory (mathematician)", "James Whitbread Lee Glaisher", "John E. Freund", "John Herschel", "Joint distribution", "Journal of the American Statistical Association", "Karl Pearson", "Kinetic theory of gases", "Kolmogorov", "Laplace", "Laplace's demon", "Law", "Legal case", "Likelihood", "Likelihood function", "List of Boolean algebra topics", "List of fallacies", "List of logic symbols", "List of logicians", "List of mathematical logic topics", "List of mathematical probabilists", "List of paradoxes", "List of probability journals", "List of rules of inference", "List of set theory topics", "Logic", "Logic in computer science", "Logical consequence", "Logical form", "Logical truth", "Machine learning", "Market (economics)", "Markov chains", "Mathematical logic", "Mathematics", "Max Born", "Meaning (linguistics)", "Measure (mathematics)", "Metalogic", "Metamathematics", "Method of least squares", "Morgan Crofton", "Mutually exclusive events", "Name", "Natural language processing", "Necessity and sufficiency", "Newtonian mechanics", "Nihilism", "Nobility", "Non-classical logic", "Notation in probability and statistics", "Objectivity (philosophy)", "Odds", "Olav Kallenberg", "Outline of logic", "Outline of probability", "Paradox", "Philosophical logic", "Philosophy", "Philosophy of logic", "Physics", "Pierre-Simon Laplace", "Pierre de Fermat", "Possibility theory", "Possible world", "Posterior probability distribution", "Power set", "Presupposition", "Presupposition (philosophy)", "Prior probability distribution", "Probability (disambiguation)", "Probability axioms", "Probability density function", "Probability interpretations", "Probability space", "Probability theory", "Probable error", "Proof (truth)", "Propensity probability", "Quantum decoherence", "Quantum fluctuation", "Quantum mechanics", "Random", "Randomness", "Real number", "Reality", "Reason", "Reference", "Reliability (statistics)", "Reliability theory of aging and longevity", "Richard Dedekind", "Richard Jeffrey", "Richard Threlkeld Cox", "Risk", "Robert Adrain", "Roger Cotes", "Roulette", "Sample space", "Schr\u00f6dinger equation", "Science", "Scientific theory", "Semantics", "Set (mathematics)", "Set theory", "Skepticism", "Solipsism", "Statement (logic)", "Statistical", "Statistical Language Model", "Statistical inference", "Statistical model", "Statistics", "Stochastic process", "Strict conditional", "Subjective probability", "Substitution (logic)", "Sylvestre Lacroix", "Syntax (logic)", "The Doctrine of Chances", "Theory", "Theory of errors", "Theory of justification", "Thomas Simpson", "Truth", "UbuWeb", "Uncertainty", "Undefined (mathematics)", "Validity (logic)", "W. F. Donkin", "Warranty", "Wave function", "Wave function collapse", "Webster's Dictionary", "Well-defined", "Witness", "\u03a3-algebra"], "references": ["http://www.britannica.com/EBchecked/topic/477530/probability-theory", "http://www.celiagreen.com/charlesmccreery/statistics/bayestutorial.pdf", "http://statprob.com/encyclopedia/AdrienMarieLegendre.html", "http://jeff560.tripod.com/mathsym.html", "http://jeff560.tripod.com/stat.html", "http://ubu.com/historical/young/index.html", "http://www.feynmanlectures.caltech.edu/I_06.html", "http://www.columbia.edu/~pg2113/index_files/Gorroochurn-Some%20Laws.pdf", "http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html", "http://archon.educ.kent.edu/Oasis/Resc/Educ/data.html", "http://plato.stanford.edu/archives/win2012/entries/probability-interpret/", "http://www.math.uah.edu/stat/", "http://wiki.stat.ucla.edu/socr/index.php/EBook", "http://bayes.wustl.edu/etj/prob/book.pdf", "http://amshistorica.unibo.it/35", "http://homepages.cwi.nl/~paulv/KOLMOGOROV.BIOGRAPHY.html", "http://bitbucket.org/shabbychef/numas_text/", "http://doi.org/10.1016%2F0001-6918(70)90012-0", "http://doi.org/10.1080%2F14459795.2011.552575", "http://www.secondmoment.org/articles/probability.php", "http://tools.wmflabs.org/ftl/cgi-bin/ftl?st=wp&su=Probability", "http://www.statslab.cam.ac.uk/~rrw1/markov/M.pdf", "http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm", "http://www.economics.soton.ac.uk/staff/aldrich/Probability%20Earliest%20Uses.htm", "http://www.bbc.co.uk/programmes/b00bqf61", "https://books.google.com/books?id=LQIsAQAAIAAJ&q=achtung-gebietend", "https://d-nb.info/gnd/4137007-7", "https://web.archive.org/web/20150428142545/http://machaut.uchicago.edu/?resource=Webster's&word=probability&use1913=on", "https://web.archive.org/web/20160119131820/http://omega.albany.edu:8008/JaynesBook.html", "https://web.archive.org/web/20160203070724/http://statprob.com/encyclopedia/AdrienMarieLegendre.html", "https://www.wikidata.org/wiki/Q9492"]}, "Rand index": {"categories": ["Clustering criteria", "Summary statistics for contingency tables"], "title": "Rand index", "method": "Rand index", "url": "https://en.wikipedia.org/wiki/Rand_index", "summary": "The Rand index or Rand measure (named after William M. Rand) in statistics, and in particular in data clustering, is a measure of the similarity between two data clusterings. A form of the Rand index may be defined that is adjusted for the chance grouping of elements, this is the adjusted Rand index. From a mathematical standpoint, Rand index is related to the accuracy, but is applicable even when class labels are not used.", "images": [], "links": ["Accuracy and precision", "Data clustering", "Digital object identifier", "Element (mathematics)", "JSTOR", "Journal of the American Statistical Association", "K-means clustering", "Partition of a set", "Set (mathematics)", "Simple matching coefficient", "Statistics"], "references": ["http://i11www.iti.uni-karlsruhe.de/extra/publications/ww-cco-06.pdf", "http://www.ima.umn.edu/~iwen/REU/10.pdf", "http://doi.org/10.1007%2FBF01908075", "http://doi.org/10.2307%2F2284239", "http://www.jmlr.org/papers/volume11/vinh10a/vinh10a.pdf", "http://www.jmlr.org/papers/volume18/17-039/17-039.pdf", "http://www.jstor.org/stable/2284239", "https://github.com/bjoern-andres/partition-comparison"]}, "Kriging": {"categories": ["All articles with failed verification", "All articles with unsourced statements", "Articles with failed verification from December 2015", "Articles with unsourced statements from August 2018", "Articles with unsourced statements from March 2016", "Commons category link is on Wikidata", "Geostatistics", "Interpolation", "Multivariate interpolation", "Webarchive template wayback links", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from November 2014"], "title": "Kriging", "method": "Kriging", "url": "https://en.wikipedia.org/wiki/Kriging", "summary": "In statistics, originally in geostatistics, kriging or Gaussian process regression is a method of interpolation for which the interpolated values are modeled by a Gaussian process governed by prior covariances. Under suitable assumptions on the priors, kriging gives the best linear unbiased prediction of the intermediate values. Interpolating methods based on other criteria such as smoothness (e.g., smoothing spline) need not yield the most likely intermediate values. The method is widely used in the domain of spatial analysis and computer experiments. The technique is also known as Wiener\u2013Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov.\n\nThe theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the Master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa. Krige sought to estimate the most likely distribution of gold based on samples from a few boreholes. The English verb is to krige and the most common noun is kriging; both are often pronounced with a hard \"g\", following the pronunciation of the name \"Krige\". The word is sometimes capitalized as Kriging in the literature.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f5/Example_of_kriging_interpolation_in_1D.png", "https://upload.wikimedia.org/wikipedia/commons/1/1d/Information_icon4.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Andrey Kolmogorov", "Astronomy", "Bayes linear statistics", "Bayesian inference", "Best linear unbiased estimator", "Best linear unbiased prediction", "Bibcode", "Carol A. Gotway Crawford", "Computer experiment", "Covariance", "Covariance function", "Covariance matrix", "Covariogram", "Curve fitting", "Danie G. Krige", "Digital object identifier", "Engineering", "Environmental science", "Expected value", "Finite element method", "Function (mathematics)", "Gaussian process", "Gauss\u2013Markov theorem", "Generalized least squares", "Geographic coordinate system", "Georges Matheron", "Geostatistics", "Gradient-Enhanced Kriging (GEK)", "Hard and soft g", "Hydrogeology", "Indicator function", "Integrated Circuit Analysis and Optimization", "International Standard Book Number", "Interpolation", "JSTOR", "Kernel (set theory)", "Lagrange multiplier", "Lagrange multipliers", "Likelihood function", "Log-normal distribution", "Logarithm", "Mathematical Geology", "Metal forming", "Metamodeling", "Mining", "Modelling of Microwave Devices", "Moment (mathematics)", "Multivariate interpolation", "Natural resource", "Nonparametric regression", "Norbert Wiener", "Normal distribution", "Optimization", "Polynomial", "Posterior probability", "Prior probability distribution", "Probability distribution", "PubMed Identifier", "Radial basis function", "Random field", "Random variable", "Real estate appraisal", "Regression-kriging", "Regression analysis", "Remote sensing", "Reproducing kernel Hilbert space", "Saraju Mohanty", "Set (mathematics)", "Smoothing spline", "Smoothness", "South Africa", "Space mapping", "Spatial analysis", "Spatial dependence", "Spline (mathematics)", "Stationary process", "Statistics", "Stochastic process", "Surrogate model", "Variogram", "Wayback Machine", "Witwatersrand"], "references": ["http://www.sumo.intec.ugent.be/ooDACE", "http://apps.nrbook.com/empanel/index.html?pg=144", "http://apps.nrbook.com/empanel/index.html?pg=836", "http://www.pykriging.com", "http://www.uqlab.com", "http://adsabs.harvard.edu/abs/1998WRR....34.1373Z", "http://web.mit.edu/dennism/www/Publications/M25_1998_Zimmerman_etal_WRR.pdf", "http://www.cse.unt.edu/~smohanty/Publications_Journals/2013/Mohanty_IET-CDS-2013Sep_Thermal-Sensor-Geostatistical.pdf", "http://press3.mcs.anl.gov/scala-gauss/", "http://www.ncbi.nlm.nih.gov/pubmed/11916123", "http://sourceforge.net/projects/kriging", "http://mgstat.sourceforge.net/", "http://doi.org/10.1002%2Fjnm.803", "http://doi.org/10.1007%2F0-306-47647-9_6", "http://doi.org/10.1007%2F978-94-011-5014-9_23", "http://doi.org/10.1007%2Fs00477-005-0234-8", "http://doi.org/10.1007%2Fs11004-005-1560-6", "http://doi.org/10.1007%2Fs12289-008-0001-8", "http://doi.org/10.1023%2FA:1023239606028", "http://doi.org/10.1029%2F98WR00003", "http://doi.org/10.1093%2Fmnras%2Fstu937", "http://doi.org/10.1093%2Fmnras%2Fstv2947", "http://doi.org/10.1093%2Fmnras%2Fstx418", "http://doi.org/10.1111%2Fj.1745-6584.2002.tb02503.x", "http://doi.org/10.1137%2F1.9781611970128", "http://www.gaussianprocess.org/gpml/code/matlab/", "http://www.jstor.org/stable/2245858", "http://www.openturns.org/", "http://scikit-learn.org/stable/", "http://scikit-learn.org/stable/modules/generated/sklearn.gaussian_process.GaussianProcessRegressor.html#sklearn.gaussian_process.GaussianProcessRegressor", "https://github.com/SMTorg/SMT", "https://github.com/bsmurphy/PyKrige", "https://github.com/modsim/KriKit", "https://web.archive.org/web/20050604080848/http://www2.imm.dtu.dk/~hbn/dace/", "https://web.archive.org/web/20140714173450/http://www.cse.unt.edu/~smohanty/Publications_Journals/2013/Mohanty_IET-CDS-2013Sep_Thermal-Sensor-Geostatistical.pdf"]}, "Non-linear iterative partial least squares": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2014", "Articles with unsourced statements from March 2011", "Articles with unsourced statements from May 2018", "CS1 maint: Multiple names: authors list", "CS1 maint: Uses authors parameter", "Commons category link from Wikidata", "Dimension reduction", "Matrix decompositions", "Wikipedia articles needing clarification from March 2011", "Wikipedia articles needing page number citations from June 2011"], "title": "Principal component analysis", "method": "Non-linear iterative partial least squares", "url": "https://en.wikipedia.org/wiki/Principal_component_analysis", "summary": "Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables (entities each of which takes on various numerical values) into a set of values of linearly uncorrelated variables called principal components. If there are \n \n \n \n n\n \n \n {\\displaystyle n}\n observations with \n \n \n \n p\n \n \n {\\displaystyle p}\n variables, then the number of distinct principal components is \n \n \n \n min\n (\n n\n \u2212\n 1\n ,\n p\n )\n \n \n {\\displaystyle \\min(n-1,p)}\n . This transformation is defined in such a way that the first principal component has the largest possible variance (that is, accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components. The resulting vectors (each being a linear combination of the variables and containing n observations) are an uncorrelated orthogonal basis set. PCA is sensitive to the relative scaling of the original variables.\nPCA was invented in 1901 by Karl Pearson, as an analogue of the principal axis theorem in mechanics; it was later independently developed and named by Harold Hotelling in the 1930s. Depending on the field of application, it is also named the discrete Karhunen\u2013Lo\u00e8ve transform (KLT) in signal processing, the Hotelling transform in multivariate quality control, proper orthogonal decomposition (POD) in mechanical engineering, singular value decomposition (SVD) of X (Golub and Van Loan, 1983), eigenvalue decomposition (EVD) of XTX in linear algebra, factor analysis (for a discussion of the differences between PCA and factor analysis see Ch. 7 of Jolliffe's Principal Component Analysis), Eckart\u2013Young theorem (Harman, 1960), or empirical orthogonal functions (EOF) in meteorological science, empirical eigenfunction decomposition (Sirovich, 1987), empirical component analysis (Lorenz, 1956), quasiharmonic modes (Brooks et al., 1988), spectral decomposition in noise and vibration, and empirical modal analysis in structural dynamics.\nPCA is mostly used as a tool in exploratory data analysis and for making predictive models. It is often used to visualize genetic distance and relatedness between populations. PCA can be done by eigenvalue decomposition of a data covariance (or correlation) matrix or singular value decomposition of a data matrix, usually after a normalization step of the initial data. The normalization of each attribute consists of mean centering \u2013 subtracting each data value from its variable\u2019s measured mean so that its empirical mean (average) is zero \u2013 and, possibly, normalizing each variable\u2019s variance to make it equal to 1; see Z-scores. The results of a PCA are usually discussed in terms of component scores, sometimes called factor scores (the transformed variable values corresponding to a particular data point), and loadings (the weight by which each standardized original variable should be multiplied to get the component score). If component scores are standardized to unit variance loadings must contain the data variance in them (and that is the magnitude of eigenvalues). If component scores are not standardized (therefore they contain the data variance) then loadings must be unit-scaled, (\"normalized\") and these weights are called eigenvectors; they are the cosines of orthogonal rotation of variables into principal components or back.\nPCA is the simplest of the true eigenvector-based multivariate analyses. Often, its operation can be thought of as revealing the internal structure of the data in a way that best explains the variance in the data. If a multivariate dataset is visualised as a set of coordinates in a high-dimensional data space (1 axis per variable), PCA can supply the user with a lower-dimensional picture, a projection of this object when viewed from its most informative viewpoint. This is done by using only the first few principal components so that the dimensionality of the transformed data is reduced.\nPCA is closely related to factor analysis. Factor analysis typically incorporates more domain specific assumptions about the underlying structure and solves eigenvectors of a slightly different matrix.\nPCA is also related to canonical correlation analysis (CCA). CCA defines coordinate systems that optimally describe the cross-covariance between two datasets while PCA defines a new orthogonal coordinate system that optimally describes variance in a single dataset.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/84/Elmap_breastcancer_wiki.png", "https://upload.wikimedia.org/wikipedia/commons/f/f2/Fractional_Residual_Variances_comparison%2C_PCA_and_NMF.pdf", "https://upload.wikimedia.org/wikipedia/commons/f/f5/GaussianScatterPCA.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/6/69/PCA_of_Haplogroup_J_using_37_STRs.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": [".NET Framework", "ALGLIB", "AbdiWilliams", 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"Blocking (statistics)", "Boosting (machine learning)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breast cancer", "Breusch\u2013Godfrey test", "C++", "CURE data clustering algorithm", "CUR matrix approximation", "Canonical correlation", "Canonical correlation analysis", "Canonical correspondence analysis", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared statistic", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational learning theory", "Conditional random field", "Conference on Neural Information Processing Systems", "Confidence interval", "Confounding", "Conjugate transpose", "Contingency table", "Contingency tables", "Continuous probability distribution", "Control chart", "Convolutional neural network", "Coordinate system", "Correlation", "Correlation and dependence", "Correlation clustering", "Correlation matrix", "Correlogram", "Correspondence analysis", "Count data", "Covariance", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curie Institute (Paris)", "Curve", "DBSCAN", "Data collection", "Data matrix (multivariate statistics)", "Data mining", "Decision tree learning", "Decomposition of time series", "DeepDream", "Deep learning", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Detrended correspondence analysis", "Diagonal", "Diagonal matrix", "Diagonalizable matrix", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension (metadata)", "Dimensionality reduction", "Discrete cosine transform", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dynamic mode decomposition", "ELKI", "Eckart\u2013Young theorem", "Econometrics", "Effect size", "Efficiency (statistics)", "Eigendecomposition", "Eigendecomposition of a matrix", "Eigenface", "Eigenvalue", "Eigenvalues", "Eigenvalues and eigenvectors", "Eigenvector", "Eigenvectors", "Eigenvectors and eigenvalues", "Elastic map", "Electric current", "Electrophysiology", "Ellipsoid", "Elliptical distribution", "Empirical component analysis", "Empirical distribution function", "Empirical eigenfunction decomposition", "Empirical mean", "Empirical orthogonal functions", "Empirical risk minimization", "Engineering statistics", "Ensemble learning", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Euclidean space", "Expectation\u2013maximization algorithm", "Experiment", "Explanatory variable", "Exploratory data analysis", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factor analysis of mixed data", "Factorial code", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feature engineering", "Feature learning", "First-hitting-time model", "Forest plot", "Fourier analysis", "Free software", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Frobenius norm", "Functional principal component analysis", "G-test", "GNU Octave", "Gated recurrent unit", "General linear model", "Generalized linear model", "Genomics", "Geographic information system", "Geometric data analysis", "Geometric mean", "Geostatistics", "Glossary of artificial intelligence", "Goodness of fit", "Grammar induction", "Gram\u2013Schmidt", "Granger causality", "Graphical model", "Grouped data", "Haplotype", "Harmonic mean", "Harold Hotelling", "Heteroscedasticity", "Hidden Markov model", "Hierarchical clustering", "High dimensional data", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "IDL (programming language)", "Iid", "Independent component analysis", "Index of dispersion", "Interaction (statistics)", "Interactive Data Language", "Interest rate derivative", "International Conference on Machine Learning", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Jean-Paul Benz\u00e9cri", "Johansen test", "Jonckheere's trend test", "Journal of Educational Psychology", "Journal of Machine Learning Research", "Julia language", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "KNIME", "Kaplan\u2013Meier estimator", "Karhunen\u2013Lo\u00e8ve theorem", "Karl Pearson", "Kendall rank correlation coefficient", "Kernel PCA", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kullback\u2013Leibler divergence", "Kurtosis", "L-moment", "L1-norm principal component analysis", "LOBPCG", "Lanczos algorithm", "Learning to rank", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear combination", "Linear discriminant analysis", "Linear regression", "Linear transformation", "List of datasets for machine-learning research", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local outlier factor", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Long short-term memory", "Loss function", "Low-rank approximation", "Lp space", "Ludovic Lebart", "M-estimator", "MATLAB", "Machine Learning (journal)", "Machine learning", "Manifold", "Mann\u2013Whitney U test", "Mathematica", "Matplotlib", "Matrix-free methods", "Matrix (mathematics)", "Matrix algebra", "Matrix decomposition", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean-shift", "Median", "Median-unbiased estimator", "Medical statistics", "Metabolomics", "Method of moments (statistics)", "Methods engineering", "Microarray", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Minimum mean square error", "Missing data", "Mixed model", "Mlpack", "Mode (statistics)", "Mode shape", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multilayer perceptron", "Multilinear principal component analysis", "Multilinear subspace learning", "Multiple comparisons", "Multiple correspondence analysis", "Multivariate Gaussian distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate dataset", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Mutual information", "NAG Numerical Library", "NMath", "Naive Bayes classifier", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Neuron", "Neuroscience", "Non-linear iterative partial least squares", "Non-negative matrix factorization", "Nonlinear dimensionality reduction", "Nonlinear 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transitions", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point distribution model", "Point estimation", "Poisson regression", "Polar decomposition", "Population (statistics)", "Population statistics", "Portfolio optimization", "Positive semidefinite matrix", "Posterior probability", "Power (statistics)", "Power iteration", "Prediction interval", "Predictive modeling", "Principal axis theorem", "Principal component analysis", "Principal component regression", "Principal diagonal", "Principal geodesic analysis", "Principle Component Analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probably approximately correct learning", "Projection (mathematics)", "Proportional hazards model", "Psychometrics", "PubMed Identifier", "Python (programming language)", "Q-learning", "Qlucore", "Quality control", "Quantitative finance", "Quasi-experiment", "Quasiharmonic modes", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Random forest", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank (linear algebra)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh quotient", "Recurrent neural network", "Regression analysis", "Regression model validation", "Reinforcement learning", "Relevance vector machine", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted Boltzmann machine", "Risk management", "Robust principal component analysis", "Robust regression", "Robust statistics", "Round-off errors", "Run chart", "SAS (software)", "Sample median", "Sample size determination", "Sample variance", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "SciPy", "Scientific control", "Scientific visualization", "Scikit-learn", "Score test", "Seasonal adjustment", "Self-organizing map", "Semi-supervised learning", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Signal-to-noise ratio", "Signal processing", "Simple linear regression", "Simultaneous equations model", "Singular spectrum analysis", "Singular value decomposition", "Skewness", "Social statistics", "Sparse PCA", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spectral theorem", "Spike-triggered covariance", "Spike sorting", "Standard deviation", "Standard error", "State\u2013action\u2013reward\u2013state\u2013action", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stock", "Stock selection criterion", "Stratified sampling", "Structural break", "Structural equation modeling", "Structured prediction", "Student's t-test", "Sufficient statistic", "Supervised learning", "Support vector machine", "Survey methodology", "Survival analysis", "Survival function", "Swap (finance)", "System identification", "T-distributed stochastic neighbor embedding", "Temporal difference learning", "The Lancet", "Time domain", "Time series", "Tolerance interval", "Transform coding", "Transpose", "Trend estimation", "Tucker decomposition", "U-Net", "U-statistic", "Uniformly most powerful test", "Unit vector", "University of Canterbury", "Unsupervised learning", "V-statistic", "Vapnik\u2013Chervonenkis theory", "Variance", "Vector autoregression", "Vector space", "Wald test", "Wavelet", "Weighted least squares", "Weka (machine learning)", "White noise", "Whitening transformation", "Whittle likelihood", "Wilcoxon signed-rank test", "Y-STR", "YouTube", "Z-score", "Z-test"], "references": ["http://www.ulb.ac.be/di/map/yleborgn/pub/NPL_PCA_07.pdf", "http://www.dsp.utoronto.ca/~haiping/Publication/SurveyMSL_PR2011.pdf", "http://stat.smmu.edu.cn/history/pearson1901.pdf", "http://www.coheris.com/produits/analytics/logiciel-data-mining/", "http://www.mathworks.com/access/helpdesk/help/techdoc/ref/eig.html#998306", "http://www.mathworks.com/matlabcentral/fileexchange/24634", "http://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_princomp_sect001.htm", "http://www.tradinginterestrates.com", "http://reference.wolfram.com/mathematica/ref/Eigenvalues.html", "http://www.cc.gatech.edu/~vempala/papers/dfkvv.pdf", "http://adsabs.harvard.edu/abs/2007AJ....133..734B", "http://adsabs.harvard.edu/abs/2008arXiv0811.4413H", "http://adsabs.harvard.edu/abs/2012ApJ...755L..28S", "http://adsabs.harvard.edu/abs/2012arXiv1205.6935G", "http://adsabs.harvard.edu/abs/2014ITSP...62.5046M", "http://adsabs.harvard.edu/abs/2014arXiv1410.6801C", "http://adsabs.harvard.edu/abs/2016ApJ...824..117P", "http://adsabs.harvard.edu/abs/2018ApJ...852..104R", "http://adsabs.harvard.edu/abs/2018ISPM...35...32V", "http://ranger.uta.edu/~chqding/papers/KmeansPCA1.pdf", "http://ranger.uta.edu/~chqding/papers/Zha-Kmeans.pdf", "http://bioinfo-out.curie.fr/projects/vidaexpert/", "http://factominer.free.fr/", "http://www.ihes.fr/~zinovyev/princmanif2006/", "http://www.ncbi.nlm.nih.gov/pubmed/19772385", "http://www.ncbi.nlm.nih.gov/pubmed/27735002", "http://www.ncbi.nlm.nih.gov/pubmed/8054384", "http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc552.htm", "http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf", "http://arxiv.org/abs/0811.1081", "http://arxiv.org/abs/0811.4413", "http://arxiv.org/abs/0912.3599", "http://arxiv.org/abs/1108.4372", "http://arxiv.org/abs/1205.6935", "http://arxiv.org/abs/1206.5538", "http://arxiv.org/abs/1207.4197", "http://arxiv.org/abs/1405.6785", "http://arxiv.org/abs/1410.6801", "http://arxiv.org/abs/1511.01245", "http://arxiv.org/abs/1604.06097", "http://arxiv.org/abs/1612.06037", "http://arxiv.org/abs/1711.09492", "http://arxiv.org/abs/1712.10317", "http://arxiv.org/abs/1804.10253", "http://arxiv.org/abs/astro-ph/0606170", "http://arxiv.org/archive/astro-ph.IM", "http://arxiv.org/archive/stat.ML", "http://doi.org/10.1002%2Fwics.101", "http://doi.org/10.1007%2F978-3-540-69497-7_27", "http://doi.org/10.1007%2Fb98835", "http://doi.org/10.1007%2Fbf00198909", "http://doi.org/10.1016%2F0003-2670(86)80028-9", "http://doi.org/10.1016%2FS0140-6736(05)17947-1", "http://doi.org/10.1016%2Fj.cosrev.2016.11.001", "http://doi.org/10.1016%2Fj.patcog.2011.01.004", "http://doi.org/10.1023%2Fb:mach.0000033113.59016.96", "http://doi.org/10.1039%2FC6IB00100A", "http://doi.org/10.1080%2F14786440109462720", "http://doi.org/10.1086%2F510127", "http://doi.org/10.1088%2F2041-8205%2F755%2F2%2FL28", "http://doi.org/10.1089%2Fcmb.2008.0221", "http://doi.org/10.1109%2F2.36", "http://doi.org/10.1109%2FMSP.2018.2826566", "http://doi.org/10.1109%2FTPAMI.2013.50", "http://doi.org/10.1109%2FTSP.2014.2338077", "http://doi.org/10.1145%2F1970392.1970395", "http://doi.org/10.1175%2F1520-0493(1987)115%3C1825:oaloma%3E2.0.co;2", "http://doi.org/10.2307%2F2333955", "http://doi.org/10.3847%2F0004-637X%2F824%2F2%2F117", "http://doi.org/10.3847%2F1538-4357%2Faaa1f2", "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6472238", "http://www.jstor.org/stable/2333955", "http://www.pnas.org/content/100/26/15522.full.pdf", "http://pubs.rsc.org/en/Content/ArticleLanding/2016/IB/C6IB00100A#!divAbstract", "https://books.google.com/books?visbn=0-12-269851-7", "https://www.springer.com/west/home/new+&+forthcoming+titles+(default)?SGWID=4-40356-22-2285433-0", "https://www.youtube.com/watch?v=BfTMmoDFXyE", "https://www.youtube.com/watch?v=UUxIXU_Ob6E", "https://www.youtube.com/watch?v=_UVHneBUBW0", "https://www.youtube.com/watch?v=ey2PE5xi9-A#t=2385", "https://stats.idre.ucla.edu/sas/output/principal-components-analysis/", "https://ijpam.eu/contents/2017-115-1/12/12.pdf", "https://www.researchgate.net/publication/271642170_Principal_Manifolds_for_Data_Visualisation_and_Dimension_Reduction_LNCSE_58", "https://ir.canterbury.ac.nz/bitstream/handle/10092/10293/thesis.pdf?sequence=1", "https://arxiv.org/abs/0809.0490", "https://arxiv.org/abs/1404.1100", "https://arxiv.org/list/cs.LG/recent", "https://arxiv.org/pdf/1108.4372.pdf"]}, "K-distribution": {"categories": ["Compound probability distributions", "Continuous distributions", "Radar signal processing", "Synthetic aperture radar"], "title": "K-distribution", "method": "K-distribution", "url": "https://en.wikipedia.org/wiki/K-distribution", "summary": "In probability and statistics, the K-distribution is a three-parameter family of continuous probability distributions. \nThe distribution arises by compounding two gamma distributions. In each case, a re-parametrization of the usual form of the family of gamma distributions is used, such that the parameters are:\n\nthe mean of the distribution, and\nthe usual shape parameter.", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Compound probability distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Eric Jakeman", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Modified Bessel function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Peter Pusey", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability density function", "Probability distribution", "Product distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Radar cross-section", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Synthetic aperture radar", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Whittaker function", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA368069", "https://doi.org/10.1103%2FPhysRevLett.40.546"]}, "Contiguous distribution": {"categories": ["All articles needing additional references", "Animal migration", "Articles needing additional references from May 2018", "Biogeography", "CS1 maint: Archived copy as title", "Ecology terminology", "Population ecology", "Population genetics"], "title": "Species distribution", "method": "Contiguous distribution", "url": "https://en.wikipedia.org/wiki/Species_distribution", "summary": "Species distribution is the manner in which a biological taxon is spatially arranged. The geographic limits of a particular taxon's distribution is its range, often represented as shaded areas on a map. Patterns of distribution change depending the scale at which they are viewed, from the arrangement of individuals within a small family unit, to patterns within a population, or the distribution of the entire species as a whole (range). Species distribution is not to be confused with dispersal, which is the movement of individuals away from their region of origin or from a population center of high density.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ce/Juniperus_communis_range_map.gif", "https://upload.wikimedia.org/wikipedia/commons/8/8f/North_America.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/1f/North_America_birds.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f6/North_America_mammals.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/3c/Population_distribution.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abiotic component", "Abiotic stress", "Abundance (ecology)", "Allee effect", "Allelopathy", "Allometry", "Alternative stable state", "Animal coloration", "Animal migration", "Antibiosis", "Antipredator adaptation", "Apex predator", "Appalachian Mountains", "Archaea", "Ascendency", "Assembly rules", "Autotroph", "Bacteriophage", "Bacterivore", "Balance of nature", "Bald eagle", "Bateman's principle", "Behavioral ecology", "Bioaccumulation", "Biodiversity", "Biogeochemical cycle", "Biogeography", "Biological data visualization", "Biological dispersal", "Biological interaction", "Biology", "Bioluminescence", "Biomagnification", "Biomass (ecology)", "Biotic component", "Biotic stress", "Bird migration", "Camouflage", "Carnivore", "Carrying capacity", "Cascade effect (ecology)", "Center of origin", "Chemoorganoheterotrophy", "Chemoorganotroph", "Chemosynthesis", "Chemotroph", "Chi-squared test", "Clade", "Clark\u2013Evans nearest neighbor method", "Climax community", "Cline (biology)", "Cold seep", "Colonisation (biology)", "Commensalism", "Community ecology", "Competition (biology)", "Competitive exclusion principle", "Consumer-resource systems", "Consumers (food chain)", "Copiotroph", "Cosmopolitan distribution", "Cross-boundary subsidy", "Dandelion", "Decomposer", "Decomposition", "Deimatic behaviour", "Density dependence", "Depensation", "Detritivore", "Detritus", "Digital object identifier", "Disjunct distribution", "Disturbance (ecology)", "Dominance (ecology)", "Ecocline", "Ecological collapse", "Ecological debt", "Ecological deficit", "Ecological economics", "Ecological effects of biodiversity", "Ecological efficiency", "Ecological energetics", "Ecological extinction", "Ecological facilitation", "Ecological footprint", "Ecological forecasting", "Ecological humanities", "Ecological indicator", "Ecological network", "Ecological niche", "Ecological pyramid", "Ecological stability", "Ecological stoichiometry", "Ecological succession", "Ecological threshold", "Ecological trap", "Ecological yield", "Ecology", "Ecology of the San Francisco Estuary", "Ecopath", "Ecosystem", "Ecosystem based fisheries", "Ecosystem diversity", "Ecosystem ecology", "Ecosystem engineer", "Ecosystem model", "Ecotone", "Ecotype", "Edaphic", "Edge effects", "Effective population size", "Effects of global warming", "Elevation", "Emergence", "Endemic species", "Endemism", "Endolith", "Energy Systems Language", "Energy flow (ecology)", "Energy quality", "Environmental microbiology", "Environmental niche modelling", "Evolutionary ecology", "Extinction debt", "F-ratio", "Feed conversion ratio", "Feeding frenzy", "Flagship species", "Food chain", "Food web", "Foraging", "Foster's rule", "Foundation species", "Functional ecology", "Generalist and specialist species", "Globalization", "Gradient analysis", "Great gerbil", "Guild (ecology)", "Habitat", "Habitat fragmentation", "Herbivore", "Herbivore adaptations to plant defense", "Heterotroph", "Heterotrophic nutrition", "Human impact on the environment", "Hydrothermal vent", "Ideal free distribution", "Indicator species", "Indigenous (ecology)", "Industrial ecology", "Insectivore", "Intermediate Disturbance Hypothesis", "International Standard Book Number", "International Standard Serial Number", "Interspecific competition", "Intertidal ecology", "Intraguild predation", "Intraspecific competition", "Introduced species", "Invasive species", "Island biogeography", "James Mauseth", "Jones and Bartlett Publishers", "Juniper", "Juniperus communis", "Kelp forest", "Keystone species", "Kleiber's law", "Lake ecosystem", "Landscape ecology", "Landscape epidemiology", "Landscape limnology", "Latitudinal gradients in species diversity", "Leucaena leucocephala", "Liebig's law of the minimum", "Limiting similarity", "List of ecology topics", "List of feeding behaviours", "Lithoautotroph", "Lithotroph", "Logistic function", "Lotka\u2013Volterra equations", "Lycaon pictus", "Macroecology", "Malthusian growth model", "Marginal value theorem", "Marine habitats", "Maximum sustainable yield", "Mesopredator", "Mesopredator release hypothesis", "Mesotrophic soil", "Metabolic theory of ecology", "Metapopulation", "Microbial cooperation", "Microbial ecology", "Microbial food web", "Microbial intelligence", "Microbial loop", "Microbial mat", "Microbial metabolism", "Microecosystem", "Microorganism", "Mimicry", "Minimum viable population", "Mixotroph", "Mutualism (biology)", "Myco-heterotrophy", "Mycotroph", "Natural environment", "Niche apportionment models", "Niche construction", "Niche differentiation", "Non-trophic networks", "North Pacific Subtropical Gyre", "Nutrient cycle", "Occupancy frequency distribution", "Occupancy\u2013abundance relationship", "Oligotroph", "Omnivore", "Optimal foraging theory", "Organotroph", "Overexploitation", "Overpopulation in wild animals", "Paradox of the plankton", "Parasitism", "Passage migrant", "Patch dynamics", "Phage ecology", "Photoheterotroph", "Photosynthesis", "Photosynthetic efficiency", "Phototroph", "Phylogenetic", "Planktivore", "Plant defense against herbivory", "Poisson distribution", "Population", "Population cycle", "Population density", "Population dynamics", "Population ecology", "Population modeling", "Population size", "Population viability analysis", "Predation", "Prey switching", "Primary nutritional groups", "Primary producers", "Primary production", "Priority effect", "Productivity (ecology)", "PubMed Central", "R/K selection theory", "Range (biology)", "Rapoport's rule", "Recruitment (biology)", "Regime shift", "Relative abundance distribution", "Relative species abundance", "Resilience (ecology)", "Resource (biology)", "Resource selection function", "River ecosystem", "Salvia leucophylla", "Season", "Seeds", "Selfish herd", "Shoaling and schooling", "Sierra Nevada (U.S.)", "Small population size", "Soil food web", "Source\u2013sink dynamics", "Spatial ecology", "Species", "Species-area curve", "Species diversity", "Species homogeneity", "Species richness", "Storage effect", "Student's t-test", "Symbiosis", "Systems ecology", "Tanker (ship)", "Taxa", "Taxon", "Terpenes", "Theoretical ecology", "Thorson's rule", "Tide pool", "Transportation", "Trophic cascade", "Trophic level", "Trophic mutualism", "Trophic state index", "Umbrella species", "Unified neutral theory of biodiversity", "Urban ecology", "Vagrancy (biology)", "Xerosere"], "references": ["http://www3.interscience.wiley.com/journal/118735253/abstract", "http://sedac.ciesin.columbia.edu/species/map_gallery.jsp", "http://www.esf.edu/efb/parry/502_reading/Colautti2004.pdf", "http://www-stat.stanford.edu/~susan/courses/s116/node31.html", "http://edis.ifas.ufl.edu/HS186", "http://www.uvm.edu/~ebuford/MB_species1.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4737218", "http://www.biology-online.org/dictionary/Abiotic_factor", "http://www.biology-online.org/dictionary/Biotic_factor", "http://doi.org/10.1016%2F0003-3472(95)80048-4", "http://doi.org/10.1016%2Fj.jag.2012.11.007", "http://doi.org/10.1046%2Fj.1472-4642.2000.00083.x", "http://doi.org/10.1111%2Fj.1365-2664.2005.01052.x", "http://doi.org/10.1111%2Fj.1366-9516.2004.00061.x", "http://doi.org/10.1111%2Fjbi.12534", "http://doi.org/10.1126%2Fscience.288.5464.328", "http://doi.org/10.2307%2F1931034", "http://www.earthsky.org/radioshows/52945/malanding-jaiteh-on-where-species-live", "http://www.worldcat.org/issn/1366-9516", "https://www.fishbase.de/glossary/Glossary.php?q=aggregated/clumped/contiguous+distribution", "https://web.archive.org/web/20081216143504/http://www.cnr.uidaho.edu/range556/Appl_BEHAVE/projects/livestock_distribution.html", "https://web.archive.org/web/20090414020826/http://www.earthsky.org/radioshows/52945/malanding-jaiteh-on-where-species-live"]}, "Cumulative frequency analysis": {"categories": ["Frequency distribution", "Use dmy dates from August 2012"], "title": "Cumulative frequency analysis", "method": "Cumulative frequency analysis", "url": "https://en.wikipedia.org/wiki/Cumulative_frequency_analysis", "summary": "Cumulative frequency analysis is the analysis of the frequency of occurrence of values of a phenomenon less than a reference value. The phenomenon may be time- or space-dependent. Cumulative frequency is also called frequency of non-exceedance.\nCumulative frequency analysis is performed to obtain insight into how often a certain phenomenon (feature) is below a certain value. This may help in describing or explaining a situation in which the phenomenon is involved, or in planning interventions, for example in flood protection. This statistical technique can be used to see how likely an event like a flood is going to happen again in the future, based on how often it happened in the past. It can be adapted to bring in things like climate change causing wetter winters and drier summers.", "images": ["https://upload.wikimedia.org/wikipedia/commons/0/0f/BinomialConfBelts.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/4a/Binomial_Distribution.PNG", "https://upload.wikimedia.org/wikipedia/commons/a/a5/CumulativeFrequency.PNG", "https://upload.wikimedia.org/wikipedia/commons/1/19/Gohana-Interval.png", "https://upload.wikimedia.org/wikipedia/commons/b/b8/GohanaCum.png", "https://upload.wikimedia.org/wikipedia/commons/5/59/Normal-Return.jpg", "https://upload.wikimedia.org/wikipedia/commons/1/19/Normal_distribution_cdf.png", "https://upload.wikimedia.org/wikipedia/commons/5/51/SampleFreqCurves.tif", "https://upload.wikimedia.org/wikipedia/commons/6/65/SanLor.png"], "links": ["Asymmetry", "Binomial distribution", "Binomial proportion confidence interval", "Confidence interval", "CumFreq", "Cumulative distribution function", "Cumulative probability", "Digital object identifier", "Distribution fitting", "El Ni\u00f1o", "Estimator", "Exponential distribution", "Frequency (statistics)", "Frequency analysis", "Frequency distribution", "Frequency of exceedance", "Fr\u00e9chet distribution", "Gumbel distribution", "Histogram", "International Standard Book Number", "L-moment", "Logistic distribution", "Loglogistic distribution", "Lognormal distribution", "MathWorks", "Maximum likelihood method", "Method of moments (statistics)", "Normal distribution", "Normal probability plot", "Pareto distribution", "Plotting position", "Probability distributions", "Probability of exceedance", "Probability plot", "Probability theory", "P\u2013P plot", "Q\u2013Q plot", "R (programming language)", "Random error", "Return period", "Software", "StatSoft", "Student's t-test", "Survival function", "Symmetrical", "The Black Swan (Taleb book)", "Wald interval", "Weibull distribution", "Wilson score interval"], "references": ["http://www.vosesoftware.com/whitepapers/Fitting%20distributions%20to%20data.pdf", "http://www.physi.uni-heidelberg.de/~nberger/teaching/ws12/statistics/Lecture11.pdf", "http://www.waterlog.info/articles.htm", "http://www.waterlog.info/cumfreq.htm", "http://www.waterlog.info/pdf/freqtxt.pdf", "http://doi.org/10.1080%2F00031305.2000.10474560", "http://doi.org/10.1080%2F01621459.1927.10502953", "http://doi.org/10.1080%2F01621459.1979.10481051", "http://doi.org/10.1080%2F01621459.1983.10477938", "http://doi.org/10.1214%2Faoms%2F1177732209"]}, "Extremum estimator": {"categories": ["Estimator"], "title": "Extremum estimator", "method": "Extremum estimator", "url": "https://en.wikipedia.org/wiki/Extremum_estimator", "summary": "In statistics and econometrics, extremum estimators is a wide class of estimators for parametric models that are calculated through maximization (or minimization) of a certain objective function, which depends on the data. The general theory of extremum estimators was developed by Amemiya (1985).\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8a/Ee_noncompactness.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/8a/20100129051538%21Ee_noncompactness.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/8/8a/20100129045306%21Ee_noncompactness.svg"], "links": ["Class (mathematics)", "Compact set", "Consistent estimator", "Continuous function", "Convergence in probability", "Daniel McFadden", "Digital object identifier", "Econometrics", "Estimator", "Generalized method of moments", "International Standard Book Number", "M-estimator", "Maximum likelihood", "Minimum distance estimation", "Objective function", "Parametric model", "Probability density function", "Real line", "Small o in probability notation", "Statistics"], "references": ["http://doi.org/10.1016/S1573-4412(05)80005-4", "https://books.google.com/books?id=0bzGQE14CwEC&pg=PA105", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA445", "https://www.ssc.wisc.edu/~xshi/econ715/Lecture_4_normality.pdf"]}, "Probability and statistics": {"categories": ["All accuracy disputes", "All articles lacking sources", "Articles lacking sources from December 2009", "Articles with disputed statements from July 2014", "Probability and statistics"], "title": "Probability and statistics", "method": "Probability and statistics", "url": "https://en.wikipedia.org/wiki/Probability_and_statistics", "summary": "Probability and Statistics or also called Statistics and Probability are two related but separate academic disciplines. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics. Moreover, many topics in statistics are independent of probability theory.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Academic discipline", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Catalog of articles in probability theory", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of probability and statistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of mathematical probabilists", "List of probability journals", "List of probability topics", "List of statistical topics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Notation in probability and statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of probability", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Probability theory", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical analysis", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.cs.sunysb.edu/~skiena/jaialai/excerpts/node12.html", "http://wiki.stat.ucla.edu/socr/index.php/EBook"]}, "CUSUM": {"categories": ["Quality control tools", "Sequential methods", "Statistical charts and diagrams"], "title": "CUSUM", "method": "CUSUM", "url": "https://en.wikipedia.org/wiki/CUSUM", "summary": "In statistical quality control, the CUSUM (or cumulative sum control chart) is a sequential analysis technique developed by E. S. Page of the University of Cambridge. It is typically used for monitoring change detection.\nCUSUM was announced in Biometrika, in 1954, a few years after the publication of Wald's SPRT algorithm.Page referred to a \"quality number\" \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n , by which he meant a parameter of the probability distribution; for example, the mean. He devised CUSUM as a method to determine changes in it, and proposed a criterion for deciding when to take corrective action. When the CUSUM method is applied to changes in mean, it can be used for step detection of a time series.\nA few years later, George Alfred Barnard developed a visualization method, the V-mask chart, to detect both increases and decreases in \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/89/Example_cusum1.png", "https://upload.wikimedia.org/wikipedia/commons/c/ca/Example_cusum2.png"], "links": ["Abraham Wald", "Biometrika", "Change detection", "Control chart", "Cumulative observed-minus-expected plots", "Digital object identifier", "E. S. Page", "George Alfred Barnard", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Journal of the Royal Statistical Society", "Likelihood function", "Mean", "Metric (mathematics)", "Neyman\u2013Pearson lemma", "Normal distribution", "Petrovaradin", "Probability distribution", "PubMed Identifier", "SPRT", "Sequential analysis", "Statistical Research Memoirs", "Statistical power", "Statistical process control", "Step detection", "Sufficient statistic", "Time series", "Type II error", "Type I error", "University of Cambridge", "Variable and attribute (research)"], "references": ["http://www.irisa.fr/sisthem/kniga/", "http://www.ncbi.nlm.nih.gov/pubmed/12665208", "http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc323.htm", "http://doi.org/10.1093%2Fbiomet%2F41.1-2.100", "http://doi.org/10.1177%2F096228020301200205", "http://www.jstor.org/stable/2333009", "http://www.jstor.org/stable/2983801", "http://www.phmsociety.org/sites/phmsociety.org/files/phm_submission/2015/ijphm_15_015.pdf", "https://www.worldcat.org/search?fq=x0:jrnl&q=n2:2153-2648"]}, "Operational sex ratio": {"categories": ["CS1 maint: Uses authors parameter", "Ecology", "Mating systems", "Reproduction", "Sexual selection"], "title": "Operational sex ratio", "method": "Operational sex ratio", "url": "https://en.wikipedia.org/wiki/Operational_sex_ratio", "summary": "In the evolutionary biology of sexual reproduction, operational sex ratio (OSR) is the ratio of sexually competing males that are ready to mate to sexually competing females that are ready to mate, or alternatively the local ratio of fertilizable females to sexually active males at any given time. This differs from physical sex ratio which simply includes all individuals, including those that are sexually inactive or do not compete for mates.\nThe theory of OSR hypothesizes that the operational sex ratio affects the mating competition of males and females in a population. This concept is especially useful in the study of sexual selection since it is a measure of how intense sexual competition is in a species, and also in the study of the relationship of sexual selection to sexual dimorphism. The OSR is closely linked to the \"potential rate of reproduction\" of the two sexes; that is, how fast they each could reproduce in ideal circumstances. Usually variation in potential reproductive rates creates bias in the OSR and this in turn will affect the strength of selection. The OSR is said to be biased toward a particular sex when sexually ready members of that sex are more abundant. For example, a male-biased OSR means that there are more sexually competing males than sexually competing females.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["CiteSeerX", "Digital object identifier", "Evolutionary biology", "Handle System", "JSTOR", "Mortality rate", "PubMed Identifier", "Sex ratio", "Sexual dimorphism", "Sexual reproduction", "Sexual selection", "Spatial distribution"], "references": ["http://linkinghub.elsevier.com/retrieve/pii/0169534796100562", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.462.3366", "http://www.ncbi.nlm.nih.gov/pubmed/18096798", "http://www.ncbi.nlm.nih.gov/pubmed/20981009", "http://www.ncbi.nlm.nih.gov/pubmed/21237764", "http://www.ncbi.nlm.nih.gov/pubmed/21460553", "http://www.ncbi.nlm.nih.gov/pubmed/327542", "http://hdl.handle.net/10400.12%2F1321", "http://doi.org/10.1006/anbe.1995.0142", "http://doi.org/10.1006/anbe.1995.9998", "http://doi.org/10.1007/bf00167335", "http://doi.org/10.1007/bf00171662", "http://doi.org/10.1007/bf00183788", "http://doi.org/10.1007/bf00300069", "http://doi.org/10.1007/bf00300566", "http://doi.org/10.1007/s00265-005-0915-9", "http://doi.org/10.1007/s002650050272", "http://doi.org/10.1007/s002650050559", "http://doi.org/10.1016/0169-5347(96)10056-2", "http://doi.org/10.1016/0169-5347(96)81045-7", "http://doi.org/10.1016/s0003-3472(05)81028-0", "http://doi.org/10.1038/346172a0", "http://doi.org/10.1038/358061a0", "http://doi.org/10.1038/nature09512", "http://doi.org/10.1086/285108", "http://doi.org/10.1086/285888", "http://doi.org/10.1086/417793", "http://doi.org/10.1086/657918", "http://doi.org/10.1093/beheco/7.2.208", "http://doi.org/10.1093/beheco/ars094", "http://doi.org/10.1126/science.1133311", "http://doi.org/10.1126/science.327542", "http://doi.org/10.2307/1938062", "http://www.jstor.org/stable/1938062", "http://www.jstor.org/stable/2463187", "http://www.jstor.org/stable/4599103", "http://beheco.oxfordjournals.org/content/early/2012/07/06/beheco.ars094.full", "http://science.sciencemag.org/content/197/4300/215"]}, "Balanced repeated replication": {"categories": ["Resampling (statistics)", "Sampling (statistics)"], "title": "Balanced repeated replication", "method": "Balanced repeated replication", "url": "https://en.wikipedia.org/wiki/Balanced_repeated_replication", "summary": "Balanced repeated replication is a statistical technique for estimating the sampling variability of a statistic obtained by stratified sampling.", "images": [], "links": ["Hadamard matrix", "International Statistical Institute", "Resampling (statistics)", "Sampling error", "Statistics", "Stratified sampling"], "references": ["http://www.jos.nu/Articles/abstract.asp?article=63223", "http://am.air.org/help/NAEPTextbook/htm/obalancedrepeatedreplication.htm", "https://www.jstor.org/stable/2240615", "https://www.jstor.org/stable/2288478"]}, "P-chart": {"categories": ["CS1 errors: external links", "Quality control tools", "Statistical charts and diagrams"], "title": "P-chart", "method": "P-chart", "url": "https://en.wikipedia.org/wiki/P-chart", "summary": "In statistical quality control, the p-chart is a type of control chart used to monitor the proportion of nonconforming units in a sample, where the sample proportion nonconforming is defined as the ratio of the number of nonconforming units to the sample size, n.The p-chart only accommodates \"pass\"/\"fail\"-type inspection as determined by one or more go-no go gauges or tests, effectively applying the specifications to the data before they are plotted on the chart. Other types of control charts display the magnitude of the quality characteristic under study, making troubleshooting possible directly from those charts.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f4/P_control_chart.svg"], "links": ["Binomial distribution", "Control chart", "Go-NoGo gauge", "Hoboken, New Jersey", "International Standard Book Number", "John Wiley & Sons", "National Institute of Standards and Technology", "Nonconformity (quality)", "Np-chart", "OCLC", "SPC Press", "Sample (statistics)", "Shewhart individuals control chart", "Specification (technical standard)", "Standard score", "Statistical process control", "Variable and attribute (research)", "Walter A. Shewhart"], "references": ["http://www.spcpress.com/", "http://www.eas.asu.edu/~masmlab/montgomery/", "http://www.itl.nist.gov/div898/handbook/index.htm", "http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc332.htm", "http://www.worldcat.org/oclc/56729567", "https://www.qualitydigest.com/inside/quality-insider-article/what-about-p-charts.html", "https://web.archive.org/web/20080620095346/http://www.eas.asu.edu/~masmlab/montgomery/"]}, "Markov blanket": {"categories": ["Bayesian networks", "Markov networks"], "title": "Markov blanket", "method": "Markov blanket", "url": "https://en.wikipedia.org/wiki/Markov_blanket", "summary": "In statistics and machine learning, the Markov blanket for a node in a graphical model contains all the variables that shield the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge needed to predict the behavior of that node and its children. The term was coined by Judea Pearl in 1988.In a Bayesian network, the values of the parents and children of a node evidently give information about that node. However, its children's parents also have to be included, because they can be used to explain away the node in question. In a Markov random field, the Markov blanket for a node is simply its adjacent nodes.\nThe Markov blanket for a node \n \n \n \n A\n \n \n {\\displaystyle A}\n in a Bayesian network is the set of nodes \n \n \n \n \u2202\n A\n \n \n {\\displaystyle \\partial A}\n composed of \n \n \n \n A\n \n \n {\\displaystyle A}\n 's parents, its children, and its children's other parents. In a Markov random field, the Markov blanket of a node is its set of neighboring nodes. The Markov blanket of A may also be denoted by \n \n \n \n MB\n \u2061\n (\n A\n )\n \n \n {\\displaystyle \\operatorname {MB} (A)}\n .\nEvery set of nodes in the network is conditionally independent of \n \n \n \n A\n \n \n {\\displaystyle A}\n when conditioned on the set \n \n \n \n \u2202\n A\n \n \n {\\displaystyle \\partial A}\n , that is, when conditioned on the Markov blanket of the node \n \n \n \n A\n \n \n {\\displaystyle A}\n . The probability has the Markov property; formally, for distinct nodes \n \n \n \n A\n \n \n {\\displaystyle A}\n and \n \n \n \n B\n \n \n {\\displaystyle B}\n :\n\n \n \n \n Pr\n (\n A\n \u2223\n \u2202\n A\n ,\n B\n )\n =\n Pr\n (\n A\n \u2223\n \u2202\n A\n )\n .\n \n \n \n {\\displaystyle \\Pr(A\\mid \\partial A,B)=\\Pr(A\\mid \\partial A).\\!}", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/eb/Diagram_of_a_Markov_blanket.svg"], "links": ["Andrey Markov", "Bayesian network", "Conditional independence", "Free energy principle", "Graphical model", "International Standard Book Number", "Judea Pearl", "Machine learning", "Markov property", "Markov random field", "Moral graph", "Separation of concerns", "Statistics", "Vertex (graph theory)"], "references": []}, "U-quadratic distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax"], "title": "U-quadratic distribution", "method": "U-quadratic distribution", "url": "https://en.wikipedia.org/wiki/U-quadratic_distribution", "summary": "In probability theory and statistics, the U-quadratic distribution is a continuous probability distribution defined by a unique convex quadratic function with lower limit a and upper limit b.\n\n \n \n \n f\n (\n x\n \n |\n \n a\n ,\n b\n ,\n \u03b1\n ,\n \u03b2\n )\n =\n \u03b1\n \n \n (\n \n x\n \u2212\n \u03b2\n \n )\n \n \n 2\n \n \n ,\n \n \n for \n \n x\n \u2208\n [\n a\n ,\n b\n ]\n .\n \n \n {\\displaystyle f(x|a,b,\\alpha ,\\beta )=\\alpha \\left(x-\\beta \\right)^{2},\\quad {\\text{for }}x\\in [a,b].}", "images": ["https://upload.wikimedia.org/wikipedia/en/2/2a/Distributions_UQuadratic_PDF.jpg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bimodal", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Convex function", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Information entropy", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": []}, "Scatterplot smoothing": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from September 2010", "Regression analysis", "Statistical charts and diagrams"], "title": "Scatterplot smoothing", "method": "Scatterplot smoothing", "url": "https://en.wikipedia.org/wiki/Scatterplot_smoothing", "summary": "In statistics, several scatterplot smoothing methods are available to fit a function through the points of a scatterplot to best represent the relationship between the variables.\nScatterplots may be smoothed by fitting a line to the data points in a diagram. This line attempts to display the non-random component of the association between the variables in a 2D scatter plot. Smoothing attempts to separate the non-random behaviour in the data from the random fluctuations, removing or reducing these fluctuations, and allows prediction of the response based value of the explanatory variable.Smoothing is normally accomplished by using any one of the techniques mentioned below.\n\nA straight line (simple linear regression)\nA quadratic or a polynomial curve\nLocal regression\nSmoothing splinesThe smoothing curve is chosen so as to provide the best fit in some sense, often defined as the fit that results in the minimum sum of the squared errors (a least squares criterion).", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Additive model", "Explanatory variable", "Generalized additive model", "International Standard Book Number", "Least squares", "Local regression", "Polynomial", "Quadratic polynomial", "Scatterplot", "Simple linear regression", "Smoothing", "Smoothing spline", "Statistics", "Sum of squared error"], "references": ["http://www.netmba.com/statistics/plot/scatter/"]}, "Misuse of statistics": {"categories": ["All articles with unsourced statements", "All pages needing cleanup", "Articles needing cleanup from November 2014", "Articles with unsourced statements from April 2010", "CS1 maint: Unfit url", "CS1 maint: Uses authors parameter", "Cleanup tagged articles with a reason field from November 2014", "Commons category link is on Wikidata", "Ethics and statistics", "Misuse of statistics", "Wikipedia pages needing cleanup from November 2014"], "title": "Misuse of statistics", "method": "Misuse of statistics", "url": "https://en.wikipedia.org/wiki/Misuse_of_statistics", "summary": "Statistics are supposed to make something easier to understand but when used in a misleading fashion can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.\nThe false statistics trap can be quite damaging for the quest for knowledge. For example, in medical science, correcting a falsehood may take decades and cost lives.\nMisuses can be easy to fall into. Professional scientists, even mathematicians and professional statisticians, can be fooled by even some simple methods, even if they are careful to check everything. Scientists have been known to fool themselves with statistics due to lack of knowledge of probability theory and lack of standardization of their tests.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fa/Wikiquote-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["68-95-99.7 rule", "American International Group", "American Society for Nondestructive Testing", "Analysis of variance", "Anscombe's quartet", "Apples and oranges", "Australasian Journal of Bone & Joint Medicine", "Biased sample", "Carl Bialik", "Central limit theorem", "Cherry picking (fallacy)", "Circular analysis", "Clothing sizes", "Confidence interval", "Consistent", "Correlation does not imply causation", "Data dredging", "Data mining", "Deception", "Descriptive statistics", "Design of experiments", "Digital object identifier", "Electromagnetic field", "Electromagnetic radiation and health", "Ethics in mathematics", "Experiment", "Extra-sensory perception", "Fallacy", "Gambler's fallacy", "Garbage in, garbage out", "How to Lie with Statistics", "Hypothesis", "Impression management", "Institutional Review Board", "Intelligence quotient", "International Standard Book Number", "International Standard Serial Number", "Journal of the Royal Statistical Society, Series A", "Lady tasting tea", "Library of Congress Control Number", "Lies, damned lies, and statistics", "Loaded question", "Ludic fallacy", "Margin of error", "Medical Register", "Misleading graph", "Null hypothesis", "Open Library", "Opinion poll", "Placebo", "Plot (graphics)", "Probability theory", "Prosecutor's fallacy", "Pseudoreplication", "PubMed Central", "PubMed Identifier", "Publication bias", "Random chance", "Regression toward the mean", "Robert P. Abelson", "Ronald Fisher", "Roy Meadow", "Sampling bias", "Sampling error", "Standardization", "Statistical literacy", "Statistical survey", "Statistical test", "Statistics", "Stephen Barrett", "Struck off", "Sudden Infant Death Syndrome", "Systemic risk", "The Design of Experiments", "The Wall Street Journal", "Theodore M. Porter", "Vanity sizing", "Viking Penguin"], "references": ["http://www.presidency.ucsb.edu/data/preferences.php", "http://lccn.loc.gov/53013322", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC558197", "http://www.ncbi.nlm.nih.gov/pubmed/12625352", "http://www.ncbi.nlm.nih.gov/pubmed/15933351", "http://www.ncbi.nlm.nih.gov/pubmed/17299669", "http://www.ndt.net/article/v04n05/oldberg/oldberg.htm", "http://www.ndt.net/article/v10n05/oldberg/oldberg.htm", "http://doi.org/10.1016%2F0031-3203(76)90044-3", "http://doi.org/10.1037%2Fh0042040", "http://doi.org/10.1080%2F08989620212968", "http://doi.org/10.1111%2Fj.1467-985X.2010.00700.x", "http://doi.org/10.1136%2Fbmj.330.7503.1290", "http://doi.org/10.1214%2F09-STS285", "http://doi.org/10.4103%2F0019-5413.30524", "http://openlibrary.org/books/OL6138576M", "http://www.quackwatch.org/01QuackeryRelatedTopics/emf.html", "http://www.worldcat.org/issn/1030-1046", "http://www.worldcat.org/issn/1744-8026", "https://books.google.com/books?id=GtSV7rG6Iu4C", "https://books.google.com/books?id=GtSV7rG6Iu4C&pg=PA25", "https://books.google.com/books?id=hT_ELDzB99gC", "https://books.google.com/books?id=wj3CQgAACAAJ", "https://web.archive.org/web/20130828175105/http://biostat.home.uludag.edu.tr/Review%20Of%20Reliability%20And%20Factors%20Affecting%20The%20Reliability%20.pdf", "https://web.archive.org/web/20131203050247/http://www.researchinformation.info/features/feature.php?feature_id=214", "https://web.archive.org/web/20140621205347/http://www.bocsar.nsw.gov.au/agdbasev7wr/bocsar/documents/pdf/cjb153.pdf", "https://web.archive.org/web/20140816043956/http://www.newscientist.com/article/dn7460-large-study-links-power-lines-to-childhood-cancer.html", "https://web.archive.org/web/20141113182754/http://www.ejgm.org/upload/sayi/1016/EJGM-00166.pdf"]}, "Statistical benchmarking": {"categories": ["All articles lacking sources", "Articles lacking sources from October 2007", "Sampling (statistics)"], "title": "Statistical benchmarking", "method": "Statistical benchmarking", "url": "https://en.wikipedia.org/wiki/Statistical_benchmarking", "summary": "In statistics, benchmarking is a method of using auxiliary information to adjust the sampling weights used in an estimation process, in order to yield more accurate estimates of totals.\nSuppose we have a population where each unit \n \n \n \n k\n \n \n {\\displaystyle k}\n has a \"value\" \n \n \n \n Y\n (\n k\n )\n \n \n {\\displaystyle Y(k)}\n associated with it. For example, \n \n \n \n Y\n (\n k\n )\n \n \n {\\displaystyle Y(k)}\n could be a wage of an employee \n \n \n \n k\n \n \n {\\displaystyle k}\n , or the cost of an item \n \n \n \n k\n \n \n {\\displaystyle k}\n . Suppose we want to estimate the sum \n \n \n \n Y\n \n \n {\\displaystyle Y}\n of all the \n \n \n \n Y\n (\n k\n )\n \n \n {\\displaystyle Y(k)}\n . So we take a sample of the \n \n \n \n k\n \n \n {\\displaystyle k}\n , get a sampling weight W(k) for all sampled \n \n \n \n k\n \n \n {\\displaystyle k}\n , and then sum up \n \n \n \n W\n (\n k\n )\n \u22c5\n Y\n (\n k\n )\n \n \n {\\displaystyle W(k)\\cdot Y(k)}\n for all sampled \n \n \n \n k\n \n \n {\\displaystyle k}\n .\nOne property usually common to the weights \n \n \n \n W\n (\n k\n )\n \n \n {\\displaystyle W(k)}\n described here is that if we sum them over all sampled \n \n \n \n k\n \n \n {\\displaystyle k}\n , then this sum is an estimate of the total number of units \n \n \n \n k\n \n \n {\\displaystyle k}\n in the population (for example, the total employment, or the total number of items). Because we have a sample, this estimate of the total number of units in the population will differ from the true population total. Similarly, the estimate of total \n \n \n \n Y\n \n \n {\\displaystyle Y}\n (where we sum \n \n \n \n W\n (\n k\n )\n \u22c5\n Y\n (\n k\n )\n \n \n {\\displaystyle W(k)\\cdot Y(k)}\n for all sampled \n \n \n \n k\n \n \n {\\displaystyle k}\n ) will also differ from true population total.\nWe do not know what the true population total \n \n \n \n Y\n \n \n {\\displaystyle Y}\n value is (if we did, there would be no point in sampling!). Yet often we do know what the sum of the \n \n \n \n W\n (\n k\n )\n \n \n {\\displaystyle W(k)}\n are over all units in the population. For example, we may not know the total earnings of the population or the total cost of the population, but often we know the total employment or total volume of sales. And even if we don't know these exactly, there often are surveys done by other organizations or at earlier times, with very accurate estimates of these auxiliary quantities. One important function of a population census is to provide data that can be used for benchmarking smaller surveys.\nThe benchmarking procedure begins by first breaking the population into benchmarking cells. Cells are formed by grouping units together that share common characteristics, for example, similar \n \n \n \n Y\n (\n k\n )\n \n \n {\\displaystyle Y(k)}\n , yet anything can be used that enhances the accuracy of the final estimates. For each cell \n \n \n \n C\n \n \n {\\displaystyle C}\n , we let \n \n \n \n W\n (\n C\n )\n \n \n {\\displaystyle W(C)}\n be the sum of all \n \n \n \n W\n (\n k\n )\n \n \n {\\displaystyle W(k)}\n , where the sum is taken over all sampled \n \n \n \n k\n \n \n {\\displaystyle k}\n in the cell \n \n \n \n C\n \n \n {\\displaystyle C}\n . For each cell \n \n \n \n C\n \n \n {\\displaystyle C}\n , we let \n \n \n \n T\n (\n C\n )\n \n \n {\\displaystyle T(C)}\n be the auxiliary value for cell \n \n \n \n C\n \n \n {\\displaystyle C}\n , which is commonly called the \"benchmark target\" for cell \n \n \n \n C\n \n \n {\\displaystyle C}\n . Next, we compute a benchmark factor \n \n \n \n F\n (\n C\n )\n =\n T\n (\n C\n )\n \n /\n \n W\n (\n C\n )\n \n \n {\\displaystyle F(C)=T(C)/W(C)}\n . Then, we adjust all weights \n \n \n \n W\n (\n k\n )\n \n \n {\\displaystyle W(k)}\n by multiplying it by its benchmark factor \n \n \n \n F\n (\n C\n )\n \n \n {\\displaystyle F(C)}\n , for its cell \n \n \n \n C\n \n \n {\\displaystyle C}\n . The net result is that the estimated \n \n \n \n W\n \n \n {\\displaystyle W}\n [formed by summing \n \n \n \n F\n (\n C\n )\n \u22c5\n W\n (\n k\n )\n \n \n {\\displaystyle F(C)\\cdot W(k)}\n ] will now equal the benchmark target total \n \n \n \n T\n \n \n {\\displaystyle T}\n . But the more important benefit is that the estimate of the total of \n \n \n \n Y\n \n \n {\\displaystyle Y}\n [formed by summing \n \n \n \n F\n (\n C\n )\n \u22c5\n F\n (\n k\n )\n \u22c5\n Y\n (\n k\n )\n \n \n {\\displaystyle F(C)\\cdot F(k)\\cdot Y(k)}\n ] will tend to be more accurate.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Census", "Estimation", "Population (statistics)", "Sample (statistics)", "Statistics", "Stratified sampling", "Summation", "Weight function"], "references": []}, "Chou's invariance theorem": {"categories": ["All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from September 2014", "Articles with multiple maintenance issues", "Bioinformatics", "Cheminformatics", "Statistical theorems", "Wikipedia articles that are too technical from September 2014", "Wikipedia articles with possible conflicts of interest from June 2012"], "title": "Chou's invariance theorem", "method": "Chou's invariance theorem", "url": "https://en.wikipedia.org/wiki/Chou%27s_invariance_theorem", "summary": "Chou's invariance theorem, named after Kuo-Chen Chou, was developed to address a problem raised in bioinformatics and cheminformatics related to multivariate statistics. Where a distance that would, in standard statistical theory, be defined as a Mahalanobis distance cannot be defined in this way because the relevant covariance matrix is singular. One effective approach to solve this problem would be to reduce the dimension of the multivariate space until the relevant covariance matrix is invertible or well defined. This can be achievable by simply omitting one or more of the original components until the matrix concerned is no longer singular. Chou's invariance theorem says that it does not matter which of the components or coordinates are selected for removal because exactly the same final value would be obtained. \n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Unbalanced_scales.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Amino acid", "Bioinformatics", "Cheminformatics", "Covariance matrix", "Digital object identifier", "Dimension (vector space)", "Invertible matrix", "Kuo-Chen Chou", "Mahalanobis distance", "Multivariate statistics", "Pseudo amino acid composition", "PubMed Identifier", "Singular matrix", "Statistical theory"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/10195282", "http://www.ncbi.nlm.nih.gov/pubmed/11354006", "http://www.ncbi.nlm.nih.gov/pubmed/12471598", "http://www.ncbi.nlm.nih.gov/pubmed/13678304", "http://www.ncbi.nlm.nih.gov/pubmed/7567954", "http://www.ncbi.nlm.nih.gov/pubmed/9988519", "http://doi.org/10.1002%2Fprot.10251", "http://doi.org/10.1002%2Fprot.1071", "http://doi.org/10.1002%2Fprot.340210406", "http://doi.org/10.1023%2FA:1020713915365", "http://doi.org/10.1023%2FA:1025350409648", "http://doi.org/10.1093%2Fprotein%2F12.2.107", "https://dx.doi.org/10.3109/10409239509083488"]}, "L-estimator": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from April 2013", "CS1 maint: Uses editors parameter", "Estimator", "Nonparametric statistics", "Robust statistics"], "title": "L-estimator", "method": "L-estimator", "url": "https://en.wikipedia.org/wiki/L-estimator", "summary": "In statistics, an L-estimator is an estimator which is an L-statistic \u2013 a linear combination of order statistics of the measurements. This can be as little as a single point, as in the median (of an odd number of values), or as many as all points, as in the mean.\nThe main benefits of L-estimators are that they are often extremely simple, and often robust statistics: assuming sorted data, they are very easy to calculate and interpret, and are often resistant to outliers. They thus are useful in robust statistics, as descriptive statistics, in statistics education, and when computation is difficult. However, they are inefficient, and in modern times robust statistics M-estimators are preferred, though these are much more difficult computationally. In many circumstances L-estimators are reasonably efficient, and thus adequate for initial estimation.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fa/Michelsonmorley-boxplot.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Arithmetic mean", "Box plot", "Breakdown point", "Central tendency", "Computer", "Consistent estimator", "Descriptive statistics", "Digital object identifier", "Efficiency (statistics)", "Electronic calculator", "Error function", "Estimator", "Expected value", "Five-number summary", "Frederick Mosteller", "Interdecile range", "International Standard Book Number", "Interquartile mean", "Interquartile range", "L-moment", "L-statistic", "Location parameter", "M-estimator", "Machine-readable data", "Median", "Mid-range", "Midhinge", "Midsummary", "Non-parametric statistics", "Nonparametric skew", "Normal distribution", "Order statistics", "Parameter estimation", "Pearson's skewness coefficients", "Population (statistics)", "Population variance", "Punch card", "Quantile", "Range (statistics)", "Robust measures of scale", "Robust statistics", "Sample (statistics)", "Sample mean", "Scale factor", "Scale parameter", "Seven-number summary", "Shape parameter", "Skewness", "Standard deviation", "Statistical dispersion", "Statistically resistant", "Statistics", "Statistics education", "Trimean", "Trimmed estimator", "Trimmed mean", "Unbiased estimator", "Winsorized mean", "Xuming He"], "references": ["http://doi.org/10.1007/978-0-387-44956-2_4", "http://doi.org/10.1007/BF02595872", "https://archive.org/details/atomicnucleus032805mbp", "https://archive.org/stream/atomicnucleus032805mbp#page/n925/mode/2up"]}, "Isomap": {"categories": ["Computational statistics"], "title": "Isomap", "method": "Isomap", "url": "https://en.wikipedia.org/wiki/Isomap", "summary": "Isomap is a nonlinear dimensionality reduction method. It is one of several widely used low-dimensional embedding methods. Isomap is used for computing a quasi-isometric, low-dimensional embedding of a set of high-dimensional data points. The algorithm provides a simple method for estimating the intrinsic geometry of a data manifold based on a rough estimate of each data point\u2019s neighbors on the manifold. Isomap is highly efficient and generally applicable to a broad range of data sources and dimensionalities.", "images": [], "links": ["Dijkstra's algorithm", "Distance matrix", "Eigenvector", "Euclidean distance", "Floyd\u2013Warshall algorithm", "Kernel PCA", "Kernel method", "Manifold", "Mercer's theorem", "Multidimensional scaling", "Nonlinear dimensionality reduction", "Positive semidefinite matrix", "Principal component analysis", "Shortest path", "Spectral clustering"], "references": ["http://web.mit.edu/cocosci/Papers/nips02-localglobal-in-press.pdf", "http://www-clmc.usc.edu/publications/T/tenenbaum-Science2000.pdf", "https://web.archive.org/web/20040411051530/http://isomap.stanford.edu/"]}, "Autoregressive model": {"categories": ["All articles lacking in-text citations", "All articles needing additional references", "All articles with unsourced statements", "Articles lacking in-text citations from March 2011", "Articles needing additional references from March 2011", "Articles with multiple maintenance issues", "Articles with unsourced statements from July 2012", "Articles with unsourced statements from October 2011", "Autocorrelation", "Signal processing", "Wikipedia articles needing page number citations from March 2011"], "title": "Autoregressive model", "method": "Autoregressive model", "url": "https://en.wikipedia.org/wiki/Autoregressive_model", "summary": "In statistics and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation.\nTogether with the moving-average (MA) model, it is a special case and key component of the more general ARMA and ARIMA models of time series, which have a more complicated stochastic structure; it is also a special case of the vector autoregressive model (VAR), which consists of a system of more than one interlocking stochastic difference equation in more than one evolving random variable.\nContrary to the moving-average model, the autoregressive model is not always stationary as it may contain a unit root.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/c/ce/ArTimeSeries.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8b/AutoCorrAR.svg", "https://upload.wikimedia.org/wikipedia/commons/6/65/AutocorrTimeAr.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Autocorrelation function", "Autocovariance", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive\u2013moving-average model", "Backshift operator", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Blue noise", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy distribution", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Confidence interval", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Cross-validation (statistics)", "C\u00e0dl\u00e0g", "Difference equation", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Economics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Forecasting", "Fourier transform", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Gilbert Walker", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Impulse response", "Independent and identically distributed random variables", "Infinite impulse response", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kronecker delta function", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Least squares regression", "Levinson recursion", "Linear difference equation", "Linear prediction", "Linear predictive coding", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Mark Thoma", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Matlab (programming language)", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "Maximum entropy spectral estimation", "Maximum likelihood estimation", "McKean\u2013Vlasov process", "Mean squared prediction error", "Method of moments (statistics)", "Mixing (mathematics)", "Moran process", "Moving-average model", "Moving average model", "Multivariate statistics", "Natural science", "Non-homogeneous Poisson process", "Normal equations", "Octave (programming language)", "Optional stopping theorem", "Ordinary least squares", "Ornstein-Uhlenbeck process", "Ornstein\u2013Uhlenbeck process", "Partial autocorrelation function", "Percolation theory", "Philosophical Transactions of the Royal Society", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Pole (complex analysis)", "Polynomial long division", "Polynomial notation", "Potts model", "Predictable process", "Predictive analytics", "Probability theory", "Proceedings of the Royal Society", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "R (programming language)", "Random dynamical system", "Random field", "Random graph", "Random process", "Random walk", "Red noise", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Resonance", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Signal processing", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Spectral density", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stochastic variable", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time constant", "Time reversibility", "Time series", "Time series analysis", "Udny Yule", "Uniform integrability", "Unit circle", "Unit root", "Usual hypotheses", "Variance", "Variance gamma process", "Vasicek model", "Vector autoregression", "Vector autoregressive model", "White noise", "Wide-sense stationary", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "YouTube"], "references": ["http://pub.ist.ac.at/~schloegl/matlab/tsa/", "http://www.mathworks.com/help/econ/autoregressive-model.html", "http://www.mathworks.com/products/econometrics/", "http://www.mathworks.com/products/sysid/", "http://finzi.psych.upenn.edu/R/library/stats/html/ar.html", "http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-56031", "http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-56224", "http://paulbourke.net/miscellaneous/ar/", "http://doi.org/10.1109%2FTIM.2002.808031", "http://www3.stat.sinica.edu.tw/statistica/oldpdf/A15n112.pdf", "https://github.com/christophmark/bayesloop", "https://www.youtube.com/watch?v=b8yslhlIsA0&list=PLD15D38DC7AA3B737&index=8#t=34m25s", "https://web.archive.org/web/20121021015413/http://www3.stat.sinica.edu.tw/statistica/oldpdf/A15n112.pdf"]}, "Negative binomial distribution": {"categories": ["CS1 maint: Multiple names: authors list", "Compound probability distributions", "Discrete distributions", "Exponential family distributions", "Factorial and binomial topics", "Infinitely divisible probability distributions", "Pages using deprecated image syntax"], "title": "Negative binomial distribution", "method": "Negative binomial distribution", "url": "https://en.wikipedia.org/wiki/Negative_binomial_distribution", "summary": "In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs. For example, if we define a 1 as failure, all non-1s as successes, and we throw a die repeatedly until 1 appears the third time (r = three failures), then the probability distribution of the number of non-1s that appeared will be a negative binomial distribution.\nThe Pascal distribution (after Blaise Pascal) and Polya distribution (for George P\u00f3lya) are special cases of the negative binomial distribution. A convention among engineers, climatologists, and others is to use \"negative binomial\" or \"Pascal\" for the case of an integer-valued stopping-time parameter r, and use \"Polya\" for the real-valued case.\nFor occurrences of \"contagious\" discrete events, like tornado outbreaks, the Polya distributions can be used to give more accurate models than the Poisson distribution by allowing the mean and variance to be different, unlike the Poisson. \"Contagious\" events have positively correlated occurrences causing a larger variance than if the occurrences were independent, due to a positive covariance term.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/83/Negbinomial.gif", "https://upload.wikimedia.org/wikipedia/commons/7/77/Open_Access_logo_PLoS_transparent.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Atlantic Ocean", "Australian & New Zealand Journal of Statistics", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Bernoulli process", "Bernoulli trial", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial coefficient", "Binomial distribution", "Binomial series", "Bioinformatics", "Biometrika", "Bivariate von Mises distribution", "Blaise Pascal", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Closed-form expression", "Complementary event", "Compound Poisson distribution", "Compound probability distribution", "Convergence in distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Coupon collector's problem", "Covariance", "Cumulant", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dice", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete probability distribution", "Discrete random variable", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Excess kurtosis", "Expectation\u2013maximization algorithm", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "Extratropical cyclone", "F-distribution", "Fisher's z-distribution", "Fisher information", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "George P\u00f3lya", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independence (probability theory)", "Independent and identically-distributed random variables", "Independent and identically distributed random variables", "Independent identically-distributed random variables", "Infinite divisibility (probability)", "Integer", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "J. B. S. Haldane", "JSTOR", "John Nelder", "Johnson's SU-distribution", "Joint probability distribution", "Journal of the Royal Statistical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Length of stay", "Library of Congress Control Number", "Linear regression", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maximum likelihood", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Meteorologische Zeitschrift", "Minimum variance unbiased estimator", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Monthly Weather Review", "Morris H. DeGroot", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative hypergeometric distribution", "Negative multinomial distribution", "Newton's binomial theorem", "Newton's method", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "OCLC", "Open access", "Overdispersion", "PLoS ONE", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Peter McCullagh", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Probability-generating function", "Probability distribution", "Probability generating function", "Probability mass function", "Probability theory", "PubMed Central", "PubMed Identifier", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Recurrence relation", "Regularized incomplete beta function", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "SAS Institute", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Statistics", "Student's t-distribution", "Sufficient statistic", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Tropical cyclone", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Vector generalized linear model", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.biomedcentral.com/1472-6947/14/26", "http://www.johndcook.com/negative_binomial.pdf", "http://www.mathworks.com/help/stats/negative-binomial-distribution.html", "http://support.sas.com/documentation/cdl/en/lefunctionsref/67960/HTML/default/viewer.htm#n0n7cce4a3gfqkn1vr0p1x0of99s.htm#n1olto4j49wrc3n11tnmuq2zibj6", "http://stattrek.com/probability-distributions/negative-binomial.aspx", "http://mathworld.wolfram.com/NegativeBinomialDistribution.html", "http://www.stat.purdue.edu/~zhanghao/STAT511/handout/Stt511%20Sec3.5.pdf", "http://www.math.uah.edu/stat/bernoulli/NegativeBinomial.html", "http://www.stat.ufl.edu/~abhisheksaha/sta4321/lect14.pdf", "http://lccn.loc.gov/84006269", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1791715", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3992140", "http://www.ncbi.nlm.nih.gov/pubmed/17299582", "http://www.ncbi.nlm.nih.gov/pubmed/17881408", "http://www.ncbi.nlm.nih.gov/pubmed/24708853", "http://www.bioconductor.org/packages/release/bioc/vignettes/DESeq2/inst/doc/DESeq2.pdf", "http://www.bioconductor.org/packages/release/bioc/vignettes/edgeR/inst/doc/edgeRUsersGuide.pdf", "http://doi.org/10.1093%2Fbioinformatics%2Fbtm453", "http://doi.org/10.1093%2Fbiomet%2F33.3.222", "http://doi.org/10.1111%2F1467-842X.00075", "http://doi.org/10.1127%2F0941-2948%2F2009%2F0393", "http://doi.org/10.1175%2F2010MWR3315.1", "http://doi.org/10.1175%2FMWR3160.1", "http://doi.org/10.1186%2F1472-6947-14-26", "http://doi.org/10.1371%2Fjournal.pone.0000180", "http://doi.org/10.2307%2F2341080", "http://www.jstor.org/stable/2332299", "http://www.jstor.org/stable/2341080", "http://www.worldcat.org/oclc/10605205", "http://www.math.ntu.edu.tw/~hchen/teaching/StatInference/notes/lecture16.pdf", "https://books.google.com/books?id=0Q_ijxOEBjMC", "https://books.google.com/books?id=XYDl0mlH-moC", "https://doi.org/10.1093/bioinformatics/btm453"]}, "Central limit theorem": {"categories": ["All articles with unsourced statements", "Articles containing proofs", "Articles with unsourced statements from April 2012", "Articles with unsourced statements from July 2016", "Articles with unsourced statements from June 2012", "Asymptotic theory (statistics)", "CS1 German-language sources (de)", "CS1 Russian-language sources (ru)", "Central limit theorem", "Commons category link from Wikidata", "Probability theorems", "Statistical theorems", "Wikipedia articles needing clarification from April 2012", "Wikipedia articles needing clarification from June 2012"], "title": "Central limit theorem", "method": "Central limit theorem", "url": "https://en.wikipedia.org/wiki/Central_limit_theorem", "summary": "In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a \"bell curve\") even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions.\nFor example, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic mean of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the distribution of the average will be closely approximated by a normal distribution. A simple example of this is that if one flips a coin many times the probability of getting a given number of heads in a series of flips will approach a normal curve, with mean equal to half the total number of flips in each series. (In the limit of an infinite number of flips, it will equal a normal curve.)\nThe central limit theorem has a number of variants. In its common form, the random variables must be identically distributed. In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, given that they comply with certain conditions.\nThe earliest version of this theorem, that the normal distribution may be used as an approximation to the binomial distribution, is now known as the de Moivre\u2013Laplace theorem.\nIn more general usage, a central limit theorem is any of a set of weak-convergence theorems in probability theory. They all express the fact that a sum of many independent and identically distributed (i.i.d.) random variables, or alternatively, random variables with specific types of dependence, will tend to be distributed according to one of a small set of attractor distributions. When the variance of the i.i.d. variables is finite, the attractor distribution is the normal distribution. In contrast, the sum of a number of i.i.d. random variables with power law tail distributions decreasing as |x|\u2212\u03b1 \u2212 1 where 0 < \u03b1 < 2 (and therefore having infinite variance) will tend to an alpha-stable distribution with stability parameter (or index of stability) of \u03b1 as the number of variables grows.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/12/Central_Limit_Theorem.png", "https://upload.wikimedia.org/wikipedia/commons/f/f3/Central_limit_thm.png", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Dice_sum_central_limit_theorem.svg", "https://upload.wikimedia.org/wikipedia/commons/2/2d/Empirical_CLT_-_Figure_-_040711.jpg", "https://upload.wikimedia.org/wikipedia/commons/7/7b/IllustrationCentralTheorem.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abraham de Moivre", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alan Turing", "Alan Turing: The Enigma", "Aleksandr Lyapunov", "Almost sure convergence", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andrew Hodges", "Andrey Markov", "Andrey Nikolaevich Kolmogorov", "Antoni Zygmund", "Applied probability", "ArXiv", "Arithmetic mean", "Assaf Naor", "Asymptotic distribution", "Asymptotic equipartition property", "Asymptotic series", "Asymptotic theory (statistics)", "Attractor", "Augustin Louis Cauchy", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Berry\u2013Esseen theorem", "Bias of an estimator", "Bibcode", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Boris Vladimirovich Gnedenko", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem for directional statistics", "Central tendency", "Characteristic function (probability theory)", "Charles Stein (statistician)", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Coin flipping", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Convergence in distribution", "Convergence in probability", "Convex hull", "Convex polytope", "Convolution", "Correlation and dependence", "Correlogram", "Count data", "Covariance matrix", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "De Moivre\u2013Laplace theorem", "Decomposition of time series", "Degrees of freedom (statistics)", "Delta method", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Discrete random variable", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erd\u0151s\u2013Kac theorem", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimating equations", "Expected value", "Experiment", "Exponential family", "Exponential function", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Forest plot", "Fourier analysis", "Fourier transform", "Francis Galton", "Franck Barthe", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Friedrich Bessel", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George P\u00f3lya", "Geostatistics", "Gibrat's law", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Haar measure", "Harald Cram\u00e9r", "Harmonic mean", "Henk Tijms", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Identically distributed", "Illustration of the central limit theorem", "Imre B\u00e1r\u00e1ny", "Independent and identically distributed", "Independent and identically distributed random variables", "Independent variable", "Index of dispersion", "Indicator function", "Information entropy", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Irwin\u2013Hall distribution", "Isotonic regression", "Jackknife resampling", "Jarl Waldemar Lindeberg", "Jarque\u2013Bera test", "Johansen test", "Joint density function", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Keith Martin Ball", "Kendall rank correlation coefficient", "King's College, Cambridge", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Law of the iterated logarithm", "Lehmann\u2013Scheff\u00e9 theorem", "Library of Congress Control Number", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Lindeberg's condition", "Linear discriminant analysis", "Linear model", "Linear regression", "Linearity of expectation", "List of fields of application of statistics", "List of statistics articles", "Little-o notation", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-normal distribution", "Log-rank test", "Logarithm", "Logarithmically concave function", "Logistic regression", "Loss function", "Lp space", "Lucien Le Cam", "L\u00e9vy continuity theorem", "M-estimator", "Mann\u2013Whitney U test", "Martingale (probability theory)", "Martingale central limit theorem", "MathWorld", "Mathematical Reviews", "Mathematical constant", "Mathematische Zeitschrift", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mixing (mathematics)", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monotonic function", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal group", "Orthogonal matrix", "Outline of statistics", "Pafnuty Chebyshev", "Pairwise independence", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Paul L\u00e9vy (mathematician)", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pierre-Simon Laplace", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson convergence theorem", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Power law", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability theory", "Proof of the law of large numbers", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random", "Random assignment", "Random sample", "Random variate", "Random vector", "Random walk", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rapha\u00ebl Salem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted expectation", "Richard von Mises", "Rick Durrett", "Robust regression", "Robust statistics", "Rotation matrix", "Run chart", "Sample (statistics)", "Sample mean", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sergei Natanovich Bernstein", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shiri Artstein", "Sign test", "Simple linear regression", "Simultaneous equations model", "Sim\u00e9on Denis Poisson", "Skewness", "Slowly varying function", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable distribution", "Standard deviation", "Standard error", "Stationary process", "Stationary sequence", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stein's method", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Summation", "Supremum", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taylor's theorem", "Time domain", "Time series", "Tolerance interval", "Toshikazu Sunada", "Total variation distance of probability measures", "Trace (linear algebra)", "Trend estimation", "Tweedie distribution", "U-statistic", "Uncorrelated", "Uniform convergence", "Uniformly most powerful test", "University of Cambridge", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Weak convergence (Hilbert space)", "Weak convergence of measures", "Whittle likelihood", "Wilcoxon signed-rank test", "Wolfram Demonstrations Project", "Z-test", "Zentralblatt MATH"], "references": ["http://demonstrations.wolfram.com/TheCentralLimitTheorem/", "http://mathworld.wolfram.com/CentralLimitTheorem.html", "http://www.gbv.de/dms/goettingen/229762905.pdf", "http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN266833020_0008", "http://www.contrib.andrew.cmu.edu/~ryanod/?p=866", "http://adsabs.harvard.edu/abs/1966RuMaS..21....1G", "http://adsabs.harvard.edu/abs/2007InMat.168...91K", "http://www.indiana.edu/~jkkteach/ExcelSampler/", "http://ccl.northwestern.edu/curriculum/ProbLab/CentralLimitTheorem.html", "http://www.socr.ucla.edu/htmls/SOCR_Experiments.html", 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"http://www.causeweb.org", "http://doi.org/10.1007%2F978-0-387-87857-7", "http://doi.org/10.1007%2FBF01206525", "http://doi.org/10.1007%2Fs00222-006-0028-8", "http://doi.org/10.1007%2Fs00440-008-0158-6", "http://doi.org/10.1016%2Fj.spl.2017.06.027", "http://doi.org/10.1070%2FRM1966v021n06ABEH001196", "http://doi.org/10.1080%2F10691898.2008.11889560", "http://doi.org/10.1090%2FS0002-9947-08-04444-9", "http://doi.org/10.1090%2FS0894-0347-04-00459-X", "http://doi.org/10.1137%2FS0040585X97981123", "http://doi.org/10.1214%2F009117906000000791", "http://doi.org/10.1214%2F154957805100000104", "http://doi.org/10.1214%2Fecp.v7-1046", "http://doi.org/10.2307%2F2245503", "http://galton.org/cgi-bin/searchImages/galton/search/books/natural-inheritance/pages/natural-inheritance_0073.htm", "http://projecteuclid.org/euclid.bsmsp/1200514239", "http://projecteuclid.org/euclid.ss/1177013818", "http://www.vias.org/simulations/simusoft_cenlimit.html", "http://zbmath.org/?format=complete&q=an:0278.60026", "http://zbmath.org/?format=complete&q=an:1226.60004", "https://books.google.com/books/about/Limit_distributions_for_sums_of_independ.html?id=rYsZAQAAIAAuJ", "https://books.google.com/books?id=6zUlh_TkWSwC", "https://statistical-engineering.com/clt-summary/", "https://jhupbooks.press.jhu.edu/content/introduction-stochastic-processes-physics", "https://web.archive.org/web/20081102151742/http://animation.yihui.name/prob:central_limit_theorem", "https://web.archive.org/web/20120529212657/http://ocw.mit.edu/courses/mathematics/18-440-probability-and-random-variables-spring-2011/lecture-notes/MIT18_440S11_Lecture31.pdf", "https://arxiv.org/pdf/math/0511078.pdf", "https://www.encyclopediaofmath.org/index.php?title=p/c021180", "https://www.khanacademy.org/math/probability/statistics-inferential/sampling_distribution/v/central-limit-theorem", "https://cran.r-project.org/package=TeachingDemos", "https://cran.r-project.org/package=animation"]}, "Q-function": {"categories": ["Articles containing proofs", "Functions related to probability distributions", "Normal distribution", "Special functions", "Webarchive template wayback links"], "title": "Q-function", "method": "Q-function", "url": "https://en.wikipedia.org/wiki/Q-function", "summary": "In statistics, the Q-function is the tail distribution function of the standard normal distribution. In other words, \n \n \n \n Q\n (\n x\n )\n \n \n {\\displaystyle Q(x)}\n is the probability that a normal (Gaussian) random variable will obtain a value larger than \n \n \n \n x\n \n \n {\\displaystyle x}\n standard deviations. Equivalently, \n \n \n \n Q\n (\n x\n )\n \n \n {\\displaystyle Q(x)}\n is the probability that a standard normal random variable takes a value larger than \n \n \n \n x\n \n \n {\\displaystyle x}\n .\nIf \n \n \n \n Y\n \n \n {\\displaystyle Y}\n is a Gaussian random variable with mean \n \n \n \n \u03bc\n \n \n {\\displaystyle \\mu }\n and variance \n \n \n \n \n \u03c3\n \n 2\n \n \n \n \n {\\displaystyle \\sigma ^{2}}\n , then \n \n \n \n X\n =\n \n \n \n Y\n \u2212\n \u03bc\n \n \u03c3\n \n \n \n \n {\\displaystyle X={\\frac {Y-\\mu }{\\sigma }}}\n is standard normal and\n\n \n \n \n P\n (\n Y\n >\n y\n )\n =\n P\n (\n X\n >\n x\n )\n =\n Q\n (\n x\n )\n \n \n {\\displaystyle P(Y>y)=P(X>x)=Q(x)}\n where \n \n \n \n x\n =\n \n \n \n y\n \u2212\n \u03bc\n \n \u03c3\n \n \n \n \n {\\displaystyle x={\\frac {y-\\mu }{\\sigma }}}\n .\nOther definitions of the Q-function, all of which are simple transformations of the normal cumulative distribution function, are also used occasionally.Because of its relation to the cumulative distribution function of the normal distribution, the Q-function can also be expressed in terms of the error function, which is an important function in applied mathematics and physics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/87/Q-factor_vs_BER.png", "https://upload.wikimedia.org/wikipedia/commons/c/c3/Q-function.png"], "links": ["ArXiv", "Chernoff bound", "Cnx.org", "Cumulative distribution function", "Decibel", "Digital object identifier", "Elementary function", "Error function", "Geometric mean", "Integration by substitution", "International Standard Book Number", "MATLAB", "Normal distribution", "Phase-shift keying", "Python (programming language)", "Quotient rule", "R (programming language)", "Signal-to-noise ratio", "Standard normal distribution", "Statistics", "Wayback Machine", "Wolfram Mathematica"], "references": ["http://www.mathworks.com/matlabcentral/fileexchange/53796", "http://mathworld.wolfram.com/NormalDistributionFunction.html", "http://wsl.stanford.edu/~ee359/craig.pdf", "http://users.auth.gr/users/9/3/028239/public_html/pdf/Q_Approxim.pdf", "http://www.eng.tau.ac.il/~jo/academic/Q.pdf", "http://campus.unibo.it/85943/1/mcddmsTranWIR2003.pdf", "http://arxiv.org/abs/1603.04166", "http://cnx.org/content/m11537/latest/", "http://doi.org/10.1109%2FWSC.2017.8247926", "http://doi.org/10.1111%2Frssb.12162", "https://web.archive.org/web/20090325160012/http://www.eng.tau.ac.il/~jo/academic/Q.pdf", "https://ieeexplore.ieee.org/document/8247926/"]}, "Generalized normal distribution": {"categories": ["Continuous distributions", "Normal distribution", "Pages using deprecated image syntax"], "title": "Generalized normal distribution", "method": "Generalized normal distribution", "url": "https://en.wikipedia.org/wiki/Generalized_normal_distribution", "summary": "The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as \"version 1\" and \"version 2\". However this is not a standard nomenclature.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/32/Generalized_normal_cdfs.svg", "https://upload.wikimedia.org/wikipedia/commons/8/81/Generalized_normal_cdfs_2.svg", "https://upload.wikimedia.org/wikipedia/commons/1/10/Generalized_normal_densities.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cb/Generalized_normal_densities_2.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARGUS distribution", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous uniform distribution", "Control chart", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Cusp (singularity)", "Dagum distribution", "Data collection", "Davis distribution", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Experiment", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "George E. P. Box", "Geostatistics", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Incomplete gamma function", "Index of dispersion", "Information entropy", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverse normal distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "J. Acoust. Soc. Am.", "Jackknife resampling", "James Clerk Maxwell", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lognormal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maximum likelihood estimation", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Naisyin Wang", "Nakagami distribution", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Newton's method", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabolic fractal distribution", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Platykurtic", "Plug-in principle", "Point estimation", "Pointwise convergence", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability distribution function", "Proportional hazards model", "Psychometrics", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrix", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rice distribution", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Smooth function", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable distribution", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Student t distribution", "Sufficient statistic", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "Symmetric distribution", "System identification", "Time domain", "Time series", "Tolerance interval", "Tracy\u2013Widom distribution", "Trend estimation", "Triangular distribution", "Trigamma function", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.cimat.mx/reportes/enlinea/I-01-18_eng.pdf", "http://doi.org/10.1016%2Fj.jmva.2008.07.006", "http://doi.org/10.1080%2F02664760500079464", "http://doi.org/10.1109%2F83.982822", "http://doi.org/10.1121%2F1.398700", "http://doi.org/10.2307%2F2371328", "http://www.cran.r-project.org/web/packages/lmomco/lmomco.pdf", "http://www3.stat.sinica.edu.tw/statistica/password.asp?vol=17&num=2&art=8", "https://web.archive.org/web/20071009233343/http://www3.stat.sinica.edu.tw/statistica/password.asp?vol=17&num=2&art=8"]}, "D/M/1 queue": {"categories": ["Single queueing nodes"], "title": "D/M/1 queue", "method": "D/M/1 queue", "url": "https://en.wikipedia.org/wiki/D/M/1_queue", "summary": "In queueing theory, a discipline within the mathematical theory of probability, a D/M/1 queue represents the queue length in a system having a single server, where arrivals occur at fixed regular intervals and job service requirements are random with an exponential distribution. The model name is written in Kendall's notation. Agner Krarup Erlang first published a solution to the stationary distribution of a D/M/1 and D/M/k queue, the model with k servers, in 1917 and 1920.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Agner Krarup Erlang", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "Data buffer", "David George Kendall", "Decomposition method (queueing theory)", "Digital object identifier", "Erlang (unit)", "Erlang distribution", "Exponential distribution", "FIFO (computing and electronics)", "First-come, first-served", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "JSTOR", "Jackson network", "John Kingman", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing Systems", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "State space", "Teletraffic engineering", "Traffic equations"], "references": ["http://alexandria.tue.nl/repository/books/641261.pdf", "http://doi.org/10.1007/s11134-009-9147-4", "http://doi.org/10.1111/j.1467-9574.2008.00395.x", "http://doi.org/10.1214/aoms/1177728975", "http://doi.org/10.1287/opre.14.2.292", "http://www.jstor.org/stable/168256", "http://www.jstor.org/stable/2236285", "http://projecteuclid.org/euclid.aoms/1177728975"]}, "Consistent estimator": {"categories": ["Asymptotic theory (statistics)", "Estimator"], "title": "Consistent estimator", "method": "Consistent estimator", "url": "https://en.wikipedia.org/wiki/Consistent_estimator", "summary": "In statistics, a consistent estimator or asymptotically consistent estimator is an estimator\u2014a rule for computing estimates of a parameter \u03b80\u2014having the property that as the number of data points used increases indefinitely, the resulting sequence of estimates converges in probability to \u03b80. This means that the distributions of the estimates become more and more concentrated near the true value of the parameter being estimated, so that the probability of the estimator being arbitrarily close to \u03b80 converges to one.\nIn practice one constructs an estimator as a function of an available sample of size n, and then imagines being able to keep collecting data and expanding the sample ad infinitum. In this way one would obtain a sequence of estimates indexed by n, and consistency is a property of what occurs as the sample size \u201cgrows to infinity\u201d. If the sequence of estimates can be mathematically shown to converge in probability to the true value \u03b80, it is called a consistent estimator; otherwise the estimator is said to be inconsistent.\nConsistency as defined here is sometimes referred to as weak consistency. When we replace convergence in probability with almost sure convergence, then the estimator is said to be strongly consistent. Consistency is related to bias; see bias versus consistency.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b2/Consistency_of_estimator.svg"], "links": ["Almost sure convergence", "Bessel's correction", "Bias of an estimator", "Biased estimator", "Chebyshev's inequality", "Consistency (statistics)", "Continuous mapping theorem", "Convergence in probability", "Cumulative distribution function", "Daniel McFadden", "Degrees of freedom (statistics)", "Efficient estimator", "Encyclopedia of Mathematics", "Estimator", "Extremum estimator", "Fisher consistency", "Iid", "International Standard Book Number", "Law of large numbers", "Mark Thoma", "Markov inequality", "Michiel Hazewinkel", "Normal distribution", "Parametric model", "Regression dilution", "Sample mean", "Sample size", "Sample standard deviation", "Sample variance", "Sampling distribution", "Slutsky\u2019s theorem", "Statistical hypothesis testing", "Statistical sample", "Statistics", "Stochastic equicontinuity", "Takeshi Amemiya", "YouTube"], "references": ["https://www.youtube.com/watch?v=TfuqBxRgRTU&list=PLD15D38DC7AA3B737&index=3#t=32m00m", "https://www.encyclopediaofmath.org/index.php?title=C/c025240"]}, "Local martingale": {"categories": ["Martingale theory"], "title": "Local martingale", "method": "Local martingale", "url": "https://en.wikipedia.org/wiki/Local_martingale", "summary": "In mathematics, a local martingale is a type of stochastic process, satisfying the localized version of the martingale property. Every martingale is a local martingale; every bounded local martingale is a martingale; in particular, every local martingale that is bounded from below is a supermartingale, and every local martingale that is bounded from above is a submartingale; however, in general a local martingale is not a martingale, because its expectation can be distorted by large values of small probability. In particular, a driftless diffusion process is a local martingale, but not necessarily a martingale.\nLocal martingales are essential in stochastic analysis, see It\u014d calculus, semimartingale, Girsanov theorem.", "images": [], "links": ["Abstract Wiener space", "Actuarial mathematics", "Adapted process", "Almost surely", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bernt \u00d8ksendal", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Bounded convergence theorem", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Dirac delta function", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Dominated convergence theorem", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (abstract algebra)", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gambler's ruin", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Harmonic function", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hitting time", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Increasing", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "It\u014d calculus", "It\u014d diffusion", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Mathematics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Partial differential equation", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability space", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Smooth function", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopped process", "Stopping rule", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": []}, "Negative relationship": {"categories": ["Independence (probability theory)", "Negative concepts"], "title": "Negative relationship", "method": "Negative relationship", "url": "https://en.wikipedia.org/wiki/Negative_relationship", "summary": "In statistics, there is a negative relationship or inverse relationship between two variables if higher values of one variable tend to be associated with lower values of the other. A negative relationship between two variables usually implies that the correlation between them is negative, or \u2014 what is in some contexts equivalent \u2014 that the slope in a corresponding graph is negative. A negative correlation between variables is also called anticorrelation or inverse correlation.\nNegative correlation can be seen geometrically when two normalized random vectors are viewed as points on a sphere, and the correlation between them is the cosine of the arc of separation of the points on the sphere. When this arc is more than a quarter-circle (\u03b8 > \u03c0/2), then the cosine is negative. Diametrically opposed points represent a correlation of \u20131 = cos(\u03c0). Any two points not in the same hemisphere have negative correlation.\nAn example would be a negative cross-sectional relationship between illness and vaccination, if it is observed that where the incidence of one is higher than average, the incidence of the other tends to be lower than average. Similarly, there would be a negative temporal relationship between illness and vaccination if it is observed in one location that times with a higher-than-average incidence of one tend to coincide with a lower-than-average incidence of the other.\nA particular inverse relationship is called inverse proportionality, and is given by \n \n \n \n y\n =\n k\n \n /\n \n x\n \n \n {\\displaystyle y=k/x}\n where k > 0 is a constant. In a Cartesian plane this relationship is displayed as a hyperbola with y decreasing as x increases.In finance, an inverse correlation between the returns on two different assets enhances the risk-reduction effect of diversifying by holding them both in the same portfolio.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/IdempotentCosineAngle.jpg"], "links": ["Cartesian plane", "Constant (mathematics)", "Correlation", "Cosine", "Cross-sectional", "Derivative", "Diametrically opposed", "Diminishing returns", "Diversification (finance)", "Finance", "Financial risk", "Hyperbola", "Oklahoma State University\u2013Stillwater", "Pearson correlation coefficient", "Positive real numbers", "Proportionality (mathematics)", "Random vector", "Rate of return", "Singular point of a curve", "Slope", "Statistics", "Time series", "University of Hawaii"], "references": ["http://www.hawaii.edu/powerkills/UC.HTM", "http://ordination.okstate.edu/STATS.htm"]}, "Statistical sample": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2017", "Sampling (statistics)", "Wikipedia articles needing clarification from March 2018", "Wikipedia articles with GND identifiers"], "title": "Sample (statistics)", "method": "Statistical sample", "url": "https://en.wikipedia.org/wiki/Sample_(statistics)", "summary": "In statistics and quantitative research methodology, a data sample is a set of data collected and/or selected from a statistical population by a defined procedure. The elements of a sample are known as sample points, sampling units or observations.\nTypically, the population is very large, making a census or a complete enumeration of all the values in the population either impractical or impossible. The sample usually represents a subset of manageable size. Samples are collected and statistics are calculated from the samples, so that one can make inferences or extrapolations from the sample to the population. \nThe data sample may be drawn from a population without replacement (i.e. no element can be selected more than once in the same sample), in which case it is a subset of a population; or with replacement (i.e. an element may appear multiple times in the one sample), in which case it is a multisubset.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/b/bf/Simple_random_sampling.PNG"], "links": ["Census", "Cluster sampling", "Convenience sample", "Data", "Digital object identifier", "Enumeration", "Estimation theory", "Extrapolation", "Independent and identically-distributed random variables", "Inference", "Integrated Authority File", "International Standard Book Number", "Johan Strydom", "Judgment sample", "Lecture Notes in Computer Science", "Mathematical Reviews", "Non-probability sample", "Non-random sampling", "Probability distribution", "Purposive sample", "Quadrature node", "Quantitative research", "Quasi-Monte Carlo method", "Quota sample", "Random sample", "Replication (statistics)", "Roxy Peck", "Sample size determination", "Sampling (statistics)", "Samuel S. Wilks", "Simple random sample", "Snowball sampling", "Statistic", "Statistical independence", "Statistical population", "Statistical unit", "Statistics", "Stratified sampling", "Subset", "Survey sampling", "Systematic sampling", "William Gemmell Cochran", "Zentralblatt MATH"], "references": ["http://www-igm.univ-mlv.fr/~berstel/Articles/1993SturmianPatriceMFCS.pdf", "http://www.socialresearchmethods.net/kb/sampstat.php", "http://doi.org/10.1007%2F3-540-57182-5_20", "http://zbmath.org/?format=complete&q=an:0925.11026", "https://books.google.com/?id=2VkNiakfaUEC&printsec=frontcover&q=", "https://d-nb.info/gnd/4057502-0", "https://mathscinet.ams.org/mathscinet-getitem?mr=1326829", "https://www.wikidata.org/wiki/Q49906"]}, "Deviation (statistics)": {"categories": ["All articles lacking sources", "Articles lacking sources from February 2007", "Statistical deviation and dispersion", "Statistical distance"], "title": "Deviation (statistics)", "method": "Deviation (statistics)", "url": "https://en.wikipedia.org/wiki/Deviation_(statistics)", "summary": "In mathematics and statistics, deviation is a measure of difference between the observed value of a variable and some other value, often that variable's mean. The sign of the deviation (positive or negative), reports the direction of that difference (the deviation is positive when the observed value exceeds the reference value). The magnitude of the value indicates the size of the difference.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Absolute difference", "Accuracy and precision", "Anomaly (natural sciences)", "Average", "Average absolute deviation", "Bias of an estimator", "Central tendency", "Data set", "Deviance (statistics)", "Errors and residuals", "Formula", "Least absolute deviation", "Level of measurement", "Mathematics", "Maximum absolute deviation", "Mean", "Mean signed deviation", "Median", "Median absolute deviation", "Nondimensionalization", "Normalization (statistics)", "Robust statistics", "Square (algebra)", "Squared deviations", "Standard deviation", "Standardizing", "Statistical dispersion", "Statistics", "Studentized residual", "Studentizing", "Variance"], "references": []}, "Kolmogorov extension theorem": {"categories": ["Theorems regarding stochastic processes"], "title": "Kolmogorov extension theorem", "method": "Kolmogorov extension theorem", "url": "https://en.wikipedia.org/wiki/Kolmogorov_extension_theorem", "summary": "In mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem or Kolmogorov consistency theorem) is a theorem that guarantees that a suitably \"consistent\" collection of finite-dimensional distributions will define a stochastic process. It is credited to the Russian mathematician Andrey Nikolaevich Kolmogorov.", "images": [], "links": ["Andrey Kolmogorov", "Brownian motion", "Finite-dimensional distribution", "Graduate Studies in Mathematics", "Hahn\u2013Kolmogorov theorem", "Hausdorff space", "Inner regular", "Inner regular measure", "International Standard Book Number", "Interval (mathematics)", "Kolmogorov continuity theorem", "Markov chain", "Mathematician", "Mathematics", "Percy John Daniell", "Permutation", "Polish space", "Probability measure", "Probability space", "Product topology", "Pushforward measure", "Radon measure", "Russia", "Sequence", "Sigma algebra", "Stochastic process", "Terence Tao", "Theorem", "Time", "United Kingdom", "Wiener process", "\u03a3-algebra"], "references": ["http://www.emis.de/journals/JEHPS/Decembre2007/Aldrich.pdf", "http://www.emis.de/journals/JEHPS/indexang.html", "https://books.google.com/books?id=HoGDAwAAQBAJ&pg=PA195", "https://books.google.com/books?id=VgQDWyihxKYC&pg=PA11"]}, "Exponential power distribution": {"categories": ["Continuous distributions", "Normal distribution", "Pages using deprecated image syntax"], "title": "Generalized normal distribution", "method": "Exponential power distribution", "url": "https://en.wikipedia.org/wiki/Generalized_normal_distribution", "summary": "The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as \"version 1\" and \"version 2\". However this is not a standard nomenclature.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/32/Generalized_normal_cdfs.svg", "https://upload.wikimedia.org/wikipedia/commons/8/81/Generalized_normal_cdfs_2.svg", "https://upload.wikimedia.org/wikipedia/commons/1/10/Generalized_normal_densities.svg", "https://upload.wikimedia.org/wikipedia/commons/c/cb/Generalized_normal_densities_2.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARGUS distribution", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arcsine distribution", "Arithmetic mean", "Asymmetric Laplace distribution", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Balding\u2013Nichols model", "Bar chart", "Bates distribution", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bias of an estimator", "Bingham distribution", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Bivariate von Mises distribution", "Blocking (statistics)", "Bootstrapping (statistics)", "Borel distribution", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burr distribution", "Canonical correlation", "Cantor distribution", "Cartography", "Categorical distribution", "Categorical variable", "Cauchy distribution", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Compound Poisson distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous uniform distribution", "Control chart", "Conway\u2013Maxwell\u2013Poisson distribution", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Cusp (singularity)", "Dagum distribution", "Data collection", "Davis distribution", "Decomposition of time series", "Degenerate distribution", "Degrees of freedom (statistics)", "Delaporte distribution", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erlang distribution", "Errors and residuals in statistics", "Estimating equations", "Ewens's sampling formula", "Excess kurtosis", "Expected value", "Experiment", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Exponential smoothing", "Extended negative binomial distribution", "F-distribution", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "Fr\u00e9chet distribution", "G-test", "Gamma/Gompertz distribution", "Gamma distribution", "Gamma function", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "General linear model", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized linear model", "Generalized normal distribution", "Geographic information system", "Geometric distribution", "Geometric mean", "Geometric stable distribution", "George E. P. Box", "Geostatistics", "Gompertz distribution", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Holtsmark distribution", "Homoscedasticity", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Incomplete gamma function", "Index of dispersion", "Information entropy", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Inverse normal distribution", "Irwin\u2013Hall distribution", "Isotonic regression", "J. Acoust. Soc. Am.", "Jackknife resampling", "James Clerk Maxwell", "Jarque\u2013Bera test", "Johansen test", "Johnson's SU-distribution", "Joint probability distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kumaraswamy distribution", "Kurtosis", "L-moment", "Landau distribution", "Laplace distribution", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of probability distributions", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Log-rank test", "Logarithmic distribution", "Logistic distribution", "Logistic regression", "Logit-normal distribution", "Lognormal distribution", "Lomax distribution", "Loss function", "Lp space", "L\u00e9vy distribution", "M-estimator", "Mann\u2013Whitney U test", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum a posteriori estimation", "Maximum entropy probability distribution", "Maximum likelihood", "Maximum likelihood estimation", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mittag-Leffler distribution", "Mixed model", "Mixture distribution", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multivariate Laplace distribution", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate statistics", "Multivariate t-distribution", "Naisyin Wang", "Nakagami distribution", "National accounts", "Natural experiment", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Nelson\u2013Aalen estimator", "Newton's method", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parabolic fractal distribution", "Parametric statistics", "Pareto distribution", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson distribution", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Phase-type distribution", "Pie chart", "Pivotal quantity", "Platykurtic", "Plug-in principle", "Point estimation", "Pointwise convergence", "Poisson binomial distribution", "Poisson distribution", "Poisson regression", "Poly-Weibull distribution", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probability distribution function", "Proportional hazards model", "Psychometrics", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Rademacher distribution", "Raised cosine distribution", "Random assignment", "Random matrix", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Regression analysis", "Regression model validation", "Relativistic Breit\u2013Wigner distribution", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rice distribution", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled inverse chi-squared distribution", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Sign test", "Simple linear regression", "Simultaneous equations model", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Skewness", "Slash distribution", "Smooth function", "Social statistics", "Soliton distribution", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Stable distribution", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Student t distribution", "Sufficient statistic", "Support (mathematics)", "Survey methodology", "Survival analysis", "Survival function", "Symmetric distribution", "System identification", "Time domain", "Time series", "Tolerance interval", "Tracy\u2013Widom distribution", "Trend estimation", "Triangular distribution", "Trigamma function", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "U-statistic", "Uniform distribution (continuous)", "Uniformly most powerful test", "V-statistic", "Variance", "Variance-gamma distribution", "Vector autoregression", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Wald test", "Wavelet", "Weibull distribution", "Whittle likelihood", "Wigner semicircle distribution", "Wilcoxon signed-rank test", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Z-test", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.cimat.mx/reportes/enlinea/I-01-18_eng.pdf", "http://doi.org/10.1016%2Fj.jmva.2008.07.006", "http://doi.org/10.1080%2F02664760500079464", "http://doi.org/10.1109%2F83.982822", "http://doi.org/10.1121%2F1.398700", "http://doi.org/10.2307%2F2371328", "http://www.cran.r-project.org/web/packages/lmomco/lmomco.pdf", "http://www3.stat.sinica.edu.tw/statistica/password.asp?vol=17&num=2&art=8", "https://web.archive.org/web/20071009233343/http://www3.stat.sinica.edu.tw/statistica/password.asp?vol=17&num=2&art=8"]}, "Life expectancy": {"categories": ["Actuarial science", "All articles needing additional references", "Articles needing additional references from June 2015", "CS1 maint: Explicit use of et al.", "CS1 maint: Multiple names: authors list", "Commons category link is defined as the pagename", "Demographic economics", "Demography", "Pages with citations having bare URLs", "Pages with citations lacking titles", "Population", "Senescence", "Use mdy dates from August 2014", "Webarchive template wayback links", "Wikipedia articles needing clarification from October 2014"], "title": "Life expectancy", "method": "Life expectancy", "url": "https://en.wikipedia.org/wiki/Life_expectancy", "summary": "Life expectancy is a statistical measure of the average time an organism is expected to live, based on the year of its birth, its current age and other demographic factors including gender. The most commonly used measure of life expectancy is at birth (LEB), which can be defined in two ways. Cohort LEB is the mean length of life of an actual birth cohort (all individuals born a given year) and can be computed only for cohorts born many decades ago, so that all their members have died. Period LEB is the mean length of life of a hypothetical cohort assumed to be exposed, from birth through death, to the mortality rates observed at a given year.National LEB figures reported by statistical national agencies and international organizations are indeed estimates of period LEB. In the Bronze Age and the Iron Age, LEB was 26 years; the 2010 world LEB was 67.2 years. For recent years, in Swaziland LEB is about 49, and in Japan, it is about 83. The combination of high infant mortality and deaths in young adulthood from accidents, epidemics, plagues, wars, and childbirth, particularly before modern medicine was widely available, significantly lowers LEB. But for those who survive early hazards, a life expectancy of 70 would not be uncommon. For example, a society with a LEB of 40 may have few people dying at precisely 40: most will die before 30 or after 55. In populations with high infant mortality rates, LEB is highly sensitive to the rate of death in the first few years of life. Because of this sensitivity to infant mortality, LEB can be subjected to gross misinterpretation, leading one to believe that a population with a low LEB will necessarily have a small proportion of older people. For example, in a hypothetical stationary population in which half the population dies before the age of five but everybody else dies at exactly 70 years old, LEB will be about 36, but about 25% of the population will be between the ages of 50 and 70. Another measure, such as life expectancy at age 5 (e5), can be used to exclude the effect of infant mortality to provide a simple measure of overall mortality rates other than in early childhood; in the hypothetical population above, life expectancy at 5 would be another 65. Aggregate population measures, such as the proportion of the population in various age groups, should also be used along individual-based measures like formal life expectancy when analyzing population structure and dynamics.\nMathematically, life expectancy is the mean number of years of life remaining at a given age, assuming age-specific mortality rates remain at their most recently measured levels. It is denoted by \n \n \n \n \n e\n \n x\n \n \n \n \n {\\displaystyle e_{x}}\n ,[a] which means the mean number of subsequent years of life for someone now aged \n \n \n \n x\n \n \n {\\displaystyle x}\n , according to a particular mortality experience. Longevity, maximum lifespan, and life expectancy are not synonyms. Life expectancy is defined statistically as the mean number of years remaining for an individual or a group of people at a given age. Longevity refers to the characteristics of the relatively long life span of some members of a population. Maximum lifespan is the age at death for the longest-lived individual of a species. Moreover, because life expectancy is an average, a particular person may die many years before or many years after the \"expected\" survival. The term \"maximum life span\" has a quite different meaning and is more related to longevity.\nLife expectancy is also used in plant or animal ecology; life tables (also known as actuarial tables). The term life expectancy may also be used in the context of manufactured objects, but the related term shelf life is used for consumer products, and the terms \"mean time to breakdown\" (MTTB) and \"mean time between failures\" (MTBF) are used in engineering.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b2/Comparison_gender_life_expectancy_CIA_factbook.svg", "https://upload.wikimedia.org/wikipedia/commons/4/41/Comparison_subsaharan_life_expectancy.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fa/Flag_of_Botswana.svg", "https://upload.wikimedia.org/wikipedia/commons/a/af/Flag_of_South_Africa.svg", "https://upload.wikimedia.org/wikipedia/commons/6/6a/Flag_of_Zimbabwe.svg", "https://upload.wikimedia.org/wikipedia/commons/6/63/LifeExpectancyBetweenFemaleAndMales.jpg", "https://upload.wikimedia.org/wikipedia/commons/0/0c/LifeExpectancy_GDPperCapita.png", "https://upload.wikimedia.org/wikipedia/commons/2/29/Life_Expectancy_at_Birth_by_Region_1950-2050.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/5/58/Smi_graph_by_Mark.png", "https://upload.wikimedia.org/wikipedia/en/8/89/Survivaltree.png"], "links": ["1918 flu pandemic", "AIDS", "ARIMA", "Accelerated aging", "Actuarial notation", "Actuary", "Age-specific death rate", "Ageing", "Ageless", "Aging-associated diseases", "Agranulocytosis", "Air pollution", "Alcoholic drink", "Ansley J. 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Gavrilov", "Life Expectancy (novel)", "Life extension", "Life history theory", "Life table", "Linda J. Young", "Lindy Effect", "List of American supercentenarians", "List of Belgian supercentenarians", "List of British supercentenarians", "List of Canadian supercentenarians", "List of Danish supercentenarians", "List of Finnish supercentenarians", "List of French supercentenarians", "List of German supercentenarians", "List of Irish supercentenarians", "List of Italian supercentenarians", "List of Japanese supercentenarians", "List of Norwegian supercentenarians", "List of Polish supercentenarians", "List of Portuguese supercentenarians", "List of Spanish supercentenarians", "List of Swedish supercentenarians", "List of centenarians (activists, non-profit leaders and philanthropists)", "List of centenarians (actors, filmmakers and entertainers)", "List of centenarians (artists, painters and sculptors)", "List of centenarians (authors, poets and journalists)", "List of centenarians (businesspeople)", "List of centenarians (educators, school administrators, social scientists and linguists)", "List of centenarians (explorers)", "List of centenarians (jurists and practitioners of law)", "List of centenarians (medical professionals)", "List of centenarians (military commanders and soldiers)", "List of centenarians (miscellaneous)", "List of centenarians (musicians, composers and music patrons)", "List of centenarians (philosophers and theologians)", "List of centenarians (politicians and civil servants)", "List of centenarians (religious figures)", "List of centenarians (royalty and nobility)", "List of centenarians (scientists and mathematicians)", "List of centenarians (sportspeople)", "List of countries by life expectancy", "List of last World War I veterans by country", "List of last surviving Canadian war veterans", "List of last surviving veterans of military insurgencies and wars", "List of last survivors of historical events", "List of living centenarians", "List of longest-living organisms", "List of longest-reigning monarchs", "List of notable surviving veterans of World War II", "List of oldest living people", "List of oldest people by country", "List of oldest twins", "List of people with the longest marriages", "List of supercentenarians by continent", "List of surviving veterans of the Spanish Civil War", "List of the verified oldest men", "List of the verified oldest people", "List of the verified oldest women", "Lists of centenarians", "Longevity", "Longevity claims", "Longevity escape velocity", "Longevity insurance", "Longevity myths", "Longevity risk", "Lung cancer", "Maternal death", "Matlab", "Maturation (disambiguation)", "Max Roser", "Maximum life span", "Mean time between failures", "Medieval demography", "Mi'kmaq", "Mitochondria", "Mitohormesis", "Mortality rate", "Mortality table", "Nanomedicine", "National Center for Health Statistics", "Natural selection", "Nature (journal)", "Negligible senescence", "Neolithic", "Occupational safety and health", "Okinawa Prefecture", "Olanzapine", "Old age", "Oldest people", "Organ printing", "Outline of life extension", "PZ Myers", "Pacific War", "Paleolithic", "Pay-as-you-go tax", "Pension", "Physical quality-of-life index", "Pollution", "Population Pyramid", "Preston curve", "Princeton University Press", "Prussia", "PubMed Central", "PubMed Identifier", "Public health", "Qing China", "R (programming language)", "Rejuvenation", "Rejuvenation (aging)", "Roadway air dispersion model", "Rob J. Hyndman", "SAS (software)", "SPSS", "Samuel de Champlain", "Science Daily", "Senescence", "Shelf life", "Shimane prefecture", "Singular value decomposition", "South Africa", "Stata", "Statistical population", "Stem-cell therapy", "Strategies for Engineered Negligible Senescence", "Stress (biology)", "Studia Islamica", "Suicide", "Supercentenarian", "Swaziland", "The Guardian", "The Lancet", "Tobacco", "Tobacco smoking", "Transhumanist politics", "Tuberculosis", "U.S. Social Security", "United States", "United States Department of Health and Human Services", "University of Michigan", "Uterus", "War", "Wayback Machine", "WebMD", "World population", "Zimbabwe"], "references": ["http://jech.bmj.com/content/59/2/158/F2.expansion", "http://www.bmj.com/content/312/7037/999", "http://www.britannica.com/EBchecked/topic/387301/modernization/12022/Population-change", "http://www.britannica.com/EBchecked/topic/393100/mortality", "http://www.channel4.com/history/microsites/H/history/guide12/part06.html", "http://www.discoverymedicine.com/S-J-Olshansky/2009/07/25/what-determines-longevity-metabolic-rate-or-stability", "http://www.google.com/publicdata/explore?ds=wb-wdi&met=sp_dyn_le00_in&idim=country:CAN&dl=en&hl=en&q=average+life+expectancy+canada#met=sp_dyn_le00_in&idim=country:USA:CHN", "http://www.immortalhumans.com/the-longevity-secret-for-tortoises-is-held-in-their-low-metabolism-rate/", "http://www.infoplease.com/ipa/A0005140.html", "http://www.livescience.com/51455-women-outlive-men.html", "http://www.medscape.com/viewarticle/861159", "http://www.medscape.com/viewarticle/863871", "http://www.newsweek.com/nearly-1-5-americans-suffer-mental-illness-each-year-230608", "http://scienceblogs.com/gregladen/2011/05/01/falsehood-if-this-was-the-ston/", "http://scienceblogs.com/pharyngula/2013/02/06/mothers-curse/", "http://www.scientificamerican.com/article/gut-feelings-the-second-brain-in-our-gastrointestinal-systems-excerpt/", "http://smart-unit-converter.com/life-expectancy.php", "http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(11)61055-6/abstract", "http://jerrymondo.tripod.com/lgev/id1.html", "http://waterfieldsllc.com/about-waterfields/social-mission/root-causes-poverty/", "http://www.webmd.com/healthy-aging/news/20050228/us-life-expectancy-best-ever-says-cdc", "http://lcfit.demog.berkeley.edu/", "http://www.brown.edu/academics/economics/sites/brown.edu.academics.economics/files/uploads/2007-14_paper.pdf", "http://www.digitalhistory.uh.edu/historyonline/usdeath.cfm", "http://www.unm.edu/~hkaplan/KaplanHillLancasterHurtado_2000_LHEvolution.pdf", "http://cdc.gov/mmwr/preview/mmwrhtml/00056796.htm", "http://minorityhealth.hhs.gov/templates/browse.aspx?lvl=2&lvlID=53", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3136028", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3997379", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4393685", "http://www.ncbi.nlm.nih.gov/pubmed/10220250", "http://www.ncbi.nlm.nih.gov/pubmed/10227303", "http://www.ncbi.nlm.nih.gov/pubmed/15510147", "http://www.ncbi.nlm.nih.gov/pubmed/16230529", "http://www.ncbi.nlm.nih.gov/pubmed/17845285", "http://www.ncbi.nlm.nih.gov/pubmed/17928583", "http://www.ncbi.nlm.nih.gov/pubmed/18087751", "http://www.ncbi.nlm.nih.gov/pubmed/18568631", "http://www.ncbi.nlm.nih.gov/pubmed/19687183", "http://www.ncbi.nlm.nih.gov/pubmed/21593516", "http://www.ncbi.nlm.nih.gov/pubmed/21772658", "http://www.ncbi.nlm.nih.gov/pubmed/21885105", "http://www.ncbi.nlm.nih.gov/pubmed/22249081", "http://www.ncbi.nlm.nih.gov/pubmed/24648481", "http://www.ncbi.nlm.nih.gov/pubmed/25262443", "http://www.ncbi.nlm.nih.gov/pubmed/27797313", "http://www.ncbi.nlm.nih.gov/pubmed/593350", "http://www.ncbi.nlm.nih.gov/pubmed/7828766", "http://www.ncbi.nlm.nih.gov/pubmed/8515788", "http://apps.who.int/gho/data/node.main.688?lang=en", 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"http://www.gapminder.org/world/#$majorMode=chart$is;shi=t;ly=2003;lb=f;il=t;fs=11;al=30;stl=t;st=t;nsl=t;se=t$wst;tts=C$ts;sp=5.59290322580644;ti=1918$zpv;v=0$inc_x;mmid=XCOORDS;iid=phAwcNAVuyj1jiMAkmq1iMg;by=ind$inc_y;mmid=YCOORDS;iid=phAwcNAVuyj2tPLxKvvnNPA;by=ind$inc_s;uniValue=8.21;iid=phAwcNAVuyj0XOoBL_n5tAQ;by=ind$inc_c;uniValue=255;gid=CATID0;by=grp$map_x;scale=log;dataMin=194;dataMax=96846$map_y;scale=lin;dataMin=23;dataMax=86$map_s;sma=49;smi=2.65$cd;bd=0$inds=;modified=75", "http://www.gapminder.org/world/#$majorMode=chart$is;shi=t;ly=2003;lb=f;il=t;fs=11;al=30;stl=t;st=t;nsl=t;se=t$wst;tts=C$ts;sp=5.59290322580644;ti=2013$zpv;v=0$inc_x;mmid=XCOORDS;iid=phAwcNAVuyj1jiMAkmq1iMg;by=ind$inc_y;mmid=YCOORDS;iid=phAwcNAVuyj2tPLxKvvnNPA;by=ind$inc_s;uniValue=8.21;iid=phAwcNAVuyj0XOoBL_n5tAQ;by=ind$inc_c;uniValue=255;gid=CATID0;by=grp$map_x;scale=log;dataMin=194;dataMax=96846$map_y;scale=lin;dataMin=23;dataMax=86$map_s;sma=49;smi=2.65$cd;bd=0$inds=;example=75", 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"http://data.worldbank.org/indicator/SP.DYN.LE00.IN/countries/1W", "http://sticerd.lse.ac.uk/seminarpapers/dg09102006.pdf", "http://news.bbc.co.uk/1/hi/health/241864.stm", "http://news.bbc.co.uk/1/hi/health/7584056.stm#Life%20expectancy", "http://news.bbc.co.uk/1/hi/scotland/glasgow_and_west/7584450.stm", "http://www.bbc.co.uk/history/british/victorians/foundling_01.shtml", "http://www.diabetes.co.uk/diabetes-life-expectancy.html", "http://www.northamptonchron.co.uk/news/inquest-told-there-was-a-lost-opportunity-to-treat-mental-health-patient-who-died-following-severe-constipation-1-5244246", "http://www.dh.gov.uk/PublicationsAndStatistics/Publications/PublicationsPolicyAndGuidance/PublicationsPolicyAndGuidanceArticle/fs/en?CONTENT_ID=4117696&chk=OXFbWI", "http://www.hscic.gov.uk/article/2543/Mortality-rate-three-times-as-high-among-mental-health-service-users-than-in-general-population", "http://www.qualitywatch.org.uk/indicator/life-expectancy#vis-ref_221", "https://www.bbc.com/news/health-18779997", "https://books.google.com/?id=0RDZdDW0EqEC&lpg=PA17&dq=zyprexa%20increase%20the%20chance%20of%20developing%20the%20disease%20of%20diabetes&pg=PA17#v=onepage&q=zyprexa%20increase%20the%20chance%20of%20developing%20the%20disease%20of%20diabetes&f=false", "https://books.google.com/books?id=Ad2PAAAAMAAJ", "https://books.google.com/books?id=T4DLK7zLxYMC&lpg=PP1&pg=PA8", "https://books.google.com/books?id=e311AAAAMAAJ&pg=PP1", "https://www.nature.com/nature/journal/v546/n7660/full/nature22786.html", "https://mobile.nytimes.com/2018/05/30/upshot/mental-illness-health-disparity-longevity.html", "https://www.nytimes.com/2007/10/06/business/06zyprexa.html", "https://academic.oup.com/ije/article/43/2/476/2901736/The-global-prevalence-of-common-mental-disorders-a", "https://www.sciencedaily.com/releases/2009/09/090928172530.htm", "https://www.sciencedaily.com/releases/2017/06/170628131500.htm", "https://www.theguardian.com/world/2011/aug/30/japan-life-expectancy-factors", "https://www.washingtonpost.com/business/economy/research-ties-economic-inequality-to-gap-in-life-expectancy/2013/03/10/c7a323c4-7094-11e2-8b8d-e0b59a1b8e2a_story.html", "https://www.cdc.gov/features/diabetesfactsheet/", "https://www.cdc.gov/nchs/data/nvsr/nvsr61/nvsr61_04.pdf", "https://www.cdc.gov/nchs/data/series/sr_02/sr02_129.pdf", "https://www.census.gov/newsroom/releases/pdf/cb10-ff06.pdf", "https://www.census.gov/popest/national/asrh/2009-nat-res.html", "https://www.cia.gov/library/publications/the-world-factbook/rankorder/2102rank.html", "https://www.cia.gov/library/publications/the-world-factbook/fields/2102.html", "https://www.cia.gov/library/publications/the-world-factbook/fields/2119.html", "https://www.cia.gov/library/publications/the-world-factbook/geos/wz.html", "https://purl.fdlp.gov/GPO/gpo41789", "https://web.archive.org/web/20060427184844/http://www.tesarta.com/www/resources/library/lifespans.html", "https://web.archive.org/web/20070713083310/http://www.plimoth.org/discover/myth/dead-at-40.php", "https://web.archive.org/web/20080527045818/https://www.cdc.gov/nchs/fastats/lifexpec.htm", "https://web.archive.org/web/20090420030845/http://hdrstats.undp.org/indicators/6.html", "https://web.archive.org/web/20100822170736/http://robjhyndman.com/software/demography/", "https://web.archive.org/web/20101230203658/http://www.digitalhistory.uh.edu/historyonline/usdeath.cfm", "https://web.archive.org/web/20120204024943/http://minorityhealth.hhs.gov/templates/browse.aspx?lvl=2&lvlid=53", "https://web.archive.org/web/20120427061404/http://www.utexas.edu/depts/classics/documents/Life.html", "https://web.archive.org/web/20131010072957/http://www.census.gov/popest/national/asrh/2009-nat-res.html", "https://web.archive.org/web/20131112164840/http://www.immortalhumans.com/the-longevity-secret-for-tortoises-is-held-in-their-low-metabolism-rate/", "https://web.archive.org/web/20150109080429/http://jech.bmj.com/content/59/2/158/F2.expansion", "https://web.archive.org/web/20160216221613/http://www.census.gov/newsroom/releases/pdf/cb10-ff06.pdf", "https://web.archive.org/web/20160331014445/http://ourworldindata.org/data/population-growth-vital-statistics/life-expectancy/", "https://www.nasmhpd.org/sites/default/files/Mortality%20and%20Morbidity%20Final%20Report%208.18.08.pdf", "https://www.un.org/esa/population/publications/WPA2009/WPA2009-report.pdf", "https://www.un.org/esa/population/publications/wpp2002/WPP2002-HIGHLIGHTSrev1.PDFUN", "https://www.bbc.co.uk/news/health-19093442"]}, "Queueing model": {"categories": ["All articles with dead external links", "All articles with unsourced statements", "Articles with dead external links from April 2018", "Articles with permanently dead external links", "Articles with unsourced statements from August 2017", "Customer experience", "Formal sciences", "Markov models", "Markov processes", "Network performance", "Operations research", "Production planning", "Queueing theory", "Rationing", "Stochastic processes", "Wikipedia articles with BNF identifiers", "Wikipedia articles with GND identifiers", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers", "Wikipedia external links cleanup from May 2017", "Wikipedia spam cleanup from May 2017"], "title": "Queueing theory", "method": "Queueing model", "url": "https://en.wikipedia.org/wiki/Queueing_theory", "summary": "Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.\nQueueing theory has its origins in research by Agner Krarup Erlang when he created models to describe the Copenhagen telephone exchange. The ideas have since seen applications including telecommunication, traffic engineering, computing\nand, particularly in industrial engineering, in the design of factories, shops, offices and hospitals, as well as in project management.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/d/d3/Fifo_queue.png", "https://upload.wikimedia.org/wikipedia/commons/6/60/Poiuy.png", "https://upload.wikimedia.org/wikipedia/commons/2/2b/ServidorParalelo.jpg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Agner Krarup Erlang", "Aleksandr Khinchin", "Andrey Markov", "Arrival theorem", "BCMP network", "Backpressure routing", "Balance equation", "Bene\u0161 method", "Biblioth\u00e8que nationale de France", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Cass Business School", "Computing", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "David George Kendall", "Decomposition method (queueing theory)", "Diffusion process", "Digital object identifier", "Ehrenfest model", "Empirical measure", "Equilibrium distribution", "Erlang (unit)", "Erlang distribution", "Erlang unit", "Erol Gelenbe", "Exponentially distributed", "FIFO (computing and electronics)", "Felix Pollaczek", "Flow-equivalent server method", "Flow control (data)", "Flow network", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "Frank Kelly (mathematician)", "G-network", "G-networks", "G/G/1 queue", "G/M/1 queue", "Gordon F. Newell", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Industrial engineering", "Information system", "Integral equation", "Integrated Authority File", "International Standard Book Number", "JSTOR", "Jackson network", "James R. Jackson", "Jeffrey P. Buzen", "John Kingman", "Journal of the ACM", "K. Mani Chandy", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Library of Congress Control Number", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/D/k queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Management Science: A Journal of the Institute for Operations Research and the Management Sciences", "Markov chain", "Markovian arrival process", "Mathematical Proceedings of the Cambridge Philosophical Society", "Matrix analytic method", "Matrix geometric method", "Mean field model", "Mean field theory", "Mean sojourn time", "Mean value analysis", "Message queue", "Mor Harchol-Balter", "National Diet Library", "Network congestion", "Network scheduler", "Network simulation", "Normalizing constant", "Onno Boxma", "Operations Research (journal)", "Operations research", "Ornstein\u2013Uhlenbeck process", "Orthant", "Peter Whittle (mathematician)", "Phase-type distribution", "Pipeline (software)", "Poisson distribution", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability distribution", "Processor sharing", "Product-form solution", "Product-form stationary distribution", "Project Production Management", "Quality of service", "Quasireversibility", "Queue area", "Queue management system", "Queueing Systems", "Queueing delay", "Queueing theory", "Queuing Rule of Thumb", "Queuing algorithm", "Random early detection", "Rational arrival process", "Reflected Brownian motion", "Renewal theory", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining processing time", "Shortest remaining time", "Stack (data structure)", "Stochastic scheduling", "Telecommunication", "Teletraffic engineering", "Throughput", "Traffic engineering (transportation)", "Traffic equations", "Traffic generation model", "Traffic jam", "Transient state", "YouTube"], "references": ["http://web2.uwindsor.ca/math/hlynka/queue.html", "http://www.eventhelix.com/RealtimeMantra/CongestionControl/queueing_theory.htm", "http://www.pennlive.com/midstate/index.ssf/2009/03/hershey_med_to_open_redesigned.html", "http://people.revoledu.com/kardi/tutorial/Queuing/index.html", "http://www.slate.com/articles/business/operations/2012/06/queueing_theory_what_people_hate_most_about_waiting_in_line_.html", "http://www.supositorio.com/rcalc/rcalclite.htm", "http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf", "http://www.cs.gmu.edu/~menasce/perfbyd/", "http://www-unix.ecs.umass.edu/~krishna/ece673/buzen.pdf", "http://www.cs.washington.edu/homes/lazowska/qsp/", "http://www.netlab.tkk.fi/opetus/s383143/kalvot/english.shtml", "http://data.bnf.fr/ark:/12148/cb12647707b", "http://queueing-systems.ens-lyon.fr/", "http://www.ee.cityu.edu.hk/~zukerman/classnotes.pdf", "http://jmt.sf.net/", "http://portal.acm.org/citation.cfm?id=79046&dl=GUIDE&coll=GUIDE", "http://doi.org/10.1007%2FBF01149260", "http://doi.org/10.1007%2Fs11134-009-9147-4", "http://doi.org/10.1007%2Fs11134-009-9151-8", "http://doi.org/10.1016%2F0169-7552(93)90073-D", "http://doi.org/10.1017%2FCBO9781139226424.039", "http://doi.org/10.1017%2FCBO9781139226424.040", "http://doi.org/10.1017%2FCBO9781139226424.041", "http://doi.org/10.1017%2FS0305004100036094", "http://doi.org/10.1080%2F15326348808807077", "http://doi.org/10.1109%2FQEST.2008.47", "http://doi.org/10.1145%2F321879.321887", "http://doi.org/10.1145%2F322186.322195", "http://doi.org/10.1145%2F362342.362345", "http://doi.org/10.1214%2Faoap%2F1029962815", "http://doi.org/10.1214%2Faoap%2F1177004602", "http://doi.org/10.1214%2Faoms%2F1177728975", "http://doi.org/10.1287%2Fmnsc.1040.0268", "http://doi.org/10.1287%2Fopre.15.2.254", "http://doi.org/10.1287%2Fopre.5.4.518", "http://doi.org/10.1287%2Fopre.50.1.227.17792", "http://doi.org/10.2307%2F3212869", "http://doi.org/10.2307%2F3214781", "http://www.jstor.org/stable/167249", "http://www.jstor.org/stable/168557", "http://www.jstor.org/stable/2236285", "http://www.jstor.org/stable/2245101", "http://www.jstor.org/stable/2627213", "http://www.jstor.org/stable/2667284", "http://www.jstor.org/stable/2984229", "http://www.jstor.org/stable/3088474", "http://www.jstor.org/stable/3212869", "http://www.jstor.org/stable/3214781", "http://projecteuclid.org/euclid.aoms/1177728975", "http://www.cass.city.ac.uk/media/stories/story_96_105659_69284.html", "http://www.stats.ox.ac.uk/~winkel/bs3a07l13-14.pdf#page=4", "http://pass.maths.org.uk/issue2/erlang/index.html", "https://books.google.com/books?id=K3lQGeCtAJgC", "https://books.google.com/books?id=d-V8c8YRJikC&pg=PA178&dq=%22First-come,+first-served%22+business&hl=en&sa=X&ved=0ahUKEwiB18-Tg9vWAhUqxlQKHcXsDIwQ6AEIKDAA#v=onepage&q=%22First-come,%20first-served%22%20business&f=false", "https://www.youtube.com/watch?v=st8HRgHOErw", "https://catalogue.bnf.fr/ark:/12148/cb12647707b", "https://id.loc.gov/authorities/subjects/sh85109832", "https://d-nb.info/gnd/4255044-0", "https://id.ndl.go.jp/auth/ndlna/00567524", "https://web.archive.org/web/20111001212934/http://oldwww.com.dtu.dk/teletraffic/erlangbook/pps131-137.pdf", "https://www.wikidata.org/wiki/Q847526"]}, "Doob's martingale inequality": {"categories": ["Martingale theory", "Probabilistic inequalities", "Statistical inequalities"], "title": "Doob's martingale inequality", "method": "Doob's martingale inequality", "url": "https://en.wikipedia.org/wiki/Doob%27s_martingale_inequality", "summary": "In mathematics, Doob's martingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a stochastic process exceeds any given value over a given interval of time. As the name suggests, the result is usually given in the case that the process is a non-negative martingale, but the result is also valid for non-negative submartingales.\nThe inequality is due to the American mathematician Joseph L. Doob.\n\n", "images": [], "links": ["Abstract Wiener space", "Actuarial mathematics", "Albert Shiryaev", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Encyclopedia of Mathematics", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Expected value", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (abstract algebra)", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Independent random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jensen's inequality", "Joseph L. Doob", "Jump diffusion", "Jump process", "Kolmogorov's inequality", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Lebesgue integration", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Mathematics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Michiel Hazewinkel", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability measure", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random field", "Random graph", "Random variable", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Sigma algebra", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stochastic processes", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["https://www.encyclopediaofmath.org/index.php?title=M/m062570"]}, "Kruskal\u2013Wallis one-way analysis of variance": {"categories": ["Analysis of variance", "Nonparametric statistics", "Statistical tests"], "title": "Kruskal\u2013Wallis one-way analysis of variance", "method": "Kruskal\u2013Wallis one-way analysis of variance", "url": "https://en.wikipedia.org/wiki/Kruskal%E2%80%93Wallis_one-way_analysis_of_variance", "summary": "The Kruskal\u2013Wallis test by ranks, Kruskal\u2013Wallis H test (named after William Kruskal and W. Allen Wallis), or one-way ANOVA on ranks is a non-parametric method for testing whether samples originate from the same distribution. It is used for comparing two or more independent samples of equal or different sample sizes. It extends the Mann\u2013Whitney U test, which is used for comparing only two groups. The parametric equivalent of the Kruskal\u2013Wallis test is the one-way analysis of variance (ANOVA). \nA significant Kruskal\u2013Wallis test indicates that at least one sample stochastically dominates one other sample. The test does not identify where this stochastic dominance occurs or for how many pairs of groups stochastic dominance obtains. For analyzing the specific sample pairs for stochastic dominance, Dunn's test, pairwise Mann-Whitney tests without Bonferroni correction, or the more powerful but less well known Conover\u2013Iman test are sometimes used.\nSince it is a non-parametric method, the Kruskal\u2013Wallis test does not assume a normal distribution of the residuals, unlike the analogous one-way analysis of variance. If the researcher can make the assumptions of an identically shaped and scaled distribution for all groups, except for any difference in medians, then the null hypothesis is that the medians of all groups are equal, and the alternative hypothesis is that at least one population median of one group is different from the population median of at least one other group.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bonferroni correction", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann-Whitney", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multiple comparisons problem", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "One way anova", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stochastic dominance", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "W. Allen Wallis", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Kruskal", "Z-test"], "references": ["http://faculty.vassar.edu/lowry/kw3.html", "http://faculty.virginia.edu/kruskal-wallis/", "http://library.lanl.gov/cgi-bin/getfile?00209046.pdf", "http://doi.org/10.1080%2F01621459.1952.10483441", "http://doi.org/10.1080%2F10485250310001634719", "http://doi.org/10.2307%2F1266041", "https://books.google.com/books?id=0hPvAAAAMAAJ&pg=PA226", "https://statistics.laerd.com/spss-tutorials/kruskal-wallis-h-test-using-spss-statistics.php"]}, "Partial correlation": {"categories": ["Autocorrelation", "Covariance and correlation", "Pages with citations having bare URLs", "Pages with citations lacking titles"], "title": "Partial correlation", "method": "Partial correlation", "url": "https://en.wikipedia.org/wiki/Partial_correlation", "summary": "In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random variables removed. If we are interested in finding whether or to what extent there is a numerical relationship between two variables of interest, using their correlation coefficient will give misleading results if there is another, confounding, variable that is numerically related to both variables of interest. This misleading information can be avoided by controlling for the confounding variable, which is done by computing the partial correlation coefficient. This is precisely the motivation for including other right-side variables in a multiple regression; but while multiple regression gives unbiased results for the effect size, it does not give a numerical value of a measure of the strength of the relationship between the two variables of interest.\nFor example, if we have economic data on the consumption, income, and wealth of various individuals and we wish to see if there is a relationship between consumption and income, failing to control for wealth when computing a correlation coefficient between consumption and income would give a misleading result, since income might be numerically related to wealth which in turn might be numerically related to consumption; a measured correlation between consumption and income might actually be contaminated by these other correlations. The use of a partial correlation avoids this problem.\nLike the correlation coefficient, the partial correlation coefficient takes on a value in the range from \u20131 to 1. The value \u20131 conveys a perfect negative correlation controlling for some variables (that is, an exact linear relationship in which higher values of one variable are associated with lower values of the other); the value 1 conveys a perfect positive linear relationship, and the value 0 conveys that there is no linear relationship.\nThe partial correlation coincides with the conditional correlation if the random variables are jointly distributed as the multivariate normal, other elliptical, multivariate hypergeometric, multivariate negative hypergeometric, multinomial or Dirichlet distribution, but not in general otherwise.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/PartialCorrelationGeometrically.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Association (statistics)", "Asymptotic theory (statistics)", "Australian and New Zealand Journal of Statistics", "Autocorrelation", "Autoregression", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias (statistics)", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of alienation", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational complexity theory", "Conditional correlation", "Conditional independence", "Confidence interval", "Confounding", "Confounding variable", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation", "Correlation and dependence", "Correlation coefficient", "Correlation matrix", "Correlogram", "Cosine", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cumulative distribution function", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dirichlet distribution", "Divergence (statistics)", "Dot product", "Durbin\u2013Watson statistic", "Dynamic programming", "Econometrics", "Economics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Encyclopedia of Mathematics", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher transformation", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian distribution", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hyperplane", "I.i.d.", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Invertible matrix", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Joint distribution", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McGraw-Hill", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Metron (journal)", "Michiel Hazewinkel", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multinomial distribution", "Multiple comparisons", "Multiple correlation", "Multiple regression", "Multivariate Gaussian", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate hypergeometric distribution", "Multivariate normal", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Negative hypergeometric distribution", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Overlapping subproblems", "Parametric statistics", "Partial autocorrelation function", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Perpendicular", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Positive-definite matrix", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability theory", "Projection (linear algebra)", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R. A. Fisher", "Radar chart", "Random assignment", "Random variables", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recursive algorithm", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spurious correlation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-test", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://digital.library.adelaide.edu.au/dspace/handle/2440/15182", "http://www.psychwiki.com/wiki/What_is_a_partial_correlation%3F", "http://www.roguewave.com/Portals/0/products/imsl-numerical-libraries/fortran-library/docs/7.0/stat/stat.htm", "http://www.statsoft.com/textbook/statistics-glossary/s/?button=0", "http://www.hawaii.edu/powerkills/UC.HTM", "http://luna.cas.usf.edu/~mbrannic/files/regression/Partial.html", "http://faculty.vassar.edu/lowry/ch3a.html", "http://doi.org/10.1111%2Fj.1467-842X.2004.00360.x", "https://web.archive.org/web/20140206182503/http://luna.cas.usf.edu/~mbrannic/files/regression/Partial.html", "https://www.encyclopediaofmath.org/index.php?title=Partial_correlation_coefficient&oldid=14288"]}, "Intervening variable": {"categories": ["Articles with imported dually licensed text", "Independence (probability theory)", "Psychometrics", "Statistical models"], "title": "Mediation (statistics)", "method": "Intervening variable", "url": "https://en.wikipedia.org/wiki/Mediation_(statistics)", "summary": "In statistics, a mediation model is one that seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator variable (also a mediating variable, intermediary variable, or intervening variable). Rather than a direct causal relationship between the independent variable and the dependent variable, a mediation model proposes that the independent variable influences the (non-observable) mediator variable, which in turn influences the dependent variable. Thus, the mediator variable serves to clarify the nature of the relationship between the independent and dependent variables.Mediation analyses are employed to understand a known relationship by exploring the underlying mechanism or process by which one variable influences another variable through a mediator variable. Mediation analysis facilitates a better understanding of the relationship between the independent and dependent variables when the variables appear to not have a definite connection. They are studied by means of operational definitions and have no existence apart.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4d/Mediation.jpg", "https://upload.wikimedia.org/wikipedia/en/d/db/Mediated_moderation_model_1.png", "https://upload.wikimedia.org/wikipedia/en/9/9a/Mediated_moderation_model_2.png", "https://upload.wikimedia.org/wikipedia/en/0/0c/Mediated_moderation_model_3.png", "https://upload.wikimedia.org/wikipedia/en/6/63/Mediated_moderation_model_4.png", "https://upload.wikimedia.org/wikipedia/en/3/37/Mediated_moderation_model_5.png"], "links": ["ArXiv", "Bayesian Networks", "Bibcode", "Bootstrapping (statistics)", "Dependent variable", "Digital object identifier", "Independent variable", "Interaction effect", "JSTOR", "James Robins", "Journal of Personality and Social Psychology", "Judea Pearl", "Moderated mediation", "Moderation (statistics)", "Morgan Kaufmann", "Non-parametric statistics", "Normal distribution", "Operational definition", "Paul E. Meehl", "Prisoner's dilemma", "PubMed Central", "PubMed Identifier", "SPSS", "Sander Greenland", "Sobel test", "Social value orientations", "Statistics", "University of Indiana"], "references": ["http:ftp://ftp.cs.ucla.edu/pub/stat_ser/r389-imai-etal-commentary-r421-reprint.pdf", "http://www2.psych.ubc.ca/~schaller/528Readings/BullockGreenHa2010.pdf", "http://www2.psych.ubc.ca/~schaller/528Readings/SpencerZannaFong2005.pdf", "http://psychclassics.yorku.ca/MacMeehl/hypcon-intvar.htm", "http://www.afhayes.com/", "http://www.afhayes.com/introduction-to-mediation-moderation-and-conditional-process-analysis.html", "http://www.afhayes.com/spss-sas-and-mplus-macros-and-code.html", "http://www.informaworld.com/smpp/ftinterface~db=all~content=a917285720~fulltext=713240930", "http://www.psychwiki.com/wiki/Mediation", "http://adsabs.harvard.edu/abs/2013arXiv1302.4929B", "http://adsabs.harvard.edu/abs/2013arXiv1302.6835P", "http://www.indiana.edu/~educy520/sec5982/week_2/variable_types.pdf", "http://www.comm.ohio-state.edu/ahayes/SPSS%20programs/indirect.htm", "http://www.comm.ohio-state.edu/ahayes/sobel.htm", "http://methodology.psu.edu/ra/causal/example", "http://ftp.cs.ucla.edu/pub/stat_ser/R273-U.pdf", "http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf", "http://www.mii.ucla.edu/causality/?p=713", "http://wexler.free.fr/library/files/tolman%20(1938)%20the%20determiners%20of%20behavior%20at%20a%20choice-point.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2819363", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2843515", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3773310", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC526390", "http://www.ncbi.nlm.nih.gov/pubmed/11928892", "http://www.ncbi.nlm.nih.gov/pubmed/12757142", "http://www.ncbi.nlm.nih.gov/pubmed/12940467", "http://www.ncbi.nlm.nih.gov/pubmed/15507130", "http://www.ncbi.nlm.nih.gov/pubmed/1576220", "http://www.ncbi.nlm.nih.gov/pubmed/16393019", "http://www.ncbi.nlm.nih.gov/pubmed/16393020", "http://www.ncbi.nlm.nih.gov/pubmed/18697684", "http://www.ncbi.nlm.nih.gov/pubmed/19234398", "http://www.ncbi.nlm.nih.gov/pubmed/20307128", "http://www.ncbi.nlm.nih.gov/pubmed/20822249", "http://www.ncbi.nlm.nih.gov/pubmed/21500915", "http://www.ncbi.nlm.nih.gov/pubmed/24885338", "http://davidakenny.net/cm/mediate.htm", "http://arxiv.org/abs/1011.1079", "http://arxiv.org/abs/1302.4929", "http://arxiv.org/abs/1302.6835", "http://doi.org/10.1023%2FA:1024649822872", "http://doi.org/10.1037%2F0022-3514.84.5.972", "http://doi.org/10.1037%2F0022-3514.89.6.845", "http://doi.org/10.1037%2F0022-3514.89.6.852", "http://doi.org/10.1037%2F1082-989x.7.1.83", "http://doi.org/10.1037%2F1082-989x.7.4.422", "http://doi.org/10.1037%2Fa0018933", "http://doi.org/10.1037%2Fa0020141", "http://doi.org/10.1037%2Fa0022658", "http://doi.org/10.1037%2Fa0036434", "http://doi.org/10.1037%2Fh0037350", "http://doi.org/10.1037%2Fh0062733", "http://doi.org/10.1080%2F03637750903310360", "http://doi.org/10.1097%2F00001648-199203000-00013", "http://doi.org/10.1097%2Fede.0b013e31818f69ce", "http://doi.org/10.1097%2Fede.0b013e31826c2bb9", "http://doi.org/10.1186%2F1742-5573-1-4", "http://doi.org/10.1214%2F09-ss057", "http://doi.org/10.1214%2F10-sts321", "http://doi.org/10.1515%2F2161-962X.1014", "http://doi.org/10.2307%2F270723", "http://doi.org/10.3758%2FBF03206553", "http://doi.org/10.3758%2FBRM.40.3.879", "http://www.jstor.org/stable/270723"]}, "Assumed mean": {"categories": ["Means"], "title": "Assumed mean", "method": "Assumed mean", "url": "https://en.wikipedia.org/wiki/Assumed_mean", "summary": "In statistics the assumed mean is a method for calculating the arithmetic mean and standard deviation of a data set. It simplifies calculating accurate values by hand. Its interest today is chiefly historical but it can be used to quickly estimate these statistics. There are other rapid calculation methods which are more suited for computers which also ensure more accurate results than the obvious methods.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407084002%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407083328%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20130407082944%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20110430032449%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20090922000234%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041048%21Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/4/40/20080713041018%21Fisher_iris_versicolor_sepalwidth.svg"], "links": ["Arithmetic mean", "Bessel's correction", "International Standard Book Number", "Standard deviation", "Statistics"], "references": []}, "Least-squares spectral analysis": {"categories": ["All articles with dead external links", "Articles with dead external links from December 2017", "Articles with permanently dead external links", "Digital signal processing", "Frequency-domain analysis"], "title": "Least-squares spectral analysis", "method": "Least-squares spectral analysis", "url": "https://en.wikipedia.org/wiki/Least-squares_spectral_analysis", "summary": "Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in long gapped records; LSSA mitigates such problems.LSSA is also known as the Van\u00ed\u010dek method after Petr Van\u00ed\u010dek, and as the Lomb method (or the Lomb periodogram) and the Lomb\u2013Scargle method (or Lomb\u2013Scargle periodogram), based on the contributions of Nicholas R. Lomb and, independently, Jeffrey D. Scargle. Closely related methods have been developed by Michael Korenberg and by Scott Chen and David Donoho.", "images": [], "links": ["Amplitude", "ArXiv", "Backslash", "Basis pursuit", "Beta distribution", "Bibcode", "Centrum Wiskunde & Informatica", "Cholesky decomposition", "Coordinate vector", "Cosine", "Data manipulation", "David Donoho", "Decibel", "Digital object identifier", "Discrete Fourier transform", "Dot product", "Fast Fourier transform", "Fourier analysis", "Fourier transform", "Frequency spectrum", "Geodesy", "Identity matrix", "International Standard Book Number", "Inverse transformation", "Kingston, Ontario", "L1 norm", "Least-squares", "Least-squares analysis", "Least squares", "Linear programming", "Linear regression", "MATLAB", "Magnitude (mathematics)", "Matching pursuit", "NASA Ames Research Center", "Natural Resources Canada", "Orthogonal functions", "Periodogram", "Petr Van\u00ed\u010dek", "PubMed Identifier", "Queen's University", "Significance level", "Sine", "Sine wave", "Sinusoidal model", "Sparse matrix", "Spectral density", "Spectral density estimation", "Time series", "Unevenly spaced time series", "University of New Brunswick", "University of Sydney", "Variance"], "references": ["http:ftp://ftp.geod.nrcan.gc.ca/pub/GSD/craymer/pubs/thesis1998.pdf", "http:ftp://ftp.geod.nrcan.gc.ca/pub/GSD/craymer/software/lssa/", "http://www.iro.umontreal.ca/~vincentp/Publications/kmp_mlj.pdf", "http://www2.unb.ca/gge/Pubs/TR84.pdf", "http://adsabs.harvard.edu/abs/1963BAN....17...22B", "http://adsabs.harvard.edu/abs/1969Ap&SS...4..387V", "http://adsabs.harvard.edu/abs/1971Ap&SS..12...10V", "http://adsabs.harvard.edu/abs/1972Ap&SS..17..357T", "http://adsabs.harvard.edu/abs/1976Ap&SS..39..447L", "http://adsabs.harvard.edu/abs/1982ApJ...263..835S", "http://adsabs.harvard.edu/abs/1997Ana...122..879K", "http://adsabs.harvard.edu/abs/1999ApJ...526..890C", "http://adsabs.harvard.edu/abs/2009A&A...496..577Z", "http://adsabs.harvard.edu/abs/2009ApJ...695..496P", "http://statweb.stanford.edu/~donoho/Reports/1994/asilomar.pdf", "http://public.lanl.gov/palmer/fastchi.html", "http://www.ncbi.nlm.nih.gov/pubmed/10643760", "http://www.ncbi.nlm.nih.gov/pubmed/2706281", "http://www.aanda.org/articles/aa/abs/2009/11/aa11296-08/aa11296-08.html", "http://arxiv.org/abs/0901.1913", "http://arxiv.org/abs/0901.2573", "http://arxiv.org/abs/astro-ph/9906466", "http://doi.org/10.1007%2FBF00204124", "http://doi.org/10.1007%2FBF00642907", "http://doi.org/10.1007%2FBF00648343", "http://doi.org/10.1007%2FBF00651344", "http://doi.org/10.1007%2FBF00656134", "http://doi.org/10.1023%2FA:1013955821559", "http://doi.org/10.1039%2Fa700902j", "http://doi.org/10.1051%2F0004-6361:200811296", "http://doi.org/10.1086%2F160554", "http://doi.org/10.1086%2F308020", "http://doi.org/10.1088%2F0004-637X%2F695%2F1%2F496", "http://doi.org/10.1177%2F074873099129000984", "http://iopscience.iop.org/article/10.1086/308020", "https://books.google.com/books?id=9GhDHTLzFDEC&pg=PA685&dq=%22spectral+analysis%22+%22vanicek%22+inauthor:press", "https://books.google.com/books?id=JCKAirWQdqkC&pg=PA314&dq=fourier-transform+orthogonal+least-squares", "https://books.google.com/books?id=LnqFIpFJ9cwC&pg=PA178&dq=Lomb-Scargle-method", "https://books.google.com/books?id=MXWypqcHECkC&pg=PA12&dq=matlab+least-squares+backslash", "https://books.google.com/books?id=P8ideTkMQisC&pg=PA289&dq=spectral+lomb+scargle", "https://books.google.com/books?id=QzGbOiZ3OnkC&pg=PA269&dq=vanicek+spectral+sinusoids", "https://books.google.com/books?id=cc9L8QWcZWsC&pg=RA3-PA263&dq=Lomb-Scargle-periodogram", "https://books.google.com/books?id=gYc4fp_ixmwC&pg=PA458&dq=vanicek+least-squares+spectral-analysis+lomb", "https://books.google.com/books?id=pH_OmkD4ZaQC&pg=PA227&dq=Lomb-periodogram"]}, "Binomial test": {"categories": ["All articles needing additional references", "Articles needing additional references from November 2016", "Statistical tests"], "title": "Binomial test", "method": "Binomial test", "url": "https://en.wikipedia.org/wiki/Binomial_test", "summary": "In statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Binomial distribution", "Board game", "Continuous distribution", "Dice", "Exact test", "G-test", "International Standard Book Number", "MATLAB", "Microsoft Excel", "Multinomial distribution", "Multinomial test", "Null hypothesis", "One- and two-tailed tests", "P-value", "Pearson's chi-squared test", "Python (programming language)", "R (programming language)", "SAS (software)", "SPSS", "SciPy", "Stata", "Statistical significance", "Statistics"], "references": ["http://www.graphpad.com/guides/prism/6/statistics/index.htm?stat_binomial.htm", "http://www.mathworks.com/matlabcentral/fileexchange/24813-binomial-test"]}, "Multiple of the median": {"categories": ["CS1 maint: Multiple names: authors list", "Medical statistics", "Medical terminology", "Medical tests", "Summary statistics"], "title": "Multiple of the median", "method": "Multiple of the median", "url": "https://en.wikipedia.org/wiki/Multiple_of_the_median", "summary": "A multiple of the median (MoM) is a measure of how far an individual test result deviates from the median. MoM is commonly used to report the results of medical screening tests, particularly where the results of the individual tests are highly variable.MoM was originally used as a method to normalize data from participating laboratories of Alpha-fetoprotein (AFP) so that individual test results could be compared. 35 years later, it is the established standard for reporting maternal serum screening results.An MoM for a test result for a patient can be determined by the following:\n\n \n \n \n M\n o\n M\n (\n P\n a\n t\n i\n e\n n\n t\n )\n =\n \n \n \n R\n e\n s\n u\n l\n t\n (\n P\n a\n t\n i\n e\n n\n t\n )\n \n \n M\n e\n d\n i\n a\n n\n (\n P\n a\n t\n i\n e\n n\n t\n P\n o\n p\n u\n l\n a\n t\n i\n o\n n\n )\n \n \n \n \n \n {\\displaystyle MoM(Patient)={\\frac {Result(Patient)}{Median(PatientPopulation)}}}\n As an example, Alpha-fetoprotein (AFP) testing is used to screen for a neural tube defect (NTD) during the second trimester of pregnancy. If the median AFP result at 16 weeks of gestation is 30 ng/mL and a pregnant woman's AFP result at that same gestational age is 60 ng/mL, then her MoM is equal to 60/30 = 2.0. In other words, her AFP result is 2 times higher than \"normal.\"\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220802%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20180605220226%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164826%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20161001164401%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160929103309%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712192103%21Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/6/65/20160712173552%21Lock-green.svg"], "links": ["Alpha-fetoprotein", "Deviation (statistics)", "Digital object identifier", "International Standard Book Number", "Median", "Neural tube defect", "PubMed Central", "PubMed Identifier", "Screening (medicine)", "Statistical dispersion"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1682205", "http://www.ncbi.nlm.nih.gov/pubmed/7679245", "http://www.pregnancylab.net/multiple-of-the-median/", "http://www.clinchem.org/cgi/content/abstract/37/5/637", "http://doi.org/10.1016%2Fs0140-6736(77)92549-1", "https://www.aphl.org/conferences/proceedings/Documents/2013/2013-Newborn-Screening-Symposium/23Berberich.pdf"]}, "Compound Poisson distribution": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from October 2010", "Compound probability distributions", "Discrete distributions", "Poisson distribution"], "title": "Compound Poisson distribution", "method": "Compound Poisson distribution", "url": "https://en.wikipedia.org/wiki/Compound_Poisson_distribution", "summary": "In probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable. In the simplest cases, the result can be either a continuous or a discrete distribution.", "images": [], "links": ["ARGUS distribution", "Actuarial science", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Bulk queue", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson process", "Continuous distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulant", "Cumulant generating function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential dispersion model", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric Poisson distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Hermite distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Independent identically-distributed random variables", "Infinite divisibility (probability)", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "Law of total cumulance", "Law of total expectation", "Law of total variance", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "Luria\u2013Delbr\u00fcck experiment", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Moment (mathematics)", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poisson process", "Poly-Weibull distribution", "Probability-generating function", "Probability distribution", "Probability generating function", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Stable distribution", "Stochastic process", "Student's t-distribution", "Survival analysis", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zero-inflated model", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://www.sciencedirect.com/science/article/pii/S0167668714001279", "http://www.tandfonline.com/doi/full/10.1080/03610926.2014.901375", "http://hdl.handle.net/2262/6987", "http://doi.org/10.1016%2Fj.insmatheco.2014.09.012", "http://doi.org/10.1080%2F03610926.2014.901375"]}, "Centerpoint (geometry)": {"categories": ["Euclidean geometry", "Means", "Multi-dimensional geometry"], "title": "Centerpoint (geometry)", "method": "Centerpoint (geometry)", "url": "https://en.wikipedia.org/wiki/Centerpoint_(geometry)", "summary": "In statistics and computational geometry, the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space. Given a set of points in d-dimensional space, a centerpoint of the set is a point such that any hyperplane that goes through that point divides the set of points in two roughly equal subsets: the smaller part should have at least a 1/(d + 1) fraction of the points. Like the median, a centerpoint need not be one of the data points. Every non-empty set of points (with no duplicates) has at least one centerpoint.", "images": [], "links": ["Approximation algorithm", "Computational geometry", "David Eppstein", "Digital object identifier", "Discrete and Computational Geometry", "Euclidean plane", "Euclidean space", "Gary Miller (professor)", "Geometric median", "Half-space (geometry)", "Helly's theorem", "Herbert Edelsbrunner", "International Standard Book Number", "John Tukey", "Kenneth L. Clarkson", "Linear time", "Mathematical Reviews", "Median", "Randomized algorithm", "Shang-Hua Teng", "Statistics", "Timothy M. Chan"], "references": ["http://www.almaden.ibm.com/u/kclarkson/center/p.pdf", "http://portal.acm.org/citation.cfm?id=982792.982853", "http://www.ams.org/mathscinet-getitem?mr=1409651", "http://doi.org/10.1007/BF02574382"]}, "Multiclass LDA": {"categories": ["All articles with dead external links", "Articles with dead external links from December 2017", "Articles with permanently dead external links", "CS1 maint: Archived copy as title", "Classification algorithms", "Market research", "Market segmentation", "Statistical classification", "Wikipedia articles needing clarification from April 2012", "Wikipedia articles needing page number citations from April 2012"], "title": "Linear discriminant analysis", "method": "Multiclass LDA", "url": "https://en.wikipedia.org/wiki/Linear_discriminant_analysis", "summary": "Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.\nLDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (i.e. the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain a categorical variable by the values of continuous independent variables. These other methods are preferable in applications where it is not reasonable to assume that the independent variables are normally distributed, which is a fundamental assumption of the LDA method.\nLDA is also closely related to principal component analysis (PCA) and factor analysis in that they both look for linear combinations of variables which best explain the data. LDA explicitly attempts to model the difference between the classes of data. PCA on the other hand does not take into account any difference in class, and factor analysis builds the feature combinations based on differences rather than similarities. Discriminant analysis is also different from factor analysis in that it is not an interdependence technique: a distinction between independent variables and dependent variables (also called criterion variables) must be made.\nLDA works when the measurements made on independent variables for each observation are continuous quantities. When dealing with categorical independent variables, the equivalent technique is discriminant correspondence analysis.Discriminant analysis is used when groups are known a priori (unlike in cluster analysis). Each case must have a score on one or more quantitative predictor measures, and a score on a group measure. In simple terms, discriminant function analysis is classification - the act of distributing things into groups, classes or categories of the same type.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/46/R._A._Fischer.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA", "Accelerated failure time model", "Actuarial science", "Affine transformation", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Eugenics", "Anomaly detection", "ArXiv", "Arithmetic mean", "Artificial intelligence", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Asymptotic theory (statistics)", "Autocorrelation", "Autoencoder", "Automated machine learning", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "BIRCH", "Bankruptcy prediction", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bias-variance dilemma", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Boosting (machine learning)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box's M test", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brian Ripley", "C. R. Rao", "CURE data clustering algorithm", "Calyampudi Radhakrishna Rao", "Canonical coordinates", "Canonical correlation", "Canonical correlation analysis", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational learning theory", "Concentration of measure", "Conditional random field", "Conference on Neural Information Processing Systems", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous variable", "Control chart", "Convolutional neural network", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curse of dimensionality", "DBSCAN", "Data collection", "Data mining", "Decision tree learning", "Decomposition of time series", "DeepDream", "Deep learning", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension reduction", "Dimensionality reduction", "Divergence (statistics)", "Dot product", "Durbin\u2013Watson statistic", "Econometrics", "Edward Altman", "Effect size", "Efficiency (statistics)", "Eigenfaces", "Eigenvalue", "Eigenvalue, eigenvector and eigenspace", "Eigenvalues and eigenvectors", "Eigenvector", "Elliptical distribution", "Empirical distribution function", "Empirical risk minimization", "Engineering statistics", "Ensemble learning", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expectation\u2013maximization algorithm", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Facial recognition system", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feature engineering", "Feature learning", "Features (pattern recognition)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gated recurrent unit", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of artificial intelligence", "Goodness of fit", "Grammar induction", "Granger causality", "Graphical model", "Grouped data", "Handle System", "Harmonic mean", "Hermitian matrix", "Heteroscedasticity", "Hidden Markov model", "Hierarchical clustering", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedastic", "Homoscedasticity", "Hyperplane", "IEEE Transactions on Pattern Analysis and Machine Intelligence", "Independent component analysis", "Independent variables", "Index of dispersion", "Instrumental variable", "Interaction (statistics)", "International Conference on Machine Learning", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Machine Learning Research", "Journal of the American Statistical Association", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kernel Fisher discriminant analysis", "Kernel trick", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latent Dirichlet allocation", "Latent variable", "Learning to rank", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear Discriminant Analysis", "Linear classifier", "Linear combination", "Linear regression", "Linear subspace", "List of datasets for machine-learning research", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local outlier factor", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logarithmically concave measure", "Logistic regression", "Logit", "Long short-term memory", "Loss function", "Lp space", "M-estimator", "MANOVA", "Machine Learning (journal)", "Machine learning", "Mann\u2013Whitney U test", "Marketing", "Mathematical Reviews", "Maximum a posteriori", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McNemar's test", "Mean", "Mean-shift", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multicollinearity", "Multidimensional scaling", "Multilayer perceptron", "Multiple comparisons", "Multiple discriminant analysis", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Naive Bayes classifier", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-negative matrix factorization", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "OPTICS algorithm", "Observational study", "Occam learning", "Official statistics", "One- and two-tailed tests", "Online machine learning", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Otsu's method", "Outline of machine learning", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pattern recognition", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perceptron", "Perceptual mapping", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Positioning (marketing)", "Posterior probability", "Power (statistics)", "Prediction interval", "Preference regression", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probably approximately correct learning", "Probit regression", "Product management", "Proportional hazards model", "Pseudo inverse", "Psychometrics", "PubMed Central", "Q-learning", "Quadratic classifier", "Quality control", "Quantitative marketing research", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R language", "Radar chart", "Random assignment", "Random forest", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recurrent neural network", "Regression analysis", "Regression model validation", "Reinforcement learning", "Relevance vector machine", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted Boltzmann machine", "Robust regression", "Robust statistics", "Ronald A. Fisher", "Ronald Fisher", "Run chart", "SAS programming language", "SPSS", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Self-organizing map", "Semi-supervised learning", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shrinkage estimator", "Sign test", "Signal-to-noise ratio", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social salience", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "State\u2013action\u2013reward\u2013state\u2013action", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical survey", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Structured prediction", "Student's t-test", "Sufficient statistic", "Supervised learning", "Support vector machine", "Surface normal", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-distributed stochastic neighbor embedding", "Talagrand's concentration inequality", "Temporal difference learning", "Time domain", "Time series", "Tolerance interval", "Training set", "Trend estimation", "U-Net", "U-statistic", "Uniformly most powerful test", "Unsupervised learning", "V-statistic", "Vapnik\u2013Chervonenkis theory", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Wilks' lambda distribution", "YouTube", "Z-Score Financial Analysis Tool", "Z-test"], "references": ["http://ajbasweb.com/old/ajbas/2010/564-576.pdf", "http://people.revoledu.com/kardi/tutorial/LDA/", "http://people.revoledu.com/kardi/tutorial/LDA/index.html", "http://www.sciencedirect.com/science/article/pii/S0031320314005214", "http://www.sciencedirect.com/science/article/pii/S0047259X00919249", "http://www.sciencedirect.com/science/article/pii/S0047259X01920342", "http://www.psychometrica.de/lds.html", "http://www.psychstat.missouristate.edu/multibook/mlt03m.html", "http://www2.chass.ncsu.edu/garson/pa765/discrim.htm", "http://www.ece.osu.edu/~aleix/pami01.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.9904", "http://userwww.sfsu.edu/~efc/classes/biol710/discrim/discrim.pdf", "http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-4389.pdf", "http://www.utdallas.edu/~herve/Abdi-DCA2007-pretty.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2976202", "http://www.alglib.net/dataanalysis/lineardiscriminantanalysis.php", "http://hdl.handle.net/2440%2F15227", "http://www.ams.org/mathscinet-getitem?mr=0999675", "http://www.ams.org/mathscinet-getitem?mr=1190469", "http://www.ams.org/mathscinet-getitem?mr=1802993", "http://arxiv.org/abs/0903.2003", "http://doi.org/10.1006%2Fjmva.2000.1924", "http://doi.org/10.1006%2Fjmva.2001.2034", "http://doi.org/10.1016%2Fj.patcog.2014.12.012", "http://doi.org/10.1016%2Fj.patrec.2004.08.005", "http://doi.org/10.1016%2Fs0031-3203(00)00162-x", "http://doi.org/10.1016%2Fs0169-2607(02)00011-1", "http://doi.org/10.1109%2F34.908974", "http://doi.org/10.1109%2F72.572105", "http://doi.org/10.1109%2FNNSP.1999.788121", "http://doi.org/10.1109%2FTIFS.2016.2569061", "http://doi.org/10.1111%2Fj.1469-1809.1936.tb02137.x", "http://doi.org/10.1128%2Faem.00726-10", "http://doi.org/10.1128%2Faem.01589-09", "http://doi.org/10.1214%2F09-aoas277", "http://doi.org/10.2307%2F2289860", "http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=572105&url=http%253A%252F%252Fieeexplore.ieee.org%252Fiel4%252F72%252F12383%252F00572105", "http://www.jstor.org/stable/2289860", "http://www.jstor.org/stable/2983775", "http://projecteuclid.org/euclid.aoas/1273584465", "http://www.worldcat.org/issn/0167-8655", "http://www.worldcat.org/issn/1045-9227", "https://github.com/mhaghighat/dcaFuse", "https://www.youtube.com/watch?v=azXCzI57Yfc", "https://www.researchgate.net/publication/326592545_Correction_of_AI_systems_by_linear_discriminants_Probabilistic_foundations", "https://web.archive.org/web/20080312065328/http://www2.chass.ncsu.edu/garson/pA765/discrim.htm", "https://web.archive.org/web/20150405124836/http://biostat.katerynakon.in.ua/en/prognosis/discriminant-analysis.html", "https://arxiv.org/list/cs.LG/recent", "https://arxiv.org/pdf/0906.2530.pdf", "https://arxiv.org/pdf/1011.0943.pdf", "https://dx.doi.org/10.1016/j.patrec.2004.08.005"]}, "Sampling design": {"categories": ["Sampling (statistics)"], "title": "Sampling design", "method": "Sampling design", "url": "https://en.wikipedia.org/wiki/Sampling_design", "summary": "In the theory of finite population sampling, a sampling design specifies for every possible sample its probability of being drawn.\n\n", "images": [], "links": ["Bernoulli sampling", "International Standard Book Number", "Mathematics", "Population", "Probability", "Sample (statistics)", "Sampling (statistics)", "Sampling error", "Sampling probability", "Statistical sampling"], "references": []}, "Census": {"categories": ["All articles with incomplete citations", "Articles containing Spanish-language text", "Articles with incomplete citations from November 2012", "Articles with short description", "Censuses", "Commons category link is on Wikidata", "Genealogy", "Latin words and phrases", "Pages containing links to subscription-only content", "Population", "Sampling (statistics)", "Survey methodology", "Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference", "Wikipedia articles with BNF identifiers", "Wikipedia articles with GND identifiers", "Wikipedia articles with NARA identifiers", "Wikipedia articles with NDL identifiers"], "title": "Census", "method": "Census", "url": "https://en.wikipedia.org/wiki/Census", "summary": "A census is the procedure of systematically acquiring and recording information about the members of a given population. The term is used mostly in connection with national population and housing censuses; other common censuses include agriculture, business, and traffic censuses. The United Nations defines the essential features of population and housing censuses as \"individual enumeration, universality within a defined territory, simultaneity and defined periodicity\", and recommends that population censuses be taken at least every 10 years. United Nations recommendations also cover census topics to be collected, official definitions, classifications and other useful information to co-ordinate international practice.The word is of Latin origin: during the Roman Republic, the census was a list that kept track of all adult males fit for military service. The modern census is essential to international comparisons of any kind of statistics, and censuses collect data on many attributes of a population, not just how many people there are. Censuses typically began as the only method of collecting national demographic data, and are now part of a larger system of different surveys. Although population estimates remain an important function of a census, including exactly the geographic distribution of the population, statistics can be produced about combinations of attributes e.g. education by age and sex in different regions. Current administrative data systems allow for other approaches to enumeration with the same level of detail but raise concerns about privacy and the possibility of biasing estimates.A census can be contrasted with sampling in which information is obtained only from a subset of a population; typically main population estimates are updated by such intercensal estimates. Modern census data are commonly used for research, business marketing, and planning, and as a baseline for designing sample surveys by providing a sampling frame such as an address register. Census counts are necessary to adjust samples to be representative of a population by weighting them as is common in opinion polling. Similarly, stratification requires knowledge of the relative sizes of different population strata which can be derived from census enumerations. In some countries, the census provides the official counts used to apportion the number of elected representatives to regions (sometimes controversially \u2013 e.g., Utah v. Evans). In many cases, a carefully chosen random sample can provide more accurate information than attempts to get a population census.", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/c1/1929_world_population_estimate.png", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/a/ae/Enumerator.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/6/6f/Volkstelling_1925_Census.jpg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Ab urbe condita (book)", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alpaca", "Amasis I", "Analysis of covariance", "Analysis of 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The word first appeared in English to describe a mathematical object called a stochastic process, but now in mathematics the terms stochastic process and random process are considered interchangeable. The word, with its current definition meaning random, came from German, but it originally came from Greek \u03c3\u03c4\u03cc\u03c7\u03bf\u03c2 (stokhos), meaning 'aim, guess'.The term stochastic is used in many different fields, particularly where stochastic or random processes are used to represent systems or phenomena that seem to change in a random way. Examples of such fields include the physical sciences such as biology, chemistry, ecology, neuroscience, and physics as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography and telecommunications. It is also used in finance, due to seemingly random changes in financial markets.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg"], "links": ["3D computer graphics", "Aleatoric music", "Aleksandr Khinchin", "Amplitude modulation", "Andrey Kolmogorov", "Artificial intelligence", "Biology", "Brownian motion", "CEMAMu", "Chemistry", "Color printing", "Commodities", "Computer graphics", "Computer music", "Computer science", "Constraint (mathematics)", "Cryptography", "Currency", "Diamorphoses", "Differential equation", "Digital object identifier", "Distributed ray tracing", "Ecology", "Engineering", "Enrico Fermi", "Ferdinand de Saussure", "Financial markets", "Frequency modulation", "Functional theories of grammar", "Game theory", "Gene expression", "Generative grammar", "Generative music", "Genetic algorithms", "Genetic programming", "Greek language", "Group theory", "Harald Cram\u00e9r", "Hydrogen bomb", "I-Ching", "Iannis Xenakis", "Illiac Suite", "Image processing", "Indeterminate music", "Information theory", "Insurance", "Integral", "Integrand", "Integrated Authority File", "Interest rates", "International Standard Book Number", "International Standard Serial Number", "Jakob Bernoulli", "Joan Bybee", "John Cage", "John Haiman", "John von Neumann", "Joseph Doob", "Julia Kristeva", "Jump process", "Ladislaus Bortkiewicz", "Langue and parole", "Lejaren Hiller", "Leonard Issacson", "Line screen", "Linguistic competence", "Linguistic performance", "Los Alamos National Laboratory", "Luce Irigaray", "Makis Solomos", "Manhattan Project", "Marianne Mithun", "Markov chain", "Markov process", "Mathematics", "Maurice Fr\u00e9chet", "Meander", "Moir\u00e9", "Monaco", "Monte Carlo Casino", "Monte Carlo method", "Music", "Music of Changes", "Neuroscience", "Neutron", "Nicholas Metropolis", "Nielsen ratings", "Nomos Alpha", "Normal distribution", "Operations research", "Oxford Dictionaries", "Oxford University Press", "Paul Hopper", "Paul L\u00e9vy (mathematician)", "Physical chemistry", "Physics", "Pierre Bourdieu", "Pithoprakta", "Probability theory", "Process control", "Promoter (biology)", "Pseudorandom number generator", "PubMed Central", "PubMed Identifier", "Quantitative analyst", "RAND Corporation", "RNA polymerase", "Randomness", "Ray tracing (graphics)", "Sandra Thompson (linguist)", "Set theory", "Siegfried Palm", "Signal processing", "Simulated annealing", "Simulation", "Sortition", "Stanis\u0142aw Ulam", "Statistical distribution", "Statistical mechanics", "Stochastic Empirical Loading and Dilution Model", "Stochastic forensics", "Stochastic matrix", "Stochastic neural network", "Stochastic optimization", "Stochastic oscillator", "Stochastic process", "Stochastic processes", "Stochastic resonance", "Stochastic screening", "Stochastic theory of hematopoiesis", "Stocks", "Systems theory", "Talmy Givon", "Technical analysis", "Technology", "Telecommunications", "U.S. Air Force", "Vestibular system", "Visual Basic for Applications", "Wiener process", "William Croft (linguist)", "William Feller", "Wolfgang Doeblin", "YouTube"], "references": ["http://www.ifa.com", "http://www.bu.edu/abl/files/fulltext.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076423", "http://www.ncbi.nlm.nih.gov/pubmed/12503175", "http://www.ncbi.nlm.nih.gov/pubmed/16287079", "http://doi.org/10.1002%2F0471667196.ess6027.pub2", "http://doi.org/10.1002%2F1439-7641(20020315)3:3%3C285::AID-CPHC285%3E3.0.CO;2-A", "http://doi.org/10.1002%2Fana.20670", "http://doi.org/10.1007%2FBF01449156", "http://doi.org/10.1007%2FBF01457949", "http://doi.org/10.1073%2Fpnas.20.6.376", "http://doi.org/10.1093%2Fbiomet%2F87.1.145", "http://doi.org/10.1214%2Faop%2F1176996025", "http://doi.org/10.1239%2Fjap%2F1110381384", "http://www.worldcat.org/issn/0006-3444", "http://www.worldcat.org/issn/0021-9002", "http://www.worldcat.org/issn/0025-5831", "http://www.worldcat.org/issn/0091-1798", "https://books.google.com/books?id=0avUelS7e7cC", "https://books.google.com/books?id=1EJZqFIGxBIC&pg=PA9", "https://books.google.com/books?id=1dcqV9mtQloC&pg=PR4", "https://books.google.com/books?id=5-lQAAAAMAAJ", "https://books.google.com/books?id=6KClauq8OekC", "https://books.google.com/books?id=CwQZCwAAQBAJ", "https://books.google.com/books?id=CyK6KAjwdYkC&pg=PR5", "https://books.google.com/books?id=H06xzeRQgV4C", "https://books.google.com/books?id=H3ZkTN2pYS4C&pg=PA1", "https://books.google.com/books?id=L6fhXh13OyMC", "https://books.google.com/books?id=N6II-6HlPxEC", "https://books.google.com/books?id=O8kD1NwQBsQC", "https://books.google.com/books?id=OWANAAAAQBAJ", "https://books.google.com/books?id=R5BGvQ3ejloC", "https://books.google.com/books?id=RaYSDAAAQBAJ", "https://books.google.com/books?id=SwZYBAAAQBAJ", "https://books.google.com/books?id=SwZYBAAAQBAJ&pg=PA1", "https://books.google.com/books?id=VWq5GG6ycxMC&pg=PT16", "https://books.google.com/books?id=XqMZAQAAIAAJ", "https://books.google.com/books?id=ddsrGdsgN9sC&pg=PA269", "https://books.google.com/books?id=ePxDAQAAIAAJ", "https://books.google.com/books?id=iojEts9YAxIC", "https://books.google.com/books?id=tfa5BAAAQBAJ&pg=PR4", "https://en.oxforddictionaries.com/definition/Stochastic", "https://www.youtube.com/watch?v=AUSKTk9ENzg", "https://www.academia.edu/249265/Set_theory_in_Xenakis_EONTA", "https://d-nb.info/gnd/4121729-9", "https://www.wikidata.org/wiki/Q1071239"]}, "Delphi method": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from July 2010", "CS1 Italian-language sources (it)", "CS1 maint: Extra text: authors list", "Estimation methods", "Forecasting", "Prediction", "Systems thinking", "Technology forecasting"], "title": "Delphi method", "method": "Delphi method", "url": "https://en.wikipedia.org/wiki/Delphi_method", "summary": "The Delphi method ( DEL-fy) is a structured communication technique or method, originally developed as a systematic, interactive forecasting method which relies on a panel of experts. The experts answer questionnaires in two or more rounds. After each round, a facilitator or change agent provides an anonymised summary of the experts' forecasts from the previous round as well as the reasons they provided for their judgments. Thus, experts are encouraged to revise their earlier answers in light of the replies of other members of their panel. It is believed that during this process the range of the answers will decrease and the group will converge towards the \"correct\" answer. Finally, the process is stopped after a predefined stop criterion (e.g., number of rounds, achievement of consensus, stability of results), and the mean or median scores of the final rounds determine the results.Delphi is based on the principle that forecasts (or decisions) from a structured group of individuals are more accurate than those from unstructured groups. The technique can also be adapted for use in face-to-face meetings, and is then called mini-Delphi or Estimate-Talk-Estimate (ETE). Delphi has been widely used for business forecasting and has certain advantages over another structured forecasting approach, prediction markets.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/35/DELPHIST.png", "https://upload.wikimedia.org/wikipedia/commons/7/7c/HYPERD.GIF"], "links": ["Automation", "Bandwagon effect", "Cold War", "Cross impact analysis", "DARPA", "David Cook", "David Passig", "Decision-making", "Digital object identifier", "Drug abuse", "E-democracy", "ELAC Action Plans", "Facilitator", "Forecasting", "Foresight: The International Journal of Applied Forecasting", "Group dynamics", "Halo effect", "Harold A. Linstone", "Henry H. Arnold", "Horizon Project", "ICT-for-development", "International Standard Book Number", "Mean", "Median", "Nicholas Rescher", "Nominal group technique", "Olaf Helmer", "Planning poker", "Policy Analysis Market", "Population control", "Prediction markets", "Project RAND", "Quantitative model", "Real-time Delphi", "Reference class forecasting", "Sales", "Senior management", "Survey methodology", "TechCast Project", "Technological Forecasting and Social Change", "Technology forecasting", "The Wisdom of Crowds", "Theoretical approach", "U.S. Army Air Corps", "War", "Wideband delphi"], "references": ["http://ejournals.library.ualberta.ca/index.php/IJQM/article/view/19025", "http://mpra.ub.uni-muenchen.de/4663/01/MPRA_paper_4663.pdf", "http://www.ebs.edu/ifk", "http://is.njit.edu/pubs/delphibook/", "http://is.njit.edu/pubs/delphibook/ch3b1.pdf", "http://is.njit.edu/pubs/delphibook/ch3b3.html", "http://www.is.njit.edu/pubs/delphibook/", "http://web.stanford.edu/group/suse-crc/cgi-bin/drupal/sites/default/files/rand-change.pdf", "http://armstrong.wharton.upenn.edu/delphi2/", "http://qbox.wharton.upenn.edu/documents/mktg/research/Delphi-WPv33.pdf", "http://scholar.lib.vt.edu/ejournals/JVTE/v15n2/custer.html", "http://martinhilbert.net/Hilbert_etal.eLACdelphi.pdf", "http://doi.org/10.1016%2FS0040-1625(01)00177-9", "http://doi.org/10.1016%2Fj.techfore.2009.01.001", "http://doi.org/10.1109%2FACCESS.2015.2424703", "http://doi.org/10.1287%2Finte.7.3.18", "http://doi.org/10.1287%2Fmnsc.9.3.458", "http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=7089162", "http://interfaces.journal.informs.org/content/7/3/18.abstract", "http://www.rand.org/international_programs/pardee/pubs/futures_method/delphi.html", "http://www.rand.org/pubs/papers/P1513/", "http://www.rand.org/pubs/papers/P3558/", "http://www.rand.org/pubs/research_memoranda/RM5888", "http://ideas.repec.org/a/for/ijafaa/y2007i8p17-20.html", "https://books.google.com/books?id=jo1Z1JZIrKIC&pg=PA5&lpg=PA5&dq=delphi+method+%22something+oracular,+something+smacking+a+little+of+the+occult%22+-wikipedia&source=bl&ots=CPxZEGMbdT&sig=VE3UTLHWtTD1w09yWE3bZI4oUuk&hl=en&sa=X&ved=0CCgQ6AEwAmoVChMI7bzWr9TxxgIVzJQNCh04oAA8#v=onepage&q=delphi%20method%20%22something%20oracular,%20something%20smacking%20a%20little%20of%20the%20occult%22%20-wikipedia&f=false", "https://www.tandfonline.com/doi/full/10.1080/13607863.2016.1261796/", "https://web.archive.org/web/20080520015240/http://is.njit.edu/pubs/delphibook/"]}, "Pareto chart": {"categories": ["Categorical data", "Product management", "Quality", "Quality control tools", "Statistical charts and diagrams", "Vilfredo Pareto"], "title": "Pareto chart", "method": "Pareto chart", "url": "https://en.wikipedia.org/wiki/Pareto_chart", "summary": "A Pareto chart, named after Vilfredo Pareto, is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line.\nThe left vertical axis is the frequency of occurrence, but it can alternatively represent cost or another important unit of measure. The right vertical axis is the cumulative percentage of the total number of occurrences, total cost, or total of the particular unit of measure. Because the values are in decreasing order, the cumulative function is a concave function. To take the example below, in order to lower the amount of late arrivals by 78%, it is sufficient to solve the first three issues.\nThe purpose of the Pareto chart is to highlight the most important among a (typically large) set of factors. In quality control, it often represents the most common sources of defects, the highest occurring type of defect, or the most frequent reasons for customer complaints, and so on. Wilkinson (2006) \ndevised an algorithm for producing statistically based acceptance limits (similar to confidence intervals) for each bar in the Pareto chart.\nThese charts can be generated by simple spreadsheet programs, such as Apache OpenOffice/LibreOffice Calc and Microsoft Excel, visualization tools such as ThoughtSpot or Tableau Software, specialized statistical software tools, and online quality charts generators.\nThe Pareto chart is one of the seven basic tools of quality control.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8a/Pareto.PNG", "https://upload.wikimedia.org/wikipedia/commons/9/93/Pareto_chart_of_titanium_investment_casting_defects.svg"], "links": ["5S (methodology)", "American Society for Quality", "Apache OpenOffice", "Bar chart", "Business process mapping", "Check sheet", "Concave function", "Confidence interval", "Control chart", "Control plan", "DMAIC", "Design of experiments", "Digital object identifier", "Failure mode and effects analysis", "Frequency probability", "Histogram", "Ishikawa diagram", "Joseph M. Juran", "Kaizen", "Leland Wilkinson", "LibreOffice Calc", "Line chart", "Microsoft Excel", "Milwaukee, Wisconsin", "Multi-vari chart", "Pareto analysis", "Pareto principle", "Poka-yoke", "Process capability", "Project charter", "Quality (business)", "Quality control", "Root cause analysis", "Scatter diagram", "Seven Basic Tools of Quality", "Seven basic tools of quality", "Six Sigma", "Statistical process control", "Statistical quality control", "Stratified sampling", "Tableau Software", "The American Statistician", "ThoughtSpot", "Units of measurement", "Value stream mapping", "Vilfredo Pareto", "Voice of the customer"], "references": ["http://best-excel-tutorial.com/56-charts/77-pareto-chart", "http://kb.tableau.com/articles/knowledgebase/pareto-analysis", "http://www.asq.org/learn-about-quality/seven-basic-quality-tools/overview/overview.html", "http://doi.org/10.1198%2F000313006x152243", "https://help.libreoffice.org/Chart/Chart_Type_Column_and_Line"]}, "Non-homogeneous Poisson process": {"categories": ["All articles to be merged", "Articles to be merged from August 2018", "L\u00e9vy processes", "Markov processes", "Point processes", "Poisson point processes", "Spatial processes"], "title": "Poisson point process", "method": "Non-homogeneous Poisson process", "url": "https://en.wikipedia.org/wiki/Poisson_point_process", "summary": "In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. This point process has convenient mathematical properties, which has led to it being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy, biology, ecology, geology, seismology, physics, economics, image processing, and telecommunications.The process is named after French mathematician Sim\u00e9on Denis Poisson despite Poisson never having studied the process. Its name derives from the fact that if a collection of random points in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution. The process was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and insurance mathematics.The Poisson point process is often defined on the real line, where it can be considered as a stochastic process. In this setting, it is used, for example, in queueing theory to model random events, such as the arrival of customers at a store, phone calls at an exchange or occurrence of earthquakes, distributed in time. In the plane, the point process, also known as a spatial Poisson process, can represent the locations of scattered objects such as transmitters in a wireless network, particles colliding into a detector, or trees in a forest. In this setting, the process is often used in mathematical models and in the related fields of spatial point processes, stochastic geometry, spatial statistics and continuum percolation theory. The Poisson point process can be defined on more abstract spaces. Beyond applications, the Poisson point process is an object of mathematical study in its own right. In all settings, the Poisson point process has the property that each point is stochastically independent to all the other points in the process, which is why it is sometimes called a purely or completely random process. Despite its wide use as a stochastic model of phenomena representable as points, the inherent nature of the process implies that it does not adequately describe phenomena where there is sufficiently strong interaction between the points. This has inspired the proposal of other point processes, some of which are constructed with the Poisson point process, that seek to capture such interaction.The point process depends on a single mathematical object, which, depending on the context, may be a constant, a locally integrable function or, in more general settings, a Radon measure. In the first case, the constant, known as the rate or intensity, is the average density of the points in the Poisson process located in some region of space. The resulting point process is called a homogeneous or stationary Poisson point process. In the second case, the point process is called an inhomogeneous or nonhomogeneous Poisson point process, and the average density of points depend on the location of the underlying space of the Poisson point process.\n The word point is often omitted, but there are other Poisson processes of objects, which, instead of points, consist of more complicated mathematical objects such as lines and polygons, and such processes can be based on the Poisson point process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/87/Inhomogeneouspoissonprocess.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4a/Marked_point_process.png", "https://upload.wikimedia.org/wikipedia/commons/0/0f/Mergefrom.svg", "https://upload.wikimedia.org/wikipedia/commons/5/5c/Sydney_skyline_at_dusk_-_Dec_2008.jpg"], "links": ["19th century", "A.K. Erlang", "Abstract Wiener space", "Abstraction (mathematics)", "Actuarial mathematics", "Aleksandr Khinchin", "Alfr\u00e9d R\u00e9nyi", "Andrey Kolmogorov", "Area", "Astronomy", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Average", "Bernoulli process", "Bernoulli trials", "Bessel process", "Biased random walk on a graph", "Binomial distribution", "Biologists", "Biology", "Birth-death process", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean model (probability theory)", "Boolean network", "Borel measurable", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Campbell's theorem (probability)", "Cartesian product", "Cauchy process", "Central limit theorem", "Chemist", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Coin flipping", "Complete spatial randomness", "Compound Poisson process", "Conny Palm", "Constant (mathematics)", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Continuum percolation theory", "Convergence of random variables", "Counting number", "Counting process", "Cox point process", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "David Cox (statistician)", "Denmark", "Density", "Diffuse", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Disjoint sets", "Dissertation", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Earthquake", "Ecologists", "Ecology", "Econometrics", "Economics", "Empirical process", "Engineers", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Ernest Rutherford", "Ernst Abbe", "Euclidean space", "Event (probability theory)", "Exchangeable random variables", "Expected value", "Exponential random variable", "Extreme value theory", "Factorial", "Factorial moment measure", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filip Lundberg", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "France", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma distribution", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geology", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Hans Geiger", "Harald Cram\u00e9r", "Harry Bateman", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Image processing", "Independent and identically distributed random variables", "Independent increments", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "International Standard Serial Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "John Kingman", "John Michell", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Ladislaus Bortkiewicz", "Laplace functional", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "Lebesgue measure", "Length", "Limit (mathematics)", "Line (geometry)", "List of inequalities", "List of stochastic processes topics", "Little-o notation", "Local martingale", "Local time (mathematics)", "Locally integrable function", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Mapping theorem (point process)", "Markov additive process", "Markov arrival process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Markov renewal process", "Markovian arrival processes", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical constant", "Mathematical finance", "Mathematical model", "Mathematical object", "Mathematical space", "Mathematical statistics", "Mathematician", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Memorylessness", "Mixing (mathematics)", "Moment measure", "Monotonic function", "Moran process", "Moving-average model", "Natural logarithm", "Nobel Laureate", "Non-homogeneous Poisson process", "One-dimension", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Palm calculus", "Particles", "Percolation theory", "Philipp Ludwig von Seidel", "Physical science", "Physics", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Plane (geometry)", "Pleiades", "Point (geometry)", "Point process", "Point process notation", "Point process operation", "Poisson distribution", "Poisson point process", "Poisson process", "Polygon", "Potts model", "Predictable process", "Probability", "Probability metric", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Prussian army", "Quadratic variation", "Queueing model", "Queueing theory", "R (programming language)", "Radon measure", "Radon\u2013Nikodym theorem", "Random", "Random dynamical system", "Random field", "Random graph", "Random number generator", "Random variable", "Random walk", "Real line", "Reflection principle (Wiener process)", "Regenerative process", "Rejection sampling", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Seismology", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Simon Newcomb", "Sim\u00e9on Denis Poisson", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Spatial statistics", "Stable process", "Star", "Stationary process", "Statistics", "Stein's method", "Stigler's law", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic geometry", "Stochastic geometry models of wireless networks", "Stochastic process", "Stochastically independent", "Stockholm University", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "Sweden", "Sydney", "System on a chip", "Tanaka equation", "Telecommunications", "Telegraph process", "Teletraffic engineering", "Theodor Svedberg", "Thesis", "Time", "Time reversibility", "Time series", "Time series analysis", "Total variation", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "Volume", "Wasserstein distance", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model", "William Feller", "Wireless network"], "references": ["http://www.vosesoftware.com/ModelRiskHelp/index.htm#Probability_theory_and_statistics/Stochastic_processes/Some_Poisson_models.htm", "http://www.math.kit.edu/stoch/~last/seite/lectures_on_the_poisson_process/media/lastpenrose2017.pdf", "http://doi.org/10.1016%2FS0169-7161(01)19014-0", "http://doi.org/10.1080%2F03461238.1969.10404602", "http://doi.org/10.1111%2Fj.1751-5823.2012.00181.x", "http://doi.org/10.1162%2FNECO_a_00548", "http://doi.org/10.1214%2Fss%2F1177013690", "http://doi.org/10.2307%2F3621649", "http://www.worldcat.org/issn/0025-5572", "http://www.worldcat.org/issn/0169-7161", "http://www.worldcat.org/issn/0306-7734", "http://www.worldcat.org/issn/0346-1238", "http://www.worldcat.org/issn/0883-4237", "https://books.google.com/books?id=0mB2CQAAQBAJ", "https://books.google.com/books?id=825NfM6Nc-EC", "https://books.google.com/books?id=CLtDhblwWEgC", "https://books.google.com/books?id=CLtDhblwWEgC&pg=PA18", "https://books.google.com/books?id=Ev2iXQKItpUC", "https://books.google.com/books?id=G3ig-0M4wSIC", "https://books.google.com/books?id=H3ZkTN2pYS4C", "https://books.google.com/books?id=ImUPAQAAMAAJ", "https://books.google.com/books?id=KAWmFYUJ5zsC", "https://books.google.com/books?id=KWF2xY6s3PoC", "https://books.google.com/books?id=Pd4cvgAACAAJ", "https://books.google.com/books?id=RK9yFrNxom8C", "https://books.google.com/books?id=VEiM-OtwDHkC", "https://books.google.com/books?id=X-m5BQAAQBAJ", "https://books.google.com/books?id=bBnvAAAAMAAJ", "https://books.google.com/books?id=c_3UBwAAQBAJ", "https://books.google.com/books?id=dBNOHvElXZ4C", "https://books.google.com/books?id=eBeNngEACAAJ", "https://books.google.com/books?id=nPENXKw5kwcC", "https://books.google.com/books?id=q7eDUjdJxIkC", "https://books.google.com/books?id=rUbxAAAAMAAJ", "https://dx.doi.org/10.1162/NECO_a_00548", "https://pubs.geoscienceworld.org/ssa/bssa/article-abstract/64/5/1363/117341/is-the-sequence-of-earthquakes-in-southern", "https://cran.r-project.org/web/packages/KFAS/vignettes/KFAS.pdf"]}, "Local asymptotic normality": {"categories": ["All articles needing expert attention", "All articles that are too technical", "Articles needing expert attention from September 2010", "Asymptotic theory (statistics)", "Wikipedia articles that are too technical from September 2010"], "title": "Local asymptotic normality", "method": "Local asymptotic normality", "url": "https://en.wikipedia.org/wiki/Local_asymptotic_normality", "summary": "In statistics, local asymptotic normality is a property of a sequence of statistical models, which allows this sequence to be asymptotically approximated by a normal location model, after a rescaling of the parameter. An important example when the local asymptotic normality holds is in the case of iid sampling from a regular parametric model.\nThe notion of local asymptotic normality was introduced by Le Cam (1960).", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Asymptotic distribution", "Big O in probability notation", "Central limit theorem", "Contiguity (probability theory)", "Convergence in distribution", "Coordinate vector", "Fisher information matrix", "Iid", "International Standard Book Number", "Law of large numbers", "Likelihood function", "Matrix (mathematics)", "Normal distribution", "Parametric statistical model", "Radon\u2013Nikodym theorem", "Regular parametric model", "Statistical model", "Statistics"], "references": []}, "Calibrated probability assessment": {"categories": ["Bayesian statistics", "Probability assessment"], "title": "Calibrated probability assessment", "method": "Calibrated probability assessment", "url": "https://en.wikipedia.org/wiki/Calibrated_probability_assessment", "summary": "Calibrated probability assessments are subjective probabilities assigned by individuals who have been trained to assess probabilities in a way that historically represents their uncertainty. For example, when a person has calibrated a situation and says they are \"80% confident\" in each of 100 predictions they made, they will get about 80% of them correct. Likewise, they will be right 90% of the time they say they are 90% certain, and so on.\nCalibration training improves subjective probabilities because most people are either \"overconfident\" or \"under-confident\" (usually the former). By practicing with a series of trivia questions, it is possible for subjects to fine-tune their ability to assess probabilities. For example, a subject may be asked:\n\nTrue or False: \"A hockey puck fits in a golf hole\"\nConfidence: Choose the probability that best represents your chance of getting this question right...\n50% 60% 70% 80% 90% 100%If a person has no idea whatsoever, they will say they are only 50% confident. If they are absolutely certain they are correct, they will say 100%. But most people will answer somewhere in between. If a calibrated person is asked a large number of such questions, they will get about as many correct as they expected. An uncalibrated person who is systematically overconfident may say they are 90% confident in a large number of questions where they only get 70% of them correct. On the other hand, an uncalibrated person who is systematically underconfident may say they are 50% confident in a large number of questions where they actually get 70% of them correct.\nAlternatively, the trainee will be asked to provide a numeric range for a question like, \"In what year did Napoleon invade Russia?\", with the instruction that the provided range is to represent a 90% confidence interval. That is, the test-taker should be 90% confident that the range contains the correct answer. \nCalibration training generally involves taking a battery of such tests. Feedback is provided between tests and the subjects refine their probabilities. Calibration training may also involve learning other techniques that help to compensate for consistent over- or under-confidence. Since subjects are better at placing odds when they pretend to bet money, subjects are taught how to convert calibration questions into a type of betting game which is shown to improve their subjective probabilities. Various collaborative methods have been developed, such as prediction market, so that subjective estimates from multiple individuals can be taken into account.\nStochastic modeling methods such as the Monte Carlo method often use subjective estimates from \"subject matter experts\". However, since research shows that such experts are very likely to be statistically overconfident, the model will tend to underestimate uncertainty and risk. The Applied Information Economics method systematically uses calibration training as part of a decision modeling process.", "images": [], "links": ["Applied Information Economics", "Calibration (statistics)", "De Finetti's game", "Monte Carlo method", "Paul J. H. Schoemaker", "Prediction market", "Subjective probability"], "references": ["http://credencecalibration.com/"]}, "Log-Laplace distribution": {"categories": ["All stub articles", "Continuous distributions", "Probability distributions with non-finite variance", "Probability stubs"], "title": "Log-Laplace distribution", "method": "Log-Laplace distribution", "url": "https://en.wikipedia.org/wiki/Log-Laplace_distribution", "summary": "In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution. If X has a Laplace distribution with parameters \u03bc and b, then Y = eX has a log-Laplace distribution. The distributional properties can be derived from the Laplace distribution.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/36/Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205908%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060623205901%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504142841%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060504141723%21Two_red_dice_01.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/3/36/20060209174242%21Two_red_dice_01.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithm", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistics", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://wolfweb.unr.edu/homepage/tkozubow/0_logs.pdf"]}, "Multiclass classification": {"categories": ["Classification algorithms", "Statistical classification"], "title": "Multiclass classification", "method": "Multiclass classification", "url": "https://en.wikipedia.org/wiki/Multiclass_classification", "summary": "Not to be confused with multi-label classification.\nIn machine learning, multiclass or multinomial classification is the problem of classifying instances into one of three or more classes. (Classifying instances into one of the two classes is called binary classification.)\nWhile some classification algorithms naturally permit the use of more than two classes, others are by nature binary algorithms; these can, however, be turned into multinomial classifiers by a variety of strategies.\nMulticlass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each instance.", "images": [], "links": ["ArXiv", "Binary classification", "Decision trees", "Digital object identifier", "Extreme Learning Machines", "Heuristic", "Hierarchical classification", "K-nearest neighbors", "Machine learning", "Multi-label classification", "Multilayer perceptron", "Naive Bayes", "Neural networks", "One-class classification", "Online machine learning", "Perceptron", "Softmax function", "Statistical classification", "Support vector machines", "Tree (data structure)"], "references": ["http://rajasekarv.wixsite.com/rajasekar-venkatesan/progressive-learning-multi-class", "http://arxiv.org/abs/1609.00085", "http://doi.org/10.1016%2Fj.neucom.2016.05.006", "https://www.cs.utah.edu/~piyush/teaching/aly05multiclass.pdf"]}, "Null hypothesis": {"categories": ["Articles that may be too long from September 2014", "Articles using small message boxes", "Articles with inconsistent citation formats", "Design of experiments", "Statistical hypothesis testing"], "title": "Null hypothesis", "method": "Null hypothesis", "url": "https://en.wikipedia.org/wiki/Null_hypothesis", "summary": "In inferential statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups. Testing (accepting, approving, rejecting, or disproving) the null hypothesis\u2014and thus concluding that there are or are not grounds for believing that there is a relationship between two phenomena (e.g. that a potential treatment has a measurable effect)\u2014is a central task in the modern practice of science; the field of statistics gives precise criteria for rejecting a null hypothesis.\nThe null hypothesis is generally assumed to be true until evidence indicates otherwise. In statistics, it is often denoted H0 (read \"H-nought\", \"H-null\", \"H-oh\", or \"H-zero\").\nThe concept of a null hypothesis is used differently in two approaches to statistical inference. In the significance testing approach of Ronald Fisher, a null hypothesis is rejected if the observed data are significantly unlikely to have occurred if the null hypothesis were true. In this case the null hypothesis is rejected and an alternative hypothesis is accepted in its place. If the data are consistent with the null hypothesis, then the null hypothesis is not rejected. In neither case is the null hypothesis or its alternative proven; the null hypothesis is tested with data and a decision is made based on how likely or unlikely the data are. This is analogous to the legal principle of presumption of innocence, in which a suspect or defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically significant degree).\nIn the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis and the two hypotheses are distinguished on the basis of data, with certain error rates.\nStatistical inference can be done without a null hypothesis, by specifying a statistical model corresponding to each candidate hypothesis and using model selection techniques to choose the most appropriate model. (The most common selection techniques are based on either Akaike information criterion or Bayes factor.)", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8e/Jerzy_Neyman2.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/46/R._A._Fischer.jpg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alternative hypothesis", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blinded experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Burden of proof (philosophy)", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Controlled experiment", "Correlation and dependence", "Correlogram", "Count data", "Counternull", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "David Cox (statistician)", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Do not reject", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Estimation statistics", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Gideon J. Mellenbergh", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Herman J. Ad\u00e8r", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homogeneity (statistics)", "Homoscedasticity", "Hypothesis", "Index of dispersion", "Inferential statistics", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lady tasting tea", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Null Hypothesis: The Journal of Unlikely Science", "Observational study", "Official statistics", "One- and two-tailed tests", "One-tailed test", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Philosophical Transactions of the Royal Society A", "Pie chart", "Pivotal quantity", "Placebo-controlled study", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Presumption of innocence", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Probability distributions", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sage Publications", "Sample (statistics)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Methods for Research Workers", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical significance", "Statistical theory", "Statistically significant", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "Testing hypotheses suggested by the data", "The Design of Experiments", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Unbiased test", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Sealy Gosset", "Z-test"], "references": ["http://davidmlane.com/hyperstat/A29337.html", "http://davidmlane.com/hyperstat/A73079.html", "http://www.leidenuniv.nl/fsw/verduin/stathist/1stword.htm", "http://doi.org/10.1016%2F0169-5347(94)90258-5", "http://doi.org/10.1037%2F1082-989X.5.4.411", "http://doi.org/10.1080%2F01621459.1993.10476404", "http://doi.org/10.1098%2Frsta.1933.0009", "http://doi.org/10.1111%2Fj.1442-9993.2009.01946.x", "http://doi.org/10.1136%2Fbmj.309.6949.248", "http://doi.org/10.1136%2Fbmj.313.7048.36", "http://doi.org/10.1198%2F016214504000000089", "http://doi.org/10.5735%2F086.046.0501", "http://www.worldcat.org/issn/1797-2450"]}, "Recursive least squares": {"categories": ["Digital signal processing", "Filter theory", "Statistical signal processing"], "title": "Recursive least squares filter", "method": "Recursive least squares", "url": "https://en.wikipedia.org/wiki/Recursive_least_squares_filter", "summary": "Recursive least squares (RLS) is an adaptive filter algorithm that recursively finds the coefficients that minimize a weighted linear least squares cost function relating to the input signals. This approach is in contrast to other algorithms such as the least mean squares (LMS) that aim to reduce the mean square error. In the derivation of the RLS, the input signals are considered deterministic, while for the LMS and similar algorithm they are considered stochastic. Compared to most of its competitors, the RLS exhibits extremely fast convergence. However, this benefit comes at the cost of high computational complexity.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f6/AdaptiveFilter_C.png"], "links": ["A posteriori", "A priori and a posteriori", "Adaptive filter", "Additive noise", "Algebraic Riccati equation", "Carl Friedrich Gauss", "Column vector", "Cross-covariance", "Deterministic system (mathematics)", "Dot product", "Finite impulse response", "Identity matrix", "International Standard Book Number", "International Standard Serial Number", "Kalman filter", "Kernel adaptive filter", "Least mean squares", "Least mean squares filter", "Least squares", "Loss function", "Matrix product", "Mean square error", "Negative feedback", "Noisy channel", "Row vector", "Sample mean and sample covariance", "Stochastic", "Transpose", "Weighted least squares", "Woodbury matrix identity", "Zero forcing equalizer"], "references": ["http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf", "http://gtas.unican.es/files/pub/stkrls_mlsp2012.pdf", "http://wwwdsp.ucd.ie/dspfiles/main_files/pdf_files/hsla_fpl2001.pdf", "https://www.worldcat.org/search?fq=x0:jrnl&q=n2:0006-3444"]}, "Traffic equations": {"categories": ["Queueing theory", "Wikipedia articles needing page number citations from December 2010"], "title": "Traffic equations", "method": "Traffic equations", "url": "https://en.wikipedia.org/wiki/Traffic_equations", "summary": "In queueing theory, a discipline within the mathematical theory of probability, traffic equations are equations that describe the mean arrival rate of traffic, allowing the arrival rates at individual nodes to be determined. Mitrani notes \"if the network is stable, the traffic equations are valid and can be solved.\"", "images": ["https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg"], "links": ["Adversarial queueing network", "Arrival theorem", "BCMP network", "Balance equation", "Bene\u0161 method", "Bulk queue", "Burke's theorem", "Buzen's algorithm", "Continuous-time Markov chain", "D/M/1 queue", "Data buffer", "Decomposition method (queueing theory)", "Digital object identifier", "Erlang (unit)", "Erlang distribution", "FIFO (computing and electronics)", "Flow-equivalent server method", "Flow control (data)", "Fluid limit", "Fluid queue", "Fork\u2013join queue", "G-network", "G/G/1 queue", "G/M/1 queue", "Gordon\u2013Newell theorem", "Heavy traffic approximation", "Information system", "International Standard Book Number", "Jackson network", "Kelly network", "Kendall's notation", "Kingman's formula", "LIFO (computing)", "Layered queueing network", "Lindley equation", "Little's law", "Loss network", "M/D/1 queue", "M/D/c queue", "M/G/1 queue", "M/G/k queue", "M/M/1 queue", "M/M/c queue", "M/M/\u221e queue", "Markovian arrival process", "Matrix analytic method", "Mean field theory", "Mean value analysis", "Message queue", "Network congestion", "Network scheduler", "Peter G. Harrison", "Pipeline (software)", "Poisson process", "Pollaczek\u2013Khinchine formula", "Polling system", "Probability theory", "Processor sharing", "Product-form solution", "Quality of service", "Quasireversibility", "Queueing theory", "Rational arrival process", "Reflected Brownian motion", "Retrial queue", "Round-robin scheduling", "Scheduling (computing)", "Shortest job first", "Shortest remaining time", "Teletraffic engineering"], "references": ["http://doi.org/10.1017/CBO9781139173087.005"]}, "Unit of observation": {"categories": ["All stub articles", "Social research", "Statistical data types", "Statistics stubs"], "title": "Unit of observation", "method": "Unit of observation", "url": "https://en.wikipedia.org/wiki/Unit_of_observation", "summary": "In statistics, a unit of observation is the unit described by the data that one analyzes. For example, in a study of the demand for money, the unit of observation might be chosen as the individual, with different observations (data points) for a given point in time differing as to which individual they refer to; or the unit of observation might be the country, with different observations differing only in regard to the country they refer to. A study may have a differing unit of observation and unit of analysis: for example, in community research, the research design may collect data at the individual level of observation but the level of analysis might be at the neighborhood level, drawing conclusions on neighborhood characteristics from data collected from individuals. Together, the unit of observation and the level of analysis define the population of a research enterprise.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Array data structure", "Boolean logic", "Category (mathematics)", "Community", "Computing", "Data", "Data collection system", "Data processing", "Datatype", "Demand for money", "Integer", "International Standard Book Number", "Level of measurement", "Money demand", "Real number", "Research design", "Sample population", "Statistical graphics", "Statistical inference", "Statistical sample", "Statistics", "Summary statistic", "Unit of analysis", "Units of measurement", "Vector space"], "references": []}, "Association scheme": {"categories": ["Algebraic combinatorics", "All articles covered by WikiProject Wikify", "All pages needing cleanup", "Analysis of variance", "Articles covered by WikiProject Wikify from March 2013", "Articles with inconsistent citation formats", "Design of experiments", "Representation theory", "Use dmy dates from September 2011", "Wikipedia introduction cleanup from March 2013"], "title": "Association scheme", "method": "Association scheme", "url": "https://en.wikipedia.org/wiki/Association_scheme", "summary": "The theory of association schemes arose in statistics, in the theory of experimental design for the analysis of variance. In mathematics, association schemes belong to both algebra and combinatorics. Indeed, in algebraic combinatorics, association schemes provide a unified approach to many topics, for example combinatorial designs and coding theory. In algebra, association schemes generalize groups, and the theory of association schemes generalizes the character theory of linear representations of groups.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abelian group", "Accelerated failure time model", "Actuarial science", "Adjacency matrix", "Adjacency relation", "Akaike information criterion", "Algebra", "Algebraic combinatorics", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Mathematical Statistics", "Anne Penfold Street", "Arithmetic mean", "Associative", "Associative algebra", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binary relation", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Block design", "Blocking (statistics)", "Bootstrapping (statistics)", "Bose\u2013Mesner algebra", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Chris Godsil", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Code", "Coding theory", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Combinatorial design", "Combinatorics", "Commutative algebra", "Commutativity", "Comparing means", "Complete graph", "Completely randomized design", "Completeness (statistics)", "Complex number", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Diagonal matrix", "Dickey\u2013Fuller test", "Digital object identifier", "Distance-regular graph", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Eigenvalues", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Finite group", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graph (discrete mathematics)", "Graphical model", "Group (mathematics)", "Group character", "Group representation", "Grouped data", "Hamming distance", "Hamming scheme", "Harmonic mean", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Idempotent", "Identity relation", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isomorphic", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Johnson scheme", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Krawtchouk polynomials", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear programming", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Mathematical Reviews", "Mathematics", "Matrix (mathematics)", "Matrix product", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Operation (mathematics)", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonal polynomials", "Orthogonality", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of a set", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Pointwise product", "Poisson regression", "Polynomial", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R. C. Bose", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relation (mathematics)", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Rosemary A. Bailey", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Sankhya (journal)", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Semisimple operator", "Sequential analysis", "Sequential probability ratio test", "Set (mathematics)", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "Symmetric matrix", "Symmetric relation", "System identification", "T-design", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tuple", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ams.org/bull/2006-43-02/S0273-0979-05-01077-3/S0273-0979-05-01077-3.pdf", "http://www.ams.org/mathscinet-getitem?mr=0102157", "http://www.ams.org/mathscinet-getitem?mr=0882540", "http://www.ams.org/mathscinet-getitem?mr=1220704", "http://www.ams.org/mathscinet-getitem?mr=2047311", "http://www.ams.org/mathscinet-getitem?mr=2214129", "http://doi.org/10.1007%2FBF02777367", "http://doi.org/10.1080%2F01621459.1952.10501161", "http://doi.org/10.1090%2FS0273-0979-05-01077-3", "http://doi.org/10.1109%2F18.720545", "http://doi.org/10.1214%2Faoms%2F1177706356", "http://www.jstor.org/stable/2237117", "http://projecteuclid.org/euclid.aoms/1177706356", "http://www.worldcat.org/issn/0021-2172", "http://www.maths.qmul.ac.uk/~rab/Asbook", "http://www.maths.qmw.ac.uk/~rab"]}, "Iteratively reweighted least squares": {"categories": ["Least squares"], "title": "Iteratively reweighted least squares", "method": "Iteratively reweighted least squares", "url": "https://en.wikipedia.org/wiki/Iteratively_reweighted_least_squares", "summary": "The method of iteratively reweighted least squares (IRLS) is used to solve certain optimization problems with objective functions of the form of a p-norm:\n\n \n \n \n \n \n \n a\n r\n g\n \n m\n i\n n\n \n \u03b2\n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n \n |\n \n \n \n y\n \n i\n \n \n \u2212\n \n f\n \n i\n \n \n (\n \n \u03b2\n \n )\n \n \n \n |\n \n \n \n p\n \n \n ,\n \n \n {\\displaystyle {\\underset {\\boldsymbol {\\beta }}{\\operatorname {arg\\,min} }}\\sum _{i=1}^{n}{\\big |}y_{i}-f_{i}({\\boldsymbol {\\beta }}){\\big |}^{p},}\n by an iterative method in which each step involves solving a weighted least squares problem of the form:\n\n \n \n \n \n \n \u03b2\n \n \n (\n t\n +\n 1\n )\n \n \n =\n \n \n \n a\n r\n g\n \n m\n i\n n\n \n \u03b2\n \n \n \n \u2211\n \n i\n =\n 1\n \n \n n\n \n \n \n w\n \n i\n \n \n (\n \n \n \u03b2\n \n \n (\n t\n )\n \n \n )\n \n \n |\n \n \n \n y\n \n i\n \n \n \u2212\n \n f\n \n i\n \n \n (\n \n \u03b2\n \n )\n \n \n \n |\n \n \n \n 2\n \n \n .\n \n \n {\\displaystyle {\\boldsymbol {\\beta }}^{(t+1)}={\\underset {\\boldsymbol {\\beta }}{\\operatorname {arg\\,min} }}\\sum _{i=1}^{n}w_{i}({\\boldsymbol {\\beta }}^{(t)}){\\big |}y_{i}-f_{i}({\\boldsymbol {\\beta }}){\\big |}^{2}.}\n IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers in an otherwise normally-distributed data set. For example, by minimizing the least absolute errors rather than the least square errors.\nAlthough not a linear regression problem, Weiszfeld's algorithm for approximating the geometric median can also be viewed as a special case of IRLS, in which the objective function is the sum of distances of the estimator from the samples.\nOne of the advantages of IRLS over linear programming and convex programming is that it can be used with Gauss\u2013Newton and Levenberg\u2013Marquardt numerical algorithms.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["ArXiv", "Bayesian linear regression", "Bayesian multivariate linear regression", "Compressed sensing", "Convex programming", "Diagonal matrix", "Digital object identifier", "Discrete choice", "Errors-in-variables models", "Errors and residuals in statistics", "Feasible generalized least squares", "Fixed effects model", "Gauss\u2013Markov theorem", "Gauss\u2013Newton", "General linear model", "Generalized least squares", "Generalized linear model", "Geometric median", "Goodness of fit", "Huber loss", "International Standard Book Number", "Isotonic regression", "Iterative method", "L1 norm", "Least-angle regression", "Least absolute deviation", "Least absolute deviations", "Least absolute errors", "Least squares", "Levenberg\u2013Marquardt", "Linear least squares", "Linear least squares (mathematics)", "Linear programming", "Linear regression", "Local regression", "Logistic regression", "Lp quasi-norm", "Lp space", "M-estimator", "Maximum likelihood", "Mean and predicted response", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Objective function", "Ordered logit", "Ordered probit", "Ordinary least squares", "P-norm", "Partial least squares regression", "Poisson regression", "Polynomial regression", "Principal component regression", "Probit model", "Quantile regression", "Random effects model", "Regression analysis", "Regression model validation", "Regularization (mathematics)", "Regularized least squares", "Restricted isometry property", "Robust regression", "Segmented regression", "Semiparametric regression", "Simple linear regression", "Statistics", "Studentized residual", "Tikhonov regularization", "Total least squares", "Weighted least squares", "Weiszfeld's algorithm", "Worcester Polytechnic Institute"], "references": ["http://graphics.stanford.edu/~jplewis/lscourse/SLIDES.pdf", "http://users.stat.umn.edu/~sandy/courses/8053/handouts/robust.pdf", "http://www.wpi.edu/Pubs/E-project/Available/E-project-050506-091720/unrestricted/IQP_Final_Report.pdf", "http://arxiv.org/abs/0807.0575", "http://doi.org/10.1002%2Fcpa.20303", "http://doi.org/10.1007%2F978-0-387-70873-7", "http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4518498", "http://www.mai.liu.se/~akbjo/LSPbook.html", "https://stemblab.github.io/irls/", "https://cnx.org/exports/92b90377-2b34-49e4-b26f-7fe572db78a1@12.pdf/iterative-reweighted-least-squares-12.pdf"]}, "Sammon projection": {"categories": ["All stub articles", "CS1 maint: Multiple names: authors list", "Dimension reduction", "Functions and mappings", "Statistics stubs"], "title": "Sammon mapping", "method": "Sammon projection", "url": "https://en.wikipedia.org/wiki/Sammon_mapping", "summary": "Sammon mapping or Sammon projection is an algorithm that maps a high-dimensional space to a space of lower dimensionality (see multidimensional scaling) by trying to preserve the structure of inter-point distances in high-dimensional space in the lower-dimension projection. It is particularly suited for use in exploratory data analysis. The method was proposed by John W. Sammon in 1969. It is considered a non-linear approach as the mapping cannot be represented as a linear combination of the original variables as possible in techniques such as principal component analysis, which also makes it more difficult to use for classification applications.Denote the distance between ith and jth objects in the original space by \n \n \n \n \n \n d\n \n i\n j\n \n \n \u2217\n \n \n \n \n \n {\\displaystyle \\scriptstyle d_{ij}^{*}}\n , and the distance between their projections by \n \n \n \n \n \n d\n \n i\n j\n \n \n\n \n \n \n \n \n {\\displaystyle \\scriptstyle d_{ij}^{}}\n . Sammon's mapping aims to minimize the following error function, which is often referred to as Sammon's stress or Sammon's error:\n\n \n \n \n E\n =\n \n \n 1\n \n \n \u2211\n \n i\n <\n j\n \n \n \n d\n \n i\n j\n \n \n \u2217\n \n \n \n \n \n \n \u2211\n \n i\n <\n j\n \n \n \n \n \n (\n \n d\n \n i\n j\n \n \n \u2217\n \n \n \u2212\n \n d\n \n i\n j\n \n \n \n )\n \n 2\n \n \n \n \n d\n \n i\n j\n \n \n \u2217\n \n \n \n \n .\n \n \n {\\displaystyle E={\\frac {1}{\\sum \\limits _{i<j}d_{ij}^{*}}}\\sum _{i<j}{\\frac {(d_{ij}^{*}-d_{ij})^{2}}{d_{ij}^{*}}}.}\n The minimization can be performed either by gradient descent, as proposed initially, or by other means, usually involving iterative methods. The number of iterations need to be experimentally determined and convergent solutions are not always guaranteed. Many implementations prefer to use the first Principal Components as a starting configuration.The Sammon mapping has been one of the most successful nonlinear metric multidimensional scaling methods since its advent in 1969, but effort has been focused on algorithm improvement rather than on the form of the stress function. The performance of the Sammon mapping has been improved by extending its stress function using left Bregman divergence \n and right Bregman divergence.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["Bregman divergence", "Digital object identifier", "Exploratory data analysis", "Gradient descent", "Map (mathematics)", "Multidimensional scaling", "Principal component analysis", "Statistics"], "references": ["http://www.codeproject.com/KB/recipes/SammonProjection.aspx", "http://hisee.sourceforge.net/", "http://doi.org/10.1007/s100440050006", "http://doi.org/10.1016/S0031-3203(97)00064-2", "http://doi.org/10.1016/j.ins.2011.10.013", "http://doi.org/10.1016/j.patcog.2010.11.013", "http://doi.org/10.1109/t-c.1969.222678", "http://theoval.cmp.uea.ac.uk/~gcc/matlab/default.html#sammon", "http://theoval.cmp.uea.ac.uk/~gcc/matlab/sammon/sammon.pdf"]}, "Doob's martingale convergence theorems": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from January 2012", "Martingale theory", "Probability theorems"], "title": "Doob's martingale convergence theorems", "method": "Doob's martingale convergence theorems", "url": "https://en.wikipedia.org/wiki/Doob%27s_martingale_convergence_theorems", "summary": "In mathematics \u2013 specifically, in the theory of stochastic processes \u2013 Doob's martingale convergence theorems are a collection of results on the long-time limits of supermartingales, named after the American mathematician Joseph L. Doob.", "images": ["https://upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg"], "links": ["Almost all", "Almost surely", "ArXiv", "Backwards martingale convergence theorem", "Bernt \u00d8ksendal", "Chebyshev's inequality", "Conditional expectation", "Continuous function", "Convergence of random variables", "Digital object identifier", "Filtered probability space", "Filtration (mathematics)", "Filtration (probability theory)", "Integral", "International Standard Book Number", "Joseph L. Doob", "Kolmogorov's zero\u2013one law", "Limit (mathematics)", "Lp space", "Martingale (probability theory)", "Mathematics", "Probability space", "Random variable", "Rick Durrett", "Sample continuous process", "Sample space", "Sigma algebra", "Stochastic processes", "Tail event", "Tautology (logic)", "Uniformly integrable"], "references": ["http://arxiv.org/abs/1410.8264", "http://doi.org/10.1134/S0081543814080070", "https://books.google.com/books/about/Probability.html?id=evbGTPhuvSoC", "https://books.google.com/books/about/Stochastic_Differential_Equations.html?id=EQZEAAAAQBAJ", "https://books.google.com/books?id=4XDpBwXEVVkC&pg=PA113", "https://books.google.com/books?id=H0PhBwAAQBAJ&pg=PA197", "https://ocw.mit.edu/courses/sloan-school-of-management/15-070j-advanced-stochastic-processes-fall-2013/lecture-notes/MIT15_070JF13_Lec11Add.pdf"]}, "Omnibus test": {"categories": ["Statistical hypothesis testing", "Statistical tests"], "title": "Omnibus test", "method": "Omnibus test", "url": "https://en.wikipedia.org/wiki/Omnibus_test", "summary": "Omnibus tests are a kind of statistical test. They test whether the explained variance in a set of data is significantly greater than the unexplained variance, overall. One example is the F-test in the analysis of variance. There can be legitimate significant effects within a model even if the omnibus test is not significant. For instance, in a model with two independent variables, if only one variable exerts a significant effect on the dependent variable and the other does not, then the omnibus test may be non-significant. This fact does not affect the conclusions that may be drawn from the one significant variable. In order to test effects within an omnibus test, researchers often use contrasts.\nIn addition, Omnibus test as a general name refers to an overall or a global test. Other names include F-test or Chi-squared test.\nOmnibus test as a statistical test is implemented on an overall hypothesis that tends to find general significance between parameters' variance, while examining parameters of the same type, such as:\nHypotheses regarding equality vs. inequality between k expectancies \u00b51=\u00b52=\u2026=\u00b5k vs. at least one pair \u00b5j\u2260\u00b5j' , where j,j'=1,...,k and j\u2260j', in Analysis Of Variance(ANOVA); \nor regarding equality between k standard deviations \u03c31= \u03c32=\u2026.= \u03c3 k vs. at least one pair \u03c3j\u2260 \u03c3j' in testing equality of variances in ANOVA; \nor regarding coefficients \u03b21= \u03b22=\u2026.= \u03b2k vs. at least one pair \u03b2j\u2260\u03b2j' in Multiple linear regression or in Logistic regression.\nUsually, it tests more than two parameters of the same type and its role is to find general significance of at least one of the parameters involved.\nOmnibus tests commonly refers to either one of those statistical tests:\n\nANOVA F test to test significance between all factor means and/or between their variances equality in Analysis of Variance procedure ;\nThe omnibus multivariate F Test in ANOVA with repeated measures ;\nF test for equality/inequality of the regression coefficients in Multiple Regression;\nChi-Square test for exploring significance differences between blocks of independent explanatory variables or their coefficients in a logistic regression.Those omnibus tests are usually conducted whenever one tends to test an overall hypothesis on a quadratic statistic (like sum of squares or variance or covariance) or rational quadratic statistic (like the ANOVA overall F test in Analysis of Variance or F Test in Analysis of covariance or the F Test in Linear Regression, or Chi-Square in Logistic Regression).\nWhile significance is founded on the omnibus test, it doesn't specify exactly where the difference is occurred, meaning, it doesn't bring specification on which parameter is significally different from the other, but it statistically determine that there is a difference, so at least two of the tested parameters are statistically different. \nIf significance was met, none of those tests will tell specifically which mean differs from the others (in ANOVA), which coefficient differs from the others (in Regression) etc.", "images": [], "links": ["Analysis of covariance", "Analysis of variance", "Bonferroni correction", "Bootstrapping (statistics)", "Chi-squared test", "Contrast (statistics)", "F-test", "Likelihood-ratio test", "Logistic regression", "Multiple linear regression", "Neyman\u2013Pearson lemma", "Normal distribution", "P-value", "Partition of sums of squares", "Post-hoc analysis", "SPSS", "Statistical significance", "Statistical test", "Stepwise regression", "Type I and type II errors", "Variance"], "references": ["http://www.math.yorku.ca/Who/Faculty/Monette/Ed-stat/0525.html", "http://www.nd.edu/~rwilliam/xsoc63993/", "http://www.sjsu.edu/people/edward.cohen/courses/c2/s1/Week_15_handout.pdf", "http://www.stat.umn.edu/geyer/aster/short/examp/reg.html"]}, "Johnson SU distribution": {"categories": ["All articles needing expert attention", "Articles needing expert attention from November 2012", "Continuous distributions", "Pages using deprecated image syntax", "Statistics articles needing expert attention"], "title": "Johnson's SU-distribution", "method": "Johnson SU distribution", "url": "https://en.wikipedia.org/wiki/Johnson%27s_SU-distribution", "summary": "The Johnson's SU-distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949. Johnson proposed it as a transformation of the normal distribution:\n\n \n \n \n z\n =\n \u03b3\n +\n \u03b4\n \n sinh\n \n \u2212\n 1\n \n \n \u2061\n \n (\n \n \n \n x\n \u2212\n \u03be\n \n \u03bb\n \n \n )\n \n \n \n {\\displaystyle z=\\gamma +\\delta \\sinh ^{-1}\\left({\\frac {x-\\xi }{\\lambda }}\\right)}\n where \n \n \n \n z\n \u223c\n \n \n N\n \n \n (\n 0\n ,\n 1\n )\n \n \n {\\displaystyle z\\sim {\\mathcal {N}}(0,1)}\n .", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/1/10/JohnsonSU.png", "https://upload.wikimedia.org/wikipedia/commons/6/6d/JohnsonSU_CDF.png"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Biometrika", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "Joint probability distribution", "Journal of the Royal Statistical Society", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Kurtosis", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Norman Lloyd Johnson", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Real number", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://doi.org/10.1080%2F00949650108812126", "http://doi.org/10.1093%2Fbiomet%2F36.3-4.297", "http://doi.org/10.1093%2Fbiomet%2Fasp053", "http://doi.org/10.2307%2F2332539", "http://www.jstor.org/stable/2332539", "http://www.jstor.org/stable/2332669", "http://oro.open.ac.uk/22510"]}, "Evidence lower bound": {"categories": ["All articles needing additional references", "All stub articles", "Articles needing additional references from May 2018", "Statistics stubs", "Theory of probability distributions"], "title": "Evidence lower bound", "method": "Evidence lower bound", "url": "https://en.wikipedia.org/wiki/Evidence_lower_bound", "summary": "In statistics, the evidence lower bound (ELBO, also variational lower bound) is the difference between the distribution of a latent variable and the distribution of the respective observed variable (See Kullback\u2013Leibler divergence)", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Kullback\u2013Leibler divergence", "Latent variable", "Probability distribution", "Statistics"], "references": ["http://legacydirs.umiacs.umd.edu/~xyang35/files/understanding-variational-lower.pdf"]}, "Quasi-likelihood": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from February 2017", "Maximum likelihood estimation"], "title": "Quasi-likelihood", "method": "Quasi-likelihood", "url": "https://en.wikipedia.org/wiki/Quasi-likelihood", "summary": "In statistics, quasi-likelihood estimation is one way of allowing for overdispersion, that is, greater variability in the data than would be expected from the statistical model used. It is most often used with models for count data or grouped binary data, i.e. data that would otherwise be modelled using the Poisson or binomial distribution.\nThe term quasi-likelihood function was introduced by Robert Wedderburn in 1974 to describe a function that has similar properties to the log-likelihood function but is not the log-likelihood corresponding to any actual probability distribution. Quasi-likelihood models can be fitted using a straightforward extension of the algorithms used to fit generalized linear models.\nInstead of specifying a probability distribution for the data, only a relationship between the mean and the variance is specified in the form of a variance function giving the variance as a function of the mean. Generally, this function is allowed to include a multiplicative factor known as the overdispersion parameter or scale parameter that is estimated from the data. Most commonly, the variance function is of a form such that fixing the overdispersion parameter at unity results in the variance-mean relationship of an actual probability distribution such as the binomial or Poisson. (For formulae, see the binomial data example and count data example under generalized linear models.)", "images": [], "links": ["Bayesian statistics", "Binomial distribution", "Count data", "Digital object identifier", "Generalized linear model", "Generalized linear models", "Hierarchical models", "International Standard Book Number", "John Nelder", "Joseph Hilbe", "Likelihood function", "Mathematical Reviews", "Mixed model", "Overdispersion", "Poisson distribution", "Probability distribution", "Random-effects models", "Robert Wedderburn (statistician)", "Statistical model", "Statistics", "Variance function"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0375592", "http://doi.org/10.1093%2Fbiomet%2F61.3.439"]}, "Risk theory": {"categories": ["Actuarial science", "Mathematical finance", "Risk", "Stochastic processes"], "title": "Ruin theory", "method": "Risk theory", "url": "https://en.wikipedia.org/wiki/Ruin_theory", "summary": "In actuarial science and applied probability ruin theory (sometimes risk theory collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin and deficit at time of ruin.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/6b/Samplepathcompoundpoisson.JPG"], "links": ["Actuarial science", "Applied Probability Trust", "Applied probability", "Compound Poisson process", "Continuous-time Markov chain", "Digital object identifier", "Filip Lundberg", "Financial risk", "Harald Cram\u00e9r", "Independent and identically distributed non-negative random variables", "International Standard Book Number", "JSTOR", "M/G/1 queue", "Michael R. Powers", "Poisson process", "Pollaczek\u2013Khinchine formula", "Queueing theory", "Renewal process", "Stochastic processes", "The Annals of Statistics"], "references": ["http://casact.net/library/astin/vol8no1/104.pdf", "http://www.actuaries.org/AFIR/Colloquia/Cairns/Gerber_Shiu.pdf", "http://doi.org/10.1002%2F9780470317044.ch5", "http://doi.org/10.1007%2F978-3-540-31343-4_1", "http://doi.org/10.1007%2F978-3-642-33483-2_2", "http://doi.org/10.1016%2F0167-6687(87)90019-9", "http://doi.org/10.1016%2F0167-6687(95)00006-E", "http://doi.org/10.1080%2F10920277.1998.10595671", "http://doi.org/10.1214%2Faos%2F1176350596", "http://www.jstor.org/stable/2241677", "http://www.jstor.org/stable/4141346"]}, "Operational confound": {"categories": ["All articles with unsourced statements", "Analysis of variance", "Articles with short description", "Articles with unsourced statements from April 2012", "Causal inference", "Design of experiments"], "title": "Confounding", "method": "Operational confound", "url": "https://en.wikipedia.org/wiki/Confounding", "summary": "In statistics, a confounder (also confounding variable, confounding factor or lurking variable) is a variable that influences both the dependent variable and independent variable causing a spurious association. Confounding is a causal concept, and as such, cannot be described in terms of correlations or associations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/d5/Confounding.PNG", "https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/b/b8/Simple_Confounding_Case.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Alaska", "American Journal of Epidemiology", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Anecdotal evidence", "Antidepressant", "ArXiv", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Berkson's paradox", "Bias of an estimator", "Bibcode", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Case-control study", "Categorical variable", "Causal inference", "Causality", "Cause", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort study", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding Factor (games company)", "Confounding factor", "Confusion", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Donald Rubin", "Double blinding", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiological method", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Health", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Human", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jerzy Neyman", "Johansen test", "Jonckheere's trend test", "Judea Pearl", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Law of large numbers", "Lehmann\u2013Scheff\u00e9 theorem", "Leslie Kish", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "Lippincott Williams & Wilkins", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Medieval Latin", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "New England Journal of Medicine", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational studies", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Peer review", "Percentile", "Permutation test", "Pesticide", "Pie chart", "Pivotal quantity", "Placebo effect", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Risk assessment", "Risk ratio", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "SSRI", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific Reports", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sherry L Mayrent", "Sign test", "Simple linear regression", "Simpson's Paradox", "Simpson's paradox", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratification (statistics)", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tricyclic antidepressant", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.une.edu.au/WebStat/unit_materials/c1_behavioural_science_research/confounds.html", "http://adsabs.harvard.edu/abs/2014NatSR...4E6085L", "http://ftp.cs.ucla.edu/pub/stat_ser/R256.pdf", "http://www.stat.yale.edu/Courses/1997-98/101/linreg.htm", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1009818", "http://www.ncbi.nlm.nih.gov/pubmed/11565527", "http://arxiv.org/abs/1304.0564", "http://doi.org/10.1037%2Fh0037350", "http://doi.org/10.1038%2Fsrep06085", "http://doi.org/10.1056%2Fnejm200109203451211", "http://doi.org/10.1093%2Faje%2F154.3.276", "http://doi.org/10.1093%2Fije%2F15.3.413", "http://doi.org/10.1136%2Fjech.2010.112565", "http://doi.org/10.1136%2Foem.46.8.505", "http://doi.org/10.1214%2F12-aos1058", "http://doi.org/10.1214%2Fss%2F1009211805"]}, "PARAFAC": {"categories": ["CS1 errors: dates", "Multilinear algebra", "Tensors"], "title": "Tensor rank decomposition", "method": "PARAFAC", "url": "https://en.wikipedia.org/wiki/Tensor_rank_decomposition", "summary": "In multilinear algebra, the tensor rank decomposition or canonical polyadic decomposition (CPD) may be regarded as a generalization of the matrix singular value decomposition (SVD) to tensors, which has found application in statistics, signal processing, psychometrics, linguistics and chemometrics. It was introduced by Hitchcock in 1927 and later rediscovered several times, notably in psychometrics. \nFor this reason, the tensor rank decomposition is sometimes historically referred to as PARAFAC or CANDECOMP.The tensor rank decomposition expresses a tensor as a minimum-length linear combination of rank-1 tensors. Such rank-1 tensors are also called simple or pure. A pure tensor is the tensor product of a collection of vectors.", "images": [], "links": ["A. Gimigliano", "A. V. Geramita", "Almost everywhere", "Alternating least squares", "Alternating slice-wise diagonalisation", "Ann Arbor", "ArXiv", "C. J. Hillar", "C. Peterson", "Chemometrics", "CiteSeerX", "Complex conjugate", "Computer-assisted proof", "Conditionally independent", "D. Bini", "Dense set", "Digital object identifier", "Euclidean topology", "F. L. Hitchcock", "F. Romani", "Field extension", "Frank Lauren Hitchcock", "Frobenius norm", "G. Blehkerman", "G. Lotti", "G. Ottaviani", "H. Abo", "Higher-order singular value decomposition", "Inner product", "International Standard Serial Number", "J. Chang", "J. D. Carroll", "J. M. Landsberg", "Journal of Mathematics and Physics", "L-BFGS", "L. Lim", "Latent class analysis", "Leopold Kronecker", "Levenberg\u2013Marquardt", "Linear Algebra and its Applications", "Linguistics", "M. V. Catalisano", "Mathematische Annalen", "Matrix multiplication algorithm", "Matrix pencil", "Multilinear algebra", "Multilinear subspace learning", "NP-hard", "Nonlinear conjugate gradient", "Psychometrics", "Psychometrika", "R programming language", "Richard A. Harshman", "SIAM Journal on Matrix Analysis and Applications", "SIAM Journal on Scientific Computing", "Signal processing", "Simultaneous diagonalization", "Simultaneous generalized Schur decomposition", "Singular value decomposition", "Statistics", "System of polynomial equations", "T. Lickteig", "Tamara G. Kolda", "Tensor (intrinsic definition)", "Tensor decomposition", "Tensor product", "Topic modeling", "Transactions of the American Mathematical Society", "Tucker decomposition", "University Microfilms", "V. de Silva", "Volker Strassen", "W state", "Weierstrass", "Z. Teitler", "Zariski topology"], "references": ["http://publish.uwo.ca/~harshman/wpppfac0.pdf", "http://www.models.life.ku.dk/~rasmus/presentations/parafac_tutorial/paraf.htm", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.2059", "http://factominer.free.fr/", "http://pubs.acs.org/doi/abs/10.1021/ac00289a052", "http://www.ams.org/jag/2013-22-01/S1056-3911-2011-00592-4/", "http://arxiv.org/abs/0911.1393", "http://arxiv.org/abs/1402.2371", "http://arxiv.org/abs/math/0607191", "http://arxiv.org/abs/math/0607647", "http://doi.org/10.1002%2Fcem.1180040105", "http://doi.org/10.1007%2F978-1-4757-2189-8", "http://doi.org/10.1007%2FBF02310791", "http://doi.org/10.1007%2Fbf02293598", "http://doi.org/10.1007%2Fs00208-014-1150-3", "http://doi.org/10.1007%2Fs10231-013-0352-8", "http://doi.org/10.1016%2F0024-3795(83)80041-x", "http://doi.org/10.1016%2F0024-3795(85)90070-9", "http://doi.org/10.1016%2Fj.difgeo.2017.07.009", "http://doi.org/10.1016%2Fj.jsc.2012.05.012", "http://doi.org/10.1016%2Fj.laa.2016.10.019", "http://doi.org/10.1016%2Fs0024-3795(02)00352-x", "http://doi.org/10.1016%2Fs0169-7439(00)00117-9", "http://doi.org/10.1021%2Fac00289a052", "http://doi.org/10.1090%2Fs0002-9947-08-04725-9", "http://doi.org/10.1090%2Fs1056-3911-10-00537-0", "http://doi.org/10.1090%2Fs1056-3911-2011-00592-4", "http://doi.org/10.1137%2F0209053", "http://doi.org/10.1137%2F06066518x", "http://doi.org/10.1137%2F0614071", "http://doi.org/10.1137%2F07070111X", "http://doi.org/10.1137%2F110829180", "http://doi.org/10.1137%2F130916084", "http://doi.org/10.1137%2F140961389", "http://doi.org/10.1137%2F16m1090132", "http://doi.org/10.1145%2F2512329", "http://epubs.siam.org/doi/10.1137/110829180", "http://epubs.siam.org/doi/10.1137/140961389", "http://epubs.siam.org/doi/10.1137/16M1090132", "http://www.worldcat.org/issn/0003-2700", "http://www.worldcat.org/issn/0024-3795", "http://www.worldcat.org/issn/0033-3123", "http://www.worldcat.org/issn/0169-7439", "http://www.worldcat.org/issn/0373-3114", "http://www.worldcat.org/issn/0747-7171", "http://www.worldcat.org/issn/0886-9383", "http://www.worldcat.org/issn/0895-4798", "http://www.worldcat.org/issn/0926-2245", "http://www.worldcat.org/issn/1056-3911", "http://www.fmrib.ox.ac.uk/analysis/techrep/tr04cb1/tr04cb1/node2.html", "https://link.springer.com/10.1007/978-1-4757-2189-8", "https://link.springer.com/article/10.1007/BF02293598", "https://link.springer.com/article/10.1007/s10231-013-0352-8", "https://web.archive.org/web/20041010092429/http://publish.uwo.ca/~harshman/wpppfac0.pdf", "https://doi.org/10.1002/cem.1180040105", "https://doi.org/10.1016/S0169-7439(00)00117-9", "https://doi.org/10.1016/j.difgeo.2017.07.009", "https://doi.org/10.1016/j.jsc.2012.05.012", "https://doi.org/10.1016/j.laa.2016.10.019", "https://doi.org/10.1137/0614071", "https://doi.org/10.1137/130916084", "https://doi.org/10.1515/crelle-2016-0067"]}, "Bernoulli scheme": {"categories": ["Ergodic theory", "Markov models", "Symbolic dynamics", "Wikipedia articles needing clarification from November 2010"], "title": "Bernoulli scheme", "method": "Bernoulli scheme", "url": "https://en.wikipedia.org/wiki/Bernoulli_scheme", "summary": "In mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes are important in the study of dynamical systems, as most such systems (such as Axiom A systems) exhibit a repellor that is the product of the Cantor set and a smooth manifold, and the dynamics on the Cantor set are isomorphic to that of the Bernoulli shift. This is essentially the Markov partition. The term shift is in reference to the shift operator, which may be used to study Bernoulli schemes. The Ornstein isomorphism theorem shows that Bernoulli shifts are isomorphic when their entropy is equal.", "images": [], "links": ["Adjacency matrix", "Amenable group", "Anosov flow", "Asymptotic equipartition property", "Axiom A system", "Bernoulli process", "Bernoulli shift", "Cantor set", "Cartesian product", "Clique (graph theory)", "Countable", "Cylinder set", "Direct product", "Discrete-time", "Discrete group", "Dynamical system", "Encyclopedia of Mathematics", "Exponential object", "Group action", "Haar measure", "Hidden Bernoulli model", "International Standard Book Number", "Isomorphism of dynamical systems", "Kolmogorov automorphism", "Kolmogorov entropy", "Markov chain", "Markov partition", "Markov shift", "Mathematics", "Measure-preserving dynamical system", "Measure-preserving transformation", "Measure (mathematics)", "Measure space", "Michiel Hazewinkel", "Ornstein isomorphism theorem", "Partition of a set", "Random variable", "Relative entropy", "Repellor", "Sample space", "Shift of finite type", "Shift operator", "Sigma-algebra", "Sinai's billiards", "Smooth manifold", "Standard probability space", "Stationary stochastic process", "Statistical independence", "Stochastic process", "Subshifts of finite type", "Symbolic dynamics", "Ya. Sinai"], "references": ["http://web.math.princeton.edu/facultypapers/Sinai/MetricEntropy2.pdf", "http://www.ams.org/journals/tran/1999-351-10/S0002-9947-99-02446-0/", "https://arxiv.org/abs/1103.4424", "https://www.encyclopediaofmath.org/index.php?title=Ornstein_isomorphism_theorem&oldid=17997"]}, "Midhinge": {"categories": ["Exploratory data analysis", "Means"], "title": "Midhinge", "method": "Midhinge", "url": "https://en.wikipedia.org/wiki/Midhinge", "summary": "In statistics, the midhinge is the average of the first and third quartiles and is thus a measure of location.\nEquivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator.\nThe midhinge is complemented by the H-spread, or interquartile range, which is the difference of the third and first quartiles and which is a measure of statistical dispersion, in sense that if one knows the midhinge and the interquartile range, one can find the first and third quartiles.\nThe use of the term \"hinge\" for the lower or upper quartiles derives from John Tukey's work on exploratory data analysis, and \"midhinge\" is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the trimean, which originated in the same context and equals the average of the median and the midhinge.\n\n", "images": [], "links": ["Exploratory data analysis", "International Standard Book Number", "Interquartile mean", "Interquartile range", "John Tukey", "L-estimator", "Location parameter", "MathWorld", "Median", "Mid-range", "Midsummary", "Quartile", "Statistical dispersion", "Statistics", "Trimean", "Trimmed estimator"], "references": ["http://mathworld.wolfram.com/H-Spread.html"]}, "Logit-normal distribution": {"categories": ["Continuous distributions", "Pages using deprecated image syntax"], "title": "Logit-normal distribution", "method": "Logit-normal distribution", "url": "https://en.wikipedia.org/wiki/Logit-normal_distribution", "summary": "In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution. If Y is a random variable with a normal distribution, and P is the standard logistic function, then X = P(Y) has a logit-normal distribution; likewise, if X is logit-normally distributed, then Y = logit(X)= log (X/(1-X)) is normally distributed. It is also known as the logistic normal distribution, which often refers to a multinomial logit version (e.g.).\nA variable might be modeled as logit-normal if it is a proportion, which is bounded by zero and one, and where values of zero and one never occur.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/52/Gaussian_and_Logistic_Normal_pdfs.pdf", "https://upload.wikimedia.org/wikipedia/commons/c/c1/Logistic_Normal_approximation_to_Dirichlet_distribution.pdf", "https://upload.wikimedia.org/wikipedia/commons/4/44/LogitnormCdfGrid2.svg", "https://upload.wikimedia.org/wikipedia/commons/a/ae/LogitnormDensityGrid.svg", "https://upload.wikimedia.org/wikipedia/commons/8/82/LogitnormalPDF.svg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compositional data", "Compound Poisson distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digamma function", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Expected value", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Serial Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "JSTOR", "John Aitchison", "John Hinde (statistician)", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kullback\u2013Leibler divergence", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logistic function", "Logit", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Median", "Mittag-Leffler distribution", "Mixture distribution", "Mode (statistics)", "Moment-generating function", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Numerical integration", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "R (programming language)", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Simplex", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard deviation", "Student's t-distribution", "Support (mathematics)", "Tracy\u2013Widom distribution", "Triangular distribution", "Trigamma function", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://brenocon.com/blog/2011/05/log-normal-and-logistic-normal-terminology/", "http://www.springerreference.com/docs/html/chapterdbid/205424.html", "http://www.tandfonline.com/doi/abs/10.1080/03610910801983178#.U1LER61dW1E", "http://people.csail.mit.edu/tomasz/papers/huang_hln_tech_report_2006.pdf", "http://www.stat.washington.edu/hoff/Preprints/nhed.ps", "http://doi.org/10.1007%2F978-3-642-04898-2_342", "http://doi.org/10.2307%2F2335470", "http://doi.org/10.2307%2F2528553", "http://www.jstor.org/stable/2528553", "http://logitnorm.r-forge.r-project.org/", "http://www.worldcat.org/issn/0006-3444", "https://www.amazon.com/The-Statistical-Analysis-Compositional-Data/dp/1930665784", "https://scholar.google.com/scholar?q=aitchison%20logistic%20normal"]}, "Item-total correlation": {"categories": ["Comparison of assessments", "Covariance and correlation", "Statistical tests"], "title": "Item-total correlation", "method": "Item-total correlation", "url": "https://en.wikipedia.org/wiki/Item-total_correlation", "summary": "The item-total correlation test arises in psychometrics in contexts where a number of tests or questions are given to an individual and where the problem is to construct a useful single quantity for each individual that can be used to compare that individual with others in a given population. The test is used to see if any of the tests or questions (\"items\") do not have responses that vary in line with those for other tests across the population. The summary measure would be an average of some form, weighted where necessary, and the item-correlation test is used to decide whether or not responses to a given test should be included in the set being averaged. In some fields of application such a summary measure is called a scale.\n\n", "images": [], "links": ["Empirical research", "International Standard Book Number", "Journal of Marketing Research", "Pearson product-moment correlation coefficient", "Psychometrics", "Scale analysis (statistics)", "Statistical population"], "references": []}, "Stochastic process": {"categories": ["Statistical data types", "Stochastic models", "Stochastic processes", "Wikipedia further reading cleanup", "Wikipedia spam cleanup from July 2018"], "title": "Stochastic process", "method": "Stochastic process", "url": "https://en.wikipedia.org/wiki/Stochastic_process", "summary": "In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables. Historically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over time, such as the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. They have applications in many disciplines including sciences such as biology, chemistry, ecology, neuroscience, and physics as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries.The term random function is also used to refer to a stochastic or random process, because a stochastic process can also be interpreted as a random element in a function space. The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. But often these two terms are used when the random variables are indexed by the integers or an interval of the real line. If the random variables are indexed by the Cartesian plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects.Based on their mathematical properties, stochastic processes can be divided into various categories, which include random walks, martingales, Markov processes, L\u00e9vy processes, Gaussian processes, random fields, renewal processes, and branching processes. The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis. The theory of stochastic processes is considered to be an important contribution to mathematics and it continues to be an active topic of research for both theoretical reasons and applications.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/4e/BMonSphere.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/3f/DriftedWienerProcess1D.svg", "https://upload.wikimedia.org/wikipedia/commons/9/96/Joseph_Doob.jpg", "https://upload.wikimedia.org/wikipedia/commons/3/38/Wiener_Zurich1932.tif", "https://upload.wikimedia.org/wikipedia/commons/f/f8/Wiener_process_3d.png", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["A.K. Erlang", "A. K. Erlang", "Abraham de Moivre", "Abstract Wiener space", "Abuse of notation", "Actuarial mathematics", "Albert Einstein", "Aleksandr Khinchin", "Alexander A. 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Doeblin", "World War II", "\u00c9mile Borel"], "references": ["http://oed.com/search?searchType=dictionary&q=Random", "http://oed.com/search?searchType=dictionary&q=Stochastic", "http://www.oxforddnb.com/help/subscribe#public", "http://adsabs.harvard.edu/abs/1934PNAS...20..376D", "http://adsabs.harvard.edu/abs/2005AmJPh..73..395B", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.114.632", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1076423", "http://arxiv.org/abs/0909.4213", "http://arxiv.org/abs/math/0609294", "http://doi.org/10.1002%2F0471667196.ess2065.pub2", "http://doi.org/10.1002%2F0471667196.ess2180.pub2", "http://doi.org/10.1002%2F0471667196.ess6027.pub2", "http://doi.org/10.1007%2F978-1-4613-0179-0_71", "http://doi.org/10.1007%2FBF00327232", "http://doi.org/10.1007%2FBF00328110", "http://doi.org/10.1007%2FBF00412958", "http://doi.org/10.1007%2FBF01449156", "http://doi.org/10.1007%2FBF01457949", "http://doi.org/10.1016%2FS0169-7161(01)19014-0", 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"https://books.google.com/books?id=c_3UBwAAQBAJ", "https://books.google.com/books?id=dBNOHvElXZ4C", "https://books.google.com/books?id=dP2JBAAAQBAJ&pg=PA1", "https://books.google.com/books?id=dQkYMjRK3fYC", "https://books.google.com/books?id=dSDxjX9nmmMC", "https://books.google.com/books?id=ddsrGdsgN9sC&pg=PA269", "https://books.google.com/books?id=e-TbA-dSrzYC", "https://books.google.com/books?id=e9saZ0YSi-AC", "https://books.google.com/books?id=eBeNngEACAAJ", "https://books.google.com/books?id=ePxDAQAAIAAJ", "https://books.google.com/books?id=evbGTPhuvSoC", "https://books.google.com/books?id=fnCQWd0GEZ8C&pg=PA113", "https://books.google.com/books?id=fsgkBAAAQBAJ&pg=PR4", "https://books.google.com/books?id=ftcsQgMp5cUC&pg=PR8", "https://books.google.com/books?id=gqriBQAAQBAJ&pg=PR10", "https://books.google.com/books?id=h3WVqBPHboAC", "https://books.google.com/books?id=hRk_AAAAQBAJ", "https://books.google.com/books?id=hRk_AAAAQBAJ&pg", "https://books.google.com/books?id=iojEts9YAxIC", "https://books.google.com/books?id=jrPVBwAAQBAJ", "https://books.google.com/books?id=kWEwk1UL42AC", "https://books.google.com/books?id=lSz_vQAACAAJ", "https://books.google.com/books?id=n3JNDAAAQBAJ&pg=PR4", "https://books.google.com/books?id=nPENXKw5kwcC", "https://books.google.com/books?id=pOQy6-qnVx8C", "https://books.google.com/books?id=pY5_DkvI-CcC&pg=PR4", "https://books.google.com/books?id=pa20eZJe4LIC", "https://books.google.com/books?id=q0lo91imeD0C", "https://books.google.com/books?id=q7dR3d5nqaUC", "https://books.google.com/books?id=q7eDUjdJxIkC", "https://books.google.com/books?id=r9r6CAAAQBAJ=PA1", "https://books.google.com/books?id=rUbxAAAAMAAJ", "https://books.google.com/books?id=ryejJmJAj28C&pg=PA1", "https://books.google.com/books?id=ryejJmJAj28C&pg=PA263", "https://books.google.com/books?id=tfa5BAAAQBAJ&pg=PR4", "https://books.google.com/books?id=tlWOphOFRgwC", "https://books.google.com/books?id=w0SgBQAAQBAJ&pg=PT5", "https://books.google.com/books?id=wGUECAAAQBAJ", "https://books.google.com/books?id=yJyLzG7N7r8C", "https://books.google.com/books?id=yJyLzG7N7r8C&pg=PR2", "https://books.google.com/books?id=yPvECi_L3bwC", "https://books.google.com/books?id=yWcvT80gQK4C", "https://books.google.co.nz/books?id=321EuQAACAAJ&dq=Stochastic+methods&hl=en&sa=X&ved=0ahUKEwiEz7bPhLHbAhUJNrwKHWdoCXcQ6AEIKTAA"]}, "Estimating equations": {"categories": ["Estimation methods"], "title": "Estimating equations", "method": "Estimating equations", "url": "https://en.wikipedia.org/wiki/Estimating_equations", "summary": "In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated. This can be thought of as a generalisation of many classical methods --- the method of moments, least squares, and maximum likelihood --- as well as some recent methods like M-estimators.\nThe basis of the method is to have, or to find, a set of simultaneous equations involving both the sample data and the unknown model parameters which are to be solved in order to define the estimates of the parameters. Various components of the equations are defined in terms of the set of observed data on which the estimates are to be based.\nImportant examples of estimating equations are the likelihood equations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Consistent estimator", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimation", "Experiment", "Exponential distribution", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized estimating equation", "Generalized linear model", "Generalized method of moments", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Least squares", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Controlling for a variable": {"categories": ["All articles needing additional references", "All stub articles", "Articles needing additional references from February 2017", "Design of experiments", "Observational study", "Statistics stubs"], "title": "Controlling for a variable", "method": "Controlling for a variable", "url": "https://en.wikipedia.org/wiki/Controlling_for_a_variable", "summary": "In statistics, controlling for a variable is the attempt to reduce the effect of confounding variables in an observational study or experiment. It means that when looking at the effect of one variable, the effects of all other variable predictors are taken into account, either by making the other variables take on a fixed value (in an experiment) or by including them in a regression to separate their effects from those of the explanatory variable of interest (in an observational study).", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Confounding", "Confounding variable", "Control variable", "Dependent and independent variables", "Experiment", "Independent variable", "Institutional review board", "International Standard Book Number", "Mixed model", "Multiple regression", "Observational study", "Omitted variable bias", "Placebo", "Regression analysis", "Sample (statistics)", "Sampling (statistics)", "Scientific control", "Statistics", "Treatment and control groups"], "references": ["http://blog.minitab.com/blog/adventures-in-statistics/a-tribute-to-regression-analysis", "https://books.google.com/books?id=mviJQgAACAAJ&dq=inauthor:%22D.+A.+Freedman%22&hl=en&sa=X&ei=alibU96YEKensATlzoGIDQ&ved=0CDYQ6AEwBA"]}, "Homogeneity (statistics)": {"categories": ["Meta-analysis", "Statistical analysis"], "title": "Homogeneity (statistics)", "method": "Homogeneity (statistics)", "url": "https://en.wikipedia.org/wiki/Homogeneity_(statistics)", "summary": "For homogeneity of variance see homoscedasticity.In statistics, homogeneity and its opposite, heterogeneity, arise in describing the properties of a dataset, or several datasets. They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part. In meta-analysis, which combines the data from several studies, homogeneity measures the differences or similarities between the several studies (see also Study heterogeneity).\nHomogeneity can be studied to several degrees of complexity. For example, considerations of homoscedasticity examine how much the variability of data-values changes throughout a dataset. However, questions of homogeneity apply to all aspects of the statistical distributions, including the location parameter. Thus, a more detailed study would examine changes to the whole of the marginal distribution. An intermediate-level study might move from looking at the variability to studying changes in the skewness. In addition to these, questions of homogeneity apply also to the joint distributions.\nThe concept of homogeneity can be applied in many different ways and, for certain types of statistical analysis, it is used to look for further properties that might need to be treated as varying within a dataset once some initial types of non-homogeneity have been dealt with.", "images": [], "links": ["Dataset", "Digital object identifier", "E-statistic", "Homogeneity and heterogeneity", "Homoscedasticity", "Hydrology", "Joint distributions", "Location parameter", "Location test", "Marginal distribution", "Meta-analysis", "Meteorological Applications", "Meteorology", "Regression analysis", "Skewness", "Statistical distribution", "Statistics", "Study heterogeneity", "Subpopulation", "Variance"], "references": ["https://web.archive.org/web/20060624164532/http://www.visualstatistics.net/Scaling/Homogeneity/Homogeneity.htm", "https://doi.org/10.1017%2FS1350482703005061"]}, "Random field": {"categories": ["Spatial processes", "Wikipedia articles needing clarification from May 2016"], "title": "Random field", "method": "Random field", "url": "https://en.wikipedia.org/wiki/Random_field", "summary": "A random field is another term for stochastic process in modern mathematics with some restriction on its index set. The modern definition of a random field or a stochastic process is a generalization of the classic naive definition of \"stochastic process\" such that the underlying parameter need no longer be a simple real or integer valued \"time\", but can instead take values that are multidimensional vectors, or points on some manifold.At its most basic, discrete case, a random field is a list of random numbers whose indices are identified with a discrete set of points in a space (for example, n-dimensional Euclidean space). When used in the natural sciences, values in a random field are often spatially correlated in one way or another. In its most basic form this might mean that adjacent values (i.e. values with adjacent indices) do not differ as much as values that are further apart. This is an example of a covariance structure, many different types of which may be modeled in a random field. More generally, the values might be defined over a continuous domain, and the random field might be thought of as a \"function valued\" random variable.", "images": [], "links": ["Abstract Wiener space", "Actuarial mathematics", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Conditional random field", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Covariance", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Digital terrain model", "Dimensional", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fluid simulation", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Gibbs random field", "Girsanov theorem", "Graphite", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Interacting particle system", "International Standard Book Number", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "John G. Kemeny", "Journal of Elasticity", "Journal of the Royal Statistical Society", "Julian Besag", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kriging", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Laurie Snell", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Manifold", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Monte Carlo method", "Moran process", "Moving-average model", "Natural sciences", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability space", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random graph", "Random variable", "Random walk", "Real coordinate space", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Representative volume element", "Resel", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic cellular automata", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Variogram", "Vasicek model", "Vector space", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://statweb.stanford.edu/~jtaylo/courses/stats352/notes/random_fields.pdf", "http://doi.org/10.1007%2Fs11831-014-9139-3", "http://doi.org/10.1016%2Fj.jnucmat.2018.09.008", "https://www.researchgate.net/publication/269332552_Practical_Application_of_the_Stochastic_Finite_Element_Method", "https://www.researchgate.net/publication/327537624_Characterisation_of_the_spatial_variability_of_material_properties_of_Gilsocarbon_and_NBG-18_using_random_fields"]}, "Backfitting algorithm": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from December 2009", "Generalized linear models", "Numerical linear algebra"], "title": "Backfitting algorithm", "method": "Backfitting algorithm", "url": "https://en.wikipedia.org/wiki/Backfitting_algorithm", "summary": "In statistics, the backfitting algorithm is a simple iterative procedure used to fit a generalized additive model. It was introduced in 1985 by Leo Breiman and Jerome Friedman along with generalized additive models. In most cases, the backfitting algorithm is equivalent to the Gauss\u2013Seidel method algorithm for solving a certain linear system of equations.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Digital object identifier", "Gauss\u2013Seidel", "Generalized additive model", "International Standard Book Number", "JSTOR", "Kernel smoothing", "Polynomial regression", "Robert Tibshirani", "Smoothing spline", "Statistics", "Trevor Hastie"], "references": ["http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode37.html", "http://doi.org/10.2307%2F2288473", "http://www.jstor.org/stable/2288473", "https://archive.is/20121211125906/http://rss.acs.unt.edu/Rdoc/library/gam/html/gam.html", "https://web.archive.org/web/20061121130651/http://pbil.univ-lyon1.fr/library/mda/html/bruto.html", "https://web.archive.org/web/20150510225240/http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/ebooks/html/spm/spmhtmlnode37.html"]}, "Diagnostic odds ratio": {"categories": ["Biostatistics", "Epidemiology", "Medical statistics", "Pages with citations having bare URLs", "Pages with citations lacking titles", "Statistical ratios", "Summary statistics for contingency tables", "Wikipedia articles needing clarification from January 2012"], "title": "Diagnostic odds ratio", "method": "Diagnostic odds ratio", "url": "https://en.wikipedia.org/wiki/Diagnostic_odds_ratio", "summary": "In medical testing with binary classification, the diagnostic odds ratio is a measure of the effectiveness of a diagnostic test. It is defined as the ratio of the odds of the test being positive if the subject has a disease relative to the odds of the test being positive if the subject does not have the disease.\nThe rationale for the diagnostic odds ratio is that it is a single indicator of test performance (like accuracy and Youden's J statistic) but which is independent of prevalence (unlike accuracy) and is presented as an odds ratio, which is familiar to medical practitioners.", "images": ["https://upload.wikimedia.org/wikipedia/commons/e/ee/Log-DiagnosticOddsRatio.svg"], "links": ["Accuracy", "Binary classification", "Confidence interval", "Confusion matrix", "Diagnostic test", "Digital object identifier", "Evaluation of binary classifiers", "Gold standard (test)", "Inverse-variance weighting", "Likelihood ratios in diagnostic testing", "Logit", "Medical test", "Meta-analysis", "Natural logarithm", "Negative predictive value", "Normal distribution", "Odds ratio", "Positive predictive value", "Prevalence", "PubMed Identifier", "Receiver operating characteristic", "Sensitivity and specificity", "Standard error (statistics)", "Youden's J statistic"], "references": ["http://www.ncbi.nlm.nih.gov/pubmed/14615004", "http://www.ncbi.nlm.nih.gov/pubmed/16861527", "http://www.ncbi.nlm.nih.gov/pubmed/17266837", "http://www.ncbi.nlm.nih.gov/pubmed/8210827", "http://srdta.cochrane.org/sites/srdta.cochrane.org/files/uploads/Chapter%2010%20-%20Version%201.0.pdf", "http://doi.org/10.1002%2Fsim.4780121403", "http://doi.org/10.1016%2FS0895-4356(03)00177-X", "http://doi.org/10.2214%2FAJR.06.0226", "http://doi.org/10.3310%2Fhta11030", "https://books.google.com/books?id=BRPvAAAAMAAJ"]}, "Time reversibility": {"categories": ["Dynamical systems", "Symmetry", "Time series"], "title": "Time reversibility", "method": "Time reversibility", "url": "https://en.wikipedia.org/wiki/Time_reversibility", "summary": "A mathematical or physical process is time-reversible if the dynamics of the process remain well-defined when the sequence of time-states is reversed.\nA deterministic process is time-reversible if the time-reversed process satisfies the same dynamic equations as the original process; in other words, the equations are invariant or symmetrical under a change in the sign of time. A stochastic process is reversible if the statistical properties of the process are the same as the statistical properties for time-reversed data from the same process.", "images": [], "links": ["ArXiv", "Attractor", "Bibcode", "Birth and death processes", "C-symmetry", "CPT symmetry", "Charge (physics)", "Classical mechanics", "Conjugate momentum", "Continuous-time Markov chain", "Critical point (mathematics)", "Detailed balance", "Deterministic system", "Digital object identifier", "Dynamic equation (disambiguation)", "Dynamical system", "Entropy", "Frank Kelly (mathematician)", "Gaussian process", "International Standard Book Number", "International Standard Serial Number", "Invariant (mathematics)", "Involution (mathematics)", "Irreversible process", "JSTOR", "James R. Norris", "Kelly's lemma", "Kolmogorov's criterion", "L\u00e9vy processes", "Markov chain", "Markov process", "Markov property", "Mathematics", "Memorylessness", "Newton's laws of motion", "One-to-one function", "P-symmetry", "Parity (physics)", "Physics", "Piecewise deterministic Markov processes", "Quantum mechanics", "Reversible computing", "Reversible process (thermodynamics)", "Sign (mathematics)", "Stochastic network", "Stochastic process", "Symmetry", "T-symmetry", "Thermodynamic process", "Time reversal signal processing", "Wave equation", "Weak nuclear force"], "references": ["http://adsabs.harvard.edu/abs/2016SMaS...25h5015P", "http://arxiv.org/abs/1110.3813", "http://doi.org/10.1088%2F0964-1726%2F25%2F8%2F085015", "http://doi.org/10.1214%2FEJP.v18-1958", "http://doi.org/10.1214%2Faop%2F1176991776", "http://doi.org/10.2307%2F1425912", "http://doi.org/10.3836%2Ftjm%2F1270133555", "http://iopscience.iop.org/article/10.1088/0964-1726/25/8/085015/pdf", "http://www.jstor.org/stable/1425912", "http://www.jstor.org/stable/2243828", "http://www.worldcat.org/issn/0964-1726"]}, "Wold's theorem": {"categories": ["Statistical theorems", "Time series", "Wikipedia articles needing clarification from December 2015"], "title": "Wold's theorem", "method": "Wold's theorem", "url": "https://en.wikipedia.org/wiki/Wold%27s_theorem", "summary": "In statistics, Wold's decomposition or the Wold representation theorem (not to be confused with the Wold theorem that is the discrete-time analog of the Wiener\u2013Khinchin theorem), named after Herman Wold, says that every covariance-stationary time series \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n can be written as the sum of two time series, one deterministic and one stochastic.\nFormally\n\n \n \n \n \n Y\n \n t\n \n \n =\n \n \u2211\n \n j\n =\n 0\n \n \n \u221e\n \n \n \n b\n \n j\n \n \n \n \u03b5\n \n t\n \u2212\n j\n \n \n +\n \n \u03b7\n \n t\n \n \n ,\n \n \n {\\displaystyle Y_{t}=\\sum _{j=0}^{\\infty }b_{j}\\varepsilon _{t-j}+\\eta _{t},}\n where:\n\n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n is the time series being considered,\n \n \n \n \n \u03b5\n \n t\n \n \n \n \n {\\displaystyle \\varepsilon _{t}}\n is an uncorrelated sequence which is the innovation process to the process \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n \u2013 that is, a white noise process that is input to the linear filter \n \n \n \n {\n \n b\n \n j\n \n \n }\n \n \n {\\displaystyle \\{b_{j}\\}}\n .\n \n \n \n b\n \n \n {\\displaystyle b}\n is the possibly infinite vector of moving average weights (coefficients or parameters)\n \n \n \n \n \u03b7\n \n t\n \n \n \n \n {\\displaystyle \\eta _{t}}\n is a deterministic time series, such as one represented by a sine wave.The moving average coefficients have these properties:\n\nStable, that is square summable \n \n \n \n \n \u2211\n \n j\n =\n 1\n \n \n \u221e\n \n \n \n |\n \n \n b\n \n j\n \n \n \n \n |\n \n \n 2\n \n \n \n \n {\\displaystyle \\sum _{j=1}^{\\infty }|b_{j}|^{2}}\n < \n \n \n \n \u221e\n \n \n {\\displaystyle \\infty }\n \nCausal (i.e. there are no terms with j < 0)\nMinimum delay\nConstant (\n \n \n \n \n b\n \n j\n \n \n \n \n {\\displaystyle b_{j}}\n independent of t)\nIt is conventional to define \n \n \n \n \n b\n \n 0\n \n \n =\n 1\n \n \n {\\displaystyle b_{0}=1}\n This theorem can be considered as an existence theorem: any stationary process has this seemingly special representation. Not only is the existence of such a simple linear and exact representation remarkable, but even more so is the special nature of the moving average model. Imagine creating a process that is a moving average but not satisfying these properties 1\u20134. For example, the coefficients \n \n \n \n \n b\n \n j\n \n \n \n \n {\\displaystyle b_{j}}\n could define an acausal and non-minimum delay model. Nevertheless the theorem assures the existence of a causal minimum delay moving average that exactly represents this process. How this all works for the case of causality and the minimum delay property is discussed in Scargle (1981), where an extension of the Wold Decomposition is discussed.\nThe usefulness of the Wold Theorem is that it allows the dynamic evolution of a variable \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n to be approximated by a linear model. If the innovations \n \n \n \n \n \u03b5\n \n t\n \n \n \n \n {\\displaystyle \\varepsilon _{t}}\n are independent, then the linear model is the only possible representation relating the observed value of \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n to its past evolution. However, when \n \n \n \n \n \u03b5\n \n t\n \n \n \n \n {\\displaystyle \\varepsilon _{t}}\n is merely an uncorrelated but not independent sequence, then the linear model exists but it is not the only representation of the dynamic dependence of the series. In this latter case, it is possible that the linear model may not be very useful, and there would be a nonlinear model relating the observed value of \n \n \n \n \n Y\n \n t\n \n \n \n \n {\\displaystyle Y_{t}}\n to its past evolution. However, in practical time series analysis, it is often the case that only linear predictors are considered, partly on the grounds of simplicity, in which case the Wold decomposition is directly relevant.\nThe Wold representation depends on an infinite number of parameters, although in practice they usually decay rapidly. The autoregressive model is an alternative that may have only a few coefficients if the corresponding moving average has many. These two models can be combined into an autoregressive-moving average (ARMA) model, or an autoregressive-integrated-moving average (ARIMA) model if non-stationarity is involved. See Scargle (1981) and references there; in addition this paper gives an extension of the Wold Theorem that allows more generality for the moving average (not necessarily stable, causal, or minimum delay) accompanied by a sharper characterization of the innovation (identically and independently distributed, not just uncorrelated). This extension allows the possibility of models that are more faithful to physical or astrophysical processes, and in particular can sense \u2033the arrow of time.\u2033", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive model", "Autoregressive moving average model", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Dynamical system", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Herman Wold", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Innovation (signal processing)", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Jeffrey Scargle", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear filter", "Linear model", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marc Nerlove", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Peter Whittle (mathematician)", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Theodore Wilbur Anderson", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uncorrelated", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wiener\u2013Khinchin theorem", "Wilcoxon signed-rank test", "Wold decomposition", "Z-test"], "references": []}, "Extreme value theory": {"categories": ["Actuarial science", "All articles lacking in-text citations", "All articles needing expert attention", "All articles that are too technical", "Articles lacking in-text citations from September 2010", "Articles needing expert attention from August 2013", "Articles needing expert attention from February 2018", "CS1 maint: Uses authors parameter", "Extreme value data", "Financial risk modeling", "Statistical theory", "Statistics articles needing expert attention", "Tails of probability distributions", "Wikipedia articles that are too technical from February 2018"], "title": "Extreme value theory", "method": "Extreme value theory", "url": "https://en.wikipedia.org/wiki/Extreme_value_theory", "summary": "Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordered sample of a given random variable, the probability of events that are more extreme than any previously observed. Extreme value analysis is widely used in many disciplines, such as structural engineering, finance, earth sciences, traffic prediction, and geological engineering. For example, EVA might be used in the field of hydrology to estimate the probability of an unusually large flooding event, such as the 100-year flood. Similarly, for the design of a breakwater, a coastal engineer would seek to estimate the 50-year wave and design the structure accordingly.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/c/ce/1755_Lisbon_earthquake.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["100-year flood", "100 metres", "1755 Lisbon earthquake", "Annals of Mathematics", "Bernoulli process", "Bibcode", "Binomial distribution", "Breakwater (structure)", "British Cotton Industry Research Association", "Coastal engineer", "Cumulative distribution function", "Degenerate distribution", "Deviation (statistics)", "Digital object identifier", "Emil Julius Gumbel", "Equity risk", "Evolution", "Extreme risk", "Extreme value theorem", "Extreme weather", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Flood", "Freak wave", "Frechet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Geometric distribution", "Gumbel distribution", "Heavy-tailed distribution", "Hydrology", "Independent and identically distributed", "Indicator function", "Insurance", "International Standard Book Number", "JSTOR", "Large deviation theory", "Laurens de Haan", "Leonard Tippett", "List of publications in statistics", "Log-correlated fields", "Market risk", "Median", "Pareto distribution", "Pickands\u2013Balkema\u2013de Haan theorem", "Pitting corrosion", "Poisson distribution", "Power law", "Probability distribution", "PubMed Identifier", "R. A. Fisher", "Random variable", "Rare events", "Sample (statistics)", "Statistical independence", "Statistics", "Tornado", "Weibull distribution", "Wildfire", "Ximelagatran"], "references": ["http://www.bankofcanada.ca/wp-content/uploads/2010/01/wp00-20.pdf", "http://www.tandfonline.com/doi/full/10.1080/02664760701234850#.VKhG7KbcuTj", "http://www.risknet.de/fileadmin/eLibrary/EVT-Paper-Roehrl-Chavez-Demoulin.pdf", "http://adsabs.harvard.edu/abs/1928PCPS...24..180F", "http://adsabs.harvard.edu/abs/2002Natur.417..506G", "http://amir.eng.uci.edu/neva.php", "http://www.vetmed.wsu.edu/org_nws/NWSci%20journal%20articles/1998%20files/Special%20addition%201/v72%20p66%20Alvarado%20et%20al.PDF", "http://www.ncbi.nlm.nih.gov/pubmed/12037557", "http://doi.org/10.1002%2Flol2.10037", "http://doi.org/10.1016%2F0167-7152(91)90107-3", "http://doi.org/10.1016%2Fj.strusafe.2006.12.001", "http://doi.org/10.1017%2Fs0305004100015681", "http://doi.org/10.1038%2F417506a", "http://doi.org/10.1080%2F02664760701234850", "http://doi.org/10.1214%2Faop%2F1176996548", "http://doi.org/10.2307%2F1968974", "http://www.fas.org/irp/agency/dod/jason/statistics.pdf", "http://www.jstor.org/stable/1968974", "http://www.jstor.org/stable/2959306", "http://archive.numdam.org/article/AIHP_1935__5_2_115_0.pdf", "http://www.numdam.org/item?id=AIHP_1935__5_2_115_0", "https://github.com/juliohm/ExtremeStats.jl", "https://books.google.com/books?id=kXCg8B5xSUwC&pg=PP1", "https://pure.uvt.nl/ws/files/1244969/j.1467-9574.2010.00470.x.pdf", "https://web.archive.org/web/20090226080558/http://www.vetmed.wsu.edu/org_nws/NWSci%20journal%20articles/1998%20files/Special%20addition%201/v72%20p66%20Alvarado%20et%20al.PDF", "https://cran.r-project.org/web/views/ExtremeValue.html"]}, "Autocorrelation plot": {"categories": ["All pages needing cleanup", "Articles needing cleanup from October 2009", "Autocorrelation", "Cleanup tagged articles without a reason field from October 2009", "Statistical charts and diagrams", "Wikipedia articles incorporating text from the National Institute of Standards and Technology", "Wikipedia pages needing cleanup from October 2009"], "title": "Correlogram", "method": "Autocorrelation plot", "url": "https://en.wikipedia.org/wiki/Correlogram", "summary": "In the analysis of data, a correlogram is an image of correlation statistics. For example, in time series analysis, a correlogram, also known as an autocorrelation plot, is a plot of the sample autocorrelations \n \n \n \n \n r\n \n h\n \n \n \n \n \n {\\displaystyle r_{h}\\,}\n versus \n \n \n \n h\n \n \n \n {\\displaystyle h\\,}\n (the time lags).\nIf cross-correlation is used, the result is called a cross-correlogram. The correlogram is a commonly used tool for checking randomness in a data set. This randomness is ascertained by computing autocorrelations for data values at varying time lags. If random, such autocorrelations should be near zero for any and all time-lag separations. If non-random, then one or more of the autocorrelations will be significantly non-zero.\nIn addition, correlograms are used in the model identification stage for Box\u2013Jenkins autoregressive moving average time series models. Autocorrelations should be near-zero for randomness; if the analyst does not check for randomness, then the validity of many of the statistical conclusions becomes suspect. The correlogram is an excellent way of checking for such randomness.\nSometimes, corrgrams, color-mapped matrices of correlation strengths in multivariate analysis, are also called correlograms.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/84/Acf.svg", "https://upload.wikimedia.org/wikipedia/commons/e/e9/Correlogram.png", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ARIMA", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autocovariance function", "Autoregressive conditional heteroskedasticity", "Autoregressive moving average", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Copyright status of work by the U.S. government", "Correlation", "Correlation and dependence", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Data set", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gaussian", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lag plot", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "M. S. Bartlett", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model identification", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Moving average model", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National Institute of Standards and Technology", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial autocorrelation plot", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile function", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R (programming language)", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Randomness", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scaled Correlation", "Scatter plot", "Scatterplot", "Scientific control", "Score test", "Seasonal adjustment", "Seasonal subseries plot", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance level", "Simple linear regression", "Simultaneous equations model", "Sine", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Spectral plot", "Standard deviation", "Standard error", "Standard normal distribution", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical test", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taylor & Francis", "The American Statistician", "Time dependence", "Time domain", "Time series", "Time series analysis", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Variance function", "Vector autoregression", "Wald test", "Wavelet", "White noise", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://euclid.psych.yorku.ca/datavis/papers/corrgram.pdf", "http://www.itl.nist.gov/div898/handbook/eda/section3/eda331.htm", "http://www.nist.gov", "http://www.statmethods.net/advgraphs/correlograms.html", "http://doi.org/10.1198%2F000313002533", "https://www.itl.nist.gov/div898/handbook/eda/section3/autocopl.htm", "https://cran.r-project.org/web/packages/corrgram/"]}, "Frisch\u2013Waugh\u2013Lovell theorem": {"categories": ["Economics theorems", "Regression analysis", "Statistical theorems"], "title": "Frisch\u2013Waugh\u2013Lovell theorem", "method": "Frisch\u2013Waugh\u2013Lovell theorem", "url": "https://en.wikipedia.org/wiki/Frisch%E2%80%93Waugh%E2%80%93Lovell_theorem", "summary": "In econometrics, the Frisch\u2013Waugh\u2013Lovell (FWL) theorem is named after the econometricians Ragnar Frisch, Frederick V. Waugh, and Michael C. Lovell.The Frisch\u2013Waugh\u2013Lovell theorem states that if the regression we are concerned with is:\n\n \n \n \n Y\n =\n \n X\n \n 1\n \n \n \n \u03b2\n \n 1\n \n \n +\n \n X\n \n 2\n \n \n \n \u03b2\n \n 2\n \n \n +\n u\n \n \n {\\displaystyle Y=X_{1}\\beta _{1}+X_{2}\\beta _{2}+u}\n where \n \n \n \n \n X\n \n 1\n \n \n \n \n {\\displaystyle X_{1}}\n and \n \n \n \n \n X\n \n 2\n \n \n \n \n {\\displaystyle X_{2}}\n are \n \n \n \n n\n \u00d7\n \n k\n \n 1\n \n \n \n \n {\\displaystyle n\\times k_{1}}\n and \n \n \n \n n\n \u00d7\n \n k\n \n 2\n \n \n \n \n {\\displaystyle n\\times k_{2}}\n matrices respectively and where \n \n \n \n \n \u03b2\n \n 1\n \n \n \n \n {\\displaystyle \\beta _{1}}\n and \n \n \n \n \n \u03b2\n \n 2\n \n \n \n \n {\\displaystyle \\beta _{2}}\n are conformable, then the estimate of \n \n \n \n \n \u03b2\n \n 2\n \n \n \n \n {\\displaystyle \\beta _{2}}\n will be the same as the estimate of it from a modified regression of the form:\n\n \n \n \n \n M\n \n \n X\n \n 1\n \n \n \n \n Y\n =\n \n M\n \n \n X\n \n 1\n \n \n \n \n \n X\n \n 2\n \n \n \n \u03b2\n \n 2\n \n \n +\n \n M\n \n \n X\n \n 1\n \n \n \n \n u\n \n ,\n \n \n {\\displaystyle M_{X_{1}}Y=M_{X_{1}}X_{2}\\beta _{2}+M_{X_{1}}u\\!,}\n where \n \n \n \n \n M\n \n \n X\n \n 1\n \n \n \n \n \n \n {\\displaystyle M_{X_{1}}}\n projects onto the orthogonal complement of the image of the projection matrix \n \n \n \n \n X\n \n 1\n \n \n (\n \n X\n \n 1\n \n \n \n T\n \n \n \n \n X\n \n 1\n \n \n \n )\n \n \u2212\n 1\n \n \n \n X\n \n 1\n \n \n \n T\n \n \n \n \n \n {\\displaystyle X_{1}(X_{1}^{\\mathsf {T}}X_{1})^{-1}X_{1}^{\\mathsf {T}}}\n . Equivalently, MX1 projects onto the orthogonal complement of the column space of X1. Specifically,\n\n \n \n \n \n M\n \n \n X\n \n 1\n \n \n \n \n =\n I\n \u2212\n \n X\n \n 1\n \n \n (\n \n X\n \n 1\n \n \n \n T\n \n \n \n \n X\n \n 1\n \n \n \n )\n \n \u2212\n 1\n \n \n \n X\n \n 1\n \n \n \n T\n \n \n \n ,\n \n \n {\\displaystyle M_{X_{1}}=I-X_{1}(X_{1}^{\\mathsf {T}}X_{1})^{-1}X_{1}^{\\mathsf {T}},}\n and this is known as the annihilator matrix or orthogonal projection matrix. This result implies that the secondary regression used for obtaining \n \n \n \n \n M\n \n \n X\n \n 1\n \n \n \n \n \n \n {\\displaystyle M_{X_{1}}}\n is unnecessary: using projection matrices to make the explanatory variables orthogonal to each other will lead to the same results as running the regression with all non-orthogonal explanators included.", "images": [], "links": ["Conformable matrix", "Digital object identifier", "Econometrica", "Econometrics", "Frederick V. Waugh", "Fumio Hayashi", "Image (mathematics)", "International Standard Book Number", "JSTOR", "Journal of Economic Education", "Journal of the American Statistical Association", "Linear regression", "Matrix (mathematics)", "Michael C. Lovell", "Orthogonal complement", "Projection matrix", "Ragnar Frisch"], "references": ["http://doi.org/10.1080%2F01621459.1963.10480682", "http://doi.org/10.3200%2FJECE.39.1.88-91", "http://www.jstor.org/stable/1907330", "https://books.google.com/books?id=DrbrDAAAQBAJ&pg=PA311", "https://books.google.com/books?id=Ot6DByCF6osC&pg=PA19", "https://books.google.com/books?id=PnVCEZOOFr0C&pg=PA54", "https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA18", "https://books.google.com/books?id=shWtvsFbxlkC&pg=PA7"]}, "List of important publications in statistics": {"categories": ["CS1 maint: Multiple names: authors list", "Lists of publications in science", "Mathematics-related lists", "Statistics-related lists", "Use dmy dates from May 2012"], "title": "List of important publications in statistics", "method": "List of important publications in statistics", "url": "https://en.wikipedia.org/wiki/List_of_important_publications_in_statistics", "summary": "This is a list of important publications in statistics, organized by field.\nSome reasons why a particular publication might be regarded as important:\n\nTopic creator \u2013 A publication that created a new topic\nBreakthrough \u2013 A publication that changed scientific knowledge significantly\nInfluence \u2013 A publication which has significantly influenced the world or has had a massive impact on the teaching of statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Abraham Wald", "Accelerated failure time model", "Actuarial science", "Admissible decision rule", "Admissible decision rules", "Akaike information criterion", "Alexey Chervonenkis", "An Essay towards solving a Problem in the Doctrine of Chances", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Statistics", "Antiquarian science books", "Applied statistics", "Arithmetic mean", "Aryeh Dvoretzky", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes' theorem", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bayesian statistics", "Bernstein\u2013von Mises theorem", "Bias of an estimator", "Bibliography of anthropology", "Bibliography of biology", "Bibliography of sociology", "Binomial regression", "Bioinformatics", "Biometrics", "Biometrics (journal)", "Biometrika", "Biometry", "Biostatistics", "Biostatistics (journal)", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Brazilian Journal of Probability and Statistics", "Breusch\u2013Godfrey test", "British Medical Journal", "Bruno de Finetti", "Calyampudi Radhakrishna Rao", "Cancer Chemotherapy Reports", "Canonical correlation", "Carl Friedrich Gauss", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Charles Roy Henderson", "Charles Sanders Peirce", "Chemometrics", "Chi-squared test", "Chilean Journal of Statistics", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Communications in Statistics", "Comparison of statistics journals", "Completeness (statistics)", "Computational learning theory", "Confidence interval", "Confounding", "Conjugate prior", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Cox model", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Current Index to Statistics", "Data collection", "David Blackwell", "David Cox (statistician)", "Decision theory", "Decomposition of time series", "Degrees of freedom (statistics)", "Delayed open access journal", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometric Theory", "Econometrica", "Econometrics", "Effect size", "Efficiency (statistics)", "Egon Pearson", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Erich Leo Lehmann", "Errors and residuals in statistics", "Estimating equations", "Eugene Garfield", "Experiment", "Experimental design", "Exponential families", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher information", "Forest plot", "Fourier analysis", "Frank P. Ramsey", "Frank Yates", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "George E.P. Box", "George E. P. Box", "George W. Snedecor", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Gwilym Jenkins", "Harald Cram\u00e9r", "Harmonic mean", "Harvard Business School", "Herman Otto Hartley", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Howard Raiffa", "Hypothesis testing", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Inverse probability", "Isotonic regression", "JSTOR", "Jack Kiefer (mathematician)", "Jackknife resampling", "Jacob Wolfowitz", "Jarque\u2013Bera test", "Johansen test", "John W. Pratt", "John Wiley & Sons", "John von Neumann", "Jonckheere's trend test", "Joseph Jastrow", "Journal of Applied Econometrics", "Journal of Applied Statistics", "Journal of Business & Economic Statistics", "Journal of Chemometrics", "Journal of Computational and Graphical Statistics", "Journal of Dairy Science", "Journal of Econometrics", "Journal of Educational and Behavioral Statistics", "Journal of Modern Applied Statistical Methods", "Journal of Official Statistics", "Journal of Statistical Computation and Simulation", "Journal of Statistical Planning and Inference", "Journal of Statistical Software", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society", "Kaplan-Meier estimator", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Laplace distribution", "Laplace transform", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratio test", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of humor research publications", "List of important publications in chemistry", "List of important publications in computer science", "List of important publications in concurrent, parallel, and distributed computing", "List of important publications in cryptography", "List of important publications in economics", "List of important publications in geology", "List of important publications in mathematics", "List of important publications in medicine", "List of important publications in philosophy", "List of important publications in physics", "List of important publications in psychology", "List of important publications in theoretical computer science", "List of scientific journals in statistics", "List of scientific publications by Albert Einstein", "List of statistics articles", "List of statistics journals", "List of systems of plant taxonomy", "Lists of important publications in science", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Logrank test", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U", "Mann\u2013Whitney U test", "Mathematical Reviews", "Mathematical economics", "Mathematical statistics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measure theory", "Median", "Median-unbiased estimator", "Medical statistics", "Meta analysis", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monotonicity", "Multiple comparisons", "Multivariate Behavioral Research", "Multivariate adaptive regression splines", "Multivariate analysis", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Nathan Mantel", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Open access journal", "Operationalization", "Operations research", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Oscar Kempthorne", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Paul Meier (statistician)", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pharmaceutical Statistics", "Pie chart", "Pierre-Simon Laplace", "Pierre Simon de Laplace", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Pragmaticism", "Pranab K. Sen", "Prediction interval", "Principal component analysis", "Prior distribution", "Prior probability", "Probabilistic design", "Probability", "Probability distribution", "Probability theory", "Proportional hazards model", "Proportional hazards models", "Propositional logic", "Psychometrics", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "REVSTAT", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Revista Colombiana de Estadistica", "Robert R. Sokal", "Robert Schlaifer", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "SORT (journal)", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Applications in Genetics and Molecular Biology", "Statistical Methods for Research Workers", "Statistical Science", "Statistical classification", "Statistical decision theory", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Statistics Surveys", "Statistics in Medicine (journal)", "Stem-and-leaf display", "Stephen M. Stigler", "Stephen Stigler", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Subjective probability", "Subscription business model", "Sufficient statistic", "Survey Methodology", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Technology Innovations in Statistics Education", "Technometrics", "The American Statistician", "The Design of Experiments", "The Review of Economics and Statistics", "Theodore Wilbur Anderson", "Thomas Bayes", "Th\u00e9orie analytique des probabilit\u00e9s", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "University of Pennsylvania", "University of York", "Uppsala", "V-statistic", "VC dimension", "VC theory", "Variance", "Variance component estimation", "Vector autoregression", "Vladimir Vapnik", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Gemmell Cochran", "Z-test"], "references": ["http://psychclassics.yorku.ca/Fisher/Methods/", "http://psychclassics.yorku.ca/Peirce/small-diffs.htm", "http://www.britannica.com/EBchecked/topic/564160/Statistical-Methods-for-Research-Workers", "http://garfield.library.upenn.edu/classics1977/A1977DU23500002.pdf", "http://garfield.library.upenn.edu/classics1980/A1980JU47400001.pdf", "http://garfield.library.upenn.edu/classics1982/A1982PJ14400001.pdf", "http://garfield.library.upenn.edu/classics1983/A1983QB30100002.pdf", "http://www.garfield.library.upenn.edu/classics.html", "http://visualiseur.bnf.fr/ark:/12148/bpt6k88764q", "http://math-doc.ujf-grenoble.fr/cgi-bin/oeitem?id=OE_LAPLACE__7_R2_0", "http://www.ncbi.nlm.nih.gov/pubmed/1757641", "http://www.ncbi.nlm.nih.gov/pubmed/20761760", "http://www.ncbi.nlm.nih.gov/pubmed/5910392", "http://www.ams.org/mathscinet-getitem?mr=0483118", "http://doi.org/10.1080%2F02664760500079373", "http://doi.org/10.1086%2F444032", "http://doi.org/10.1214%2Faos%2F1176344123", "http://doi.org/10.1214%2Fss%2F1030037906", "http://doi.org/10.1214%2Fss%2F1177013111", "http://doi.org/10.2307%2F2289251", "http://doi.org/10.2307%2F2528399", "http://doi.org/10.2307%2F2682986", "http://doi.org/10.3102%2F00028312003003223", "http://doi.org/10.3168%2Fjds.S0022-0302(91)78599-8", "http://www.jstor.org/stable/2245530", "http://www.jstor.org/stable/2289251", "http://www.jstor.org/stable/2528399", "http://www.jstor.org/stable/2682986", "http://www.jstor.org/stable/2958876", "http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ss/1030037906", "http://projecteuclid.org/euclid.aos/1176344123", "http://www.worldcat.org/issn/0022-0302", "http://www.worldcat.org/issn/0162-1459", "http://www.worldcat.org/issn/0883-4237", "http://www.york.ac.uk/depts/maths/histstat/essay.pdf", "https://archive.org/details/thorieanalytiqu01laplgoog", "https://web.archive.org/web/20051213222222/http://www.library.adelaide.edu.au/digitised/fisher/18pt1.pdf", "https://web.archive.org/web/20080227205205/http://cepa.newschool.edu/het//texts/ramsey/ramsess.pdf", "https://doi.org/10.1093%2Fbiomet%2F30.1-2.134", "https://doi.org/10.1093%2Fbiomet%2F52.1-2.203", "https://doi.org/10.1093%2Fbiomet%2F54.1-2.93", "https://doi.org/10.1093%2Fbiomet%2F58.3.545", "https://doi.org/10.1137%2F1116025", "https://www.jstor.org/stable/2281868", "https://www.jstor.org/stable/2985181"]}, "Ratio distribution": {"categories": ["Algebra of random variables", "All articles with unsourced statements", "Articles with unsourced statements from April 2013", "Statistical ratios", "Types of probability distributions"], "title": "Ratio distribution", "method": "Ratio distribution", "url": "https://en.wikipedia.org/wiki/Ratio_distribution", "summary": "A ratio distribution (or quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions.\nGiven two (usually independent) random variables X and Y, the distribution of the random variable Z that is formed as the ratio\n\n \n \n \n Z\n =\n X\n \n /\n \n Y\n \n \n {\\displaystyle Z=X/Y}\n is a ratio distribution.\n(See also Relationships among probability distributions.)\nThe Cauchy distribution is an example of a ratio distribution. The random variable associated with this distribution comes about as the ratio of two Gaussian (normal) distributed variables with zero mean. \nThus the Cauchy distribution is also called the normal ratio distribution.\nA number of researchers have considered more general ratio distributions.\nTwo distributions often used in test-statistics, the t-distribution and the F-distribution, are also ratio distributions: \nThe t-distributed random variable is the ratio of a Gaussian random variable divided by an independent chi-distributed random variable (i.e., the square root of a chi-squared distribution), \nwhile the F-distributed random variable is the ratio of two independent chi-squared distributed random variables.\nOften the ratio distributions are heavy-tailed, and it may be difficult to work with such distributions and develop an associated statistical test.\nA method based on the median has been suggested as a \"work-around\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9b/Ratiodist2.jpg", "https://upload.wikimedia.org/wikipedia/commons/8/80/WikiPic4.jpg"], "links": ["Algebra of random variables", "Beta distribution", "Beta prime distribution", "Biometrika", "Cauchy distribution", "Chi-squared distribution", "Chi distribution", "Chi square distribution", "Confluent hypergeometric function", "D. V. Hinkley", "David Hinkley", "Defense Technical Information Center", "Degrees of freedom", "Determinant", "Difference distribution", "Digital object identifier", "F-distribution", "F distribution", "Gamma distribution", "Gaussian distribution", "Generalized gamma distribution", "George Marsaglia", "Heavy-tailed", "Hermite function", "International Standard Book Number", "Inverse distribution", "JSTOR", "Jack Hayya", "John Wiley & Sons", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society", "Laplace distribution", "Management Science (journal)", "MathWorld", "Median", "Mellin transform", "Melvin D. Springer", "Multivariate analysis", "Normal distribution", "Pearson product-moment correlation coefficient", "Probability density function", "Probability distribution", "Proc Natl Acad Sci U S A", "Product distribution", "PubMed Central", "PubMed Identifier", "Random variable", "Ratio", "Ratio estimator", "Relationships among probability distributions", "Roy C. Geary", "Slash distribution", "Statistical test", "Statistically independent", "Stephen R. Quake", "Student's t-distribution", "Student's t distribution", "Sum distribution", "Taylor & Francis", "The Annals of Mathematical Statistics", "Uniform distribution (continuous)", "Wilks' lambda distribution", "Wishart distribution"], "references": ["http://www.mathpages.com/home/kmath042/kmath042.htm", "http://mathworld.wolfram.com/NormalRatioDistribution.html", "http://mathworld.wolfram.com/RatioDistribution.html", "http://authors.library.caltech.edu/685/1/BROpnas02.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC130571", "http://www.ncbi.nlm.nih.gov/pubmed/12235357", "http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/slappf.htm", "http://www.dtic.mil/dtic/tr/fulltext/u2/600972.pdf", "http://www.dtic.mil/get-tr-doc/pdf?AD=AD0600972", "http://doi.org/10.1073%2Fpnas.162468199", "http://doi.org/10.1080%2F03610920600683689", "http://doi.org/10.1214%2Faoms%2F1177731679", "http://doi.org/10.1287%2Fmnsc.21.11.1338", "http://doi.org/10.2307%2F2283145", "http://doi.org/10.2307%2F2331976", "http://doi.org/10.2307%2F2334671", "http://doi.org/10.2307%2F2342070", "http://www.jstor.org/stable/2235953", "http://www.jstor.org/stable/2283145", "http://www.jstor.org/stable/2331976", "http://www.jstor.org/stable/2334671", "http://www.jstor.org/stable/2342070", "http://www.jstor.org/stable/2629897", "http://biomet.oxfordjournals.org/cgi/content/citation/24/3-4/428"]}, "Index (economics)": {"categories": ["All Wikipedia articles lacking focus", "All Wikipedia articles needing clarification", "All articles covered by WikiProject Wikify", "All articles with unsourced statements", "All pages needing cleanup", "Articles covered by WikiProject Wikify from July 2018", "Articles needing cleanup from January 2011", "Articles needing cleanup from July 2010", "Articles with multiple maintenance issues", "Articles with unsourced statements from February 2012", "Business terms", "Cleanup tagged articles without a reason field from January 2011", "Economic growth", "Economic indicators", "Index numbers", "Mathematical and quantitative methods (economics)", "Wikipedia articles lacking focus from July 2018", "Wikipedia articles needing clarification from July 2018", "Wikipedia articles with LCCN identifiers", "Wikipedia articles with NDL identifiers", "Wikipedia introduction cleanup from July 2018", "Wikipedia list cleanup from July 2010", "Wikipedia pages needing cleanup from January 2011"], "title": "Index (economics)", "method": "Index (economics)", "url": "https://en.wikipedia.org/wiki/Index_(economics)", "summary": "In economics and finance, an index is a statistical measure of changes in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, and employment. Economic indices track economic health from different perspectives. Influential global financial indices such as the Global Dow, and the NASDAQ Composite track the performance of selected large and powerful companies in order to evaluate and predict economic trends. The Dow Jones Industrial Average and the S&P 500 primarily track U.S. markets, though some legacy international companies are included. The consumer price index tracks the variation in prices for different consumer goods and services over time in a constant geographical location, and is integral to calculations used to adjust salaries, bond interest rates, and tax thresholds for inflation. The GDP Deflator Index, or real GDP, measures the level of prices of all new, domestically produced, final goods and services in an economy. Market performance indices include the labour market index/job index and proprietary stock market index investment instruments offered by brokerage houses.\nSome indices display market variations that cannot be captured in other ways. For example, the Economist provides a Big Mac Index that expresses the adjusted cost of a globally ubiquitous Big Mac as a percentage over or under the cost of a Big Mac in the U.S. in USD (estimated: $3.57). The least relatively expensive Big Mac price occurs in Hong Kong, at a 52% reduction from U.S. prices, or $1.71 U.S. Such indices can be used to help forecast currency values. From this example, it would be assumed that Hong Kong currency is undervalued, and provides a currency investment opportunity.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Adam Smith", "Adaptive expectations", "Aggregate demand", "Aggregation problem", "Agricultural economics", "Alfred Marshall", "Amartya Sen", "Anarchist economics", "Ancient economic thought", "Applied economics", "Asia-Pacific Economic Cooperation", "Asset-backed securities index", "Austrian School", "Average cost", "BSE Sensex", "Balance of payments", "Behavioral economics", "Big Mac Index", "Bilateral monopoly", "Bombay Stock Exchange", "Brokerage house", "Buddhist economics", "Budget set", "Bureau of Labor Statistics", "Business cycle", "Business economics", "Capacity utilization", "Capital flight", "Case\u2013Shiller index", "Central bank", "Chemical plant cost indexes", "Chicago school of economics", "Classical economics", "Commodity", "Competition (economics)", "Computational economics", "Consumer choice", "Consumer confidence", "Consumer price index", "Convexity in economics", "Cost-of-living index", "Cost of living", "Cost\u2013benefit analysis", "Credit default swap index", "Cryptocurrency", "Currency", "David Ricardo", "Deadweight loss", "Decision theory", "Deflation", "Demand for money", "Demand shock", "Demographic economics", "Depression (economics)", "Development economics", "Distribution (economics)", "Dow Jones & Company", "Dow Jones Indexes", "Dow Jones Industrial Average", "Dynamic stochastic general equilibrium", "Ecological economics", "Econometrics", "Economic Cooperation Organization", "Economic cost", "Economic data", "Economic equilibrium", "Economic geography", "Economic growth", "Economic history", "Economic indicator", "Economic methodology", "Economic planning", "Economic policy", "Economic rent", "Economic sociology", "Economic statistics", "Economic surplus", "Economic system", "Economic theory", "Economics", "Economies of scale", "Economies of scope", "Economist", "Education economics", "Effective demand", "Elasticity (economics)", "Employment", "Engineering economics", "Environmental economics", "Euro Stoxx 50", "European Free Trade Association", "Evolutionary economics", "Expected utility hypothesis", "Experimental economics", "Externality", "FTSE/Athex Large Cap", "FTSE4Good Index", "FTSE 100 Index", "FTSE 250 Index", "FTSE 350 Index", "FTSE AIM UK 50 Index", "FTSE All-Share Index", "FTSE Bursa Malaysia Index", "FTSE Fledgling Index", "FTSE Group", "FTSE Italia Mid Cap", "FTSE MIB", "FTSE SmallCap Index", "FTSE techMARK 100", "FTSEurofirst 300 Index", "Feminist economics", "Finance", "Financial economics", "Fiscal policy", "Francis Ysidro Edgeworth", "Friedrich Hayek", "GDP Deflator", "Game theory", "Gary Becker", "General equilibrium theory", "Georgism", "Global Dow", "Great Depression", "Harold Hotelling", "Health economics", "Herbert A. Simon", "Heterodox economics", "Historic Automobile Group", "Historical school of economics", "History of economic thought", "Hyperinflation", "IS\u2013LM model", "ITraxx", "Index of economics articles", "Indexation", "Indifference curve", "Industrial organization", "Inflation", "Input\u2013output model", "Institutional economics", "Interest", "Interest rate", "International Monetary Fund", "International Standard Book Number", "International economics", "International organization", "Intertemporal choice", "Investment (macroeconomics)", "JEL classification codes", "Jacob Marschak", "Job index", "John Eatwell, Baron Eatwell", "John Maynard Keynes", "John von Neumann", "Joseph Schumpeter", "Karl Marx", "Kenneth Arrow", "Keynesian economics", "Knowledge economy", "Labour economics", "Labour market index", "Lausanne School", "Law and economics", "Library of Congress Control Number", "List of important publications in economics", "List of stock market indices", "L\u00e9on Walras", "MSCI EAFE", "MSCI Inc.", "MSCI World", "Macroeconomics", "Mainstream economics", "Malthusianism", "Marginal cost", "Marginal utility", "Marginalism", "Market (economics)", "Market failure", "Market structure", "Markit Group Limited", "Marxian economics", "Mathematical economics", "Mathematical finance", "Measures of national income and output", "Mechanism design", "Mercantilism", "Microeconomics", "Microfoundations", "Milton Friedman", "Monetary economics", "Monetary policy", "Money", "Money supply", "Monopolistic competition", "Monopoly", "Monopsony", "Mutualism (economic theory)", "NAIRU", "NASDAQ Composite", "National Diet Library", "National accounts", "Natural resource economics", "Neo-Keynesian economics", "Neo-Marxian economics", "Neoclassical economics", "New Keynesian economics", "New classical macroeconomics", "New institutional economics", "Non-convexity (economics)", "Number", "OECD", "Oligopoly", "Oligopsony", "Operations research", "Opportunity cost", "Outline of economics", "Pareto efficiency", "Paul Krugman", "Paul Samuelson", "Perfect competition", "Physiocracy", "Political economy", "Post-Keynesian economics", "Preference (economics)", "Price", "Price index", "Price level", "Producer price index", "Production set", "Profit (economics)", "Public choice", "Public economics", "Public good", "Purchasing power parity", "Ragnar Frisch", "Rate of profit", "Ratio", "Rational expectations", "Rationing", "Real business-cycle theory", "Recession", "Regional economics", "Retail price", "Returns to scale", "Reuters", "Reuters-CRB Index", "Richard Thaler", "Risk aversion", "Robert Lucas Jr.", "Robert Solow", "Russell 1000 Index", "Russell 2000 Index", "Russell 3000 Index", "Russell Investments", "Russell Midcap Index", "S&P/ASX 200", "S&P/TSX Composite Index", "S&P 1500", "S&P 400", "S&P 500", "S&P 600", "S&P Global 1200", "S&P Leveraged Loan Index", "STOXX", "STOXX Europe 50", "STOXX Europe 600", "Saving", "Scarcity", "Schools of economic thought", "Service economy", "Shortage", "Shrinkflation", "Social choice theory", "Social cost", "Socialist economics", "Socioeconomics", "Stagflation", "Standard & Poor's", "Stock market index", "Stockholm school (economics)", "Sunk cost", "Supply-side economics", "Supply and demand", "Supply shock", "The Economist", "The General Theory of Employment, Interest and Money", "The New Palgrave: A Dictionary of Economics", "Theory of the firm", "Thermoeconomics", "Time series", "Tjalling Koopmans", "Trade", "Transaction cost", "Transport economics", "USD", "Uncertainty", "Unemployment", "Urban economics", "Utility", "Value (economics)", "Vilfredo Pareto", "Wage", "Welfare economics", "World Bank", "World Trade Organization"], "references": ["http://www.djindexes.com/", "http://www.investopedia.com/university/indexes/index1.asp", "http://www.kroijer.com", "http://www.oanda.com/currency/big-mac-index", "http://www.politonomist.com/gdp-deflator-and-measuring-inflation-00491/", "http://www.sgindex.com/", "http://www2.standardandpoors.com/portal/site/sp/en/us/page.category/indices/2,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0.html?lid=us_topnav_indicies", "http://www.humboldt.edu/~indexhum/", "https://books.google.com/books?id=HOqcFW9b5VoC&pg=PA11&dq=Superlative+index+number&as_brr=3&sig=0pz8BjGjaNoB-HEPK8o09xOH57Q#PPA11,M1", "https://id.loc.gov/authorities/subjects/sh85064859", "https://id.ndl.go.jp/auth/ndlna/00565457", "https://web.archive.org/web/20090117035026/http://www.politonomist.com/gdp-deflator-and-measuring-inflation-00491/", "https://www.wikidata.org/wiki/Q2272475"]}, "Randomized response": {"categories": ["Survey methodology"], "title": "Randomized response", "method": "Randomized response", "url": "https://en.wikipedia.org/wiki/Randomized_response", "summary": "Randomised response is a research method used in structured survey interview. It was first proposed by S. L. Warner in 1965 and later modified by B. G. Greenberg in 1969. It allows respondents to respond to sensitive issues (such as criminal behavior or sexuality) while maintaining confidentiality. Chance decides, unknown to the interviewer, whether the question is to be answered truthfully, or \"yes\", regardless of the truth.\nFor example, social scientists have used it to ask people whether they use drugs, whether they have illegally installed telephones, or whether they have evaded paying taxes. Before abortions were legal, social scientists used the method to ask women whether they have had abortions.\nThe concept is somewhat similar to plausible deniability. Plausible deniability allows the subject to credibly say he did not make a statement, while the randomized response technique allows the subject to credibly say he had not been truthful when making a statement.\n\n", "images": [], "links": ["Abortion", "Bogus pipeline", "Dichotomy", "Differential privacy", "Digital object identifier", "JSTOR", "Journal of the American Statistical Association", "Law of large numbers", "Plausible deniability", "Prostitute", "Survey research", "Taylor & Francis", "Unmatched count"], "references": ["http://doi.org/10.1080%2F01621459.1965.10480775", "http://doi.org/10.2307%2F2283636", "http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6883988&queryText%3Daoki+sezaki", "http://www.jstor.org/stable/2283137", "http://www.jstor.org/stable/2283636", "http://www.cl.cam.ac.uk/~dq209/publications/spotme.pdf", "https://books.google.com/books?hl=de&lr=&id=ieKmQUgYvCgC&oi=fnd&pg=PR5&dq=boruch%2B1971%2Brandomized%2Bresponse&ots=XVpzeJDjlK&sig=xPkZC2aHHXwfuzVQa6zBZW8G1io#v=onepage&q=&f=false"]}, "Order of a kernel": {"categories": ["All stub articles", "Nonparametric statistics", "Statistics stubs"], "title": "Order of a kernel", "method": "Order of a kernel", "url": "https://en.wikipedia.org/wiki/Order_of_a_kernel", "summary": "In statistics, the order of a kernel is the degree of the first non-zero moment of a kernel.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/df/Bellcurve.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/d/df/20111024150224%21Bellcurve.svg"], "links": ["International Standard Book Number", "Kernel (statistics)", "Moment (mathematics)", "Statistics"], "references": ["https://books.google.com/books?id=Zsa7ofamTIUC&pg=PT63"]}, "Repeated measures design": {"categories": ["All articles covered by WikiProject Wikify", "All pages needing cleanup", "Analysis of variance", "Articles covered by WikiProject Wikify from August 2017", "CS1 maint: Uses editors parameter", "Design of experiments", "Science experiments", "Wikipedia introduction cleanup from August 2017"], "title": "Repeated measures design", "method": "Repeated measures design", "url": "https://en.wikipedia.org/wiki/Repeated_measures_design", "summary": "Repeated measures design uses the same subjects with every branch of research, including the control. For instance, repeated measurements are collected in a longitudinal study in which change over time is assessed. Other (non-repeated measures) studies compare the same measure under two or more different conditions. For instance, to test the effects of caffeine on cognitive function, a subject's math ability might be tested once after they consume caffeine and another time when they consume a placebo.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Academic discipline", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blind experiment", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Clinical trial protocol", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Controlled experiment", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover design", "Crossover studies", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Education", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Experimental unit", "Exponential family", "Exponential smoothing", "External validity", "F-test", "F statistic", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Fractional factorial design", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Growth curve (statistics)", "Harmonic mean", "Health-care", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear model", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Longitudinal study", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Marie Davidian", "Mauchly's sphericity test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mixed models", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Nuisance variable", "Observational studies", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Panel analysis", "Panel data", "Panel study", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pharmaceutical science", "Pie chart", "Pivotal quantity", "Placebo", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Poisson regression", "Polynomial and rational function modeling", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychology", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Standard treatment", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "Tuple", "Type 1 error", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.experiment-resources.com/repeated-measures-design.html#ixzz1cl4ahmlq", "http://biostat.mc.vanderbilt.edu/twiki/pub/Main/ClinStat/repmeas.PDF", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3764084", "http://www.ncbi.nlm.nih.gov/pubmed/24004855", "http://ericae.net/ft/tamu/Rm.htm", "http://doi.org/10.1001%2Farchpsyc.61.3.310", "http://doi.org/10.1002%2Fsim.4780121807", "http://doi.org/10.1037%2F1082-989x.8.4.434", "http://doi.org/10.1080%2F01621459.1989.10478802", "http://doi.org/10.1111%2Fj.1469-8986.1987.tb00324.x", "http://doi.org/10.1177%2F1099800404267682", "http://doi.org/10.1289%2Fehp.121-A282", "http://doi.org/10.3758%2Fbf03192707", "http://www.southampton.ac.uk/~cpd/anovas/datasets/index.htm", "https://www.researchgate.net/publication/256484739_Retina_mirovasculature_in_Science_selection_in_EHP"]}, "Discrete choice": {"categories": ["Choice modelling", "Economics models", "Mathematical and quantitative methods (economics)"], "title": "Discrete choice", "method": "Discrete choice", "url": "https://en.wikipedia.org/wiki/Discrete_choice", "summary": "In economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives, such as entering or not entering the labor market, or choosing between modes of transport. Such choices contrast with standard consumption models in which the quantity of each good consumed is assumed to be a continuous variable. In the continuous case, calculus methods (e.g. first-order conditions) can be used to determine the optimum amount chosen, and demand can be modeled empirically using regression analysis. On the other hand, discrete choice analysis examines situations in which the potential outcomes are discrete, such that the optimum is not characterized by standard first-order conditions. Thus, instead of examining \u201chow much\u201d as in problems with continuous choice variables, discrete choice analysis examines \u201cwhich one.\u201d However, discrete choice analysis can also be used to examine the chosen quantity when only a few distinct quantities must be chosen from, such as the number of vehicles a household chooses to own and the number of minutes of telecommunications service a customer decides to purchase. Techniques such as logistic regression and probit regression can be used for empirical analysis of discrete choice.\nEstimation of such models is usually done via parametric, semi-parametric and non-parametric maximum likelihood methods.Discrete choice models theoretically or empirically model choices made by people among a finite set of alternatives. The models have been used to examine, e.g., the choice of which car to buy, where to go to college, which mode of transport (car, bus, rail) to take to work among numerous other applications. Discrete choice models are also used to examine choices by organizations, such as firms or government agencies. In the discussion below, the decision-making unit is assumed to be a person, though the concepts are applicable more generally. Daniel McFadden won the Nobel prize in 2000 for his pioneering work in developing the theoretical basis for discrete choice.\nDiscrete choice models statistically relate the choice made by each person to the attributes of the person and the attributes of the alternatives available to the person. For example, the choice of which car a person buys is statistically related to the person\u2019s income and age as well as to price, fuel efficiency, size, and other attributes of each available car. The models estimate the probability that a person chooses a particular alternative. The models are often used to forecast how people\u2019s choices will change under changes in demographics and/or attributes of the alternatives.\nDiscrete choice models specify the probability that an individual chooses an option among a set of alternatives. The probabilistic description of discrete choice behavior is used not to reflect individual behavior that is viewed as intrinsically probabilistic. Rather, it is the lack of information that leads us to describe choice in a probabilistic fashion. In practice, we cannot know all factors affecting individual choice decisions as their determinants are partially observed or imperfectly measured. Therefore, discrete choice models rely on stochastic assumptions and specifications to account for unobserved factors related to a) choice alternatives, b) taste variation over people (interpersonal heterogeneity) and over time (intra-individual choice dynamics), and c) heterogeneous choice sets. The different formulations have been summarized and classified into groups of models.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/3a/Linear_regression.svg"], "links": ["Artelys Knitro", "Bayesian linear regression", "Bayesian multivariate linear regression", "Bellman equation", "Charles F. Manski", "Collectively exhaustive events", "Constrained optimization", "Consumer theory", "Continuous variable", "Counterfactual conditional", "Cumulative normal", "Daniel McFadden", "Demand curve", "Digital object identifier", "Discounting", "Discrete variable", "Dynamic programming", "Econometrica", "Economics", "Errors-in-variables models", "Errors and residuals in statistics", "Extreme value distribution", "Fixed effects model", "G. S. Maddala", "Gauss\u2013Markov theorem", "General linear model", "Generalized extreme value distribution", "Generalized least squares", "Generalized linear model", "Goodness of fit", "Gumbel distribution", "Heteroscedasticity", "Iid", "Independence of irrelevant alternatives", "Initial condition", "International Economic Review", "International Standard Book Number", "International Standard Serial Number", "Isotonic regression", "Iteratively reweighted least squares", "JSTOR", "Jerry Hausman", "John Rust", "Journal of Applied Econometrics", "Journal of Econometrics", "Journal of Human Resources", "Kenneth E. Train", "Kenneth Judd", "Kronecker delta", "Labor market", "Least-angle regression", "Least absolute deviations", "Least squares", "Linear least squares", "Linear regression", "Local regression", "Logistic distribution", "Logistic function", "Logistic regression", "Markov chain", "Markov decision process", "Maximum likelihood estimation", "Mean and predicted response", "Method of simulated moments", "Mixed logit", "Mixed model", "Multilevel model", "Multinomial logit", "Multinomial probit", "Mutual exclusivity", "New product development", "Nobel Memorial Prize in Economic Sciences", "Non-linear least squares", "Non-negative least squares", "Nonlinear regression", "Nonparametric regression", "Normal distribution", "Ordered logit", "Ordered probit", "Ordinary least squares", "Partial least squares regression", "Plackett\u2013Luce model", "Poisson regression", "Polynomial regression", "Polytomous choice", "Present value", "Pricing", "Principal component regression", "Probit model", "Probit regression", "Quantile regression", "Random effects model", "Rapid transit", "Regression analysis", "Regression model validation", "Regularized least squares", "Review of Economics and Statistics", "Robust regression", "Scion (automobile)", "Segmented regression", "Semiparametric regression", "Simple linear regression", "State variable", "Statistics", "Structural estimation", "Studentized residual", "Tikhonov regularization", "Time horizon", "Total least squares", "Transport", "Utility theory", "Weighted least squares", "William Greene (economist)"], "references": ["http://roso.epfl.ch/mbi/handbook-final.pdf", "http://trb.metapress.com/content/126847136p81w0p3/", "http://trb.metapress.com/content/l341607q38j850j7/", "http://www.sciencedirect.com/science/article/pii/S0167947316302596", "http://www2.informatik.hu-berlin.de/alkox/lehre/lvws0809/verkehr/logit.pdf", "http://elsa.berkeley.edu/choice2/ch5.pdf", "http://elsa.berkeley.edu/choice2/ch6.pdf", "http://elsa.berkeley.edu/reprints/misc/multinomial.pdf", "http://elsa.berkeley.edu/wp/mcfadden1198/mcfadden1198.pdf", "http://elsa.berkeley.edu/~train/valtrb.pdf", "http://emlab.berkeley.edu/books/choice.html", "http://dspace.mit.edu/handle/1721.1/49797", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.4879", "http://cowles.econ.yale.edu/P/cd/d04b/d0477.pdf", "http://doi.org/10.1002%2F1099-1255(200009%2F10)15:5%3C447::AID-JAE570%3E3.0.CO;2-1", "http://doi.org/10.1016%2F0041-1647(78)90120-x", "http://doi.org/10.1016%2F0304-4076(81)90056-7", "http://doi.org/10.1016%2FS0148-2963(99)00058-2", "http://doi.org/10.1016%2Fj.csda.2016.10.024", "http://doi.org/10.1016%2Fj.labeco.2007.04.003", "http://doi.org/10.1016%2Fj.red.2008.07.001", "http://doi.org/10.1016%2Fj.ssci.2013.10.004", "http://doi.org/10.1111%2Fj.1468-2354.2007.00471.x", "http://doi.org/10.1162%2F003465398557735", "http://doi.org/10.2307%2F1911259", "http://doi.org/10.2307%2F2298122", "http://doi.org/10.2307%2F3147053", "http://doi.org/10.3141%2F1805-10", "http://doi.org/10.3982%2FECTA12605", "http://doi.org/10.3982%2FECTA7925", "http://dx.doi.org/10.2307/2298122", "http://www.jstor.org/stable/145612", "http://www.jstor.org/stable/1911259", "http://www.jstor.org/stable/1913909", "http://www.jstor.org/stable/2346567", "http://www.jstor.org/stable/2555538", "http://www.jstor.org/stable/2646846", "http://www.worldcat.org/issn/0012-9682", "http://www.worldcat.org/issn/1468-0262", "https://editorialexpress.com/jrust/nfxp.html", "https://archive.is/20120717185534/http://trb.metapress.com/content/126847136p81w0p3/", "https://archive.is/20130129010708/http://trb.metapress.com/content/l341607q38j850j7/", "https://doi.org/10.3982/ECTA12605", "https://dx.doi.org/10.3982/ECTA7925"]}, "Pivotal quantity": {"categories": ["Statistical theory"], "title": "Pivotal quantity", "method": "Pivotal quantity", "url": "https://en.wikipedia.org/wiki/Pivotal_quantity", "summary": "In statistics, a pivotal quantity or pivot is a function of observations and unobservable parameters such that the function's probability distribution does not depend on the unknown parameters (including nuisance parameters). A pivot quantity need not be a statistic\u2014the function and its value can depend on the parameters of the model, but its distribution must not. If it is a statistic, then it is known as an ancillary statistic.\nMore formally, let \n \n \n \n X\n =\n (\n \n X\n \n 1\n \n \n ,\n \n X\n \n 2\n \n \n ,\n \u2026\n ,\n \n X\n \n n\n \n \n )\n \n \n {\\displaystyle X=(X_{1},X_{2},\\ldots ,X_{n})}\n be a random sample from a distribution that depends on a parameter (or vector of parameters) \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n . Let \n \n \n \n g\n (\n X\n ,\n \u03b8\n )\n \n \n {\\displaystyle g(X,\\theta )}\n be a random variable whose distribution is the same for all \n \n \n \n \u03b8\n \n \n {\\displaystyle \\theta }\n . Then \n \n \n \n g\n \n \n {\\displaystyle g}\n is called a pivotal quantity (or simply a pivot).\nPivotal quantities are commonly used for normalization to allow data from different data sets to be compared. It is relatively easy to construct pivots for location and scale parameters: for the former we form differences so that location cancels, for the latter ratios so that scale cancels.\nPivotal quantities are fundamental to the construction of test statistics, as they allow the statistic to not depend on parameters \u2013 for example, Student's t-statistic is for a normal distribution with unknown variance (and mean). They also provide one method of constructing confidence intervals, and the use of pivotal quantities improves performance of the bootstrap. In the form of ancillary statistics, they can be used to construct frequentist prediction intervals (predictive confidence intervals).\n\n", "images": [], "links": ["Ancillary statistic", "Asymptotic normality", "Bootstrapping (statistics)", "Confidence interval", "Correlation", "Fisher transformation", "International Standard Book Number", "Normal distribution", "Normalization (statistics)", "Nuisance parameter", "Parameter", "Prediction interval", "Probability distribution", "Robust statistics", "Sample variance", "Statistic", "Statistics", "Student's t-distribution", "Student's t-statistic", "Test statistic", "Variance-stabilizing transformation", "Z-score"], "references": ["https://books.google.com/books?id=_bEPBwAAQBAJ&pg=PA471"]}, "List of national and international statistical services": {"categories": ["All articles with dead external links", "Articles with French-language external links", "Articles with Japanese-language external links", "Articles with dead external links from January 2018", "Articles with permanently dead external links", "Demography", "Lists of government agencies", "National statistical services", "Official statistics", "Statistics-related lists"], "title": "List of national and international statistical services", "method": "List of national and international statistical services", "url": "https://en.wikipedia.org/wiki/List_of_national_and_international_statistical_services", "summary": "The following is a list of national and international statistical services.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/9a/Flag_of_Afghanistan.svg", "https://upload.wikimedia.org/wikipedia/commons/3/36/Flag_of_Albania.svg", "https://upload.wikimedia.org/wikipedia/commons/7/77/Flag_of_Algeria.svg", "https://upload.wikimedia.org/wikipedia/commons/1/19/Flag_of_Andorra.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9d/Flag_of_Angola.svg", "https://upload.wikimedia.org/wikipedia/commons/8/89/Flag_of_Antigua_and_Barbuda.svg", 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"https://web.archive.org/web/20160930004308/http://stat.gov.sx/", "https://web.archive.org/web/20171019205734/http://web.dos.gov.jo/", "https://www.gmm-mercosul.org/selecionarTema?x=XNZKsPGJUz1EMCAh3JYNTfkd822f1-yGdrTm9RewcoGJ*7flyiAZgw", "https://www.un.org/en/development/desa/index.html", "https://www.un.org/popin/", "https://www.unescwa.org/our-work/statistics", "https://unhabitat.org/urban-knowledge/", "https://www.unido.org/researchers/statistical-databases", "https://psa.gov.ph", "https://www.stats.gov.sa/en/", "https://www.stat.gov.tw", "https://www.ons.gov.uk"]}, "Optional stopping theorem": {"categories": ["All articles needing additional references", "Articles containing proofs", "Articles needing additional references from February 2012", "CS1 maint: Archived copy as title", "Martingale theory", "Probability theorems", "Statistical theorems"], "title": "Optional stopping theorem", "method": "Optional stopping theorem", "url": "https://en.wikipedia.org/wiki/Optional_stopping_theorem", "summary": "In probability theory, the optional stopping theorem (or Doob's optional sampling theorem) says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value. Since martingales can be used to model the wealth of a gambler participating in a fair game, the optional stopping theorem says that, on average, nothing can be gained by stopping play based on the information obtainable so far (i.e., without looking into the future). Certain conditions are necessary for this result to hold true. In particular, the theorem applies to doubling strategies.\nThe optional stopping theorem is an important tool of mathematical finance in the context of the fundamental theorem of asset pricing.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Almost surely", "Conditional expectation", "Dominated convergence theorem", "Expected value", "Filtration (probability theory)", "Fundamental theorem of asset pricing", "International Standard Book Number", "Join and meet", "Joseph L. Doob", "Markov chain", "Martingale (betting system)", "Martingale (probability theory)", "Martingale convergence theorem", "Mathematical constant", "Mathematical finance", "Monotone convergence theorem", "Probability theory", "Random walk", "Stopped process", "Stopping time", "Submartingale", "Supermartingale"], "references": ["http://math.mit.edu/~sheffield/martingalenote.pdf", "https://www.scribd.com/doc/28125042/Unit-Betting-System", "https://web.archive.org/web/20160305022324/https://www.scribd.com/doc/28125042/Unit-Betting-System"]}, "Elastic map": {"categories": ["Data mining", "Dimension reduction"], "title": "Elastic map", "method": "Elastic map", "url": "https://en.wikipedia.org/wiki/Elastic_map", "summary": "Elastic maps provide a tool for nonlinear dimensionality reduction. By their construction, they are a system of elastic springs embedded in the data\nspace. This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructured k-means clustering (zero elasticity) to the estimators located closely to linear PCA manifolds (for high bending and low stretching modules). With some intermediate values of the elasticity coefficients, this system effectively approximates non-linear principal manifolds. This approach is based on a mechanical analogy between principal manifolds, that are passing through \"the middle\" of the data distribution, and elastic membranes and plates. The method was developed by A.N. Gorban, A.Y. Zinovyev and A.A. Pitenko in 1996\u20131998.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/84/Elmap_breastcancer_wiki.png", "https://upload.wikimedia.org/wikipedia/commons/4/48/SlideQualityLife.png"], "links": ["Alexander Nikolaevich Gorban", "Artificial neural network", "Backpropagation", "Breast cancer", "Curie Institute (Paris)", "Elastic net", "Elastic net regularization", "Elasticity coefficient", "Euclidean space", "Expectation-maximization algorithm", "Financial portfolio", "Geodesic", "Gross domestic product", "Independent Component Analysis", "Infant mortality", "Institut des Hautes \u00c9tudes Scientifiques", "International Journal of Neural Systems", "International Standard Book Number", "K-means", "K-means clustering", "Life expectancy", "Machine learning", "Mechanical equilibrium", "Mechanics", "Microarray", "Multiphase flow", "Nonlinear dimensionality reduction", "Principal Component Analysis", "Principal component analysis", "Probability density function", "Scientific visualization", "Self-organizing map", "Spring (device)", "Standard deviation", "Support vector machine", "Trichomes", "Tuberculosis", "United Nations"], "references": ["http://knowledge.sagepub.com/view/intlpoliticalscience/n129.xml", "http://www.sciencedirect.com/science/article/pii/S0301932214000159", "http://www.springerlink.com/content/6416210h727016t5/", "http://bioinfo-out.curie.fr/projects/vidaexpert/", "http://www.ihes.fr", "http://www.ihes.fr/~zinovyev", "http://www.ihes.fr/~zinovyev/princmanif2006/", "http://www.ihes.fr/~zinovyev/vida/ViDaExpert/ViDaOverView.pdf", "http://www.ploscompbiol.org/article/info:doi%2F10.1371%2Fjournal.pcbi.1003029#pcbi-1003029-g005", "http://pca.narod.ru/ElNetChakon.pdf", "http://pca.narod.ru/contentsgkwz.htm", "https://www.springer.com/gp/book/9783319214399", "https://arxiv.org/abs/0809.0490", "https://arxiv.org/abs/1001.1122", "https://arxiv.org/abs/1008.1188", "https://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.08.012"]}, "Infinite divisibility (probability)": {"categories": ["Infinitely divisible probability distributions", "Theory of probability distributions", "Types of probability distributions"], "title": "Infinite divisibility (probability)", "method": "Infinite divisibility (probability)", "url": "https://en.wikipedia.org/wiki/Infinite_divisibility_(probability)", "summary": "In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distributed random variables. The characteristic function of any infinitely divisible distribution is then called an infinitely divisible characteristic function.More rigorously, the probability distribution F is infinitely divisible if, for every positive integer n, there exist n independent identically distributed random variables Xn1, ..., Xnn whose sum Sn = Xn1 + \u2026 + Xnn has the distribution F.\nThe concept of infinite divisibility of probability distributions was introduced in 1929 by Bruno de Finetti. This type of decomposition of a distribution is used in probability and statistics to find families of probability distributions that might be natural choices for certain models or applications. Infinitely divisible distributions play an important role in probability theory in the context of limit theorems.\n\n", "images": [], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Bruno de Finetti", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Central limit theorem", "Characteristic function (probability theory)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Convergence in distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cram\u00e9r\u2019s decomposition theorem", "Dagum distribution", "Davis distribution", "Decomposable distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Discrete Weibull distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "Indecomposable distribution", "Independent and identically distributed random variables", "Independent increments", "International Standard Book Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irrational number", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "L\u00e9vy process", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poisson limit theorem", "Poly-Weibull distribution", "Probability", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rational number", "Rayleigh distribution", "Reciprocal distribution", "Rectified Gaussian distribution", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Statistical independence", "Statistics", "Stochastic process", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular array", "Triangular distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Variance", "Variance-gamma distribution", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["https://doi.org/10.1016%2Fj.spl.2006.09.014"]}, "B\u00fchlmann model": {"categories": ["Actuarial science", "All articles lacking in-text citations", "Analysis of variance", "Articles lacking in-text citations from October 2010"], "title": "B\u00fchlmann model", "method": "B\u00fchlmann model", "url": "https://en.wikipedia.org/wiki/B%C3%BChlmann_model", "summary": "In credibility theory, a branch of study in actuarial science, the B\u00fchlmann model is a random effects model (or \"variance components model\" or hierarchical linear model) used in to determine the appropriate premium for a group of insurance contracts. The model is named after Hans B\u00fchlmann who first published a description in 1967.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Abstract Wiener space", "Actuarial mathematics", "Actuarial science", "Arg min", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Bernoulli process", "Bessel process", "Biased random walk on a graph", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Bulk queue", "Burkholder\u2013Davis\u2013Gundy inequalities", "Cameron\u2013Martin formula", "Cauchy process", "Central limit theorem", "Chen model", "Chinese restaurant process", "Classical Wiener space", "Compound Poisson process", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous stochastic process", "Convergence of random variables", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Credibility theory", "C\u00e0dl\u00e0g", "Diffusion process", "Digital object identifier", "Dirichlet process", "Discrete-time stochastic process", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynkin's formula", "Econometrics", "Empirical process", "Ergodic theorem", "Ergodic theory", "Ergodicity", "Exchangeable random variables", "Extreme value theory", "Feller-continuous process", "Feller process", "Feynman\u2013Kac formula", "Filtration (probability theory)", "Fisher\u2013Tippett\u2013Gnedenko theorem", "Fleming\u2013Viot process", "Fluid queue", "Fractional Brownian motion", "G-network", "Galton\u2013Watson process", "Galves\u2013L\u00f6cherbach model", "Gamma process", "Garman\u2013Kohlhagen model", "Gaussian process", "Gaussian random field", "Gauss\u2013Markov process", "Geometric Brownian motion", "Gibbs measure", "Girsanov theorem", "Heath\u2013Jarrow\u2013Morton framework", "Heston model", "Hidden Markov model", "Hierarchical linear model", "Hopfield model", "Ho\u2013Lee model", "Hull\u2013White model", "Hunt process", "Independent and identically distributed", "Independent and identically distributed random variables", "Infinitesimal generator (stochastic processes)", "Insurance premium", "Interacting particle system", "Ising model", "It\u00f4's lemma", "It\u00f4 diffusion", "It\u00f4 integral", "It\u00f4 process", "Jump diffusion", "Jump process", "Kolmogorov continuity theorem", "Kolmogorov extension theorem", "Kunita\u2013Watanabe inequality", "LIBOR market model", "Large deviation principle", "Large deviations theory", "Law of large numbers", "Law of the iterated logarithm", "List of inequalities", "List of stochastic processes topics", "Local martingale", "Local time (mathematics)", "Loop-erased random walk", "L\u00e9vy process", "L\u00e9vy\u2013Prokhorov metric", "M/G/1 queue", "M/M/1 queue", "M/M/c queue", "Machine learning", "Malliavin calculus", "Markov additive process", "Markov chain", "Markov process", "Markov property", "Markov random field", "Martingale (probability theory)", "Martingale difference sequence", "Martingale representation theorem", "Mathematical finance", "Mathematical statistics", "Maximal Entropy Random Walk", "Maximal ergodic theorem", "McKean\u2013Vlasov process", "Mixing (mathematics)", "Moran process", "Moving-average model", "Non-homogeneous Poisson process", "Optional stopping theorem", "Ornstein\u2013Uhlenbeck process", "Percolation theory", "Piecewise deterministic Markov process", "Pitman\u2013Yor process", "Point process", "Poisson point process", "Poisson process", "Potts model", "Predictable process", "Probability theory", "Progressively measurable process", "Prokhorov's theorem", "Quadratic variation", "Queueing model", "Queueing theory", "Random dynamical system", "Random effects model", "Random field", "Random graph", "Random walk", "Reflection principle (Wiener process)", "Regenerative process", "Rendleman\u2013Bartter model", "Renewal process", "Renewal theory", "Risk process", "Ruin theory", "SABR volatility model", "Sample-continuous process", "Sanov's theorem", "Schramm\u2013Loewner evolution", "Self-avoiding walk", "Self-similar process", "Semimartingale", "Sigma-martingale", "Skorokhod's representation theorem", "Skorokhod integral", "Skorokhod space", "Snell envelope", "Sparre\u2013Anderson model", "Stable process", "Stationary process", "Statistics", "Stochastic analysis", "Stochastic chains with memory of variable length", "Stochastic differential equation", "Stochastic process", "Stopping time", "Stratonovich integral", "Submartingale", "Supermartingale", "Superprocess", "System on a chip", "Tanaka equation", "Telegraph process", "Time reversibility", "Time series", "Time series analysis", "Uniform integrability", "Usual hypotheses", "Variance gamma process", "Vasicek model", "White noise", "Wiener process", "Wiener sausage", "Wiener space", "Wilkie investment model"], "references": ["http://www.math.ku.dk/~schmidli/rt.pdf", "http://www.casact.org/library/astin/vol4no3/199.pdf", "http://doi.org/10.1016%2FS0167-6687(98)00055-9", "https://web.archive.org/web/20130811041617/http://www.math.ku.dk/~schmidli/rt.pdf"]}, "Truncated mean": {"categories": ["All articles needing additional references", "All articles with unsourced statements", "Articles needing additional references from July 2010", "Articles with unsourced statements from October 2016", "Means", "Robust statistics"], "title": "Truncated mean", "method": "Truncated mean", "url": "https://en.wikipedia.org/wiki/Truncated_mean", "summary": "A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both. This number of points to be discarded is usually given as a percentage of the total number of points, but may also be given as a fixed number of points.\nFor most statistical applications, 5 to 25 percent of the ends are discarded; the 25% trimmed mean (when the lowest 25% and the highest 25% are discarded) is known as the interquartile mean. For example, given a set of 8 points, trimming by 12.5% would discard the minimum and maximum value in the sample: the smallest and largest values, and would compute the mean of the remaining 6 points. \nThe median can be regarded as a fully truncated mean and is most robust. As with other trimmed estimators, the main advantage of the trimmed mean is robustness and higher efficiency for mixed distributions and heavy-tailed distribution (like the Cauchy distribution), at the cost of lower efficiency for some other less heavily-tailed distributions (such as the normal distribution). For intermediate distributions the differences between the efficiency of the mean and the median are not very big, e.g. for the student-t distribution with 2 degrees of freedom the variances for mean and median are nearly equal.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Average", "Average Crop Revenue Election", "Bias of an estimator", "Cauchy distribution", "Central Europe", "Digital object identifier", "Efficiency (statistics)", "Figure skating", "ISU Judging System", "Interquartile mean", "JSTOR", "Libor", "Location parameter", "Maximum likelihood", "Mean", "Median", "Normal distribution", "Order statistics", "Outlier", "Probability distribution", "R (programming language)", "Robust statistics", "Sample (statistics)", "Sampling (statistics)", "Sport", "Statistics", "Student's t-test", "Symmetry", "Trimean", "Trimmed estimator", "Weighted average", "Winsorising", "Winsorized mean"], "references": ["http://www.bbalibor.com/explained/the-basics", "http://farmdocdaily.illinois.edu/2012/08/lessons_from_libor.html", "http://doi.org/10.1080%2F01621459.1964.10482170", "http://doi.org/10.1080%2F01621459.1966.10480912", "http://doi.org/10.1080%2F01621459.1978.10480031", "http://www.jstor.org/stable/2282794", "http://www.jstor.org/stable/2286549", "https://books.google.com/books?id=2qcyNld-bHwC&pg=PA458&lpg=PA458&dq=Modified+mean", "https://online.wsj.com/news/articles/SB10000872396390443477104577551253521597214", "https://cran.r-project.org/web/packages/DescTools/", "https://cran.r-project.org/web/packages/WRS2/"]}, "Fisher's linear discriminator": {"categories": ["All articles with dead external links", "Articles with dead external links from December 2017", "Articles with permanently dead external links", "CS1 maint: Archived copy as title", "Classification algorithms", "Market research", "Market segmentation", "Statistical classification", "Wikipedia articles needing clarification from April 2012", "Wikipedia articles needing page number citations from April 2012"], "title": "Linear discriminant analysis", "method": "Fisher's linear discriminator", "url": "https://en.wikipedia.org/wiki/Linear_discriminant_analysis", "summary": "Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.\nLDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (i.e. the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain a categorical variable by the values of continuous independent variables. These other methods are preferable in applications where it is not reasonable to assume that the independent variables are normally distributed, which is a fundamental assumption of the LDA method.\nLDA is also closely related to principal component analysis (PCA) and factor analysis in that they both look for linear combinations of variables which best explain the data. LDA explicitly attempts to model the difference between the classes of data. PCA on the other hand does not take into account any difference in class, and factor analysis builds the feature combinations based on differences rather than similarities. Discriminant analysis is also different from factor analysis in that it is not an interdependence technique: a distinction between independent variables and dependent variables (also called criterion variables) must be made.\nLDA works when the measurements made on independent variables for each observation are continuous quantities. When dealing with categorical independent variables, the equivalent technique is discriminant correspondence analysis.Discriminant analysis is used when groups are known a priori (unlike in cluster analysis). Each case must have a score on one or more quantitative predictor measures, and a score on a group measure. In simple terms, discriminant function analysis is classification - the act of distributing things into groups, classes or categories of the same type.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fe/Kernel_Machine.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/4/46/R._A._Fischer.jpg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ANOVA", "Accelerated failure time model", "Actuarial science", "Affine transformation", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Annals of Eugenics", "Anomaly detection", "ArXiv", "Arithmetic mean", "Artificial intelligence", "Artificial neural network", "Artificial neural networks", "Association rule learning", "Asymptotic theory (statistics)", "Autocorrelation", "Autoencoder", "Automated machine learning", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "BIRCH", "Bankruptcy prediction", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian network", "Bayesian probability", "Bias-variance dilemma", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Boosting (machine learning)", "Bootstrap aggregating", "Bootstrapping (statistics)", "Box's M test", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Brian Ripley", "C. R. Rao", "CURE data clustering algorithm", "Calyampudi Radhakrishna Rao", "Canonical coordinates", "Canonical correlation", "Canonical correlation analysis", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Computational learning theory", "Concentration of measure", "Conditional random field", "Conference on Neural Information Processing Systems", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous variable", "Control chart", "Convolutional neural network", "Correlation and dependence", "Correlogram", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Curse of dimensionality", "DBSCAN", "Data collection", "Data mining", "Decision tree learning", "Decomposition of time series", "DeepDream", "Deep learning", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent variable", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Dimension reduction", "Dimensionality reduction", "Divergence (statistics)", "Dot product", "Durbin\u2013Watson statistic", "Econometrics", "Edward Altman", "Effect size", "Efficiency (statistics)", "Eigenfaces", "Eigenvalue", "Eigenvalue, eigenvector and eigenspace", "Eigenvalues and eigenvectors", "Eigenvector", "Elliptical distribution", "Empirical distribution function", "Empirical risk minimization", "Engineering statistics", "Ensemble learning", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Expectation\u2013maximization algorithm", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Facial recognition system", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "Feature engineering", "Feature learning", "Features (pattern recognition)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "Gated recurrent unit", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of artificial intelligence", "Goodness of fit", "Grammar induction", "Granger causality", "Graphical model", "Grouped data", "Handle System", "Harmonic mean", "Hermitian matrix", "Heteroscedasticity", "Hidden Markov model", "Hierarchical clustering", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedastic", "Homoscedasticity", "Hyperplane", "IEEE Transactions on Pattern Analysis and Machine Intelligence", "Independent component analysis", "Independent variables", "Index of dispersion", "Instrumental variable", "Interaction (statistics)", "International Conference on Machine Learning", "International Standard Book Number", "International Standard Serial Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of Machine Learning Research", "Journal of the American Statistical Association", "K-means clustering", "K-nearest neighbors algorithm", "K-nearest neighbors classification", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kernel Fisher discriminant analysis", "Kernel trick", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latent Dirichlet allocation", "Latent variable", "Learning to rank", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear Discriminant Analysis", "Linear classifier", "Linear combination", "Linear regression", "Linear subspace", "List of datasets for machine-learning research", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Local outlier factor", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logarithmically concave measure", "Logistic regression", "Logit", "Long short-term memory", "Loss function", "Lp space", "M-estimator", "MANOVA", "Machine Learning (journal)", "Machine learning", "Mann\u2013Whitney U test", "Marketing", "Mathematical Reviews", "Maximum a posteriori", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimation", "McNemar's test", "Mean", "Mean-shift", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multicollinearity", "Multidimensional scaling", "Multilayer perceptron", "Multiple comparisons", "Multiple discriminant analysis", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "Naive Bayes classifier", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-negative matrix factorization", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "OPTICS algorithm", "Observational study", "Occam learning", "Official statistics", "One- and two-tailed tests", "Online machine learning", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Otsu's method", "Outline of machine learning", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pattern recognition", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Perceptron", "Perceptual mapping", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Positioning (marketing)", "Posterior probability", "Power (statistics)", "Prediction interval", "Preference regression", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability density function", "Probability distribution", "Probably approximately correct learning", "Probit regression", "Product management", "Proportional hazards model", "Pseudo inverse", "Psychometrics", "PubMed Central", "Q-learning", "Quadratic classifier", "Quality control", "Quantitative marketing research", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "R language", "Radar chart", "Random assignment", "Random forest", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Recurrent neural network", "Regression analysis", "Regression model validation", "Reinforcement learning", "Relevance vector machine", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Restricted Boltzmann machine", "Robust regression", "Robust statistics", "Ronald A. Fisher", "Ronald Fisher", "Run chart", "SAS programming language", "SPSS", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Self-organizing map", "Semi-supervised learning", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Shrinkage estimator", "Sign test", "Signal-to-noise ratio", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social salience", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "State\u2013action\u2013reward\u2013state\u2013action", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical learning theory", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical survey", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Structured prediction", "Student's t-test", "Sufficient statistic", "Supervised learning", "Support vector machine", "Surface normal", "Survey methodology", "Survival analysis", "Survival function", "System identification", "T-distributed stochastic neighbor embedding", "Talagrand's concentration inequality", "Temporal difference learning", "Time domain", "Time series", "Tolerance interval", "Training set", "Trend estimation", "U-Net", "U-statistic", "Uniformly most powerful test", "Unsupervised learning", "V-statistic", "Vapnik\u2013Chervonenkis theory", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Wilks' lambda distribution", "YouTube", "Z-Score Financial Analysis Tool", "Z-test"], "references": ["http://ajbasweb.com/old/ajbas/2010/564-576.pdf", "http://people.revoledu.com/kardi/tutorial/LDA/", "http://people.revoledu.com/kardi/tutorial/LDA/index.html", "http://www.sciencedirect.com/science/article/pii/S0031320314005214", "http://www.sciencedirect.com/science/article/pii/S0047259X00919249", "http://www.sciencedirect.com/science/article/pii/S0047259X01920342", "http://www.psychometrica.de/lds.html", "http://www.psychstat.missouristate.edu/multibook/mlt03m.html", "http://www2.chass.ncsu.edu/garson/pa765/discrim.htm", "http://www.ece.osu.edu/~aleix/pami01.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.9904", "http://userwww.sfsu.edu/~efc/classes/biol710/discrim/discrim.pdf", "http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-4389.pdf", "http://www.utdallas.edu/~herve/Abdi-DCA2007-pretty.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2976202", "http://www.alglib.net/dataanalysis/lineardiscriminantanalysis.php", "http://hdl.handle.net/2440%2F15227", "http://www.ams.org/mathscinet-getitem?mr=0999675", "http://www.ams.org/mathscinet-getitem?mr=1190469", "http://www.ams.org/mathscinet-getitem?mr=1802993", "http://arxiv.org/abs/0903.2003", "http://doi.org/10.1006%2Fjmva.2000.1924", "http://doi.org/10.1006%2Fjmva.2001.2034", "http://doi.org/10.1016%2Fj.patcog.2014.12.012", "http://doi.org/10.1016%2Fj.patrec.2004.08.005", "http://doi.org/10.1016%2Fs0031-3203(00)00162-x", "http://doi.org/10.1016%2Fs0169-2607(02)00011-1", "http://doi.org/10.1109%2F34.908974", "http://doi.org/10.1109%2F72.572105", "http://doi.org/10.1109%2FNNSP.1999.788121", "http://doi.org/10.1109%2FTIFS.2016.2569061", "http://doi.org/10.1111%2Fj.1469-1809.1936.tb02137.x", "http://doi.org/10.1128%2Faem.00726-10", "http://doi.org/10.1128%2Faem.01589-09", "http://doi.org/10.1214%2F09-aoas277", "http://doi.org/10.2307%2F2289860", "http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=572105&url=http%253A%252F%252Fieeexplore.ieee.org%252Fiel4%252F72%252F12383%252F00572105", "http://www.jstor.org/stable/2289860", "http://www.jstor.org/stable/2983775", "http://projecteuclid.org/euclid.aoas/1273584465", "http://www.worldcat.org/issn/0167-8655", "http://www.worldcat.org/issn/1045-9227", "https://github.com/mhaghighat/dcaFuse", "https://www.youtube.com/watch?v=azXCzI57Yfc", "https://www.researchgate.net/publication/326592545_Correction_of_AI_systems_by_linear_discriminants_Probabilistic_foundations", "https://web.archive.org/web/20080312065328/http://www2.chass.ncsu.edu/garson/pA765/discrim.htm", "https://web.archive.org/web/20150405124836/http://biostat.katerynakon.in.ua/en/prognosis/discriminant-analysis.html", "https://arxiv.org/list/cs.LG/recent", "https://arxiv.org/pdf/0906.2530.pdf", "https://arxiv.org/pdf/1011.0943.pdf", "https://dx.doi.org/10.1016/j.patrec.2004.08.005"]}, "Halton sequence": {"categories": ["Articles with example pseudocode", "Quasirandomness", "Sequences and series"], "title": "Halton sequence", "method": "Halton sequence", "url": "https://en.wikipedia.org/wiki/Halton_sequence", "summary": "In statistics, Halton sequences are sequences used to generate points in space for numerical methods such as Monte Carlo simulations. Although these sequences are deterministic, they are of low discrepancy, that is, appear to be random for many purposes. They were first introduced in 1960 and are an example of a quasi-random number sequence. They generalise the one-dimensional van der Corput sequences.", "images": ["https://upload.wikimedia.org/wikipedia/commons/5/51/Halton_sequence_2D.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a5/Halton_sequence_2_3.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Pseudorandom_sequence_2D.svg"], "links": ["Association for Computing Machinery", "Constructions of low-discrepancy sequences", "Coprime integers", "Deterministic system (mathematics)", "Digital object identifier", "Dover Publications", "Harald Niederreiter", "International Standard Book Number", "Linear correlation", "Low-discrepancy sequence", "Monte Carlo simulations", "Quasi-random number", "Random", "Sequence", "Society for Industrial and Applied Mathematics", "Statistics", "Van der Corput sequence"], "references": ["http://doi.org/10.1145%2F264029.264064", "http://doi.org/10.1145%2F355588.365104"]}, "Generalized additive model for location, scale and shape": {"categories": ["Generalized linear models", "Semi-parametric models", "Use dmy dates from September 2011"], "title": "Generalized additive model for location, scale and shape", "method": "Generalized additive model for location, scale and shape", "url": "https://en.wikipedia.org/wiki/Generalized_additive_model_for_location,_scale_and_shape", "summary": "The Generalized Additive Model for Location, Scale and Shape (GAMLSS) is about statistical modelling and learning. GAMLSS is a modern distribution based approach to (semiparametric) regression analysis. A parametric distribution is assumed for the response (target) variable but the parameters of this distribution can vary according to explanatory variables using linear, nonlinear or smooth functions. In data science language GAMLSS is about supervised machine learning.\nA guiding principle of GAMLSS is how to learn from data generated in many fields. In particular, the GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the distribution of response variable has any parametric distribution which might be heavy or light-tailed, and positively or negatively skewed. In addition, all the parameters of the distribution [location (e.g., mean), scale (e.g., variance) and shape (skewness and kurtosis)] can be modelled as linear, nonlinear or smooth functions of explanatory variables.", "images": [], "links": ["Continuous distribution", "Count data", "Dependent and independent variables", "Digital object identifier", "Discrete distribution", "Explanatory variable", "Exponential family", "Generalized additive model", "Generalized linear model", "Kurtosis", "Leptokurtic", "Location parameter", "Mean", "Non-parametric", "Over-dispersion", "Platykurtic", "Probability distribution", "PubMed Identifier", "R (programming language)", "Random effect", "Scale parameter", "Semiparametric", "Shape parameter", "Skewness", "Statistical model"], "references": ["http://arrow.unisa.edu.au:8081/1959.8/62400", "http://www.springerlink.com/content/j02v6t04m5833876/", "http://www.springerlink.com/content/w6231707326g8233/", "http://www3.interscience.wiley.com/journal/121547617/abstract", "http://epub.ub.uni-muenchen.de/6260/", "http://www.ncbi.nlm.nih.gov/pubmed/16143968", "http://www.who.int/childgrowth/en", "http://www.agu.org/pubs/crossref/2009/2008WR007645.shtml", "http://doi.org/10.1002/joc.3393", "http://doi.org/10.1002/sim.1861", "http://doi.org/10.1002/sim.2227", "http://doi.org/10.1007/s00180-006-0017-9", "http://doi.org/10.1016/j.advwatres.2010.03.013", "http://doi.org/10.1016/j.coastaleng.2011.05.010", "http://doi.org/10.1016/j.eneco.2011.05.001", "http://doi.org/10.1029/2008wr007645", "http://doi.org/10.18637/jss.v023.i07", "http://doi.org/10.5194/hessd-8-681-2011", "http://gamlss.org/images/stories/papers/Distributions-2010-onlyThetable.pdf", "http://gamlss.org/images/stories/papers/gamlssreferencecard.pdf", "http://manual.gamlss.org/", "http://packages.gamlss.org", "http://packages.gamlss.org/", "http://www.gamlss.org/", "http://www.gamlss.org/images/stories/papers/book-2008-27-6-08.pdf", "http://www.jstatsoft.org/v23/i07", "https://doi.org/10.1186%2F1471-2288-8-59"]}, "Factorial moment": {"categories": ["Factorial and binomial topics", "Moment (mathematics)"], "title": "Factorial moment", "method": "Factorial moment", "url": "https://en.wikipedia.org/wiki/Factorial_moment", "summary": "In probability theory, the factorial moment is a mathematical quantity defined as the expectation or average of the falling factorial of a random variable. Factorial moments are useful for studying non-negative integer-valued random variables, and arise in the use of probability-generating functions to derive the moments of discrete random variables.\nFactorial moments serve as analytic tools in the mathematical field of combinatorics, which is the study of discrete mathematical structures.", "images": [], "links": ["Beta-binomial distribution", "Binomial distribution", "Combinatorics", "Cumulant", "Digital object identifier", "Expected value", "Factorial moment generating function", "Factorial moment measure", "Falling factorial", "Hypergeometric distribution", "Integer", "John Riordan (mathematician)", "Moment (mathematics)", "Non-negative", "Operator (mathematics)", "Pochhammer symbol", "Poisson distribution", "Probability-generating function", "Probability distribution", "Probability theory", "Random variable", "Rising factorial", "Special function", "Stirling numbers of the second kind"], "references": ["http://dlmf.nist.gov/", "http://doi.org/10.1071%2Fph530498"]}, "Balanced incomplete block design": {"categories": ["Combinatorics", "Design of experiments", "Design theory", "Set families"], "title": "Block design", "method": "Balanced incomplete block design", "url": "https://en.wikipedia.org/wiki/Block_design", "summary": "In combinatorial mathematics, a block design is a set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties that are deemed useful for a particular application. These applications come from many areas, including experimental design, finite geometry, software testing, cryptography, and algebraic geometry. Many variations have been examined, but the most intensely studied are the balanced incomplete block designs (BIBDs or 2-designs) which historically were related to statistical issues in the design of experiments.A block design in which all the blocks have the same size is called uniform. The designs discussed in this article are all uniform. Pairwise balanced designs (PBDs) are examples of block designs that are not necessarily uniform.", "images": [], "links": ["15 schoolgirl problem", "Affine plane (incidence geometry)", "Algebraic geometry", "Analysis of covariance", "Analysis of variance", "Annals of Eugenics", "Annals of Mathematical Statistics", "Anne Penfold Street", "ArXiv", "Association scheme", "Bayesian experimental design", "Bayesian linear regression", "Bhat-Nayak Vasanti N.", "Binary relation", "Blind experiment", "Block code", "Blocking (statistics)", "Box\u2013Behnken design", "Bruck\u2013Ryser\u2013Chowla theorem", "Cambridge University Press", "Central composite design", "Cochran's theorem", "Combinatorial design", "Combinatorics", "Comparing means", "Completely randomized design", "Confounding", "Contrast (statistics)", "Covariate", "Crossover study", "Cryptography", "Damaraju Raghavarao", "Design of experiments", "Digital object identifier", "Digon", "Effect size", "Eric W. Weisstein", "Error correcting code", "Experiment", "Experimental design", "Experimental unit", "External validity", "Factorial experiment", "Family of sets", "Fano plane", "Finite geometry", "Fisher's inequality", "Fractional factorial design", "Generalized randomized block design", "Glossary of experimental design", "Graeco-Latin square", "H. J. Ryser", "Hadamard matrix", "Hierarchical Bayes model", "Hierarchical linear modeling", "Identity relation", "Incidence geometry", "Incidence matrix", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Journal of Combinatorial Theory", "Latin hypercube sampling", "Latin square", "Linear regression", "List of statistics articles", "MathWorld", "Mathematical Reviews", "Mathematics", "Mixed model", "Multiple comparison", "Multivariate analysis of variance", "M\u00f6bius plane", "Nuisance variable", "Optimal design", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Ovoid (projective geometry)", "Paley construction", "Paley digraph", "Partition of a set", "Peter Cameron (mathematician)", "Plackett-Burman design", "Polynomial and rational function modeling", "Projective linear group", "Projective plane", "Projective special linear group", "Pulse-position modulation", "Quadratic form", "Quadric (projective geometry)", "R", "R. C. Bose", "Random assignment", "Random effect", "Randomization", "Randomized block design", "Randomized controlled trial", "Raymond Paley", "Regular Hadamard matrix", "Repeated measures design", "Replication (statistics)", "Response surface methodology", "Restricted randomization", "Ronald Fisher", "S. S. Shrikhande", "Sample size", "Scientific control", "Scientific method", "Sequential analysis", "Sequential probability ratio test", "Set (mathematics)", "Software testing", "Statistical inference", "Statistical model", "Statistics", "Steiner system", "Taguchi methods", "Validity (statistics)"], "references": ["http://mathworld.wolfram.com/BlockDesign.html", "http://www.ams.org/mathscinet-getitem?mr=2384014", "http://arxiv.org/abs/1203.5378", "http://designtheory.org", "http://doi.org/10.1002%2Fjcd.20145", "http://doi.org/10.1016%2F0097-3165(71)90054-9", "http://doi.org/10.1016%2F0097-3165(78)90002-X", "http://doi.org/10.1080%2F01621459.1952.10501161", "http://doi.org/10.1109%2FLCOMM.2012.042512.120457", "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6205424", "http://www.neverendingbooks.org/DATA/biplanesingerman.pdf", "http://www.maths.qmul.ac.uk/~pjc/design/resources.html", "https://cran.r-project.org/package=agricolae"]}, "Bayesian brain": {"categories": ["Bayesian statistics", "Cognitive neuroscience", "Computational neuroscience", "Probabilistic models"], "title": "Bayesian approaches to brain function", "method": "Bayesian brain", "url": "https://en.wikipedia.org/wiki/Bayesian_approaches_to_brain_function", "summary": "Bayesian approaches to brain function investigate the capacity of the nervous system to operate in situations of uncertainty in a fashion that is close to the optimal prescribed by Bayesian statistics. This term is used in behavioural sciences and neuroscience and studies associated with this term often strive to explain the brain's cognitive abilities based on statistical principles. It is frequently assumed that the nervous system maintains internal probabilistic models that are updated by neural processing of sensory information using methods approximating those of Bayesian probability.", "images": ["https://upload.wikimedia.org/wikipedia/commons/9/96/Gray739.png", "https://upload.wikimedia.org/wikipedia/commons/8/89/Symbol_book_class2.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Affective neuroscience", "Artificial neural network", "Basic research", "Bayesian cognitive science", "Bayesian inference in motor learning", "Bayesian probability", "Bayesian statistics", "Behavioral epigenetics", "Behavioral neurology", "Behavioral neuroscience", "Behavioural genetics", "Biological neural network", "Brain\u2013computer interface", "Cellular neuroscience", "Chronobiology", "Clinical neurophysiology", "Clinical neuroscience", "Cognitive architecture", "Cognitive neuroscience", "Computational neuroscience", "Connectomics", "Consumer neuroscience", "Cultural neuroscience", "Detection theory", "Digital object identifier", "Educational neuroscience", "Edwin Thompson Jaynes", "Evolutionary neuroscience", "Experimental psychology", "Geoffrey Hinton", "Harold Jeffreys", "Helmholtz machine", "Hermann Helmholtz", "Hierarchical temporal memory", "Human brain", "Imaging genetics", "Integrative neuroscience", "Intraoperative neurophysiological monitoring", "Jeff Hawkins", "Kalman filter", "Karl Friston", "Machine learning", "Markov chain", "Mental model", "Michael S. Landy", "Michael Shadlen", "Mismatch negativity", "Molecular cellular cognition", "Molecular neuroscience", "Motor control", "Neural computation", "Neural development", "Neural engineering", "Neuro-ophthalmology", "Neuroanatomy", "Neuroanthropology", "Neurobioengineering", "Neurobiotics", "Neurocardiology", "Neurochemistry", "Neurochip", "Neurocriminology", "Neurodegeneration", "Neurodevelopmental disorder", "Neurodiversity", "Neuroeconomics", "Neuroendocrinology", "Neuroepidemiology", "Neuroepistemology", "Neuroesthetics", "Neuroethics", "Neuroethology", "Neurogastroenterology", "Neurogenesis", "Neurogenetics", "Neurohistory", "Neuroimaging", "Neuroimmune system", "Neuroimmunology", "Neuroinformatics", "Neurointensive care", "Neurolaw", "Neurolinguistics", "Neurology", "Neuromanagement", "Neuromarketing", "Neurometrics", "Neuromodulation", "Neuromorphology", "Neurooncology", "Neuropathology", "Neuropharmacology", "Neurophenomenology", "Neurophilosophy", "Neurophysics", "Neurophysiology", "Neuroplasticity", "Neuropolitics", "Neuroprosthetics", "Neuropsychiatry", "Neuropsychology", "Neuroradiology", "Neurorehabilitation", "Neurorobotics", "Neuroscience", "Neurosurgery", "Neurotechnology", "Neurotheology", "Neurotology", "Neurotoxin", "Neurovirology", "New Scientist", "Nutritional neuroscience", "Outline of neuroscience", "Paleoneurobiology", "Peter Dayan", "Pierre-Simon Laplace", "Predictive coding", "Priming (psychology)", "Probabilistic model", "Psychiatry", "Psychology", "PubMed Central", "PubMed Identifier", "Richard Threlkeld Cox", "Science News", "Sensory neuroscience", "Social neuroscience", "Systems neuroscience", "The free energy principle", "Thermodynamic free energy", "Thomas Bayes", "Two-alternative forced choice", "Unsupervised learning", "Variational Bayes", "Zoubin Ghahramani"], "references": ["http://www.ingentaconnect.com/content/brill/sp/2012/00000025/F0020003/art00007", "http://www.nature.com/nature/journal/v427/n6971/full/nature02169.html", "http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T0W-3X3BTP4-D&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=839657cf68a414de392abcfaca2e198f", "http://www.universaldarwinism.com/Friston%20Karl.htm", "http://www.cs.toronto.edu/~hinton/", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1828626", "http://www.ncbi.nlm.nih.gov/pubmed/17389923", "http://www.ncbi.nlm.nih.gov/pubmed/22564398", "http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=2660582&blobtype=pdf", "http://doi.org/10.1163%2F187847612X634445", "http://doi.org/10.1371%2Fjournal.pone.0000333", "http://doi.org/10.3389%2Ffpsyg.2013.00221", "http://www.frontiersin.org/consciousness_research/10.3389/fpsyg.2013.00221/abstract", "http://www.jneurosci.org/cgi/content/abstract/26/40/10154", "http://journalofvision.org//5/2/2/", "http://journalofvision.org//7/8/13/", "http://www.opticsinfobase.org/abstract.cfm?URI=josaa-20-7-1391", "http://jn.physiology.org/cgi/content/abstract/92/5/3161", "http://www.ploscompbiol.org/article/info:doi%2F10.1371%2Fjournal.pcbi.1000130", "http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000333", "http://www.fil.ion.ucl.ac.uk/~karl/", "http://www.fil.ion.ucl.ac.uk/~karl/A%20free%20energy%20principle%20for%20the%20brain.pdf", "http://www.fil.ion.ucl.ac.uk/~karl/A%20theory%20of%20cortical%20responses.pdf", "http://www.fil.ion.ucl.ac.uk/~karl/Action%20and%20behavior%20A%20free-energy%20formulation.pdf", "http://www.fil.ion.ucl.ac.uk/~karl/The%20free-energy%20principle%20A%20unified%20brain%20theory.pdf", "https://books.google.com/books?id=UjixarjDFH0C", "https://www.newscientist.com/article/mg19826586.100-is-this-a-unified-theory-of-the-brain.html", "https://www.cs.toronto.edu/~hinton/absps/cvq.pdf", "https://doi.org/10.1017%2Fs0140525x12000477", "https://doi.org/10.1371%2Fjournal.pcbi.1000532", "https://www.sciencenews.org/article/bayesian-reasoning-implicated-some-mental-disorders"]}, "Eaton's inequality": {"categories": ["All articles lacking reliable references", "All articles with unsourced statements", "Articles lacking reliable references from April 2013", "Articles with unsourced statements from April 2013", "Probabilistic inequalities", "Statistical inequalities", "Wikipedia articles needing clarification from April 2013"], "title": "Eaton's inequality", "method": "Eaton's inequality", "url": "https://en.wikipedia.org/wiki/Eaton%27s_inequality", "summary": "In probability theory, Eaton's inequality is a bound on the largest values of a linear combination of bounded random variables. This inequality was described in 1974 by Morris L. Eaton.", "images": ["https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171208221057%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20171207131032%21Question_book-new.svg", "https://upload.wikimedia.org/wikipedia/en/archive/9/99/20160612140736%21Question_book-new.svg"], "links": ["Cumulative distribution function", "Expected value", "Hoeffding's inequality", "Infimum", "Mean", "Probability density function", "Probability theory", "Rademacher distribution", "Random variables", "Riesz\u2013Fischer theorem", "Standard deviation", "Standard normal distribution", "Variance"], "references": ["https://arxiv.org/abs/1112.4988"]}, "Ceiling effect (statistics)": {"categories": ["All articles to be expanded", "All articles with empty sections", "All articles with specifically marked weasel-worded phrases", "Articles to be expanded from December 2011", "Articles using small message boxes", "Articles with empty sections from December 2011", "Articles with specifically marked weasel-worded phrases from January 2011", "Covariance and correlation", "Medical statistics", "Use dmy dates from July 2011"], "title": "Ceiling effect (statistics)", "method": "Ceiling effect (statistics)", "url": "https://en.wikipedia.org/wiki/Ceiling_effect_(statistics)", "summary": "The ceiling effect is observed when an independent variable no longer has an effect on a dependent variable, or the level above which variance in an independent variable is no longer measurable. The specific application varies slightly in differentiating between two areas of use for this term: pharmacological or statistical. An example of use in the first area, a ceiling effect in treatment, is pain relief by some kinds of analgesic drugs, which have no further effect on pain above a particular dosage level (see also: ceiling effect in pharmacology). An example of use in the second area, a ceiling effect in data-gathering, is a survey that groups all respondents into income categories, not distinguishing incomes of respondents above the highest level measured in the survey instrument. The maximum income level able to be reported creates a \u201cceiling\u201d that results in measurement inaccuracy, as the dependent variable range is not inclusive of the true values above that point. The ceiling effect can occur any time a measure involves a set range in which a normal distribution predicts multiple scores at or above the maximum value for the dependent variable.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128143823%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128140726%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110427033551%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110424212543%21Wiki_letter_w_cropped.svg"], "links": ["Alan S. 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Roughly speaking, a process satisfies the Markov property if one can make predictions for the future of the process based solely on its present state just as well as one could knowing the process's full history, hence independently from such history; i.e., conditional on the present state of the system, its future and past states are independent.\nA Markov chain is a type of Markov process that has either a discrete state space or a discrete index set (often representing time), but the precise definition of a Markov chain varies. For example, it is common to define a Markov chain as a Markov process in either discrete or continuous time with a countable state space (thus regardless of the nature of time), but it is also common to define a Markov chain as having discrete time in either countable or continuous state space (thus regardless of the state space).Markov studied Markov processes in the early 20th century, publishing his first paper on the topic in 1906. Random walks based on integers and the gambler's ruin problem are examples of Markov processes. Some variations of these processes were studied hundreds of years earlier in the context of independent variables. Two important examples of Markov processes are the Wiener process, also known as the Brownian motion process, and the Poisson process, which are considered the most important and central stochastic processes in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after 1906, in various settings. These two processes are Markov processes in continuous time, while random walks on the integers and the gambler's ruin problem are examples of Markov processes in discrete time.Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, exchange rates of currencies, storage systems such as dams, and population growths of certain animal species. The algorithm known as PageRank, which was originally proposed for the internet search engine Google, is based on a Markov process.Markov processes are the basis for general stochastic simulation methods known as Gibbs sampling and Markov chain Monte Carlo. Furthermore, they are used for simulating random objects with specific probability distributions, and have found extensive application in Bayesian statistics.The adjective Markovian is used to describe something that is related to a Markov process.", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/70/AAMarkov.jpg", "https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg", "https://upload.wikimedia.org/wikipedia/commons/7/73/Blue_pencil.svg", "https://upload.wikimedia.org/wikipedia/commons/9/95/Finance_Markov_chain_example_state_space.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a6/Financial_Markov_process.svg", "https://upload.wikimedia.org/wikipedia/commons/0/07/Intensities_vs_transition_probabilities.svg", "https://upload.wikimedia.org/wikipedia/commons/d/da/Markov_Chains_prediction_on_50_discrete_steps..png", "https://upload.wikimedia.org/wikipedia/commons/8/86/Markov_Chains_prediction_on_n%3D3..png", "https://upload.wikimedia.org/wikipedia/commons/f/f3/Markov_chain_extremly_simple1.png", "https://upload.wikimedia.org/wikipedia/commons/2/2b/Markovkate_01.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0b/Mchain_simple_corrected_C1.png", "https://upload.wikimedia.org/wikipedia/commons/5/5b/Mvchain_approx_C2.png", "https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/9/9a/Transition_graph_pac-man.png", "https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["A Mathematical Theory of Communication", "Absorbing Markov chain", "Abstract Wiener space", "Actuarial mathematics", "Agner Krarup Erlang", "Alexander Pushkin", "Algorithmic composition", "Andrei Kolmogorov", "Andrey Markov", "Arithmetic coding", "AstroTurf", "Authoritarian", "Autoregressive conditional heteroskedasticity", "Autoregressive integrated moving average", "Autoregressive model", "Autoregressive\u2013moving-average model", "Base stealing", "Bayesian inference", "Bayesian statistics", "Bear market", "Bernoulli process", "Bernoulli scheme", "Bessel process", "Biased random walk on a graph", "Bibcode", "Bioinformatics", "Bipartite graph", "Birth-death process", "Birth\u2013death process", "Black\u2013Derman\u2013Toy model", "Black\u2013Karasinski model", "Black\u2013Scholes model", "Boolean network", "Branching process", "Brownian bridge", "Brownian excursion", "Brownian meander", "Brownian motion", "Bulk queue", "Bull market", "Bunt (baseball)", "Burkholder\u2013Davis\u2013Gundy inequalities", "B\u00fchlmann model", "Cameron\u2013Martin formula", "Capitalism", "Cauchy process", "Central limit theorem", "Chapman\u2013Kolmogorov equation", "Chen model", "Chinese restaurant process", "CiteSeerX", "Classical Wiener space", "Claude Shannon", "Compound Poisson process", "Conditional probability", "Conditional probability distribution", "Connected component (graph theory)", "Constant elasticity of variance model", "Contact process (mathematics)", "Continuous-time Markov process", "Continuous-time random walk", "Continuous-time stochastic process", "Continuous or discrete variable", "Continuous stochastic process", "Convergence of random variables", "Copolymer", "Countable set", "Cox process", "Cox\u2013Ingersoll\u2013Ross model", "Cram\u00e9r\u2013Lundberg model", "Credit rating agency", "Cruise control", "Csound", "C\u00e0dl\u00e0g", "Dam", "Das Kapital", "Data compression", "Defective matrix", "Democratic regime", "Detailed balance", "Diagonal matrix", "Diffusion equation", "Diffusion process", "Digital object identifier", "Directed acyclic graph", "Directed graph", "Dirichlet process", "Discrete-time stochastic process", "Dissociated press", "Dol\u00e9ans-Dade exponential", "Donsker's theorem", "Doob's martingale convergence theorems", "Doob's martingale inequality", "Doob's optional stopping theorem", "Doob decomposition theorem", "Doob\u2013Meyer decomposition theorem", "Dynamics of Markovian particles", "Dynkin's formula", "Econometrics", "Economic development", "Edmund F. 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"https://web.archive.org/web/20170921211826/http://meyer.math.ncsu.edu/Meyer/PS_Files/ReorderingPageRank.pdf", "https://web.archive.org/web/20171120031137/https://books.google.com/books?id=0mB2CQAAQBAJ", "https://web.archive.org/web/20171120031137/https://books.google.com/books?id=7Bu8jgEACAAJ", "https://web.archive.org/web/20171120031137/https://books.google.com/books?id=c_3UBwAAQBAJ", "https://www.encyclopediaofmath.org/index.php?title=p/m062350", "https://www.wikidata.org/wiki/Q176645", "https://www.worldcat.org/oclc/10533049", "https://www.worldcat.org/oclc/982373850"]}, "Queuing delay": {"categories": ["All articles with dead external links", "Articles with dead external links from June 2016", "Computer engineering", "Computer networking", "Queueing theory", "Telecommunications engineering", "Wikipedia articles incorporating text from MIL-STD-188", "Wikipedia articles incorporating text from the Federal Standard 1037C"], "title": "Queuing delay", "method": "Queuing delay", "url": "https://en.wikipedia.org/wiki/Queuing_delay", "summary": "In telecommunication and computer engineering, the queuing delay or queueing delay is the time a job waits in a queue until it can be executed. It is a key component of network delay. In a switched network, queuing delay is the time between the completion of signaling by the call originator and the arrival of a ringing signal at the call receiver. Queuing delay may be caused by delays at the originating switch, intermediate switches, or the call receiver servicing switch. In a data network, queuing delay is the sum of the delays between the request for service and the establishment of a circuit to the called data terminal equipment (DTE). In a packet-switched network, queuing delay is the sum of the delays encountered by a packet between the time of insertion into the network and the time of delivery to the address. This term is most often used in reference to routers. When packets arrive at a router, they have to be processed and transmitted. A router can only process one packet at a time. If packets arrive faster than the router can process them (such as in a burst transmission) the router puts them into the queue (also called the buffer) until it can get around to transmitting them. Delay can also vary from packet to packet so averages and statistics are usually generated when measuring and evaluating queuing delay. As a queue begins to fill up due to traffic arriving faster than it can be processed, the amount of delay a packet experiences going through the queue increases. The speed at which the contents of a queue can be processed is a function of the transmission rate of the facility. This leads to the classic delay curve. The average delay any given packet is likely to experience is given by the formula 1/(\u03bc-\u03bb) where \u03bc is the number of packets per second the facility can sustain and \u03bb is the average rate at which packets are arriving to be serviced. This formula can be used when no packets are dropped from the queue. \nThe maximum queuing delay is proportional to buffer size. The longer the line of packets waiting to be transmitted, the longer the average waiting time is. The router queue of packets waiting to be sent also introduces a potential cause of packet loss. Since the router has a finite amount of buffer memory to hold the queue, a router which receives packets at too high a rate may experience a full queue. In this case, the router has no other option than to simply discard excess packets.\nWhen the transmission protocol uses the dropped-packets symptom of filled buffers to regulate its transmit rate, as the Internet's TCP does, bandwidth is fairly shared at near theoretical capacity with minimal network congestion delays. Absent this feedback mechanism the delays become both unpredictable and rise sharply, a symptom also seen as freeways approach capacity; metered onramps are the most effective solution there, just as TCP's self-regulation is the most effective solution when the traffic is packets instead of cars). This result is both hard to model mathematically and quite counterintuitive to people who lack experience with mathematics or real networks. Failing to drop packets, choosing instead to buffer an ever-increasing number of them, produces bufferbloat.\nIn Kendall's notation, the M/M/1/K queuing model, where K is the size of the buffer, may be used to analyze the queuing delay in a specific system. Kendall's notation should be used to calculate the queuing delay when packets are dropped from the queue. The M/M/1/K queuing model is the most basic and important queuing model for network analysis.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/62/PD-icon.svg"], "links": ["Broadcast delay", "Buffer (computer science)", "Bufferbloat", "Burst transmission", "Computer engineering", "Copyright status of work by the U.S. government", "Delay encoding", "End-to-end delay", "General Services Administration", "Kendall's notation", "Lag", "Little's law", "MIL-STD-188", "Network congestion", "Network delay", "Packet (information technology)", "Packet loss", "Processing delay", "Queue (data structure)", "Queueing theory", "Router (computing)", "Telecommunication", "Transmission delay"], "references": ["http://59.67.152.66:8000/newenglish/delay.htm", "http://www.hill2dot0.com/wiki/index.php?title=Queuing_delay", "http://streaming.stat.iastate.edu/~stat330/notes/day30.pdf", "http://www.its.bldrdoc.gov/fs-1037/dir-029/_4318.htm", "http://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm", "https://archive.is/20130114163812/http://59.67.152.66:8000/newenglish/delay.htm", "https://web.archive.org/web/20150904041151/http://www.hill2dot0.com/wiki/index.php?title=Queuing_delay"]}, "Likelihood principle": {"categories": ["Estimation theory", "Statistical principles"], "title": "Likelihood principle", "method": "Likelihood principle", "url": "https://en.wikipedia.org/wiki/Likelihood_principle", "summary": "In statistics, the likelihood principle is that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function.\nA likelihood function arises from a probability density function considered as a function of its distributional parameterization argument. For example, consider a model which gives the probability density function \u0192X(x | \u03b8) of observable random variable X as a function of a parameter \u03b8. Then for a specific value x of X, the function \n \n \n \n \n \n L\n \n \n \n \n {\\displaystyle {\\mathcal {L}}}\n (\u03b8 | x) = \u0192X(x | \u03b8) is a likelihood function of \u03b8: it gives a measure of how \"likely\" any particular value of \u03b8 is, if we know that X has the value x. The density function may be a density with respect to counting measure, i.e. a probability mass function.\nTwo likelihood functions are equivalent if one is a scalar multiple of the other. The likelihood principle is this: all information from the data that is relevant to inferences about the value of the model parameters is in the equivalence class to which the likelihood function belongs. The strong likelihood principle applies this same criterion to cases such as sequential experiments where the sample of data that is available results from applying a stopping rule to the observations earlier in the experiment.", "images": [], "links": ["A. W. F. Edwards", "Allan Birnbaum", "Bayes factor", "Bernoulli trial", "Bibcode", "British Journal for the Philosophy of Science", "Conditionality principle", "Deborah Mayo", "Design of experiments", "Digital object identifier", "Fisher's exact test", "Frequentist", "George Alfred Barnard", "Harold Jeffreys", "Ian Hacking", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "James Berger (statistician)", "Leonard J. Savage", "Likelihood-ratio test", "Likelihood function", "Mathematical Reviews", "Maximum likelihood", "Null hypothesis", "Optional stopping", "P-value", "P-values", "Pearson's chi-squared test", "Philosophical Transactions of the Royal Society A", "Philosophy of science", "Probability density function", "Probability mass function", "Random variable", "Ronald A. Fisher", "Sampling (statistics)", "Statistical Science", "Statistical hypothesis testing", "Statistical independence", "Statistical model", "Statistics", "Stopping rule", "Sufficiency principle", "Sufficient statistic"], "references": ["http://digital.library.adelaide.edu.au/dspace/handle/2440/15172", "http://jeff560.tripod.com/l.html", "http://www2.isye.gatech.edu/~brani/isyebayes/bank/handout2.pdf", "http://adsabs.harvard.edu/abs/1922RSPTA.222..309F", "http://www.phil.vt.edu/dmayo/personal_website/ch%207%20mayo%20birnbaum%20proof.pdf", "http://www.cimat.mx/reportes/enlinea/D-99-10.html", "http://www.ams.org/mathscinet-getitem?mr=0138176", "http://www.ams.org/mathscinet-getitem?mr=0353514", "http://doi.org/10.1098%2Frsta.1922.0009", "http://doi.org/10.2307%2F1402681", "http://doi.org/10.2307%2F2281640", "http://doi.org/10.2307%2F2982406", "http://www.jstor.org/stable/1402681", "http://www.jstor.org/stable/2281640", "http://www.jstor.org/stable/2982406", "http://projecteuclid.org/euclid.lnms/1215466210", "http://www.worldcat.org/issn/0035-9238", "http://www.worldcat.org/issn/0162-1459", "http://www.worldcat.org/issn/0306-7734", "http://www.economics.soton.ac.uk/staff/aldrich/fisherguide/prob+lik.htm", "https://arxiv.org/abs/1302.5468", "https://doi.org/10.1093%2Fbjps%2Faxt039", "https://projecteuclid.org/euclid.ss/1408368565"]}, "Spherical design": {"categories": ["Algebra", "Design of experiments"], "title": "Spherical design", "method": "Spherical design", "url": "https://en.wikipedia.org/wiki/Spherical_design", "summary": "A spherical design, part of combinatorial design theory in mathematics, is a finite set of N points on the d-dimensional unit d-sphere Sd such that the average value of any polynomial f of degree t or less on the set equals the average value of f on the whole sphere (that is, the integral of f over Sd divided by the area or measure of Sd). Such a set is often called a spherical t-design to indicate the value of t, which is a fundamental parameter.\nSpherical designs can be of value in approximation theory, in statistics for experimental design (being usable to construct rotatable designs), in combinatorics, and in geometry. The main problem is to find examples, given d and t, that are not too large; however, such examples may be hard to come by.\nSpherical t-designs have also recently been appropriated in quantum mechanics in the form of quantum t-designs with various applications to quantum information theory, quantum computing and POVMs.\nThe concept of a spherical design is due to Delsarte, Goethals, and Seidel (1977).", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Advances in Mathematics", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Andriy Bondarenko", "Annals of Mathematics", "Approximation theory", "ArXiv", "Arithmetic 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design", "Combinatorics", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Crossover study", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "European 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(statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maryna Viazovska", "Mathematical Reviews", "Mathematics", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Measure (mathematics)", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "N-sphere", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuisance variable", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", 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"Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Robust regression", "Robust statistics", "Rotatable design", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Taguchi methods", "Thomas Zaslavsky", "Thomson problem", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Validity (statistics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://neilsloane.com/sphdesigns/", "http://www.ams.org/mathscinet-getitem?mr=0485471", "http://www.ams.org/mathscinet-getitem?mr=0679209", "http://www.ams.org/mathscinet-getitem?mr=0744857", "http://www.ams.org/mathscinet-getitem?mr=1116326", "http://www.ams.org/mathscinet-getitem?mr=3071504", "http://arxiv.org/abs/1009.4407", "http://doi.org/10.1016%2F0001-8708(84)90022-7", "http://doi.org/10.1016%2FS0195-6698(82)80036-X", "http://doi.org/10.4007%2Fannals.2013.178.2.2", "http://www.iop.org/EJ/article/1538-4357/470/2/L81/5407.text.html"]}, "Samuelson's inequality": {"categories": ["All articles to be expanded", "Articles to be expanded from July 2017", "Articles using small message boxes", "Statistical inequalities"], "title": "Samuelson's inequality", "method": "Samuelson's inequality", "url": "https://en.wikipedia.org/wiki/Samuelson%27s_inequality", "summary": "In statistics, Samuelson's inequality, named after the economist Paul Samuelson, also called the Laguerre\u2013Samuelson inequality, after the mathematician Edmond Laguerre, states that every one of any collection x1, ..., xn, is within \u221an \u2212 1 uncorrected sample standard deviations of their sample mean.", "images": ["https://upload.wikimedia.org/wikipedia/commons/1/1c/Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128143823%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20151128140726%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110427033551%21Wiki_letter_w_cropped.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/1/1c/20110424212543%21Wiki_letter_w_cropped.svg"], "links": ["Chebychev's inequality", "Chebyshev's inequality", "Descartes' rule of signs", "Digital object identifier", "Edmond Laguerre", "Equation solving", "If and only if", "International Standard Book Number", "JSTOR", "Journal of the American Statistical Association", "Laguerre", "McGill University", "Mean", "Paul Samuelson", "Polynomial", "Standard deviation", "Statistics", "Studentized residual", "Studentized residuals"], "references": ["http://www.collectionscanada.gc.ca/obj/s4/f2/dsk1/tape10/PQDD_0027/MQ50799.pdf", "http://doi.org/10.1007/978-94-011-4577-0_10", "http://doi.org/10.2307/2285901", "http://www.jstor.org/stable/2285901"]}, "Blind experiment": {"categories": ["All articles that may contain original research", "All articles with incomplete citations", "All articles with specifically marked weasel-worded phrases", "Articles that may contain original research from September 2018", "Articles with incomplete citations from November 2012", "Articles with specifically marked weasel-worded phrases from March 2018", "Clinical research", "Design of experiments", "French inventions", "Scientific method", "Webarchive template wayback links"], "title": "Blinded experiment", "method": "Blind experiment", "url": "https://en.wikipedia.org/wiki/Blinded_experiment", "summary": "A blind or blinded-experiment is an experiment in which information about the test is masked (kept) from the participant, to reduce or eliminate bias, until after a trial outcome is known. It is understood that bias may be intentional or subconscious, thus no dishonesty is implied by blinding. If both tester and subject are blinded, the trial is called a double-blind experiment.\nBlind testing is used wherever items are to be compared without influences from testers' preferences or expectations, for example in clinical trials to evaluate the effectiveness of medicinal drugs and procedures without placebo effect, observer bias, or conscious deception; and comparative testing of commercial products to objectively assess user preferences without being influenced by branding and other properties not being tested.\nBlinding can be imposed on researchers, technicians, or subjects. The opposite of a blind trial is an open trial. Blind experiments are an important tool of the scientific method, in many fields of research\u2014medicine, psychology and the social sciences, natural sciences such as physics and biology, applied sciences such as market research, and many others. In some disciplines, such as medicinal drug testing, blind experiments are considered essential.\nIn some cases, while blind experiments would be useful, they are impractical or unethical; an example is in the field of developmental psychology: although it would be informative to raise children under arbitrary experimental conditions, such as on a remote island with a fabricated enculturation, it is a violation of ethics and human rights.\nThe terms blind (adjective) or to blind (transitive verb) when used in this sense are figurative extensions of the literal idea of blindfolding someone. The terms masked or to mask may be used for the same concept; this is commonly the case in ophthalmology, where the word 'blind' is often used in the literal sense.\nSome argue that the use of the term \"blind\" for academic review or experiments is offensive and prefer the alternative term \"masked\" or \"anonymous\".", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8b/Nuvola_apps_kalzium.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["ABX test", "Academic clinical trials", "Accelerated failure time model", "Actuarial science", "Adaptive clinical trial", "Adjective", "Age of Enlightenment", "Akaike information criterion", "Analysis of clinical trials", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Animal magnetism", "Animal testing", "Animal testing on non-human primates", "Antoine Lavoisier", "Applied science", "Arithmetic mean", "Asymptotic theory (statistics)", "Attributable fraction among the exposed", "Attributable fraction for the population", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "B meson", "BaBar", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian experimental design", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Benjamin Franklin", "Bias", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biology", "Biostatistics", "Biplot", "Blind audition", "Blind experiment", "Blindfold", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Behnken design", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Case fatality rate", "Case report", "Case series", "Case study", "Case\u2013control study", "Categorical variable", "Census", "Central composite design", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Claude Bernard", "Clinical endpoint", "Clinical protocol", "Clinical research", "Clinical study design", "Clinical trial", "Clinical trials", "Cluster analysis", "Cluster sampling", "Cochran's theorem", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cohort study", "Cointegration", "Collider Detector at Fermilab", "Comparing means", "Completely randomized design", "Completeness (statistics)", "Confidence interval", "Conflict of interest", "Confounding", "Contingency table", "Continuous probability distribution", "Contrast (statistics)", "Control chart", "Control group", "Correlation and dependence", "Correlation does not imply causation", "Correlogram", "Count data", "Covariate", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-sectional study", "Cross-validation (statistics)", "Crossover study", "Cumulative incidence", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Developmental psychology", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Double bind", "Double blind", "Durbin\u2013Watson statistic", "Ecological study", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiological methods", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Ethics", "Evidence-based medicine", "Experiment", "Experimental unit", "Experimenter's bias", "Exponential family", "Exponential smoothing", "External validity", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "First-in-man study", "Forest plot", "Fourier analysis", "Fractional factorial design", "Franz Mesmer", "French Academy of Sciences", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Generalized randomized block design", "Geographic information system", "Geometric mean", "Geostatistics", "Glossary of clinical research", "Glossary of experimental design", "Goodness of fit", "Graeco-Latin square", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Hazard ratio", "Heteroscedasticity", "Hierarchical Bayes model", "Hierarchical linear modeling", "Hierarchy of evidence", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Humphry Davy", "In vitro", "In vivo", "Incidence (epidemiology)", "Index of dispersion", "Infectivity", "Intention-to-treat analysis", "Interaction (statistics)", "Internal validity", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Latin hypercube sampling", "Latin square", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Likelihood ratios in diagnostic testing", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of clinical research topics", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Longitudinal study", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Market research", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Medicine", "Mesmerism", "Meta-analysis", "Meta analysis", "Method of moments (statistics)", "Methods engineering", "MiniBooNE", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Morbidity", "Mortality rate", "Multicenter trial", "Multiple comparison", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Natural sciences", "Nelson\u2013Aalen estimator", "Nested case\u2013control study", "Neutrino", "Nitrous oxide", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Nuclear physics", "Nuisance variable", "Null result", "Number needed to harm", "Number needed to treat", "Observational study", "Observer-expectancy effect", "Observer bias", "Observer effect (psychology)", "Odds ratio", "Official statistics", "One- and two-tailed tests", "Open-label trial", "Ophthalmology", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Orthogonal array", "Orthogonality", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Particle physics", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Pepsi Challenge", "Percentile", "Period prevalence", "Permutation test", "Physics", "Pie chart", "Pivotal quantity", "Placebo", "Plackett-Burman design", "Plug-in principle", "Point estimation", "Point prevalence", "Poisson regression", "Police lineup", "Polynomial and rational function modeling", "Population (statistics)", "Population Impact Measures", "Population statistics", "Posterior probability", "Power (statistics)", "Pre- and post-test probability", "Prediction interval", "Prevalence", "Preventable fraction among the unexposed", "Preventable fraction for the population", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Prospective cohort study", "Protocol (science)", "Psychology", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random effect", "Random sample", "Randomization", "Randomization test", "Randomized block design", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Relative risk reduction", "Reliability engineering", "Repeated measures design", "Replication (statistics)", "Reproducibility", "Resampling (statistics)", "Response surface methodology", "Restricted randomization", "Retrospective cohort study", "Risk difference", "Risk ratio", "Risk\u2013benefit ratio", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Scientific method", "Score test", "Seasonal adjustment", "Seeding trial", "Selection bias", "Semiparametric regression", "Sequential analysis", "Sequential probability ratio test", "Sham surgery", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social sciences", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Specificity and sensitivity", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stradivarius", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sudbury Neutrino Observatory", "Sufficient statistic", "Super-Kamiokande", "Survey methodology", "Survival analysis", "Survival function", "Survivorship bias", "System identification", "Systematic error", "Systematic review", "Taguchi methods", "Time domain", "Time series", "Tolerance interval", "Transitive verb", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Vaccine trial", "Validity (statistics)", "Variance", "Vector autoregression", "Virulence", "W. H. R. Rivers", "Wald test", "Wavelet", "Wayback Machine", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.oxfordreference.com/view/10.1093/oi/authority.20110803095728138", "http://www.pharmaclinicalresearch.com/", "http://skepdic.com/control.html", "http://www.cebm.net/oxford-centre-evidence-based-medicine-levels-evidence-march-2009/", "http://www.apa.org/monitor/julaug04/accuracy.html", "http://doi.org/10.1089%2Facm.2009.0515", "http://www.legalaffairs.org/issues/July-August-2002/review_koerner_julaug2002.msp", "http://news.bbc.co.uk/2/hi/health/6176209.stm", "http://www.pharmaschool.co.uk/", "https://books.google.com/books?id=1hp9p_nmvGUC&pg=PT130", "https://books.google.com/books?id=UEMQAAAAYAAJ&pg=RA1-PA249", "https://books.google.com/books?id=fnjICgAAQBAJ&pg=PA78&lpg=PA78", "https://books.google.com/books?id=ybY3AQAAIAAJ&pg=PA356", "https://books.google.com/books?id=zpPWwBS1C60C", "https://www.nytimes.com/2006/12/13/health/13cnd-hiv.html?pagewanted=print", "https://web.archive.org/web/20051130042924/http://www.apa.org/monitor/julaug04/accuracy.html", "https://web.archive.org/web/20090324141638/http://news.bbc.co.uk/2/hi/health/6176209.stm", "https://web.archive.org/web/20150623064014/http://www.nytimes.com/2006/12/13/health/13cnd-hiv.html?pagewanted=print", "https://web.archive.org/web/20170320061110/http://www.oxfordreference.com/view/10.1093/oi/authority.20110803095728138", "https://web.archive.org/web/20171026195451/http://www.cebm.net/oxford-centre-evidence-based-medicine-levels-evidence-march-2009/", "https://web.archive.org/web/20180320202349/http://pharmaclinicalresearch.com/"]}, "Stochastic modelling (insurance)": {"categories": ["Actuarial science", "Monte Carlo methods in finance", "Stochastic models"], "title": "Stochastic modelling (insurance)", "method": "Stochastic modelling (insurance)", "url": "https://en.wikipedia.org/wiki/Stochastic_modelling_(insurance)", "summary": "This page is concerned with the stochastic modelling as applied to the insurance industry. For other stochastic modelling applications, please see Monte Carlo method and Stochastic asset models. For mathematical definition, please see Stochastic process.\n\"Stochastic\" means being or having a random variable. A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques. Distributions of potential outcomes are derived from a large number of simulations (stochastic projections) which reflect the random variation in the input(s).\nIts application initially started in physics. It is now being applied in engineering, life sciences, social sciences, and finance. See also Economic capital.", "images": [], "links": ["Actuarial Society of South Africa", "Assets", "Discounted cash flow", "Economic capital", "Engineering", "Falcon Model", "Finance", "Insurer", "Liability (financial accounting)", "Life sciences", "Mean", "Monte Carlo method", "Percentile", "Physics", "Probability density function", "Probability distribution", "Random variable", "Reinsurance", "Simulation", "Social science", "Stochastic", "Stochastic asset model", "Stochastic investment model", "Stochastic process", "Thompson Model", "Time-series", "Wilkie investment model"], "references": ["http://www.actuaries.asn.au/Library/Vol12_Issue4(web).pdf", "http://www.actuaries.org.uk/files/pdf/life_insurance/GN47notes_20050902.pdf", "http://www.actuarialsociety.org.za/Portals/2/Documents/Convention-StocasticModellingForDummies-PW-YH-2007.pdf"]}, "Location estimation": {"categories": ["Summary statistics"], "title": "Summary statistics", "method": "Location estimation", "url": "https://en.wikipedia.org/wiki/Summary_statistics", "summary": "In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in\n\na measure of location, or central tendency, such as the arithmetic mean\na measure of statistical dispersion like the standard deviation\na measure of the shape of the distribution like skewness or kurtosis\nif more than one variable is measured, a measure of statistical dependence such as a correlation coefficientA common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.\nEntries in an analysis of variance table can also be regarded as summary statistics.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/fa/Michelsonmorley-boxplot.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Absolute deviation", "Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Distance correlation", "Distance standard deviation", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Five-number summary", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Gini coefficient", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile mean", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Mean absolute difference", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Michelson\u2013Morley experiment", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observation", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Order statistics", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Percentiles", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "PubMed Central", "PubMed Identifier", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Seven-number summary", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4381997", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4500174", "http://www.ncbi.nlm.nih.gov/pubmed/23761928", "http://www.ncbi.nlm.nih.gov/pubmed/26180505", "http://www.ncbi.nlm.nih.gov/pubmed/26317396", "http://doi.org/10.1080%2F13506285.2014.890989", "http://doi.org/10.1167%2F15.4.8", "http://doi.org/10.1177%2F0956797612473759"]}, "Spearman's rank correlation coefficient": {"categories": ["All articles with specifically marked weasel-worded phrases", "All articles with unsourced statements", "Articles with specifically marked weasel-worded phrases from February 2018", "Articles with unsourced statements from February 2018", "Articles with unsourced statements from September 2015", "CS1 maint: Multiple names: authors list", "Covariance and correlation", "Information retrieval evaluation", "Nonparametric statistics", "Statistical tests", "Vague or ambiguous geographic scope from February 2018"], "title": "Spearman's rank correlation coefficient", "method": "Spearman's rank correlation coefficient", "url": "https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient", "summary": "In statistics, Spearman's rank correlation coefficient or Spearman's rho, named after Charles Spearman and often denoted by the Greek letter \n \n \n \n \u03c1\n \n \n {\\displaystyle \\rho }\n (rho) or as \n \n \n \n \n r\n \n s\n \n \n \n \n {\\displaystyle r_{s}}\n , is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function.\nThe Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not). If there are no repeated data values, a perfect Spearman correlation of +1 or \u22121 occurs when each of the variables is a perfect monotone function of the other.\nIntuitively, the Spearman correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations have a dissimilar (or fully opposed for a correlation of \u22121) rank between the two variables.\nSpearman's coefficient is appropriate for both continuous and discrete ordinal variables. Both Spearman's \n \n \n \n \u03c1\n \n \n {\\displaystyle \\rho }\n and Kendall's \n \n \n \n \u03c4\n \n \n {\\displaystyle \\tau }\n can be formulated as special cases of a more general correlation coefficient.", "images": ["https://upload.wikimedia.org/wikipedia/commons/4/40/Fisher_iris_versicolor_sepalwidth.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8f/Spearman%27s_Rank_chart.png", "https://upload.wikimedia.org/wikipedia/commons/4/4e/Spearman_fig1.svg", "https://upload.wikimedia.org/wikipedia/commons/8/80/Spearman_fig2.svg", "https://upload.wikimedia.org/wikipedia/commons/6/67/Spearman_fig3.svg", "https://upload.wikimedia.org/wikipedia/commons/a/a6/Spearman_fig4.svg", "https://upload.wikimedia.org/wikipedia/commons/7/71/Spearman_fig5.svg", "https://upload.wikimedia.org/wikipedia/commons/9/91/Wikiversity-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biometrika", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Charles Spearman", "Chebyshev's sum inequality", "Chemometrics", "Chi-squared test", "CiteSeerX", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confidence intervals", "Confounding", "Contingency table", "Continuous probability distribution", "Continuous variable", "Control chart", "Correlation and dependence", "Correlogram", "Correspondence analysis", "Count data", "Covariance", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Distance correlation", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Fisher transformation", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General correlation coefficient", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Grade correspondence analysis", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Hypothesis test", "IQ", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall's tau", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Level of measurement", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Monotonic", "Monotonic function", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Non-parametric statistics", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "OCLC", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal variable", "Ordinary least squares", "Outline of statistics", "P-value", "Page's trend test", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Polychoric correlation", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Ranking", "Ranking (statistics)", "Rao\u2013Blackwell theorem", "Raw score", "Rearrangement inequality", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Rho (letter)", "Robust regression", "Robust statistics", "Royal Geographical Society", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spectral density estimation", "Standard deviation", "Standard error", "Standard score", "Stationary process", "Statistic", "Statistical classification", "Statistical dependence", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical independence", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Student's t distribution", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "TV", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variable (mathematics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.474.9634", "http://aimsciences.org/journals/pdfs.jsp?paperID=2265&mode=abstract", "http://doi.org/10.1007%2Fbf02294183", "http://doi.org/10.1093%2Fbiomet%2F44.3-4.470", "http://doi.org/10.1093%2Fbiomet%2F64.3.645", "http://doi.org/10.1177%2F0013164497057004009", "http://doi.org/10.2307%2F1412159", "http://doi.org/10.2307%2F2282965", "http://www.jstor.org/stable/1412159", "http://www.jstor.org/stable/2282965", "http://www.worldcat.org/oclc/136868", "http://www.worldcat.org/oclc/520735", "http://www.sussex.ac.uk/Users/grahamh/RM1web/Rhotable.htm", "https://books.google.com/books?id=0hPvAAAAMAAJ&pg=PA358", "https://www.rgs.org/NR/rdonlyres/4844E3AB-B36D-4B14-8A20-3A3C28FAC087/0/OASpearmansRankExcelGuidePDF.pdf"]}, "Exchange paradox": {"categories": ["All articles lacking reliable references", "All articles with style issues", "Articles lacking reliable references from November 2017", "CS1 Greek-language sources (el)", "Decision-making paradoxes", "Probability problems", "Probability theory paradoxes", "Wikipedia articles with style issues from August 2013"], "title": "Two envelopes problem", "method": "Exchange paradox", "url": "https://en.wikipedia.org/wiki/Two_envelopes_problem", "summary": "The two envelopes problem, also known as the exchange paradox, is a brain teaser, puzzle, or paradox in logic, probability, and recreational mathematics. It is of special interest in decision theory, and for the Bayesian interpretation of probability theory. Historically, it arose as a variant of the necktie paradox.\nThe problem typically is introduced by formulating a hypothetical challenge of the following type: \n\nIt seems obvious that there is no point in switching envelopes as the situation is symmetric. However, because you stand to gain twice as much money if you switch while risking only a loss of half of what you currently have, it is possible to argue that it is more beneficial to switch. The problem is to show what is wrong with this argument.", "images": ["https://upload.wikimedia.org/wikipedia/en/f/f2/Edit-clear.svg"], "links": ["Alfred A. Knopf", "Analysis (journal)", "ArXiv", "Barry Nalebuff", "Bayes' rule", "Bayesian probability", "Belgian", "Bertrand's paradox (probability)", "Bibcode", "Boy or Girl paradox", "Brain teaser", "Conditional expectation", "Conditional probability", "Counterfactual thinking", "David Chalmers", "Decision theory", "Derek Abbott", "Digital object identifier", "Envelope", "Erwin Schroedinger", "Expectation value", "Expected utility", "Expected value", "Exponential distribution", "F. Thomas Bruss", "Franz Thomas Bruss", "Game theory", "International Standard Book Number", "John Broome (philosopher)", "John Edensor Littlewood", "Laplace", "Logic", "Mark D. McDonnell", "Martin Gardner", "Maurice Kraitchik", "Michael R. Powers", "Mind (journal)", "Minimax theorem", "Monty Hall problem", "Necktie paradox", "Newcomb's paradox", "Paradox", "Philosophy", "Principle of insufficient reason", "Prior probability", "Probability", "Probability distribution", "Proceedings of the Royal Society A", "Puzzle", "Randomized algorithm", "Raymond Smullyan", "Recreational mathematics", "Siegel's paradox", "Sleeping Beauty problem", "Springer-Verlag", "St. Petersburg paradox", "Statistical randomness", "Subjectivist", "Thomas M. Cover", "Two envelopes problem", "Von Neumann"], "references": ["http://philosophy.utoronto.ca/people/linked-documents-people/c%20two%20envelope%20with%20no%20probability.pdf", "http://www.aplusclick.com/pdf/LeslieGreenTwoEnvelopes.pdf", "http://adsabs.harvard.edu/abs/2009RSPSA.465.3309M", "http://adsabs.harvard.edu/abs/2011RSPSA.467.2825M", "http://adsabs.harvard.edu/abs/2012arXiv1202.4669B", "http://adsabs.harvard.edu/abs/2014arXiv1411.2823T", "http://www.mit.edu/~emin/writings/envelopes.html", "http://arxiv.org/abs/1202.4669", "http://arxiv.org/abs/1411.2823", "http://consequently.org/papers/envelopes.pdf", "http://doi.org/10.1080%2F00031305.1991.10475791", "http://doi.org/10.1080%2F00031305.1992.10475902", "http://doi.org/10.1080%2F00031305.1993.10475966", "http://doi.org/10.1080%2F00031305.1994.10476075", "http://doi.org/10.1080%2F00031305.1996.10473551", "http://doi.org/10.1093%2Fanalys%2F55.1.6", "http://doi.org/10.1093%2Fanalys%2F62.2.155", "http://doi.org/10.1093%2Fanalys%2F62.2.157", "http://doi.org/10.1093%2Fmind%2F109.435.415", "http://doi.org/10.1093%2Fmind%2Ffzm903", "http://doi.org/10.1098%2Frspa.2009.0312", "http://doi.org/10.1098%2Frspa.2010.0541", "http://doi.org/10.1111%2Fj.1467-9639.2008.00318.x", "http://doi.org/10.1111%2Fj.1467-9639.2009.00346.x", "http://doi.org/10.1257%2Fjep.3.1.171", "http://doi.org/10.3390%2Frisks3010026", "http://sorites.org/Issue_20/sorites20.pdf", "https://web.archive.org/web/20071114230748/http://www.mit.edu/~emin/writings/envelopes.html", "https://web.archive.org/web/20110929034017/http://philosophy.utoronto.ca/people/linked-documents-people/c%20two%20envelope%20with%20no%20probability.pdf"]}, "Azuma's inequality": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from July 2010", "CS1 Russian-language sources (ru)", "CS1 uses Russian-language script (ru)", "Martingale theory", "Probabilistic inequalities"], "title": "Azuma's inequality", "method": "Azuma's inequality", "url": "https://en.wikipedia.org/wiki/Azuma%27s_inequality", "summary": "In probability theory, the Azuma\u2013Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences.\nSuppose { Xk : k = 0, 1, 2, 3, ... } is a martingale (or super-martingale) and\n\n \n \n \n \n |\n \n \n X\n \n k\n \n \n \u2212\n \n X\n \n k\n \u2212\n 1\n \n \n \n |\n \n <\n \n c\n \n k\n \n \n ,\n \n \n \n {\\displaystyle |X_{k}-X_{k-1}|<c_{k},\\,}\n almost surely. Then for all positive integers N and all positive reals t,\n\n \n \n \n P\n (\n \n X\n \n N\n \n \n \u2212\n \n X\n \n 0\n \n \n \u2265\n t\n )\n \u2264\n exp\n \u2061\n \n (\n \n \n \n \u2212\n \n t\n \n 2\n \n \n \n \n 2\n \n \u2211\n \n k\n =\n 1\n \n \n N\n \n \n \n c\n \n k\n \n \n 2\n \n \n \n \n \n )\n \n .\n \n \n {\\displaystyle P(X_{N}-X_{0}\\geq t)\\leq \\exp \\left({-t^{2} \\over 2\\sum _{k=1}^{N}c_{k}^{2}}\\right).}\n And symmetrically (when Xk is a sub-martingale):\n\n \n \n \n P\n (\n \n X\n \n N\n \n \n \u2212\n \n X\n \n 0\n \n \n \u2264\n \u2212\n t\n )\n \u2264\n exp\n \u2061\n \n (\n \n \n \n \u2212\n \n t\n \n 2\n \n \n \n \n 2\n \n \u2211\n \n k\n =\n 1\n \n \n N\n \n \n \n c\n \n k\n \n \n 2\n \n \n \n \n \n )\n \n .\n \n \n {\\displaystyle P(X_{N}-X_{0}\\leq -t)\\leq \\exp \\left({-t^{2} \\over 2\\sum _{k=1}^{N}c_{k}^{2}}\\right).}\n If X is a martingale, using both inequalities above and applying the union bound allows one to obtain a two-sided bound:\n\n \n \n \n P\n (\n \n |\n \n \n X\n \n N\n \n \n \u2212\n \n X\n \n 0\n \n \n \n |\n \n \u2265\n t\n )\n \u2264\n 2\n exp\n \u2061\n \n (\n \n \n \n \u2212\n \n t\n \n 2\n \n \n \n \n 2\n \n \u2211\n \n k\n =\n 1\n \n \n N\n \n \n \n c\n \n k\n \n \n 2\n \n \n \n \n \n )\n \n .\n \n \n {\\displaystyle P(|X_{N}-X_{0}|\\geq t)\\leq 2\\exp \\left({-t^{2} \\over 2\\sum _{k=1}^{N}c_{k}^{2}}\\right).}\n Azuma's inequality applied to the Doob martingale gives McDiarmid's inequality which is common in the analysis of randomized algorithms.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Almost surely", "Bernstein inequalities (probability theory)", "Concentration inequality", "Digital object identifier", "Doob martingale", "Exponential decay", "Kazuoki Azuma", "Martingale (probability theory)", "Mathematical Reviews", "Probability theory", "Randomized algorithm", "Real number", "Sergei Bernstein", "Sergei Natanovich Bernstein", "T\u00f4hoku Mathematical Journal", "Union bound", "Wassily Hoeffding"], "references": ["http://www.ams.org/mathscinet-getitem?mr=0144363", "http://www.ams.org/mathscinet-getitem?mr=0221571", "http://www.ams.org/mathscinet-getitem?mr=1036755", "http://www.ams.org/mathscinet-getitem?mr=1630408", "http://doi.org/10.2307%2F2282952", "http://doi.org/10.2748%2Ftmj%2F1178243286", "http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.tmj/1178243286"]}, "Complementary event": {"categories": ["Experiment (probability theory)"], "title": "Complementary event", "method": "Complementary event", "url": "https://en.wikipedia.org/wiki/Complementary_event", "summary": "In probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. The event A and its complement [not A] are mutually exclusive and exhaustive. Generally, there is only one event B such that A and B are both mutually exclusive and exhaustive; that event is the complement of A. The complement of an event A is usually denoted as A\u2032, Ac or A. Given an event, the event and its complementary event define a Bernoulli trial: did the event occur or not?\nFor example, if a typical coin is tossed and one assumes that it cannot land on its edge, then it can either land showing \"heads\" or \"tails.\" Because these two outcomes are mutually exclusive (i.e. the coin cannot simultaneously show both heads and tails) and collectively exhaustive (i.e. there are no other possible outcomes not represented between these two), they are therefore each other's complements. This means that [heads] is logically equivalent to [not tails], and [tails] is equivalent to [not heads].", "images": ["https://upload.wikimedia.org/wikipedia/commons/7/77/Nuvola_apps_atlantik.png"], "links": ["Bayes' theorem", "Bernoulli trial", "Binomial probability", "Boole's inequality", "Collectively exhaustive events", "Conditional independence", "Conditional probability", "Elementary event", "Event (probability theory)", "Exclusive disjunction", "Experiment (probability theory)", "Google Books", "Independence (probability theory)", "International Standard Book Number", "Joint probability distribution", "Law of large numbers", "Law of total probability", "Marginal distribution", "McGraw-Hill", "Mutually exclusive", "Mutually exclusive events", "Negation", "Outcome (probability)", "Principle of inclusion-exclusion", "Probability axioms", "Probability measure", "Probability space", "Probability theory", "Random variable", "Sample space", "Statistics", "Tree diagram (probability theory)", "Unity (mathematics)", "Venn diagram", "W. H. Freeman and Company"], "references": ["http://highered.mcgraw-hill.com/sites/dl/free/0072549076/79746/ch04_p175.pdf", "http://bcs.whfreeman.com/yates2e/", "https://books.google.com/books?id=DWCAh7jWO98C&pg=PA229"]}, "Rectified Gaussian distribution": {"categories": ["Normal distribution", "Probability distributions"], "title": "Rectified Gaussian distribution", "method": "Rectified Gaussian distribution", "url": "https://en.wikipedia.org/wiki/Rectified_Gaussian_distribution", "summary": "In probability theory, the rectified Gaussian distribution is a modification of the Gaussian distribution when its negative elements are reset to 0 (analogous to an electronic rectifier). It is essentially a mixture of a discrete distribution (constant 0) and a continuous distribution (a truncated Gaussian distribution with interval \n \n \n \n (\n 0\n ,\n \u221e\n )\n \n \n {\\displaystyle (0,\\infty )}\n ) as a result of censoring.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b6/Truncated_Gaussian.jpg"], "links": ["ARGUS distribution", "Arcsine distribution", "Asymmetric Laplace distribution", "Balding\u2013Nichols model", "Bates distribution", "Benford's law", "Benini distribution", "Benktander type II distribution", "Benktander type I distribution", "Bernoulli distribution", "Beta-binomial distribution", "Beta distribution", "Beta negative binomial distribution", "Beta prime distribution", "Beta rectangular distribution", "Bingham distribution", "Binomial distribution", "Bivariate von Mises distribution", "Borel distribution", "Burr distribution", "Cantor distribution", "Categorical distribution", "Cauchy distribution", "Censoring (statistics)", "Chi-squared distribution", "Chi distribution", "Circular distribution", "Circular uniform distribution", "Compound Poisson distribution", "Computational biology", "Continuous distribution", "Conway\u2013Maxwell\u2013Poisson distribution", "Cumulative distribution function", "Dagum distribution", "Davis distribution", "Degenerate distribution", "Delaporte distribution", "Digital object identifier", "Dirac delta function", "Directional statistics", "Dirichlet-multinomial distribution", "Dirichlet distribution", "Dirichlet process", "Discrete Weibull distribution", "Discrete distribution", "Discrete phase-type distribution", "Discrete uniform distribution", "Elliptical distribution", "Erlang distribution", "Ewens's sampling formula", "Exponential-logarithmic distribution", "Exponential distribution", "Exponential family", "Extended negative binomial distribution", "F-distribution", "Factor analysis", "Fisher's z-distribution", "Flory\u2013Schulz distribution", "Folded normal distribution", "Fr\u00e9chet distribution", "Gamma/Gompertz distribution", "Gamma distribution", "Gaussian distribution", "Gaussian q-distribution", "Gauss\u2013Kuzmin distribution", "Gene regulatory network", "Generalised hyperbolic distribution", "Generalized Dirichlet distribution", "Generalized Pareto distribution", "Generalized extreme value distribution", "Generalized inverse Gaussian distribution", "Generalized normal distribution", "Geometric distribution", "Geometric stable distribution", "Gompertz distribution", "Gumbel distribution", "Half-logistic distribution", "Half-normal distribution", "Holtsmark distribution", "Hotelling's T-squared distribution", "Hyper-Erlang distribution", "Hyperbolic secant distribution", "Hyperexponential distribution", "Hypergeometric distribution", "Hypoexponential distribution", "International Standard Serial Number", "Inverse-Wishart distribution", "Inverse-chi-squared distribution", "Inverse-gamma distribution", "Inverse Gaussian distribution", "Inverse matrix gamma distribution", "Irwin\u2013Hall distribution", "Johnson's SU-distribution", "Joint probability distribution", "Kent distribution", "Kolmogorov\u2013Smirnov test", "Kumaraswamy distribution", "Landau distribution", "Laplace distribution", "List of probability distributions", "Location\u2013scale family", "Log-Cauchy distribution", "Log-Laplace distribution", "Log-logistic distribution", "Log-normal distribution", "Logarithmic distribution", "Logistic distribution", "Logit-normal distribution", "Lomax distribution", "L\u00e9vy distribution", "Marchenko\u2013Pastur distribution", "Matrix-exponential distribution", "Matrix gamma distribution", "Matrix normal distribution", "Matrix t-distribution", "Maximum entropy probability distribution", "Maxwell\u2013Boltzmann distribution", "Maxwell\u2013J\u00fcttner distribution", "Mean", "Mean-preserving contraction", "Mittag-Leffler distribution", "Mixture distribution", "Multinomial distribution", "Multivariate Laplace distribution", "Multivariate normal distribution", "Multivariate stable distribution", "Multivariate t-distribution", "Nakagami distribution", "Natural exponential family", "Negative binomial distribution", "Negative multinomial distribution", "Noncentral beta distribution", "Noncentral chi-squared distribution", "Noncentral t-distribution", "Normal-Wishart distribution", "Normal-gamma distribution", "Normal-inverse-Wishart distribution", "Normal-inverse-gamma distribution", "Normal-inverse Gaussian distribution", "Normal distribution", "Parabolic fractal distribution", "Pareto distribution", "Pearson distribution", "Phase-type distribution", "Poisson binomial distribution", "Poisson distribution", "Poly-Weibull distribution", "Probability density function", "Probability distribution", "Probability theory", "Q-Gaussian distribution", "Q-Weibull distribution", "Q-exponential distribution", "Rademacher distribution", "Raised cosine distribution", "Random matrix", "Random variable", "Rayleigh distribution", "Reciprocal distribution", "Rectifier", "Relativistic Breit\u2013Wigner distribution", "Rice distribution", "Scaled inverse chi-squared distribution", "Shifted Gompertz distribution", "Shifted log-logistic distribution", "Singular distribution", "Skellam distribution", "Skew normal distribution", "Slash distribution", "Soliton distribution", "Stable distribution", "Standard normal distribution", "Student's t-distribution", "Tracy\u2013Widom distribution", "Triangular distribution", "Truncated Gaussian distribution", "Truncated normal distribution", "Tukey lambda distribution", "Tweedie distribution", "Type-1 Gumbel distribution", "Type-2 Gumbel distribution", "U-quadratic distribution", "Uniform distribution (continuous)", "Unit step function", "Variance", "Variance-gamma distribution", "Variational Bayesian methods", "Voigt profile", "Von Mises distribution", "Von Mises\u2013Fisher distribution", "Weibull distribution", "Wigner semicircle distribution", "Wilks's lambda distribution", "Wishart distribution", "Wrapped Cauchy distribution", "Wrapped L\u00e9vy distribution", "Wrapped asymmetric Laplace distribution", "Wrapped distribution", "Wrapped exponential distribution", "Wrapped normal distribution", "Yule\u2013Simon distribution", "Zeta distribution", "Zipf's law", "Zipf\u2013Mandelbrot law"], "references": ["http://doi.org/10.1016%2Fj.sigpro.2006.06.006", "http://doi.org/10.1186%2F1477-5956-9-S1-S9", "http://www.worldcat.org/issn/1477-5956"]}, "Secretary problem": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from June 2016", "CS1 maint: Multiple names: authors list", "Decision theory", "Matching", "Mathematical optimization in business", "Optimal decisions", "Probability problems", "Sequential methods", "Use dmy dates from September 2010"], "title": "Secretary problem", "method": "Secretary problem", "url": "https://en.wikipedia.org/wiki/Secretary_problem", "summary": "The secretary problem is a problem that demonstrates a scenario involving optimal stopping theory. The problem has been studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.\nThe basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of \n \n \n \n n\n \n \n {\\displaystyle n}\n rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator can rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant. If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end. The difficulty is that the decision must be made immediately.\nThe problem has an elegant solution, and the shortest rigorous proof known so far is provided by the odds algorithm (Bruss 2000). An easy analysis implies that the optimal win probability is always at least \n \n \n \n 1\n \n /\n \n e\n \n \n {\\displaystyle 1/e}\n , and that the latter holds even in a much greater generality (2003). The optimal stopping rule prescribes always rejecting the first \n \n \n \n \u223c\n n\n \n /\n \n e\n \n \n {\\displaystyle \\sim n/e}\n applicants that are interviewed (where e is the base of the natural logarithm) and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the \n \n \n \n 1\n \n /\n \n e\n \n \n {\\displaystyle 1/e}\n stopping rule, because the probability of stopping at the best applicant with this strategy is about \n \n \n \n 1\n \n /\n \n e\n \n \n {\\displaystyle 1/e}\n already for moderate values of \n \n \n \n n\n \n \n {\\displaystyle n}\n . One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.", "images": ["https://upload.wikimedia.org/wikipedia/en/6/67/SecretaryProblemHeuristicPlot.png"], "links": ["American Scientist", "Anterior cingulate", "Applied probability", "Arthur Cayley", "Assignment problem", "Behavioral operations research", "CiteSeerX", "Decision making", "Decision theory", "Digital object identifier", "Dorsolateral prefrontal cortex", "Dynamic programming", "E (mathematical constant)", "Eric W. Weisstein", "Expected value", "Experimental economics", "Experimental psychology", "F. Thomas Bruss", "Functional MRI", "I.i.d.", "Insular cortex", "International Standard Book Number", "International Standard Serial Number", "JSTOR", "Johannes Kepler", "Leo Moser", "Leonard Gillman", "Markov decision process", "Martin Gardner", "MathWorld", "Merrill M. Flood", "Minimax", "Natural logarithm", "Neuroscience", "Odds algorithm", "Optimal stopping", "Parietal cortex", "PubMed Central", "PubMed Identifier", "Purdue University", "Random variable", "Reward system", "Robbins' problem", "Robert J. Vanderbei", "Samuel Karlin", "Scientific American", "Search theory", "Selection algorithm", "Stable marriage problem", "Statistics", "Stopping rule", "Theodore P. Hill", "Thomas M. Cover", "Uniform distribution (continuous)", "Ventral striatum", "Zero-sum game"], "references": ["http://www.spotlightmind.com/optimal-search", "http://mathworld.wolfram.com/SultansDowryProblem.html", "http://www.princeton.edu/~rvdb/tex/PostdocProblem/PostdocProb.pdf", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.41", "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.497.6468", "http://www.math.ucla.edu/~tom/Stopping/Contents.html", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC40102", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4366612", "http://www.ncbi.nlm.nih.gov/pubmed/18464792", "http://www.ncbi.nlm.nih.gov/pubmed/24142842", "http://www.ncbi.nlm.nih.gov/pubmed/8570606", "http://www.americanscientist.org/issues/feature/2009/2/knowing-when-to-stop/1", "http://doi.org/10.1006%2Fobhd.1997.2683", "http://doi.org/10.1007%2F978-3-642-40450-4_50", "http://doi.org/10.1016%2FS0377-2217(02)00601-X", "http://doi.org/10.1016%2Fj.jmp.2005.08.002", "http://doi.org/10.1016%2Fj.jmp.2005.11.003", "http://doi.org/10.1038%2Fnrn2374", "http://doi.org/10.1073%2Fpnas.93.2.628", "http://doi.org/10.1093%2Fcercor%2Fbht286", "http://doi.org/10.1109%2FCRV.2009.30", "http://doi.org/10.1214%2Faop%2F1019160340", "http://doi.org/10.1214%2Faop%2F1068646368", "http://doi.org/10.1214%2Faop%2F1176988613", "http://doi.org/10.1214%2Faop%2F1176993237", "http://doi.org/10.1214%2Fss%2F1177012493", "http://doi.org/10.1287%2Fmnsc.1060.0535", "http://doi.org/10.1287%2Fmoor.5.4.481", "http://doi.org/10.1511%2F2009.77.126", "http://doi.org/10.2307%2F1402748", "http://doi.org/10.2307%2F2589677", "http://www.jstor.org/stable/1402748", "http://www.jstor.org/stable/2589677", "http://www.worldcat.org/issn/1545-2786", "https://web.archive.org/web/20110721020330/http://www.pourlascience.fr/ewb_pages/f/fiche-article-savoir-quand-s-arreter-22670.php", "https://oeis.org/A054404"]}, "Generalized p-value": {"categories": ["All articles lacking in-text citations", "Articles lacking in-text citations from January 2017", "Statistical hypothesis testing"], "title": "Generalized p-value", "method": "Generalized p-value", "url": "https://en.wikipedia.org/wiki/Generalized_p-value", "summary": "In statistics, a generalized p-value is an extended version of the classical p-value, which except in a limited number of applications, provides only approximate solutions.\nConventional statistical methods do not provide exact solutions to many statistical problems, such as those arising in mixed models and MANOVA, especially when the problem involves a number of nuisance parameters. As a result, practitioners often resort to approximate statistical methods or asymptotic statistical methods that are valid only when the sample size is large. With small samples, such methods often have poor performance. Use of approximate and asymptotic methods may lead to misleading conclusions or may fail to detect truly significant results from experiments.\nTests based on generalized p-values are exact statistical methods in that they are based on exact probability statements. While conventional statistical methods do not provide exact solutions to such problems as testing variance components or ANOVA under unequal variances, exact tests for such problems can be obtained based on generalized p-values.In order to overcome the shortcomings of the classical p-values, Tsui and Weerahandi extended the classical definition so that one can obtain exact solutions for such problems as the Behrens\u2013Fisher problem and testing variance components. This is accomplished by allowing test variables to depend on observable random vectors as well as their observed values, as in the Bayesian treatment of the problem, but without having to treat constant parameters as random variables.", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["ANOVA", "Asymptotic theory (statistics)", "Behrens\u2013Fisher problem", "Experiment", "International Standard Book Number", "Journal of the American Statistical Association", "MANOVA", "Mixed model", "Nuisance parameter", "P-value", "Statistical significance", "Statistics", "Variance components"], "references": ["http://www.x-techniques.com/", "https://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-40621-3", "https://www.jstor.org/stable/2289949"]}, "Cohort (statistics)": {"categories": ["Actuarial science", "Applied statistics", "Biostatistics", "Demography"], "title": "Cohort (statistics)", "method": "Cohort (statistics)", "url": "https://en.wikipedia.org/wiki/Cohort_(statistics)", "summary": "In statistics, marketing and demography, a cohort is a group of subjects who share a defining characteristic (typically subjects who experienced a common event in a selected time period, such as birth or graduation).\nCohort data can oftentimes be more advantageous to demographers than period data. Because cohort data is honed to a specific time period, it is usually more accurate. It is more accurate because it can be tuned to retrieve custom data for a specific study.\nIn addition, cohort data is not affected by tempo effects, unlike period data. On the contrary; cohort data can be disadvantageous in the sense that it can take a long amount of time to collect the data necessary for the cohort study. Another disadvantage of cohort studies is that it can be extremely costly to carry out, since the study will go on for a long period of time, demographers often require sufficient funds to fuel the study.\nDemography often contrasts cohort perspectives and period perspectives. For instance, the total cohort fertility rate is an index of the average completed family size for cohorts of women, but since it can only be known for women who have finished child-bearing, it cannot be measured for currently fertile women. It can be calculated as the sum of the cohort's age-specific fertility rates that obtain as it ages through time. In contrast, the total period fertility rate uses current age-specific fertility rates to calculate the completed family size for a notional woman, were she to experience these fertility rates through her life.\nA study on a cohort is a cohort study.\nTwo important aspects of cohort studies are: \n\nProspective Cohort Study: In this type of study, there is a collection of exposure data (baseline data) from the subjects recruited before development of the outcomes of interest. The subjects are then followed through time (future) to record when the subject develops the outcome of interest. Ways to follow-up with subjects of the study include: phone interviews, face-to-face interviews, physical exams, medical/laboratory tests, and mail questionnaires. An example of a prospective cohort study is, for instance, if a demographer wanted to measure all the males births in the year 2018. The demographer would have to wait for the event to be over, the year 2018 must come to an end in order for the demographer to have all the necessary data.\nRetrospective Cohort Study: Retrospective Studies start with subjects that are at risk to have the outcome or disease of interest and identifies the outcome starting from where the subject is when the study starts to the past of the subject to identify the exposure. Retrospective use records: clinical, educational, birth certificates, death certificates, etc. but that may be difficult because there may not be data for the study that is being initiated. These studies may have multiple exposures which may make this study difficult. On the other hand, an example of a retrospective cohort study is, if a demographer was examining a group of people born in year 1970 who have type 1 diabetes. The demographer would begin by looking at historical data. However, if the demographer was looking at ineffective data in attempts to deduce the source of type 1 diabetes, the demographers results would not be accurate.", "images": ["https://upload.wikimedia.org/wikipedia/commons/b/b5/ExplainingCaseControlSJW.jpg"], "links": ["Age grade", "Bureau of Labor Statistics", "Case mix", "Cohort (disambiguation)", "Cohort perspective", "Cohort study", "Demography", "Fertility rate", "Generational cohort", "Marketing", "National Longitudinal Surveys", "Period perspective", "Prospective cohort study", "Research subject", "Statistics", "Tempo effect", "U.S. Bureau of Labor Statistics Division of Information Services"], "references": ["http://www.statsref.com/HTML/index.html?cohort_studies2.html", "http://sphweb.bumc.bu.edu/otlt/MPH-Modules/EP/EP713_CohortStudies/EP713_CohortStudies_print.html", "http://sphweb.bumc.bu.edu/otlt/MPH-Modules/EP/EP713_CohortStudies/EP713_CohortStudies5.html", "http://www.bls.gov/bls/glossary.htm", "http://www.cls.ioe.ac.uk"]}, "Goldfeld\u2013Quandt test": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2010", "Regression diagnostics", "Statistical deviation and dispersion", "Statistical tests"], "title": "Goldfeld\u2013Quandt test", "method": "Goldfeld\u2013Quandt test", "url": "https://en.wikipedia.org/wiki/Goldfeld%E2%80%93Quandt_test", "summary": "In statistics, the Goldfeld\u2013Quandt test checks for homoscedasticity in regression analyses. It does this by dividing a dataset into two parts or groups, and hence the test is sometimes called a two-group test. The Goldfeld\u2013Quandt test is one of two tests proposed in a 1965 paper by Stephen Goldfeld and Richard Quandt. Both a parametric and nonparametric test are described in the paper, but the term \"Goldfeld\u2013Quandt test\" is usually associated only with the former.", "images": ["https://upload.wikimedia.org/wikipedia/commons/d/dc/NPGQPlota.svg", "https://upload.wikimedia.org/wikipedia/en/0/0b/GQplot.svg"], "links": ["Breusch\u2013Pagan test", "Design matrix", "Digital object identifier", "Explanatory variable", "F-test of equality of variances", "Glejser test", "Herbert Glejser", "Homoscedasticity", "International Standard Book Number", "JSTOR", "Least squares", "Mark Thoma", "Monotonic function", "Monte Carlo method", "Multiple regression", "Nonparametric test", "Normal distribution", "Parametric statistics", "Permutation test", "Quadratic function", "R (programming language)", "Ramsey RESET test", "Richard Quandt", "Robust statistics", "Specification (regression)", "Statistical power", "Statistics", "Stephen Goldfeld", "Test statistic", "Type I and type II errors", "YouTube"], "references": ["http://doi.org/10.1080%2F01621459.1965.10480811", "http://doi.org/10.1080%2F01621459.1969.10500976", "http://doi.org/10.1093%2Fbiomet%2F70.1.1", "http://doi.org/10.2307%2F1924311", "http://www.jstor.org/stable/1924311", "http://www.jstor.org/stable/2282689", "http://www.jstor.org/stable/2283741", "http://www.jstor.org/stable/2335938", "https://books.google.com/books?id=86rWI7WzFScC&pg=PA102", "https://books.google.com/books?id=PnVCEZOOFr0C&pg=PA424", "https://books.google.com/books?id=ax1QcAAACAAJ&pg=PA116", "https://www.youtube.com/watch?v=6jEy5YSJd8w&list=PLD15D38DC7AA3B737&index=4#t=49m23s", "https://cran.r-project.org/web/packages/lmtest/index.html"]}, "Choropleth map": {"categories": ["All articles needing additional references", "Articles needing additional references from March 2009", "Color scales", "Map types", "Statistical charts and diagrams", "Use dmy dates from September 2015"], "title": "Choropleth map", "method": "Choropleth map", "url": "https://en.wikipedia.org/wiki/Choropleth_map", "summary": "A choropleth map (from Greek \u03c7\u1ff6\u03c1\u03bf\u03c2 (\"area/region\") + \u03c0\u03bb\u1fc6\u03b8\u03bf\u03c2 (\"multitude\")) is a thematic map in which areas are shaded or patterned in proportion to the measurement of the statistical variable being displayed on the map, such as population density or per-capita income. \nChoropleth maps provide an easy way to visualize how a measurement varies across a geographic area or show the level of variability within a region. A heat map is similar but does not use geographic boundaries.", "images": ["https://upload.wikimedia.org/wikipedia/commons/f/f7/Australian_Census_2011_demographic_map_-_Australia_by_SLA_-_BCP_field_2715_Christianity_Anglican_Persons.svg", "https://upload.wikimedia.org/wikipedia/commons/c/c8/Choropleth-density.png", "https://upload.wikimedia.org/wikipedia/commons/1/15/Color_progression_examples_bi-polar.svg", "https://upload.wikimedia.org/wikipedia/commons/3/33/Color_progression_examples_blended_hue.svg", "https://upload.wikimedia.org/wikipedia/commons/4/4c/Color_progression_examples_full-spectral.svg", "https://upload.wikimedia.org/wikipedia/commons/0/0a/Color_progression_examples_partial_spectral.svg", "https://upload.wikimedia.org/wikipedia/commons/e/ee/Color_progression_examples_single_hue.svg", "https://upload.wikimedia.org/wikipedia/commons/f/fe/Color_progression_examples_value_progression.svg", "https://upload.wikimedia.org/wikipedia/commons/6/60/DasymapBG_Bay_Area_choropleth_and_dasymetric_maps.jpg", "https://upload.wikimedia.org/wikipedia/commons/f/f5/Terra.png", "https://upload.wikimedia.org/wikipedia/commons/9/99/Wiktionary-logo-en-v2.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg", "https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg"], "links": ["Anglican", "Atlas", "Australians", "Boston", "Cartogram", "Cartography", "Charles Dupin", "Color blindness", "Contour line", "Dasymetric map", "Dichromacy", "Digital object identifier", "Early world maps", "Ecological fallacy", "Geography", "Geologic map", "Greek language", "HSL and HSV", "Head/tail Breaks", "Heat map", "History of cartography", "Hue", "International Standard Book Number", "Jenks natural breaks optimization", "John Kirtland Wright", "Linguistic map", "List of cartographers", "MacChoro", "Map", "Map projection", "Mark Monmonier", "Michael Friendly", "Modifiable areal unit problem", "Nautical chart", "Per-capita income", "Pictorial map", "Room temperature", "San Francisco Bay Area", "Thematic map", "Topographic map", "Topography", "Weather map"], "references": ["http://www.math.yorku.ca/SCS/Gallery/milestone/milestone.pdf", "http://artsbeat.blogs.nytimes.com/2011/08/09/what-digital-maps-can-tell-us-about-the-american-way", "http://geography.wr.usgs.gov/science/dasymetric/", "http://colorbrewer2.org/", "http://doi.org/10.1029%2F2004EO400002", "http://choropleth.us/", "https://www.worldcat.org/oclc/5160537/"]}, "Goodman and Kruskal's gamma": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from August 2010", "Rankings", "Statistical tests", "Summary statistics for contingency tables"], "title": "Goodman and Kruskal's gamma", "method": "Goodman and Kruskal's gamma", "url": "https://en.wikipedia.org/wiki/Goodman_and_Kruskal%27s_gamma", "summary": "In statistics, Goodman and Kruskal's gamma is a measure of rank correlation, i.e., the similarity of the orderings of the data when ranked by each of the quantities. It measures the strength of association of the cross tabulated data when both variables are measured at the ordinal level. It makes no adjustment for either table size or ties. Values range from \u22121 (100% negative association, or perfect inversion) to +1 (100% positive association, or perfect agreement). A value of zero indicates the absence of association.\nThis statistic (which is distinct from Goodman and Kruskal's lambda) is named after Leo Goodman and William Kruskal, who proposed it in a series of papers from 1954 to 1972.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Association (statistics)", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of colligation", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Concordant pair", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Cross tabulation", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodman and Kruskal's lambda", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "JSTOR", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Journal of the American Statistical Association", "Journal of the Royal Statistical Society", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kendall tau rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Leo Goodman", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "Maximum likelihood estimator", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinal level", "Ordinary least squares", "Outline of statistics", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Student t distribution", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variable (mathematics)", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "William Kruskal", "Yule's Y", "Z-test"], "references": ["http://doi.org/10.1080%2F01621459.1959.10501503", "http://doi.org/10.1080%2F01621459.1963.10500850", "http://doi.org/10.1080%2F01621459.1972.10482401", "http://doi.org/10.2307%2F2281536", "http://www.jstor.org/stable/2281536", "http://www.jstor.org/stable/2282143", "http://www.jstor.org/stable/2283271", "http://www.jstor.org/stable/2284396", "http://www.jstor.org/stable/2340126"]}, "Preferential attachment": {"categories": ["Stochastic processes"], "title": "Preferential attachment", "method": "Preferential attachment", "url": "https://en.wikipedia.org/wiki/Preferential_attachment", "summary": "A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who are already wealthy receive more than those who are not. \"Preferential attachment\" is only the most recent of many names that have been given to such processes. They are also referred to under the names \"Yule process\", \"cumulative advantage\", \"the rich get richer\", and, less correctly, the \"Matthew effect\". They are also related to Gibrat's law. The principal reason for scientific interest in preferential attachment is that it can, under suitable circumstances, generate power law distributions.\n\n", "images": [], "links": ["ArXiv", "Assortative mixing", "BA model", "Barab\u00e1si-Albert model", "Beta function", "Bibcode", "Bible", "Bibliogram", "Bose\u2013Einstein condensation: a network theory approach", "Bradford's law", "Capital accumulation", "Chinese restaurant process", "Complex network", "Derek J. de Solla Price", "Digital object identifier", "Double jeopardy (marketing)", "Gamma function", "Genus", "Gibrat's law", "Gospel of Matthew", "Herbert A. Simon", "Linear", "Link-centric preferential attachment", "Lotka's law", "Master equation", "Matthew effect", "Matthew effect (sociology)", "Maximum likelihood estimation", "New International Version", "Pareto distribution", "Philosophical Transactions of the Royal Society B", "Power law", "Price's model", "PubMed Central", "PubMed Identifier", "Robert K. Merton", "Scale-free network", "Simon model", "Speciation", "Species", "Stochastic process", "Stochastic processes", "Taxon", "Udny Yule", "Urn problem", "Wealth condensation", "Yule distribution", "Yule\u2013Simon distribution"], "references": ["http://adsabs.harvard.edu/abs/1968Sci...159...56M", "http://adsabs.harvard.edu/abs/1999Sci...286..509B", "http://adsabs.harvard.edu/abs/2015PLoSO..1037796P", "http://garfield.library.upenn.edu/price/pricetheory1976.pdf", "http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4574777", "http://www.ncbi.nlm.nih.gov/pubmed/10521342", "http://www.ncbi.nlm.nih.gov/pubmed/17737466", "http://www.ncbi.nlm.nih.gov/pubmed/26378457", "http://arxiv.org/abs/cond-mat/0412004", "http://arxiv.org/abs/cond-mat/9910332", "http://doi.org/10.1002%2Fasi.4630270505", "http://doi.org/10.1080%2F00107510500052444", "http://doi.org/10.1093%2Fbiomet%2F42.3-4.425", "http://doi.org/10.1098%2Frstb.1925.0002", "http://doi.org/10.1126%2Fscience.159.3810.56", "http://doi.org/10.1126%2Fscience.286.5439.509", "http://doi.org/10.1371%2Fjournal.pone.0137796", "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0137796"]}, "Bessel's correction": {"categories": ["All articles lacking in-text citations", "Articles containing proofs", "Articles lacking in-text citations from November 2010", "Estimation methods", "Statistical deviation and dispersion"], "title": "Bessel's correction", "method": "Bessel's correction", "url": "https://en.wikipedia.org/wiki/Bessel%27s_correction", "summary": "In statistics, Bessel's correction is the use of n \u2212 1 instead of n in the formula for the sample variance and sample standard deviation, where n is the number of observations in a sample. This method corrects the bias in the estimation of the population variance. It also partially corrects the bias in the estimation of the population standard deviation. However, the correction often increases the mean squared error in these estimations. This technique is named after Friedrich Bessel.\nIn estimating the population variance from a sample when the population mean is unknown, the uncorrected sample variance is the mean of the squares of deviations of sample values from the sample mean (i.e. using a multiplicative factor 1/n). In this case, the sample variance is a biased estimator of the population variance.\nMultiplying the uncorrected sample variance by the factor\n\n \n \n \n \n \n n\n \n n\n \u2212\n 1\n \n \n \n \n \n {\\displaystyle {\\frac {n}{n-1}}}\n gives an unbiased estimator of the population variance. In some literature, the above factor is called Bessel's correction.\nOne can understand Bessel's correction as the degrees of freedom in the residuals vector (residuals, not errors, because the population mean is unknown):\n\n \n \n \n (\n \n x\n \n 1\n \n \n \u2212\n \n \n x\n \u00af\n \n \n ,\n \n \u2026\n ,\n \n \n x\n \n n\n \n \n \u2212\n \n \n x\n \u00af\n \n \n )\n ,\n \n \n {\\displaystyle (x_{1}-{\\overline {x}},\\,\\dots ,\\,x_{n}-{\\overline {x}}),}\n where \n \n \n \n \n \n x\n \u00af\n \n \n \n \n {\\displaystyle {\\overline {x}}}\n is the sample mean. While there are n independent observations in the sample, there are only n \u2212 1 independent residuals, as they sum to 0. For a more intuitive explanation of the need for Bessel's correction, see \u00a7 Source of bias.\nGenerally Bessel's correction is an approach to reduce the bias due to finite sample size. Such finite-sample bias correction is also needed for other estimates like skew and kurtosis, but in these the inaccuracies are often significantly larger. To fully remove such bias it is necessary to do a more complex multi-parameter estimation. For instance a correct correction for the standard deviation depends on the kurtosis (normalized central 4th moment), but this again has a finite sample bias and it depends on the standard deviation, i.e. both estimations have to be merged.\n\n", "images": ["https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_with_red_question_mark.svg", "https://upload.wikimedia.org/wikipedia/commons/archive/a/a4/20070810173321%21Text_document_with_red_question_mark.svg"], "links": ["Bias of an estimator", "Biased estimator", "Binomial theorem", "Concave function", "Degrees of freedom (statistics)", "Eric W. Weisstein", "Errors and residuals in statistics", "Estimation theory", "Excess kurtosis", "Friedrich Bessel", "International Standard Book Number", "Jensen's inequality", "Kurtosis", "Linearity of expectation", "MathWorld", "Mean squared error", "Sample standard deviation", "Sample variance", "Skewness", "Square root", "Standard deviation", "Statistics", "Unbiased estimation of standard deviation", "Variance"], "references": ["http://mathworld.wolfram.com/BesselsCorrection.html", "http://www.khanacademy.org/cs/fishy-statistics-unbiased-estimate-of-population-variance/1183564841"]}, "Numerical parameter": {"categories": ["Statistical parameters"], "title": "Statistical parameter", "method": "Numerical parameter", "url": "https://en.wikipedia.org/wiki/Statistical_parameter", "summary": "A statistical parameter or population parameter is a quantity that indexes a family of probability distributions. It can be regarded as a numerical characteristic of a population or a statistical model.", "images": ["https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bias of an estimator", "Binomial distribution", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Cambridge University Press", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Concentration parameter", "Conditional probability distribution", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Dependent and independent variables", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Indexed family", "Interaction (statistics)", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Observational study", "Official statistics", "One- and two-tailed tests", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "Parameter", "Parametric family", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson distribution", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Precision (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Random sample", "Random variables", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression coefficient", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Run chart", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical population", "Statistical power", "Statistical process control", "Statistical sample", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": []}, "Two-tailed test": {"categories": ["Statistical tests"], "title": "One- and two-tailed tests", "method": "Two-tailed test", "url": "https://en.wikipedia.org/wiki/One-_and_two-tailed_tests", "summary": "In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value may be more than or less than the reference value, for example, whether a test taker may score above or below the historical average. \nA one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, for example, whether a machine produces more than one-percent defective products. Alternative names are one-sided and two-sided tests; the terminology \"tail\" is used because the extreme portions of distributions, where observations lead to rejection of the null hypothesis, are small and often \"tail off\" toward zero as in the normal distribution or \"bell curve\", pictured on the right.", "images": ["https://upload.wikimedia.org/wikipedia/commons/8/8e/Chi-square_distributionCDF-English.png", "https://upload.wikimedia.org/wikipedia/commons/9/96/DisNormal06.svg", "https://upload.wikimedia.org/wikipedia/commons/3/37/People_icon.svg", "https://upload.wikimedia.org/wikipedia/commons/8/8c/Standard_deviation_diagram.svg", "https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg", "https://upload.wikimedia.org/wikipedia/en/4/48/Folder_Hexagonal_Icon.svg", "https://upload.wikimedia.org/wikipedia/en/0/00/P-value_Graph.png", "https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg"], "links": ["Accelerated failure time model", "Actuarial science", "Akaike information criterion", "Analysis of covariance", "Analysis of variance", "Anderson\u2013Darling test", "Arithmetic mean", "Asymptotic theory (statistics)", "Autocorrelation", "Autoregressive conditional heteroskedasticity", "Autoregressive\u2013moving-average model", "Bar chart", "Bayes estimator", "Bayes factor", "Bayesian inference", "Bayesian information criterion", "Bayesian linear regression", "Bayesian probability", "Bernoulli trial", "Bias of an estimator", "Binomial regression", "Bioinformatics", "Biostatistics", "Biplot", "Blocking (statistics)", "Bootstrapping (statistics)", "Box plot", "Box\u2013Jenkins method", "Breusch\u2013Godfrey test", "Canonical correlation", "Cartography", "Categorical variable", "Census", "Central limit theorem", "Central tendency", "Checking whether a coin is fair", "Chemometrics", "Chi-squared distribution", "Chi-squared test", "Clinical study design", "Clinical trial", "Cluster analysis", "Cluster sampling", "Coefficient of determination", "Coefficient of variation", "Cohen's kappa", "Cointegration", "Completeness (statistics)", "Confidence interval", "Confounding", "Contingency table", "Continuous probability distribution", "Control chart", "Correlation and dependence", "Correlogram", "Count data", "Credible interval", "Crime statistics", "Critical values", "Cross-correlation", "Cross-validation (statistics)", "Data collection", "Decomposition of time series", "Degrees of freedom (statistics)", "Demographic statistics", "Density estimation", "Descriptive statistics", "Design of experiments", "Dickey\u2013Fuller test", "Digital object identifier", "Divergence (statistics)", "Durbin\u2013Watson statistic", "Econometrics", "Effect size", "Efficiency (statistics)", "Elliptical distribution", "Empirical distribution function", "Engineering statistics", "Environmental statistics", "Epidemiology", "Errors and residuals in statistics", "Estimating equations", "Experiment", "Exponential family", "Exponential smoothing", "F-test", "Factor analysis", "Factorial experiment", "Failure rate", "Fan chart (statistics)", "First-hitting-time model", "Forest plot", "Fourier analysis", "Frequency distribution", "Frequency domain", "Frequentist inference", "Friedman test", "G-test", "General linear model", "Generalized linear model", "Geographic information system", "Geometric mean", "Geostatistics", "Goodness-of-fit", "Goodness of fit", "Granger causality", "Graphical model", "Grouped data", "Harmonic mean", "Heteroscedasticity", "Histogram", "Hodges\u2013Lehmann estimator", "Homoscedasticity", "Index of dispersion", "Interaction (statistics)", "International Standard Book Number", "Interquartile range", "Interval estimation", "Isotonic regression", "Jackknife resampling", "Jarque\u2013Bera test", "Johansen test", "John E. Freund", "Jonckheere's trend test", "Kaplan\u2013Meier estimator", "Karl Pearson", "Kendall rank correlation coefficient", "Kolmogorov\u2013Smirnov test", "Kriging", "Kruskal\u2013Wallis one-way analysis of variance", "Kurtosis", "L-moment", "Lady tasting tea", "Lehmann\u2013Scheff\u00e9 theorem", "Likelihood-ratio test", "Likelihood function", "Likelihood interval", "Lilliefors test", "Linear discriminant analysis", "Linear regression", "List of fields of application of statistics", "List of statistics articles", "Ljung\u2013Box test", "Location parameter", "Location\u2013scale family", "Log-rank test", "Logistic regression", "Loss function", "Lp space", "M-estimator", "Mann\u2013Whitney U test", "Maximum a posteriori estimation", "Maximum likelihood", "McNemar's test", "Mean", "Median", "Median-unbiased estimator", "Medical statistics", "Method of moments (statistics)", "Methods engineering", "Minimum-variance unbiased estimator", "Minimum distance estimation", "Missing data", "Mixed model", "Mode (statistics)", "Model selection", "Moment (mathematics)", "Monotone likelihood ratio", "Multiple comparisons", "Multivariate adaptive regression splines", "Multivariate analysis of variance", "Multivariate distribution", "Multivariate normal distribution", "Multivariate statistics", "National accounts", "Natural experiment", "Nelson\u2013Aalen estimator", "Nonlinear regression", "Nonparametric regression", "Nonparametric statistics", "Normal distribution", "Null hypothesis", "Observational study", "Official statistics", "Opinion poll", "Optimal decision", "Optimal design", "Order statistic", "Ordinary least squares", "Outline of statistics", "P-value", "Paired difference test", "Parameter", "Parametric statistics", "Partial autocorrelation function", "Partial correlation", "Partition of sums of squares", "Pearson's chi-squared test", "Pearson correlation coefficient", "Pearson product-moment correlation coefficient", "Percentile", "Permutation test", "Pie chart", "Pivotal quantity", "Plug-in principle", "Point estimation", "Poisson regression", "Population (statistics)", "Population statistics", "Posterior probability", "Power (statistics)", "Prediction interval", "Principal component analysis", "Prior probability", "Probabilistic design", "Probability distribution", "Proportional hazards model", "Psychometrics", "Quality control", "Quantile function", "Quasi-experiment", "Questionnaire", "Q\u2013Q plot", "Radar chart", "Random assignment", "Randomization test", "Randomized controlled trial", "Randomized experiment", "Range (statistics)", "Rank correlation", "Rank statistics", "Rao\u2013Blackwell theorem", "Regression analysis", "Regression model validation", "Reliability engineering", "Replication (statistics)", "Resampling (statistics)", "Robust regression", "Robust statistics", "Ronald Fisher", "Run chart", "Sample mean", "Sample median", "Sample size determination", "Sampling (statistics)", "Sampling distribution", "Scale parameter", "Scatter plot", "Scientific control", "Score test", "Seasonal adjustment", "Semiparametric regression", "Shape of the distribution", "Shape parameter", "Shapiro\u2013Wilk test", "Sign test", "Significance testing", "Simple linear regression", "Simultaneous equations model", "Skewness", "Social statistics", "Spatial analysis", "Spearman's rank correlation coefficient", "Spectral density estimation", "Standard deviation", "Standard error", "Stationary process", "Statistic", "Statistical Methods for Research Workers", "Statistical classification", "Statistical dispersion", "Statistical distance", "Statistical graphics", "Statistical hypothesis testing", "Statistical inference", "Statistical model", "Statistical parameter", "Statistical power", "Statistical process control", "Statistical significance", "Statistical theory", "Statistics", "Stem-and-leaf display", "Stratified sampling", "Structural break", "Structural equation modeling", "Student's t-distribution", "Student's t-test", "Sufficient statistic", "Survey methodology", "Survival analysis", "Survival function", "System identification", "Test statistic", "The Design of Experiments", "Time domain", "Time series", "Tolerance interval", "Trend estimation", "U-statistic", "Uniformly most powerful test", "V-statistic", "Variance", "Vector autoregression", "Wald test", "Wavelet", "Whittle likelihood", "Wilcoxon signed-rank test", "Z-test"], "references": ["http://edr.sagepub.com/content/20/9/13.short", "http://www.sciencedirect.com/science/article/pii/S0003347298907564", "http://doi.org/10.1080%2F14786440009463897", "http://www.economics.soton.ac.uk/staff/aldrich/1900.pdf", "https://drive.google.com/file/d/0B76EXfrQqs3ha255TkliQk1ONEE/view"]}, "Circular analysis": {"categories": ["All articles with unsourced statements", "Articles with unsourced statements from April 2013", "Misuse of statistics", "Model selection"], "title": "Circular analysis", "method": "Circular analysis", "url": "https://en.wikipedia.org/wiki/Circular_analysis", "summary": "In statistics, circular analysis is the selection of the details of a data analysis using the data that is being analysed. It is often referred to as double dipping, as one uses the same data twice. Circular analysis unjustifiably inflates the apparent statistical strength of any results reported and, at the most extreme, can lead to the apparently significant result being found in data that consists only of noise. In particular, where an experiment is implemented to study a postulated effect, it is a misuse of statistics to initially reduce the complete dataset by selecting a subset of data in ways that are aligned to the effects being studied. A second misuse occurs where the performance of a fitted model or classification rule is reported as a raw result, without allowing for the effects of model-sel